id	sid	tid	token	lemma	pos
fuelectenerg-400	1	1	400.indd	400.indd	NUM
fuelectenerg-400	1	2	facta	facta	PROPN
fuelectenerg-400	1	3	universitatis	universitatis	PROPN
fuelectenerg-400	1	4	series	series	NOUN
fuelectenerg-400	1	5	:	:	PUNCT
fuelectenerg-400	1	6	electronics	electronic	NOUN
fuelectenerg-400	1	7	and	and	CCONJ
fuelectenerg-400	1	8	energetics	energetics	NOUN
fuelectenerg-400	1	9	vol	vol	NOUN
fuelectenerg-400	1	10	.	.	PUNCT
fuelectenerg-400	1	11	27	27	NUM
fuelectenerg-400	1	12	,	,	PUNCT
fuelectenerg-400	1	13	no	no	DET
fuelectenerg-400	1	14	4	4	NUM
fuelectenerg-400	1	15	,	,	PUNCT
fuelectenerg-400	1	16	december	december	PROPN
fuelectenerg-400	1	17	2014	2014	NUM
fuelectenerg-400	1	18	,	,	PUNCT
fuelectenerg-400	1	19	pp	pp	ADV
fuelectenerg-400	1	20	.	.	PUNCT
fuelectenerg-400	2	1	521	521	NUM
fuelectenerg-400	2	2	542	542	NUM
fuelectenerg-400	2	3	lozenge	lozenge	NOUN
fuelectenerg-400	2	4	tiling	tile	VERB
fuelectenerg-400	2	5	constrained	constrained	ADJ
fuelectenerg-400	2	6	codes	code	NOUN
fuelectenerg-400	2	7	bane	bane	NOUN
fuelectenerg-400	2	8	vasić1	vasić1	NOUN
fuelectenerg-400	2	9	and	and	CCONJ
fuelectenerg-400	2	10	anantha	anantha	PROPN
fuelectenerg-400	2	11	raman	raman	PROPN
fuelectenerg-400	2	12	krishnan2	krishnan2	PROPN
fuelectenerg-400	3	1	1department	1department	NUM
fuelectenerg-400	3	2	of	of	ADP
fuelectenerg-400	3	3	electrical	electrical	ADJ
fuelectenerg-400	3	4	and	and	CCONJ
fuelectenerg-400	3	5	computer	computer	NOUN
fuelectenerg-400	3	6	engineering	engineering	NOUN
fuelectenerg-400	3	7	,	,	PUNCT
fuelectenerg-400	3	8	university	university	PROPN
fuelectenerg-400	3	9	of	of	ADP
fuelectenerg-400	3	10	arizona	arizona	PROPN
fuelectenerg-400	3	11	,	,	PUNCT
fuelectenerg-400	3	12	tucson	tucson	PROPN
fuelectenerg-400	3	13	,	,	PUNCT
fuelectenerg-400	3	14	az	az	PROPN
fuelectenerg-400	3	15	,	,	PUNCT
fuelectenerg-400	3	16	85721	85721	NUM
fuelectenerg-400	3	17	,	,	PUNCT
fuelectenerg-400	3	18	usa	usa	PROPN
fuelectenerg-400	3	19	2western	2western	NUM
fuelectenerg-400	3	20	digital	digital	ADJ
fuelectenerg-400	3	21	corporation	corporation	NOUN
fuelectenerg-400	3	22	,	,	PUNCT
fuelectenerg-400	3	23	irvine	irvine	PROPN
fuelectenerg-400	3	24	,	,	PUNCT
fuelectenerg-400	3	25	ca	ca	PROPN
fuelectenerg-400	3	26	92612	92612	NUM
fuelectenerg-400	3	27	,	,	PUNCT
fuelectenerg-400	3	28	usa	usa	PROPN
fuelectenerg-400	3	29	abstract	abstract	PROPN
fuelectenerg-400	3	30	:	:	PUNCT
fuelectenerg-400	3	31	while	while	SCONJ
fuelectenerg-400	3	32	the	the	DET
fuelectenerg-400	3	33	field	field	NOUN
fuelectenerg-400	3	34	of	of	ADP
fuelectenerg-400	3	35	one	one	NUM
fuelectenerg-400	3	36	-	-	PUNCT
fuelectenerg-400	3	37	dimensional	dimensional	ADJ
fuelectenerg-400	3	38	constrained	constrained	ADJ
fuelectenerg-400	3	39	codes	code	NOUN
fuelectenerg-400	3	40	is	be	AUX
fuelectenerg-400	3	41	mature	mature	ADJ
fuelectenerg-400	3	42	,	,	PUNCT
fuelectenerg-400	3	43	with	with	ADP
fuelectenerg-400	3	44	theoretical	theoretical	ADJ
fuelectenerg-400	3	45	as	as	ADV
fuelectenerg-400	3	46	well	well	ADV
fuelectenerg-400	3	47	as	as	ADP
fuelectenerg-400	3	48	practical	practical	ADJ
fuelectenerg-400	3	49	aspects	aspect	NOUN
fuelectenerg-400	3	50	of	of	ADP
fuelectenerg-400	3	51	codeand	codeand	NOUN
fuelectenerg-400	3	52	decoder	decoder	NOUN
fuelectenerg-400	3	53	-	-	PUNCT
fuelectenerg-400	3	54	design	design	NOUN
fuelectenerg-400	3	55	being	be	AUX
fuelectenerg-400	3	56	well	well	ADV
fuelectenerg-400	3	57	-	-	PUNCT
fuelectenerg-400	3	58	established	establish	VERB
fuelectenerg-400	3	59	,	,	PUNCT
fuelectenerg-400	3	60	such	such	DET
fuelectenerg-400	3	61	a	a	DET
fuelectenerg-400	3	62	theoretical	theoretical	ADJ
fuelectenerg-400	3	63	treatment	treatment	NOUN
fuelectenerg-400	3	64	of	of	ADP
fuelectenerg-400	3	65	its	its	PRON
fuelectenerg-400	3	66	two	two	NUM
fuelectenerg-400	3	67	-	-	PUNCT
fuelectenerg-400	3	68	dimensional	dimensional	ADJ
fuelectenerg-400	3	69	(	(	PUNCT
fuelectenerg-400	3	70	2d	2d	NOUN
fuelectenerg-400	3	71	)	)	PUNCT
fuelectenerg-400	3	72	counterpart	counterpart	NOUN
fuelectenerg-400	3	73	is	be	AUX
fuelectenerg-400	3	74	still	still	ADV
fuelectenerg-400	3	75	unavailable	unavailable	ADJ
fuelectenerg-400	3	76	.	.	PUNCT
fuelectenerg-400	4	1	research	research	NOUN
fuelectenerg-400	4	2	has	have	AUX
fuelectenerg-400	4	3	been	be	AUX
fuelectenerg-400	4	4	conducted	conduct	VERB
fuelectenerg-400	4	5	on	on	ADP
fuelectenerg-400	4	6	a	a	DET
fuelectenerg-400	4	7	few	few	ADJ
fuelectenerg-400	4	8	exemplar	exemplar	ADJ
fuelectenerg-400	4	9	2d	2d	NUM
fuelectenerg-400	4	10	constraints	constraint	NOUN
fuelectenerg-400	4	11	,	,	PUNCT
fuelectenerg-400	4	12	e.g.	e.g.	ADV
fuelectenerg-400	4	13	,	,	PUNCT
fuelectenerg-400	4	14	the	the	DET
fuelectenerg-400	4	15	hard	hard	ADJ
fuelectenerg-400	4	16	triangle	triangle	NOUN
fuelectenerg-400	4	17	model	model	NOUN
fuelectenerg-400	4	18	,	,	PUNCT
fuelectenerg-400	4	19	run	run	ADJ
fuelectenerg-400	4	20	-	-	PUNCT
fuelectenerg-400	4	21	length	length	NOUN
fuelectenerg-400	4	22	limited	limited	ADJ
fuelectenerg-400	4	23	constraints	constraint	NOUN
fuelectenerg-400	4	24	on	on	ADP
fuelectenerg-400	4	25	the	the	DET
fuelectenerg-400	4	26	square	square	ADJ
fuelectenerg-400	4	27	lattice	lattice	NOUN
fuelectenerg-400	4	28	,	,	PUNCT
fuelectenerg-400	4	29	and	and	CCONJ
fuelectenerg-400	4	30	2d	2d	NUM
fuelectenerg-400	4	31	checkerboard	checkerboard	NOUN
fuelectenerg-400	4	32	constraints	constraint	NOUN
fuelectenerg-400	4	33	.	.	PUNCT
fuelectenerg-400	5	1	excluding	exclude	VERB
fuelectenerg-400	5	2	these	these	DET
fuelectenerg-400	5	3	results	result	NOUN
fuelectenerg-400	5	4	,	,	PUNCT
fuelectenerg-400	5	5	2d	2d	NUM
fuelectenerg-400	5	6	constrained	constrain	VERB
fuelectenerg-400	5	7	systems	system	NOUN
fuelectenerg-400	5	8	remain	remain	VERB
fuelectenerg-400	5	9	largely	largely	ADV
fuelectenerg-400	5	10	uncharacterized	uncharacterized	ADJ
fuelectenerg-400	5	11	mathematically	mathematically	ADV
fuelectenerg-400	5	12	,	,	PUNCT
fuelectenerg-400	5	13	with	with	ADP
fuelectenerg-400	5	14	only	only	ADJ
fuelectenerg-400	5	15	loose	loose	ADJ
fuelectenerg-400	5	16	bounds	bound	NOUN
fuelectenerg-400	5	17	of	of	ADP
fuelectenerg-400	5	18	capacities	capacity	NOUN
fuelectenerg-400	5	19	present	present	ADJ
fuelectenerg-400	5	20	.	.	PUNCT
fuelectenerg-400	6	1	in	in	ADP
fuelectenerg-400	6	2	this	this	DET
fuelectenerg-400	6	3	paper	paper	NOUN
fuelectenerg-400	6	4	we	we	PRON
fuelectenerg-400	6	5	present	present	VERB
fuelectenerg-400	6	6	a	a	DET
fuelectenerg-400	6	7	lozenge	lozenge	NOUN
fuelectenerg-400	6	8	constraint	constraint	NOUN
fuelectenerg-400	6	9	on	on	ADP
fuelectenerg-400	6	10	a	a	DET
fuelectenerg-400	6	11	regular	regular	ADJ
fuelectenerg-400	6	12	triangular	triangular	NOUN
fuelectenerg-400	6	13	lattice	lattice	NOUN
fuelectenerg-400	6	14	and	and	CCONJ
fuelectenerg-400	6	15	derive	derive	VERB
fuelectenerg-400	6	16	shannon	shannon	PROPN
fuelectenerg-400	6	17	noiseless	noiseless	PROPN
fuelectenerg-400	6	18	capacity	capacity	NOUN
fuelectenerg-400	6	19	bounds	bound	NOUN
fuelectenerg-400	6	20	.	.	PUNCT
fuelectenerg-400	7	1	to	to	PART
fuelectenerg-400	7	2	estimate	estimate	VERB
fuelectenerg-400	7	3	capacity	capacity	NOUN
fuelectenerg-400	7	4	of	of	ADP
fuelectenerg-400	7	5	lozenge	lozenge	NOUN
fuelectenerg-400	7	6	tiling	tile	VERB
fuelectenerg-400	7	7	we	we	PRON
fuelectenerg-400	7	8	make	make	VERB
fuelectenerg-400	7	9	use	use	NOUN
fuelectenerg-400	7	10	of	of	ADP
fuelectenerg-400	7	11	the	the	DET
fuelectenerg-400	7	12	bijection	bijection	NOUN
fuelectenerg-400	7	13	between	between	ADP
fuelectenerg-400	7	14	the	the	DET
fuelectenerg-400	7	15	counting	counting	NOUN
fuelectenerg-400	7	16	of	of	ADP
fuelectenerg-400	7	17	lozenge	lozenge	NOUN
fuelectenerg-400	7	18	tiling	tiling	NOUN
fuelectenerg-400	7	19	and	and	CCONJ
fuelectenerg-400	7	20	the	the	DET
fuelectenerg-400	7	21	counting	counting	NOUN
fuelectenerg-400	7	22	of	of	ADP
fuelectenerg-400	7	23	boxed	boxed	ADJ
fuelectenerg-400	7	24	plane	plane	NOUN
fuelectenerg-400	7	25	partitions	partition	NOUN
fuelectenerg-400	7	26	.	.	PUNCT
fuelectenerg-400	8	1	keywords	keyword	NOUN
fuelectenerg-400	8	2	:	:	PUNCT
fuelectenerg-400	8	3	2d	2d	NUM
fuelectenerg-400	8	4	constrained	constrain	VERB
fuelectenerg-400	8	5	codes	code	NOUN
fuelectenerg-400	8	6	,	,	PUNCT
fuelectenerg-400	8	7	2d	2d	NUM
fuelectenerg-400	8	8	constraints	constraint	NOUN
fuelectenerg-400	8	9	,	,	PUNCT
fuelectenerg-400	8	10	lozenge	lozenge	NOUN
fuelectenerg-400	8	11	tiling	tiling	NOUN
fuelectenerg-400	8	12	,	,	PUNCT
fuelectenerg-400	8	13	colored	colored	ADJ
fuelectenerg-400	8	14	tiling	tiling	NOUN
fuelectenerg-400	8	15	.	.	PUNCT
fuelectenerg-400	9	1	1	1	NUM
fuelectenerg-400	9	2	introduction	introduction	NOUN
fuelectenerg-400	9	3	real	real	ADJ
fuelectenerg-400	9	4	-	-	PUNCT
fuelectenerg-400	9	5	world	world	NOUN
fuelectenerg-400	9	6	communications	communication	NOUN
fuelectenerg-400	9	7	channels	channel	NOUN
fuelectenerg-400	9	8	,	,	PUNCT
fuelectenerg-400	9	9	in	in	ADP
fuelectenerg-400	9	10	contrast	contrast	NOUN
fuelectenerg-400	9	11	to	to	ADP
fuelectenerg-400	9	12	channels	channel	NOUN
fuelectenerg-400	9	13	of	of	ADP
fuelectenerg-400	9	14	theoretical	theoretical	ADJ
fuelectenerg-400	9	15	interest	interest	NOUN
fuelectenerg-400	9	16	,	,	PUNCT
fuelectenerg-400	9	17	often	often	ADV
fuelectenerg-400	9	18	suffer	suffer	VERB
fuelectenerg-400	9	19	from	from	ADP
fuelectenerg-400	9	20	physical	physical	ADJ
fuelectenerg-400	9	21	and	and	CCONJ
fuelectenerg-400	9	22	systemic	systemic	ADJ
fuelectenerg-400	9	23	limitations	limitation	NOUN
fuelectenerg-400	9	24	that	that	PRON
fuelectenerg-400	9	25	constrain	constrain	VERB
fuelectenerg-400	9	26	the	the	DET
fuelectenerg-400	9	27	nature	nature	NOUN
fuelectenerg-400	9	28	of	of	ADP
fuelectenerg-400	9	29	data	datum	NOUN
fuelectenerg-400	9	30	that	that	PRON
fuelectenerg-400	9	31	may	may	AUX
fuelectenerg-400	9	32	be	be	AUX
fuelectenerg-400	9	33	transmitted	transmit	VERB
fuelectenerg-400	9	34	through	through	ADP
fuelectenerg-400	9	35	them	they	PRON
fuelectenerg-400	9	36	.	.	PUNCT
fuelectenerg-400	10	1	one	one	NUM
fuelectenerg-400	10	2	such	such	ADJ
fuelectenerg-400	10	3	often	often	ADV
fuelectenerg-400	10	4	-	-	PUNCT
fuelectenerg-400	10	5	quoted	quote	VERB
fuelectenerg-400	10	6	example	example	NOUN
fuelectenerg-400	10	7	is	be	AUX
fuelectenerg-400	10	8	the	the	DET
fuelectenerg-400	10	9	magnetic	magnetic	ADJ
fuelectenerg-400	10	10	recording	recording	NOUN
fuelectenerg-400	10	11	system	system	NOUN
fuelectenerg-400	10	12	,	,	PUNCT
fuelectenerg-400	10	13	where	where	SCONJ
fuelectenerg-400	10	14	information	information	NOUN
fuelectenerg-400	10	15	is	be	AUX
fuelectenerg-400	10	16	translated	translate	VERB
fuelectenerg-400	10	17	to	to	ADP
fuelectenerg-400	10	18	a	a	DET
fuelectenerg-400	10	19	direction	direction	NOUN
fuelectenerg-400	10	20	of	of	ADP
fuelectenerg-400	10	21	magnetization	magnetization	NOUN
fuelectenerg-400	10	22	of	of	ADP
fuelectenerg-400	10	23	the	the	DET
fuelectenerg-400	10	24	recording	recording	NOUN
fuelectenerg-400	10	25	medium	medium	NOUN
fuelectenerg-400	10	26	.	.	PUNCT
fuelectenerg-400	11	1	magnetic	magnetic	ADJ
fuelectenerg-400	11	2	recording	recording	NOUN
fuelectenerg-400	11	3	systems	system	NOUN
fuelectenerg-400	11	4	place	place	NOUN
fuelectenerg-400	11	5	constraints	constraint	NOUN
fuelectenerg-400	11	6	on	on	ADP
fuelectenerg-400	11	7	the	the	DET
fuelectenerg-400	11	8	duration	duration	NOUN
fuelectenerg-400	11	9	between	between	ADP
fuelectenerg-400	11	10	two	two	NUM
fuelectenerg-400	11	11	consecutive	consecutive	ADJ
fuelectenerg-400	11	12	transitions	transition	NOUN
fuelectenerg-400	11	13	of	of	ADP
fuelectenerg-400	11	14	manuscript	manuscript	NOUN
fuelectenerg-400	11	15	received	receive	VERB
fuelectenerg-400	11	16	august	august	PROPN
fuelectenerg-400	11	17	9	9	NUM
fuelectenerg-400	11	18	,	,	PUNCT
fuelectenerg-400	11	19	2014	2014	NUM
fuelectenerg-400	11	20	corresponding	correspond	VERB
fuelectenerg-400	11	21	author	author	NOUN
fuelectenerg-400	11	22	:	:	PUNCT
fuelectenerg-400	11	23	bane	bane	NOUN
fuelectenerg-400	11	24	vasić	vasić	NOUN
fuelectenerg-400	11	25	is	be	AUX
fuelectenerg-400	11	26	with	with	ADP
fuelectenerg-400	11	27	the	the	DET
fuelectenerg-400	11	28	department	department	NOUN
fuelectenerg-400	11	29	of	of	ADP
fuelectenerg-400	11	30	electrical	electrical	ADJ
fuelectenerg-400	11	31	and	and	CCONJ
fuelectenerg-400	11	32	computer	computer	NOUN
fuelectenerg-400	11	33	engineering	engineering	NOUN
fuelectenerg-400	11	34	,	,	PUNCT
fuelectenerg-400	11	35	university	university	PROPN
fuelectenerg-400	11	36	of	of	ADP
fuelectenerg-400	11	37	arizona	arizona	PROPN
fuelectenerg-400	11	38	,	,	PUNCT
fuelectenerg-400	11	39	tucson	tucson	PROPN
fuelectenerg-400	11	40	,	,	PUNCT
fuelectenerg-400	11	41	az	az	PROPN
fuelectenerg-400	11	42	,	,	PUNCT
fuelectenerg-400	11	43	85721	85721	NUM
fuelectenerg-400	11	44	,	,	PUNCT
fuelectenerg-400	11	45	usa	usa	PROPN
fuelectenerg-400	11	46	(	(	PUNCT
fuelectenerg-400	11	47	e	e	NOUN
fuelectenerg-400	11	48	-	-	NOUN
fuelectenerg-400	11	49	mail	mail	NOUN
fuelectenerg-400	11	50	:	:	PUNCT
fuelectenerg-400	11	51	vasic@ece.arizona.edu	vasic@ece.arizona.edu	NOUN
fuelectenerg-400	11	52	)	)	PUNCT
fuelectenerg-400	11	53	.	.	PUNCT
fuelectenerg-400	12	1	521	521	NUM
fuelectenerg-400	12	2	facta	facta	NOUN
fuelectenerg-400	12	3	universitatis	universitatis	PROPN
fuelectenerg-400	12	4	series	series	NOUN
fuelectenerg-400	12	5	:	:	PUNCT
fuelectenerg-400	12	6	electronics	electronic	NOUN
fuelectenerg-400	12	7	and	and	CCONJ
fuelectenerg-400	12	8	energetics	energetics	NOUN
fuelectenerg-400	12	9	vol	vol	NOUN
fuelectenerg-400	12	10	.	.	PUNCT
fuelectenerg-400	12	11	27	27	NUM
fuelectenerg-400	12	12	,	,	PUNCT
fuelectenerg-400	12	13	no	no	DET
fuelectenerg-400	12	14	4	4	NUM
fuelectenerg-400	12	15	,	,	PUNCT
fuelectenerg-400	12	16	december	december	PROPN
fuelectenerg-400	12	17	2014	2014	NUM
fuelectenerg-400	12	18	,	,	PUNCT
fuelectenerg-400	12	19	pp	pp	ADV
fuelectenerg-400	12	20	.	.	PUNCT
fuelectenerg-400	12	21	521	521	NUM
fuelectenerg-400	12	22	542	542	NUM
fuelectenerg-400	12	23	doi	doi	NOUN
fuelectenerg-400	12	24	:	:	PUNCT
fuelectenerg-400	12	25	10.2298	10.2298	NUM
fuelectenerg-400	12	26	/	/	SYM
fuelectenerg-400	12	27	fuee1404521v	fuee1404521v	PROPN
fuelectenerg-400	12	28	received	receive	VERB
fuelectenerg-400	12	29	august	august	PROPN
fuelectenerg-400	12	30	9	9	NUM
fuelectenerg-400	12	31	,	,	PUNCT
fuelectenerg-400	12	32	2014	2014	NUM
fuelectenerg-400	12	33	corresponding	correspond	VERB
fuelectenerg-400	12	34	author	author	NOUN
fuelectenerg-400	12	35	:	:	PUNCT
fuelectenerg-400	12	36	bane	bane	NOUN
fuelectenerg-400	12	37	vasic	vasic	ADJ
fuelectenerg-400	12	38	department	department	PROPN
fuelectenerg-400	12	39	of	of	ADP
fuelectenerg-400	12	40	electrical	electrical	ADJ
fuelectenerg-400	12	41	and	and	CCONJ
fuelectenerg-400	12	42	computer	computer	NOUN
fuelectenerg-400	12	43	engineering	engineering	NOUN
fuelectenerg-400	12	44	,	,	PUNCT
fuelectenerg-400	12	45	university	university	PROPN
fuelectenerg-400	12	46	of	of	ADP
fuelectenerg-400	12	47	arizona	arizona	PROPN
fuelectenerg-400	12	48	,	,	PUNCT
fuelectenerg-400	12	49	tucson	tucson	PROPN
fuelectenerg-400	12	50	,	,	PUNCT
fuelectenerg-400	12	51	az	az	PROPN
fuelectenerg-400	12	52	,	,	PUNCT
fuelectenerg-400	12	53	85721	85721	NUM
fuelectenerg-400	12	54	,	,	PUNCT
fuelectenerg-400	12	55	usa	usa	PROPN
fuelectenerg-400	12	56	(	(	PUNCT
fuelectenerg-400	12	57	e	e	NOUN
fuelectenerg-400	12	58	-	-	NOUN
fuelectenerg-400	12	59	mail	mail	NOUN
fuelectenerg-400	12	60	:	:	PUNCT
fuelectenerg-400	12	61	vasic@ece.arizona.edu	vasic@ece.arizona.edu	NOUN
fuelectenerg-400	12	62	)	)	PUNCT
fuelectenerg-400	12	63	522	522	NUM
fuelectenerg-400	12	64	a.	a.	NOUN
fuelectenerg-400	12	65	r.	r.	PROPN
fuelectenerg-400	12	66	krishnanan	krishnanan	PROPN
fuelectenerg-400	12	67	and	and	CCONJ
fuelectenerg-400	12	68	b.	b.	PROPN
fuelectenerg-400	12	69	vasić	vasić	PROPN
fuelectenerg-400	12	70	magnetization	magnetization	NOUN
fuelectenerg-400	12	71	direction	direction	NOUN
fuelectenerg-400	12	72	[	[	X
fuelectenerg-400	12	73	1	1	NUM
fuelectenerg-400	12	74	]	]	PUNCT
fuelectenerg-400	12	75	.	.	PUNCT
fuelectenerg-400	13	1	transitions	transition	NOUN
fuelectenerg-400	13	2	too	too	ADV
fuelectenerg-400	13	3	close	close	ADV
fuelectenerg-400	13	4	to	to	ADP
fuelectenerg-400	13	5	each	each	DET
fuelectenerg-400	13	6	other	other	ADJ
fuelectenerg-400	13	7	degrades	degrade	VERB
fuelectenerg-400	13	8	the	the	DET
fuelectenerg-400	13	9	signal	signal	NOUN
fuelectenerg-400	13	10	-	-	PUNCT
fuelectenerg-400	13	11	to	to	ADP
fuelectenerg-400	13	12	-	-	PUNCT
fuelectenerg-400	13	13	noise	noise	NOUN
fuelectenerg-400	13	14	ratio	ratio	NOUN
fuelectenerg-400	13	15	(	(	PUNCT
fuelectenerg-400	13	16	snr	snr	PROPN
fuelectenerg-400	13	17	)	)	PUNCT
fuelectenerg-400	13	18	during	during	ADP
fuelectenerg-400	13	19	readback	readback	NOUN
fuelectenerg-400	13	20	.	.	PUNCT
fuelectenerg-400	14	1	on	on	ADP
fuelectenerg-400	14	2	the	the	DET
fuelectenerg-400	14	3	other	other	ADJ
fuelectenerg-400	14	4	hand	hand	NOUN
fuelectenerg-400	14	5	,	,	PUNCT
fuelectenerg-400	14	6	transitions	transition	NOUN
fuelectenerg-400	14	7	too	too	ADV
fuelectenerg-400	14	8	far	far	ADV
fuelectenerg-400	14	9	apart	apart	ADV
fuelectenerg-400	14	10	make	make	VERB
fuelectenerg-400	14	11	vulnerable	vulnerable	ADJ
fuelectenerg-400	14	12	to	to	ADP
fuelectenerg-400	14	13	failure	failure	NOUN
fuelectenerg-400	14	14	the	the	DET
fuelectenerg-400	14	15	timing	timing	NOUN
fuelectenerg-400	14	16	-	-	PUNCT
fuelectenerg-400	14	17	recovery	recovery	NOUN
fuelectenerg-400	14	18	sub	sub	NOUN
fuelectenerg-400	14	19	-	-	NOUN
fuelectenerg-400	14	20	systems	system	NOUN
fuelectenerg-400	14	21	which	which	PRON
fuelectenerg-400	14	22	typically	typically	ADV
fuelectenerg-400	14	23	rely	rely	VERB
fuelectenerg-400	14	24	on	on	ADP
fuelectenerg-400	14	25	these	these	DET
fuelectenerg-400	14	26	transitions	transition	NOUN
fuelectenerg-400	14	27	to	to	PART
fuelectenerg-400	14	28	derive	derive	VERB
fuelectenerg-400	14	29	symbol	symbol	NOUN
fuelectenerg-400	14	30	-	-	PUNCT
fuelectenerg-400	14	31	level	level	NOUN
fuelectenerg-400	14	32	timing	timing	NOUN
fuelectenerg-400	14	33	information	information	NOUN
fuelectenerg-400	14	34	.	.	PUNCT
fuelectenerg-400	15	1	a	a	DET
fuelectenerg-400	15	2	solution	solution	NOUN
fuelectenerg-400	15	3	to	to	PART
fuelectenerg-400	15	4	satisfy	satisfy	VERB
fuelectenerg-400	15	5	channel	channel	NOUN
fuelectenerg-400	15	6	constraints	constraint	NOUN
fuelectenerg-400	15	7	is	be	AUX
fuelectenerg-400	15	8	to	to	PART
fuelectenerg-400	15	9	use	use	VERB
fuelectenerg-400	15	10	constrained	constrained	ADJ
fuelectenerg-400	15	11	codes	code	NOUN
fuelectenerg-400	15	12	(	(	PUNCT
fuelectenerg-400	15	13	or	or	CCONJ
fuelectenerg-400	15	14	modulation	modulation	NOUN
fuelectenerg-400	15	15	codes	code	NOUN
fuelectenerg-400	15	16	)	)	PUNCT
fuelectenerg-400	15	17	–	–	PUNCT
fuelectenerg-400	15	18	codes	code	NOUN
fuelectenerg-400	15	19	that	that	PRON
fuelectenerg-400	15	20	transform	transform	VERB
fuelectenerg-400	15	21	user	user	NOUN
fuelectenerg-400	15	22	information	information	NOUN
fuelectenerg-400	15	23	to	to	ADP
fuelectenerg-400	15	24	symbol	symbol	NOUN
fuelectenerg-400	15	25	-	-	PUNCT
fuelectenerg-400	15	26	sequences	sequence	NOUN
fuelectenerg-400	15	27	that	that	PRON
fuelectenerg-400	15	28	satisfy	satisfy	VERB
fuelectenerg-400	15	29	the	the	DET
fuelectenerg-400	15	30	constraints	constraint	NOUN
fuelectenerg-400	15	31	.	.	PUNCT
fuelectenerg-400	16	1	one	one	NUM
fuelectenerg-400	16	2	dimensional	dimensional	ADJ
fuelectenerg-400	16	3	(	(	PUNCT
fuelectenerg-400	16	4	1d	1d	NUM
fuelectenerg-400	16	5	)	)	PUNCT
fuelectenerg-400	16	6	constraints	constraint	NOUN
fuelectenerg-400	16	7	have	have	AUX
fuelectenerg-400	16	8	been	be	AUX
fuelectenerg-400	16	9	well	well	ADV
fuelectenerg-400	16	10	-	-	PUNCT
fuelectenerg-400	16	11	studied	study	VERB
fuelectenerg-400	16	12	.	.	PUNCT
fuelectenerg-400	17	1	the	the	DET
fuelectenerg-400	17	2	mathematical	mathematical	ADJ
fuelectenerg-400	17	3	framework	framework	NOUN
fuelectenerg-400	17	4	for	for	ADP
fuelectenerg-400	17	5	determining	determine	VERB
fuelectenerg-400	17	6	the	the	DET
fuelectenerg-400	17	7	shannon	shannon	PROPN
fuelectenerg-400	17	8	noiseless	noiseless	ADJ
fuelectenerg-400	17	9	capacity	capacity	NOUN
fuelectenerg-400	17	10	of	of	ADP
fuelectenerg-400	17	11	1d	1d	NUM
fuelectenerg-400	17	12	constraints	constraint	NOUN
fuelectenerg-400	17	13	–	–	PUNCT
fuelectenerg-400	17	14	the	the	DET
fuelectenerg-400	17	15	growth	growth	NOUN
fuelectenerg-400	17	16	rate	rate	NOUN
fuelectenerg-400	17	17	of	of	ADP
fuelectenerg-400	17	18	the	the	DET
fuelectenerg-400	17	19	number	number	NOUN
fuelectenerg-400	17	20	of	of	ADP
fuelectenerg-400	17	21	sequences	sequence	NOUN
fuelectenerg-400	17	22	satisfying	satisfy	VERB
fuelectenerg-400	17	23	a	a	DET
fuelectenerg-400	17	24	given	give	VERB
fuelectenerg-400	17	25	constraint	constraint	NOUN
fuelectenerg-400	17	26	–	–	PUNCT
fuelectenerg-400	17	27	has	have	AUX
fuelectenerg-400	17	28	been	be	AUX
fuelectenerg-400	17	29	comprehensively	comprehensively	ADV
fuelectenerg-400	17	30	laid	lay	VERB
fuelectenerg-400	17	31	out	out	ADP
fuelectenerg-400	17	32	.	.	PUNCT
fuelectenerg-400	18	1	further	far	ADV
fuelectenerg-400	18	2	,	,	PUNCT
fuelectenerg-400	18	3	development	development	NOUN
fuelectenerg-400	18	4	of	of	ADP
fuelectenerg-400	18	5	1d	1d	NUM
fuelectenerg-400	18	6	constrained	constrain	VERB
fuelectenerg-400	18	7	codes	code	NOUN
fuelectenerg-400	18	8	and	and	CCONJ
fuelectenerg-400	18	9	decoders	decoder	NOUN
fuelectenerg-400	18	10	is	be	AUX
fuelectenerg-400	18	11	mature	mature	ADJ
fuelectenerg-400	18	12	(	(	PUNCT
fuelectenerg-400	18	13	refer	refer	VERB
fuelectenerg-400	18	14	[	[	X
fuelectenerg-400	18	15	1	1	NUM
fuelectenerg-400	18	16	]	]	PUNCT
fuelectenerg-400	18	17	for	for	ADP
fuelectenerg-400	18	18	a	a	DET
fuelectenerg-400	18	19	review	review	NOUN
fuelectenerg-400	18	20	on	on	ADP
fuelectenerg-400	18	21	this	this	DET
fuelectenerg-400	18	22	topic	topic	NOUN
fuelectenerg-400	18	23	)	)	PUNCT
fuelectenerg-400	18	24	.	.	PUNCT
fuelectenerg-400	19	1	in	in	ADP
fuelectenerg-400	19	2	contrast	contrast	NOUN
fuelectenerg-400	19	3	,	,	PUNCT
fuelectenerg-400	19	4	analysis	analysis	NOUN
fuelectenerg-400	19	5	and	and	CCONJ
fuelectenerg-400	19	6	code	code	NOUN
fuelectenerg-400	19	7	development	development	NOUN
fuelectenerg-400	19	8	for	for	ADP
fuelectenerg-400	19	9	two	two	NUM
fuelectenerg-400	19	10	-	-	PUNCT
fuelectenerg-400	19	11	dimensional	dimensional	ADJ
fuelectenerg-400	19	12	(	(	PUNCT
fuelectenerg-400	19	13	2d	2d	NOUN
fuelectenerg-400	19	14	)	)	PUNCT
fuelectenerg-400	19	15	constraint	constraint	NOUN
fuelectenerg-400	19	16	systems	system	NOUN
fuelectenerg-400	19	17	have	have	AUX
fuelectenerg-400	19	18	been	be	AUX
fuelectenerg-400	19	19	less	less	ADV
fuelectenerg-400	19	20	successful	successful	ADJ
fuelectenerg-400	19	21	.	.	PUNCT
fuelectenerg-400	20	1	initial	initial	ADJ
fuelectenerg-400	20	2	work	work	NOUN
fuelectenerg-400	20	3	on	on	ADP
fuelectenerg-400	20	4	2d	2d	NUM
fuelectenerg-400	20	5	constraints	constraint	NOUN
fuelectenerg-400	20	6	was	be	AUX
fuelectenerg-400	20	7	done	do	VERB
fuelectenerg-400	20	8	by	by	ADP
fuelectenerg-400	20	9	ashley	ashley	PROPN
fuelectenerg-400	20	10	and	and	CCONJ
fuelectenerg-400	20	11	marcus	marcus	PROPN
fuelectenerg-400	21	1	[	[	X
fuelectenerg-400	21	2	2	2	X
fuelectenerg-400	21	3	]	]	PUNCT
fuelectenerg-400	21	4	who	who	PRON
fuelectenerg-400	21	5	considered	consider	VERB
fuelectenerg-400	21	6	2d	2d	NUM
fuelectenerg-400	21	7	low	low	ADJ
fuelectenerg-400	21	8	-	-	PUNCT
fuelectenerg-400	21	9	pass	pass	NOUN
fuelectenerg-400	21	10	filtering	filter	VERB
fuelectenerg-400	21	11	codes	code	NOUN
fuelectenerg-400	21	12	for	for	ADP
fuelectenerg-400	21	13	eliminating	eliminate	VERB
fuelectenerg-400	21	14	bit	bit	NOUN
fuelectenerg-400	21	15	-	-	PUNCT
fuelectenerg-400	21	16	patterns	pattern	NOUN
fuelectenerg-400	21	17	with	with	ADP
fuelectenerg-400	21	18	large	large	ADJ
fuelectenerg-400	21	19	highfrequency	highfrequency	NOUN
fuelectenerg-400	21	20	components	component	NOUN
fuelectenerg-400	21	21	.	.	PUNCT
fuelectenerg-400	22	1	subsequently	subsequently	ADV
fuelectenerg-400	22	2	,	,	PUNCT
fuelectenerg-400	22	3	considerable	considerable	ADJ
fuelectenerg-400	22	4	research	research	NOUN
fuelectenerg-400	22	5	was	be	AUX
fuelectenerg-400	22	6	conducted	conduct	VERB
fuelectenerg-400	22	7	on	on	ADP
fuelectenerg-400	22	8	numerous	numerous	ADJ
fuelectenerg-400	22	9	classes	class	NOUN
fuelectenerg-400	22	10	of	of	ADP
fuelectenerg-400	22	11	2d	2d	NUM
fuelectenerg-400	22	12	constraints	constraint	NOUN
fuelectenerg-400	22	13	,	,	PUNCT
fuelectenerg-400	22	14	e.g.	e.g.	ADV
fuelectenerg-400	22	15	,	,	PUNCT
fuelectenerg-400	22	16	[	[	X
fuelectenerg-400	22	17	3–9	3–9	NOUN
fuelectenerg-400	22	18	]	]	PUNCT
fuelectenerg-400	22	19	.	.	PUNCT
fuelectenerg-400	23	1	in	in	ADP
fuelectenerg-400	23	2	spite	spite	NOUN
fuelectenerg-400	23	3	of	of	ADP
fuelectenerg-400	23	4	these	these	DET
fuelectenerg-400	23	5	efforts	effort	NOUN
fuelectenerg-400	23	6	,	,	PUNCT
fuelectenerg-400	23	7	these	these	DET
fuelectenerg-400	23	8	constrained	constrain	VERB
fuelectenerg-400	23	9	systems	system	NOUN
fuelectenerg-400	23	10	remain	remain	VERB
fuelectenerg-400	23	11	largely	largely	ADV
fuelectenerg-400	23	12	uncharacterized	uncharacterized	ADJ
fuelectenerg-400	23	13	mathematically	mathematically	ADV
fuelectenerg-400	23	14	with	with	ADP
fuelectenerg-400	23	15	only	only	ADJ
fuelectenerg-400	23	16	loose	loose	ADJ
fuelectenerg-400	23	17	bounds	bound	NOUN
fuelectenerg-400	23	18	of	of	ADP
fuelectenerg-400	23	19	capacities	capacity	NOUN
fuelectenerg-400	23	20	existing	exist	VERB
fuelectenerg-400	23	21	.	.	PUNCT
fuelectenerg-400	24	1	with	with	ADP
fuelectenerg-400	24	2	an	an	DET
fuelectenerg-400	24	3	exception	exception	NOUN
fuelectenerg-400	24	4	of	of	ADP
fuelectenerg-400	24	5	a	a	DET
fuelectenerg-400	24	6	few	few	ADJ
fuelectenerg-400	24	7	cases	case	NOUN
fuelectenerg-400	24	8	,	,	PUNCT
fuelectenerg-400	24	9	the	the	DET
fuelectenerg-400	24	10	channel	channel	NOUN
fuelectenerg-400	24	11	capacity	capacity	NOUN
fuelectenerg-400	24	12	of	of	ADP
fuelectenerg-400	24	13	2d	2d	NUM
fuelectenerg-400	24	14	constrained	constrain	VERB
fuelectenerg-400	24	15	channels	channel	NOUN
fuelectenerg-400	24	16	is	be	AUX
fuelectenerg-400	24	17	unknown	unknown	ADJ
fuelectenerg-400	24	18	(	(	PUNCT
fuelectenerg-400	24	19	see	see	VERB
fuelectenerg-400	24	20	[	[	X
fuelectenerg-400	24	21	10	10	NUM
fuelectenerg-400	24	22	]	]	NUM
fuelectenerg-400	24	23	)	)	PUNCT
fuelectenerg-400	24	24	,	,	PUNCT
fuelectenerg-400	24	25	and	and	CCONJ
fuelectenerg-400	24	26	there	there	PRON
fuelectenerg-400	24	27	is	be	VERB
fuelectenerg-400	24	28	no	no	DET
fuelectenerg-400	24	29	systematic	systematic	ADJ
fuelectenerg-400	24	30	procedure	procedure	NOUN
fuelectenerg-400	24	31	to	to	PART
fuelectenerg-400	24	32	design	design	VERB
fuelectenerg-400	24	33	encoders	encoder	NOUN
fuelectenerg-400	24	34	and	and	CCONJ
fuelectenerg-400	24	35	decoders	decoder	NOUN
fuelectenerg-400	24	36	.	.	PUNCT
fuelectenerg-400	25	1	nonetheless	nonetheless	ADV
fuelectenerg-400	25	2	,	,	PUNCT
fuelectenerg-400	25	3	the	the	DET
fuelectenerg-400	25	4	need	need	ADJ
fuelectenerg-400	25	5	two	two	NUM
fuelectenerg-400	25	6	-	-	PUNCT
fuelectenerg-400	25	7	dimensional	dimensional	ADJ
fuelectenerg-400	25	8	constrained	constrain	VERB
fuelectenerg-400	25	9	codes	code	NOUN
fuelectenerg-400	25	10	has	have	AUX
fuelectenerg-400	25	11	come	come	VERB
fuelectenerg-400	25	12	to	to	ADP
fuelectenerg-400	25	13	the	the	DET
fuelectenerg-400	25	14	fore	fore	NOUN
fuelectenerg-400	25	15	in	in	ADP
fuelectenerg-400	25	16	light	light	NOUN
fuelectenerg-400	25	17	of	of	ADP
fuelectenerg-400	25	18	the	the	DET
fuelectenerg-400	25	19	recent	recent	ADJ
fuelectenerg-400	25	20	work	work	NOUN
fuelectenerg-400	25	21	in	in	ADP
fuelectenerg-400	25	22	two	two	NUM
fuelectenerg-400	25	23	-	-	PUNCT
fuelectenerg-400	25	24	dimensional	dimensional	ADJ
fuelectenerg-400	25	25	magnetic	magnetic	ADJ
fuelectenerg-400	25	26	recording	recording	NOUN
fuelectenerg-400	25	27	(	(	PUNCT
fuelectenerg-400	25	28	tdmr	tdmr	NOUN
fuelectenerg-400	25	29	)	)	PUNCT
fuelectenerg-400	25	30	.	.	PUNCT
fuelectenerg-400	26	1	in	in	ADP
fuelectenerg-400	26	2	[	[	X
fuelectenerg-400	26	3	11	11	NUM
fuelectenerg-400	26	4	]	]	PUNCT
fuelectenerg-400	26	5	,	,	PUNCT
fuelectenerg-400	26	6	it	it	PRON
fuelectenerg-400	26	7	was	be	AUX
fuelectenerg-400	26	8	shown	show	VERB
fuelectenerg-400	26	9	that	that	SCONJ
fuelectenerg-400	26	10	constrained	constrain	VERB
fuelectenerg-400	26	11	coding	coding	NOUN
fuelectenerg-400	26	12	which	which	PRON
fuelectenerg-400	26	13	restricts	restrict	VERB
fuelectenerg-400	26	14	the	the	DET
fuelectenerg-400	26	15	occurrence	occurrence	NOUN
fuelectenerg-400	26	16	of	of	ADP
fuelectenerg-400	26	17	certain	certain	ADJ
fuelectenerg-400	26	18	2d	2d	NOUN
fuelectenerg-400	26	19	patterns	pattern	NOUN
fuelectenerg-400	26	20	greatly	greatly	ADV
fuelectenerg-400	26	21	reduces	reduce	VERB
fuelectenerg-400	26	22	system	system	NOUN
fuelectenerg-400	26	23	complexity	complexity	NOUN
fuelectenerg-400	26	24	and	and	CCONJ
fuelectenerg-400	26	25	improves	improve	VERB
fuelectenerg-400	26	26	the	the	DET
fuelectenerg-400	26	27	detection	detection	NOUN
fuelectenerg-400	26	28	performance	performance	NOUN
fuelectenerg-400	26	29	.	.	PUNCT
fuelectenerg-400	27	1	also	also	ADV
fuelectenerg-400	27	2	,	,	PUNCT
fuelectenerg-400	27	3	there	there	PRON
fuelectenerg-400	27	4	exist	exist	VERB
fuelectenerg-400	27	5	media	medium	NOUN
fuelectenerg-400	27	6	models	model	NOUN
fuelectenerg-400	27	7	for	for	ADP
fuelectenerg-400	27	8	tdmr	tdmr	NOUN
fuelectenerg-400	27	9	that	that	PRON
fuelectenerg-400	27	10	rely	rely	VERB
fuelectenerg-400	27	11	on	on	ADP
fuelectenerg-400	27	12	polyomino	polyomino	NOUN
fuelectenerg-400	27	13	tiling	tile	VERB
fuelectenerg-400	27	14	[	[	X
fuelectenerg-400	27	15	12,13	12,13	NUM
fuelectenerg-400	27	16	]	]	PUNCT
fuelectenerg-400	27	17	,	,	PUNCT
fuelectenerg-400	27	18	which	which	PRON
fuelectenerg-400	27	19	are	be	AUX
fuelectenerg-400	27	20	closely	closely	ADV
fuelectenerg-400	27	21	related	relate	VERB
fuelectenerg-400	27	22	to	to	ADP
fuelectenerg-400	27	23	the	the	DET
fuelectenerg-400	27	24	2d	2d	NUM
fuelectenerg-400	27	25	constrained	constrain	VERB
fuelectenerg-400	27	26	systems	system	NOUN
fuelectenerg-400	27	27	.	.	PUNCT
fuelectenerg-400	28	1	in	in	ADP
fuelectenerg-400	28	2	this	this	DET
fuelectenerg-400	28	3	paper	paper	NOUN
fuelectenerg-400	28	4	,	,	PUNCT
fuelectenerg-400	28	5	we	we	PRON
fuelectenerg-400	28	6	consider	consider	VERB
fuelectenerg-400	28	7	a	a	DET
fuelectenerg-400	28	8	class	class	NOUN
fuelectenerg-400	28	9	of	of	ADP
fuelectenerg-400	28	10	low	low	ADJ
fuelectenerg-400	28	11	-	-	PUNCT
fuelectenerg-400	28	12	pass	pass	NOUN
fuelectenerg-400	28	13	constraint	constraint	NOUN
fuelectenerg-400	28	14	on	on	ADP
fuelectenerg-400	28	15	the	the	DET
fuelectenerg-400	28	16	triangular	triangular	NOUN
fuelectenerg-400	28	17	lattice	lattice	NOUN
fuelectenerg-400	28	18	termed	term	VERB
fuelectenerg-400	28	19	segregation	segregation	NOUN
fuelectenerg-400	28	20	constraint	constraint	NOUN
fuelectenerg-400	28	21	and	and	CCONJ
fuelectenerg-400	28	22	it	it	PRON
fuelectenerg-400	28	23	special	special	ADJ
fuelectenerg-400	28	24	case	case	NOUN
fuelectenerg-400	28	25	,	,	PUNCT
fuelectenerg-400	28	26	no	no	DET
fuelectenerg-400	28	27	isolated	isolated	ADJ
fuelectenerg-400	28	28	bit	bit	NOUN
fuelectenerg-400	28	29	(	(	PUNCT
fuelectenerg-400	28	30	nib	nib	NOUN
fuelectenerg-400	28	31	)	)	PUNCT
fuelectenerg-400	28	32	constraint	constraint	NOUN
fuelectenerg-400	28	33	.	.	PUNCT
fuelectenerg-400	29	1	we	we	PRON
fuelectenerg-400	29	2	provide	provide	VERB
fuelectenerg-400	29	3	an	an	DET
fuelectenerg-400	29	4	upper	upper	ADJ
fuelectenerg-400	29	5	bound	bind	VERB
fuelectenerg-400	29	6	on	on	ADP
fuelectenerg-400	29	7	the	the	DET
fuelectenerg-400	29	8	shannon	shannon	PROPN
fuelectenerg-400	29	9	noiseless	noiseless	PROPN
fuelectenerg-400	29	10	capacity	capacity	NOUN
fuelectenerg-400	29	11	for	for	ADP
fuelectenerg-400	29	12	this	this	DET
fuelectenerg-400	29	13	constraint	constraint	NOUN
fuelectenerg-400	29	14	.	.	PUNCT
fuelectenerg-400	30	1	the	the	DET
fuelectenerg-400	30	2	key	key	ADJ
fuelectenerg-400	30	3	novelty	novelty	NOUN
fuelectenerg-400	30	4	of	of	ADP
fuelectenerg-400	30	5	the	the	DET
fuelectenerg-400	30	6	our	our	PRON
fuelectenerg-400	30	7	approach	approach	NOUN
fuelectenerg-400	30	8	is	be	AUX
fuelectenerg-400	30	9	to	to	PART
fuelectenerg-400	30	10	view	view	VERB
fuelectenerg-400	30	11	our	our	PRON
fuelectenerg-400	30	12	2d	2d	PROPN
fuelectenerg-400	30	13	constraint	constraint	NOUN
fuelectenerg-400	30	14	as	as	ADP
fuelectenerg-400	30	15	a	a	DET
fuelectenerg-400	30	16	colored	colored	ADJ
fuelectenerg-400	30	17	tiling	tiling	NOUN
fuelectenerg-400	30	18	of	of	ADP
fuelectenerg-400	30	19	a	a	DET
fuelectenerg-400	30	20	plane	plane	NOUN
fuelectenerg-400	30	21	.	.	PUNCT
fuelectenerg-400	31	1	thus	thus	ADV
fuelectenerg-400	31	2	,	,	PUNCT
fuelectenerg-400	31	3	the	the	DET
fuelectenerg-400	31	4	estimation	estimation	NOUN
fuelectenerg-400	31	5	of	of	ADP
fuelectenerg-400	31	6	the	the	DET
fuelectenerg-400	31	7	number	number	NOUN
fuelectenerg-400	31	8	of	of	ADP
fuelectenerg-400	31	9	permissible	permissible	ADJ
fuelectenerg-400	31	10	colored	colored	ADJ
fuelectenerg-400	31	11	tilings	tiling	NOUN
fuelectenerg-400	31	12	leads	lead	VERB
fuelectenerg-400	31	13	to	to	ADP
fuelectenerg-400	31	14	upper	upper	ADJ
fuelectenerg-400	31	15	bounds	bound	NOUN
fuelectenerg-400	31	16	on	on	ADP
fuelectenerg-400	31	17	shannon	shannon	PROPN
fuelectenerg-400	31	18	noiseless	noiseless	PROPN
fuelectenerg-400	31	19	capacity	capacity	NOUN
fuelectenerg-400	31	20	of	of	ADP
fuelectenerg-400	31	21	2d	2d	NUM
fuelectenerg-400	31	22	channels	channel	NOUN
fuelectenerg-400	31	23	represented	represent	VERB
fuelectenerg-400	31	24	by	by	ADP
fuelectenerg-400	31	25	this	this	DET
fuelectenerg-400	31	26	constraint	constraint	NOUN
fuelectenerg-400	31	27	.	.	PUNCT
fuelectenerg-400	32	1	in	in	ADP
fuelectenerg-400	32	2	addition	addition	NOUN
fuelectenerg-400	32	3	,	,	PUNCT
fuelectenerg-400	32	4	the	the	DET
fuelectenerg-400	32	5	tools	tool	NOUN
fuelectenerg-400	32	6	used	use	VERB
fuelectenerg-400	32	7	for	for	ADP
fuelectenerg-400	32	8	analysis	analysis	NOUN
fuelectenerg-400	32	9	also	also	ADV
fuelectenerg-400	32	10	lead	lead	VERB
fuelectenerg-400	32	11	to	to	ADP
fuelectenerg-400	32	12	a	a	DET
fuelectenerg-400	32	13	framework	framework	NOUN
fuelectenerg-400	32	14	for	for	ADP
fuelectenerg-400	32	15	encoders	encoder	NOUN
fuelectenerg-400	32	16	and	and	CCONJ
fuelectenerg-400	32	17	decoders	decoder	NOUN
fuelectenerg-400	32	18	for	for	ADP
fuelectenerg-400	32	19	the	the	DET
fuelectenerg-400	32	20	constraint	constraint	NOUN
fuelectenerg-400	32	21	.	.	PUNCT
fuelectenerg-400	33	1	the	the	DET
fuelectenerg-400	33	2	rest	rest	NOUN
fuelectenerg-400	33	3	of	of	ADP
fuelectenerg-400	33	4	the	the	DET
fuelectenerg-400	33	5	paper	paper	NOUN
fuelectenerg-400	33	6	is	be	AUX
fuelectenerg-400	33	7	organized	organize	VERB
fuelectenerg-400	33	8	as	as	SCONJ
fuelectenerg-400	33	9	follows	follow	VERB
fuelectenerg-400	33	10	.	.	PUNCT
fuelectenerg-400	34	1	section	section	NOUN
fuelectenerg-400	34	2	2	2	NUM
fuelectenerg-400	34	3	gives	give	VERB
fuelectenerg-400	34	4	the	the	DET
fuelectenerg-400	34	5	necessary	necessary	ADJ
fuelectenerg-400	34	6	background	background	NOUN
fuelectenerg-400	34	7	and	and	CCONJ
fuelectenerg-400	34	8	motivation	motivation	NOUN
fuelectenerg-400	34	9	of	of	ADP
fuelectenerg-400	34	10	the	the	DET
fuelectenerg-400	34	11	problem	problem	NOUN
fuelectenerg-400	34	12	.	.	PUNCT
fuelectenerg-400	35	1	in	in	ADP
fuelectenerg-400	35	2	section	section	NOUN
fuelectenerg-400	35	3	3	3	NUM
fuelectenerg-400	35	4	,	,	PUNCT
fuelectenerg-400	35	5	we	we	PRON
fuelectenerg-400	35	6	define	define	VERB
fuelectenerg-400	35	7	lozenge	lozenge	NOUN
fuelectenerg-400	35	8	codes	code	NOUN
fuelectenerg-400	35	9	and	and	CCONJ
fuelectenerg-400	35	10	establish	establish	VERB
fuelectenerg-400	35	11	their	their	PRON
fuelectenerg-400	35	12	connection	connection	NOUN
fuelectenerg-400	35	13	with	with	ADP
fuelectenerg-400	35	14	boxed	boxed	ADJ
fuelectenerg-400	35	15	plane	plane	NOUN
fuelectenerg-400	35	16	partitions	partition	NOUN
fuelectenerg-400	35	17	,	,	PUNCT
fuelectenerg-400	35	18	and	and	CCONJ
fuelectenerg-400	35	19	in	in	ADP
fuelectenerg-400	35	20	section	section	NOUN
fuelectenerg-400	35	21	4	4	NUM
fuelectenerg-400	35	22	we	we	PRON
fuelectenerg-400	35	23	derive	derive	VERB
fuelectenerg-400	35	24	bounds	bound	NOUN
fuelectenerg-400	35	25	on	on	ADP
fuelectenerg-400	35	26	capacity	capacity	NOUN
fuelectenerg-400	35	27	.	.	PUNCT
fuelectenerg-400	36	1	section	section	NOUN
fuelectenerg-400	36	2	5	5	NUM
fuelectenerg-400	36	3	introduces	introduce	NOUN
fuelectenerg-400	36	4	encoding	encode	VERB
fuelectenerg-400	36	5	and	and	CCONJ
fuelectenerg-400	36	6	decoding	decode	VERB
fuelectenerg-400	36	7	schemes	scheme	NOUN
fuelectenerg-400	36	8	for	for	ADP
fuelectenerg-400	36	9	lozenge	lozenge	NOUN
fuelectenerg-400	36	10	codes	code	NOUN
fuelectenerg-400	36	11	,	,	PUNCT
fuelectenerg-400	36	12	and	and	CCONJ
fuelectenerg-400	36	13	section	section	NOUN
fuelectenerg-400	36	14	6	6	NUM
fuelectenerg-400	36	15	concludes	conclude	VERB
fuelectenerg-400	36	16	the	the	DET
fuelectenerg-400	36	17	paper	paper	NOUN
fuelectenerg-400	36	18	.	.	PUNCT
fuelectenerg-400	37	1	detection	detection	NOUN
fuelectenerg-400	37	2	and	and	CCONJ
fuelectenerg-400	37	3	coding	code	VERB
fuelectenerg-400	37	4	for	for	ADP
fuelectenerg-400	37	5	tdmr	tdmr	NOUN
fuelectenerg-400	37	6	channel	channel	NOUN
fuelectenerg-400	37	7	523	523	NUM
fuelectenerg-400	37	8	2	2	NUM
fuelectenerg-400	37	9	preliminaries	preliminary	NOUN
fuelectenerg-400	37	10	a	a	DET
fuelectenerg-400	37	11	two	two	NUM
fuelectenerg-400	37	12	-	-	PUNCT
fuelectenerg-400	37	13	dimensional	dimensional	ADJ
fuelectenerg-400	37	14	constrained	constrain	VERB
fuelectenerg-400	37	15	encoder	encoder	NOUN
fuelectenerg-400	37	16	may	may	AUX
fuelectenerg-400	37	17	be	be	AUX
fuelectenerg-400	37	18	visualized	visualize	VERB
fuelectenerg-400	37	19	as	as	ADP
fuelectenerg-400	37	20	a	a	DET
fuelectenerg-400	37	21	mapping	mapping	NOUN
fuelectenerg-400	37	22	from	from	ADP
fuelectenerg-400	37	23	an	an	DET
fuelectenerg-400	37	24	unconstrained	unconstrained	ADJ
fuelectenerg-400	37	25	binary	binary	ADJ
fuelectenerg-400	37	26	sequence	sequence	NOUN
fuelectenerg-400	37	27	into	into	ADP
fuelectenerg-400	37	28	a	a	DET
fuelectenerg-400	37	29	colored	colored	ADJ
fuelectenerg-400	37	30	tiling	tiling	NOUN
fuelectenerg-400	37	31	.	.	PUNCT
fuelectenerg-400	38	1	a	a	DET
fuelectenerg-400	38	2	tiling	tiling	NOUN
fuelectenerg-400	38	3	of	of	ADP
fuelectenerg-400	38	4	the	the	DET
fuelectenerg-400	38	5	plane	plane	NOUN
fuelectenerg-400	38	6	is	be	AUX
fuelectenerg-400	38	7	a	a	DET
fuelectenerg-400	38	8	collection	collection	NOUN
fuelectenerg-400	38	9	of	of	ADP
fuelectenerg-400	38	10	plane	plane	NOUN
fuelectenerg-400	38	11	figures	figure	NOUN
fuelectenerg-400	38	12	that	that	PRON
fuelectenerg-400	38	13	fills	fill	VERB
fuelectenerg-400	38	14	the	the	DET
fuelectenerg-400	38	15	plane	plane	NOUN
fuelectenerg-400	38	16	with	with	ADP
fuelectenerg-400	38	17	no	no	DET
fuelectenerg-400	38	18	overlaps	overlap	NOUN
fuelectenerg-400	38	19	and	and	CCONJ
fuelectenerg-400	38	20	no	no	DET
fuelectenerg-400	38	21	gaps	gap	NOUN
fuelectenerg-400	38	22	.	.	PUNCT
fuelectenerg-400	39	1	the	the	DET
fuelectenerg-400	39	2	plane	plane	NOUN
fuelectenerg-400	39	3	figures	figure	NOUN
fuelectenerg-400	39	4	used	use	VERB
fuelectenerg-400	39	5	as	as	ADP
fuelectenerg-400	39	6	building	build	VERB
fuelectenerg-400	39	7	blocks	block	NOUN
fuelectenerg-400	39	8	for	for	ADP
fuelectenerg-400	39	9	tilings	tiling	NOUN
fuelectenerg-400	39	10	are	be	AUX
fuelectenerg-400	39	11	called	call	VERB
fuelectenerg-400	39	12	tiles	tile	NOUN
fuelectenerg-400	39	13	.	.	PUNCT
fuelectenerg-400	40	1	two	two	NUM
fuelectenerg-400	40	2	tiles	tile	NOUN
fuelectenerg-400	40	3	are	be	AUX
fuelectenerg-400	40	4	said	say	VERB
fuelectenerg-400	40	5	to	to	PART
fuelectenerg-400	40	6	be	be	AUX
fuelectenerg-400	40	7	neigbors	neigbor	NOUN
fuelectenerg-400	40	8	if	if	SCONJ
fuelectenerg-400	40	9	they	they	PRON
fuelectenerg-400	40	10	share	share	VERB
fuelectenerg-400	40	11	an	an	DET
fuelectenerg-400	40	12	edge	edge	NOUN
fuelectenerg-400	40	13	(	(	PUNCT
fuelectenerg-400	40	14	side	side	NOUN
fuelectenerg-400	40	15	)	)	PUNCT
fuelectenerg-400	40	16	,	,	PUNCT
fuelectenerg-400	40	17	and	and	CCONJ
fuelectenerg-400	40	18	to	to	PART
fuelectenerg-400	40	19	be	be	AUX
fuelectenerg-400	40	20	touching	touch	VERB
fuelectenerg-400	40	21	if	if	SCONJ
fuelectenerg-400	40	22	they	they	PRON
fuelectenerg-400	40	23	share	share	VERB
fuelectenerg-400	40	24	only	only	ADV
fuelectenerg-400	40	25	a	a	DET
fuelectenerg-400	40	26	single	single	ADJ
fuelectenerg-400	40	27	vertex	vertex	NOUN
fuelectenerg-400	40	28	.	.	PUNCT
fuelectenerg-400	41	1	a	a	DET
fuelectenerg-400	41	2	regular	regular	ADJ
fuelectenerg-400	41	3	tiling	tiling	NOUN
fuelectenerg-400	41	4	uses	use	VERB
fuelectenerg-400	41	5	congruent	congruent	ADJ
fuelectenerg-400	41	6	regular	regular	ADJ
fuelectenerg-400	41	7	polygons	polygon	NOUN
fuelectenerg-400	41	8	as	as	ADP
fuelectenerg-400	41	9	tiles	tile	NOUN
fuelectenerg-400	41	10	.	.	PUNCT
fuelectenerg-400	42	1	there	there	PRON
fuelectenerg-400	42	2	are	be	VERB
fuelectenerg-400	42	3	only	only	ADV
fuelectenerg-400	42	4	three	three	NUM
fuelectenerg-400	42	5	regular	regular	ADJ
fuelectenerg-400	42	6	tilings	tiling	NOUN
fuelectenerg-400	42	7	:	:	PUNCT
fuelectenerg-400	42	8	triangular	triangular	NOUN
fuelectenerg-400	42	9	,	,	PUNCT
fuelectenerg-400	42	10	square	square	ADJ
fuelectenerg-400	42	11	,	,	PUNCT
fuelectenerg-400	42	12	and	and	CCONJ
fuelectenerg-400	42	13	hexagonal	hexagonal	ADJ
fuelectenerg-400	42	14	.	.	PUNCT
fuelectenerg-400	43	1	figure	figure	NOUN
fuelectenerg-400	43	2	1	1	NUM
fuelectenerg-400	43	3	illustrates	illustrate	VERB
fuelectenerg-400	43	4	each	each	PRON
fuelectenerg-400	43	5	of	of	ADP
fuelectenerg-400	43	6	these	these	DET
fuelectenerg-400	43	7	tilings	tiling	NOUN
fuelectenerg-400	43	8	.	.	PUNCT
fuelectenerg-400	44	1	a	a	DET
fuelectenerg-400	44	2	tiling	tiling	NOUN
fuelectenerg-400	44	3	of	of	ADP
fuelectenerg-400	44	4	a	a	DET
fuelectenerg-400	44	5	plane	plane	NOUN
fuelectenerg-400	44	6	figure	figure	NOUN
fuelectenerg-400	44	7	or	or	CCONJ
fuelectenerg-400	44	8	finite	finite	ADJ
fuelectenerg-400	44	9	region	region	NOUN
fuelectenerg-400	44	10	can	can	AUX
fuelectenerg-400	44	11	be	be	AUX
fuelectenerg-400	44	12	defined	define	VERB
fuelectenerg-400	44	13	analogously	analogously	ADV
fuelectenerg-400	44	14	.	.	PUNCT
fuelectenerg-400	45	1	a	a	DET
fuelectenerg-400	45	2	tiling	tiling	NOUN
fuelectenerg-400	45	3	is	be	AUX
fuelectenerg-400	45	4	said	say	VERB
fuelectenerg-400	45	5	to	to	PART
fuelectenerg-400	45	6	be	be	AUX
fuelectenerg-400	45	7	colored	color	VERB
fuelectenerg-400	45	8	or	or	CCONJ
fuelectenerg-400	45	9	labelled	label	VERB
fuelectenerg-400	45	10	if	if	SCONJ
fuelectenerg-400	45	11	each	each	PRON
fuelectenerg-400	45	12	of	of	ADP
fuelectenerg-400	45	13	its	its	PRON
fuelectenerg-400	45	14	tiles	tile	NOUN
fuelectenerg-400	45	15	is	be	AUX
fuelectenerg-400	45	16	asigned	asigne	VERB
fuelectenerg-400	45	17	a	a	DET
fuelectenerg-400	45	18	color	color	NOUN
fuelectenerg-400	45	19	/	/	SYM
fuelectenerg-400	45	20	symbol	symbol	NOUN
fuelectenerg-400	45	21	from	from	ADP
fuelectenerg-400	45	22	a	a	DET
fuelectenerg-400	45	23	finite	finite	ADJ
fuelectenerg-400	45	24	set	set	NOUN
fuelectenerg-400	45	25	of	of	ADP
fuelectenerg-400	45	26	colors	color	NOUN
fuelectenerg-400	45	27	/	/	SYM
fuelectenerg-400	45	28	symbols	symbol	NOUN
fuelectenerg-400	45	29	.	.	PUNCT
fuelectenerg-400	46	1	a	a	DET
fuelectenerg-400	46	2	colored	colored	ADJ
fuelectenerg-400	46	3	tiling	tiling	NOUN
fuelectenerg-400	46	4	is	be	AUX
fuelectenerg-400	46	5	also	also	ADV
fuelectenerg-400	46	6	referred	refer	VERB
fuelectenerg-400	46	7	as	as	ADP
fuelectenerg-400	46	8	a	a	DET
fuelectenerg-400	46	9	pattern	pattern	NOUN
fuelectenerg-400	46	10	or	or	CCONJ
fuelectenerg-400	46	11	a	a	DET
fuelectenerg-400	46	12	configuration	configuration	NOUN
fuelectenerg-400	46	13	.	.	PUNCT
fuelectenerg-400	47	1	a	a	DET
fuelectenerg-400	47	2	binary	binary	ADJ
fuelectenerg-400	47	3	coloring	coloring	NOUN
fuelectenerg-400	47	4	employs	employ	VERB
fuelectenerg-400	47	5	black	black	ADJ
fuelectenerg-400	47	6	and	and	CCONJ
fuelectenerg-400	47	7	white	white	ADJ
fuelectenerg-400	47	8	tiles	tile	NOUN
fuelectenerg-400	47	9	,	,	PUNCT
fuelectenerg-400	47	10	while	while	SCONJ
fuelectenerg-400	47	11	generally	generally	ADV
fuelectenerg-400	47	12	in	in	ADP
fuelectenerg-400	47	13	m	m	PRON
fuelectenerg-400	47	14	-ary	-ary	VERB
fuelectenerg-400	47	15	coloring	coloring	NOUN
fuelectenerg-400	47	16	each	each	DET
fuelectenerg-400	47	17	tile	tile	NOUN
fuelectenerg-400	47	18	is	be	AUX
fuelectenerg-400	47	19	colored	color	VERB
fuelectenerg-400	47	20	by	by	ADP
fuelectenerg-400	47	21	one	one	NUM
fuelectenerg-400	47	22	of	of	ADP
fuelectenerg-400	47	23	m	m	PROPN
fuelectenerg-400	47	24	>	>	X
fuelectenerg-400	47	25	1	1	NUM
fuelectenerg-400	47	26	colors	color	NOUN
fuelectenerg-400	47	27	.	.	PUNCT
fuelectenerg-400	48	1	consequent	consequent	ADJ
fuelectenerg-400	48	2	to	to	ADP
fuelectenerg-400	48	3	the	the	DET
fuelectenerg-400	48	4	definitions	definition	NOUN
fuelectenerg-400	48	5	above	above	ADV
fuelectenerg-400	48	6	,	,	PUNCT
fuelectenerg-400	48	7	a	a	DET
fuelectenerg-400	48	8	two	two	NUM
fuelectenerg-400	48	9	-	-	PUNCT
fuelectenerg-400	48	10	dimensional	dimensional	ADJ
fuelectenerg-400	48	11	constraint	constraint	NOUN
fuelectenerg-400	48	12	can	can	AUX
fuelectenerg-400	48	13	be	be	AUX
fuelectenerg-400	48	14	expressed	express	VERB
fuelectenerg-400	48	15	as	as	ADP
fuelectenerg-400	48	16	a	a	DET
fuelectenerg-400	48	17	restriction	restriction	NOUN
fuelectenerg-400	48	18	on	on	ADP
fuelectenerg-400	48	19	a	a	DET
fuelectenerg-400	48	20	coloring	coloring	NOUN
fuelectenerg-400	48	21	(	(	PUNCT
fuelectenerg-400	48	22	or	or	CCONJ
fuelectenerg-400	48	23	labeling	labeling	NOUN
fuelectenerg-400	48	24	)	)	PUNCT
fuelectenerg-400	48	25	of	of	ADP
fuelectenerg-400	48	26	tiles	tile	NOUN
fuelectenerg-400	48	27	in	in	ADP
fuelectenerg-400	48	28	a	a	DET
fuelectenerg-400	48	29	regular	regular	ADJ
fuelectenerg-400	48	30	tiling	tiling	NOUN
fuelectenerg-400	48	31	.	.	PUNCT
fuelectenerg-400	49	1	the	the	DET
fuelectenerg-400	49	2	most	most	ADV
fuelectenerg-400	49	3	famous	famous	ADJ
fuelectenerg-400	49	4	example	example	NOUN
fuelectenerg-400	49	5	is	be	AUX
fuelectenerg-400	49	6	a	a	DET
fuelectenerg-400	49	7	hard	hard	ADJ
fuelectenerg-400	49	8	-	-	PUNCT
fuelectenerg-400	49	9	hexagon	hexagon	NOUN
fuelectenerg-400	49	10	constraint	constraint	NOUN
fuelectenerg-400	50	1	[	[	X
fuelectenerg-400	50	2	14	14	NUM
fuelectenerg-400	50	3	]	]	PUNCT
fuelectenerg-400	50	4	–	–	PUNCT
fuelectenerg-400	50	5	a	a	DET
fuelectenerg-400	50	6	planar	planar	ADJ
fuelectenerg-400	50	7	hexagonal	hexagonal	ADJ
fuelectenerg-400	50	8	lattice	lattice	NOUN
fuelectenerg-400	50	9	with	with	ADP
fuelectenerg-400	50	10	nearest	near	ADJ
fuelectenerg-400	50	11	-	-	PUNCT
fuelectenerg-400	50	12	neighbor	neighbor	NOUN
fuelectenerg-400	50	13	exclusion	exclusion	NOUN
fuelectenerg-400	50	14	.	.	PUNCT
fuelectenerg-400	51	1	this	this	PRON
fuelectenerg-400	51	2	is	be	AUX
fuelectenerg-400	51	3	used	use	VERB
fuelectenerg-400	51	4	as	as	ADP
fuelectenerg-400	51	5	a	a	DET
fuelectenerg-400	51	6	gas	gas	NOUN
fuelectenerg-400	51	7	model	model	NOUN
fuelectenerg-400	51	8	in	in	ADP
fuelectenerg-400	51	9	statistical	statistical	ADJ
fuelectenerg-400	51	10	mechanics	mechanic	NOUN
fuelectenerg-400	51	11	.	.	PUNCT
fuelectenerg-400	52	1	the	the	DET
fuelectenerg-400	52	2	hard	hard	ADJ
fuelectenerg-400	52	3	-	-	PUNCT
fuelectenerg-400	52	4	hexagon	hexagon	NOUN
fuelectenerg-400	52	5	constraint	constraint	NOUN
fuelectenerg-400	52	6	allows	allow	VERB
fuelectenerg-400	52	7	only	only	ADV
fuelectenerg-400	52	8	those	those	DET
fuelectenerg-400	52	9	(	(	PUNCT
fuelectenerg-400	52	10	binary	binary	ADJ
fuelectenerg-400	52	11	)	)	PUNCT
fuelectenerg-400	52	12	colorings	coloring	NOUN
fuelectenerg-400	52	13	in	in	ADP
fuelectenerg-400	52	14	which	which	PRON
fuelectenerg-400	52	15	black	black	ADJ
fuelectenerg-400	52	16	hexagons	hexagon	NOUN
fuelectenerg-400	52	17	are	be	AUX
fuelectenerg-400	52	18	isolated	isolate	VERB
fuelectenerg-400	52	19	,	,	PUNCT
fuelectenerg-400	52	20	i.e.	i.e.	X
fuelectenerg-400	52	21	,	,	PUNCT
fuelectenerg-400	52	22	have	have	VERB
fuelectenerg-400	52	23	all	all	DET
fuelectenerg-400	52	24	white	white	ADJ
fuelectenerg-400	52	25	neighbors	neighbor	NOUN
fuelectenerg-400	52	26	.	.	PUNCT
fuelectenerg-400	53	1	a	a	DET
fuelectenerg-400	53	2	hard	hard	ADJ
fuelectenerg-400	53	3	-	-	PUNCT
fuelectenerg-400	53	4	triangle	triangle	NOUN
fuelectenerg-400	53	5	[	[	X
fuelectenerg-400	53	6	3	3	NUM
fuelectenerg-400	53	7	]	]	PUNCT
fuelectenerg-400	53	8	and	and	CCONJ
fuelectenerg-400	53	9	hard	hard	ADJ
fuelectenerg-400	53	10	-	-	PUNCT
fuelectenerg-400	53	11	square	square	ADJ
fuelectenerg-400	53	12	constraints	constraint	NOUN
fuelectenerg-400	53	13	are	be	AUX
fuelectenerg-400	53	14	defined	define	VERB
fuelectenerg-400	53	15	similarly	similarly	ADV
fuelectenerg-400	53	16	.	.	PUNCT
fuelectenerg-400	54	1	a	a	DET
fuelectenerg-400	54	2	twodimensional	twodimensional	ADJ
fuelectenerg-400	54	3	runlength	runlength	NOUN
fuelectenerg-400	54	4	(	(	PUNCT
fuelectenerg-400	54	5	d	d	NOUN
fuelectenerg-400	54	6	,	,	PUNCT
fuelectenerg-400	54	7	k	k	NOUN
fuelectenerg-400	54	8	)	)	PUNCT
fuelectenerg-400	54	9	constraint	constraint	NOUN
fuelectenerg-400	54	10	is	be	AUX
fuelectenerg-400	54	11	a	a	DET
fuelectenerg-400	54	12	restriction	restriction	NOUN
fuelectenerg-400	54	13	on	on	ADP
fuelectenerg-400	54	14	the	the	DET
fuelectenerg-400	54	15	separation	separation	NOUN
fuelectenerg-400	54	16	space	space	NOUN
fuelectenerg-400	54	17	between	between	ADP
fuelectenerg-400	54	18	black	black	ADJ
fuelectenerg-400	54	19	tiles	tile	NOUN
fuelectenerg-400	54	20	,	,	PUNCT
fuelectenerg-400	54	21	so	so	SCONJ
fuelectenerg-400	54	22	that	that	SCONJ
fuelectenerg-400	54	23	the	the	DET
fuelectenerg-400	54	24	number	number	NOUN
fuelectenerg-400	54	25	of	of	ADP
fuelectenerg-400	54	26	white	white	ADJ
fuelectenerg-400	54	27	tiles	tile	NOUN
fuelectenerg-400	54	28	between	between	ADP
fuelectenerg-400	54	29	two	two	NUM
fuelectenerg-400	54	30	black	black	ADJ
fuelectenerg-400	54	31	tiles	tile	NOUN
fuelectenerg-400	54	32	in	in	ADP
fuelectenerg-400	54	33	any	any	DET
fuelectenerg-400	54	34	direction	direction	NOUN
fuelectenerg-400	54	35	is	be	AUX
fuelectenerg-400	54	36	at	at	ADP
fuelectenerg-400	54	37	least	least	ADJ
fuelectenerg-400	54	38	d	d	NOUN
fuelectenerg-400	54	39	and	and	CCONJ
fuelectenerg-400	54	40	at	at	ADP
fuelectenerg-400	54	41	most	most	ADJ
fuelectenerg-400	54	42	k	k	X
fuelectenerg-400	54	43	(	(	PUNCT
fuelectenerg-400	54	44	0	0	NUM
fuelectenerg-400	54	45	≤	≤	NUM
fuelectenerg-400	55	1	d	d	X
fuelectenerg-400	55	2	<	<	X
fuelectenerg-400	55	3	k	k	X
fuelectenerg-400	55	4	)	)	PUNCT
fuelectenerg-400	55	5	.	.	PUNCT
fuelectenerg-400	56	1	indeed	indeed	ADV
fuelectenerg-400	56	2	,	,	PUNCT
fuelectenerg-400	56	3	it	it	PRON
fuelectenerg-400	56	4	can	can	AUX
fuelectenerg-400	56	5	be	be	AUX
fuelectenerg-400	56	6	seen	see	VERB
fuelectenerg-400	56	7	that	that	SCONJ
fuelectenerg-400	56	8	the	the	DET
fuelectenerg-400	56	9	hard	hard	ADV
fuelectenerg-400	56	10	-	-	PUNCT
fuelectenerg-400	56	11	hexagon	hexagon	NOUN
fuelectenerg-400	56	12	,	,	PUNCT
fuelectenerg-400	56	13	hard	hard	ADJ
fuelectenerg-400	56	14	-	-	PUNCT
fuelectenerg-400	56	15	triangle	triangle	NOUN
fuelectenerg-400	56	16	and	and	CCONJ
fuelectenerg-400	56	17	hard	hard	ADJ
fuelectenerg-400	56	18	-	-	PUNCT
fuelectenerg-400	56	19	square	square	ADJ
fuelectenerg-400	56	20	constraints	constraint	NOUN
fuelectenerg-400	56	21	are	be	AUX
fuelectenerg-400	56	22	instances	instance	NOUN
fuelectenerg-400	56	23	of	of	ADP
fuelectenerg-400	56	24	the	the	DET
fuelectenerg-400	56	25	(	(	PUNCT
fuelectenerg-400	56	26	d	d	PROPN
fuelectenerg-400	56	27	,	,	PUNCT
fuelectenerg-400	56	28	k	k	NOUN
fuelectenerg-400	56	29	)	)	PUNCT
fuelectenerg-400	56	30	constraints	constraint	NOUN
fuelectenerg-400	56	31	.	.	PUNCT
fuelectenerg-400	57	1	in	in	ADP
fuelectenerg-400	57	2	particular	particular	ADJ
fuelectenerg-400	57	3	,	,	PUNCT
fuelectenerg-400	57	4	they	they	PRON
fuelectenerg-400	57	5	are	be	AUX
fuelectenerg-400	57	6	(	(	PUNCT
fuelectenerg-400	57	7	d	d	NOUN
fuelectenerg-400	57	8	,	,	PUNCT
fuelectenerg-400	57	9	k	k	NOUN
fuelectenerg-400	57	10	)	)	PUNCT
fuelectenerg-400	57	11	=	=	SYM
fuelectenerg-400	57	12	(	(	PUNCT
fuelectenerg-400	57	13	1,∞	1,∞	NUM
fuelectenerg-400	57	14	)	)	PUNCT
fuelectenerg-400	57	15	runlength	runlength	NOUN
fuelectenerg-400	57	16	constraints	constraint	NOUN
fuelectenerg-400	57	17	on	on	ADP
fuelectenerg-400	57	18	their	their	PRON
fuelectenerg-400	57	19	respective	respective	ADJ
fuelectenerg-400	57	20	lattices	lattice	NOUN
fuelectenerg-400	57	21	.	.	PUNCT
fuelectenerg-400	58	1	constraints	constraint	NOUN
fuelectenerg-400	58	2	for	for	ADP
fuelectenerg-400	58	3	which	which	PRON
fuelectenerg-400	58	4	a	a	DET
fuelectenerg-400	58	5	coloring	coloring	NOUN
fuelectenerg-400	58	6	depends	depend	VERB
fuelectenerg-400	58	7	on	on	ADP
fuelectenerg-400	58	8	both	both	CCONJ
fuelectenerg-400	58	9	neigboring	neigbore	VERB
fuelectenerg-400	58	10	and	and	CCONJ
fuelectenerg-400	58	11	touching	touching	ADJ
fuelectenerg-400	58	12	tiles	tile	NOUN
fuelectenerg-400	58	13	is	be	AUX
fuelectenerg-400	58	14	referred	refer	VERB
fuelectenerg-400	58	15	to	to	ADP
fuelectenerg-400	58	16	as	as	ADP
fuelectenerg-400	58	17	a	a	DET
fuelectenerg-400	58	18	checkerboard	checkerboard	NOUN
fuelectenerg-400	58	19	constraint	constraint	NOUN
fuelectenerg-400	58	20	[	[	X
fuelectenerg-400	58	21	9	9	NUM
fuelectenerg-400	58	22	]	]	PUNCT
fuelectenerg-400	58	23	.	.	PUNCT
fuelectenerg-400	59	1	one	one	NUM
fuelectenerg-400	59	2	example	example	NOUN
fuelectenerg-400	59	3	of	of	ADP
fuelectenerg-400	59	4	a	a	DET
fuelectenerg-400	59	5	checkerboard	checkerboard	NOUN
fuelectenerg-400	59	6	constraint	constraint	NOUN
fuelectenerg-400	59	7	is	be	AUX
fuelectenerg-400	59	8	a	a	DET
fuelectenerg-400	59	9	square	square	ADJ
fuelectenerg-400	59	10	tiling	tiling	NOUN
fuelectenerg-400	59	11	in	in	ADP
fuelectenerg-400	59	12	which	which	PRON
fuelectenerg-400	59	13	black	black	ADJ
fuelectenerg-400	59	14	squares	square	NOUN
fuelectenerg-400	59	15	are	be	AUX
fuelectenerg-400	59	16	not	not	PART
fuelectenerg-400	59	17	permitted	permit	VERB
fuelectenerg-400	59	18	to	to	PART
fuelectenerg-400	59	19	share	share	VERB
fuelectenerg-400	59	20	a	a	DET
fuelectenerg-400	59	21	vertex	vertex	NOUN
fuelectenerg-400	59	22	.	.	PUNCT
fuelectenerg-400	60	1	as	as	SCONJ
fuelectenerg-400	60	2	mentioned	mention	VERB
fuelectenerg-400	60	3	previously	previously	ADV
fuelectenerg-400	60	4	,	,	PUNCT
fuelectenerg-400	60	5	both	both	PRON
fuelectenerg-400	60	6	runlength	runlength	NOUN
fuelectenerg-400	60	7	and	and	CCONJ
fuelectenerg-400	60	8	checkerboard	checkerboard	NOUN
fuelectenerg-400	60	9	constraints	constraint	NOUN
fuelectenerg-400	60	10	have	have	AUX
fuelectenerg-400	60	11	been	be	AUX
fuelectenerg-400	60	12	an	an	DET
fuelectenerg-400	60	13	active	active	ADJ
fuelectenerg-400	60	14	area	area	NOUN
fuelectenerg-400	60	15	of	of	ADP
fuelectenerg-400	60	16	research	research	NOUN
fuelectenerg-400	60	17	,	,	PUNCT
fuelectenerg-400	60	18	but	but	CCONJ
fuelectenerg-400	60	19	the	the	DET
fuelectenerg-400	60	20	progress	progress	NOUN
fuelectenerg-400	60	21	has	have	AUX
fuelectenerg-400	60	22	been	be	AUX
fuelectenerg-400	60	23	slow	slow	ADJ
fuelectenerg-400	60	24	because	because	SCONJ
fuelectenerg-400	60	25	of	of	ADP
fuelectenerg-400	60	26	inherent	inherent	ADJ
fuelectenerg-400	60	27	hardness	hardness	NOUN
fuelectenerg-400	60	28	of	of	ADP
fuelectenerg-400	60	29	two	two	NUM
fuelectenerg-400	60	30	-	-	PUNCT
fuelectenerg-400	60	31	dimensional	dimensional	ADJ
fuelectenerg-400	60	32	tiling	tiling	NOUN
fuelectenerg-400	60	33	problems	problem	NOUN
fuelectenerg-400	60	34	.	.	PUNCT
fuelectenerg-400	61	1	3	3	NUM
fuelectenerg-400	61	2	lozenge	lozenge	NOUN
fuelectenerg-400	61	3	codes	code	NOUN
fuelectenerg-400	61	4	consider	consider	VERB
fuelectenerg-400	61	5	a	a	DET
fuelectenerg-400	61	6	regular	regular	ADJ
fuelectenerg-400	61	7	tiling	tiling	NOUN
fuelectenerg-400	61	8	of	of	ADP
fuelectenerg-400	61	9	a	a	DET
fuelectenerg-400	61	10	plane	plane	NOUN
fuelectenerg-400	61	11	.	.	PUNCT
fuelectenerg-400	62	1	a	a	DET
fuelectenerg-400	62	2	(	(	PUNCT
fuelectenerg-400	62	3	d	d	NOUN
fuelectenerg-400	62	4	,	,	PUNCT
fuelectenerg-400	62	5	k	k	NOUN
fuelectenerg-400	62	6	)	)	PUNCT
fuelectenerg-400	62	7	segregation	segregation	NOUN
fuelectenerg-400	62	8	constraint	constraint	NOUN
fuelectenerg-400	62	9	is	be	AUX
fuelectenerg-400	62	10	a	a	DET
fuelectenerg-400	62	11	tiling	tiling	NOUN
fuelectenerg-400	62	12	that	that	PRON
fuelectenerg-400	62	13	limits	limit	VERB
fuelectenerg-400	62	14	the	the	DET
fuelectenerg-400	62	15	number	number	NOUN
fuelectenerg-400	62	16	of	of	ADP
fuelectenerg-400	62	17	neighboring	neighboring	NOUN
fuelectenerg-400	62	18	tiles	tile	NOUN
fuelectenerg-400	62	19	(	(	PUNCT
fuelectenerg-400	62	20	neighborhood	neighborhood	NOUN
fuelectenerg-400	62	21	size	size	NOUN
fuelectenerg-400	62	22	)	)	PUNCT
fuelectenerg-400	62	23	of	of	ADP
fuelectenerg-400	62	24	same	same	ADJ
fuelectenerg-400	62	25	color	color	NOUN
fuelectenerg-400	62	26	to	to	PART
fuelectenerg-400	62	27	be	be	AUX
fuelectenerg-400	62	28	no	no	PRON
fuelectenerg-400	62	29	less	less	ADJ
fuelectenerg-400	62	30	than	than	ADP
fuelectenerg-400	62	31	d+1	d+1	PROPN
fuelectenerg-400	62	32	and	and	CCONJ
fuelectenerg-400	62	33	no	no	PRON
fuelectenerg-400	62	34	more	more	ADJ
fuelectenerg-400	62	35	than	than	ADP
fuelectenerg-400	62	36	k+1	k+1	PROPN
fuelectenerg-400	62	37	.	.	PUNCT
fuelectenerg-400	63	1	a	a	DET
fuelectenerg-400	63	2	2d	2d	NUM
fuelectenerg-400	63	3	bit	bit	NOUN
fuelectenerg-400	63	4	pattern	pattern	NOUN
fuelectenerg-400	63	5	is	be	AUX
fuelectenerg-400	63	6	said	say	VERB
fuelectenerg-400	63	7	to	to	PART
fuelectenerg-400	63	8	satisfy	satisfy	VERB
fuelectenerg-400	63	9	a	a	DET
fuelectenerg-400	63	10	no	no	DET
fuelectenerg-400	63	11	isolated	isolated	ADJ
fuelectenerg-400	63	12	bit	bit	NOUN
fuelectenerg-400	63	13	(	(	PUNCT
fuelectenerg-400	63	14	nib	nib	NOUN
fuelectenerg-400	63	15	)	)	PUNCT
fuelectenerg-400	63	16	constraint	constraint	NOUN
fuelectenerg-400	63	17	if	if	SCONJ
fuelectenerg-400	63	18	every	every	DET
fuelectenerg-400	63	19	bit	bit	NOUN
fuelectenerg-400	63	20	has	have	VERB
fuelectenerg-400	63	21	at	at	ADV
fuelectenerg-400	63	22	least	least	ADV
fuelectenerg-400	63	23	one	one	NUM
fuelectenerg-400	63	24	bit	bit	NOUN
fuelectenerg-400	63	25	of	of	ADP
fuelectenerg-400	63	26	the	the	DET
fuelectenerg-400	63	27	same	same	ADJ
fuelectenerg-400	63	28	polarity	polarity	NOUN
fuelectenerg-400	63	29	adjacent	adjacent	ADJ
fuelectenerg-400	63	30	to	to	ADP
fuelectenerg-400	63	31	it	it	PRON
fuelectenerg-400	63	32	.	.	PUNCT
fuelectenerg-400	64	1	thus	thus	ADV
fuelectenerg-400	64	2	the	the	DET
fuelectenerg-400	64	3	nib	nib	NOUN
fuelectenerg-400	64	4	is	be	AUX
fuelectenerg-400	64	5	a	a	DET
fuelectenerg-400	64	6	(	(	PUNCT
fuelectenerg-400	64	7	d	d	NOUN
fuelectenerg-400	64	8	,	,	PUNCT
fuelectenerg-400	64	9	k	k	NOUN
fuelectenerg-400	64	10	)	)	PUNCT
fuelectenerg-400	64	11	=	=	SYM
fuelectenerg-400	64	12	(	(	PUNCT
fuelectenerg-400	64	13	1,∞	1,∞	NUM
fuelectenerg-400	64	14	)	)	PUNCT
fuelectenerg-400	64	15	segregation	segregation	NOUN
fuelectenerg-400	64	16	constraint	constraint	NOUN
fuelectenerg-400	64	17	.	.	PUNCT
fuelectenerg-400	65	1	note	note	VERB
fuelectenerg-400	65	2	that	that	SCONJ
fuelectenerg-400	65	3	the	the	DET
fuelectenerg-400	65	4	parameters	parameter	NOUN
fuelectenerg-400	65	5	d	d	PROPN
fuelectenerg-400	65	6	and	and	CCONJ
fuelectenerg-400	65	7	k	k	PROPN
fuelectenerg-400	65	8	in	in	ADP
fuelectenerg-400	65	9	runlength	runlength	NOUN
fuelectenerg-400	65	10	and	and	CCONJ
fuelectenerg-400	65	11	segregation	segregation	NOUN
fuelectenerg-400	65	12	constraints	constraint	NOUN
fuelectenerg-400	65	13	have	have	VERB
fuelectenerg-400	65	14	different	different	ADJ
fuelectenerg-400	65	15	meanings	meaning	NOUN
fuelectenerg-400	65	16	.	.	PUNCT
fuelectenerg-400	66	1	in	in	ADP
fuelectenerg-400	66	2	rectangular	rectangular	ADJ
fuelectenerg-400	66	3	latices	latex	NOUN
fuelectenerg-400	66	4	runlength	runlength	NOUN
fuelectenerg-400	66	5	constraint	constraint	NOUN
fuelectenerg-400	66	6	can	can	AUX
fuelectenerg-400	66	7	be	be	AUX
fuelectenerg-400	66	8	converted	convert	VERB
fuelectenerg-400	66	9	522	522	NUM
fuelectenerg-400	66	10	b.	b.	NOUN
fuelectenerg-400	66	11	vasic	vasic	NOUN
fuelectenerg-400	66	12	,	,	PUNCT
fuelectenerg-400	66	13	a.	a.	PROPN
fuelectenerg-400	66	14	r.	r.	PROPN
fuelectenerg-400	66	15	krishnan	krishnan	PROPN
fuelectenerg-400	66	16	lozenge	lozenge	PROPN
fuelectenerg-400	66	17	tiling	tile	VERB
fuelectenerg-400	66	18	constrained	constrain	VERB
fuelectenerg-400	66	19	codes	code	NOUN
fuelectenerg-400	66	20	523	523	NUM
fuelectenerg-400	66	21	522	522	NUM
fuelectenerg-400	66	22	a.	a.	NOUN
fuelectenerg-400	66	23	r.	r.	PROPN
fuelectenerg-400	66	24	krishnanan	krishnanan	PROPN
fuelectenerg-400	66	25	and	and	CCONJ
fuelectenerg-400	66	26	b.	b.	PROPN
fuelectenerg-400	66	27	vasić	vasić	PROPN
fuelectenerg-400	66	28	magnetization	magnetization	NOUN
fuelectenerg-400	66	29	direction	direction	NOUN
fuelectenerg-400	66	30	[	[	X
fuelectenerg-400	66	31	1	1	NUM
fuelectenerg-400	66	32	]	]	PUNCT
fuelectenerg-400	66	33	.	.	PUNCT
fuelectenerg-400	67	1	transitions	transition	NOUN
fuelectenerg-400	67	2	too	too	ADV
fuelectenerg-400	67	3	close	close	ADV
fuelectenerg-400	67	4	to	to	ADP
fuelectenerg-400	67	5	each	each	DET
fuelectenerg-400	67	6	other	other	ADJ
fuelectenerg-400	67	7	degrades	degrade	VERB
fuelectenerg-400	67	8	the	the	DET
fuelectenerg-400	67	9	signal	signal	NOUN
fuelectenerg-400	67	10	-	-	PUNCT
fuelectenerg-400	67	11	to	to	ADP
fuelectenerg-400	67	12	-	-	PUNCT
fuelectenerg-400	67	13	noise	noise	NOUN
fuelectenerg-400	67	14	ratio	ratio	NOUN
fuelectenerg-400	67	15	(	(	PUNCT
fuelectenerg-400	67	16	snr	snr	PROPN
fuelectenerg-400	67	17	)	)	PUNCT
fuelectenerg-400	67	18	during	during	ADP
fuelectenerg-400	67	19	readback	readback	NOUN
fuelectenerg-400	67	20	.	.	PUNCT
fuelectenerg-400	68	1	on	on	ADP
fuelectenerg-400	68	2	the	the	DET
fuelectenerg-400	68	3	other	other	ADJ
fuelectenerg-400	68	4	hand	hand	NOUN
fuelectenerg-400	68	5	,	,	PUNCT
fuelectenerg-400	68	6	transitions	transition	NOUN
fuelectenerg-400	68	7	too	too	ADV
fuelectenerg-400	68	8	far	far	ADV
fuelectenerg-400	68	9	apart	apart	ADV
fuelectenerg-400	68	10	make	make	VERB
fuelectenerg-400	68	11	vulnerable	vulnerable	ADJ
fuelectenerg-400	68	12	to	to	ADP
fuelectenerg-400	68	13	failure	failure	NOUN
fuelectenerg-400	68	14	the	the	DET
fuelectenerg-400	68	15	timing	timing	NOUN
fuelectenerg-400	68	16	-	-	PUNCT
fuelectenerg-400	68	17	recovery	recovery	NOUN
fuelectenerg-400	68	18	sub	sub	NOUN
fuelectenerg-400	68	19	-	-	NOUN
fuelectenerg-400	68	20	systems	system	NOUN
fuelectenerg-400	68	21	which	which	PRON
fuelectenerg-400	68	22	typically	typically	ADV
fuelectenerg-400	68	23	rely	rely	VERB
fuelectenerg-400	68	24	on	on	ADP
fuelectenerg-400	68	25	these	these	DET
fuelectenerg-400	68	26	transitions	transition	NOUN
fuelectenerg-400	68	27	to	to	PART
fuelectenerg-400	68	28	derive	derive	VERB
fuelectenerg-400	68	29	symbol	symbol	NOUN
fuelectenerg-400	68	30	-	-	PUNCT
fuelectenerg-400	68	31	level	level	NOUN
fuelectenerg-400	68	32	timing	timing	NOUN
fuelectenerg-400	68	33	information	information	NOUN
fuelectenerg-400	68	34	.	.	PUNCT
fuelectenerg-400	69	1	a	a	DET
fuelectenerg-400	69	2	solution	solution	NOUN
fuelectenerg-400	69	3	to	to	PART
fuelectenerg-400	69	4	satisfy	satisfy	VERB
fuelectenerg-400	69	5	channel	channel	NOUN
fuelectenerg-400	69	6	constraints	constraint	NOUN
fuelectenerg-400	69	7	is	be	AUX
fuelectenerg-400	69	8	to	to	PART
fuelectenerg-400	69	9	use	use	VERB
fuelectenerg-400	69	10	constrained	constrained	ADJ
fuelectenerg-400	69	11	codes	code	NOUN
fuelectenerg-400	69	12	(	(	PUNCT
fuelectenerg-400	69	13	or	or	CCONJ
fuelectenerg-400	69	14	modulation	modulation	NOUN
fuelectenerg-400	69	15	codes	code	NOUN
fuelectenerg-400	69	16	)	)	PUNCT
fuelectenerg-400	69	17	–	–	PUNCT
fuelectenerg-400	69	18	codes	code	NOUN
fuelectenerg-400	69	19	that	that	PRON
fuelectenerg-400	69	20	transform	transform	VERB
fuelectenerg-400	69	21	user	user	NOUN
fuelectenerg-400	69	22	information	information	NOUN
fuelectenerg-400	69	23	to	to	ADP
fuelectenerg-400	69	24	symbol	symbol	NOUN
fuelectenerg-400	69	25	-	-	PUNCT
fuelectenerg-400	69	26	sequences	sequence	NOUN
fuelectenerg-400	69	27	that	that	PRON
fuelectenerg-400	69	28	satisfy	satisfy	VERB
fuelectenerg-400	69	29	the	the	DET
fuelectenerg-400	69	30	constraints	constraint	NOUN
fuelectenerg-400	69	31	.	.	PUNCT
fuelectenerg-400	70	1	one	one	NUM
fuelectenerg-400	70	2	dimensional	dimensional	ADJ
fuelectenerg-400	70	3	(	(	PUNCT
fuelectenerg-400	70	4	1d	1d	NUM
fuelectenerg-400	70	5	)	)	PUNCT
fuelectenerg-400	70	6	constraints	constraint	NOUN
fuelectenerg-400	70	7	have	have	AUX
fuelectenerg-400	70	8	been	be	AUX
fuelectenerg-400	70	9	well	well	ADV
fuelectenerg-400	70	10	-	-	PUNCT
fuelectenerg-400	70	11	studied	study	VERB
fuelectenerg-400	70	12	.	.	PUNCT
fuelectenerg-400	71	1	the	the	DET
fuelectenerg-400	71	2	mathematical	mathematical	ADJ
fuelectenerg-400	71	3	framework	framework	NOUN
fuelectenerg-400	71	4	for	for	ADP
fuelectenerg-400	71	5	determining	determine	VERB
fuelectenerg-400	71	6	the	the	DET
fuelectenerg-400	71	7	shannon	shannon	PROPN
fuelectenerg-400	71	8	noiseless	noiseless	ADJ
fuelectenerg-400	71	9	capacity	capacity	NOUN
fuelectenerg-400	71	10	of	of	ADP
fuelectenerg-400	71	11	1d	1d	NUM
fuelectenerg-400	71	12	constraints	constraint	NOUN
fuelectenerg-400	71	13	–	–	PUNCT
fuelectenerg-400	71	14	the	the	DET
fuelectenerg-400	71	15	growth	growth	NOUN
fuelectenerg-400	71	16	rate	rate	NOUN
fuelectenerg-400	71	17	of	of	ADP
fuelectenerg-400	71	18	the	the	DET
fuelectenerg-400	71	19	number	number	NOUN
fuelectenerg-400	71	20	of	of	ADP
fuelectenerg-400	71	21	sequences	sequence	NOUN
fuelectenerg-400	71	22	satisfying	satisfy	VERB
fuelectenerg-400	71	23	a	a	DET
fuelectenerg-400	71	24	given	give	VERB
fuelectenerg-400	71	25	constraint	constraint	NOUN
fuelectenerg-400	71	26	–	–	PUNCT
fuelectenerg-400	71	27	has	have	AUX
fuelectenerg-400	71	28	been	be	AUX
fuelectenerg-400	71	29	comprehensively	comprehensively	ADV
fuelectenerg-400	71	30	laid	lay	VERB
fuelectenerg-400	71	31	out	out	ADP
fuelectenerg-400	71	32	.	.	PUNCT
fuelectenerg-400	72	1	further	far	ADV
fuelectenerg-400	72	2	,	,	PUNCT
fuelectenerg-400	72	3	development	development	NOUN
fuelectenerg-400	72	4	of	of	ADP
fuelectenerg-400	72	5	1d	1d	NUM
fuelectenerg-400	72	6	constrained	constrain	VERB
fuelectenerg-400	72	7	codes	code	NOUN
fuelectenerg-400	72	8	and	and	CCONJ
fuelectenerg-400	72	9	decoders	decoder	NOUN
fuelectenerg-400	72	10	is	be	AUX
fuelectenerg-400	72	11	mature	mature	ADJ
fuelectenerg-400	72	12	(	(	PUNCT
fuelectenerg-400	72	13	refer	refer	VERB
fuelectenerg-400	72	14	[	[	X
fuelectenerg-400	72	15	1	1	NUM
fuelectenerg-400	72	16	]	]	PUNCT
fuelectenerg-400	72	17	for	for	ADP
fuelectenerg-400	72	18	a	a	DET
fuelectenerg-400	72	19	review	review	NOUN
fuelectenerg-400	72	20	on	on	ADP
fuelectenerg-400	72	21	this	this	DET
fuelectenerg-400	72	22	topic	topic	NOUN
fuelectenerg-400	72	23	)	)	PUNCT
fuelectenerg-400	72	24	.	.	PUNCT
fuelectenerg-400	73	1	in	in	ADP
fuelectenerg-400	73	2	contrast	contrast	NOUN
fuelectenerg-400	73	3	,	,	PUNCT
fuelectenerg-400	73	4	analysis	analysis	NOUN
fuelectenerg-400	73	5	and	and	CCONJ
fuelectenerg-400	73	6	code	code	NOUN
fuelectenerg-400	73	7	development	development	NOUN
fuelectenerg-400	73	8	for	for	ADP
fuelectenerg-400	73	9	two	two	NUM
fuelectenerg-400	73	10	-	-	PUNCT
fuelectenerg-400	73	11	dimensional	dimensional	ADJ
fuelectenerg-400	73	12	(	(	PUNCT
fuelectenerg-400	73	13	2d	2d	NOUN
fuelectenerg-400	73	14	)	)	PUNCT
fuelectenerg-400	73	15	constraint	constraint	NOUN
fuelectenerg-400	73	16	systems	system	NOUN
fuelectenerg-400	73	17	have	have	AUX
fuelectenerg-400	73	18	been	be	AUX
fuelectenerg-400	73	19	less	less	ADV
fuelectenerg-400	73	20	successful	successful	ADJ
fuelectenerg-400	73	21	.	.	PUNCT
fuelectenerg-400	74	1	initial	initial	ADJ
fuelectenerg-400	74	2	work	work	NOUN
fuelectenerg-400	74	3	on	on	ADP
fuelectenerg-400	74	4	2d	2d	NUM
fuelectenerg-400	74	5	constraints	constraint	NOUN
fuelectenerg-400	74	6	was	be	AUX
fuelectenerg-400	74	7	done	do	VERB
fuelectenerg-400	74	8	by	by	ADP
fuelectenerg-400	74	9	ashley	ashley	PROPN
fuelectenerg-400	74	10	and	and	CCONJ
fuelectenerg-400	74	11	marcus	marcus	PROPN
fuelectenerg-400	75	1	[	[	X
fuelectenerg-400	75	2	2	2	X
fuelectenerg-400	75	3	]	]	PUNCT
fuelectenerg-400	75	4	who	who	PRON
fuelectenerg-400	75	5	considered	consider	VERB
fuelectenerg-400	75	6	2d	2d	NUM
fuelectenerg-400	75	7	low	low	ADJ
fuelectenerg-400	75	8	-	-	PUNCT
fuelectenerg-400	75	9	pass	pass	NOUN
fuelectenerg-400	75	10	filtering	filter	VERB
fuelectenerg-400	75	11	codes	code	NOUN
fuelectenerg-400	75	12	for	for	ADP
fuelectenerg-400	75	13	eliminating	eliminate	VERB
fuelectenerg-400	75	14	bit	bit	NOUN
fuelectenerg-400	75	15	-	-	PUNCT
fuelectenerg-400	75	16	patterns	pattern	NOUN
fuelectenerg-400	75	17	with	with	ADP
fuelectenerg-400	75	18	large	large	ADJ
fuelectenerg-400	75	19	highfrequency	highfrequency	NOUN
fuelectenerg-400	75	20	components	component	NOUN
fuelectenerg-400	75	21	.	.	PUNCT
fuelectenerg-400	76	1	subsequently	subsequently	ADV
fuelectenerg-400	76	2	,	,	PUNCT
fuelectenerg-400	76	3	considerable	considerable	ADJ
fuelectenerg-400	76	4	research	research	NOUN
fuelectenerg-400	76	5	was	be	AUX
fuelectenerg-400	76	6	conducted	conduct	VERB
fuelectenerg-400	76	7	on	on	ADP
fuelectenerg-400	76	8	numerous	numerous	ADJ
fuelectenerg-400	76	9	classes	class	NOUN
fuelectenerg-400	76	10	of	of	ADP
fuelectenerg-400	76	11	2d	2d	NUM
fuelectenerg-400	76	12	constraints	constraint	NOUN
fuelectenerg-400	76	13	,	,	PUNCT
fuelectenerg-400	76	14	e.g.	e.g.	ADV
fuelectenerg-400	76	15	,	,	PUNCT
fuelectenerg-400	76	16	[	[	X
fuelectenerg-400	76	17	3–9	3–9	NOUN
fuelectenerg-400	76	18	]	]	PUNCT
fuelectenerg-400	76	19	.	.	PUNCT
fuelectenerg-400	77	1	in	in	ADP
fuelectenerg-400	77	2	spite	spite	NOUN
fuelectenerg-400	77	3	of	of	ADP
fuelectenerg-400	77	4	these	these	DET
fuelectenerg-400	77	5	efforts	effort	NOUN
fuelectenerg-400	77	6	,	,	PUNCT
fuelectenerg-400	77	7	these	these	DET
fuelectenerg-400	77	8	constrained	constrain	VERB
fuelectenerg-400	77	9	systems	system	NOUN
fuelectenerg-400	77	10	remain	remain	VERB
fuelectenerg-400	77	11	largely	largely	ADV
fuelectenerg-400	77	12	uncharacterized	uncharacterized	ADJ
fuelectenerg-400	77	13	mathematically	mathematically	ADV
fuelectenerg-400	77	14	with	with	ADP
fuelectenerg-400	77	15	only	only	ADJ
fuelectenerg-400	77	16	loose	loose	ADJ
fuelectenerg-400	77	17	bounds	bound	NOUN
fuelectenerg-400	77	18	of	of	ADP
fuelectenerg-400	77	19	capacities	capacity	NOUN
fuelectenerg-400	77	20	existing	exist	VERB
fuelectenerg-400	77	21	.	.	PUNCT
fuelectenerg-400	78	1	with	with	ADP
fuelectenerg-400	78	2	an	an	DET
fuelectenerg-400	78	3	exception	exception	NOUN
fuelectenerg-400	78	4	of	of	ADP
fuelectenerg-400	78	5	a	a	DET
fuelectenerg-400	78	6	few	few	ADJ
fuelectenerg-400	78	7	cases	case	NOUN
fuelectenerg-400	78	8	,	,	PUNCT
fuelectenerg-400	78	9	the	the	DET
fuelectenerg-400	78	10	channel	channel	NOUN
fuelectenerg-400	78	11	capacity	capacity	NOUN
fuelectenerg-400	78	12	of	of	ADP
fuelectenerg-400	78	13	2d	2d	NUM
fuelectenerg-400	78	14	constrained	constrain	VERB
fuelectenerg-400	78	15	channels	channel	NOUN
fuelectenerg-400	78	16	is	be	AUX
fuelectenerg-400	78	17	unknown	unknown	ADJ
fuelectenerg-400	78	18	(	(	PUNCT
fuelectenerg-400	78	19	see	see	VERB
fuelectenerg-400	78	20	[	[	X
fuelectenerg-400	78	21	10	10	NUM
fuelectenerg-400	78	22	]	]	NUM
fuelectenerg-400	78	23	)	)	PUNCT
fuelectenerg-400	78	24	,	,	PUNCT
fuelectenerg-400	78	25	and	and	CCONJ
fuelectenerg-400	78	26	there	there	PRON
fuelectenerg-400	78	27	is	be	VERB
fuelectenerg-400	78	28	no	no	DET
fuelectenerg-400	78	29	systematic	systematic	ADJ
fuelectenerg-400	78	30	procedure	procedure	NOUN
fuelectenerg-400	78	31	to	to	PART
fuelectenerg-400	78	32	design	design	VERB
fuelectenerg-400	78	33	encoders	encoder	NOUN
fuelectenerg-400	78	34	and	and	CCONJ
fuelectenerg-400	78	35	decoders	decoder	NOUN
fuelectenerg-400	78	36	.	.	PUNCT
fuelectenerg-400	79	1	nonetheless	nonetheless	ADV
fuelectenerg-400	79	2	,	,	PUNCT
fuelectenerg-400	79	3	the	the	DET
fuelectenerg-400	79	4	need	need	ADJ
fuelectenerg-400	79	5	two	two	NUM
fuelectenerg-400	79	6	-	-	PUNCT
fuelectenerg-400	79	7	dimensional	dimensional	ADJ
fuelectenerg-400	79	8	constrained	constrain	VERB
fuelectenerg-400	79	9	codes	code	NOUN
fuelectenerg-400	79	10	has	have	AUX
fuelectenerg-400	79	11	come	come	VERB
fuelectenerg-400	79	12	to	to	ADP
fuelectenerg-400	79	13	the	the	DET
fuelectenerg-400	79	14	fore	fore	NOUN
fuelectenerg-400	79	15	in	in	ADP
fuelectenerg-400	79	16	light	light	NOUN
fuelectenerg-400	79	17	of	of	ADP
fuelectenerg-400	79	18	the	the	DET
fuelectenerg-400	79	19	recent	recent	ADJ
fuelectenerg-400	79	20	work	work	NOUN
fuelectenerg-400	79	21	in	in	ADP
fuelectenerg-400	79	22	two	two	NUM
fuelectenerg-400	79	23	-	-	PUNCT
fuelectenerg-400	79	24	dimensional	dimensional	ADJ
fuelectenerg-400	79	25	magnetic	magnetic	ADJ
fuelectenerg-400	79	26	recording	recording	NOUN
fuelectenerg-400	79	27	(	(	PUNCT
fuelectenerg-400	79	28	tdmr	tdmr	NOUN
fuelectenerg-400	79	29	)	)	PUNCT
fuelectenerg-400	79	30	.	.	PUNCT
fuelectenerg-400	80	1	in	in	ADP
fuelectenerg-400	80	2	[	[	X
fuelectenerg-400	80	3	11	11	NUM
fuelectenerg-400	80	4	]	]	PUNCT
fuelectenerg-400	80	5	,	,	PUNCT
fuelectenerg-400	80	6	it	it	PRON
fuelectenerg-400	80	7	was	be	AUX
fuelectenerg-400	80	8	shown	show	VERB
fuelectenerg-400	80	9	that	that	SCONJ
fuelectenerg-400	80	10	constrained	constrain	VERB
fuelectenerg-400	80	11	coding	coding	NOUN
fuelectenerg-400	80	12	which	which	PRON
fuelectenerg-400	80	13	restricts	restrict	VERB
fuelectenerg-400	80	14	the	the	DET
fuelectenerg-400	80	15	occurrence	occurrence	NOUN
fuelectenerg-400	80	16	of	of	ADP
fuelectenerg-400	80	17	certain	certain	ADJ
fuelectenerg-400	80	18	2d	2d	NOUN
fuelectenerg-400	80	19	patterns	pattern	NOUN
fuelectenerg-400	80	20	greatly	greatly	ADV
fuelectenerg-400	80	21	reduces	reduce	VERB
fuelectenerg-400	80	22	system	system	NOUN
fuelectenerg-400	80	23	complexity	complexity	NOUN
fuelectenerg-400	80	24	and	and	CCONJ
fuelectenerg-400	80	25	improves	improve	VERB
fuelectenerg-400	80	26	the	the	DET
fuelectenerg-400	80	27	detection	detection	NOUN
fuelectenerg-400	80	28	performance	performance	NOUN
fuelectenerg-400	80	29	.	.	PUNCT
fuelectenerg-400	81	1	also	also	ADV
fuelectenerg-400	81	2	,	,	PUNCT
fuelectenerg-400	81	3	there	there	PRON
fuelectenerg-400	81	4	exist	exist	VERB
fuelectenerg-400	81	5	media	medium	NOUN
fuelectenerg-400	81	6	models	model	NOUN
fuelectenerg-400	81	7	for	for	ADP
fuelectenerg-400	81	8	tdmr	tdmr	NOUN
fuelectenerg-400	81	9	that	that	PRON
fuelectenerg-400	81	10	rely	rely	VERB
fuelectenerg-400	81	11	on	on	ADP
fuelectenerg-400	81	12	polyomino	polyomino	NOUN
fuelectenerg-400	81	13	tiling	tile	VERB
fuelectenerg-400	81	14	[	[	X
fuelectenerg-400	81	15	12,13	12,13	NUM
fuelectenerg-400	81	16	]	]	PUNCT
fuelectenerg-400	81	17	,	,	PUNCT
fuelectenerg-400	81	18	which	which	PRON
fuelectenerg-400	81	19	are	be	AUX
fuelectenerg-400	81	20	closely	closely	ADV
fuelectenerg-400	81	21	related	relate	VERB
fuelectenerg-400	81	22	to	to	ADP
fuelectenerg-400	81	23	the	the	DET
fuelectenerg-400	81	24	2d	2d	NUM
fuelectenerg-400	81	25	constrained	constrain	VERB
fuelectenerg-400	81	26	systems	system	NOUN
fuelectenerg-400	81	27	.	.	PUNCT
fuelectenerg-400	82	1	in	in	ADP
fuelectenerg-400	82	2	this	this	DET
fuelectenerg-400	82	3	paper	paper	NOUN
fuelectenerg-400	82	4	,	,	PUNCT
fuelectenerg-400	82	5	we	we	PRON
fuelectenerg-400	82	6	consider	consider	VERB
fuelectenerg-400	82	7	a	a	DET
fuelectenerg-400	82	8	class	class	NOUN
fuelectenerg-400	82	9	of	of	ADP
fuelectenerg-400	82	10	low	low	ADJ
fuelectenerg-400	82	11	-	-	PUNCT
fuelectenerg-400	82	12	pass	pass	NOUN
fuelectenerg-400	82	13	constraint	constraint	NOUN
fuelectenerg-400	82	14	on	on	ADP
fuelectenerg-400	82	15	the	the	DET
fuelectenerg-400	82	16	triangular	triangular	NOUN
fuelectenerg-400	82	17	lattice	lattice	NOUN
fuelectenerg-400	82	18	termed	term	VERB
fuelectenerg-400	82	19	segregation	segregation	NOUN
fuelectenerg-400	82	20	constraint	constraint	NOUN
fuelectenerg-400	82	21	and	and	CCONJ
fuelectenerg-400	82	22	it	it	PRON
fuelectenerg-400	82	23	special	special	ADJ
fuelectenerg-400	82	24	case	case	NOUN
fuelectenerg-400	82	25	,	,	PUNCT
fuelectenerg-400	82	26	no	no	DET
fuelectenerg-400	82	27	isolated	isolated	ADJ
fuelectenerg-400	82	28	bit	bit	NOUN
fuelectenerg-400	82	29	(	(	PUNCT
fuelectenerg-400	82	30	nib	nib	NOUN
fuelectenerg-400	82	31	)	)	PUNCT
fuelectenerg-400	82	32	constraint	constraint	NOUN
fuelectenerg-400	82	33	.	.	PUNCT
fuelectenerg-400	83	1	we	we	PRON
fuelectenerg-400	83	2	provide	provide	VERB
fuelectenerg-400	83	3	an	an	DET
fuelectenerg-400	83	4	upper	upper	ADJ
fuelectenerg-400	83	5	bound	bind	VERB
fuelectenerg-400	83	6	on	on	ADP
fuelectenerg-400	83	7	the	the	DET
fuelectenerg-400	83	8	shannon	shannon	PROPN
fuelectenerg-400	83	9	noiseless	noiseless	PROPN
fuelectenerg-400	83	10	capacity	capacity	NOUN
fuelectenerg-400	83	11	for	for	ADP
fuelectenerg-400	83	12	this	this	DET
fuelectenerg-400	83	13	constraint	constraint	NOUN
fuelectenerg-400	83	14	.	.	PUNCT
fuelectenerg-400	84	1	the	the	DET
fuelectenerg-400	84	2	key	key	ADJ
fuelectenerg-400	84	3	novelty	novelty	NOUN
fuelectenerg-400	84	4	of	of	ADP
fuelectenerg-400	84	5	the	the	DET
fuelectenerg-400	84	6	our	our	PRON
fuelectenerg-400	84	7	approach	approach	NOUN
fuelectenerg-400	84	8	is	be	AUX
fuelectenerg-400	84	9	to	to	PART
fuelectenerg-400	84	10	view	view	VERB
fuelectenerg-400	84	11	our	our	PRON
fuelectenerg-400	84	12	2d	2d	PROPN
fuelectenerg-400	84	13	constraint	constraint	NOUN
fuelectenerg-400	84	14	as	as	ADP
fuelectenerg-400	84	15	a	a	DET
fuelectenerg-400	84	16	colored	colored	ADJ
fuelectenerg-400	84	17	tiling	tiling	NOUN
fuelectenerg-400	84	18	of	of	ADP
fuelectenerg-400	84	19	a	a	DET
fuelectenerg-400	84	20	plane	plane	NOUN
fuelectenerg-400	84	21	.	.	PUNCT
fuelectenerg-400	85	1	thus	thus	ADV
fuelectenerg-400	85	2	,	,	PUNCT
fuelectenerg-400	85	3	the	the	DET
fuelectenerg-400	85	4	estimation	estimation	NOUN
fuelectenerg-400	85	5	of	of	ADP
fuelectenerg-400	85	6	the	the	DET
fuelectenerg-400	85	7	number	number	NOUN
fuelectenerg-400	85	8	of	of	ADP
fuelectenerg-400	85	9	permissible	permissible	ADJ
fuelectenerg-400	85	10	colored	colored	ADJ
fuelectenerg-400	85	11	tilings	tiling	NOUN
fuelectenerg-400	85	12	leads	lead	VERB
fuelectenerg-400	85	13	to	to	ADP
fuelectenerg-400	85	14	upper	upper	ADJ
fuelectenerg-400	85	15	bounds	bound	NOUN
fuelectenerg-400	85	16	on	on	ADP
fuelectenerg-400	85	17	shannon	shannon	PROPN
fuelectenerg-400	85	18	noiseless	noiseless	PROPN
fuelectenerg-400	85	19	capacity	capacity	NOUN
fuelectenerg-400	85	20	of	of	ADP
fuelectenerg-400	85	21	2d	2d	NUM
fuelectenerg-400	85	22	channels	channel	NOUN
fuelectenerg-400	85	23	represented	represent	VERB
fuelectenerg-400	85	24	by	by	ADP
fuelectenerg-400	85	25	this	this	DET
fuelectenerg-400	85	26	constraint	constraint	NOUN
fuelectenerg-400	85	27	.	.	PUNCT
fuelectenerg-400	86	1	in	in	ADP
fuelectenerg-400	86	2	addition	addition	NOUN
fuelectenerg-400	86	3	,	,	PUNCT
fuelectenerg-400	86	4	the	the	DET
fuelectenerg-400	86	5	tools	tool	NOUN
fuelectenerg-400	86	6	used	use	VERB
fuelectenerg-400	86	7	for	for	ADP
fuelectenerg-400	86	8	analysis	analysis	NOUN
fuelectenerg-400	86	9	also	also	ADV
fuelectenerg-400	86	10	lead	lead	VERB
fuelectenerg-400	86	11	to	to	ADP
fuelectenerg-400	86	12	a	a	DET
fuelectenerg-400	86	13	framework	framework	NOUN
fuelectenerg-400	86	14	for	for	ADP
fuelectenerg-400	86	15	encoders	encoder	NOUN
fuelectenerg-400	86	16	and	and	CCONJ
fuelectenerg-400	86	17	decoders	decoder	NOUN
fuelectenerg-400	86	18	for	for	ADP
fuelectenerg-400	86	19	the	the	DET
fuelectenerg-400	86	20	constraint	constraint	NOUN
fuelectenerg-400	86	21	.	.	PUNCT
fuelectenerg-400	87	1	the	the	DET
fuelectenerg-400	87	2	rest	rest	NOUN
fuelectenerg-400	87	3	of	of	ADP
fuelectenerg-400	87	4	the	the	DET
fuelectenerg-400	87	5	paper	paper	NOUN
fuelectenerg-400	87	6	is	be	AUX
fuelectenerg-400	87	7	organized	organize	VERB
fuelectenerg-400	87	8	as	as	SCONJ
fuelectenerg-400	87	9	follows	follow	VERB
fuelectenerg-400	87	10	.	.	PUNCT
fuelectenerg-400	88	1	section	section	NOUN
fuelectenerg-400	88	2	2	2	NUM
fuelectenerg-400	88	3	gives	give	VERB
fuelectenerg-400	88	4	the	the	DET
fuelectenerg-400	88	5	necessary	necessary	ADJ
fuelectenerg-400	88	6	background	background	NOUN
fuelectenerg-400	88	7	and	and	CCONJ
fuelectenerg-400	88	8	motivation	motivation	NOUN
fuelectenerg-400	88	9	of	of	ADP
fuelectenerg-400	88	10	the	the	DET
fuelectenerg-400	88	11	problem	problem	NOUN
fuelectenerg-400	88	12	.	.	PUNCT
fuelectenerg-400	89	1	in	in	ADP
fuelectenerg-400	89	2	section	section	NOUN
fuelectenerg-400	89	3	3	3	NUM
fuelectenerg-400	89	4	,	,	PUNCT
fuelectenerg-400	89	5	we	we	PRON
fuelectenerg-400	89	6	define	define	VERB
fuelectenerg-400	89	7	lozenge	lozenge	NOUN
fuelectenerg-400	89	8	codes	code	NOUN
fuelectenerg-400	89	9	and	and	CCONJ
fuelectenerg-400	89	10	establish	establish	VERB
fuelectenerg-400	89	11	their	their	PRON
fuelectenerg-400	89	12	connection	connection	NOUN
fuelectenerg-400	89	13	with	with	ADP
fuelectenerg-400	89	14	boxed	boxed	ADJ
fuelectenerg-400	89	15	plane	plane	NOUN
fuelectenerg-400	89	16	partitions	partition	NOUN
fuelectenerg-400	89	17	,	,	PUNCT
fuelectenerg-400	89	18	and	and	CCONJ
fuelectenerg-400	89	19	in	in	ADP
fuelectenerg-400	89	20	section	section	NOUN
fuelectenerg-400	89	21	4	4	NUM
fuelectenerg-400	89	22	we	we	PRON
fuelectenerg-400	89	23	derive	derive	VERB
fuelectenerg-400	89	24	bounds	bound	NOUN
fuelectenerg-400	89	25	on	on	ADP
fuelectenerg-400	89	26	capacity	capacity	NOUN
fuelectenerg-400	89	27	.	.	PUNCT
fuelectenerg-400	90	1	section	section	NOUN
fuelectenerg-400	90	2	5	5	NUM
fuelectenerg-400	90	3	introduces	introduce	NOUN
fuelectenerg-400	90	4	encoding	encode	VERB
fuelectenerg-400	90	5	and	and	CCONJ
fuelectenerg-400	90	6	decoding	decode	VERB
fuelectenerg-400	90	7	schemes	scheme	NOUN
fuelectenerg-400	90	8	for	for	ADP
fuelectenerg-400	90	9	lozenge	lozenge	NOUN
fuelectenerg-400	90	10	codes	code	NOUN
fuelectenerg-400	90	11	,	,	PUNCT
fuelectenerg-400	90	12	and	and	CCONJ
fuelectenerg-400	90	13	section	section	NOUN
fuelectenerg-400	90	14	6	6	NUM
fuelectenerg-400	90	15	concludes	conclude	VERB
fuelectenerg-400	90	16	the	the	DET
fuelectenerg-400	90	17	paper	paper	NOUN
fuelectenerg-400	90	18	.	.	PUNCT
fuelectenerg-400	91	1	detection	detection	NOUN
fuelectenerg-400	91	2	and	and	CCONJ
fuelectenerg-400	91	3	coding	code	VERB
fuelectenerg-400	91	4	for	for	ADP
fuelectenerg-400	91	5	tdmr	tdmr	NOUN
fuelectenerg-400	91	6	channel	channel	NOUN
fuelectenerg-400	91	7	523	523	NUM
fuelectenerg-400	91	8	2	2	NUM
fuelectenerg-400	91	9	preliminaries	preliminary	NOUN
fuelectenerg-400	91	10	a	a	DET
fuelectenerg-400	91	11	two	two	NUM
fuelectenerg-400	91	12	-	-	PUNCT
fuelectenerg-400	91	13	dimensional	dimensional	ADJ
fuelectenerg-400	91	14	constrained	constrain	VERB
fuelectenerg-400	91	15	encoder	encoder	NOUN
fuelectenerg-400	91	16	may	may	AUX
fuelectenerg-400	91	17	be	be	AUX
fuelectenerg-400	91	18	visualized	visualize	VERB
fuelectenerg-400	91	19	as	as	ADP
fuelectenerg-400	91	20	a	a	DET
fuelectenerg-400	91	21	mapping	mapping	NOUN
fuelectenerg-400	91	22	from	from	ADP
fuelectenerg-400	91	23	an	an	DET
fuelectenerg-400	91	24	unconstrained	unconstrained	ADJ
fuelectenerg-400	91	25	binary	binary	ADJ
fuelectenerg-400	91	26	sequence	sequence	NOUN
fuelectenerg-400	91	27	into	into	ADP
fuelectenerg-400	91	28	a	a	DET
fuelectenerg-400	91	29	colored	colored	ADJ
fuelectenerg-400	91	30	tiling	tiling	NOUN
fuelectenerg-400	91	31	.	.	PUNCT
fuelectenerg-400	92	1	a	a	DET
fuelectenerg-400	92	2	tiling	tiling	NOUN
fuelectenerg-400	92	3	of	of	ADP
fuelectenerg-400	92	4	the	the	DET
fuelectenerg-400	92	5	plane	plane	NOUN
fuelectenerg-400	92	6	is	be	AUX
fuelectenerg-400	92	7	a	a	DET
fuelectenerg-400	92	8	collection	collection	NOUN
fuelectenerg-400	92	9	of	of	ADP
fuelectenerg-400	92	10	plane	plane	NOUN
fuelectenerg-400	92	11	figures	figure	NOUN
fuelectenerg-400	92	12	that	that	PRON
fuelectenerg-400	92	13	fills	fill	VERB
fuelectenerg-400	92	14	the	the	DET
fuelectenerg-400	92	15	plane	plane	NOUN
fuelectenerg-400	92	16	with	with	ADP
fuelectenerg-400	92	17	no	no	DET
fuelectenerg-400	92	18	overlaps	overlap	NOUN
fuelectenerg-400	92	19	and	and	CCONJ
fuelectenerg-400	92	20	no	no	DET
fuelectenerg-400	92	21	gaps	gap	NOUN
fuelectenerg-400	92	22	.	.	PUNCT
fuelectenerg-400	93	1	the	the	DET
fuelectenerg-400	93	2	plane	plane	NOUN
fuelectenerg-400	93	3	figures	figure	NOUN
fuelectenerg-400	93	4	used	use	VERB
fuelectenerg-400	93	5	as	as	ADP
fuelectenerg-400	93	6	building	build	VERB
fuelectenerg-400	93	7	blocks	block	NOUN
fuelectenerg-400	93	8	for	for	ADP
fuelectenerg-400	93	9	tilings	tiling	NOUN
fuelectenerg-400	93	10	are	be	AUX
fuelectenerg-400	93	11	called	call	VERB
fuelectenerg-400	93	12	tiles	tile	NOUN
fuelectenerg-400	93	13	.	.	PUNCT
fuelectenerg-400	94	1	two	two	NUM
fuelectenerg-400	94	2	tiles	tile	NOUN
fuelectenerg-400	94	3	are	be	AUX
fuelectenerg-400	94	4	said	say	VERB
fuelectenerg-400	94	5	to	to	PART
fuelectenerg-400	94	6	be	be	AUX
fuelectenerg-400	94	7	neigbors	neigbor	NOUN
fuelectenerg-400	94	8	if	if	SCONJ
fuelectenerg-400	94	9	they	they	PRON
fuelectenerg-400	94	10	share	share	VERB
fuelectenerg-400	94	11	an	an	DET
fuelectenerg-400	94	12	edge	edge	NOUN
fuelectenerg-400	94	13	(	(	PUNCT
fuelectenerg-400	94	14	side	side	NOUN
fuelectenerg-400	94	15	)	)	PUNCT
fuelectenerg-400	94	16	,	,	PUNCT
fuelectenerg-400	94	17	and	and	CCONJ
fuelectenerg-400	94	18	to	to	PART
fuelectenerg-400	94	19	be	be	AUX
fuelectenerg-400	94	20	touching	touch	VERB
fuelectenerg-400	94	21	if	if	SCONJ
fuelectenerg-400	94	22	they	they	PRON
fuelectenerg-400	94	23	share	share	VERB
fuelectenerg-400	94	24	only	only	ADV
fuelectenerg-400	94	25	a	a	DET
fuelectenerg-400	94	26	single	single	ADJ
fuelectenerg-400	94	27	vertex	vertex	NOUN
fuelectenerg-400	94	28	.	.	PUNCT
fuelectenerg-400	95	1	a	a	DET
fuelectenerg-400	95	2	regular	regular	ADJ
fuelectenerg-400	95	3	tiling	tiling	NOUN
fuelectenerg-400	95	4	uses	use	VERB
fuelectenerg-400	95	5	congruent	congruent	ADJ
fuelectenerg-400	95	6	regular	regular	ADJ
fuelectenerg-400	95	7	polygons	polygon	NOUN
fuelectenerg-400	95	8	as	as	ADP
fuelectenerg-400	95	9	tiles	tile	NOUN
fuelectenerg-400	95	10	.	.	PUNCT
fuelectenerg-400	96	1	there	there	PRON
fuelectenerg-400	96	2	are	be	VERB
fuelectenerg-400	96	3	only	only	ADV
fuelectenerg-400	96	4	three	three	NUM
fuelectenerg-400	96	5	regular	regular	ADJ
fuelectenerg-400	96	6	tilings	tiling	NOUN
fuelectenerg-400	96	7	:	:	PUNCT
fuelectenerg-400	96	8	triangular	triangular	NOUN
fuelectenerg-400	96	9	,	,	PUNCT
fuelectenerg-400	96	10	square	square	ADJ
fuelectenerg-400	96	11	,	,	PUNCT
fuelectenerg-400	96	12	and	and	CCONJ
fuelectenerg-400	96	13	hexagonal	hexagonal	ADJ
fuelectenerg-400	96	14	.	.	PUNCT
fuelectenerg-400	97	1	figure	figure	NOUN
fuelectenerg-400	97	2	1	1	NUM
fuelectenerg-400	97	3	illustrates	illustrate	VERB
fuelectenerg-400	97	4	each	each	PRON
fuelectenerg-400	97	5	of	of	ADP
fuelectenerg-400	97	6	these	these	DET
fuelectenerg-400	97	7	tilings	tiling	NOUN
fuelectenerg-400	97	8	.	.	PUNCT
fuelectenerg-400	98	1	a	a	DET
fuelectenerg-400	98	2	tiling	tiling	NOUN
fuelectenerg-400	98	3	of	of	ADP
fuelectenerg-400	98	4	a	a	DET
fuelectenerg-400	98	5	plane	plane	NOUN
fuelectenerg-400	98	6	figure	figure	NOUN
fuelectenerg-400	98	7	or	or	CCONJ
fuelectenerg-400	98	8	finite	finite	ADJ
fuelectenerg-400	98	9	region	region	NOUN
fuelectenerg-400	98	10	can	can	AUX
fuelectenerg-400	98	11	be	be	AUX
fuelectenerg-400	98	12	defined	define	VERB
fuelectenerg-400	98	13	analogously	analogously	ADV
fuelectenerg-400	98	14	.	.	PUNCT
fuelectenerg-400	99	1	a	a	DET
fuelectenerg-400	99	2	tiling	tiling	NOUN
fuelectenerg-400	99	3	is	be	AUX
fuelectenerg-400	99	4	said	say	VERB
fuelectenerg-400	99	5	to	to	PART
fuelectenerg-400	99	6	be	be	AUX
fuelectenerg-400	99	7	colored	color	VERB
fuelectenerg-400	99	8	or	or	CCONJ
fuelectenerg-400	99	9	labelled	label	VERB
fuelectenerg-400	99	10	if	if	SCONJ
fuelectenerg-400	99	11	each	each	PRON
fuelectenerg-400	99	12	of	of	ADP
fuelectenerg-400	99	13	its	its	PRON
fuelectenerg-400	99	14	tiles	tile	NOUN
fuelectenerg-400	99	15	is	be	AUX
fuelectenerg-400	99	16	asigned	asigne	VERB
fuelectenerg-400	99	17	a	a	DET
fuelectenerg-400	99	18	color	color	NOUN
fuelectenerg-400	99	19	/	/	SYM
fuelectenerg-400	99	20	symbol	symbol	NOUN
fuelectenerg-400	99	21	from	from	ADP
fuelectenerg-400	99	22	a	a	DET
fuelectenerg-400	99	23	finite	finite	ADJ
fuelectenerg-400	99	24	set	set	NOUN
fuelectenerg-400	99	25	of	of	ADP
fuelectenerg-400	99	26	colors	color	NOUN
fuelectenerg-400	99	27	/	/	SYM
fuelectenerg-400	99	28	symbols	symbol	NOUN
fuelectenerg-400	99	29	.	.	PUNCT
fuelectenerg-400	100	1	a	a	DET
fuelectenerg-400	100	2	colored	colored	ADJ
fuelectenerg-400	100	3	tiling	tiling	NOUN
fuelectenerg-400	100	4	is	be	AUX
fuelectenerg-400	100	5	also	also	ADV
fuelectenerg-400	100	6	referred	refer	VERB
fuelectenerg-400	100	7	as	as	ADP
fuelectenerg-400	100	8	a	a	DET
fuelectenerg-400	100	9	pattern	pattern	NOUN
fuelectenerg-400	100	10	or	or	CCONJ
fuelectenerg-400	100	11	a	a	DET
fuelectenerg-400	100	12	configuration	configuration	NOUN
fuelectenerg-400	100	13	.	.	PUNCT
fuelectenerg-400	101	1	a	a	DET
fuelectenerg-400	101	2	binary	binary	ADJ
fuelectenerg-400	101	3	coloring	coloring	NOUN
fuelectenerg-400	101	4	employs	employ	VERB
fuelectenerg-400	101	5	black	black	ADJ
fuelectenerg-400	101	6	and	and	CCONJ
fuelectenerg-400	101	7	white	white	ADJ
fuelectenerg-400	101	8	tiles	tile	NOUN
fuelectenerg-400	101	9	,	,	PUNCT
fuelectenerg-400	101	10	while	while	SCONJ
fuelectenerg-400	101	11	generally	generally	ADV
fuelectenerg-400	101	12	in	in	ADP
fuelectenerg-400	101	13	m	m	PRON
fuelectenerg-400	101	14	-ary	-ary	VERB
fuelectenerg-400	101	15	coloring	coloring	NOUN
fuelectenerg-400	101	16	each	each	DET
fuelectenerg-400	101	17	tile	tile	NOUN
fuelectenerg-400	101	18	is	be	AUX
fuelectenerg-400	101	19	colored	color	VERB
fuelectenerg-400	101	20	by	by	ADP
fuelectenerg-400	101	21	one	one	NUM
fuelectenerg-400	101	22	of	of	ADP
fuelectenerg-400	101	23	m	m	PROPN
fuelectenerg-400	101	24	>	>	X
fuelectenerg-400	101	25	1	1	NUM
fuelectenerg-400	101	26	colors	color	NOUN
fuelectenerg-400	101	27	.	.	PUNCT
fuelectenerg-400	102	1	consequent	consequent	ADJ
fuelectenerg-400	102	2	to	to	ADP
fuelectenerg-400	102	3	the	the	DET
fuelectenerg-400	102	4	definitions	definition	NOUN
fuelectenerg-400	102	5	above	above	ADV
fuelectenerg-400	102	6	,	,	PUNCT
fuelectenerg-400	102	7	a	a	DET
fuelectenerg-400	102	8	two	two	NUM
fuelectenerg-400	102	9	-	-	PUNCT
fuelectenerg-400	102	10	dimensional	dimensional	ADJ
fuelectenerg-400	102	11	constraint	constraint	NOUN
fuelectenerg-400	102	12	can	can	AUX
fuelectenerg-400	102	13	be	be	AUX
fuelectenerg-400	102	14	expressed	express	VERB
fuelectenerg-400	102	15	as	as	ADP
fuelectenerg-400	102	16	a	a	DET
fuelectenerg-400	102	17	restriction	restriction	NOUN
fuelectenerg-400	102	18	on	on	ADP
fuelectenerg-400	102	19	a	a	DET
fuelectenerg-400	102	20	coloring	coloring	NOUN
fuelectenerg-400	102	21	(	(	PUNCT
fuelectenerg-400	102	22	or	or	CCONJ
fuelectenerg-400	102	23	labeling	labeling	NOUN
fuelectenerg-400	102	24	)	)	PUNCT
fuelectenerg-400	102	25	of	of	ADP
fuelectenerg-400	102	26	tiles	tile	NOUN
fuelectenerg-400	102	27	in	in	ADP
fuelectenerg-400	102	28	a	a	DET
fuelectenerg-400	102	29	regular	regular	ADJ
fuelectenerg-400	102	30	tiling	tiling	NOUN
fuelectenerg-400	102	31	.	.	PUNCT
fuelectenerg-400	103	1	the	the	DET
fuelectenerg-400	103	2	most	most	ADV
fuelectenerg-400	103	3	famous	famous	ADJ
fuelectenerg-400	103	4	example	example	NOUN
fuelectenerg-400	103	5	is	be	AUX
fuelectenerg-400	103	6	a	a	DET
fuelectenerg-400	103	7	hard	hard	ADJ
fuelectenerg-400	103	8	-	-	PUNCT
fuelectenerg-400	103	9	hexagon	hexagon	NOUN
fuelectenerg-400	103	10	constraint	constraint	NOUN
fuelectenerg-400	104	1	[	[	X
fuelectenerg-400	104	2	14	14	NUM
fuelectenerg-400	104	3	]	]	PUNCT
fuelectenerg-400	104	4	–	–	PUNCT
fuelectenerg-400	104	5	a	a	DET
fuelectenerg-400	104	6	planar	planar	ADJ
fuelectenerg-400	104	7	hexagonal	hexagonal	ADJ
fuelectenerg-400	104	8	lattice	lattice	NOUN
fuelectenerg-400	104	9	with	with	ADP
fuelectenerg-400	104	10	nearest	near	ADJ
fuelectenerg-400	104	11	-	-	PUNCT
fuelectenerg-400	104	12	neighbor	neighbor	NOUN
fuelectenerg-400	104	13	exclusion	exclusion	NOUN
fuelectenerg-400	104	14	.	.	PUNCT
fuelectenerg-400	105	1	this	this	PRON
fuelectenerg-400	105	2	is	be	AUX
fuelectenerg-400	105	3	used	use	VERB
fuelectenerg-400	105	4	as	as	ADP
fuelectenerg-400	105	5	a	a	DET
fuelectenerg-400	105	6	gas	gas	NOUN
fuelectenerg-400	105	7	model	model	NOUN
fuelectenerg-400	105	8	in	in	ADP
fuelectenerg-400	105	9	statistical	statistical	ADJ
fuelectenerg-400	105	10	mechanics	mechanic	NOUN
fuelectenerg-400	105	11	.	.	PUNCT
fuelectenerg-400	106	1	the	the	DET
fuelectenerg-400	106	2	hard	hard	ADJ
fuelectenerg-400	106	3	-	-	PUNCT
fuelectenerg-400	106	4	hexagon	hexagon	NOUN
fuelectenerg-400	106	5	constraint	constraint	NOUN
fuelectenerg-400	106	6	allows	allow	VERB
fuelectenerg-400	106	7	only	only	ADV
fuelectenerg-400	106	8	those	those	DET
fuelectenerg-400	106	9	(	(	PUNCT
fuelectenerg-400	106	10	binary	binary	ADJ
fuelectenerg-400	106	11	)	)	PUNCT
fuelectenerg-400	106	12	colorings	coloring	NOUN
fuelectenerg-400	106	13	in	in	ADP
fuelectenerg-400	106	14	which	which	PRON
fuelectenerg-400	106	15	black	black	ADJ
fuelectenerg-400	106	16	hexagons	hexagon	NOUN
fuelectenerg-400	106	17	are	be	AUX
fuelectenerg-400	106	18	isolated	isolate	VERB
fuelectenerg-400	106	19	,	,	PUNCT
fuelectenerg-400	106	20	i.e.	i.e.	X
fuelectenerg-400	106	21	,	,	PUNCT
fuelectenerg-400	106	22	have	have	VERB
fuelectenerg-400	106	23	all	all	DET
fuelectenerg-400	106	24	white	white	ADJ
fuelectenerg-400	106	25	neighbors	neighbor	NOUN
fuelectenerg-400	106	26	.	.	PUNCT
fuelectenerg-400	107	1	a	a	DET
fuelectenerg-400	107	2	hard	hard	ADJ
fuelectenerg-400	107	3	-	-	PUNCT
fuelectenerg-400	107	4	triangle	triangle	NOUN
fuelectenerg-400	107	5	[	[	X
fuelectenerg-400	107	6	3	3	NUM
fuelectenerg-400	107	7	]	]	PUNCT
fuelectenerg-400	107	8	and	and	CCONJ
fuelectenerg-400	107	9	hard	hard	ADJ
fuelectenerg-400	107	10	-	-	PUNCT
fuelectenerg-400	107	11	square	square	ADJ
fuelectenerg-400	107	12	constraints	constraint	NOUN
fuelectenerg-400	107	13	are	be	AUX
fuelectenerg-400	107	14	defined	define	VERB
fuelectenerg-400	107	15	similarly	similarly	ADV
fuelectenerg-400	107	16	.	.	PUNCT
fuelectenerg-400	108	1	a	a	DET
fuelectenerg-400	108	2	twodimensional	twodimensional	ADJ
fuelectenerg-400	108	3	runlength	runlength	NOUN
fuelectenerg-400	108	4	(	(	PUNCT
fuelectenerg-400	108	5	d	d	NOUN
fuelectenerg-400	108	6	,	,	PUNCT
fuelectenerg-400	108	7	k	k	NOUN
fuelectenerg-400	108	8	)	)	PUNCT
fuelectenerg-400	108	9	constraint	constraint	NOUN
fuelectenerg-400	108	10	is	be	AUX
fuelectenerg-400	108	11	a	a	DET
fuelectenerg-400	108	12	restriction	restriction	NOUN
fuelectenerg-400	108	13	on	on	ADP
fuelectenerg-400	108	14	the	the	DET
fuelectenerg-400	108	15	separation	separation	NOUN
fuelectenerg-400	108	16	space	space	NOUN
fuelectenerg-400	108	17	between	between	ADP
fuelectenerg-400	108	18	black	black	ADJ
fuelectenerg-400	108	19	tiles	tile	NOUN
fuelectenerg-400	108	20	,	,	PUNCT
fuelectenerg-400	108	21	so	so	SCONJ
fuelectenerg-400	108	22	that	that	SCONJ
fuelectenerg-400	108	23	the	the	DET
fuelectenerg-400	108	24	number	number	NOUN
fuelectenerg-400	108	25	of	of	ADP
fuelectenerg-400	108	26	white	white	ADJ
fuelectenerg-400	108	27	tiles	tile	NOUN
fuelectenerg-400	108	28	between	between	ADP
fuelectenerg-400	108	29	two	two	NUM
fuelectenerg-400	108	30	black	black	ADJ
fuelectenerg-400	108	31	tiles	tile	NOUN
fuelectenerg-400	108	32	in	in	ADP
fuelectenerg-400	108	33	any	any	DET
fuelectenerg-400	108	34	direction	direction	NOUN
fuelectenerg-400	108	35	is	be	AUX
fuelectenerg-400	108	36	at	at	ADP
fuelectenerg-400	108	37	least	least	ADJ
fuelectenerg-400	108	38	d	d	NOUN
fuelectenerg-400	108	39	and	and	CCONJ
fuelectenerg-400	108	40	at	at	ADP
fuelectenerg-400	108	41	most	most	ADJ
fuelectenerg-400	108	42	k	k	X
fuelectenerg-400	108	43	(	(	PUNCT
fuelectenerg-400	108	44	0	0	NUM
fuelectenerg-400	108	45	≤	≤	NUM
fuelectenerg-400	109	1	d	d	X
fuelectenerg-400	109	2	<	<	X
fuelectenerg-400	109	3	k	k	X
fuelectenerg-400	109	4	)	)	PUNCT
fuelectenerg-400	109	5	.	.	PUNCT
fuelectenerg-400	110	1	indeed	indeed	ADV
fuelectenerg-400	110	2	,	,	PUNCT
fuelectenerg-400	110	3	it	it	PRON
fuelectenerg-400	110	4	can	can	AUX
fuelectenerg-400	110	5	be	be	AUX
fuelectenerg-400	110	6	seen	see	VERB
fuelectenerg-400	110	7	that	that	SCONJ
fuelectenerg-400	110	8	the	the	DET
fuelectenerg-400	110	9	hard	hard	ADV
fuelectenerg-400	110	10	-	-	PUNCT
fuelectenerg-400	110	11	hexagon	hexagon	NOUN
fuelectenerg-400	110	12	,	,	PUNCT
fuelectenerg-400	110	13	hard	hard	ADJ
fuelectenerg-400	110	14	-	-	PUNCT
fuelectenerg-400	110	15	triangle	triangle	NOUN
fuelectenerg-400	110	16	and	and	CCONJ
fuelectenerg-400	110	17	hard	hard	ADJ
fuelectenerg-400	110	18	-	-	PUNCT
fuelectenerg-400	110	19	square	square	ADJ
fuelectenerg-400	110	20	constraints	constraint	NOUN
fuelectenerg-400	110	21	are	be	AUX
fuelectenerg-400	110	22	instances	instance	NOUN
fuelectenerg-400	110	23	of	of	ADP
fuelectenerg-400	110	24	the	the	DET
fuelectenerg-400	110	25	(	(	PUNCT
fuelectenerg-400	110	26	d	d	PROPN
fuelectenerg-400	110	27	,	,	PUNCT
fuelectenerg-400	110	28	k	k	NOUN
fuelectenerg-400	110	29	)	)	PUNCT
fuelectenerg-400	110	30	constraints	constraint	NOUN
fuelectenerg-400	110	31	.	.	PUNCT
fuelectenerg-400	111	1	in	in	ADP
fuelectenerg-400	111	2	particular	particular	ADJ
fuelectenerg-400	111	3	,	,	PUNCT
fuelectenerg-400	111	4	they	they	PRON
fuelectenerg-400	111	5	are	be	AUX
fuelectenerg-400	111	6	(	(	PUNCT
fuelectenerg-400	111	7	d	d	NOUN
fuelectenerg-400	111	8	,	,	PUNCT
fuelectenerg-400	111	9	k	k	NOUN
fuelectenerg-400	111	10	)	)	PUNCT
fuelectenerg-400	111	11	=	=	SYM
fuelectenerg-400	111	12	(	(	PUNCT
fuelectenerg-400	111	13	1,∞	1,∞	NUM
fuelectenerg-400	111	14	)	)	PUNCT
fuelectenerg-400	111	15	runlength	runlength	NOUN
fuelectenerg-400	111	16	constraints	constraint	NOUN
fuelectenerg-400	111	17	on	on	ADP
fuelectenerg-400	111	18	their	their	PRON
fuelectenerg-400	111	19	respective	respective	ADJ
fuelectenerg-400	111	20	lattices	lattice	NOUN
fuelectenerg-400	111	21	.	.	PUNCT
fuelectenerg-400	112	1	constraints	constraint	NOUN
fuelectenerg-400	112	2	for	for	ADP
fuelectenerg-400	112	3	which	which	PRON
fuelectenerg-400	112	4	a	a	DET
fuelectenerg-400	112	5	coloring	coloring	NOUN
fuelectenerg-400	112	6	depends	depend	VERB
fuelectenerg-400	112	7	on	on	ADP
fuelectenerg-400	112	8	both	both	CCONJ
fuelectenerg-400	112	9	neigboring	neigbore	VERB
fuelectenerg-400	112	10	and	and	CCONJ
fuelectenerg-400	112	11	touching	touching	ADJ
fuelectenerg-400	112	12	tiles	tile	NOUN
fuelectenerg-400	112	13	is	be	AUX
fuelectenerg-400	112	14	referred	refer	VERB
fuelectenerg-400	112	15	to	to	ADP
fuelectenerg-400	112	16	as	as	ADP
fuelectenerg-400	112	17	a	a	DET
fuelectenerg-400	112	18	checkerboard	checkerboard	NOUN
fuelectenerg-400	112	19	constraint	constraint	NOUN
fuelectenerg-400	112	20	[	[	X
fuelectenerg-400	112	21	9	9	NUM
fuelectenerg-400	112	22	]	]	PUNCT
fuelectenerg-400	112	23	.	.	PUNCT
fuelectenerg-400	113	1	one	one	NUM
fuelectenerg-400	113	2	example	example	NOUN
fuelectenerg-400	113	3	of	of	ADP
fuelectenerg-400	113	4	a	a	DET
fuelectenerg-400	113	5	checkerboard	checkerboard	NOUN
fuelectenerg-400	113	6	constraint	constraint	NOUN
fuelectenerg-400	113	7	is	be	AUX
fuelectenerg-400	113	8	a	a	DET
fuelectenerg-400	113	9	square	square	ADJ
fuelectenerg-400	113	10	tiling	tiling	NOUN
fuelectenerg-400	113	11	in	in	ADP
fuelectenerg-400	113	12	which	which	PRON
fuelectenerg-400	113	13	black	black	ADJ
fuelectenerg-400	113	14	squares	square	NOUN
fuelectenerg-400	113	15	are	be	AUX
fuelectenerg-400	113	16	not	not	PART
fuelectenerg-400	113	17	permitted	permit	VERB
fuelectenerg-400	113	18	to	to	PART
fuelectenerg-400	113	19	share	share	VERB
fuelectenerg-400	113	20	a	a	DET
fuelectenerg-400	113	21	vertex	vertex	NOUN
fuelectenerg-400	113	22	.	.	PUNCT
fuelectenerg-400	114	1	as	as	SCONJ
fuelectenerg-400	114	2	mentioned	mention	VERB
fuelectenerg-400	114	3	previously	previously	ADV
fuelectenerg-400	114	4	,	,	PUNCT
fuelectenerg-400	114	5	both	both	PRON
fuelectenerg-400	114	6	runlength	runlength	NOUN
fuelectenerg-400	114	7	and	and	CCONJ
fuelectenerg-400	114	8	checkerboard	checkerboard	NOUN
fuelectenerg-400	114	9	constraints	constraint	NOUN
fuelectenerg-400	114	10	have	have	AUX
fuelectenerg-400	114	11	been	be	AUX
fuelectenerg-400	114	12	an	an	DET
fuelectenerg-400	114	13	active	active	ADJ
fuelectenerg-400	114	14	area	area	NOUN
fuelectenerg-400	114	15	of	of	ADP
fuelectenerg-400	114	16	research	research	NOUN
fuelectenerg-400	114	17	,	,	PUNCT
fuelectenerg-400	114	18	but	but	CCONJ
fuelectenerg-400	114	19	the	the	DET
fuelectenerg-400	114	20	progress	progress	NOUN
fuelectenerg-400	114	21	has	have	AUX
fuelectenerg-400	114	22	been	be	AUX
fuelectenerg-400	114	23	slow	slow	ADJ
fuelectenerg-400	114	24	because	because	SCONJ
fuelectenerg-400	114	25	of	of	ADP
fuelectenerg-400	114	26	inherent	inherent	ADJ
fuelectenerg-400	114	27	hardness	hardness	NOUN
fuelectenerg-400	114	28	of	of	ADP
fuelectenerg-400	114	29	two	two	NUM
fuelectenerg-400	114	30	-	-	PUNCT
fuelectenerg-400	114	31	dimensional	dimensional	ADJ
fuelectenerg-400	114	32	tiling	tiling	NOUN
fuelectenerg-400	114	33	problems	problem	NOUN
fuelectenerg-400	114	34	.	.	PUNCT
fuelectenerg-400	115	1	3	3	NUM
fuelectenerg-400	115	2	lozenge	lozenge	NOUN
fuelectenerg-400	115	3	codes	code	NOUN
fuelectenerg-400	115	4	consider	consider	VERB
fuelectenerg-400	115	5	a	a	DET
fuelectenerg-400	115	6	regular	regular	ADJ
fuelectenerg-400	115	7	tiling	tiling	NOUN
fuelectenerg-400	115	8	of	of	ADP
fuelectenerg-400	115	9	a	a	DET
fuelectenerg-400	115	10	plane	plane	NOUN
fuelectenerg-400	115	11	.	.	PUNCT
fuelectenerg-400	116	1	a	a	DET
fuelectenerg-400	116	2	(	(	PUNCT
fuelectenerg-400	116	3	d	d	NOUN
fuelectenerg-400	116	4	,	,	PUNCT
fuelectenerg-400	116	5	k	k	NOUN
fuelectenerg-400	116	6	)	)	PUNCT
fuelectenerg-400	116	7	segregation	segregation	NOUN
fuelectenerg-400	116	8	constraint	constraint	NOUN
fuelectenerg-400	116	9	is	be	AUX
fuelectenerg-400	116	10	a	a	DET
fuelectenerg-400	116	11	tiling	tiling	NOUN
fuelectenerg-400	116	12	that	that	PRON
fuelectenerg-400	116	13	limits	limit	VERB
fuelectenerg-400	116	14	the	the	DET
fuelectenerg-400	116	15	number	number	NOUN
fuelectenerg-400	116	16	of	of	ADP
fuelectenerg-400	116	17	neighboring	neighboring	NOUN
fuelectenerg-400	116	18	tiles	tile	NOUN
fuelectenerg-400	116	19	(	(	PUNCT
fuelectenerg-400	116	20	neighborhood	neighborhood	NOUN
fuelectenerg-400	116	21	size	size	NOUN
fuelectenerg-400	116	22	)	)	PUNCT
fuelectenerg-400	116	23	of	of	ADP
fuelectenerg-400	116	24	same	same	ADJ
fuelectenerg-400	116	25	color	color	NOUN
fuelectenerg-400	116	26	to	to	PART
fuelectenerg-400	116	27	be	be	AUX
fuelectenerg-400	116	28	no	no	PRON
fuelectenerg-400	116	29	less	less	ADJ
fuelectenerg-400	116	30	than	than	ADP
fuelectenerg-400	116	31	d+1	d+1	PROPN
fuelectenerg-400	116	32	and	and	CCONJ
fuelectenerg-400	116	33	no	no	PRON
fuelectenerg-400	116	34	more	more	ADJ
fuelectenerg-400	116	35	than	than	ADP
fuelectenerg-400	116	36	k+1	k+1	PROPN
fuelectenerg-400	116	37	.	.	PUNCT
fuelectenerg-400	117	1	a	a	DET
fuelectenerg-400	117	2	2d	2d	NUM
fuelectenerg-400	117	3	bit	bit	NOUN
fuelectenerg-400	117	4	pattern	pattern	NOUN
fuelectenerg-400	117	5	is	be	AUX
fuelectenerg-400	117	6	said	say	VERB
fuelectenerg-400	117	7	to	to	PART
fuelectenerg-400	117	8	satisfy	satisfy	VERB
fuelectenerg-400	117	9	a	a	DET
fuelectenerg-400	117	10	no	no	DET
fuelectenerg-400	117	11	isolated	isolated	ADJ
fuelectenerg-400	117	12	bit	bit	NOUN
fuelectenerg-400	117	13	(	(	PUNCT
fuelectenerg-400	117	14	nib	nib	NOUN
fuelectenerg-400	117	15	)	)	PUNCT
fuelectenerg-400	117	16	constraint	constraint	NOUN
fuelectenerg-400	117	17	if	if	SCONJ
fuelectenerg-400	117	18	every	every	DET
fuelectenerg-400	117	19	bit	bit	NOUN
fuelectenerg-400	117	20	has	have	VERB
fuelectenerg-400	117	21	at	at	ADV
fuelectenerg-400	117	22	least	least	ADV
fuelectenerg-400	117	23	one	one	NUM
fuelectenerg-400	117	24	bit	bit	NOUN
fuelectenerg-400	117	25	of	of	ADP
fuelectenerg-400	117	26	the	the	DET
fuelectenerg-400	117	27	same	same	ADJ
fuelectenerg-400	117	28	polarity	polarity	NOUN
fuelectenerg-400	117	29	adjacent	adjacent	ADJ
fuelectenerg-400	117	30	to	to	ADP
fuelectenerg-400	117	31	it	it	PRON
fuelectenerg-400	117	32	.	.	PUNCT
fuelectenerg-400	118	1	thus	thus	ADV
fuelectenerg-400	118	2	the	the	DET
fuelectenerg-400	118	3	nib	nib	NOUN
fuelectenerg-400	118	4	is	be	AUX
fuelectenerg-400	118	5	a	a	DET
fuelectenerg-400	118	6	(	(	PUNCT
fuelectenerg-400	118	7	d	d	NOUN
fuelectenerg-400	118	8	,	,	PUNCT
fuelectenerg-400	118	9	k	k	NOUN
fuelectenerg-400	118	10	)	)	PUNCT
fuelectenerg-400	118	11	=	=	SYM
fuelectenerg-400	118	12	(	(	PUNCT
fuelectenerg-400	118	13	1,∞	1,∞	NUM
fuelectenerg-400	118	14	)	)	PUNCT
fuelectenerg-400	118	15	segregation	segregation	NOUN
fuelectenerg-400	118	16	constraint	constraint	NOUN
fuelectenerg-400	118	17	.	.	PUNCT
fuelectenerg-400	119	1	note	note	VERB
fuelectenerg-400	119	2	that	that	SCONJ
fuelectenerg-400	119	3	the	the	DET
fuelectenerg-400	119	4	parameters	parameter	NOUN
fuelectenerg-400	119	5	d	d	PROPN
fuelectenerg-400	119	6	and	and	CCONJ
fuelectenerg-400	119	7	k	k	PROPN
fuelectenerg-400	119	8	in	in	ADP
fuelectenerg-400	119	9	runlength	runlength	NOUN
fuelectenerg-400	119	10	and	and	CCONJ
fuelectenerg-400	119	11	segregation	segregation	NOUN
fuelectenerg-400	119	12	constraints	constraint	NOUN
fuelectenerg-400	119	13	have	have	VERB
fuelectenerg-400	119	14	different	different	ADJ
fuelectenerg-400	119	15	meanings	meaning	NOUN
fuelectenerg-400	119	16	.	.	PUNCT
fuelectenerg-400	120	1	in	in	ADP
fuelectenerg-400	120	2	rectangular	rectangular	ADJ
fuelectenerg-400	120	3	latices	latex	NOUN
fuelectenerg-400	120	4	runlength	runlength	NOUN
fuelectenerg-400	120	5	constraint	constraint	NOUN
fuelectenerg-400	120	6	can	can	AUX
fuelectenerg-400	120	7	be	be	AUX
fuelectenerg-400	120	8	converted	convert	VERB
fuelectenerg-400	120	9	522	522	NUM
fuelectenerg-400	120	10	b.	b.	NOUN
fuelectenerg-400	120	11	vasic	vasic	NOUN
fuelectenerg-400	120	12	,	,	PUNCT
fuelectenerg-400	120	13	a.	a.	PROPN
fuelectenerg-400	120	14	r.	r.	PROPN
fuelectenerg-400	120	15	krishnan	krishnan	PROPN
fuelectenerg-400	120	16	lozenge	lozenge	PROPN
fuelectenerg-400	120	17	tiling	tile	VERB
fuelectenerg-400	120	18	constrained	constrain	VERB
fuelectenerg-400	120	19	codes	code	NOUN
fuelectenerg-400	120	20	523	523	NUM
fuelectenerg-400	120	21	524	524	NUM
fuelectenerg-400	120	22	a.	a.	NOUN
fuelectenerg-400	120	23	r.	r.	PROPN
fuelectenerg-400	120	24	krishnanan	krishnanan	PROPN
fuelectenerg-400	120	25	and	and	CCONJ
fuelectenerg-400	120	26	b.	b.	PROPN
fuelectenerg-400	120	27	vasić	vasić	PROPN
fuelectenerg-400	120	28	to	to	ADP
fuelectenerg-400	120	29	a	a	DET
fuelectenerg-400	120	30	segregation	segregation	NOUN
fuelectenerg-400	120	31	constraint	constraint	NOUN
fuelectenerg-400	120	32	by	by	ADP
fuelectenerg-400	120	33	precoding	precode	VERB
fuelectenerg-400	120	34	[	[	X
fuelectenerg-400	120	35	1	1	NUM
fuelectenerg-400	120	36	]	]	PUNCT
fuelectenerg-400	120	37	,	,	PUNCT
fuelectenerg-400	120	38	while	while	SCONJ
fuelectenerg-400	120	39	for	for	ADP
fuelectenerg-400	120	40	other	other	ADJ
fuelectenerg-400	120	41	two	two	NUM
fuelectenerg-400	120	42	latices	latex	NOUN
fuelectenerg-400	120	43	in	in	ADP
fuelectenerg-400	120	44	fig	fig	NOUN
fuelectenerg-400	120	45	.	.	PUNCT
fuelectenerg-400	121	1	1(a	1(a	NUM
fuelectenerg-400	121	2	)	)	PUNCT
fuelectenerg-400	121	3	this	this	PRON
fuelectenerg-400	121	4	is	be	AUX
fuelectenerg-400	121	5	not	not	PART
fuelectenerg-400	121	6	the	the	DET
fuelectenerg-400	121	7	case	case	NOUN
fuelectenerg-400	121	8	.	.	PUNCT
fuelectenerg-400	122	1	in	in	ADP
fuelectenerg-400	122	2	other	other	ADJ
fuelectenerg-400	122	3	words	word	NOUN
fuelectenerg-400	122	4	segregation	segregation	NOUN
fuelectenerg-400	122	5	constraints	constraint	NOUN
fuelectenerg-400	122	6	are	be	AUX
fuelectenerg-400	122	7	not	not	PART
fuelectenerg-400	122	8	in	in	ADP
fuelectenerg-400	122	9	bijection	bijection	NOUN
fuelectenerg-400	122	10	to	to	ADP
fuelectenerg-400	122	11	simple	simple	ADJ
fuelectenerg-400	122	12	runlength	runlength	NOUN
fuelectenerg-400	122	13	(	(	PUNCT
fuelectenerg-400	122	14	d	d	NOUN
fuelectenerg-400	122	15	,	,	PUNCT
fuelectenerg-400	122	16	k	k	NOUN
fuelectenerg-400	122	17	)	)	PUNCT
fuelectenerg-400	122	18	constraints	constraint	NOUN
fuelectenerg-400	122	19	.	.	PUNCT
fuelectenerg-400	123	1	using	use	VERB
fuelectenerg-400	123	2	fig	fig	NOUN
fuelectenerg-400	123	3	.	.	PUNCT
fuelectenerg-400	124	1	1	1	NUM
fuelectenerg-400	124	2	,	,	PUNCT
fuelectenerg-400	124	3	the	the	DET
fuelectenerg-400	124	4	nib	nib	NOUN
fuelectenerg-400	124	5	constraint	constraint	NOUN
fuelectenerg-400	124	6	can	can	AUX
fuelectenerg-400	124	7	be	be	AUX
fuelectenerg-400	124	8	explained	explain	VERB
fuelectenerg-400	124	9	as	as	SCONJ
fuelectenerg-400	124	10	follows	follow	VERB
fuelectenerg-400	124	11	:	:	PUNCT
fuelectenerg-400	124	12	for	for	ADP
fuelectenerg-400	124	13	any	any	DET
fuelectenerg-400	124	14	given	give	VERB
fuelectenerg-400	124	15	tile	tile	NOUN
fuelectenerg-400	124	16	(	(	PUNCT
fuelectenerg-400	124	17	for	for	ADP
fuelectenerg-400	124	18	example	example	NOUN
fuelectenerg-400	124	19	,	,	PUNCT
fuelectenerg-400	124	20	the	the	DET
fuelectenerg-400	124	21	tile	tile	NOUN
fuelectenerg-400	124	22	marked	mark	VERB
fuelectenerg-400	124	23	gray	gray	ADJ
fuelectenerg-400	124	24	in	in	ADP
fuelectenerg-400	124	25	the	the	DET
fuelectenerg-400	124	26	figure	figure	NOUN
fuelectenerg-400	124	27	)	)	PUNCT
fuelectenerg-400	124	28	,	,	PUNCT
fuelectenerg-400	124	29	if	if	SCONJ
fuelectenerg-400	124	30	none	none	NOUN
fuelectenerg-400	124	31	of	of	ADP
fuelectenerg-400	124	32	its	its	PRON
fuelectenerg-400	124	33	neighbouring	neighbouring	ADJ
fuelectenerg-400	124	34	tiles	tile	NOUN
fuelectenerg-400	124	35	(	(	PUNCT
fuelectenerg-400	124	36	tiles	tile	NOUN
fuelectenerg-400	124	37	marked	mark	VERB
fuelectenerg-400	124	38	black	black	ADJ
fuelectenerg-400	124	39	)	)	PUNCT
fuelectenerg-400	124	40	are	be	AUX
fuelectenerg-400	124	41	of	of	ADP
fuelectenerg-400	124	42	the	the	DET
fuelectenerg-400	124	43	same	same	ADJ
fuelectenerg-400	124	44	colour	colour	NOUN
fuelectenerg-400	124	45	,	,	PUNCT
fuelectenerg-400	124	46	then	then	ADV
fuelectenerg-400	124	47	the	the	DET
fuelectenerg-400	124	48	nib	nib	NOUN
fuelectenerg-400	124	49	constraint	constraint	NOUN
fuelectenerg-400	124	50	is	be	AUX
fuelectenerg-400	124	51	said	say	VERB
fuelectenerg-400	124	52	to	to	PART
fuelectenerg-400	124	53	be	be	AUX
fuelectenerg-400	124	54	violated	violate	VERB
fuelectenerg-400	124	55	.	.	PUNCT
fuelectenerg-400	125	1	our	our	PRON
fuelectenerg-400	125	2	recent	recent	ADJ
fuelectenerg-400	125	3	experimental	experimental	ADJ
fuelectenerg-400	125	4	results	result	NOUN
fuelectenerg-400	125	5	show	show	VERB
fuelectenerg-400	125	6	that	that	SCONJ
fuelectenerg-400	125	7	if	if	SCONJ
fuelectenerg-400	125	8	input	input	NOUN
fuelectenerg-400	125	9	bits	bit	NOUN
fuelectenerg-400	125	10	are	be	AUX
fuelectenerg-400	125	11	mapped	map	VERB
fuelectenerg-400	125	12	to	to	PART
fuelectenerg-400	125	13	bit	bit	NOUN
fuelectenerg-400	125	14	patterns	pattern	NOUN
fuelectenerg-400	125	15	satisfying	satisfy	VERB
fuelectenerg-400	125	16	the	the	DET
fuelectenerg-400	125	17	nib	nib	NOUN
fuelectenerg-400	125	18	constraint	constraint	NOUN
fuelectenerg-400	125	19	,	,	PUNCT
fuelectenerg-400	125	20	then	then	ADV
fuelectenerg-400	125	21	the	the	DET
fuelectenerg-400	125	22	probability	probability	NOUN
fuelectenerg-400	125	23	of	of	ADP
fuelectenerg-400	125	24	rewriting	rewrite	VERB
fuelectenerg-400	125	25	a	a	DET
fuelectenerg-400	125	26	grain	grain	NOUN
fuelectenerg-400	125	27	is	be	AUX
fuelectenerg-400	125	28	reduced	reduce	VERB
fuelectenerg-400	125	29	[	[	X
fuelectenerg-400	125	30	12,15	12,15	NUM
fuelectenerg-400	125	31	]	]	X
fuelectenerg-400	125	32	.	.	PUNCT
fuelectenerg-400	126	1	the	the	DET
fuelectenerg-400	126	2	goal	goal	NOUN
fuelectenerg-400	126	3	of	of	ADP
fuelectenerg-400	126	4	this	this	DET
fuelectenerg-400	126	5	paper	paper	NOUN
fuelectenerg-400	126	6	is	be	AUX
fuelectenerg-400	126	7	to	to	PART
fuelectenerg-400	126	8	establish	establish	VERB
fuelectenerg-400	126	9	a	a	DET
fuelectenerg-400	126	10	bound	bind	VERB
fuelectenerg-400	126	11	of	of	ADP
fuelectenerg-400	126	12	shannon	shannon	PROPN
fuelectenerg-400	126	13	noiseless	noiseless	PROPN
fuelectenerg-400	126	14	capacity	capacity	NOUN
fuelectenerg-400	126	15	and	and	CCONJ
fuelectenerg-400	126	16	designing	designing	NOUN
fuelectenerg-400	126	17	of	of	ADP
fuelectenerg-400	126	18	encoders	encoder	NOUN
fuelectenerg-400	126	19	and	and	CCONJ
fuelectenerg-400	126	20	decoders	decoder	NOUN
fuelectenerg-400	126	21	for	for	ADP
fuelectenerg-400	126	22	nib	nib	NOUN
fuelectenerg-400	126	23	constraint	constraint	NOUN
fuelectenerg-400	126	24	on	on	ADP
fuelectenerg-400	126	25	the	the	DET
fuelectenerg-400	126	26	triangular	triangular	NOUN
fuelectenerg-400	126	27	lattice	lattice	NOUN
fuelectenerg-400	126	28	.	.	PUNCT
fuelectenerg-400	127	1	(	(	PUNCT
fuelectenerg-400	127	2	a	a	X
fuelectenerg-400	127	3	)	)	PUNCT
fuelectenerg-400	127	4	(	(	PUNCT
fuelectenerg-400	127	5	b	b	X
fuelectenerg-400	127	6	)	)	PUNCT
fuelectenerg-400	127	7	(	(	PUNCT
fuelectenerg-400	127	8	c	c	X
fuelectenerg-400	127	9	)	)	PUNCT
fuelectenerg-400	127	10	fig	fig	NOUN
fuelectenerg-400	127	11	.	.	PUNCT
fuelectenerg-400	128	1	1	1	X
fuelectenerg-400	128	2	.	.	X
fuelectenerg-400	128	3	regular	regular	ADJ
fuelectenerg-400	128	4	two	two	NUM
fuelectenerg-400	128	5	-	-	PUNCT
fuelectenerg-400	128	6	dimensional	dimensional	ADJ
fuelectenerg-400	128	7	tilings	tiling	NOUN
fuelectenerg-400	128	8	(	(	PUNCT
fuelectenerg-400	128	9	a	a	PRON
fuelectenerg-400	128	10	)	)	PUNCT
fuelectenerg-400	128	11	triangular	triangular	NOUN
fuelectenerg-400	128	12	,	,	PUNCT
fuelectenerg-400	128	13	(	(	PUNCT
fuelectenerg-400	128	14	b	b	NOUN
fuelectenerg-400	128	15	)	)	PUNCT
fuelectenerg-400	128	16	square	square	NOUN
fuelectenerg-400	128	17	,	,	PUNCT
fuelectenerg-400	128	18	and	and	CCONJ
fuelectenerg-400	128	19	(	(	PUNCT
fuelectenerg-400	128	20	c	c	NOUN
fuelectenerg-400	128	21	)	)	PUNCT
fuelectenerg-400	128	22	hexagonal	hexagonal	ADJ
fuelectenerg-400	128	23	tiling	tiling	NOUN
fuelectenerg-400	128	24	.	.	PUNCT
fuelectenerg-400	129	1	in	in	ADP
fuelectenerg-400	129	2	the	the	DET
fuelectenerg-400	129	3	triangular	triangular	NOUN
fuelectenerg-400	129	4	,	,	PUNCT
fuelectenerg-400	129	5	square	square	ADJ
fuelectenerg-400	129	6	and	and	CCONJ
fuelectenerg-400	129	7	hexagonal	hexagonal	ADJ
fuelectenerg-400	129	8	tilings	tiling	NOUN
fuelectenerg-400	129	9	,	,	PUNCT
fuelectenerg-400	129	10	each	each	DET
fuelectenerg-400	129	11	tile	tile	NOUN
fuelectenerg-400	129	12	has	have	VERB
fuelectenerg-400	129	13	three	three	NUM
fuelectenerg-400	129	14	,	,	PUNCT
fuelectenerg-400	129	15	four	four	NUM
fuelectenerg-400	129	16	and	and	CCONJ
fuelectenerg-400	129	17	six	six	NUM
fuelectenerg-400	129	18	neighbors	neighbor	NOUN
fuelectenerg-400	129	19	,	,	PUNCT
fuelectenerg-400	129	20	respectively	respectively	ADV
fuelectenerg-400	129	21	.	.	PUNCT
fuelectenerg-400	130	1	the	the	DET
fuelectenerg-400	130	2	tiles	tile	NOUN
fuelectenerg-400	130	3	shaded	shade	VERB
fuelectenerg-400	130	4	black	black	ADJ
fuelectenerg-400	130	5	are	be	AUX
fuelectenerg-400	130	6	the	the	DET
fuelectenerg-400	130	7	neighbors	neighbor	NOUN
fuelectenerg-400	130	8	that	that	PRON
fuelectenerg-400	130	9	share	share	VERB
fuelectenerg-400	130	10	an	an	DET
fuelectenerg-400	130	11	edge	edge	NOUN
fuelectenerg-400	130	12	with	with	ADP
fuelectenerg-400	130	13	the	the	DET
fuelectenerg-400	130	14	tile	tile	NOUN
fuelectenerg-400	130	15	shaded	shade	VERB
fuelectenerg-400	130	16	gray	gray	ADJ
fuelectenerg-400	130	17	.	.	PUNCT
fuelectenerg-400	131	1	to	to	PART
fuelectenerg-400	131	2	describe	describe	VERB
fuelectenerg-400	131	3	lozenge	lozenge	NOUN
fuelectenerg-400	131	4	codes	code	NOUN
fuelectenerg-400	131	5	,	,	PUNCT
fuelectenerg-400	131	6	we	we	PRON
fuelectenerg-400	131	7	start	start	VERB
fuelectenerg-400	131	8	by	by	ADP
fuelectenerg-400	131	9	considering	consider	VERB
fuelectenerg-400	131	10	a	a	DET
fuelectenerg-400	131	11	hexagon	hexagon	NOUN
fuelectenerg-400	131	12	h	h	NOUN
fuelectenerg-400	131	13	with	with	ADP
fuelectenerg-400	131	14	sides	side	NOUN
fuelectenerg-400	131	15	of	of	ADP
fuelectenerg-400	131	16	lengths	length	NOUN
fuelectenerg-400	131	17	a	a	DET
fuelectenerg-400	131	18	,	,	PUNCT
fuelectenerg-400	131	19	b	b	NOUN
fuelectenerg-400	131	20	,	,	PUNCT
fuelectenerg-400	131	21	c	c	NOUN
fuelectenerg-400	131	22	,	,	PUNCT
fuelectenerg-400	131	23	a	a	DET
fuelectenerg-400	131	24	,	,	PUNCT
fuelectenerg-400	131	25	b	b	NOUN
fuelectenerg-400	131	26	,	,	PUNCT
fuelectenerg-400	131	27	c	c	NOUN
fuelectenerg-400	131	28	and	and	CCONJ
fuelectenerg-400	131	29	angles	angle	NOUN
fuelectenerg-400	131	30	of	of	ADP
fuelectenerg-400	131	31	2π/3	2π/3	NUM
fuelectenerg-400	131	32	,	,	PUNCT
fuelectenerg-400	131	33	subdivided	subdivide	VERB
fuelectenerg-400	131	34	into	into	ADP
fuelectenerg-400	131	35	equilateral	equilateral	ADJ
fuelectenerg-400	131	36	triangles	triangle	NOUN
fuelectenerg-400	131	37	of	of	ADP
fuelectenerg-400	131	38	unit	unit	NOUN
fuelectenerg-400	131	39	side	side	NOUN
fuelectenerg-400	131	40	by	by	ADP
fuelectenerg-400	131	41	lines	line	NOUN
fuelectenerg-400	131	42	parallel	parallel	ADJ
fuelectenerg-400	131	43	to	to	ADP
fuelectenerg-400	131	44	the	the	DET
fuelectenerg-400	131	45	hexagon	hexagon	NOUN
fuelectenerg-400	131	46	sides	side	NOUN
fuelectenerg-400	131	47	.	.	PUNCT
fuelectenerg-400	132	1	we	we	PRON
fuelectenerg-400	132	2	will	will	AUX
fuelectenerg-400	132	3	henceforth	henceforth	ADV
fuelectenerg-400	132	4	refer	refer	VERB
fuelectenerg-400	132	5	to	to	ADP
fuelectenerg-400	132	6	such	such	ADJ
fuelectenerg-400	132	7	equi	equi	NOUN
fuelectenerg-400	132	8	-	-	PUNCT
fuelectenerg-400	132	9	angular	angular	ADJ
fuelectenerg-400	132	10	triangularized	triangularize	VERB
fuelectenerg-400	132	11	hexagons	hexagon	NOUN
fuelectenerg-400	132	12	as	as	ADP
fuelectenerg-400	132	13	(	(	PUNCT
fuelectenerg-400	132	14	a	a	PRON
fuelectenerg-400	132	15	,	,	PUNCT
fuelectenerg-400	132	16	b	b	NOUN
fuelectenerg-400	132	17	,	,	PUNCT
fuelectenerg-400	132	18	c	c	NOUN
fuelectenerg-400	132	19	)	)	PUNCT
fuelectenerg-400	132	20	hexagons	hexagon	NOUN
fuelectenerg-400	132	21	.	.	PUNCT
fuelectenerg-400	133	1	figure	figure	NOUN
fuelectenerg-400	133	2	2(a	2(a	NUM
fuelectenerg-400	133	3	)	)	PUNCT
fuelectenerg-400	133	4	shows	show	VERB
fuelectenerg-400	133	5	such	such	DET
fuelectenerg-400	133	6	a	a	DET
fuelectenerg-400	133	7	(	(	PUNCT
fuelectenerg-400	133	8	2	2	NUM
fuelectenerg-400	133	9	,	,	PUNCT
fuelectenerg-400	133	10	3	3	NUM
fuelectenerg-400	133	11	,	,	PUNCT
fuelectenerg-400	133	12	4	4	NUM
fuelectenerg-400	133	13	)	)	PUNCT
fuelectenerg-400	133	14	hexagon	hexagon	NOUN
fuelectenerg-400	133	15	.	.	PUNCT
fuelectenerg-400	134	1	as	as	SCONJ
fuelectenerg-400	134	2	mentioned	mention	VERB
fuelectenerg-400	134	3	earlier	early	ADV
fuelectenerg-400	134	4	,	,	PUNCT
fuelectenerg-400	134	5	two	two	NUM
fuelectenerg-400	134	6	triangles	triangle	NOUN
fuelectenerg-400	134	7	are	be	AUX
fuelectenerg-400	134	8	neighbors	neighbor	NOUN
fuelectenerg-400	134	9	if	if	SCONJ
fuelectenerg-400	134	10	they	they	PRON
fuelectenerg-400	134	11	share	share	VERB
fuelectenerg-400	134	12	a	a	DET
fuelectenerg-400	134	13	side	side	NOUN
fuelectenerg-400	134	14	.	.	PUNCT
fuelectenerg-400	135	1	(	(	PUNCT
fuelectenerg-400	135	2	a	a	X
fuelectenerg-400	135	3	)	)	PUNCT
fuelectenerg-400	135	4	(	(	PUNCT
fuelectenerg-400	135	5	b	b	X
fuelectenerg-400	135	6	)	)	PUNCT
fuelectenerg-400	135	7	fig	fig	NOUN
fuelectenerg-400	135	8	.	.	PUNCT
fuelectenerg-400	136	1	2	2	X
fuelectenerg-400	136	2	.	.	X
fuelectenerg-400	136	3	lozenge	lozenge	ADJ
fuelectenerg-400	136	4	tilings	tiling	NOUN
fuelectenerg-400	136	5	in	in	ADP
fuelectenerg-400	136	6	a	a	DET
fuelectenerg-400	136	7	triangular	triangular	NOUN
fuelectenerg-400	136	8	lattice	lattice	NOUN
fuelectenerg-400	136	9	:	:	PUNCT
fuelectenerg-400	136	10	(	(	PUNCT
fuelectenerg-400	136	11	a	a	X
fuelectenerg-400	136	12	)	)	PUNCT
fuelectenerg-400	136	13	a	a	PRON
fuelectenerg-400	136	14	(	(	PUNCT
fuelectenerg-400	136	15	2	2	NUM
fuelectenerg-400	136	16	,	,	PUNCT
fuelectenerg-400	136	17	3	3	NUM
fuelectenerg-400	136	18	,	,	PUNCT
fuelectenerg-400	136	19	4	4	X
fuelectenerg-400	136	20	)	)	PUNCT
fuelectenerg-400	136	21	hexagon	hexagon	NOUN
fuelectenerg-400	136	22	h	h	PROPN
fuelectenerg-400	136	23	embedded	embed	VERB
fuelectenerg-400	136	24	in	in	ADP
fuelectenerg-400	136	25	a	a	DET
fuelectenerg-400	136	26	triangular	triangular	NOUN
fuelectenerg-400	136	27	lattice	lattice	NOUN
fuelectenerg-400	136	28	.	.	PUNCT
fuelectenerg-400	137	1	(	(	PUNCT
fuelectenerg-400	137	2	b	b	X
fuelectenerg-400	137	3	)	)	PUNCT
fuelectenerg-400	137	4	colored	colored	ADJ
fuelectenerg-400	137	5	tiling	tiling	NOUN
fuelectenerg-400	137	6	of	of	ADP
fuelectenerg-400	137	7	a	a	DET
fuelectenerg-400	137	8	(	(	PUNCT
fuelectenerg-400	137	9	2,3,4	2,3,4	NUM
fuelectenerg-400	137	10	)	)	PUNCT
fuelectenerg-400	137	11	hexagon	hexagon	NOUN
fuelectenerg-400	137	12	.	.	PUNCT
fuelectenerg-400	138	1	detection	detection	NOUN
fuelectenerg-400	138	2	and	and	CCONJ
fuelectenerg-400	138	3	coding	code	VERB
fuelectenerg-400	138	4	for	for	ADP
fuelectenerg-400	138	5	tdmr	tdmr	NOUN
fuelectenerg-400	138	6	channel	channel	NOUN
fuelectenerg-400	138	7	525	525	NUM
fuelectenerg-400	138	8	(	(	PUNCT
fuelectenerg-400	138	9	a	a	NOUN
fuelectenerg-400	138	10	)	)	PUNCT
fuelectenerg-400	138	11	(	(	PUNCT
fuelectenerg-400	138	12	b	b	X
fuelectenerg-400	138	13	)	)	PUNCT
fuelectenerg-400	138	14	(	(	PUNCT
fuelectenerg-400	138	15	c	c	X
fuelectenerg-400	138	16	)	)	PUNCT
fuelectenerg-400	138	17	fig	fig	NOUN
fuelectenerg-400	138	18	.	.	PUNCT
fuelectenerg-400	139	1	3	3	X
fuelectenerg-400	139	2	.	.	X
fuelectenerg-400	139	3	the	the	DET
fuelectenerg-400	139	4	prototype	prototype	NOUN
fuelectenerg-400	139	5	tiles	tile	NOUN
fuelectenerg-400	139	6	used	use	VERB
fuelectenerg-400	139	7	in	in	ADP
fuelectenerg-400	139	8	the	the	DET
fuelectenerg-400	139	9	tiling	tiling	NOUN
fuelectenerg-400	139	10	of	of	ADP
fuelectenerg-400	139	11	hexagons	hexagon	NOUN
fuelectenerg-400	139	12	.	.	PUNCT
fuelectenerg-400	140	1	we	we	PRON
fuelectenerg-400	140	2	are	be	AUX
fuelectenerg-400	140	3	interested	interested	ADJ
fuelectenerg-400	140	4	in	in	ADP
fuelectenerg-400	140	5	coloring	color	VERB
fuelectenerg-400	140	6	the	the	DET
fuelectenerg-400	140	7	triangles	triangle	NOUN
fuelectenerg-400	140	8	using	use	VERB
fuelectenerg-400	140	9	m	m	VERB
fuelectenerg-400	140	10	>	>	X
fuelectenerg-400	140	11	1	1	NUM
fuelectenerg-400	140	12	different	different	ADJ
fuelectenerg-400	140	13	colors	color	NOUN
fuelectenerg-400	140	14	in	in	ADP
fuelectenerg-400	140	15	such	such	DET
fuelectenerg-400	140	16	a	a	DET
fuelectenerg-400	140	17	way	way	NOUN
fuelectenerg-400	140	18	that	that	PRON
fuelectenerg-400	140	19	no	no	DET
fuelectenerg-400	140	20	isolated	isolated	ADJ
fuelectenerg-400	140	21	triangle	triangle	NOUN
fuelectenerg-400	140	22	is	be	AUX
fuelectenerg-400	140	23	colored	color	VERB
fuelectenerg-400	140	24	differently	differently	ADV
fuelectenerg-400	140	25	than	than	ADP
fuelectenerg-400	140	26	its	its	PRON
fuelectenerg-400	140	27	neighbors	neighbor	NOUN
fuelectenerg-400	140	28	.	.	PUNCT
fuelectenerg-400	141	1	in	in	ADP
fuelectenerg-400	141	2	the	the	DET
fuelectenerg-400	141	3	paper	paper	NOUN
fuelectenerg-400	141	4	we	we	PRON
fuelectenerg-400	141	5	focus	focus	VERB
fuelectenerg-400	141	6	on	on	ADP
fuelectenerg-400	141	7	the	the	DET
fuelectenerg-400	141	8	m	m	NOUN
fuelectenerg-400	141	9	=	=	SYM
fuelectenerg-400	141	10	2	2	NUM
fuelectenerg-400	141	11	case	case	NOUN
fuelectenerg-400	141	12	.	.	PUNCT
fuelectenerg-400	142	1	we	we	PRON
fuelectenerg-400	142	2	require	require	VERB
fuelectenerg-400	142	3	a	a	DET
fuelectenerg-400	142	4	segregation	segregation	NOUN
fuelectenerg-400	142	5	of	of	ADP
fuelectenerg-400	142	6	at	at	ADV
fuelectenerg-400	142	7	least	least	ADV
fuelectenerg-400	142	8	two	two	NUM
fuelectenerg-400	142	9	neighboring	neighboring	NOUN
fuelectenerg-400	142	10	triangles	triangle	NOUN
fuelectenerg-400	142	11	of	of	ADP
fuelectenerg-400	142	12	the	the	DET
fuelectenerg-400	142	13	same	same	ADJ
fuelectenerg-400	142	14	color	color	NOUN
fuelectenerg-400	142	15	.	.	PUNCT
fuelectenerg-400	143	1	fig	fig	NOUN
fuelectenerg-400	143	2	.	.	PUNCT
fuelectenerg-400	144	1	2(b	2(b	NUM
fuelectenerg-400	144	2	)	)	PUNCT
fuelectenerg-400	144	3	shows	show	VERB
fuelectenerg-400	144	4	one	one	NUM
fuelectenerg-400	144	5	such	such	ADJ
fuelectenerg-400	144	6	coloring	coloring	NOUN
fuelectenerg-400	144	7	of	of	ADP
fuelectenerg-400	144	8	the	the	DET
fuelectenerg-400	144	9	(	(	PUNCT
fuelectenerg-400	144	10	2	2	NUM
fuelectenerg-400	144	11	,	,	PUNCT
fuelectenerg-400	144	12	3	3	NUM
fuelectenerg-400	144	13	,	,	PUNCT
fuelectenerg-400	144	14	4	4	X
fuelectenerg-400	144	15	)	)	PUNCT
fuelectenerg-400	144	16	hexagon	hexagon	NOUN
fuelectenerg-400	144	17	shown	show	VERB
fuelectenerg-400	144	18	in	in	ADP
fuelectenerg-400	144	19	fig	fig	NOUN
fuelectenerg-400	144	20	.	.	PUNCT
fuelectenerg-400	145	1	2(a	2(a	NUM
fuelectenerg-400	145	2	)	)	PUNCT
fuelectenerg-400	145	3	.	.	PUNCT
fuelectenerg-400	146	1	two	two	NUM
fuelectenerg-400	146	2	neighboring	neighboring	NOUN
fuelectenerg-400	146	3	triangles	triangle	NOUN
fuelectenerg-400	146	4	form	form	VERB
fuelectenerg-400	146	5	a	a	DET
fuelectenerg-400	146	6	rhombus	rhombus	NOUN
fuelectenerg-400	146	7	with	with	ADP
fuelectenerg-400	146	8	side	side	NOUN
fuelectenerg-400	146	9	of	of	ADP
fuelectenerg-400	146	10	unit	unit	NOUN
fuelectenerg-400	146	11	length	length	NOUN
fuelectenerg-400	146	12	and	and	CCONJ
fuelectenerg-400	146	13	internal	internal	ADJ
fuelectenerg-400	146	14	angles	angle	NOUN
fuelectenerg-400	146	15	π	π	PROPN
fuelectenerg-400	146	16	3	3	NUM
fuelectenerg-400	146	17	and	and	CCONJ
fuelectenerg-400	146	18	2π	2π	PROPN
fuelectenerg-400	146	19	3	3	NUM
fuelectenerg-400	146	20	.	.	PUNCT
fuelectenerg-400	147	1	such	such	DET
fuelectenerg-400	147	2	a	a	DET
fuelectenerg-400	147	3	rhombus	rhombus	NOUN
fuelectenerg-400	147	4	is	be	AUX
fuelectenerg-400	147	5	known	know	VERB
fuelectenerg-400	147	6	as	as	ADP
fuelectenerg-400	147	7	a	a	DET
fuelectenerg-400	147	8	lozenge	lozenge	NOUN
fuelectenerg-400	147	9	.	.	PUNCT
fuelectenerg-400	148	1	a	a	DET
fuelectenerg-400	148	2	lozenge	lozenge	NOUN
fuelectenerg-400	148	3	created	create	VERB
fuelectenerg-400	148	4	in	in	ADP
fuelectenerg-400	148	5	this	this	DET
fuelectenerg-400	148	6	way	way	NOUN
fuelectenerg-400	148	7	may	may	AUX
fuelectenerg-400	148	8	have	have	VERB
fuelectenerg-400	148	9	three	three	NUM
fuelectenerg-400	148	10	different	different	ADJ
fuelectenerg-400	148	11	orientations	orientation	NOUN
fuelectenerg-400	148	12	.	.	PUNCT
fuelectenerg-400	149	1	fig	fig	NOUN
fuelectenerg-400	149	2	.	.	PUNCT
fuelectenerg-400	150	1	3	3	NUM
fuelectenerg-400	150	2	shows	show	VERB
fuelectenerg-400	150	3	these	these	DET
fuelectenerg-400	150	4	orientations	orientation	NOUN
fuelectenerg-400	150	5	.	.	PUNCT
fuelectenerg-400	151	1	we	we	PRON
fuelectenerg-400	151	2	refer	refer	VERB
fuelectenerg-400	151	3	to	to	ADP
fuelectenerg-400	151	4	the	the	DET
fuelectenerg-400	151	5	prototiles	prototile	NOUN
fuelectenerg-400	151	6	shown	show	VERB
fuelectenerg-400	151	7	in	in	ADP
fuelectenerg-400	151	8	fig	fig	NOUN
fuelectenerg-400	151	9	.	.	PUNCT
fuelectenerg-400	152	1	3(a	3(a	NUM
fuelectenerg-400	152	2	)	)	PUNCT
fuelectenerg-400	152	3	,	,	PUNCT
fuelectenerg-400	153	1	3(b	3(b	NUM
fuelectenerg-400	153	2	)	)	PUNCT
fuelectenerg-400	153	3	and	and	CCONJ
fuelectenerg-400	153	4	3(c	3(c	NUM
fuelectenerg-400	153	5	)	)	PUNCT
fuelectenerg-400	153	6	as	as	ADP
fuelectenerg-400	153	7	to	to	PART
fuelectenerg-400	153	8	type	type	VERB
fuelectenerg-400	153	9	-	-	PUNCT
fuelectenerg-400	153	10	a	a	NOUN
fuelectenerg-400	153	11	,	,	PUNCT
fuelectenerg-400	153	12	type	type	NOUN
fuelectenerg-400	153	13	-	-	PUNCT
fuelectenerg-400	153	14	b	b	NOUN
fuelectenerg-400	153	15	and	and	CCONJ
fuelectenerg-400	153	16	type	type	NOUN
fuelectenerg-400	153	17	-	-	PUNCT
fuelectenerg-400	153	18	c	c	NOUN
fuelectenerg-400	153	19	lozenges	lozenge	NOUN
fuelectenerg-400	153	20	,	,	PUNCT
fuelectenerg-400	153	21	respectively	respectively	ADV
fuelectenerg-400	153	22	.	.	PUNCT
fuelectenerg-400	154	1	the	the	DET
fuelectenerg-400	154	2	last	last	ADJ
fuelectenerg-400	154	3	two	two	NUM
fuelectenerg-400	154	4	prototiles	prototile	NOUN
fuelectenerg-400	154	5	are	be	AUX
fuelectenerg-400	154	6	referred	refer	VERB
fuelectenerg-400	154	7	to	to	ADP
fuelectenerg-400	154	8	as	as	ADP
fuelectenerg-400	154	9	vertical	vertical	ADJ
fuelectenerg-400	154	10	lozenges	lozenge	NOUN
fuelectenerg-400	154	11	.	.	PUNCT
fuelectenerg-400	155	1	now	now	ADV
fuelectenerg-400	155	2	,	,	PUNCT
fuelectenerg-400	155	3	suppose	suppose	VERB
fuelectenerg-400	155	4	each	each	PRON
fuelectenerg-400	155	5	of	of	ADP
fuelectenerg-400	155	6	the	the	DET
fuelectenerg-400	155	7	lozenges	lozenge	NOUN
fuelectenerg-400	155	8	is	be	AUX
fuelectenerg-400	155	9	colored	color	VERB
fuelectenerg-400	155	10	independently	independently	ADV
fuelectenerg-400	155	11	,	,	PUNCT
fuelectenerg-400	155	12	we	we	PRON
fuelectenerg-400	155	13	can	can	AUX
fuelectenerg-400	155	14	ensure	ensure	VERB
fuelectenerg-400	155	15	that	that	SCONJ
fuelectenerg-400	155	16	for	for	ADP
fuelectenerg-400	155	17	any	any	DET
fuelectenerg-400	155	18	triangle	triangle	NOUN
fuelectenerg-400	155	19	there	there	PRON
fuelectenerg-400	155	20	is	be	VERB
fuelectenerg-400	155	21	at	at	ADV
fuelectenerg-400	155	22	least	least	ADJ
fuelectenerg-400	155	23	one	one	NUM
fuelectenerg-400	155	24	neighboring	neighboring	NOUN
fuelectenerg-400	155	25	triangle	triangle	NOUN
fuelectenerg-400	155	26	with	with	ADP
fuelectenerg-400	155	27	the	the	DET
fuelectenerg-400	155	28	same	same	ADJ
fuelectenerg-400	155	29	color	color	NOUN
fuelectenerg-400	155	30	,	,	PUNCT
fuelectenerg-400	155	31	i.e.	i.e.	X
fuelectenerg-400	155	32	(	(	PUNCT
fuelectenerg-400	155	33	d	d	NOUN
fuelectenerg-400	155	34	,	,	PUNCT
fuelectenerg-400	155	35	k	k	NOUN
fuelectenerg-400	155	36	)	)	PUNCT
fuelectenerg-400	155	37	=	=	SYM
fuelectenerg-400	155	38	(	(	PUNCT
fuelectenerg-400	155	39	1,∞	1,∞	NUM
fuelectenerg-400	155	40	)	)	PUNCT
fuelectenerg-400	155	41	.	.	PUNCT
fuelectenerg-400	156	1	the	the	DET
fuelectenerg-400	156	2	constrained	constrain	VERB
fuelectenerg-400	156	3	coding	coding	NOUN
fuelectenerg-400	156	4	problem	problem	NOUN
fuelectenerg-400	156	5	can	can	AUX
fuelectenerg-400	156	6	be	be	AUX
fuelectenerg-400	156	7	now	now	ADV
fuelectenerg-400	156	8	formulated	formulate	VERB
fuelectenerg-400	156	9	as	as	SCONJ
fuelectenerg-400	156	10	follows	follow	VERB
fuelectenerg-400	156	11	:	:	PUNCT
fuelectenerg-400	156	12	given	give	VERB
fuelectenerg-400	156	13	a	a	DET
fuelectenerg-400	156	14	hexagonal	hexagonal	ADJ
fuelectenerg-400	156	15	region	region	NOUN
fuelectenerg-400	156	16	of	of	ADP
fuelectenerg-400	156	17	a	a	DET
fuelectenerg-400	156	18	triangular	triangular	NOUN
fuelectenerg-400	156	19	lattice	lattice	NOUN
fuelectenerg-400	156	20	,	,	PUNCT
fuelectenerg-400	156	21	one	one	PRON
fuelectenerg-400	156	22	would	would	AUX
fuelectenerg-400	156	23	like	like	VERB
fuelectenerg-400	156	24	to	to	PART
fuelectenerg-400	156	25	find	find	VERB
fuelectenerg-400	156	26	a	a	DET
fuelectenerg-400	156	27	one	one	NUM
fuelectenerg-400	156	28	-	-	PUNCT
fuelectenerg-400	156	29	to	to	ADP
fuelectenerg-400	156	30	-	-	PUNCT
fuelectenerg-400	156	31	one	one	NUM
fuelectenerg-400	156	32	mapping	mapping	NOUN
fuelectenerg-400	156	33	from	from	ADP
fuelectenerg-400	156	34	a	a	DET
fuelectenerg-400	156	35	set	set	NOUN
fuelectenerg-400	156	36	of	of	ADP
fuelectenerg-400	156	37	integers	integer	NOUN
fuelectenerg-400	156	38	representing	represent	VERB
fuelectenerg-400	156	39	user	user	NOUN
fuelectenerg-400	156	40	’s	’s	PART
fuelectenerg-400	156	41	binary	binary	ADJ
fuelectenerg-400	156	42	data	datum	NOUN
fuelectenerg-400	156	43	(	(	PUNCT
fuelectenerg-400	156	44	this	this	DET
fuelectenerg-400	156	45	bijection	bijection	NOUN
fuelectenerg-400	156	46	is	be	AUX
fuelectenerg-400	156	47	trivial	trivial	ADJ
fuelectenerg-400	156	48	)	)	PUNCT
fuelectenerg-400	156	49	to	to	ADP
fuelectenerg-400	156	50	a	a	DET
fuelectenerg-400	156	51	set	set	NOUN
fuelectenerg-400	156	52	of	of	ADP
fuelectenerg-400	156	53	nib	nib	NOUN
fuelectenerg-400	156	54	-	-	PUNCT
fuelectenerg-400	156	55	permissible	permissible	ADJ
fuelectenerg-400	156	56	colored	colored	ADJ
fuelectenerg-400	156	57	tilings	tiling	NOUN
fuelectenerg-400	156	58	.	.	PUNCT
fuelectenerg-400	157	1	in	in	ADP
fuelectenerg-400	157	2	addition	addition	NOUN
fuelectenerg-400	157	3	,	,	PUNCT
fuelectenerg-400	157	4	due	due	ADP
fuelectenerg-400	157	5	to	to	ADP
fuelectenerg-400	157	6	complexity	complexity	NOUN
fuelectenerg-400	157	7	constrains	constrain	NOUN
fuelectenerg-400	157	8	,	,	PUNCT
fuelectenerg-400	157	9	it	it	PRON
fuelectenerg-400	157	10	is	be	AUX
fuelectenerg-400	157	11	desirable	desirable	ADJ
fuelectenerg-400	157	12	that	that	SCONJ
fuelectenerg-400	157	13	the	the	DET
fuelectenerg-400	157	14	mapping	mapping	NOUN
fuelectenerg-400	157	15	is	be	AUX
fuelectenerg-400	157	16	described	describe	VERB
fuelectenerg-400	157	17	by	by	ADP
fuelectenerg-400	157	18	an	an	DET
fuelectenerg-400	157	19	algorithm	algorithm	NOUN
fuelectenerg-400	157	20	which	which	PRON
fuelectenerg-400	157	21	operates	operate	VERB
fuelectenerg-400	157	22	locally	locally	ADV
fuelectenerg-400	157	23	on	on	ADP
fuelectenerg-400	157	24	a	a	DET
fuelectenerg-400	157	25	small	small	ADJ
fuelectenerg-400	157	26	lattice	lattice	NOUN
fuelectenerg-400	157	27	region	region	NOUN
fuelectenerg-400	157	28	.	.	PUNCT
fuelectenerg-400	158	1	we	we	PRON
fuelectenerg-400	158	2	propose	propose	VERB
fuelectenerg-400	158	3	a	a	DET
fuelectenerg-400	158	4	mapping	mapping	NOUN
fuelectenerg-400	158	5	which	which	PRON
fuelectenerg-400	158	6	is	be	AUX
fuelectenerg-400	158	7	a	a	DET
fuelectenerg-400	158	8	composition	composition	NOUN
fuelectenerg-400	158	9	of	of	ADP
fuelectenerg-400	158	10	two	two	NUM
fuelectenerg-400	158	11	mappings	mapping	NOUN
fuelectenerg-400	158	12	:	:	PUNCT
fuelectenerg-400	158	13	tiling	tile	VERB
fuelectenerg-400	158	14	and	and	CCONJ
fuelectenerg-400	158	15	coloring	coloring	NOUN
fuelectenerg-400	158	16	.	.	PUNCT
fuelectenerg-400	159	1	now	now	ADV
fuelectenerg-400	159	2	the	the	DET
fuelectenerg-400	159	3	nib	nib	NOUN
fuelectenerg-400	159	4	coloring	coloring	NOUN
fuelectenerg-400	159	5	can	can	AUX
fuelectenerg-400	159	6	be	be	AUX
fuelectenerg-400	159	7	separated	separate	VERB
fuelectenerg-400	159	8	into	into	ADP
fuelectenerg-400	159	9	two	two	NUM
fuelectenerg-400	159	10	steps	step	NOUN
fuelectenerg-400	159	11	as	as	SCONJ
fuelectenerg-400	159	12	illustrated	illustrate	VERB
fuelectenerg-400	159	13	in	in	ADP
fuelectenerg-400	159	14	fig	fig	NOUN
fuelectenerg-400	159	15	.	.	PUNCT
fuelectenerg-400	160	1	4	4	X
fuelectenerg-400	160	2	.	.	X
fuelectenerg-400	160	3	first	first	ADV
fuelectenerg-400	160	4	,	,	PUNCT
fuelectenerg-400	160	5	the	the	DET
fuelectenerg-400	160	6	hexagon	hexagon	NOUN
fuelectenerg-400	160	7	(	(	PUNCT
fuelectenerg-400	160	8	fig	fig	NOUN
fuelectenerg-400	160	9	.	.	PUNCT
fuelectenerg-400	161	1	4(a	4(a	NUM
fuelectenerg-400	161	2	)	)	PUNCT
fuelectenerg-400	161	3	)	)	PUNCT
fuelectenerg-400	162	1	is	be	AUX
fuelectenerg-400	162	2	tiled	tile	VERB
fuelectenerg-400	162	3	with	with	ADP
fuelectenerg-400	162	4	(	(	PUNCT
fuelectenerg-400	162	5	uncolored	uncolored	ADJ
fuelectenerg-400	162	6	)	)	PUNCT
fuelectenerg-400	162	7	lozenges	lozenge	NOUN
fuelectenerg-400	162	8	(	(	PUNCT
fuelectenerg-400	162	9	to	to	PART
fuelectenerg-400	162	10	obtain	obtain	VERB
fuelectenerg-400	162	11	lozenge	lozenge	NOUN
fuelectenerg-400	162	12	tiling	tile	VERB
fuelectenerg-400	162	13	in	in	ADP
fuelectenerg-400	162	14	fig	fig	NOUN
fuelectenerg-400	162	15	.	.	PUNCT
fuelectenerg-400	163	1	4(b	4(b	NUM
fuelectenerg-400	163	2	)	)	PUNCT
fuelectenerg-400	163	3	)	)	PUNCT
fuelectenerg-400	163	4	,	,	PUNCT
fuelectenerg-400	163	5	and	and	CCONJ
fuelectenerg-400	163	6	then	then	ADV
fuelectenerg-400	163	7	the	the	DET
fuelectenerg-400	163	8	lozenges	lozenge	NOUN
fuelectenerg-400	163	9	are	be	AUX
fuelectenerg-400	163	10	colored	color	VERB
fuelectenerg-400	163	11	,	,	PUNCT
fuelectenerg-400	163	12	(	(	PUNCT
fuelectenerg-400	163	13	to	to	PART
fuelectenerg-400	163	14	obtain	obtain	VERB
fuelectenerg-400	163	15	colored	colored	ADJ
fuelectenerg-400	163	16	tiling	tile	VERB
fuelectenerg-400	163	17	in	in	ADP
fuelectenerg-400	163	18	fig	fig	NOUN
fuelectenerg-400	163	19	.	.	PUNCT
fuelectenerg-400	164	1	4(c	4(c	NUM
fuelectenerg-400	164	2	)	)	PUNCT
fuelectenerg-400	164	3	)	)	PUNCT
fuelectenerg-400	164	4	.	.	PUNCT
fuelectenerg-400	165	1	it	it	PRON
fuelectenerg-400	165	2	is	be	AUX
fuelectenerg-400	165	3	important	important	ADJ
fuelectenerg-400	165	4	to	to	PART
fuelectenerg-400	165	5	note	note	VERB
fuelectenerg-400	165	6	that	that	SCONJ
fuelectenerg-400	165	7	the	the	DET
fuelectenerg-400	165	8	reader	reader	NOUN
fuelectenerg-400	165	9	does	do	AUX
fuelectenerg-400	165	10	not	not	PART
fuelectenerg-400	165	11	have	have	VERB
fuelectenerg-400	165	12	knowledge	knowledge	NOUN
fuelectenerg-400	165	13	of	of	ADP
fuelectenerg-400	165	14	the	the	DET
fuelectenerg-400	165	15	tiling	tiling	NOUN
fuelectenerg-400	165	16	and	and	CCONJ
fuelectenerg-400	165	17	retrieves	retrieve	NOUN
fuelectenerg-400	165	18	encoded	encode	VERB
fuelectenerg-400	165	19	bits	bit	NOUN
fuelectenerg-400	165	20	solely	solely	ADV
fuelectenerg-400	165	21	based	base	VERB
fuelectenerg-400	165	22	on	on	ADP
fuelectenerg-400	165	23	the	the	DET
fuelectenerg-400	165	24	colored	colored	ADJ
fuelectenerg-400	165	25	pattern	pattern	NOUN
fuelectenerg-400	165	26	.	.	PUNCT
fuelectenerg-400	166	1	thus	thus	ADV
fuelectenerg-400	166	2	,	,	PUNCT
fuelectenerg-400	166	3	not	not	PART
fuelectenerg-400	166	4	all	all	DET
fuelectenerg-400	166	5	colorings	coloring	NOUN
fuelectenerg-400	166	6	can	can	AUX
fuelectenerg-400	166	7	guaranty	guaranty	VERB
fuelectenerg-400	166	8	retrievability	retrievability	NOUN
fuelectenerg-400	166	9	.	.	PUNCT
fuelectenerg-400	167	1	of	of	ADP
fuelectenerg-400	167	2	interest	interest	NOUN
fuelectenerg-400	167	3	are	be	AUX
fuelectenerg-400	167	4	only	only	ADV
fuelectenerg-400	167	5	those	those	DET
fuelectenerg-400	167	6	colorings	coloring	NOUN
fuelectenerg-400	167	7	that	that	PRON
fuelectenerg-400	167	8	ensure	ensure	VERB
fuelectenerg-400	167	9	retrievability	retrievability	NOUN
fuelectenerg-400	167	10	.	.	PUNCT
fuelectenerg-400	168	1	dividing	divide	VERB
fuelectenerg-400	168	2	the	the	DET
fuelectenerg-400	168	3	hard	hard	ADJ
fuelectenerg-400	168	4	coloring	color	VERB
fuelectenerg-400	168	5	hard	hard	ADJ
fuelectenerg-400	168	6	problem	problem	NOUN
fuelectenerg-400	168	7	into	into	ADP
fuelectenerg-400	168	8	two	two	NUM
fuelectenerg-400	168	9	manageable	manageable	ADJ
fuelectenerg-400	168	10	operations	operation	NOUN
fuelectenerg-400	168	11	results	result	NOUN
fuelectenerg-400	168	12	into	into	ADP
fuelectenerg-400	168	13	an	an	DET
fuelectenerg-400	168	14	unavoidable	unavoidable	ADJ
fuelectenerg-400	168	15	rate	rate	NOUN
fuelectenerg-400	168	16	penalty	penalty	NOUN
fuelectenerg-400	168	17	,	,	PUNCT
fuelectenerg-400	168	18	however	however	ADV
fuelectenerg-400	168	19	the	the	DET
fuelectenerg-400	168	20	rate	rate	NOUN
fuelectenerg-400	168	21	penalty	penalty	NOUN
fuelectenerg-400	168	22	due	due	ADJ
fuelectenerg-400	168	23	this	this	DET
fuelectenerg-400	168	24	simplification	simplification	NOUN
fuelectenerg-400	168	25	is	be	AUX
fuelectenerg-400	168	26	a	a	DET
fuelectenerg-400	168	27	tradeoff	tradeoff	NOUN
fuelectenerg-400	168	28	for	for	ADP
fuelectenerg-400	168	29	tractability	tractability	NOUN
fuelectenerg-400	168	30	.	.	PUNCT
fuelectenerg-400	169	1	as	as	SCONJ
fuelectenerg-400	169	2	we	we	PRON
fuelectenerg-400	169	3	show	show	VERB
fuelectenerg-400	169	4	in	in	ADP
fuelectenerg-400	169	5	the	the	DET
fuelectenerg-400	169	6	following	follow	VERB
fuelectenerg-400	169	7	sections	section	NOUN
fuelectenerg-400	169	8	,	,	PUNCT
fuelectenerg-400	169	9	it	it	PRON
fuelectenerg-400	169	10	is	be	AUX
fuelectenerg-400	169	11	now	now	ADV
fuelectenerg-400	169	12	possible	possible	ADJ
fuelectenerg-400	169	13	to	to	PART
fuelectenerg-400	169	14	use	use	VERB
fuelectenerg-400	169	15	elegant	elegant	ADJ
fuelectenerg-400	169	16	combinatorial	combinatorial	ADJ
fuelectenerg-400	169	17	methods	method	NOUN
fuelectenerg-400	169	18	to	to	PART
fuelectenerg-400	169	19	design	design	VERB
fuelectenerg-400	169	20	encoders	encoder	NOUN
fuelectenerg-400	169	21	and	and	CCONJ
fuelectenerg-400	169	22	decoders	decoder	NOUN
fuelectenerg-400	169	23	.	.	PUNCT
fuelectenerg-400	170	1	moreover	moreover	ADV
fuelectenerg-400	170	2	we	we	PRON
fuelectenerg-400	170	3	can	can	AUX
fuelectenerg-400	170	4	establish	establish	VERB
fuelectenerg-400	170	5	bounds	bound	NOUN
fuelectenerg-400	170	6	on	on	ADP
fuelectenerg-400	170	7	capacities	capacity	NOUN
fuelectenerg-400	170	8	,	,	PUNCT
fuelectenerg-400	170	9	i.e.	i.e.	X
fuelectenerg-400	170	10	,	,	PUNCT
fuelectenerg-400	170	11	achievable	achievable	ADJ
fuelectenerg-400	170	12	density	density	NOUN
fuelectenerg-400	170	13	.	.	PUNCT
fuelectenerg-400	171	1	we	we	PRON
fuelectenerg-400	171	2	start	start	VERB
fuelectenerg-400	171	3	with	with	ADP
fuelectenerg-400	171	4	deriving	derive	VERB
fuelectenerg-400	171	5	the	the	DET
fuelectenerg-400	171	6	capacity	capacity	NOUN
fuelectenerg-400	171	7	bounds	bound	NOUN
fuelectenerg-400	171	8	.	.	PUNCT
fuelectenerg-400	172	1	524	524	NUM
fuelectenerg-400	172	2	b.	b.	PROPN
fuelectenerg-400	172	3	vasic	vasic	PROPN
fuelectenerg-400	172	4	,	,	PUNCT
fuelectenerg-400	172	5	a.	a.	PROPN
fuelectenerg-400	172	6	r.	r.	PROPN
fuelectenerg-400	172	7	krishnan	krishnan	PROPN
fuelectenerg-400	172	8	lozenge	lozenge	PROPN
fuelectenerg-400	172	9	tiling	tile	VERB
fuelectenerg-400	172	10	constrained	constrained	ADJ
fuelectenerg-400	172	11	codes	code	NOUN
fuelectenerg-400	172	12	525	525	NUM
fuelectenerg-400	172	13	524	524	NUM
fuelectenerg-400	172	14	a.	a.	NOUN
fuelectenerg-400	172	15	r.	r.	PROPN
fuelectenerg-400	172	16	krishnanan	krishnanan	PROPN
fuelectenerg-400	172	17	and	and	CCONJ
fuelectenerg-400	172	18	b.	b.	PROPN
fuelectenerg-400	172	19	vasić	vasić	PROPN
fuelectenerg-400	172	20	to	to	ADP
fuelectenerg-400	172	21	a	a	DET
fuelectenerg-400	172	22	segregation	segregation	NOUN
fuelectenerg-400	172	23	constraint	constraint	NOUN
fuelectenerg-400	172	24	by	by	ADP
fuelectenerg-400	172	25	precoding	precode	VERB
fuelectenerg-400	172	26	[	[	X
fuelectenerg-400	172	27	1	1	NUM
fuelectenerg-400	172	28	]	]	PUNCT
fuelectenerg-400	172	29	,	,	PUNCT
fuelectenerg-400	172	30	while	while	SCONJ
fuelectenerg-400	172	31	for	for	ADP
fuelectenerg-400	172	32	other	other	ADJ
fuelectenerg-400	172	33	two	two	NUM
fuelectenerg-400	172	34	latices	latex	NOUN
fuelectenerg-400	172	35	in	in	ADP
fuelectenerg-400	172	36	fig	fig	NOUN
fuelectenerg-400	172	37	.	.	PUNCT
fuelectenerg-400	173	1	1(a	1(a	NUM
fuelectenerg-400	173	2	)	)	PUNCT
fuelectenerg-400	173	3	this	this	PRON
fuelectenerg-400	173	4	is	be	AUX
fuelectenerg-400	173	5	not	not	PART
fuelectenerg-400	173	6	the	the	DET
fuelectenerg-400	173	7	case	case	NOUN
fuelectenerg-400	173	8	.	.	PUNCT
fuelectenerg-400	174	1	in	in	ADP
fuelectenerg-400	174	2	other	other	ADJ
fuelectenerg-400	174	3	words	word	NOUN
fuelectenerg-400	174	4	segregation	segregation	NOUN
fuelectenerg-400	174	5	constraints	constraint	NOUN
fuelectenerg-400	174	6	are	be	AUX
fuelectenerg-400	174	7	not	not	PART
fuelectenerg-400	174	8	in	in	ADP
fuelectenerg-400	174	9	bijection	bijection	NOUN
fuelectenerg-400	174	10	to	to	ADP
fuelectenerg-400	174	11	simple	simple	ADJ
fuelectenerg-400	174	12	runlength	runlength	NOUN
fuelectenerg-400	174	13	(	(	PUNCT
fuelectenerg-400	174	14	d	d	NOUN
fuelectenerg-400	174	15	,	,	PUNCT
fuelectenerg-400	174	16	k	k	NOUN
fuelectenerg-400	174	17	)	)	PUNCT
fuelectenerg-400	174	18	constraints	constraint	NOUN
fuelectenerg-400	174	19	.	.	PUNCT
fuelectenerg-400	175	1	using	use	VERB
fuelectenerg-400	175	2	fig	fig	NOUN
fuelectenerg-400	175	3	.	.	PUNCT
fuelectenerg-400	176	1	1	1	NUM
fuelectenerg-400	176	2	,	,	PUNCT
fuelectenerg-400	176	3	the	the	DET
fuelectenerg-400	176	4	nib	nib	NOUN
fuelectenerg-400	176	5	constraint	constraint	NOUN
fuelectenerg-400	176	6	can	can	AUX
fuelectenerg-400	176	7	be	be	AUX
fuelectenerg-400	176	8	explained	explain	VERB
fuelectenerg-400	176	9	as	as	SCONJ
fuelectenerg-400	176	10	follows	follow	VERB
fuelectenerg-400	176	11	:	:	PUNCT
fuelectenerg-400	176	12	for	for	ADP
fuelectenerg-400	176	13	any	any	DET
fuelectenerg-400	176	14	given	give	VERB
fuelectenerg-400	176	15	tile	tile	NOUN
fuelectenerg-400	176	16	(	(	PUNCT
fuelectenerg-400	176	17	for	for	ADP
fuelectenerg-400	176	18	example	example	NOUN
fuelectenerg-400	176	19	,	,	PUNCT
fuelectenerg-400	176	20	the	the	DET
fuelectenerg-400	176	21	tile	tile	NOUN
fuelectenerg-400	176	22	marked	mark	VERB
fuelectenerg-400	176	23	gray	gray	ADJ
fuelectenerg-400	176	24	in	in	ADP
fuelectenerg-400	176	25	the	the	DET
fuelectenerg-400	176	26	figure	figure	NOUN
fuelectenerg-400	176	27	)	)	PUNCT
fuelectenerg-400	176	28	,	,	PUNCT
fuelectenerg-400	176	29	if	if	SCONJ
fuelectenerg-400	176	30	none	none	NOUN
fuelectenerg-400	176	31	of	of	ADP
fuelectenerg-400	176	32	its	its	PRON
fuelectenerg-400	176	33	neighbouring	neighbouring	ADJ
fuelectenerg-400	176	34	tiles	tile	NOUN
fuelectenerg-400	176	35	(	(	PUNCT
fuelectenerg-400	176	36	tiles	tile	NOUN
fuelectenerg-400	176	37	marked	mark	VERB
fuelectenerg-400	176	38	black	black	ADJ
fuelectenerg-400	176	39	)	)	PUNCT
fuelectenerg-400	176	40	are	be	AUX
fuelectenerg-400	176	41	of	of	ADP
fuelectenerg-400	176	42	the	the	DET
fuelectenerg-400	176	43	same	same	ADJ
fuelectenerg-400	176	44	colour	colour	NOUN
fuelectenerg-400	176	45	,	,	PUNCT
fuelectenerg-400	176	46	then	then	ADV
fuelectenerg-400	176	47	the	the	DET
fuelectenerg-400	176	48	nib	nib	NOUN
fuelectenerg-400	176	49	constraint	constraint	NOUN
fuelectenerg-400	176	50	is	be	AUX
fuelectenerg-400	176	51	said	say	VERB
fuelectenerg-400	176	52	to	to	PART
fuelectenerg-400	176	53	be	be	AUX
fuelectenerg-400	176	54	violated	violate	VERB
fuelectenerg-400	176	55	.	.	PUNCT
fuelectenerg-400	177	1	our	our	PRON
fuelectenerg-400	177	2	recent	recent	ADJ
fuelectenerg-400	177	3	experimental	experimental	ADJ
fuelectenerg-400	177	4	results	result	NOUN
fuelectenerg-400	177	5	show	show	VERB
fuelectenerg-400	177	6	that	that	SCONJ
fuelectenerg-400	177	7	if	if	SCONJ
fuelectenerg-400	177	8	input	input	NOUN
fuelectenerg-400	177	9	bits	bit	NOUN
fuelectenerg-400	177	10	are	be	AUX
fuelectenerg-400	177	11	mapped	map	VERB
fuelectenerg-400	177	12	to	to	PART
fuelectenerg-400	177	13	bit	bit	NOUN
fuelectenerg-400	177	14	patterns	pattern	NOUN
fuelectenerg-400	177	15	satisfying	satisfy	VERB
fuelectenerg-400	177	16	the	the	DET
fuelectenerg-400	177	17	nib	nib	NOUN
fuelectenerg-400	177	18	constraint	constraint	NOUN
fuelectenerg-400	177	19	,	,	PUNCT
fuelectenerg-400	177	20	then	then	ADV
fuelectenerg-400	177	21	the	the	DET
fuelectenerg-400	177	22	probability	probability	NOUN
fuelectenerg-400	177	23	of	of	ADP
fuelectenerg-400	177	24	rewriting	rewrite	VERB
fuelectenerg-400	177	25	a	a	DET
fuelectenerg-400	177	26	grain	grain	NOUN
fuelectenerg-400	177	27	is	be	AUX
fuelectenerg-400	177	28	reduced	reduce	VERB
fuelectenerg-400	177	29	[	[	X
fuelectenerg-400	177	30	12,15	12,15	NUM
fuelectenerg-400	177	31	]	]	X
fuelectenerg-400	177	32	.	.	PUNCT
fuelectenerg-400	178	1	the	the	DET
fuelectenerg-400	178	2	goal	goal	NOUN
fuelectenerg-400	178	3	of	of	ADP
fuelectenerg-400	178	4	this	this	DET
fuelectenerg-400	178	5	paper	paper	NOUN
fuelectenerg-400	178	6	is	be	AUX
fuelectenerg-400	178	7	to	to	PART
fuelectenerg-400	178	8	establish	establish	VERB
fuelectenerg-400	178	9	a	a	DET
fuelectenerg-400	178	10	bound	bind	VERB
fuelectenerg-400	178	11	of	of	ADP
fuelectenerg-400	178	12	shannon	shannon	PROPN
fuelectenerg-400	178	13	noiseless	noiseless	PROPN
fuelectenerg-400	178	14	capacity	capacity	NOUN
fuelectenerg-400	178	15	and	and	CCONJ
fuelectenerg-400	178	16	designing	designing	NOUN
fuelectenerg-400	178	17	of	of	ADP
fuelectenerg-400	178	18	encoders	encoder	NOUN
fuelectenerg-400	178	19	and	and	CCONJ
fuelectenerg-400	178	20	decoders	decoder	NOUN
fuelectenerg-400	178	21	for	for	ADP
fuelectenerg-400	178	22	nib	nib	NOUN
fuelectenerg-400	178	23	constraint	constraint	NOUN
fuelectenerg-400	178	24	on	on	ADP
fuelectenerg-400	178	25	the	the	DET
fuelectenerg-400	178	26	triangular	triangular	NOUN
fuelectenerg-400	178	27	lattice	lattice	NOUN
fuelectenerg-400	178	28	.	.	PUNCT
fuelectenerg-400	179	1	(	(	PUNCT
fuelectenerg-400	179	2	a	a	X
fuelectenerg-400	179	3	)	)	PUNCT
fuelectenerg-400	179	4	(	(	PUNCT
fuelectenerg-400	179	5	b	b	X
fuelectenerg-400	179	6	)	)	PUNCT
fuelectenerg-400	179	7	(	(	PUNCT
fuelectenerg-400	179	8	c	c	X
fuelectenerg-400	179	9	)	)	PUNCT
fuelectenerg-400	179	10	fig	fig	NOUN
fuelectenerg-400	179	11	.	.	PUNCT
fuelectenerg-400	180	1	1	1	X
fuelectenerg-400	180	2	.	.	X
fuelectenerg-400	180	3	regular	regular	ADJ
fuelectenerg-400	180	4	two	two	NUM
fuelectenerg-400	180	5	-	-	PUNCT
fuelectenerg-400	180	6	dimensional	dimensional	ADJ
fuelectenerg-400	180	7	tilings	tiling	NOUN
fuelectenerg-400	180	8	(	(	PUNCT
fuelectenerg-400	180	9	a	a	PRON
fuelectenerg-400	180	10	)	)	PUNCT
fuelectenerg-400	180	11	triangular	triangular	NOUN
fuelectenerg-400	180	12	,	,	PUNCT
fuelectenerg-400	180	13	(	(	PUNCT
fuelectenerg-400	180	14	b	b	NOUN
fuelectenerg-400	180	15	)	)	PUNCT
fuelectenerg-400	180	16	square	square	NOUN
fuelectenerg-400	180	17	,	,	PUNCT
fuelectenerg-400	180	18	and	and	CCONJ
fuelectenerg-400	180	19	(	(	PUNCT
fuelectenerg-400	180	20	c	c	NOUN
fuelectenerg-400	180	21	)	)	PUNCT
fuelectenerg-400	180	22	hexagonal	hexagonal	ADJ
fuelectenerg-400	180	23	tiling	tiling	NOUN
fuelectenerg-400	180	24	.	.	PUNCT
fuelectenerg-400	181	1	in	in	ADP
fuelectenerg-400	181	2	the	the	DET
fuelectenerg-400	181	3	triangular	triangular	NOUN
fuelectenerg-400	181	4	,	,	PUNCT
fuelectenerg-400	181	5	square	square	ADJ
fuelectenerg-400	181	6	and	and	CCONJ
fuelectenerg-400	181	7	hexagonal	hexagonal	ADJ
fuelectenerg-400	181	8	tilings	tiling	NOUN
fuelectenerg-400	181	9	,	,	PUNCT
fuelectenerg-400	181	10	each	each	DET
fuelectenerg-400	181	11	tile	tile	NOUN
fuelectenerg-400	181	12	has	have	VERB
fuelectenerg-400	181	13	three	three	NUM
fuelectenerg-400	181	14	,	,	PUNCT
fuelectenerg-400	181	15	four	four	NUM
fuelectenerg-400	181	16	and	and	CCONJ
fuelectenerg-400	181	17	six	six	NUM
fuelectenerg-400	181	18	neighbors	neighbor	NOUN
fuelectenerg-400	181	19	,	,	PUNCT
fuelectenerg-400	181	20	respectively	respectively	ADV
fuelectenerg-400	181	21	.	.	PUNCT
fuelectenerg-400	182	1	the	the	DET
fuelectenerg-400	182	2	tiles	tile	NOUN
fuelectenerg-400	182	3	shaded	shade	VERB
fuelectenerg-400	182	4	black	black	ADJ
fuelectenerg-400	182	5	are	be	AUX
fuelectenerg-400	182	6	the	the	DET
fuelectenerg-400	182	7	neighbors	neighbor	NOUN
fuelectenerg-400	182	8	that	that	PRON
fuelectenerg-400	182	9	share	share	VERB
fuelectenerg-400	182	10	an	an	DET
fuelectenerg-400	182	11	edge	edge	NOUN
fuelectenerg-400	182	12	with	with	ADP
fuelectenerg-400	182	13	the	the	DET
fuelectenerg-400	182	14	tile	tile	NOUN
fuelectenerg-400	182	15	shaded	shade	VERB
fuelectenerg-400	182	16	gray	gray	ADJ
fuelectenerg-400	182	17	.	.	PUNCT
fuelectenerg-400	183	1	to	to	PART
fuelectenerg-400	183	2	describe	describe	VERB
fuelectenerg-400	183	3	lozenge	lozenge	NOUN
fuelectenerg-400	183	4	codes	code	NOUN
fuelectenerg-400	183	5	,	,	PUNCT
fuelectenerg-400	183	6	we	we	PRON
fuelectenerg-400	183	7	start	start	VERB
fuelectenerg-400	183	8	by	by	ADP
fuelectenerg-400	183	9	considering	consider	VERB
fuelectenerg-400	183	10	a	a	DET
fuelectenerg-400	183	11	hexagon	hexagon	NOUN
fuelectenerg-400	183	12	h	h	NOUN
fuelectenerg-400	183	13	with	with	ADP
fuelectenerg-400	183	14	sides	side	NOUN
fuelectenerg-400	183	15	of	of	ADP
fuelectenerg-400	183	16	lengths	length	NOUN
fuelectenerg-400	183	17	a	a	DET
fuelectenerg-400	183	18	,	,	PUNCT
fuelectenerg-400	183	19	b	b	NOUN
fuelectenerg-400	183	20	,	,	PUNCT
fuelectenerg-400	183	21	c	c	NOUN
fuelectenerg-400	183	22	,	,	PUNCT
fuelectenerg-400	183	23	a	a	DET
fuelectenerg-400	183	24	,	,	PUNCT
fuelectenerg-400	183	25	b	b	NOUN
fuelectenerg-400	183	26	,	,	PUNCT
fuelectenerg-400	183	27	c	c	NOUN
fuelectenerg-400	183	28	and	and	CCONJ
fuelectenerg-400	183	29	angles	angle	NOUN
fuelectenerg-400	183	30	of	of	ADP
fuelectenerg-400	183	31	2π/3	2π/3	NUM
fuelectenerg-400	183	32	,	,	PUNCT
fuelectenerg-400	183	33	subdivided	subdivide	VERB
fuelectenerg-400	183	34	into	into	ADP
fuelectenerg-400	183	35	equilateral	equilateral	ADJ
fuelectenerg-400	183	36	triangles	triangle	NOUN
fuelectenerg-400	183	37	of	of	ADP
fuelectenerg-400	183	38	unit	unit	NOUN
fuelectenerg-400	183	39	side	side	NOUN
fuelectenerg-400	183	40	by	by	ADP
fuelectenerg-400	183	41	lines	line	NOUN
fuelectenerg-400	183	42	parallel	parallel	ADJ
fuelectenerg-400	183	43	to	to	ADP
fuelectenerg-400	183	44	the	the	DET
fuelectenerg-400	183	45	hexagon	hexagon	NOUN
fuelectenerg-400	183	46	sides	side	NOUN
fuelectenerg-400	183	47	.	.	PUNCT
fuelectenerg-400	184	1	we	we	PRON
fuelectenerg-400	184	2	will	will	AUX
fuelectenerg-400	184	3	henceforth	henceforth	ADV
fuelectenerg-400	184	4	refer	refer	VERB
fuelectenerg-400	184	5	to	to	ADP
fuelectenerg-400	184	6	such	such	ADJ
fuelectenerg-400	184	7	equi	equi	NOUN
fuelectenerg-400	184	8	-	-	PUNCT
fuelectenerg-400	184	9	angular	angular	ADJ
fuelectenerg-400	184	10	triangularized	triangularize	VERB
fuelectenerg-400	184	11	hexagons	hexagon	NOUN
fuelectenerg-400	184	12	as	as	ADP
fuelectenerg-400	184	13	(	(	PUNCT
fuelectenerg-400	184	14	a	a	PRON
fuelectenerg-400	184	15	,	,	PUNCT
fuelectenerg-400	184	16	b	b	NOUN
fuelectenerg-400	184	17	,	,	PUNCT
fuelectenerg-400	184	18	c	c	NOUN
fuelectenerg-400	184	19	)	)	PUNCT
fuelectenerg-400	184	20	hexagons	hexagon	NOUN
fuelectenerg-400	184	21	.	.	PUNCT
fuelectenerg-400	185	1	figure	figure	NOUN
fuelectenerg-400	185	2	2(a	2(a	NUM
fuelectenerg-400	185	3	)	)	PUNCT
fuelectenerg-400	185	4	shows	show	VERB
fuelectenerg-400	185	5	such	such	DET
fuelectenerg-400	185	6	a	a	DET
fuelectenerg-400	185	7	(	(	PUNCT
fuelectenerg-400	185	8	2	2	NUM
fuelectenerg-400	185	9	,	,	PUNCT
fuelectenerg-400	185	10	3	3	NUM
fuelectenerg-400	185	11	,	,	PUNCT
fuelectenerg-400	185	12	4	4	NUM
fuelectenerg-400	185	13	)	)	PUNCT
fuelectenerg-400	185	14	hexagon	hexagon	NOUN
fuelectenerg-400	185	15	.	.	PUNCT
fuelectenerg-400	186	1	as	as	SCONJ
fuelectenerg-400	186	2	mentioned	mention	VERB
fuelectenerg-400	186	3	earlier	early	ADV
fuelectenerg-400	186	4	,	,	PUNCT
fuelectenerg-400	186	5	two	two	NUM
fuelectenerg-400	186	6	triangles	triangle	NOUN
fuelectenerg-400	186	7	are	be	AUX
fuelectenerg-400	186	8	neighbors	neighbor	NOUN
fuelectenerg-400	186	9	if	if	SCONJ
fuelectenerg-400	186	10	they	they	PRON
fuelectenerg-400	186	11	share	share	VERB
fuelectenerg-400	186	12	a	a	DET
fuelectenerg-400	186	13	side	side	NOUN
fuelectenerg-400	186	14	.	.	PUNCT
fuelectenerg-400	187	1	(	(	PUNCT
fuelectenerg-400	187	2	a	a	X
fuelectenerg-400	187	3	)	)	PUNCT
fuelectenerg-400	187	4	(	(	PUNCT
fuelectenerg-400	187	5	b	b	X
fuelectenerg-400	187	6	)	)	PUNCT
fuelectenerg-400	187	7	fig	fig	NOUN
fuelectenerg-400	187	8	.	.	PUNCT
fuelectenerg-400	188	1	2	2	X
fuelectenerg-400	188	2	.	.	X
fuelectenerg-400	188	3	lozenge	lozenge	ADJ
fuelectenerg-400	188	4	tilings	tiling	NOUN
fuelectenerg-400	188	5	in	in	ADP
fuelectenerg-400	188	6	a	a	DET
fuelectenerg-400	188	7	triangular	triangular	NOUN
fuelectenerg-400	188	8	lattice	lattice	NOUN
fuelectenerg-400	188	9	:	:	PUNCT
fuelectenerg-400	188	10	(	(	PUNCT
fuelectenerg-400	188	11	a	a	X
fuelectenerg-400	188	12	)	)	PUNCT
fuelectenerg-400	188	13	a	a	PRON
fuelectenerg-400	188	14	(	(	PUNCT
fuelectenerg-400	188	15	2	2	NUM
fuelectenerg-400	188	16	,	,	PUNCT
fuelectenerg-400	188	17	3	3	NUM
fuelectenerg-400	188	18	,	,	PUNCT
fuelectenerg-400	188	19	4	4	X
fuelectenerg-400	188	20	)	)	PUNCT
fuelectenerg-400	188	21	hexagon	hexagon	NOUN
fuelectenerg-400	188	22	h	h	PROPN
fuelectenerg-400	188	23	embedded	embed	VERB
fuelectenerg-400	188	24	in	in	ADP
fuelectenerg-400	188	25	a	a	DET
fuelectenerg-400	188	26	triangular	triangular	NOUN
fuelectenerg-400	188	27	lattice	lattice	NOUN
fuelectenerg-400	188	28	.	.	PUNCT
fuelectenerg-400	189	1	(	(	PUNCT
fuelectenerg-400	189	2	b	b	X
fuelectenerg-400	189	3	)	)	PUNCT
fuelectenerg-400	189	4	colored	colored	ADJ
fuelectenerg-400	189	5	tiling	tiling	NOUN
fuelectenerg-400	189	6	of	of	ADP
fuelectenerg-400	189	7	a	a	DET
fuelectenerg-400	189	8	(	(	PUNCT
fuelectenerg-400	189	9	2,3,4	2,3,4	NUM
fuelectenerg-400	189	10	)	)	PUNCT
fuelectenerg-400	189	11	hexagon	hexagon	NOUN
fuelectenerg-400	189	12	.	.	PUNCT
fuelectenerg-400	190	1	detection	detection	NOUN
fuelectenerg-400	190	2	and	and	CCONJ
fuelectenerg-400	190	3	coding	code	VERB
fuelectenerg-400	190	4	for	for	ADP
fuelectenerg-400	190	5	tdmr	tdmr	NOUN
fuelectenerg-400	190	6	channel	channel	NOUN
fuelectenerg-400	190	7	525	525	NUM
fuelectenerg-400	190	8	(	(	PUNCT
fuelectenerg-400	190	9	a	a	NOUN
fuelectenerg-400	190	10	)	)	PUNCT
fuelectenerg-400	190	11	(	(	PUNCT
fuelectenerg-400	190	12	b	b	X
fuelectenerg-400	190	13	)	)	PUNCT
fuelectenerg-400	190	14	(	(	PUNCT
fuelectenerg-400	190	15	c	c	X
fuelectenerg-400	190	16	)	)	PUNCT
fuelectenerg-400	190	17	fig	fig	NOUN
fuelectenerg-400	190	18	.	.	PUNCT
fuelectenerg-400	191	1	3	3	X
fuelectenerg-400	191	2	.	.	X
fuelectenerg-400	191	3	the	the	DET
fuelectenerg-400	191	4	prototype	prototype	NOUN
fuelectenerg-400	191	5	tiles	tile	NOUN
fuelectenerg-400	191	6	used	use	VERB
fuelectenerg-400	191	7	in	in	ADP
fuelectenerg-400	191	8	the	the	DET
fuelectenerg-400	191	9	tiling	tiling	NOUN
fuelectenerg-400	191	10	of	of	ADP
fuelectenerg-400	191	11	hexagons	hexagon	NOUN
fuelectenerg-400	191	12	.	.	PUNCT
fuelectenerg-400	192	1	we	we	PRON
fuelectenerg-400	192	2	are	be	AUX
fuelectenerg-400	192	3	interested	interested	ADJ
fuelectenerg-400	192	4	in	in	ADP
fuelectenerg-400	192	5	coloring	color	VERB
fuelectenerg-400	192	6	the	the	DET
fuelectenerg-400	192	7	triangles	triangle	NOUN
fuelectenerg-400	192	8	using	use	VERB
fuelectenerg-400	192	9	m	m	VERB
fuelectenerg-400	192	10	>	>	X
fuelectenerg-400	192	11	1	1	NUM
fuelectenerg-400	192	12	different	different	ADJ
fuelectenerg-400	192	13	colors	color	NOUN
fuelectenerg-400	192	14	in	in	ADP
fuelectenerg-400	192	15	such	such	DET
fuelectenerg-400	192	16	a	a	DET
fuelectenerg-400	192	17	way	way	NOUN
fuelectenerg-400	192	18	that	that	PRON
fuelectenerg-400	192	19	no	no	DET
fuelectenerg-400	192	20	isolated	isolated	ADJ
fuelectenerg-400	192	21	triangle	triangle	NOUN
fuelectenerg-400	192	22	is	be	AUX
fuelectenerg-400	192	23	colored	color	VERB
fuelectenerg-400	192	24	differently	differently	ADV
fuelectenerg-400	192	25	than	than	ADP
fuelectenerg-400	192	26	its	its	PRON
fuelectenerg-400	192	27	neighbors	neighbor	NOUN
fuelectenerg-400	192	28	.	.	PUNCT
fuelectenerg-400	193	1	in	in	ADP
fuelectenerg-400	193	2	the	the	DET
fuelectenerg-400	193	3	paper	paper	NOUN
fuelectenerg-400	193	4	we	we	PRON
fuelectenerg-400	193	5	focus	focus	VERB
fuelectenerg-400	193	6	on	on	ADP
fuelectenerg-400	193	7	the	the	DET
fuelectenerg-400	193	8	m	m	NOUN
fuelectenerg-400	193	9	=	=	SYM
fuelectenerg-400	193	10	2	2	NUM
fuelectenerg-400	193	11	case	case	NOUN
fuelectenerg-400	193	12	.	.	PUNCT
fuelectenerg-400	194	1	we	we	PRON
fuelectenerg-400	194	2	require	require	VERB
fuelectenerg-400	194	3	a	a	DET
fuelectenerg-400	194	4	segregation	segregation	NOUN
fuelectenerg-400	194	5	of	of	ADP
fuelectenerg-400	194	6	at	at	ADV
fuelectenerg-400	194	7	least	least	ADV
fuelectenerg-400	194	8	two	two	NUM
fuelectenerg-400	194	9	neighboring	neighboring	NOUN
fuelectenerg-400	194	10	triangles	triangle	NOUN
fuelectenerg-400	194	11	of	of	ADP
fuelectenerg-400	194	12	the	the	DET
fuelectenerg-400	194	13	same	same	ADJ
fuelectenerg-400	194	14	color	color	NOUN
fuelectenerg-400	194	15	.	.	PUNCT
fuelectenerg-400	195	1	fig	fig	NOUN
fuelectenerg-400	195	2	.	.	PUNCT
fuelectenerg-400	196	1	2(b	2(b	NUM
fuelectenerg-400	196	2	)	)	PUNCT
fuelectenerg-400	196	3	shows	show	VERB
fuelectenerg-400	196	4	one	one	NUM
fuelectenerg-400	196	5	such	such	ADJ
fuelectenerg-400	196	6	coloring	coloring	NOUN
fuelectenerg-400	196	7	of	of	ADP
fuelectenerg-400	196	8	the	the	DET
fuelectenerg-400	196	9	(	(	PUNCT
fuelectenerg-400	196	10	2	2	NUM
fuelectenerg-400	196	11	,	,	PUNCT
fuelectenerg-400	196	12	3	3	NUM
fuelectenerg-400	196	13	,	,	PUNCT
fuelectenerg-400	196	14	4	4	X
fuelectenerg-400	196	15	)	)	PUNCT
fuelectenerg-400	196	16	hexagon	hexagon	NOUN
fuelectenerg-400	196	17	shown	show	VERB
fuelectenerg-400	196	18	in	in	ADP
fuelectenerg-400	196	19	fig	fig	NOUN
fuelectenerg-400	196	20	.	.	PUNCT
fuelectenerg-400	197	1	2(a	2(a	NUM
fuelectenerg-400	197	2	)	)	PUNCT
fuelectenerg-400	197	3	.	.	PUNCT
fuelectenerg-400	198	1	two	two	NUM
fuelectenerg-400	198	2	neighboring	neighboring	NOUN
fuelectenerg-400	198	3	triangles	triangle	NOUN
fuelectenerg-400	198	4	form	form	VERB
fuelectenerg-400	198	5	a	a	DET
fuelectenerg-400	198	6	rhombus	rhombus	NOUN
fuelectenerg-400	198	7	with	with	ADP
fuelectenerg-400	198	8	side	side	NOUN
fuelectenerg-400	198	9	of	of	ADP
fuelectenerg-400	198	10	unit	unit	NOUN
fuelectenerg-400	198	11	length	length	NOUN
fuelectenerg-400	198	12	and	and	CCONJ
fuelectenerg-400	198	13	internal	internal	ADJ
fuelectenerg-400	198	14	angles	angle	NOUN
fuelectenerg-400	198	15	π	π	PROPN
fuelectenerg-400	198	16	3	3	NUM
fuelectenerg-400	198	17	and	and	CCONJ
fuelectenerg-400	198	18	2π	2π	PROPN
fuelectenerg-400	198	19	3	3	NUM
fuelectenerg-400	198	20	.	.	PUNCT
fuelectenerg-400	199	1	such	such	DET
fuelectenerg-400	199	2	a	a	DET
fuelectenerg-400	199	3	rhombus	rhombus	NOUN
fuelectenerg-400	199	4	is	be	AUX
fuelectenerg-400	199	5	known	know	VERB
fuelectenerg-400	199	6	as	as	ADP
fuelectenerg-400	199	7	a	a	DET
fuelectenerg-400	199	8	lozenge	lozenge	NOUN
fuelectenerg-400	199	9	.	.	PUNCT
fuelectenerg-400	200	1	a	a	DET
fuelectenerg-400	200	2	lozenge	lozenge	NOUN
fuelectenerg-400	200	3	created	create	VERB
fuelectenerg-400	200	4	in	in	ADP
fuelectenerg-400	200	5	this	this	DET
fuelectenerg-400	200	6	way	way	NOUN
fuelectenerg-400	200	7	may	may	AUX
fuelectenerg-400	200	8	have	have	VERB
fuelectenerg-400	200	9	three	three	NUM
fuelectenerg-400	200	10	different	different	ADJ
fuelectenerg-400	200	11	orientations	orientation	NOUN
fuelectenerg-400	200	12	.	.	PUNCT
fuelectenerg-400	201	1	fig	fig	NOUN
fuelectenerg-400	201	2	.	.	PUNCT
fuelectenerg-400	202	1	3	3	NUM
fuelectenerg-400	202	2	shows	show	VERB
fuelectenerg-400	202	3	these	these	DET
fuelectenerg-400	202	4	orientations	orientation	NOUN
fuelectenerg-400	202	5	.	.	PUNCT
fuelectenerg-400	203	1	we	we	PRON
fuelectenerg-400	203	2	refer	refer	VERB
fuelectenerg-400	203	3	to	to	ADP
fuelectenerg-400	203	4	the	the	DET
fuelectenerg-400	203	5	prototiles	prototile	NOUN
fuelectenerg-400	203	6	shown	show	VERB
fuelectenerg-400	203	7	in	in	ADP
fuelectenerg-400	203	8	fig	fig	NOUN
fuelectenerg-400	203	9	.	.	PUNCT
fuelectenerg-400	204	1	3(a	3(a	NUM
fuelectenerg-400	204	2	)	)	PUNCT
fuelectenerg-400	204	3	,	,	PUNCT
fuelectenerg-400	205	1	3(b	3(b	NUM
fuelectenerg-400	205	2	)	)	PUNCT
fuelectenerg-400	205	3	and	and	CCONJ
fuelectenerg-400	205	4	3(c	3(c	NUM
fuelectenerg-400	205	5	)	)	PUNCT
fuelectenerg-400	205	6	as	as	ADP
fuelectenerg-400	205	7	to	to	PART
fuelectenerg-400	205	8	type	type	VERB
fuelectenerg-400	205	9	-	-	PUNCT
fuelectenerg-400	205	10	a	a	NOUN
fuelectenerg-400	205	11	,	,	PUNCT
fuelectenerg-400	205	12	type	type	NOUN
fuelectenerg-400	205	13	-	-	PUNCT
fuelectenerg-400	205	14	b	b	NOUN
fuelectenerg-400	205	15	and	and	CCONJ
fuelectenerg-400	205	16	type	type	NOUN
fuelectenerg-400	205	17	-	-	PUNCT
fuelectenerg-400	205	18	c	c	NOUN
fuelectenerg-400	205	19	lozenges	lozenge	NOUN
fuelectenerg-400	205	20	,	,	PUNCT
fuelectenerg-400	205	21	respectively	respectively	ADV
fuelectenerg-400	205	22	.	.	PUNCT
fuelectenerg-400	206	1	the	the	DET
fuelectenerg-400	206	2	last	last	ADJ
fuelectenerg-400	206	3	two	two	NUM
fuelectenerg-400	206	4	prototiles	prototile	NOUN
fuelectenerg-400	206	5	are	be	AUX
fuelectenerg-400	206	6	referred	refer	VERB
fuelectenerg-400	206	7	to	to	ADP
fuelectenerg-400	206	8	as	as	ADP
fuelectenerg-400	206	9	vertical	vertical	ADJ
fuelectenerg-400	206	10	lozenges	lozenge	NOUN
fuelectenerg-400	206	11	.	.	PUNCT
fuelectenerg-400	207	1	now	now	ADV
fuelectenerg-400	207	2	,	,	PUNCT
fuelectenerg-400	207	3	suppose	suppose	VERB
fuelectenerg-400	207	4	each	each	PRON
fuelectenerg-400	207	5	of	of	ADP
fuelectenerg-400	207	6	the	the	DET
fuelectenerg-400	207	7	lozenges	lozenge	NOUN
fuelectenerg-400	207	8	is	be	AUX
fuelectenerg-400	207	9	colored	color	VERB
fuelectenerg-400	207	10	independently	independently	ADV
fuelectenerg-400	207	11	,	,	PUNCT
fuelectenerg-400	207	12	we	we	PRON
fuelectenerg-400	207	13	can	can	AUX
fuelectenerg-400	207	14	ensure	ensure	VERB
fuelectenerg-400	207	15	that	that	SCONJ
fuelectenerg-400	207	16	for	for	ADP
fuelectenerg-400	207	17	any	any	DET
fuelectenerg-400	207	18	triangle	triangle	NOUN
fuelectenerg-400	207	19	there	there	PRON
fuelectenerg-400	207	20	is	be	VERB
fuelectenerg-400	207	21	at	at	ADV
fuelectenerg-400	207	22	least	least	ADJ
fuelectenerg-400	207	23	one	one	NUM
fuelectenerg-400	207	24	neighboring	neighboring	NOUN
fuelectenerg-400	207	25	triangle	triangle	NOUN
fuelectenerg-400	207	26	with	with	ADP
fuelectenerg-400	207	27	the	the	DET
fuelectenerg-400	207	28	same	same	ADJ
fuelectenerg-400	207	29	color	color	NOUN
fuelectenerg-400	207	30	,	,	PUNCT
fuelectenerg-400	207	31	i.e.	i.e.	X
fuelectenerg-400	207	32	(	(	PUNCT
fuelectenerg-400	207	33	d	d	NOUN
fuelectenerg-400	207	34	,	,	PUNCT
fuelectenerg-400	207	35	k	k	NOUN
fuelectenerg-400	207	36	)	)	PUNCT
fuelectenerg-400	207	37	=	=	SYM
fuelectenerg-400	207	38	(	(	PUNCT
fuelectenerg-400	207	39	1,∞	1,∞	NUM
fuelectenerg-400	207	40	)	)	PUNCT
fuelectenerg-400	207	41	.	.	PUNCT
fuelectenerg-400	208	1	the	the	DET
fuelectenerg-400	208	2	constrained	constrain	VERB
fuelectenerg-400	208	3	coding	coding	NOUN
fuelectenerg-400	208	4	problem	problem	NOUN
fuelectenerg-400	208	5	can	can	AUX
fuelectenerg-400	208	6	be	be	AUX
fuelectenerg-400	208	7	now	now	ADV
fuelectenerg-400	208	8	formulated	formulate	VERB
fuelectenerg-400	208	9	as	as	SCONJ
fuelectenerg-400	208	10	follows	follow	VERB
fuelectenerg-400	208	11	:	:	PUNCT
fuelectenerg-400	208	12	given	give	VERB
fuelectenerg-400	208	13	a	a	DET
fuelectenerg-400	208	14	hexagonal	hexagonal	ADJ
fuelectenerg-400	208	15	region	region	NOUN
fuelectenerg-400	208	16	of	of	ADP
fuelectenerg-400	208	17	a	a	DET
fuelectenerg-400	208	18	triangular	triangular	NOUN
fuelectenerg-400	208	19	lattice	lattice	NOUN
fuelectenerg-400	208	20	,	,	PUNCT
fuelectenerg-400	208	21	one	one	PRON
fuelectenerg-400	208	22	would	would	AUX
fuelectenerg-400	208	23	like	like	VERB
fuelectenerg-400	208	24	to	to	PART
fuelectenerg-400	208	25	find	find	VERB
fuelectenerg-400	208	26	a	a	DET
fuelectenerg-400	208	27	one	one	NUM
fuelectenerg-400	208	28	-	-	PUNCT
fuelectenerg-400	208	29	to	to	ADP
fuelectenerg-400	208	30	-	-	PUNCT
fuelectenerg-400	208	31	one	one	NUM
fuelectenerg-400	208	32	mapping	mapping	NOUN
fuelectenerg-400	208	33	from	from	ADP
fuelectenerg-400	208	34	a	a	DET
fuelectenerg-400	208	35	set	set	NOUN
fuelectenerg-400	208	36	of	of	ADP
fuelectenerg-400	208	37	integers	integer	NOUN
fuelectenerg-400	208	38	representing	represent	VERB
fuelectenerg-400	208	39	user	user	NOUN
fuelectenerg-400	208	40	’s	’s	PART
fuelectenerg-400	208	41	binary	binary	ADJ
fuelectenerg-400	208	42	data	datum	NOUN
fuelectenerg-400	208	43	(	(	PUNCT
fuelectenerg-400	208	44	this	this	DET
fuelectenerg-400	208	45	bijection	bijection	NOUN
fuelectenerg-400	208	46	is	be	AUX
fuelectenerg-400	208	47	trivial	trivial	ADJ
fuelectenerg-400	208	48	)	)	PUNCT
fuelectenerg-400	208	49	to	to	ADP
fuelectenerg-400	208	50	a	a	DET
fuelectenerg-400	208	51	set	set	NOUN
fuelectenerg-400	208	52	of	of	ADP
fuelectenerg-400	208	53	nib	nib	NOUN
fuelectenerg-400	208	54	-	-	PUNCT
fuelectenerg-400	208	55	permissible	permissible	ADJ
fuelectenerg-400	208	56	colored	colored	ADJ
fuelectenerg-400	208	57	tilings	tiling	NOUN
fuelectenerg-400	208	58	.	.	PUNCT
fuelectenerg-400	209	1	in	in	ADP
fuelectenerg-400	209	2	addition	addition	NOUN
fuelectenerg-400	209	3	,	,	PUNCT
fuelectenerg-400	209	4	due	due	ADP
fuelectenerg-400	209	5	to	to	ADP
fuelectenerg-400	209	6	complexity	complexity	NOUN
fuelectenerg-400	209	7	constrains	constrain	NOUN
fuelectenerg-400	209	8	,	,	PUNCT
fuelectenerg-400	209	9	it	it	PRON
fuelectenerg-400	209	10	is	be	AUX
fuelectenerg-400	209	11	desirable	desirable	ADJ
fuelectenerg-400	209	12	that	that	SCONJ
fuelectenerg-400	209	13	the	the	DET
fuelectenerg-400	209	14	mapping	mapping	NOUN
fuelectenerg-400	209	15	is	be	AUX
fuelectenerg-400	209	16	described	describe	VERB
fuelectenerg-400	209	17	by	by	ADP
fuelectenerg-400	209	18	an	an	DET
fuelectenerg-400	209	19	algorithm	algorithm	NOUN
fuelectenerg-400	209	20	which	which	PRON
fuelectenerg-400	209	21	operates	operate	VERB
fuelectenerg-400	209	22	locally	locally	ADV
fuelectenerg-400	209	23	on	on	ADP
fuelectenerg-400	209	24	a	a	DET
fuelectenerg-400	209	25	small	small	ADJ
fuelectenerg-400	209	26	lattice	lattice	NOUN
fuelectenerg-400	209	27	region	region	NOUN
fuelectenerg-400	209	28	.	.	PUNCT
fuelectenerg-400	210	1	we	we	PRON
fuelectenerg-400	210	2	propose	propose	VERB
fuelectenerg-400	210	3	a	a	DET
fuelectenerg-400	210	4	mapping	mapping	NOUN
fuelectenerg-400	210	5	which	which	PRON
fuelectenerg-400	210	6	is	be	AUX
fuelectenerg-400	210	7	a	a	DET
fuelectenerg-400	210	8	composition	composition	NOUN
fuelectenerg-400	210	9	of	of	ADP
fuelectenerg-400	210	10	two	two	NUM
fuelectenerg-400	210	11	mappings	mapping	NOUN
fuelectenerg-400	210	12	:	:	PUNCT
fuelectenerg-400	210	13	tiling	tile	VERB
fuelectenerg-400	210	14	and	and	CCONJ
fuelectenerg-400	210	15	coloring	coloring	NOUN
fuelectenerg-400	210	16	.	.	PUNCT
fuelectenerg-400	211	1	now	now	ADV
fuelectenerg-400	211	2	the	the	DET
fuelectenerg-400	211	3	nib	nib	NOUN
fuelectenerg-400	211	4	coloring	coloring	NOUN
fuelectenerg-400	211	5	can	can	AUX
fuelectenerg-400	211	6	be	be	AUX
fuelectenerg-400	211	7	separated	separate	VERB
fuelectenerg-400	211	8	into	into	ADP
fuelectenerg-400	211	9	two	two	NUM
fuelectenerg-400	211	10	steps	step	NOUN
fuelectenerg-400	211	11	as	as	SCONJ
fuelectenerg-400	211	12	illustrated	illustrate	VERB
fuelectenerg-400	211	13	in	in	ADP
fuelectenerg-400	211	14	fig	fig	NOUN
fuelectenerg-400	211	15	.	.	PUNCT
fuelectenerg-400	212	1	4	4	X
fuelectenerg-400	212	2	.	.	X
fuelectenerg-400	212	3	first	first	ADV
fuelectenerg-400	212	4	,	,	PUNCT
fuelectenerg-400	212	5	the	the	DET
fuelectenerg-400	212	6	hexagon	hexagon	NOUN
fuelectenerg-400	212	7	(	(	PUNCT
fuelectenerg-400	212	8	fig	fig	NOUN
fuelectenerg-400	212	9	.	.	PUNCT
fuelectenerg-400	213	1	4(a	4(a	NUM
fuelectenerg-400	213	2	)	)	PUNCT
fuelectenerg-400	213	3	)	)	PUNCT
fuelectenerg-400	214	1	is	be	AUX
fuelectenerg-400	214	2	tiled	tile	VERB
fuelectenerg-400	214	3	with	with	ADP
fuelectenerg-400	214	4	(	(	PUNCT
fuelectenerg-400	214	5	uncolored	uncolored	ADJ
fuelectenerg-400	214	6	)	)	PUNCT
fuelectenerg-400	214	7	lozenges	lozenge	NOUN
fuelectenerg-400	214	8	(	(	PUNCT
fuelectenerg-400	214	9	to	to	PART
fuelectenerg-400	214	10	obtain	obtain	VERB
fuelectenerg-400	214	11	lozenge	lozenge	NOUN
fuelectenerg-400	214	12	tiling	tile	VERB
fuelectenerg-400	214	13	in	in	ADP
fuelectenerg-400	214	14	fig	fig	NOUN
fuelectenerg-400	214	15	.	.	PUNCT
fuelectenerg-400	215	1	4(b	4(b	NUM
fuelectenerg-400	215	2	)	)	PUNCT
fuelectenerg-400	215	3	)	)	PUNCT
fuelectenerg-400	215	4	,	,	PUNCT
fuelectenerg-400	215	5	and	and	CCONJ
fuelectenerg-400	215	6	then	then	ADV
fuelectenerg-400	215	7	the	the	DET
fuelectenerg-400	215	8	lozenges	lozenge	NOUN
fuelectenerg-400	215	9	are	be	AUX
fuelectenerg-400	215	10	colored	color	VERB
fuelectenerg-400	215	11	,	,	PUNCT
fuelectenerg-400	215	12	(	(	PUNCT
fuelectenerg-400	215	13	to	to	PART
fuelectenerg-400	215	14	obtain	obtain	VERB
fuelectenerg-400	215	15	colored	colored	ADJ
fuelectenerg-400	215	16	tiling	tile	VERB
fuelectenerg-400	215	17	in	in	ADP
fuelectenerg-400	215	18	fig	fig	NOUN
fuelectenerg-400	215	19	.	.	PUNCT
fuelectenerg-400	216	1	4(c	4(c	NUM
fuelectenerg-400	216	2	)	)	PUNCT
fuelectenerg-400	216	3	)	)	PUNCT
fuelectenerg-400	216	4	.	.	PUNCT
fuelectenerg-400	217	1	it	it	PRON
fuelectenerg-400	217	2	is	be	AUX
fuelectenerg-400	217	3	important	important	ADJ
fuelectenerg-400	217	4	to	to	PART
fuelectenerg-400	217	5	note	note	VERB
fuelectenerg-400	217	6	that	that	SCONJ
fuelectenerg-400	217	7	the	the	DET
fuelectenerg-400	217	8	reader	reader	NOUN
fuelectenerg-400	217	9	does	do	AUX
fuelectenerg-400	217	10	not	not	PART
fuelectenerg-400	217	11	have	have	VERB
fuelectenerg-400	217	12	knowledge	knowledge	NOUN
fuelectenerg-400	217	13	of	of	ADP
fuelectenerg-400	217	14	the	the	DET
fuelectenerg-400	217	15	tiling	tiling	NOUN
fuelectenerg-400	217	16	and	and	CCONJ
fuelectenerg-400	217	17	retrieves	retrieve	NOUN
fuelectenerg-400	217	18	encoded	encode	VERB
fuelectenerg-400	217	19	bits	bit	NOUN
fuelectenerg-400	217	20	solely	solely	ADV
fuelectenerg-400	217	21	based	base	VERB
fuelectenerg-400	217	22	on	on	ADP
fuelectenerg-400	217	23	the	the	DET
fuelectenerg-400	217	24	colored	colored	ADJ
fuelectenerg-400	217	25	pattern	pattern	NOUN
fuelectenerg-400	217	26	.	.	PUNCT
fuelectenerg-400	218	1	thus	thus	ADV
fuelectenerg-400	218	2	,	,	PUNCT
fuelectenerg-400	218	3	not	not	PART
fuelectenerg-400	218	4	all	all	DET
fuelectenerg-400	218	5	colorings	coloring	NOUN
fuelectenerg-400	218	6	can	can	AUX
fuelectenerg-400	218	7	guaranty	guaranty	VERB
fuelectenerg-400	218	8	retrievability	retrievability	NOUN
fuelectenerg-400	218	9	.	.	PUNCT
fuelectenerg-400	219	1	of	of	ADP
fuelectenerg-400	219	2	interest	interest	NOUN
fuelectenerg-400	219	3	are	be	AUX
fuelectenerg-400	219	4	only	only	ADV
fuelectenerg-400	219	5	those	those	DET
fuelectenerg-400	219	6	colorings	coloring	NOUN
fuelectenerg-400	219	7	that	that	PRON
fuelectenerg-400	219	8	ensure	ensure	VERB
fuelectenerg-400	219	9	retrievability	retrievability	NOUN
fuelectenerg-400	219	10	.	.	PUNCT
fuelectenerg-400	220	1	dividing	divide	VERB
fuelectenerg-400	220	2	the	the	DET
fuelectenerg-400	220	3	hard	hard	ADJ
fuelectenerg-400	220	4	coloring	color	VERB
fuelectenerg-400	220	5	hard	hard	ADJ
fuelectenerg-400	220	6	problem	problem	NOUN
fuelectenerg-400	220	7	into	into	ADP
fuelectenerg-400	220	8	two	two	NUM
fuelectenerg-400	220	9	manageable	manageable	ADJ
fuelectenerg-400	220	10	operations	operation	NOUN
fuelectenerg-400	220	11	results	result	NOUN
fuelectenerg-400	220	12	into	into	ADP
fuelectenerg-400	220	13	an	an	DET
fuelectenerg-400	220	14	unavoidable	unavoidable	ADJ
fuelectenerg-400	220	15	rate	rate	NOUN
fuelectenerg-400	220	16	penalty	penalty	NOUN
fuelectenerg-400	220	17	,	,	PUNCT
fuelectenerg-400	220	18	however	however	ADV
fuelectenerg-400	220	19	the	the	DET
fuelectenerg-400	220	20	rate	rate	NOUN
fuelectenerg-400	220	21	penalty	penalty	NOUN
fuelectenerg-400	220	22	due	due	ADJ
fuelectenerg-400	220	23	this	this	DET
fuelectenerg-400	220	24	simplification	simplification	NOUN
fuelectenerg-400	220	25	is	be	AUX
fuelectenerg-400	220	26	a	a	DET
fuelectenerg-400	220	27	tradeoff	tradeoff	NOUN
fuelectenerg-400	220	28	for	for	ADP
fuelectenerg-400	220	29	tractability	tractability	NOUN
fuelectenerg-400	220	30	.	.	PUNCT
fuelectenerg-400	221	1	as	as	SCONJ
fuelectenerg-400	221	2	we	we	PRON
fuelectenerg-400	221	3	show	show	VERB
fuelectenerg-400	221	4	in	in	ADP
fuelectenerg-400	221	5	the	the	DET
fuelectenerg-400	221	6	following	follow	VERB
fuelectenerg-400	221	7	sections	section	NOUN
fuelectenerg-400	221	8	,	,	PUNCT
fuelectenerg-400	221	9	it	it	PRON
fuelectenerg-400	221	10	is	be	AUX
fuelectenerg-400	221	11	now	now	ADV
fuelectenerg-400	221	12	possible	possible	ADJ
fuelectenerg-400	221	13	to	to	PART
fuelectenerg-400	221	14	use	use	VERB
fuelectenerg-400	221	15	elegant	elegant	ADJ
fuelectenerg-400	221	16	combinatorial	combinatorial	ADJ
fuelectenerg-400	221	17	methods	method	NOUN
fuelectenerg-400	221	18	to	to	PART
fuelectenerg-400	221	19	design	design	VERB
fuelectenerg-400	221	20	encoders	encoder	NOUN
fuelectenerg-400	221	21	and	and	CCONJ
fuelectenerg-400	221	22	decoders	decoder	NOUN
fuelectenerg-400	221	23	.	.	PUNCT
fuelectenerg-400	222	1	moreover	moreover	ADV
fuelectenerg-400	222	2	we	we	PRON
fuelectenerg-400	222	3	can	can	AUX
fuelectenerg-400	222	4	establish	establish	VERB
fuelectenerg-400	222	5	bounds	bound	NOUN
fuelectenerg-400	222	6	on	on	ADP
fuelectenerg-400	222	7	capacities	capacity	NOUN
fuelectenerg-400	222	8	,	,	PUNCT
fuelectenerg-400	222	9	i.e.	i.e.	X
fuelectenerg-400	222	10	,	,	PUNCT
fuelectenerg-400	222	11	achievable	achievable	ADJ
fuelectenerg-400	222	12	density	density	NOUN
fuelectenerg-400	222	13	.	.	PUNCT
fuelectenerg-400	223	1	we	we	PRON
fuelectenerg-400	223	2	start	start	VERB
fuelectenerg-400	223	3	with	with	ADP
fuelectenerg-400	223	4	deriving	derive	VERB
fuelectenerg-400	223	5	the	the	DET
fuelectenerg-400	223	6	capacity	capacity	NOUN
fuelectenerg-400	223	7	bounds	bound	NOUN
fuelectenerg-400	223	8	.	.	PUNCT
fuelectenerg-400	224	1	524	524	NUM
fuelectenerg-400	224	2	b.	b.	PROPN
fuelectenerg-400	224	3	vasic	vasic	PROPN
fuelectenerg-400	224	4	,	,	PUNCT
fuelectenerg-400	224	5	a.	a.	PROPN
fuelectenerg-400	224	6	r.	r.	PROPN
fuelectenerg-400	224	7	krishnan	krishnan	PROPN
fuelectenerg-400	224	8	lozenge	lozenge	PROPN
fuelectenerg-400	224	9	tiling	tile	VERB
fuelectenerg-400	224	10	constrained	constrained	ADJ
fuelectenerg-400	224	11	codes	code	NOUN
fuelectenerg-400	224	12	525	525	NUM
fuelectenerg-400	224	13	526	526	NUM
fuelectenerg-400	224	14	a.	a.	NOUN
fuelectenerg-400	224	15	r.	r.	PROPN
fuelectenerg-400	224	16	krishnanan	krishnanan	PROPN
fuelectenerg-400	224	17	and	and	CCONJ
fuelectenerg-400	224	18	b.	b.	PROPN
fuelectenerg-400	224	19	vasić	vasić	PROPN
fuelectenerg-400	224	20	(	(	PUNCT
fuelectenerg-400	224	21	a	a	X
fuelectenerg-400	224	22	)	)	PUNCT
fuelectenerg-400	224	23	(	(	PUNCT
fuelectenerg-400	224	24	b	b	X
fuelectenerg-400	224	25	)	)	PUNCT
fuelectenerg-400	224	26	(	(	PUNCT
fuelectenerg-400	224	27	c	c	X
fuelectenerg-400	224	28	)	)	PUNCT
fuelectenerg-400	224	29	fig	fig	NOUN
fuelectenerg-400	224	30	.	.	PUNCT
fuelectenerg-400	225	1	4	4	X
fuelectenerg-400	225	2	.	.	X
fuelectenerg-400	225	3	colored	color	VERB
fuelectenerg-400	225	4	lozenge	lozenge	NOUN
fuelectenerg-400	225	5	tilings	tiling	NOUN
fuelectenerg-400	225	6	in	in	ADP
fuelectenerg-400	225	7	a	a	DET
fuelectenerg-400	225	8	triangular	triangular	NOUN
fuelectenerg-400	225	9	lattice	lattice	NOUN
fuelectenerg-400	225	10	:	:	PUNCT
fuelectenerg-400	225	11	(	(	PUNCT
fuelectenerg-400	225	12	a	a	X
fuelectenerg-400	225	13	)	)	PUNCT
fuelectenerg-400	225	14	a	a	DET
fuelectenerg-400	225	15	hexagon	hexagon	NOUN
fuelectenerg-400	225	16	with	with	ADP
fuelectenerg-400	225	17	side	side	NOUN
fuelectenerg-400	225	18	-	-	PUNCT
fuelectenerg-400	225	19	length	length	NOUN
fuelectenerg-400	225	20	of	of	ADP
fuelectenerg-400	225	21	6	6	NUM
fuelectenerg-400	225	22	embedded	embed	VERB
fuelectenerg-400	225	23	in	in	ADP
fuelectenerg-400	225	24	a	a	DET
fuelectenerg-400	225	25	triangular	triangular	NOUN
fuelectenerg-400	225	26	lattice	lattice	NOUN
fuelectenerg-400	225	27	.	.	PUNCT
fuelectenerg-400	226	1	(	(	PUNCT
fuelectenerg-400	226	2	b	b	X
fuelectenerg-400	226	3	)	)	PUNCT
fuelectenerg-400	226	4	an	an	DET
fuelectenerg-400	226	5	uncolored	uncolored	ADJ
fuelectenerg-400	226	6	lozenge	lozenge	NOUN
fuelectenerg-400	226	7	tiling	tiling	NOUN
fuelectenerg-400	226	8	of	of	ADP
fuelectenerg-400	226	9	the	the	DET
fuelectenerg-400	226	10	hexagon	hexagon	NOUN
fuelectenerg-400	226	11	.	.	PUNCT
fuelectenerg-400	227	1	(	(	PUNCT
fuelectenerg-400	227	2	c	c	X
fuelectenerg-400	227	3	)	)	PUNCT
fuelectenerg-400	227	4	a	a	DET
fuelectenerg-400	227	5	colored	colored	ADJ
fuelectenerg-400	227	6	lozenge	lozenge	NOUN
fuelectenerg-400	227	7	tiling	tiling	NOUN
fuelectenerg-400	227	8	of	of	ADP
fuelectenerg-400	227	9	the	the	DET
fuelectenerg-400	227	10	hexagon	hexagon	NOUN
fuelectenerg-400	227	11	.	.	PUNCT
fuelectenerg-400	228	1	4	4	NUM
fuelectenerg-400	228	2	bounds	bound	NOUN
fuelectenerg-400	228	3	on	on	ADP
fuelectenerg-400	228	4	capacity	capacity	NOUN
fuelectenerg-400	228	5	for	for	ADP
fuelectenerg-400	228	6	the	the	DET
fuelectenerg-400	228	7	nib	nib	NOUN
fuelectenerg-400	228	8	constraint	constraint	NOUN
fuelectenerg-400	228	9	defined	define	VERB
fuelectenerg-400	228	10	above	above	ADV
fuelectenerg-400	228	11	,	,	PUNCT
fuelectenerg-400	228	12	we	we	PRON
fuelectenerg-400	228	13	can	can	AUX
fuelectenerg-400	228	14	define	define	VERB
fuelectenerg-400	228	15	the	the	DET
fuelectenerg-400	228	16	shannon	shannon	PROPN
fuelectenerg-400	228	17	noiseless	noiseless	PROPN
fuelectenerg-400	228	18	capacity	capacity	NOUN
fuelectenerg-400	228	19	using	use	VERB
fuelectenerg-400	228	20	an	an	DET
fuelectenerg-400	228	21	(	(	PUNCT
fuelectenerg-400	228	22	n	n	CCONJ
fuelectenerg-400	228	23	,	,	PUNCT
fuelectenerg-400	228	24	n	n	CCONJ
fuelectenerg-400	228	25	,	,	PUNCT
fuelectenerg-400	228	26	n	n	CCONJ
fuelectenerg-400	228	27	)	)	PUNCT
fuelectenerg-400	228	28	hexagon	hexagon	NOUN
fuelectenerg-400	228	29	as	as	SCONJ
fuelectenerg-400	228	30	follows	follow	VERB
fuelectenerg-400	228	31	:	:	PUNCT
fuelectenerg-400	228	32	c	c	X
fuelectenerg-400	228	33	=	=	SYM
fuelectenerg-400	228	34	lim	lim	PROPN
fuelectenerg-400	228	35	n→∞	n→∞	NUM
fuelectenerg-400	229	1	log2	log2	PROPN
fuelectenerg-400	229	2	m(n	m(n	PROPN
fuelectenerg-400	229	3	,	,	PUNCT
fuelectenerg-400	229	4	n	n	CCONJ
fuelectenerg-400	229	5	,	,	PUNCT
fuelectenerg-400	229	6	n	n	CCONJ
fuelectenerg-400	229	7	)	)	PUNCT
fuelectenerg-400	229	8	log226n2	log226n2	ADV
fuelectenerg-400	229	9	(	(	PUNCT
fuelectenerg-400	229	10	1	1	NUM
fuelectenerg-400	229	11	)	)	PUNCT
fuelectenerg-400	229	12	=	=	VERB
fuelectenerg-400	230	1	lim	lim	PROPN
fuelectenerg-400	230	2	n→∞	n→∞	NUM
fuelectenerg-400	230	3	log2	log2	PROPN
fuelectenerg-400	230	4	m(n	m(n	PROPN
fuelectenerg-400	230	5	,	,	PUNCT
fuelectenerg-400	230	6	n	n	CCONJ
fuelectenerg-400	230	7	,	,	PUNCT
fuelectenerg-400	230	8	n	n	CCONJ
fuelectenerg-400	230	9	)	)	PUNCT
fuelectenerg-400	230	10	6n2	6n2	NUM
fuelectenerg-400	230	11	.	.	PUNCT
fuelectenerg-400	231	1	(	(	PUNCT
fuelectenerg-400	231	2	2	2	X
fuelectenerg-400	231	3	)	)	PUNCT
fuelectenerg-400	231	4	note	note	NOUN
fuelectenerg-400	231	5	that	that	SCONJ
fuelectenerg-400	231	6	since	since	SCONJ
fuelectenerg-400	231	7	the	the	DET
fuelectenerg-400	231	8	number	number	NOUN
fuelectenerg-400	231	9	of	of	ADP
fuelectenerg-400	231	10	triangles	triangle	NOUN
fuelectenerg-400	231	11	constituting	constitute	VERB
fuelectenerg-400	231	12	the	the	DET
fuelectenerg-400	231	13	(	(	PUNCT
fuelectenerg-400	231	14	n	n	X
fuelectenerg-400	231	15	,	,	PUNCT
fuelectenerg-400	231	16	n	n	CCONJ
fuelectenerg-400	231	17	,	,	PUNCT
fuelectenerg-400	231	18	n	n	CCONJ
fuelectenerg-400	231	19	)	)	PUNCT
fuelectenerg-400	231	20	hexagon	hexagon	PROPN
fuelectenerg-400	231	21	is	be	AUX
fuelectenerg-400	231	22	6n2	6n2	NUM
fuelectenerg-400	231	23	,	,	PUNCT
fuelectenerg-400	231	24	in	in	ADP
fuelectenerg-400	231	25	eqn	eqn	NOUN
fuelectenerg-400	231	26	.	.	PUNCT
fuelectenerg-400	232	1	1	1	NUM
fuelectenerg-400	232	2	,	,	PUNCT
fuelectenerg-400	232	3	the	the	DET
fuelectenerg-400	232	4	denominator	denominator	NOUN
fuelectenerg-400	232	5	is	be	AUX
fuelectenerg-400	232	6	logarithm	logarithm	NOUN
fuelectenerg-400	232	7	of	of	ADP
fuelectenerg-400	232	8	the	the	DET
fuelectenerg-400	232	9	total	total	ADJ
fuelectenerg-400	232	10	number	number	NOUN
fuelectenerg-400	232	11	of	of	ADP
fuelectenerg-400	232	12	independent	independent	ADJ
fuelectenerg-400	232	13	colorings	coloring	NOUN
fuelectenerg-400	232	14	of	of	ADP
fuelectenerg-400	232	15	the	the	DET
fuelectenerg-400	232	16	constituent	constituent	NOUN
fuelectenerg-400	232	17	triangles	triangle	NOUN
fuelectenerg-400	232	18	.	.	PUNCT
fuelectenerg-400	233	1	the	the	DET
fuelectenerg-400	233	2	numerator	numerator	NOUN
fuelectenerg-400	233	3	m(n	m(n	PROPN
fuelectenerg-400	233	4	,	,	PUNCT
fuelectenerg-400	233	5	n	n	CCONJ
fuelectenerg-400	233	6	,	,	PUNCT
fuelectenerg-400	233	7	n	n	CCONJ
fuelectenerg-400	233	8	)	)	PUNCT
fuelectenerg-400	233	9	is	be	AUX
fuelectenerg-400	233	10	the	the	DET
fuelectenerg-400	233	11	logarithm	logarithm	NOUN
fuelectenerg-400	233	12	of	of	ADP
fuelectenerg-400	233	13	the	the	DET
fuelectenerg-400	233	14	number	number	NOUN
fuelectenerg-400	233	15	of	of	ADP
fuelectenerg-400	233	16	colorings	coloring	NOUN
fuelectenerg-400	233	17	of	of	ADP
fuelectenerg-400	233	18	the	the	DET
fuelectenerg-400	233	19	constituent	constituent	NOUN
fuelectenerg-400	233	20	triangles	triangle	NOUN
fuelectenerg-400	233	21	that	that	PRON
fuelectenerg-400	233	22	satisfy	satisfy	VERB
fuelectenerg-400	233	23	the	the	DET
fuelectenerg-400	233	24	nib	nib	NOUN
fuelectenerg-400	233	25	constraint	constraint	NOUN
fuelectenerg-400	233	26	.	.	PUNCT
fuelectenerg-400	234	1	similarly	similarly	ADV
fuelectenerg-400	234	2	,	,	PUNCT
fuelectenerg-400	234	3	if	if	SCONJ
fuelectenerg-400	234	4	n(n	n(n	PROPN
fuelectenerg-400	234	5	,	,	PUNCT
fuelectenerg-400	234	6	n	n	CCONJ
fuelectenerg-400	234	7	,	,	PUNCT
fuelectenerg-400	234	8	n	n	CCONJ
fuelectenerg-400	234	9	)	)	PUNCT
fuelectenerg-400	234	10	denotes	denote	VERB
fuelectenerg-400	234	11	the	the	DET
fuelectenerg-400	234	12	number	number	NOUN
fuelectenerg-400	234	13	of	of	ADP
fuelectenerg-400	234	14	uncolored	uncolored	ADJ
fuelectenerg-400	234	15	patterns	pattern	NOUN
fuelectenerg-400	234	16	(	(	PUNCT
fuelectenerg-400	234	17	tilings	tiling	NOUN
fuelectenerg-400	234	18	)	)	PUNCT
fuelectenerg-400	234	19	,	,	PUNCT
fuelectenerg-400	234	20	the	the	DET
fuelectenerg-400	234	21	asymptotic	asymptotic	ADJ
fuelectenerg-400	234	22	growth	growth	NOUN
fuelectenerg-400	234	23	rate	rate	NOUN
fuelectenerg-400	234	24	of	of	ADP
fuelectenerg-400	234	25	n(n	n(n	PROPN
fuelectenerg-400	234	26	,	,	PUNCT
fuelectenerg-400	234	27	n	n	CCONJ
fuelectenerg-400	234	28	,	,	PUNCT
fuelectenerg-400	234	29	n	n	CCONJ
fuelectenerg-400	234	30	)	)	PUNCT
fuelectenerg-400	234	31	–	–	PUNCT
fuelectenerg-400	234	32	we	we	PRON
fuelectenerg-400	234	33	call	call	VERB
fuelectenerg-400	234	34	it	it	PRON
fuelectenerg-400	234	35	tiling	tile	VERB
fuelectenerg-400	234	36	capacity	capacity	NOUN
fuelectenerg-400	234	37	(	(	PUNCT
fuelectenerg-400	234	38	ct	ct	NOUN
fuelectenerg-400	234	39	)	)	PUNCT
fuelectenerg-400	234	40	is	be	AUX
fuelectenerg-400	234	41	defined	define	VERB
fuelectenerg-400	234	42	as	as	ADP
fuelectenerg-400	234	43	ct	ct	PROPN
fuelectenerg-400	234	44	=	=	PROPN
fuelectenerg-400	234	45	lim	lim	PROPN
fuelectenerg-400	234	46	n→∞	n→∞	NUM
fuelectenerg-400	234	47	log2	log2	PROPN
fuelectenerg-400	234	48	n(n	n(n	PROPN
fuelectenerg-400	234	49	,	,	PUNCT
fuelectenerg-400	234	50	n	n	CCONJ
fuelectenerg-400	234	51	,	,	PUNCT
fuelectenerg-400	234	52	n	n	CCONJ
fuelectenerg-400	234	53	)	)	PUNCT
fuelectenerg-400	234	54	log226n2	log226n2	ADV
fuelectenerg-400	234	55	.	.	PUNCT
fuelectenerg-400	235	1	(	(	PUNCT
fuelectenerg-400	235	2	3	3	X
fuelectenerg-400	235	3	)	)	PUNCT
fuelectenerg-400	235	4	finally	finally	ADV
fuelectenerg-400	235	5	,	,	PUNCT
fuelectenerg-400	235	6	we	we	PRON
fuelectenerg-400	235	7	define	define	VERB
fuelectenerg-400	235	8	a	a	DET
fuelectenerg-400	235	9	coloring	coloring	NOUN
fuelectenerg-400	235	10	capacity	capacity	NOUN
fuelectenerg-400	235	11	(	(	PUNCT
fuelectenerg-400	235	12	cc	cc	NOUN
fuelectenerg-400	235	13	)	)	PUNCT
fuelectenerg-400	235	14	based	base	VERB
fuelectenerg-400	235	15	on	on	ADP
fuelectenerg-400	235	16	the	the	DET
fuelectenerg-400	235	17	number	number	NOUN
fuelectenerg-400	235	18	of	of	ADP
fuelectenerg-400	235	19	distinct	distinct	ADJ
fuelectenerg-400	235	20	patterns	pattern	NOUN
fuelectenerg-400	235	21	,	,	PUNCT
fuelectenerg-400	235	22	i.e.	i.e.	X
fuelectenerg-400	235	23	number	number	NOUN
fuelectenerg-400	235	24	k(n	k(n	PROPN
fuelectenerg-400	235	25	,	,	PUNCT
fuelectenerg-400	235	26	n	n	CCONJ
fuelectenerg-400	235	27	,	,	PUNCT
fuelectenerg-400	235	28	n	n	CCONJ
fuelectenerg-400	235	29	)	)	PUNCT
fuelectenerg-400	235	30	of	of	ADP
fuelectenerg-400	235	31	ways	way	NOUN
fuelectenerg-400	235	32	of	of	ADP
fuelectenerg-400	235	33	distinctly	distinctly	ADV
fuelectenerg-400	235	34	coloring	color	VERB
fuelectenerg-400	235	35	a	a	DET
fuelectenerg-400	235	36	lozenge	lozenge	NOUN
fuelectenerg-400	235	37	tiling	tile	VERB
fuelectenerg-400	235	38	so	so	SCONJ
fuelectenerg-400	235	39	that	that	SCONJ
fuelectenerg-400	235	40	the	the	DET
fuelectenerg-400	235	41	constraints	constraint	NOUN
fuelectenerg-400	235	42	are	be	AUX
fuelectenerg-400	235	43	satisfied	satisfied	ADJ
fuelectenerg-400	235	44	.	.	PUNCT
fuelectenerg-400	236	1	this	this	PRON
fuelectenerg-400	236	2	is	be	AUX
fuelectenerg-400	236	3	defined	define	VERB
fuelectenerg-400	236	4	as	as	SCONJ
fuelectenerg-400	236	5	follows	follow	VERB
fuelectenerg-400	236	6	:	:	PUNCT
fuelectenerg-400	236	7	cc	cc	PROPN
fuelectenerg-400	236	8	=	=	PROPN
fuelectenerg-400	236	9	lim	lim	PROPN
fuelectenerg-400	236	10	n→∞	n→∞	NUM
fuelectenerg-400	236	11	log2	log2	PROPN
fuelectenerg-400	236	12	k(n	k(n	PROPN
fuelectenerg-400	236	13	,	,	PUNCT
fuelectenerg-400	236	14	n	n	CCONJ
fuelectenerg-400	236	15	,	,	PUNCT
fuelectenerg-400	236	16	n	n	CCONJ
fuelectenerg-400	236	17	)	)	PUNCT
fuelectenerg-400	236	18	log226n2	log226n2	ADV
fuelectenerg-400	236	19	.	.	PUNCT
fuelectenerg-400	237	1	(	(	PUNCT
fuelectenerg-400	237	2	4	4	X
fuelectenerg-400	237	3	)	)	PUNCT
fuelectenerg-400	237	4	we	we	PRON
fuelectenerg-400	237	5	are	be	AUX
fuelectenerg-400	237	6	interested	interested	ADJ
fuelectenerg-400	237	7	in	in	ADP
fuelectenerg-400	237	8	calculating	calculate	VERB
fuelectenerg-400	237	9	the	the	DET
fuelectenerg-400	237	10	number	number	NOUN
fuelectenerg-400	237	11	of	of	ADP
fuelectenerg-400	237	12	colored	colored	ADJ
fuelectenerg-400	237	13	lozenge	lozenge	NOUN
fuelectenerg-400	237	14	tilings	tiling	NOUN
fuelectenerg-400	237	15	of	of	ADP
fuelectenerg-400	237	16	a	a	DET
fuelectenerg-400	237	17	given	give	VERB
fuelectenerg-400	237	18	lattice	lattice	NOUN
fuelectenerg-400	237	19	.	.	PUNCT
fuelectenerg-400	238	1	observe	observe	VERB
fuelectenerg-400	238	2	that	that	SCONJ
fuelectenerg-400	238	3	this	this	PRON
fuelectenerg-400	238	4	will	will	AUX
fuelectenerg-400	238	5	yield	yield	VERB
fuelectenerg-400	238	6	bounds	bound	NOUN
fuelectenerg-400	238	7	on	on	ADP
fuelectenerg-400	238	8	the	the	DET
fuelectenerg-400	238	9	capacity	capacity	NOUN
fuelectenerg-400	238	10	of	of	ADP
fuelectenerg-400	238	11	the	the	DET
fuelectenerg-400	238	12	nib	nib	NOUN
fuelectenerg-400	238	13	constraint	constraint	NOUN
fuelectenerg-400	238	14	because	because	SCONJ
fuelectenerg-400	238	15	the	the	DET
fuelectenerg-400	238	16	capacity	capacity	NOUN
fuelectenerg-400	238	17	c(1,∞	c(1,∞	PROPN
fuelectenerg-400	238	18	)	)	PUNCT
fuelectenerg-400	238	19	of	of	ADP
fuelectenerg-400	238	20	the	the	DET
fuelectenerg-400	238	21	nib	nib	NOUN
fuelectenerg-400	238	22	constraint	constraint	NOUN
fuelectenerg-400	238	23	for	for	ADP
fuelectenerg-400	238	24	the	the	DET
fuelectenerg-400	238	25	triangular	triangular	NOUN
fuelectenerg-400	238	26	lattice	lattice	NOUN
fuelectenerg-400	238	27	model	model	NOUN
fuelectenerg-400	238	28	,	,	PUNCT
fuelectenerg-400	238	29	can	can	AUX
fuelectenerg-400	238	30	be	be	AUX
fuelectenerg-400	238	31	bounded	bound	VERB
fuelectenerg-400	238	32	by	by	ADP
fuelectenerg-400	238	33	the	the	DET
fuelectenerg-400	238	34	tiling	tile	VERB
fuelectenerg-400	238	35	density	density	NOUN
fuelectenerg-400	238	36	and	and	CCONJ
fuelectenerg-400	238	37	coloring	coloring	NOUN
fuelectenerg-400	238	38	densuty	densuty	NOUN
fuelectenerg-400	238	39	,	,	PUNCT
fuelectenerg-400	238	40	ct	ct	PROPN
fuelectenerg-400	238	41	and	and	CCONJ
fuelectenerg-400	238	42	cc	cc	PROPN
fuelectenerg-400	238	43	,	,	PUNCT
fuelectenerg-400	238	44	respectively	respectively	ADV
fuelectenerg-400	238	45	,	,	PUNCT
fuelectenerg-400	238	46	as	as	ADP
fuelectenerg-400	238	47	c(1,∞	c(1,∞	PROPN
fuelectenerg-400	238	48	)	)	PUNCT
fuelectenerg-400	238	49	≥	≥	NOUN
fuelectenerg-400	239	1	ct	ct	NUM
fuelectenerg-400	240	1	+	+	NUM
fuelectenerg-400	240	2	cc	cc	X
fuelectenerg-400	240	3	(	(	PUNCT
fuelectenerg-400	240	4	5	5	NUM
fuelectenerg-400	240	5	)	)	PUNCT
fuelectenerg-400	240	6	detection	detection	NOUN
fuelectenerg-400	240	7	and	and	CCONJ
fuelectenerg-400	240	8	coding	code	VERB
fuelectenerg-400	240	9	for	for	ADP
fuelectenerg-400	240	10	tdmr	tdmr	NOUN
fuelectenerg-400	240	11	channel	channel	NOUN
fuelectenerg-400	240	12	527	527	NUM
fuelectenerg-400	240	13	to	to	PART
fuelectenerg-400	240	14	estimate	estimate	VERB
fuelectenerg-400	240	15	capacity	capacity	NOUN
fuelectenerg-400	240	16	of	of	ADP
fuelectenerg-400	240	17	lozenge	lozenge	NOUN
fuelectenerg-400	240	18	tiling	tile	VERB
fuelectenerg-400	240	19	we	we	PRON
fuelectenerg-400	240	20	make	make	VERB
fuelectenerg-400	240	21	use	use	NOUN
fuelectenerg-400	240	22	of	of	ADP
fuelectenerg-400	240	23	the	the	DET
fuelectenerg-400	240	24	bijection	bijection	NOUN
fuelectenerg-400	240	25	between	between	ADP
fuelectenerg-400	240	26	the	the	DET
fuelectenerg-400	240	27	two	two	NUM
fuelectenerg-400	240	28	enumeration	enumeration	NOUN
fuelectenerg-400	240	29	problems	problem	NOUN
fuelectenerg-400	240	30	:	:	PUNCT
fuelectenerg-400	240	31	the	the	DET
fuelectenerg-400	240	32	counting	counting	NOUN
fuelectenerg-400	240	33	of	of	ADP
fuelectenerg-400	240	34	lozenge	lozenge	NOUN
fuelectenerg-400	240	35	tiling	tiling	NOUN
fuelectenerg-400	240	36	and	and	CCONJ
fuelectenerg-400	240	37	the	the	DET
fuelectenerg-400	240	38	counting	counting	NOUN
fuelectenerg-400	240	39	of	of	ADP
fuelectenerg-400	240	40	boxed	boxed	ADJ
fuelectenerg-400	240	41	plane	plane	NOUN
fuelectenerg-400	240	42	partition	partition	NOUN
fuelectenerg-400	240	43	.	.	PUNCT
fuelectenerg-400	241	1	then	then	ADV
fuelectenerg-400	241	2	,	,	PUNCT
fuelectenerg-400	241	3	we	we	PRON
fuelectenerg-400	241	4	will	will	AUX
fuelectenerg-400	241	5	make	make	VERB
fuelectenerg-400	241	6	use	use	NOUN
fuelectenerg-400	241	7	of	of	ADP
fuelectenerg-400	241	8	the	the	DET
fuelectenerg-400	241	9	work	work	NOUN
fuelectenerg-400	241	10	of	of	ADP
fuelectenerg-400	241	11	macmahon	macmahon	PROPN
fuelectenerg-400	241	12	on	on	ADP
fuelectenerg-400	241	13	calculating	calculate	VERB
fuelectenerg-400	241	14	the	the	DET
fuelectenerg-400	241	15	number	number	NOUN
fuelectenerg-400	241	16	of	of	ADP
fuelectenerg-400	241	17	boxed	boxed	ADJ
fuelectenerg-400	241	18	plane	plane	NOUN
fuelectenerg-400	241	19	partition	partition	NOUN
fuelectenerg-400	241	20	[	[	X
fuelectenerg-400	241	21	16	16	NUM
fuelectenerg-400	241	22	]	]	PUNCT
fuelectenerg-400	241	23	to	to	PART
fuelectenerg-400	241	24	determine	determine	VERB
fuelectenerg-400	241	25	ct	ct	PROPN
fuelectenerg-400	241	26	.	.	PUNCT
fuelectenerg-400	242	1	before	before	ADP
fuelectenerg-400	242	2	this	this	PRON
fuelectenerg-400	242	3	,	,	PUNCT
fuelectenerg-400	242	4	we	we	PRON
fuelectenerg-400	242	5	briefly	briefly	ADV
fuelectenerg-400	242	6	discuss	discuss	VERB
fuelectenerg-400	242	7	the	the	DET
fuelectenerg-400	242	8	problem	problem	NOUN
fuelectenerg-400	242	9	of	of	ADP
fuelectenerg-400	242	10	enumeration	enumeration	NOUN
fuelectenerg-400	242	11	of	of	ADP
fuelectenerg-400	242	12	boxed	boxed	ADJ
fuelectenerg-400	242	13	plane	plane	NOUN
fuelectenerg-400	242	14	partition	partition	NOUN
fuelectenerg-400	242	15	.	.	PUNCT
fuelectenerg-400	243	1	the	the	DET
fuelectenerg-400	243	2	use	use	NOUN
fuelectenerg-400	243	3	of	of	ADP
fuelectenerg-400	243	4	colored	colored	ADJ
fuelectenerg-400	243	5	tilings	tiling	NOUN
fuelectenerg-400	243	6	to	to	PART
fuelectenerg-400	243	7	estimate	estimate	VERB
fuelectenerg-400	243	8	capacity	capacity	NOUN
fuelectenerg-400	243	9	is	be	AUX
fuelectenerg-400	243	10	attractive	attractive	ADJ
fuelectenerg-400	243	11	due	due	ADP
fuelectenerg-400	243	12	to	to	ADP
fuelectenerg-400	243	13	the	the	DET
fuelectenerg-400	243	14	fact	fact	NOUN
fuelectenerg-400	243	15	that	that	SCONJ
fuelectenerg-400	243	16	the	the	DET
fuelectenerg-400	243	17	theory	theory	NOUN
fuelectenerg-400	243	18	of	of	ADP
fuelectenerg-400	243	19	counting	count	VERB
fuelectenerg-400	243	20	domino	domino	NOUN
fuelectenerg-400	243	21	tilings	tiling	NOUN
fuelectenerg-400	243	22	is	be	AUX
fuelectenerg-400	243	23	well	well	ADV
fuelectenerg-400	243	24	-	-	PUNCT
fuelectenerg-400	243	25	explored	explore	VERB
fuelectenerg-400	243	26	[	[	X
fuelectenerg-400	243	27	17,18	17,18	NUM
fuelectenerg-400	243	28	]	]	PUNCT
fuelectenerg-400	243	29	.	.	PUNCT
fuelectenerg-400	244	1	early	early	ADJ
fuelectenerg-400	244	2	work	work	NOUN
fuelectenerg-400	244	3	in	in	ADP
fuelectenerg-400	244	4	counting	count	VERB
fuelectenerg-400	244	5	domino	domino	NOUN
fuelectenerg-400	244	6	tilings	tiling	NOUN
fuelectenerg-400	244	7	includes	include	VERB
fuelectenerg-400	244	8	the	the	DET
fuelectenerg-400	244	9	work	work	NOUN
fuelectenerg-400	244	10	of	of	ADP
fuelectenerg-400	244	11	kasteleyn	kasteleyn	NOUN
fuelectenerg-400	244	12	[	[	X
fuelectenerg-400	244	13	19	19	NUM
fuelectenerg-400	244	14	]	]	PUNCT
fuelectenerg-400	244	15	,	,	PUNCT
fuelectenerg-400	244	16	who	who	PRON
fuelectenerg-400	244	17	calculated	calculate	VERB
fuelectenerg-400	244	18	the	the	DET
fuelectenerg-400	244	19	number	number	NOUN
fuelectenerg-400	244	20	of	of	ADP
fuelectenerg-400	244	21	domino	domino	NOUN
fuelectenerg-400	244	22	tilings	tiling	NOUN
fuelectenerg-400	244	23	of	of	ADP
fuelectenerg-400	244	24	a	a	DET
fuelectenerg-400	244	25	square	square	ADJ
fuelectenerg-400	244	26	lattice	lattice	NOUN
fuelectenerg-400	244	27	.	.	PUNCT
fuelectenerg-400	245	1	another	another	DET
fuelectenerg-400	245	2	work	work	NOUN
fuelectenerg-400	245	3	is	be	AUX
fuelectenerg-400	245	4	that	that	PRON
fuelectenerg-400	245	5	of	of	ADP
fuelectenerg-400	245	6	macmahon	macmahon	PROPN
fuelectenerg-400	246	1	[	[	X
fuelectenerg-400	246	2	16	16	NUM
fuelectenerg-400	246	3	]	]	PUNCT
fuelectenerg-400	246	4	in	in	ADP
fuelectenerg-400	246	5	which	which	PRON
fuelectenerg-400	246	6	the	the	DET
fuelectenerg-400	246	7	number	number	NOUN
fuelectenerg-400	246	8	of	of	ADP
fuelectenerg-400	246	9	lozenge	lozenge	ADJ
fuelectenerg-400	246	10	tilings	tiling	NOUN
fuelectenerg-400	246	11	of	of	ADP
fuelectenerg-400	246	12	a	a	DET
fuelectenerg-400	246	13	hexagon	hexagon	NOUN
fuelectenerg-400	246	14	embedded	embed	VERB
fuelectenerg-400	246	15	in	in	ADP
fuelectenerg-400	246	16	a	a	DET
fuelectenerg-400	246	17	triangular	triangular	NOUN
fuelectenerg-400	246	18	lattice	lattice	NOUN
fuelectenerg-400	246	19	was	be	AUX
fuelectenerg-400	246	20	calculated	calculate	VERB
fuelectenerg-400	246	21	.	.	PUNCT
fuelectenerg-400	247	1	desreux	desreux	NOUN
fuelectenerg-400	247	2	and	and	CCONJ
fuelectenerg-400	247	3	remila	remila	NOUN
fuelectenerg-400	248	1	[	[	X
fuelectenerg-400	248	2	20	20	NUM
fuelectenerg-400	248	3	]	]	PUNCT
fuelectenerg-400	248	4	gave	give	VERB
fuelectenerg-400	248	5	optimal	optimal	ADJ
fuelectenerg-400	248	6	algorithms	algorithm	NOUN
fuelectenerg-400	248	7	for	for	ADP
fuelectenerg-400	248	8	the	the	DET
fuelectenerg-400	248	9	generation	generation	NOUN
fuelectenerg-400	248	10	of	of	ADP
fuelectenerg-400	248	11	domino	domino	NOUN
fuelectenerg-400	248	12	tilings	tiling	NOUN
fuelectenerg-400	248	13	and	and	CCONJ
fuelectenerg-400	248	14	lozenge	lozenge	ADJ
fuelectenerg-400	248	15	tilings	tiling	NOUN
fuelectenerg-400	248	16	.	.	PUNCT
fuelectenerg-400	249	1	4.1	4.1	NUM
fuelectenerg-400	249	2	a	a	DET
fuelectenerg-400	249	3	method	method	NOUN
fuelectenerg-400	249	4	based	base	VERB
fuelectenerg-400	249	5	on	on	ADP
fuelectenerg-400	249	6	boxed	boxed	ADJ
fuelectenerg-400	249	7	plane	plane	NOUN
fuelectenerg-400	249	8	partitions	partition	NOUN
fuelectenerg-400	249	9	a	a	DET
fuelectenerg-400	249	10	plane	plane	NOUN
fuelectenerg-400	249	11	partition	partition	NOUN
fuelectenerg-400	249	12	π	π	NOUN
fuelectenerg-400	249	13	is	be	AUX
fuelectenerg-400	249	14	a	a	DET
fuelectenerg-400	249	15	collection	collection	NOUN
fuelectenerg-400	249	16	of	of	ADP
fuelectenerg-400	249	17	non	non	ADJ
fuelectenerg-400	249	18	-	-	ADJ
fuelectenerg-400	249	19	negative	negative	ADJ
fuelectenerg-400	249	20	integers	integer	NOUN
fuelectenerg-400	249	21	πx	πx	NOUN
fuelectenerg-400	249	22	,	,	PUNCT
fuelectenerg-400	249	23	y	y	PROPN
fuelectenerg-400	249	24	indexed	index	VERB
fuelectenerg-400	249	25	by	by	ADP
fuelectenerg-400	249	26	non	non	ADJ
fuelectenerg-400	249	27	-	-	ADJ
fuelectenerg-400	249	28	negative	negative	ADJ
fuelectenerg-400	249	29	integers	integer	NOUN
fuelectenerg-400	249	30	x	x	X
fuelectenerg-400	249	31	,	,	PUNCT
fuelectenerg-400	249	32	y	y	PROPN
fuelectenerg-400	249	33	such	such	ADJ
fuelectenerg-400	249	34	that	that	SCONJ
fuelectenerg-400	249	35	(	(	PUNCT
fuelectenerg-400	249	36	a	a	X
fuelectenerg-400	249	37	)	)	PUNCT
fuelectenerg-400	249	38	only	only	ADV
fuelectenerg-400	249	39	finite	finite	ADJ
fuelectenerg-400	249	40	number	number	NOUN
fuelectenerg-400	249	41	of	of	ADP
fuelectenerg-400	249	42	πx	πx	NOUN
fuelectenerg-400	249	43	,	,	PUNCT
fuelectenerg-400	249	44	y	y	PROPN
fuelectenerg-400	249	45	are	be	AUX
fuelectenerg-400	249	46	non	non	ADJ
fuelectenerg-400	249	47	-	-	ADJ
fuelectenerg-400	249	48	zero	zero	NUM
fuelectenerg-400	249	49	and	and	CCONJ
fuelectenerg-400	249	50	,	,	PUNCT
fuelectenerg-400	249	51	(	(	PUNCT
fuelectenerg-400	249	52	b	b	X
fuelectenerg-400	249	53	)	)	PUNCT
fuelectenerg-400	249	54	∀x	∀x	NUM
fuelectenerg-400	249	55	,	,	PUNCT
fuelectenerg-400	249	56	y	y	PROPN
fuelectenerg-400	249	57	πx	πx	PROPN
fuelectenerg-400	249	58	,	,	PUNCT
fuelectenerg-400	249	59	y	y	PROPN
fuelectenerg-400	249	60	≤	≤	NUM
fuelectenerg-400	249	61	πx	πx	ADP
fuelectenerg-400	249	62	,	,	PUNCT
fuelectenerg-400	249	63	y+1	y+1	PRON
fuelectenerg-400	249	64	and	and	CCONJ
fuelectenerg-400	249	65	πx	πx	ADJ
fuelectenerg-400	249	66	,	,	PUNCT
fuelectenerg-400	249	67	y	y	PROPN
fuelectenerg-400	249	68	≤	≤	PROPN
fuelectenerg-400	249	69	πx+1,y	πx+1,y	PROPN
fuelectenerg-400	249	70	.	.	PUNCT
fuelectenerg-400	250	1	the	the	DET
fuelectenerg-400	250	2	plane	plane	NOUN
fuelectenerg-400	250	3	partition	partition	NOUN
fuelectenerg-400	250	4	is	be	AUX
fuelectenerg-400	250	5	said	say	VERB
fuelectenerg-400	250	6	to	to	PART
fuelectenerg-400	250	7	fit	fit	VERB
fuelectenerg-400	250	8	inside	inside	ADP
fuelectenerg-400	250	9	a	a	DET
fuelectenerg-400	250	10	box	box	NOUN
fuelectenerg-400	250	11	of	of	ADP
fuelectenerg-400	250	12	dimension	dimension	NOUN
fuelectenerg-400	250	13	a	a	DET
fuelectenerg-400	250	14	×	×	NOUN
fuelectenerg-400	250	15	b	b	NOUN
fuelectenerg-400	250	16	×	×	NOUN
fuelectenerg-400	250	17	c	c	NOUN
fuelectenerg-400	251	1	if	if	SCONJ
fuelectenerg-400	251	2	there	there	PRON
fuelectenerg-400	251	3	exist	exist	VERB
fuelectenerg-400	251	4	integers	integer	NOUN
fuelectenerg-400	251	5	a	a	DET
fuelectenerg-400	251	6	,	,	PUNCT
fuelectenerg-400	251	7	b	b	NOUN
fuelectenerg-400	251	8	,	,	PUNCT
fuelectenerg-400	251	9	c	c	X
fuelectenerg-400	251	10	such	such	ADJ
fuelectenerg-400	251	11	that	that	SCONJ
fuelectenerg-400	251	12	πx	πx	NOUN
fuelectenerg-400	251	13	,	,	PUNCT
fuelectenerg-400	251	14	y	y	PROPN
fuelectenerg-400	251	15	≤	≤	PROPN
fuelectenerg-400	251	16	c	c	NOUN
fuelectenerg-400	251	17	for	for	ADP
fuelectenerg-400	251	18	all	all	DET
fuelectenerg-400	251	19	x	x	NOUN
fuelectenerg-400	251	20	,	,	PUNCT
fuelectenerg-400	251	21	y	y	PROPN
fuelectenerg-400	251	22	and	and	CCONJ
fuelectenerg-400	251	23	πx	πx	PROPN
fuelectenerg-400	251	24	,	,	PUNCT
fuelectenerg-400	251	25	y	y	PROPN
fuelectenerg-400	251	26	=	=	NOUN
fuelectenerg-400	251	27	0	0	NUM
fuelectenerg-400	251	28	for	for	ADP
fuelectenerg-400	251	29	all	all	PRON
fuelectenerg-400	252	1	x	x	SYM
fuelectenerg-400	252	2	>	>	X
fuelectenerg-400	252	3	a	a	X
fuelectenerg-400	252	4	,	,	PUNCT
fuelectenerg-400	252	5	y	y	PROPN
fuelectenerg-400	252	6	>	>	X
fuelectenerg-400	252	7	b.	b.	PROPN
fuelectenerg-400	253	1	such	such	ADJ
fuelectenerg-400	253	2	partitions	partition	NOUN
fuelectenerg-400	253	3	are	be	AUX
fuelectenerg-400	253	4	called	call	VERB
fuelectenerg-400	253	5	boxed	boxed	ADJ
fuelectenerg-400	253	6	plane	plane	NOUN
fuelectenerg-400	253	7	partitions	partition	NOUN
fuelectenerg-400	253	8	.	.	PUNCT
fuelectenerg-400	254	1	a	a	DET
fuelectenerg-400	254	2	more	more	ADV
fuelectenerg-400	254	3	intuitive	intuitive	ADJ
fuelectenerg-400	254	4	way	way	NOUN
fuelectenerg-400	254	5	of	of	ADP
fuelectenerg-400	254	6	visualizing	visualize	VERB
fuelectenerg-400	254	7	the	the	DET
fuelectenerg-400	254	8	boxed	box	VERB
fuelectenerg-400	254	9	plane	plane	NOUN
fuelectenerg-400	254	10	partitions	partition	NOUN
fuelectenerg-400	254	11	is	be	AUX
fuelectenerg-400	254	12	by	by	ADP
fuelectenerg-400	254	13	constructing	construct	VERB
fuelectenerg-400	254	14	the	the	DET
fuelectenerg-400	254	15	young	young	ADJ
fuelectenerg-400	254	16	’s	’s	PART
fuelectenerg-400	254	17	solid	solid	ADJ
fuelectenerg-400	254	18	diagram	diagram	NOUN
fuelectenerg-400	254	19	corresponding	correspond	VERB
fuelectenerg-400	254	20	to	to	ADP
fuelectenerg-400	254	21	a	a	DET
fuelectenerg-400	254	22	boxed	box	VERB
fuelectenerg-400	254	23	partition	partition	NOUN
fuelectenerg-400	254	24	π	π	NOUN
fuelectenerg-400	254	25	.	.	PUNCT
fuelectenerg-400	255	1	for	for	ADP
fuelectenerg-400	255	2	instance	instance	NOUN
fuelectenerg-400	255	3	,	,	PUNCT
fuelectenerg-400	255	4	consider	consider	VERB
fuelectenerg-400	255	5	the	the	DET
fuelectenerg-400	255	6	following	follow	VERB
fuelectenerg-400	255	7	partition	partition	NOUN
fuelectenerg-400	255	8	boxed	box	VERB
fuelectenerg-400	255	9	within	within	ADP
fuelectenerg-400	255	10	a	a	DET
fuelectenerg-400	255	11	box	box	NOUN
fuelectenerg-400	255	12	of	of	ADP
fuelectenerg-400	255	13	dimension	dimension	NOUN
fuelectenerg-400	255	14	2	2	NUM
fuelectenerg-400	255	15	×	×	NOUN
fuelectenerg-400	255	16	3	3	NUM
fuelectenerg-400	255	17	×	×	NOUN
fuelectenerg-400	255	18	4	4	NUM
fuelectenerg-400	255	19	.	.	PUNCT
fuelectenerg-400	256	1	π	π	X
fuelectenerg-400	256	2	=	=	PUNCT
fuelectenerg-400	256	3	(	(	PUNCT
fuelectenerg-400	256	4	4	4	NUM
fuelectenerg-400	256	5	2	2	NUM
fuelectenerg-400	256	6	2	2	NUM
fuelectenerg-400	256	7	2	2	NUM
fuelectenerg-400	256	8	1	1	NUM
fuelectenerg-400	256	9	1	1	NUM
fuelectenerg-400	256	10	)	)	PUNCT
fuelectenerg-400	256	11	the	the	DET
fuelectenerg-400	256	12	dimension	dimension	NOUN
fuelectenerg-400	256	13	of	of	ADP
fuelectenerg-400	256	14	the	the	DET
fuelectenerg-400	256	15	matrix	matrix	NOUN
fuelectenerg-400	256	16	is	be	AUX
fuelectenerg-400	256	17	2	2	NUM
fuelectenerg-400	256	18	×	×	NOUN
fuelectenerg-400	256	19	3	3	NUM
fuelectenerg-400	256	20	with	with	ADP
fuelectenerg-400	256	21	all	all	DET
fuelectenerg-400	256	22	entries	entry	NOUN
fuelectenerg-400	256	23	≤	≤	ADJ
fuelectenerg-400	256	24	4	4	NUM
fuelectenerg-400	256	25	.	.	PUNCT
fuelectenerg-400	256	26	to	to	PART
fuelectenerg-400	256	27	build	build	VERB
fuelectenerg-400	256	28	its	its	PRON
fuelectenerg-400	256	29	corresponding	corresponding	ADJ
fuelectenerg-400	256	30	young	young	ADJ
fuelectenerg-400	256	31	’s	’s	PART
fuelectenerg-400	256	32	solid	solid	ADJ
fuelectenerg-400	256	33	diagram	diagram	NOUN
fuelectenerg-400	256	34	,	,	PUNCT
fuelectenerg-400	256	35	we	we	PRON
fuelectenerg-400	256	36	first	first	ADV
fuelectenerg-400	256	37	consider	consider	VERB
fuelectenerg-400	256	38	a	a	DET
fuelectenerg-400	256	39	box	box	NOUN
fuelectenerg-400	256	40	of	of	ADP
fuelectenerg-400	256	41	dimension	dimension	NOUN
fuelectenerg-400	256	42	2×3×4	2×3×4	NOUN
fuelectenerg-400	256	43	.	.	PUNCT
fuelectenerg-400	257	1	to	to	ADP
fuelectenerg-400	257	2	one	one	NUM
fuelectenerg-400	257	3	of	of	ADP
fuelectenerg-400	257	4	the	the	DET
fuelectenerg-400	257	5	vertices	vertex	NOUN
fuelectenerg-400	257	6	,	,	PUNCT
fuelectenerg-400	257	7	we	we	PRON
fuelectenerg-400	257	8	assign	assign	VERB
fuelectenerg-400	257	9	the	the	DET
fuelectenerg-400	257	10	cartesian	cartesian	ADJ
fuelectenerg-400	257	11	co	co	NOUN
fuelectenerg-400	257	12	-	-	NOUN
fuelectenerg-400	257	13	ordinate	ordinate	ADJ
fuelectenerg-400	257	14	(	(	PUNCT
fuelectenerg-400	257	15	0	0	NUM
fuelectenerg-400	257	16	,	,	PUNCT
fuelectenerg-400	257	17	0	0	NUM
fuelectenerg-400	257	18	,	,	PUNCT
fuelectenerg-400	257	19	0	0	NUM
fuelectenerg-400	257	20	)	)	PUNCT
fuelectenerg-400	257	21	.	.	PUNCT
fuelectenerg-400	258	1	to	to	ADP
fuelectenerg-400	258	2	the	the	DET
fuelectenerg-400	258	3	opposite	opposite	ADJ
fuelectenerg-400	258	4	vertex	vertex	NOUN
fuelectenerg-400	258	5	we	we	PRON
fuelectenerg-400	258	6	assign	assign	VERB
fuelectenerg-400	258	7	the	the	DET
fuelectenerg-400	258	8	co	co	NOUN
fuelectenerg-400	258	9	-	-	NOUN
fuelectenerg-400	258	10	ordinate	ordinate	NOUN
fuelectenerg-400	258	11	(	(	PUNCT
fuelectenerg-400	258	12	2	2	NUM
fuelectenerg-400	258	13	,	,	PUNCT
fuelectenerg-400	258	14	3	3	NUM
fuelectenerg-400	258	15	,	,	PUNCT
fuelectenerg-400	258	16	4	4	NUM
fuelectenerg-400	258	17	)	)	PUNCT
fuelectenerg-400	258	18	.	.	PUNCT
fuelectenerg-400	259	1	for	for	ADP
fuelectenerg-400	259	2	each	each	DET
fuelectenerg-400	259	3	x	x	SYM
fuelectenerg-400	259	4	≤	≤	NOUN
fuelectenerg-400	259	5	2	2	NUM
fuelectenerg-400	259	6	,	,	PUNCT
fuelectenerg-400	259	7	y	y	PROPN
fuelectenerg-400	259	8	≤	≤	PROPN
fuelectenerg-400	259	9	3	3	NUM
fuelectenerg-400	259	10	,	,	PUNCT
fuelectenerg-400	259	11	we	we	PRON
fuelectenerg-400	259	12	start	start	VERB
fuelectenerg-400	259	13	at	at	ADP
fuelectenerg-400	259	14	(	(	PUNCT
fuelectenerg-400	259	15	x	x	SYM
fuelectenerg-400	259	16	−	−	PROPN
fuelectenerg-400	259	17	1	1	NUM
fuelectenerg-400	259	18	,	,	PUNCT
fuelectenerg-400	259	19	y	y	PROPN
fuelectenerg-400	259	20	−	−	PROPN
fuelectenerg-400	259	21	1	1	NUM
fuelectenerg-400	259	22	,	,	PUNCT
fuelectenerg-400	259	23	0	0	NUM
fuelectenerg-400	259	24	)	)	PUNCT
fuelectenerg-400	259	25	and	and	CCONJ
fuelectenerg-400	259	26	stack	stack	VERB
fuelectenerg-400	259	27	πx	πx	NOUN
fuelectenerg-400	259	28	,	,	PUNCT
fuelectenerg-400	259	29	y	y	PROPN
fuelectenerg-400	259	30	cubes	cube	NOUN
fuelectenerg-400	259	31	of	of	ADP
fuelectenerg-400	259	32	unit	unit	NOUN
fuelectenerg-400	259	33	side	side	NOUN
fuelectenerg-400	259	34	length	length	NOUN
fuelectenerg-400	259	35	.	.	PUNCT
fuelectenerg-400	260	1	this	this	DET
fuelectenerg-400	260	2	construction	construction	NOUN
fuelectenerg-400	260	3	will	will	AUX
fuelectenerg-400	260	4	fit	fit	VERB
fuelectenerg-400	260	5	inside	inside	ADP
fuelectenerg-400	260	6	the	the	DET
fuelectenerg-400	260	7	box	box	NOUN
fuelectenerg-400	260	8	.	.	PUNCT
fuelectenerg-400	261	1	fig	fig	NOUN
fuelectenerg-400	261	2	.	.	PUNCT
fuelectenerg-400	262	1	5	5	X
fuelectenerg-400	262	2	.	.	X
fuelectenerg-400	262	3	tiling	tile	VERB
fuelectenerg-400	262	4	corresponding	correspond	VERB
fuelectenerg-400	262	5	to	to	ADP
fuelectenerg-400	262	6	the	the	DET
fuelectenerg-400	262	7	boxed	box	VERB
fuelectenerg-400	262	8	plane	plane	NOUN
fuelectenerg-400	262	9	partition	partition	NOUN
fuelectenerg-400	262	10	π	π	NOUN
fuelectenerg-400	262	11	.	.	PUNCT
fuelectenerg-400	263	1	the	the	DET
fuelectenerg-400	263	2	tiling	tiling	NOUN
fuelectenerg-400	263	3	given	give	VERB
fuelectenerg-400	263	4	in	in	ADP
fuelectenerg-400	263	5	fig	fig	NOUN
fuelectenerg-400	263	6	.	.	PUNCT
fuelectenerg-400	264	1	5	5	NUM
fuelectenerg-400	264	2	corresponds	correspond	NOUN
fuelectenerg-400	264	3	to	to	ADP
fuelectenerg-400	264	4	the	the	DET
fuelectenerg-400	264	5	boxed	box	VERB
fuelectenerg-400	264	6	plane	plane	NOUN
fuelectenerg-400	264	7	partition	partition	NOUN
fuelectenerg-400	264	8	π	π	PROPN
fuelectenerg-400	264	9	given	give	VERB
fuelectenerg-400	264	10	526	526	NUM
fuelectenerg-400	264	11	b.	b.	NOUN
fuelectenerg-400	264	12	vasic	vasic	NOUN
fuelectenerg-400	264	13	,	,	PUNCT
fuelectenerg-400	264	14	a.	a.	PROPN
fuelectenerg-400	264	15	r.	r.	PROPN
fuelectenerg-400	264	16	krishnan	krishnan	PROPN
fuelectenerg-400	264	17	lozenge	lozenge	PROPN
fuelectenerg-400	264	18	tiling	tile	VERB
fuelectenerg-400	264	19	constrained	constrained	ADJ
fuelectenerg-400	264	20	codes	code	NOUN
fuelectenerg-400	264	21	527	527	NUM
fuelectenerg-400	264	22	526	526	NUM
fuelectenerg-400	264	23	a.	a.	NOUN
fuelectenerg-400	264	24	r.	r.	PROPN
fuelectenerg-400	264	25	krishnanan	krishnanan	PROPN
fuelectenerg-400	264	26	and	and	CCONJ
fuelectenerg-400	264	27	b.	b.	PROPN
fuelectenerg-400	264	28	vasić	vasić	PROPN
fuelectenerg-400	264	29	(	(	PUNCT
fuelectenerg-400	264	30	a	a	X
fuelectenerg-400	264	31	)	)	PUNCT
fuelectenerg-400	264	32	(	(	PUNCT
fuelectenerg-400	264	33	b	b	X
fuelectenerg-400	264	34	)	)	PUNCT
fuelectenerg-400	264	35	(	(	PUNCT
fuelectenerg-400	264	36	c	c	X
fuelectenerg-400	264	37	)	)	PUNCT
fuelectenerg-400	264	38	fig	fig	NOUN
fuelectenerg-400	264	39	.	.	PUNCT
fuelectenerg-400	265	1	4	4	X
fuelectenerg-400	265	2	.	.	X
fuelectenerg-400	265	3	colored	color	VERB
fuelectenerg-400	265	4	lozenge	lozenge	NOUN
fuelectenerg-400	265	5	tilings	tiling	NOUN
fuelectenerg-400	265	6	in	in	ADP
fuelectenerg-400	265	7	a	a	DET
fuelectenerg-400	265	8	triangular	triangular	NOUN
fuelectenerg-400	265	9	lattice	lattice	NOUN
fuelectenerg-400	265	10	:	:	PUNCT
fuelectenerg-400	265	11	(	(	PUNCT
fuelectenerg-400	265	12	a	a	X
fuelectenerg-400	265	13	)	)	PUNCT
fuelectenerg-400	265	14	a	a	DET
fuelectenerg-400	265	15	hexagon	hexagon	NOUN
fuelectenerg-400	265	16	with	with	ADP
fuelectenerg-400	265	17	side	side	NOUN
fuelectenerg-400	265	18	-	-	PUNCT
fuelectenerg-400	265	19	length	length	NOUN
fuelectenerg-400	265	20	of	of	ADP
fuelectenerg-400	265	21	6	6	NUM
fuelectenerg-400	265	22	embedded	embed	VERB
fuelectenerg-400	265	23	in	in	ADP
fuelectenerg-400	265	24	a	a	DET
fuelectenerg-400	265	25	triangular	triangular	NOUN
fuelectenerg-400	265	26	lattice	lattice	NOUN
fuelectenerg-400	265	27	.	.	PUNCT
fuelectenerg-400	266	1	(	(	PUNCT
fuelectenerg-400	266	2	b	b	X
fuelectenerg-400	266	3	)	)	PUNCT
fuelectenerg-400	266	4	an	an	DET
fuelectenerg-400	266	5	uncolored	uncolored	ADJ
fuelectenerg-400	266	6	lozenge	lozenge	NOUN
fuelectenerg-400	266	7	tiling	tiling	NOUN
fuelectenerg-400	266	8	of	of	ADP
fuelectenerg-400	266	9	the	the	DET
fuelectenerg-400	266	10	hexagon	hexagon	NOUN
fuelectenerg-400	266	11	.	.	PUNCT
fuelectenerg-400	267	1	(	(	PUNCT
fuelectenerg-400	267	2	c	c	X
fuelectenerg-400	267	3	)	)	PUNCT
fuelectenerg-400	267	4	a	a	DET
fuelectenerg-400	267	5	colored	colored	ADJ
fuelectenerg-400	267	6	lozenge	lozenge	NOUN
fuelectenerg-400	267	7	tiling	tiling	NOUN
fuelectenerg-400	267	8	of	of	ADP
fuelectenerg-400	267	9	the	the	DET
fuelectenerg-400	267	10	hexagon	hexagon	NOUN
fuelectenerg-400	267	11	.	.	PUNCT
fuelectenerg-400	268	1	4	4	NUM
fuelectenerg-400	268	2	bounds	bound	NOUN
fuelectenerg-400	268	3	on	on	ADP
fuelectenerg-400	268	4	capacity	capacity	NOUN
fuelectenerg-400	268	5	for	for	ADP
fuelectenerg-400	268	6	the	the	DET
fuelectenerg-400	268	7	nib	nib	NOUN
fuelectenerg-400	268	8	constraint	constraint	NOUN
fuelectenerg-400	268	9	defined	define	VERB
fuelectenerg-400	268	10	above	above	ADV
fuelectenerg-400	268	11	,	,	PUNCT
fuelectenerg-400	268	12	we	we	PRON
fuelectenerg-400	268	13	can	can	AUX
fuelectenerg-400	268	14	define	define	VERB
fuelectenerg-400	268	15	the	the	DET
fuelectenerg-400	268	16	shannon	shannon	PROPN
fuelectenerg-400	268	17	noiseless	noiseless	PROPN
fuelectenerg-400	268	18	capacity	capacity	NOUN
fuelectenerg-400	268	19	using	use	VERB
fuelectenerg-400	268	20	an	an	DET
fuelectenerg-400	268	21	(	(	PUNCT
fuelectenerg-400	268	22	n	n	CCONJ
fuelectenerg-400	268	23	,	,	PUNCT
fuelectenerg-400	268	24	n	n	CCONJ
fuelectenerg-400	268	25	,	,	PUNCT
fuelectenerg-400	268	26	n	n	CCONJ
fuelectenerg-400	268	27	)	)	PUNCT
fuelectenerg-400	268	28	hexagon	hexagon	NOUN
fuelectenerg-400	268	29	as	as	SCONJ
fuelectenerg-400	268	30	follows	follow	VERB
fuelectenerg-400	268	31	:	:	PUNCT
fuelectenerg-400	268	32	c	c	X
fuelectenerg-400	268	33	=	=	SYM
fuelectenerg-400	268	34	lim	lim	PROPN
fuelectenerg-400	268	35	n→∞	n→∞	NUM
fuelectenerg-400	269	1	log2	log2	PROPN
fuelectenerg-400	269	2	m(n	m(n	PROPN
fuelectenerg-400	269	3	,	,	PUNCT
fuelectenerg-400	269	4	n	n	CCONJ
fuelectenerg-400	269	5	,	,	PUNCT
fuelectenerg-400	269	6	n	n	CCONJ
fuelectenerg-400	269	7	)	)	PUNCT
fuelectenerg-400	269	8	log226n2	log226n2	ADV
fuelectenerg-400	269	9	(	(	PUNCT
fuelectenerg-400	269	10	1	1	NUM
fuelectenerg-400	269	11	)	)	PUNCT
fuelectenerg-400	269	12	=	=	VERB
fuelectenerg-400	270	1	lim	lim	PROPN
fuelectenerg-400	270	2	n→∞	n→∞	NUM
fuelectenerg-400	270	3	log2	log2	PROPN
fuelectenerg-400	270	4	m(n	m(n	PROPN
fuelectenerg-400	270	5	,	,	PUNCT
fuelectenerg-400	270	6	n	n	CCONJ
fuelectenerg-400	270	7	,	,	PUNCT
fuelectenerg-400	270	8	n	n	CCONJ
fuelectenerg-400	270	9	)	)	PUNCT
fuelectenerg-400	270	10	6n2	6n2	NUM
fuelectenerg-400	270	11	.	.	PUNCT
fuelectenerg-400	271	1	(	(	PUNCT
fuelectenerg-400	271	2	2	2	X
fuelectenerg-400	271	3	)	)	PUNCT
fuelectenerg-400	271	4	note	note	NOUN
fuelectenerg-400	271	5	that	that	SCONJ
fuelectenerg-400	271	6	since	since	SCONJ
fuelectenerg-400	271	7	the	the	DET
fuelectenerg-400	271	8	number	number	NOUN
fuelectenerg-400	271	9	of	of	ADP
fuelectenerg-400	271	10	triangles	triangle	NOUN
fuelectenerg-400	271	11	constituting	constitute	VERB
fuelectenerg-400	271	12	the	the	DET
fuelectenerg-400	271	13	(	(	PUNCT
fuelectenerg-400	271	14	n	n	X
fuelectenerg-400	271	15	,	,	PUNCT
fuelectenerg-400	271	16	n	n	CCONJ
fuelectenerg-400	271	17	,	,	PUNCT
fuelectenerg-400	271	18	n	n	CCONJ
fuelectenerg-400	271	19	)	)	PUNCT
fuelectenerg-400	271	20	hexagon	hexagon	PROPN
fuelectenerg-400	271	21	is	be	AUX
fuelectenerg-400	271	22	6n2	6n2	NUM
fuelectenerg-400	271	23	,	,	PUNCT
fuelectenerg-400	271	24	in	in	ADP
fuelectenerg-400	271	25	eqn	eqn	NOUN
fuelectenerg-400	271	26	.	.	PUNCT
fuelectenerg-400	272	1	1	1	NUM
fuelectenerg-400	272	2	,	,	PUNCT
fuelectenerg-400	272	3	the	the	DET
fuelectenerg-400	272	4	denominator	denominator	NOUN
fuelectenerg-400	272	5	is	be	AUX
fuelectenerg-400	272	6	logarithm	logarithm	NOUN
fuelectenerg-400	272	7	of	of	ADP
fuelectenerg-400	272	8	the	the	DET
fuelectenerg-400	272	9	total	total	ADJ
fuelectenerg-400	272	10	number	number	NOUN
fuelectenerg-400	272	11	of	of	ADP
fuelectenerg-400	272	12	independent	independent	ADJ
fuelectenerg-400	272	13	colorings	coloring	NOUN
fuelectenerg-400	272	14	of	of	ADP
fuelectenerg-400	272	15	the	the	DET
fuelectenerg-400	272	16	constituent	constituent	NOUN
fuelectenerg-400	272	17	triangles	triangle	NOUN
fuelectenerg-400	272	18	.	.	PUNCT
fuelectenerg-400	273	1	the	the	DET
fuelectenerg-400	273	2	numerator	numerator	NOUN
fuelectenerg-400	273	3	m(n	m(n	PROPN
fuelectenerg-400	273	4	,	,	PUNCT
fuelectenerg-400	273	5	n	n	CCONJ
fuelectenerg-400	273	6	,	,	PUNCT
fuelectenerg-400	273	7	n	n	CCONJ
fuelectenerg-400	273	8	)	)	PUNCT
fuelectenerg-400	273	9	is	be	AUX
fuelectenerg-400	273	10	the	the	DET
fuelectenerg-400	273	11	logarithm	logarithm	NOUN
fuelectenerg-400	273	12	of	of	ADP
fuelectenerg-400	273	13	the	the	DET
fuelectenerg-400	273	14	number	number	NOUN
fuelectenerg-400	273	15	of	of	ADP
fuelectenerg-400	273	16	colorings	coloring	NOUN
fuelectenerg-400	273	17	of	of	ADP
fuelectenerg-400	273	18	the	the	DET
fuelectenerg-400	273	19	constituent	constituent	NOUN
fuelectenerg-400	273	20	triangles	triangle	NOUN
fuelectenerg-400	273	21	that	that	PRON
fuelectenerg-400	273	22	satisfy	satisfy	VERB
fuelectenerg-400	273	23	the	the	DET
fuelectenerg-400	273	24	nib	nib	NOUN
fuelectenerg-400	273	25	constraint	constraint	NOUN
fuelectenerg-400	273	26	.	.	PUNCT
fuelectenerg-400	274	1	similarly	similarly	ADV
fuelectenerg-400	274	2	,	,	PUNCT
fuelectenerg-400	274	3	if	if	SCONJ
fuelectenerg-400	274	4	n(n	n(n	PROPN
fuelectenerg-400	274	5	,	,	PUNCT
fuelectenerg-400	274	6	n	n	CCONJ
fuelectenerg-400	274	7	,	,	PUNCT
fuelectenerg-400	274	8	n	n	CCONJ
fuelectenerg-400	274	9	)	)	PUNCT
fuelectenerg-400	274	10	denotes	denote	VERB
fuelectenerg-400	274	11	the	the	DET
fuelectenerg-400	274	12	number	number	NOUN
fuelectenerg-400	274	13	of	of	ADP
fuelectenerg-400	274	14	uncolored	uncolored	ADJ
fuelectenerg-400	274	15	patterns	pattern	NOUN
fuelectenerg-400	274	16	(	(	PUNCT
fuelectenerg-400	274	17	tilings	tiling	NOUN
fuelectenerg-400	274	18	)	)	PUNCT
fuelectenerg-400	274	19	,	,	PUNCT
fuelectenerg-400	274	20	the	the	DET
fuelectenerg-400	274	21	asymptotic	asymptotic	ADJ
fuelectenerg-400	274	22	growth	growth	NOUN
fuelectenerg-400	274	23	rate	rate	NOUN
fuelectenerg-400	274	24	of	of	ADP
fuelectenerg-400	274	25	n(n	n(n	PROPN
fuelectenerg-400	274	26	,	,	PUNCT
fuelectenerg-400	274	27	n	n	CCONJ
fuelectenerg-400	274	28	,	,	PUNCT
fuelectenerg-400	274	29	n	n	CCONJ
fuelectenerg-400	274	30	)	)	PUNCT
fuelectenerg-400	274	31	–	–	PUNCT
fuelectenerg-400	274	32	we	we	PRON
fuelectenerg-400	274	33	call	call	VERB
fuelectenerg-400	274	34	it	it	PRON
fuelectenerg-400	274	35	tiling	tile	VERB
fuelectenerg-400	274	36	capacity	capacity	NOUN
fuelectenerg-400	274	37	(	(	PUNCT
fuelectenerg-400	274	38	ct	ct	NOUN
fuelectenerg-400	274	39	)	)	PUNCT
fuelectenerg-400	274	40	is	be	AUX
fuelectenerg-400	274	41	defined	define	VERB
fuelectenerg-400	274	42	as	as	ADP
fuelectenerg-400	274	43	ct	ct	PROPN
fuelectenerg-400	274	44	=	=	PROPN
fuelectenerg-400	274	45	lim	lim	PROPN
fuelectenerg-400	274	46	n→∞	n→∞	NUM
fuelectenerg-400	274	47	log2	log2	PROPN
fuelectenerg-400	274	48	n(n	n(n	PROPN
fuelectenerg-400	274	49	,	,	PUNCT
fuelectenerg-400	274	50	n	n	CCONJ
fuelectenerg-400	274	51	,	,	PUNCT
fuelectenerg-400	274	52	n	n	CCONJ
fuelectenerg-400	274	53	)	)	PUNCT
fuelectenerg-400	274	54	log226n2	log226n2	ADV
fuelectenerg-400	274	55	.	.	PUNCT
fuelectenerg-400	275	1	(	(	PUNCT
fuelectenerg-400	275	2	3	3	X
fuelectenerg-400	275	3	)	)	PUNCT
fuelectenerg-400	275	4	finally	finally	ADV
fuelectenerg-400	275	5	,	,	PUNCT
fuelectenerg-400	275	6	we	we	PRON
fuelectenerg-400	275	7	define	define	VERB
fuelectenerg-400	275	8	a	a	DET
fuelectenerg-400	275	9	coloring	coloring	NOUN
fuelectenerg-400	275	10	capacity	capacity	NOUN
fuelectenerg-400	275	11	(	(	PUNCT
fuelectenerg-400	275	12	cc	cc	NOUN
fuelectenerg-400	275	13	)	)	PUNCT
fuelectenerg-400	275	14	based	base	VERB
fuelectenerg-400	275	15	on	on	ADP
fuelectenerg-400	275	16	the	the	DET
fuelectenerg-400	275	17	number	number	NOUN
fuelectenerg-400	275	18	of	of	ADP
fuelectenerg-400	275	19	distinct	distinct	ADJ
fuelectenerg-400	275	20	patterns	pattern	NOUN
fuelectenerg-400	275	21	,	,	PUNCT
fuelectenerg-400	275	22	i.e.	i.e.	X
fuelectenerg-400	275	23	number	number	NOUN
fuelectenerg-400	275	24	k(n	k(n	PROPN
fuelectenerg-400	275	25	,	,	PUNCT
fuelectenerg-400	275	26	n	n	CCONJ
fuelectenerg-400	275	27	,	,	PUNCT
fuelectenerg-400	275	28	n	n	CCONJ
fuelectenerg-400	275	29	)	)	PUNCT
fuelectenerg-400	275	30	of	of	ADP
fuelectenerg-400	275	31	ways	way	NOUN
fuelectenerg-400	275	32	of	of	ADP
fuelectenerg-400	275	33	distinctly	distinctly	ADV
fuelectenerg-400	275	34	coloring	color	VERB
fuelectenerg-400	275	35	a	a	DET
fuelectenerg-400	275	36	lozenge	lozenge	NOUN
fuelectenerg-400	275	37	tiling	tile	VERB
fuelectenerg-400	275	38	so	so	SCONJ
fuelectenerg-400	275	39	that	that	SCONJ
fuelectenerg-400	275	40	the	the	DET
fuelectenerg-400	275	41	constraints	constraint	NOUN
fuelectenerg-400	275	42	are	be	AUX
fuelectenerg-400	275	43	satisfied	satisfied	ADJ
fuelectenerg-400	275	44	.	.	PUNCT
fuelectenerg-400	276	1	this	this	PRON
fuelectenerg-400	276	2	is	be	AUX
fuelectenerg-400	276	3	defined	define	VERB
fuelectenerg-400	276	4	as	as	SCONJ
fuelectenerg-400	276	5	follows	follow	VERB
fuelectenerg-400	276	6	:	:	PUNCT
fuelectenerg-400	276	7	cc	cc	PROPN
fuelectenerg-400	276	8	=	=	PROPN
fuelectenerg-400	276	9	lim	lim	PROPN
fuelectenerg-400	276	10	n→∞	n→∞	NUM
fuelectenerg-400	276	11	log2	log2	PROPN
fuelectenerg-400	276	12	k(n	k(n	PROPN
fuelectenerg-400	276	13	,	,	PUNCT
fuelectenerg-400	276	14	n	n	CCONJ
fuelectenerg-400	276	15	,	,	PUNCT
fuelectenerg-400	276	16	n	n	CCONJ
fuelectenerg-400	276	17	)	)	PUNCT
fuelectenerg-400	276	18	log226n2	log226n2	ADV
fuelectenerg-400	276	19	.	.	PUNCT
fuelectenerg-400	277	1	(	(	PUNCT
fuelectenerg-400	277	2	4	4	X
fuelectenerg-400	277	3	)	)	PUNCT
fuelectenerg-400	277	4	we	we	PRON
fuelectenerg-400	277	5	are	be	AUX
fuelectenerg-400	277	6	interested	interested	ADJ
fuelectenerg-400	277	7	in	in	ADP
fuelectenerg-400	277	8	calculating	calculate	VERB
fuelectenerg-400	277	9	the	the	DET
fuelectenerg-400	277	10	number	number	NOUN
fuelectenerg-400	277	11	of	of	ADP
fuelectenerg-400	277	12	colored	colored	ADJ
fuelectenerg-400	277	13	lozenge	lozenge	NOUN
fuelectenerg-400	277	14	tilings	tiling	NOUN
fuelectenerg-400	277	15	of	of	ADP
fuelectenerg-400	277	16	a	a	DET
fuelectenerg-400	277	17	given	give	VERB
fuelectenerg-400	277	18	lattice	lattice	NOUN
fuelectenerg-400	277	19	.	.	PUNCT
fuelectenerg-400	278	1	observe	observe	VERB
fuelectenerg-400	278	2	that	that	SCONJ
fuelectenerg-400	278	3	this	this	PRON
fuelectenerg-400	278	4	will	will	AUX
fuelectenerg-400	278	5	yield	yield	VERB
fuelectenerg-400	278	6	bounds	bound	NOUN
fuelectenerg-400	278	7	on	on	ADP
fuelectenerg-400	278	8	the	the	DET
fuelectenerg-400	278	9	capacity	capacity	NOUN
fuelectenerg-400	278	10	of	of	ADP
fuelectenerg-400	278	11	the	the	DET
fuelectenerg-400	278	12	nib	nib	NOUN
fuelectenerg-400	278	13	constraint	constraint	NOUN
fuelectenerg-400	278	14	because	because	SCONJ
fuelectenerg-400	278	15	the	the	DET
fuelectenerg-400	278	16	capacity	capacity	NOUN
fuelectenerg-400	278	17	c(1,∞	c(1,∞	PROPN
fuelectenerg-400	278	18	)	)	PUNCT
fuelectenerg-400	278	19	of	of	ADP
fuelectenerg-400	278	20	the	the	DET
fuelectenerg-400	278	21	nib	nib	NOUN
fuelectenerg-400	278	22	constraint	constraint	NOUN
fuelectenerg-400	278	23	for	for	ADP
fuelectenerg-400	278	24	the	the	DET
fuelectenerg-400	278	25	triangular	triangular	NOUN
fuelectenerg-400	278	26	lattice	lattice	NOUN
fuelectenerg-400	278	27	model	model	NOUN
fuelectenerg-400	278	28	,	,	PUNCT
fuelectenerg-400	278	29	can	can	AUX
fuelectenerg-400	278	30	be	be	AUX
fuelectenerg-400	278	31	bounded	bound	VERB
fuelectenerg-400	278	32	by	by	ADP
fuelectenerg-400	278	33	the	the	DET
fuelectenerg-400	278	34	tiling	tile	VERB
fuelectenerg-400	278	35	density	density	NOUN
fuelectenerg-400	278	36	and	and	CCONJ
fuelectenerg-400	278	37	coloring	coloring	NOUN
fuelectenerg-400	278	38	densuty	densuty	NOUN
fuelectenerg-400	278	39	,	,	PUNCT
fuelectenerg-400	278	40	ct	ct	PROPN
fuelectenerg-400	278	41	and	and	CCONJ
fuelectenerg-400	278	42	cc	cc	PROPN
fuelectenerg-400	278	43	,	,	PUNCT
fuelectenerg-400	278	44	respectively	respectively	ADV
fuelectenerg-400	278	45	,	,	PUNCT
fuelectenerg-400	278	46	as	as	ADP
fuelectenerg-400	278	47	c(1,∞	c(1,∞	PROPN
fuelectenerg-400	278	48	)	)	PUNCT
fuelectenerg-400	278	49	≥	≥	NOUN
fuelectenerg-400	279	1	ct	ct	NUM
fuelectenerg-400	280	1	+	+	NUM
fuelectenerg-400	280	2	cc	cc	X
fuelectenerg-400	280	3	(	(	PUNCT
fuelectenerg-400	280	4	5	5	NUM
fuelectenerg-400	280	5	)	)	PUNCT
fuelectenerg-400	280	6	detection	detection	NOUN
fuelectenerg-400	280	7	and	and	CCONJ
fuelectenerg-400	280	8	coding	code	VERB
fuelectenerg-400	280	9	for	for	ADP
fuelectenerg-400	280	10	tdmr	tdmr	NOUN
fuelectenerg-400	280	11	channel	channel	NOUN
fuelectenerg-400	280	12	527	527	NUM
fuelectenerg-400	280	13	to	to	PART
fuelectenerg-400	280	14	estimate	estimate	VERB
fuelectenerg-400	280	15	capacity	capacity	NOUN
fuelectenerg-400	280	16	of	of	ADP
fuelectenerg-400	280	17	lozenge	lozenge	NOUN
fuelectenerg-400	280	18	tiling	tile	VERB
fuelectenerg-400	280	19	we	we	PRON
fuelectenerg-400	280	20	make	make	VERB
fuelectenerg-400	280	21	use	use	NOUN
fuelectenerg-400	280	22	of	of	ADP
fuelectenerg-400	280	23	the	the	DET
fuelectenerg-400	280	24	bijection	bijection	NOUN
fuelectenerg-400	280	25	between	between	ADP
fuelectenerg-400	280	26	the	the	DET
fuelectenerg-400	280	27	two	two	NUM
fuelectenerg-400	280	28	enumeration	enumeration	NOUN
fuelectenerg-400	280	29	problems	problem	NOUN
fuelectenerg-400	280	30	:	:	PUNCT
fuelectenerg-400	280	31	the	the	DET
fuelectenerg-400	280	32	counting	counting	NOUN
fuelectenerg-400	280	33	of	of	ADP
fuelectenerg-400	280	34	lozenge	lozenge	NOUN
fuelectenerg-400	280	35	tiling	tiling	NOUN
fuelectenerg-400	280	36	and	and	CCONJ
fuelectenerg-400	280	37	the	the	DET
fuelectenerg-400	280	38	counting	counting	NOUN
fuelectenerg-400	280	39	of	of	ADP
fuelectenerg-400	280	40	boxed	boxed	ADJ
fuelectenerg-400	280	41	plane	plane	NOUN
fuelectenerg-400	280	42	partition	partition	NOUN
fuelectenerg-400	280	43	.	.	PUNCT
fuelectenerg-400	281	1	then	then	ADV
fuelectenerg-400	281	2	,	,	PUNCT
fuelectenerg-400	281	3	we	we	PRON
fuelectenerg-400	281	4	will	will	AUX
fuelectenerg-400	281	5	make	make	VERB
fuelectenerg-400	281	6	use	use	NOUN
fuelectenerg-400	281	7	of	of	ADP
fuelectenerg-400	281	8	the	the	DET
fuelectenerg-400	281	9	work	work	NOUN
fuelectenerg-400	281	10	of	of	ADP
fuelectenerg-400	281	11	macmahon	macmahon	PROPN
fuelectenerg-400	281	12	on	on	ADP
fuelectenerg-400	281	13	calculating	calculate	VERB
fuelectenerg-400	281	14	the	the	DET
fuelectenerg-400	281	15	number	number	NOUN
fuelectenerg-400	281	16	of	of	ADP
fuelectenerg-400	281	17	boxed	boxed	ADJ
fuelectenerg-400	281	18	plane	plane	NOUN
fuelectenerg-400	281	19	partition	partition	NOUN
fuelectenerg-400	281	20	[	[	X
fuelectenerg-400	281	21	16	16	NUM
fuelectenerg-400	281	22	]	]	PUNCT
fuelectenerg-400	281	23	to	to	PART
fuelectenerg-400	281	24	determine	determine	VERB
fuelectenerg-400	281	25	ct	ct	PROPN
fuelectenerg-400	281	26	.	.	PUNCT
fuelectenerg-400	282	1	before	before	ADP
fuelectenerg-400	282	2	this	this	PRON
fuelectenerg-400	282	3	,	,	PUNCT
fuelectenerg-400	282	4	we	we	PRON
fuelectenerg-400	282	5	briefly	briefly	ADV
fuelectenerg-400	282	6	discuss	discuss	VERB
fuelectenerg-400	282	7	the	the	DET
fuelectenerg-400	282	8	problem	problem	NOUN
fuelectenerg-400	282	9	of	of	ADP
fuelectenerg-400	282	10	enumeration	enumeration	NOUN
fuelectenerg-400	282	11	of	of	ADP
fuelectenerg-400	282	12	boxed	boxed	ADJ
fuelectenerg-400	282	13	plane	plane	NOUN
fuelectenerg-400	282	14	partition	partition	NOUN
fuelectenerg-400	282	15	.	.	PUNCT
fuelectenerg-400	283	1	the	the	DET
fuelectenerg-400	283	2	use	use	NOUN
fuelectenerg-400	283	3	of	of	ADP
fuelectenerg-400	283	4	colored	colored	ADJ
fuelectenerg-400	283	5	tilings	tiling	NOUN
fuelectenerg-400	283	6	to	to	PART
fuelectenerg-400	283	7	estimate	estimate	VERB
fuelectenerg-400	283	8	capacity	capacity	NOUN
fuelectenerg-400	283	9	is	be	AUX
fuelectenerg-400	283	10	attractive	attractive	ADJ
fuelectenerg-400	283	11	due	due	ADP
fuelectenerg-400	283	12	to	to	ADP
fuelectenerg-400	283	13	the	the	DET
fuelectenerg-400	283	14	fact	fact	NOUN
fuelectenerg-400	283	15	that	that	SCONJ
fuelectenerg-400	283	16	the	the	DET
fuelectenerg-400	283	17	theory	theory	NOUN
fuelectenerg-400	283	18	of	of	ADP
fuelectenerg-400	283	19	counting	count	VERB
fuelectenerg-400	283	20	domino	domino	NOUN
fuelectenerg-400	283	21	tilings	tiling	NOUN
fuelectenerg-400	283	22	is	be	AUX
fuelectenerg-400	283	23	well	well	ADV
fuelectenerg-400	283	24	-	-	PUNCT
fuelectenerg-400	283	25	explored	explore	VERB
fuelectenerg-400	283	26	[	[	X
fuelectenerg-400	283	27	17,18	17,18	NUM
fuelectenerg-400	283	28	]	]	PUNCT
fuelectenerg-400	283	29	.	.	PUNCT
fuelectenerg-400	284	1	early	early	ADJ
fuelectenerg-400	284	2	work	work	NOUN
fuelectenerg-400	284	3	in	in	ADP
fuelectenerg-400	284	4	counting	count	VERB
fuelectenerg-400	284	5	domino	domino	NOUN
fuelectenerg-400	284	6	tilings	tiling	NOUN
fuelectenerg-400	284	7	includes	include	VERB
fuelectenerg-400	284	8	the	the	DET
fuelectenerg-400	284	9	work	work	NOUN
fuelectenerg-400	284	10	of	of	ADP
fuelectenerg-400	284	11	kasteleyn	kasteleyn	NOUN
fuelectenerg-400	284	12	[	[	X
fuelectenerg-400	284	13	19	19	NUM
fuelectenerg-400	284	14	]	]	PUNCT
fuelectenerg-400	284	15	,	,	PUNCT
fuelectenerg-400	284	16	who	who	PRON
fuelectenerg-400	284	17	calculated	calculate	VERB
fuelectenerg-400	284	18	the	the	DET
fuelectenerg-400	284	19	number	number	NOUN
fuelectenerg-400	284	20	of	of	ADP
fuelectenerg-400	284	21	domino	domino	NOUN
fuelectenerg-400	284	22	tilings	tiling	NOUN
fuelectenerg-400	284	23	of	of	ADP
fuelectenerg-400	284	24	a	a	DET
fuelectenerg-400	284	25	square	square	ADJ
fuelectenerg-400	284	26	lattice	lattice	NOUN
fuelectenerg-400	284	27	.	.	PUNCT
fuelectenerg-400	285	1	another	another	DET
fuelectenerg-400	285	2	work	work	NOUN
fuelectenerg-400	285	3	is	be	AUX
fuelectenerg-400	285	4	that	that	PRON
fuelectenerg-400	285	5	of	of	ADP
fuelectenerg-400	285	6	macmahon	macmahon	PROPN
fuelectenerg-400	286	1	[	[	X
fuelectenerg-400	286	2	16	16	NUM
fuelectenerg-400	286	3	]	]	PUNCT
fuelectenerg-400	286	4	in	in	ADP
fuelectenerg-400	286	5	which	which	PRON
fuelectenerg-400	286	6	the	the	DET
fuelectenerg-400	286	7	number	number	NOUN
fuelectenerg-400	286	8	of	of	ADP
fuelectenerg-400	286	9	lozenge	lozenge	ADJ
fuelectenerg-400	286	10	tilings	tiling	NOUN
fuelectenerg-400	286	11	of	of	ADP
fuelectenerg-400	286	12	a	a	DET
fuelectenerg-400	286	13	hexagon	hexagon	NOUN
fuelectenerg-400	286	14	embedded	embed	VERB
fuelectenerg-400	286	15	in	in	ADP
fuelectenerg-400	286	16	a	a	DET
fuelectenerg-400	286	17	triangular	triangular	NOUN
fuelectenerg-400	286	18	lattice	lattice	NOUN
fuelectenerg-400	286	19	was	be	AUX
fuelectenerg-400	286	20	calculated	calculate	VERB
fuelectenerg-400	286	21	.	.	PUNCT
fuelectenerg-400	287	1	desreux	desreux	NOUN
fuelectenerg-400	287	2	and	and	CCONJ
fuelectenerg-400	287	3	remila	remila	NOUN
fuelectenerg-400	288	1	[	[	X
fuelectenerg-400	288	2	20	20	NUM
fuelectenerg-400	288	3	]	]	PUNCT
fuelectenerg-400	288	4	gave	give	VERB
fuelectenerg-400	288	5	optimal	optimal	ADJ
fuelectenerg-400	288	6	algorithms	algorithm	NOUN
fuelectenerg-400	288	7	for	for	ADP
fuelectenerg-400	288	8	the	the	DET
fuelectenerg-400	288	9	generation	generation	NOUN
fuelectenerg-400	288	10	of	of	ADP
fuelectenerg-400	288	11	domino	domino	NOUN
fuelectenerg-400	288	12	tilings	tiling	NOUN
fuelectenerg-400	288	13	and	and	CCONJ
fuelectenerg-400	288	14	lozenge	lozenge	ADJ
fuelectenerg-400	288	15	tilings	tiling	NOUN
fuelectenerg-400	288	16	.	.	PUNCT
fuelectenerg-400	289	1	4.1	4.1	NUM
fuelectenerg-400	289	2	a	a	DET
fuelectenerg-400	289	3	method	method	NOUN
fuelectenerg-400	289	4	based	base	VERB
fuelectenerg-400	289	5	on	on	ADP
fuelectenerg-400	289	6	boxed	boxed	ADJ
fuelectenerg-400	289	7	plane	plane	NOUN
fuelectenerg-400	289	8	partitions	partition	NOUN
fuelectenerg-400	289	9	a	a	DET
fuelectenerg-400	289	10	plane	plane	NOUN
fuelectenerg-400	289	11	partition	partition	NOUN
fuelectenerg-400	289	12	π	π	NOUN
fuelectenerg-400	289	13	is	be	AUX
fuelectenerg-400	289	14	a	a	DET
fuelectenerg-400	289	15	collection	collection	NOUN
fuelectenerg-400	289	16	of	of	ADP
fuelectenerg-400	289	17	non	non	ADJ
fuelectenerg-400	289	18	-	-	ADJ
fuelectenerg-400	289	19	negative	negative	ADJ
fuelectenerg-400	289	20	integers	integer	NOUN
fuelectenerg-400	289	21	πx	πx	NOUN
fuelectenerg-400	289	22	,	,	PUNCT
fuelectenerg-400	289	23	y	y	PROPN
fuelectenerg-400	289	24	indexed	index	VERB
fuelectenerg-400	289	25	by	by	ADP
fuelectenerg-400	289	26	non	non	ADJ
fuelectenerg-400	289	27	-	-	ADJ
fuelectenerg-400	289	28	negative	negative	ADJ
fuelectenerg-400	289	29	integers	integer	NOUN
fuelectenerg-400	289	30	x	x	X
fuelectenerg-400	289	31	,	,	PUNCT
fuelectenerg-400	289	32	y	y	PROPN
fuelectenerg-400	289	33	such	such	ADJ
fuelectenerg-400	289	34	that	that	SCONJ
fuelectenerg-400	289	35	(	(	PUNCT
fuelectenerg-400	289	36	a	a	X
fuelectenerg-400	289	37	)	)	PUNCT
fuelectenerg-400	289	38	only	only	ADV
fuelectenerg-400	289	39	finite	finite	ADJ
fuelectenerg-400	289	40	number	number	NOUN
fuelectenerg-400	289	41	of	of	ADP
fuelectenerg-400	289	42	πx	πx	NOUN
fuelectenerg-400	289	43	,	,	PUNCT
fuelectenerg-400	289	44	y	y	PROPN
fuelectenerg-400	289	45	are	be	AUX
fuelectenerg-400	289	46	non	non	ADJ
fuelectenerg-400	289	47	-	-	ADJ
fuelectenerg-400	289	48	zero	zero	NUM
fuelectenerg-400	289	49	and	and	CCONJ
fuelectenerg-400	289	50	,	,	PUNCT
fuelectenerg-400	289	51	(	(	PUNCT
fuelectenerg-400	289	52	b	b	X
fuelectenerg-400	289	53	)	)	PUNCT
fuelectenerg-400	289	54	∀x	∀x	NUM
fuelectenerg-400	289	55	,	,	PUNCT
fuelectenerg-400	289	56	y	y	PROPN
fuelectenerg-400	289	57	πx	πx	PROPN
fuelectenerg-400	289	58	,	,	PUNCT
fuelectenerg-400	289	59	y	y	PROPN
fuelectenerg-400	289	60	≤	≤	NUM
fuelectenerg-400	289	61	πx	πx	ADP
fuelectenerg-400	289	62	,	,	PUNCT
fuelectenerg-400	289	63	y+1	y+1	PRON
fuelectenerg-400	289	64	and	and	CCONJ
fuelectenerg-400	289	65	πx	πx	ADJ
fuelectenerg-400	289	66	,	,	PUNCT
fuelectenerg-400	289	67	y	y	PROPN
fuelectenerg-400	289	68	≤	≤	PROPN
fuelectenerg-400	289	69	πx+1,y	πx+1,y	PROPN
fuelectenerg-400	289	70	.	.	PUNCT
fuelectenerg-400	290	1	the	the	DET
fuelectenerg-400	290	2	plane	plane	NOUN
fuelectenerg-400	290	3	partition	partition	NOUN
fuelectenerg-400	290	4	is	be	AUX
fuelectenerg-400	290	5	said	say	VERB
fuelectenerg-400	290	6	to	to	PART
fuelectenerg-400	290	7	fit	fit	VERB
fuelectenerg-400	290	8	inside	inside	ADP
fuelectenerg-400	290	9	a	a	DET
fuelectenerg-400	290	10	box	box	NOUN
fuelectenerg-400	290	11	of	of	ADP
fuelectenerg-400	290	12	dimension	dimension	NOUN
fuelectenerg-400	290	13	a	a	DET
fuelectenerg-400	290	14	×	×	NOUN
fuelectenerg-400	290	15	b	b	NOUN
fuelectenerg-400	290	16	×	×	NOUN
fuelectenerg-400	290	17	c	c	NOUN
fuelectenerg-400	291	1	if	if	SCONJ
fuelectenerg-400	291	2	there	there	PRON
fuelectenerg-400	291	3	exist	exist	VERB
fuelectenerg-400	291	4	integers	integer	NOUN
fuelectenerg-400	291	5	a	a	DET
fuelectenerg-400	291	6	,	,	PUNCT
fuelectenerg-400	291	7	b	b	NOUN
fuelectenerg-400	291	8	,	,	PUNCT
fuelectenerg-400	291	9	c	c	X
fuelectenerg-400	291	10	such	such	ADJ
fuelectenerg-400	291	11	that	that	SCONJ
fuelectenerg-400	291	12	πx	πx	NOUN
fuelectenerg-400	291	13	,	,	PUNCT
fuelectenerg-400	291	14	y	y	PROPN
fuelectenerg-400	291	15	≤	≤	PROPN
fuelectenerg-400	291	16	c	c	NOUN
fuelectenerg-400	291	17	for	for	ADP
fuelectenerg-400	291	18	all	all	DET
fuelectenerg-400	291	19	x	x	NOUN
fuelectenerg-400	291	20	,	,	PUNCT
fuelectenerg-400	291	21	y	y	PROPN
fuelectenerg-400	291	22	and	and	CCONJ
fuelectenerg-400	291	23	πx	πx	PROPN
fuelectenerg-400	291	24	,	,	PUNCT
fuelectenerg-400	291	25	y	y	PROPN
fuelectenerg-400	291	26	=	=	NOUN
fuelectenerg-400	291	27	0	0	NUM
fuelectenerg-400	291	28	for	for	ADP
fuelectenerg-400	291	29	all	all	PRON
fuelectenerg-400	292	1	x	x	SYM
fuelectenerg-400	292	2	>	>	X
fuelectenerg-400	292	3	a	a	X
fuelectenerg-400	292	4	,	,	PUNCT
fuelectenerg-400	292	5	y	y	PROPN
fuelectenerg-400	292	6	>	>	X
fuelectenerg-400	292	7	b.	b.	PROPN
fuelectenerg-400	293	1	such	such	ADJ
fuelectenerg-400	293	2	partitions	partition	NOUN
fuelectenerg-400	293	3	are	be	AUX
fuelectenerg-400	293	4	called	call	VERB
fuelectenerg-400	293	5	boxed	boxed	ADJ
fuelectenerg-400	293	6	plane	plane	NOUN
fuelectenerg-400	293	7	partitions	partition	NOUN
fuelectenerg-400	293	8	.	.	PUNCT
fuelectenerg-400	294	1	a	a	DET
fuelectenerg-400	294	2	more	more	ADV
fuelectenerg-400	294	3	intuitive	intuitive	ADJ
fuelectenerg-400	294	4	way	way	NOUN
fuelectenerg-400	294	5	of	of	ADP
fuelectenerg-400	294	6	visualizing	visualize	VERB
fuelectenerg-400	294	7	the	the	DET
fuelectenerg-400	294	8	boxed	box	VERB
fuelectenerg-400	294	9	plane	plane	NOUN
fuelectenerg-400	294	10	partitions	partition	NOUN
fuelectenerg-400	294	11	is	be	AUX
fuelectenerg-400	294	12	by	by	ADP
fuelectenerg-400	294	13	constructing	construct	VERB
fuelectenerg-400	294	14	the	the	DET
fuelectenerg-400	294	15	young	young	ADJ
fuelectenerg-400	294	16	’s	’s	PART
fuelectenerg-400	294	17	solid	solid	ADJ
fuelectenerg-400	294	18	diagram	diagram	NOUN
fuelectenerg-400	294	19	corresponding	correspond	VERB
fuelectenerg-400	294	20	to	to	ADP
fuelectenerg-400	294	21	a	a	DET
fuelectenerg-400	294	22	boxed	box	VERB
fuelectenerg-400	294	23	partition	partition	NOUN
fuelectenerg-400	294	24	π	π	NOUN
fuelectenerg-400	294	25	.	.	PUNCT
fuelectenerg-400	295	1	for	for	ADP
fuelectenerg-400	295	2	instance	instance	NOUN
fuelectenerg-400	295	3	,	,	PUNCT
fuelectenerg-400	295	4	consider	consider	VERB
fuelectenerg-400	295	5	the	the	DET
fuelectenerg-400	295	6	following	follow	VERB
fuelectenerg-400	295	7	partition	partition	NOUN
fuelectenerg-400	295	8	boxed	box	VERB
fuelectenerg-400	295	9	within	within	ADP
fuelectenerg-400	295	10	a	a	DET
fuelectenerg-400	295	11	box	box	NOUN
fuelectenerg-400	295	12	of	of	ADP
fuelectenerg-400	295	13	dimension	dimension	NOUN
fuelectenerg-400	295	14	2	2	NUM
fuelectenerg-400	295	15	×	×	NOUN
fuelectenerg-400	295	16	3	3	NUM
fuelectenerg-400	295	17	×	×	NOUN
fuelectenerg-400	295	18	4	4	NUM
fuelectenerg-400	295	19	.	.	PUNCT
fuelectenerg-400	296	1	π	π	X
fuelectenerg-400	296	2	=	=	PUNCT
fuelectenerg-400	296	3	(	(	PUNCT
fuelectenerg-400	296	4	4	4	NUM
fuelectenerg-400	296	5	2	2	NUM
fuelectenerg-400	296	6	2	2	NUM
fuelectenerg-400	296	7	2	2	NUM
fuelectenerg-400	296	8	1	1	NUM
fuelectenerg-400	296	9	1	1	NUM
fuelectenerg-400	296	10	)	)	PUNCT
fuelectenerg-400	296	11	the	the	DET
fuelectenerg-400	296	12	dimension	dimension	NOUN
fuelectenerg-400	296	13	of	of	ADP
fuelectenerg-400	296	14	the	the	DET
fuelectenerg-400	296	15	matrix	matrix	NOUN
fuelectenerg-400	296	16	is	be	AUX
fuelectenerg-400	296	17	2	2	NUM
fuelectenerg-400	296	18	×	×	NOUN
fuelectenerg-400	296	19	3	3	NUM
fuelectenerg-400	296	20	with	with	ADP
fuelectenerg-400	296	21	all	all	DET
fuelectenerg-400	296	22	entries	entry	NOUN
fuelectenerg-400	296	23	≤	≤	ADJ
fuelectenerg-400	296	24	4	4	NUM
fuelectenerg-400	296	25	.	.	PUNCT
fuelectenerg-400	296	26	to	to	PART
fuelectenerg-400	296	27	build	build	VERB
fuelectenerg-400	296	28	its	its	PRON
fuelectenerg-400	296	29	corresponding	corresponding	ADJ
fuelectenerg-400	296	30	young	young	ADJ
fuelectenerg-400	296	31	’s	’s	PART
fuelectenerg-400	296	32	solid	solid	ADJ
fuelectenerg-400	296	33	diagram	diagram	NOUN
fuelectenerg-400	296	34	,	,	PUNCT
fuelectenerg-400	296	35	we	we	PRON
fuelectenerg-400	296	36	first	first	ADV
fuelectenerg-400	296	37	consider	consider	VERB
fuelectenerg-400	296	38	a	a	DET
fuelectenerg-400	296	39	box	box	NOUN
fuelectenerg-400	296	40	of	of	ADP
fuelectenerg-400	296	41	dimension	dimension	NOUN
fuelectenerg-400	296	42	2×3×4	2×3×4	NOUN
fuelectenerg-400	296	43	.	.	PUNCT
fuelectenerg-400	297	1	to	to	ADP
fuelectenerg-400	297	2	one	one	NUM
fuelectenerg-400	297	3	of	of	ADP
fuelectenerg-400	297	4	the	the	DET
fuelectenerg-400	297	5	vertices	vertex	NOUN
fuelectenerg-400	297	6	,	,	PUNCT
fuelectenerg-400	297	7	we	we	PRON
fuelectenerg-400	297	8	assign	assign	VERB
fuelectenerg-400	297	9	the	the	DET
fuelectenerg-400	297	10	cartesian	cartesian	ADJ
fuelectenerg-400	297	11	co	co	NOUN
fuelectenerg-400	297	12	-	-	NOUN
fuelectenerg-400	297	13	ordinate	ordinate	ADJ
fuelectenerg-400	297	14	(	(	PUNCT
fuelectenerg-400	297	15	0	0	NUM
fuelectenerg-400	297	16	,	,	PUNCT
fuelectenerg-400	297	17	0	0	NUM
fuelectenerg-400	297	18	,	,	PUNCT
fuelectenerg-400	297	19	0	0	NUM
fuelectenerg-400	297	20	)	)	PUNCT
fuelectenerg-400	297	21	.	.	PUNCT
fuelectenerg-400	298	1	to	to	ADP
fuelectenerg-400	298	2	the	the	DET
fuelectenerg-400	298	3	opposite	opposite	ADJ
fuelectenerg-400	298	4	vertex	vertex	NOUN
fuelectenerg-400	298	5	we	we	PRON
fuelectenerg-400	298	6	assign	assign	VERB
fuelectenerg-400	298	7	the	the	DET
fuelectenerg-400	298	8	co	co	NOUN
fuelectenerg-400	298	9	-	-	NOUN
fuelectenerg-400	298	10	ordinate	ordinate	NOUN
fuelectenerg-400	298	11	(	(	PUNCT
fuelectenerg-400	298	12	2	2	NUM
fuelectenerg-400	298	13	,	,	PUNCT
fuelectenerg-400	298	14	3	3	NUM
fuelectenerg-400	298	15	,	,	PUNCT
fuelectenerg-400	298	16	4	4	NUM
fuelectenerg-400	298	17	)	)	PUNCT
fuelectenerg-400	298	18	.	.	PUNCT
fuelectenerg-400	299	1	for	for	ADP
fuelectenerg-400	299	2	each	each	DET
fuelectenerg-400	299	3	x	x	SYM
fuelectenerg-400	299	4	≤	≤	NOUN
fuelectenerg-400	299	5	2	2	NUM
fuelectenerg-400	299	6	,	,	PUNCT
fuelectenerg-400	299	7	y	y	PROPN
fuelectenerg-400	299	8	≤	≤	PROPN
fuelectenerg-400	299	9	3	3	NUM
fuelectenerg-400	299	10	,	,	PUNCT
fuelectenerg-400	299	11	we	we	PRON
fuelectenerg-400	299	12	start	start	VERB
fuelectenerg-400	299	13	at	at	ADP
fuelectenerg-400	299	14	(	(	PUNCT
fuelectenerg-400	299	15	x	x	SYM
fuelectenerg-400	299	16	−	−	PROPN
fuelectenerg-400	299	17	1	1	NUM
fuelectenerg-400	299	18	,	,	PUNCT
fuelectenerg-400	299	19	y	y	PROPN
fuelectenerg-400	299	20	−	−	PROPN
fuelectenerg-400	299	21	1	1	NUM
fuelectenerg-400	299	22	,	,	PUNCT
fuelectenerg-400	299	23	0	0	NUM
fuelectenerg-400	299	24	)	)	PUNCT
fuelectenerg-400	299	25	and	and	CCONJ
fuelectenerg-400	299	26	stack	stack	VERB
fuelectenerg-400	299	27	πx	πx	NOUN
fuelectenerg-400	299	28	,	,	PUNCT
fuelectenerg-400	299	29	y	y	PROPN
fuelectenerg-400	299	30	cubes	cube	NOUN
fuelectenerg-400	299	31	of	of	ADP
fuelectenerg-400	299	32	unit	unit	NOUN
fuelectenerg-400	299	33	side	side	NOUN
fuelectenerg-400	299	34	length	length	NOUN
fuelectenerg-400	299	35	.	.	PUNCT
fuelectenerg-400	300	1	this	this	DET
fuelectenerg-400	300	2	construction	construction	NOUN
fuelectenerg-400	300	3	will	will	AUX
fuelectenerg-400	300	4	fit	fit	VERB
fuelectenerg-400	300	5	inside	inside	ADP
fuelectenerg-400	300	6	the	the	DET
fuelectenerg-400	300	7	box	box	NOUN
fuelectenerg-400	300	8	.	.	PUNCT
fuelectenerg-400	301	1	fig	fig	NOUN
fuelectenerg-400	301	2	.	.	PUNCT
fuelectenerg-400	302	1	5	5	X
fuelectenerg-400	302	2	.	.	X
fuelectenerg-400	302	3	tiling	tile	VERB
fuelectenerg-400	302	4	corresponding	correspond	VERB
fuelectenerg-400	302	5	to	to	ADP
fuelectenerg-400	302	6	the	the	DET
fuelectenerg-400	302	7	boxed	box	VERB
fuelectenerg-400	302	8	plane	plane	NOUN
fuelectenerg-400	302	9	partition	partition	NOUN
fuelectenerg-400	302	10	π	π	NOUN
fuelectenerg-400	302	11	.	.	PUNCT
fuelectenerg-400	303	1	the	the	DET
fuelectenerg-400	303	2	tiling	tiling	NOUN
fuelectenerg-400	303	3	given	give	VERB
fuelectenerg-400	303	4	in	in	ADP
fuelectenerg-400	303	5	fig	fig	NOUN
fuelectenerg-400	303	6	.	.	PUNCT
fuelectenerg-400	304	1	5	5	NUM
fuelectenerg-400	304	2	corresponds	correspond	NOUN
fuelectenerg-400	304	3	to	to	ADP
fuelectenerg-400	304	4	the	the	DET
fuelectenerg-400	304	5	boxed	box	VERB
fuelectenerg-400	304	6	plane	plane	NOUN
fuelectenerg-400	304	7	partition	partition	NOUN
fuelectenerg-400	304	8	π	π	PROPN
fuelectenerg-400	304	9	given	give	VERB
fuelectenerg-400	304	10	526	526	NUM
fuelectenerg-400	304	11	b.	b.	NOUN
fuelectenerg-400	304	12	vasic	vasic	NOUN
fuelectenerg-400	304	13	,	,	PUNCT
fuelectenerg-400	304	14	a.	a.	PROPN
fuelectenerg-400	304	15	r.	r.	PROPN
fuelectenerg-400	304	16	krishnan	krishnan	PROPN
fuelectenerg-400	304	17	lozenge	lozenge	PROPN
fuelectenerg-400	304	18	tiling	tile	VERB
fuelectenerg-400	304	19	constrained	constrained	ADJ
fuelectenerg-400	304	20	codes	code	NOUN
fuelectenerg-400	304	21	527	527	NUM
fuelectenerg-400	304	22	528	528	NUM
fuelectenerg-400	304	23	a.	a.	NOUN
fuelectenerg-400	304	24	r.	r.	PROPN
fuelectenerg-400	304	25	krishnanan	krishnanan	PROPN
fuelectenerg-400	304	26	and	and	CCONJ
fuelectenerg-400	304	27	b.	b.	PROPN
fuelectenerg-400	304	28	vasić	vasić	PROPN
fuelectenerg-400	304	29	above	above	ADV
fuelectenerg-400	304	30	.	.	PUNCT
fuelectenerg-400	305	1	the	the	DET
fuelectenerg-400	305	2	young	young	PROPN
fuelectenerg-400	305	3	’s	’s	PART
fuelectenerg-400	305	4	solid	solid	ADJ
fuelectenerg-400	305	5	diagram	diagram	NOUN
fuelectenerg-400	305	6	construction	construction	NOUN
fuelectenerg-400	305	7	is	be	AUX
fuelectenerg-400	305	8	also	also	ADV
fuelectenerg-400	305	9	apparent	apparent	ADJ
fuelectenerg-400	305	10	if	if	SCONJ
fuelectenerg-400	305	11	the	the	DET
fuelectenerg-400	305	12	tiled	tile	VERB
fuelectenerg-400	305	13	(	(	PUNCT
fuelectenerg-400	305	14	2	2	NUM
fuelectenerg-400	305	15	,	,	PUNCT
fuelectenerg-400	305	16	3	3	NUM
fuelectenerg-400	305	17	,	,	PUNCT
fuelectenerg-400	305	18	4	4	X
fuelectenerg-400	305	19	)	)	PUNCT
fuelectenerg-400	305	20	hexagon	hexagon	NOUN
fuelectenerg-400	305	21	is	be	AUX
fuelectenerg-400	305	22	visualized	visualize	VERB
fuelectenerg-400	305	23	as	as	ADP
fuelectenerg-400	305	24	a	a	DET
fuelectenerg-400	305	25	2	2	NUM
fuelectenerg-400	305	26	×	×	NOUN
fuelectenerg-400	305	27	3	3	NUM
fuelectenerg-400	305	28	×	×	NOUN
fuelectenerg-400	305	29	4	4	NUM
fuelectenerg-400	305	30	box	box	NOUN
fuelectenerg-400	305	31	.	.	PUNCT
fuelectenerg-400	306	1	for	for	ADP
fuelectenerg-400	306	2	ease	ease	NOUN
fuelectenerg-400	306	3	of	of	ADP
fuelectenerg-400	306	4	visualization	visualization	NOUN
fuelectenerg-400	306	5	,	,	PUNCT
fuelectenerg-400	306	6	the	the	DET
fuelectenerg-400	306	7	top	top	ADJ
fuelectenerg-400	306	8	face	face	NOUN
fuelectenerg-400	306	9	of	of	ADP
fuelectenerg-400	306	10	the	the	DET
fuelectenerg-400	306	11	topmost	topmost	PROPN
fuelectenerg-400	306	12	box	box	NOUN
fuelectenerg-400	306	13	is	be	AUX
fuelectenerg-400	306	14	colored	color	VERB
fuelectenerg-400	306	15	black	black	ADJ
fuelectenerg-400	306	16	.	.	PUNCT
fuelectenerg-400	307	1	the	the	DET
fuelectenerg-400	307	2	relationship	relationship	NOUN
fuelectenerg-400	307	3	between	between	ADP
fuelectenerg-400	307	4	lozenge	lozenge	NOUN
fuelectenerg-400	307	5	tiling	tile	VERB
fuelectenerg-400	307	6	and	and	CCONJ
fuelectenerg-400	307	7	boxed	boxed	ADJ
fuelectenerg-400	307	8	plane	plane	NOUN
fuelectenerg-400	307	9	partition	partition	NOUN
fuelectenerg-400	307	10	is	be	AUX
fuelectenerg-400	307	11	given	give	VERB
fuelectenerg-400	307	12	by	by	ADP
fuelectenerg-400	307	13	the	the	DET
fuelectenerg-400	307	14	theorem	theorem	NOUN
fuelectenerg-400	307	15	1	1	NUM
fuelectenerg-400	307	16	in	in	ADP
fuelectenerg-400	307	17	[	[	X
fuelectenerg-400	307	18	18	18	NUM
fuelectenerg-400	307	19	]	]	PUNCT
fuelectenerg-400	307	20	.	.	PUNCT
fuelectenerg-400	308	1	lemma	lemma	PROPN
fuelectenerg-400	308	2	1	1	NUM
fuelectenerg-400	308	3	the	the	DET
fuelectenerg-400	308	4	number	number	NOUN
fuelectenerg-400	308	5	of	of	ADP
fuelectenerg-400	308	6	boxed	boxed	ADJ
fuelectenerg-400	308	7	plane	plane	NOUN
fuelectenerg-400	308	8	partitions	partition	NOUN
fuelectenerg-400	308	9	fitting	fit	VERB
fuelectenerg-400	308	10	inside	inside	ADP
fuelectenerg-400	308	11	a	a	DET
fuelectenerg-400	308	12	a	a	DET
fuelectenerg-400	308	13	×	×	NOUN
fuelectenerg-400	308	14	b	b	PROPN
fuelectenerg-400	308	15	×	×	PROPN
fuelectenerg-400	308	16	c	c	PROPN
fuelectenerg-400	308	17	box	box	PROPN
fuelectenerg-400	308	18	is	be	AUX
fuelectenerg-400	308	19	equal	equal	ADJ
fuelectenerg-400	308	20	to	to	ADP
fuelectenerg-400	308	21	the	the	DET
fuelectenerg-400	308	22	number	number	NOUN
fuelectenerg-400	308	23	of	of	ADP
fuelectenerg-400	308	24	lozenge	lozenge	ADJ
fuelectenerg-400	308	25	tilings	tiling	NOUN
fuelectenerg-400	308	26	of	of	ADP
fuelectenerg-400	308	27	an	an	DET
fuelectenerg-400	308	28	(	(	PUNCT
fuelectenerg-400	308	29	a	a	PROPN
fuelectenerg-400	308	30	,	,	PUNCT
fuelectenerg-400	308	31	b	b	NOUN
fuelectenerg-400	308	32	,	,	PUNCT
fuelectenerg-400	308	33	c	c	NOUN
fuelectenerg-400	308	34	)	)	PUNCT
fuelectenerg-400	308	35	hexagon	hexagon	NOUN
fuelectenerg-400	308	36	.	.	PUNCT
fuelectenerg-400	309	1	proof	proof	NOUN
fuelectenerg-400	309	2	:	:	PUNCT
fuelectenerg-400	309	3	the	the	DET
fuelectenerg-400	309	4	proof	proof	NOUN
fuelectenerg-400	309	5	is	be	AUX
fuelectenerg-400	309	6	based	base	VERB
fuelectenerg-400	309	7	on	on	ADP
fuelectenerg-400	309	8	macmahon	macmahon	PROPN
fuelectenerg-400	310	1	[	[	X
fuelectenerg-400	310	2	16	16	NUM
fuelectenerg-400	310	3	]	]	PUNCT
fuelectenerg-400	310	4	formula	formula	NOUN
fuelectenerg-400	310	5	.	.	PUNCT
fuelectenerg-400	311	1	4.2	4.2	NUM
fuelectenerg-400	311	2	bounds	bound	NOUN
fuelectenerg-400	311	3	on	on	ADP
fuelectenerg-400	311	4	ct	ct	NUM
fuelectenerg-400	311	5	by	by	ADP
fuelectenerg-400	311	6	lemma	lemma	PROPN
fuelectenerg-400	311	7	1	1	NUM
fuelectenerg-400	311	8	,	,	PUNCT
fuelectenerg-400	311	9	the	the	DET
fuelectenerg-400	311	10	number	number	NOUN
fuelectenerg-400	311	11	of	of	ADP
fuelectenerg-400	311	12	lozenge	lozenge	NOUN
fuelectenerg-400	311	13	tiling	tiling	NOUN
fuelectenerg-400	311	14	of	of	ADP
fuelectenerg-400	311	15	any	any	DET
fuelectenerg-400	311	16	(	(	PUNCT
fuelectenerg-400	311	17	a	a	PRON
fuelectenerg-400	311	18	,	,	PUNCT
fuelectenerg-400	311	19	b	b	NOUN
fuelectenerg-400	311	20	,	,	PUNCT
fuelectenerg-400	311	21	c	c	NOUN
fuelectenerg-400	311	22	)	)	PUNCT
fuelectenerg-400	311	23	hexagon	hexagon	NOUN
fuelectenerg-400	311	24	is	be	AUX
fuelectenerg-400	311	25	equal	equal	ADJ
fuelectenerg-400	311	26	to	to	ADP
fuelectenerg-400	311	27	the	the	DET
fuelectenerg-400	311	28	number	number	NOUN
fuelectenerg-400	311	29	of	of	ADP
fuelectenerg-400	311	30	boxed	boxed	ADJ
fuelectenerg-400	311	31	partitions	partition	NOUN
fuelectenerg-400	311	32	fitting	fitting	ADJ
fuelectenerg-400	311	33	inside	inside	ADP
fuelectenerg-400	311	34	an	an	DET
fuelectenerg-400	311	35	a×b×c	a×b×c	PROPN
fuelectenerg-400	311	36	box	box	NOUN
fuelectenerg-400	311	37	.	.	PUNCT
fuelectenerg-400	312	1	macmahon	macmahon	PROPN
fuelectenerg-400	313	1	[	[	X
fuelectenerg-400	313	2	16	16	NUM
fuelectenerg-400	313	3	]	]	PUNCT
fuelectenerg-400	313	4	found	find	VERB
fuelectenerg-400	313	5	the	the	DET
fuelectenerg-400	313	6	number	number	NOUN
fuelectenerg-400	313	7	of	of	ADP
fuelectenerg-400	313	8	such	such	ADJ
fuelectenerg-400	313	9	partitions	partition	NOUN
fuelectenerg-400	313	10	,	,	PUNCT
fuelectenerg-400	313	11	n(a	n(a	PROPN
fuelectenerg-400	313	12	,	,	PUNCT
fuelectenerg-400	313	13	b	b	NOUN
fuelectenerg-400	313	14	,	,	PUNCT
fuelectenerg-400	313	15	c	c	NOUN
fuelectenerg-400	313	16	)	)	PUNCT
fuelectenerg-400	313	17	,	,	PUNCT
fuelectenerg-400	313	18	to	to	PART
fuelectenerg-400	313	19	be	be	AUX
fuelectenerg-400	313	20	n(a	n(a	PROPN
fuelectenerg-400	313	21	,	,	PUNCT
fuelectenerg-400	313	22	b	b	NOUN
fuelectenerg-400	313	23	,	,	PUNCT
fuelectenerg-400	313	24	c	c	NOUN
fuelectenerg-400	313	25	)	)	PUNCT
fuelectenerg-400	313	26	=	=	PRON
fuelectenerg-400	313	27	∏a	∏a	VERB
fuelectenerg-400	313	28	i=1(c+	i=1(c+	PROPN
fuelectenerg-400	313	29	i)b/(i)b	i)b/(i)b	PROPN
fuelectenerg-400	313	30	where	where	SCONJ
fuelectenerg-400	313	31	(	(	PUNCT
fuelectenerg-400	313	32	i)n	i)n	VERB
fuelectenerg-400	313	33	:	:	PUNCT
fuelectenerg-400	313	34	=	=	SYM
fuelectenerg-400	313	35	i(i	i(i	PROPN
fuelectenerg-400	313	36	+	+	CCONJ
fuelectenerg-400	313	37	1)(i	1)(i	NUM
fuelectenerg-400	313	38	+	+	CCONJ
fuelectenerg-400	313	39	2	2	NUM
fuelectenerg-400	313	40	)	)	PUNCT
fuelectenerg-400	313	41	.	.	PUNCT
fuelectenerg-400	313	42	.	.	PUNCT
fuelectenerg-400	314	1	.	.	PUNCT
fuelectenerg-400	315	1	(	(	PUNCT
fuelectenerg-400	315	2	i	i	PRON
fuelectenerg-400	315	3	+	+	CCONJ
fuelectenerg-400	315	4	n	n	CCONJ
fuelectenerg-400	315	5	−	−	PROPN
fuelectenerg-400	315	6	1	1	NUM
fuelectenerg-400	315	7	)	)	PUNCT
fuelectenerg-400	315	8	is	be	AUX
fuelectenerg-400	315	9	the	the	DET
fuelectenerg-400	315	10	rising	rise	VERB
fuelectenerg-400	315	11	factorial	factorial	NOUN
fuelectenerg-400	315	12	.	.	PUNCT
fuelectenerg-400	316	1	for	for	ADP
fuelectenerg-400	316	2	an	an	DET
fuelectenerg-400	316	3	equilateral	equilateral	ADJ
fuelectenerg-400	316	4	hexagon	hexagon	NOUN
fuelectenerg-400	316	5	,	,	PUNCT
fuelectenerg-400	316	6	we	we	PRON
fuelectenerg-400	316	7	were	be	AUX
fuelectenerg-400	316	8	able	able	ADJ
fuelectenerg-400	316	9	to	to	PART
fuelectenerg-400	316	10	find	find	VERB
fuelectenerg-400	316	11	the	the	DET
fuelectenerg-400	316	12	capacity	capacity	NOUN
fuelectenerg-400	316	13	of	of	ADP
fuelectenerg-400	316	14	tiling	tile	VERB
fuelectenerg-400	316	15	(	(	PUNCT
fuelectenerg-400	316	16	without	without	ADP
fuelectenerg-400	316	17	coloring	color	VERB
fuelectenerg-400	316	18	)	)	PUNCT
fuelectenerg-400	316	19	in	in	ADP
fuelectenerg-400	316	20	a	a	DET
fuelectenerg-400	316	21	closed	closed	ADJ
fuelectenerg-400	316	22	form	form	NOUN
fuelectenerg-400	316	23	.	.	PUNCT
fuelectenerg-400	317	1	it	it	PRON
fuelectenerg-400	317	2	is	be	AUX
fuelectenerg-400	317	3	given	give	VERB
fuelectenerg-400	317	4	by	by	ADP
fuelectenerg-400	317	5	theorem	theorem	NOUN
fuelectenerg-400	317	6	1	1	NUM
fuelectenerg-400	317	7	.	.	PUNCT
fuelectenerg-400	317	8	theorem	theorem	VERB
fuelectenerg-400	317	9	1	1	NUM
fuelectenerg-400	317	10	the	the	DET
fuelectenerg-400	317	11	capacity	capacity	NOUN
fuelectenerg-400	317	12	of	of	ADP
fuelectenerg-400	317	13	the	the	DET
fuelectenerg-400	317	14	lozenge	lozenge	NOUN
fuelectenerg-400	317	15	tiling	tile	VERB
fuelectenerg-400	317	16	for	for	ADP
fuelectenerg-400	317	17	an	an	DET
fuelectenerg-400	317	18	equilateral	equilateral	ADJ
fuelectenerg-400	317	19	hexagon	hexagon	NOUN
fuelectenerg-400	317	20	is	be	AUX
fuelectenerg-400	318	1	ct	ct	NOUN
fuelectenerg-400	318	2	=	=	SYM
fuelectenerg-400	318	3	3	3	NUM
fuelectenerg-400	318	4	4	4	NUM
fuelectenerg-400	318	5	log2	log2	NOUN
fuelectenerg-400	318	6	3	3	NUM
fuelectenerg-400	318	7	−	−	NOUN
fuelectenerg-400	318	8	1	1	NUM
fuelectenerg-400	318	9	.	.	PUNCT
fuelectenerg-400	318	10	proof	proof	NOUN
fuelectenerg-400	318	11	:	:	PUNCT
fuelectenerg-400	318	12	the	the	DET
fuelectenerg-400	318	13	proof	proof	NOUN
fuelectenerg-400	318	14	follows	follow	VERB
fuelectenerg-400	318	15	from	from	ADP
fuelectenerg-400	318	16	lemma	lemma	PROPN
fuelectenerg-400	318	17	1	1	NUM
fuelectenerg-400	318	18	as	as	SCONJ
fuelectenerg-400	318	19	given	give	VERB
fuelectenerg-400	318	20	in	in	ADP
fuelectenerg-400	318	21	appendix	appendix	ADJ
fuelectenerg-400	318	22	7	7	NUM
fuelectenerg-400	318	23	note	note	NOUN
fuelectenerg-400	318	24	that	that	PRON
fuelectenerg-400	318	25	closed	close	VERB
fuelectenerg-400	318	26	forms	form	NOUN
fuelectenerg-400	318	27	solutions	solution	NOUN
fuelectenerg-400	318	28	for	for	ADP
fuelectenerg-400	318	29	the	the	DET
fuelectenerg-400	318	30	capacity	capacity	NOUN
fuelectenerg-400	318	31	such	such	ADJ
fuelectenerg-400	318	32	as	as	ADP
fuelectenerg-400	318	33	one	one	NUM
fuelectenerg-400	318	34	given	give	VERB
fuelectenerg-400	318	35	by	by	ADP
fuelectenerg-400	318	36	the	the	DET
fuelectenerg-400	318	37	above	above	ADJ
fuelectenerg-400	318	38	theorem	theorem	NOUN
fuelectenerg-400	318	39	are	be	AUX
fuelectenerg-400	318	40	quite	quite	ADV
fuelectenerg-400	318	41	rare	rare	ADJ
fuelectenerg-400	318	42	in	in	ADP
fuelectenerg-400	318	43	problems	problem	NOUN
fuelectenerg-400	318	44	involving	involve	VERB
fuelectenerg-400	318	45	2d	2d	NUM
fuelectenerg-400	318	46	constraints	constraint	NOUN
fuelectenerg-400	318	47	.	.	PUNCT
fuelectenerg-400	319	1	4.3	4.3	NUM
fuelectenerg-400	319	2	bounds	bound	NOUN
fuelectenerg-400	319	3	on	on	ADP
fuelectenerg-400	319	4	cc	cc	ADP
fuelectenerg-400	319	5	the	the	DET
fuelectenerg-400	319	6	capacity	capacity	NOUN
fuelectenerg-400	319	7	of	of	ADP
fuelectenerg-400	319	8	the	the	DET
fuelectenerg-400	319	9	coloring	coloring	NOUN
fuelectenerg-400	319	10	problem	problem	NOUN
fuelectenerg-400	319	11	,	,	PUNCT
fuelectenerg-400	319	12	cc	cc	NOUN
fuelectenerg-400	319	13	,	,	PUNCT
fuelectenerg-400	319	14	can	can	AUX
fuelectenerg-400	319	15	be	be	AUX
fuelectenerg-400	319	16	estimated	estimate	VERB
fuelectenerg-400	319	17	by	by	ADP
fuelectenerg-400	319	18	counting	count	VERB
fuelectenerg-400	319	19	the	the	DET
fuelectenerg-400	319	20	number	number	NOUN
fuelectenerg-400	319	21	of	of	ADP
fuelectenerg-400	319	22	ways	way	NOUN
fuelectenerg-400	319	23	the	the	DET
fuelectenerg-400	319	24	lozenges	lozenge	NOUN
fuelectenerg-400	319	25	constituting	constitute	VERB
fuelectenerg-400	319	26	a	a	DET
fuelectenerg-400	319	27	lozenge	lozenge	NOUN
fuelectenerg-400	319	28	tiling	tiling	NOUN
fuelectenerg-400	319	29	can	can	AUX
fuelectenerg-400	319	30	be	be	AUX
fuelectenerg-400	319	31	colored	color	VERB
fuelectenerg-400	319	32	.	.	PUNCT
fuelectenerg-400	320	1	given	give	VERB
fuelectenerg-400	320	2	a	a	DET
fuelectenerg-400	320	3	lozenge	lozenge	NOUN
fuelectenerg-400	320	4	tiling	tiling	NOUN
fuelectenerg-400	320	5	of	of	ADP
fuelectenerg-400	320	6	an	an	DET
fuelectenerg-400	320	7	(	(	PUNCT
fuelectenerg-400	320	8	n	n	X
fuelectenerg-400	320	9	,	,	PUNCT
fuelectenerg-400	320	10	n	n	CCONJ
fuelectenerg-400	320	11	,	,	PUNCT
fuelectenerg-400	320	12	n	n	CCONJ
fuelectenerg-400	320	13	)	)	PUNCT
fuelectenerg-400	320	14	hexagon	hexagon	PROPN
fuelectenerg-400	320	15	,	,	PUNCT
fuelectenerg-400	320	16	h	h	NOUN
fuelectenerg-400	320	17	,	,	PUNCT
fuelectenerg-400	320	18	the	the	DET
fuelectenerg-400	320	19	coloring	coloring	NOUN
fuelectenerg-400	320	20	of	of	ADP
fuelectenerg-400	320	21	the	the	DET
fuelectenerg-400	320	22	lozenges	lozenge	NOUN
fuelectenerg-400	320	23	can	can	AUX
fuelectenerg-400	320	24	not	not	PART
fuelectenerg-400	320	25	be	be	AUX
fuelectenerg-400	320	26	done	do	VERB
fuelectenerg-400	320	27	arbitrarily	arbitrarily	ADV
fuelectenerg-400	320	28	.	.	PUNCT
fuelectenerg-400	321	1	to	to	PART
fuelectenerg-400	321	2	explain	explain	VERB
fuelectenerg-400	321	3	this	this	PRON
fuelectenerg-400	321	4	,	,	PUNCT
fuelectenerg-400	321	5	we	we	PRON
fuelectenerg-400	321	6	consider	consider	VERB
fuelectenerg-400	321	7	a	a	DET
fuelectenerg-400	321	8	colored	colored	ADJ
fuelectenerg-400	321	9	lozenge	lozenge	NOUN
fuelectenerg-400	321	10	tiling	tiling	NOUN
fuelectenerg-400	321	11	of	of	ADP
fuelectenerg-400	321	12	the	the	DET
fuelectenerg-400	321	13	(	(	PUNCT
fuelectenerg-400	321	14	2	2	NUM
fuelectenerg-400	321	15	,	,	PUNCT
fuelectenerg-400	321	16	1	1	NUM
fuelectenerg-400	321	17	,	,	PUNCT
fuelectenerg-400	321	18	1	1	NUM
fuelectenerg-400	321	19	)	)	PUNCT
fuelectenerg-400	321	20	hexagon	hexagon	NOUN
fuelectenerg-400	321	21	which	which	PRON
fuelectenerg-400	321	22	is	be	AUX
fuelectenerg-400	321	23	shown	show	VERB
fuelectenerg-400	321	24	in	in	ADP
fuelectenerg-400	321	25	figure	figure	NOUN
fuelectenerg-400	321	26	6	6	NUM
fuelectenerg-400	321	27	.	.	PUNCT
fuelectenerg-400	321	28	figure	figure	NOUN
fuelectenerg-400	321	29	6(a	6(a	NUM
fuelectenerg-400	321	30	)	)	PUNCT
fuelectenerg-400	321	31	shows	show	VERB
fuelectenerg-400	321	32	the	the	DET
fuelectenerg-400	321	33	colored	colored	ADJ
fuelectenerg-400	321	34	lozenge	lozenge	NOUN
fuelectenerg-400	321	35	tiling	tile	VERB
fuelectenerg-400	321	36	without	without	ADP
fuelectenerg-400	321	37	any	any	DET
fuelectenerg-400	321	38	boundaries	boundary	NOUN
fuelectenerg-400	321	39	.	.	PUNCT
fuelectenerg-400	322	1	in	in	ADP
fuelectenerg-400	322	2	the	the	DET
fuelectenerg-400	322	3	absence	absence	NOUN
fuelectenerg-400	322	4	of	of	ADP
fuelectenerg-400	322	5	the	the	DET
fuelectenerg-400	322	6	tiling	tile	VERB
fuelectenerg-400	322	7	information	information	NOUN
fuelectenerg-400	322	8	,	,	PUNCT
fuelectenerg-400	322	9	the	the	DET
fuelectenerg-400	322	10	decoder	decoder	NOUN
fuelectenerg-400	322	11	would	would	AUX
fuelectenerg-400	322	12	not	not	PART
fuelectenerg-400	322	13	be	be	AUX
fuelectenerg-400	322	14	able	able	ADJ
fuelectenerg-400	322	15	to	to	PART
fuelectenerg-400	322	16	decode	decode	VERB
fuelectenerg-400	322	17	this	this	DET
fuelectenerg-400	322	18	tiling	tile	VERB
fuelectenerg-400	322	19	correctly	correctly	ADV
fuelectenerg-400	322	20	.	.	PUNCT
fuelectenerg-400	323	1	figures	figure	NOUN
fuelectenerg-400	323	2	6(b	6(b	NUM
fuelectenerg-400	323	3	)	)	PUNCT
fuelectenerg-400	323	4	and	and	CCONJ
fuelectenerg-400	323	5	6(c	6(c	NUM
fuelectenerg-400	323	6	)	)	PUNCT
fuelectenerg-400	323	7	show	show	VERB
fuelectenerg-400	323	8	two	two	NUM
fuelectenerg-400	323	9	possible	possible	ADJ
fuelectenerg-400	323	10	lozenge	lozenge	NOUN
fuelectenerg-400	323	11	tilings	tiling	NOUN
fuelectenerg-400	323	12	this	this	PRON
fuelectenerg-400	323	13	can	can	AUX
fuelectenerg-400	323	14	be	be	AUX
fuelectenerg-400	323	15	decoded	decode	VERB
fuelectenerg-400	323	16	to	to	ADP
fuelectenerg-400	323	17	.	.	PUNCT
fuelectenerg-400	324	1	this	this	PRON
fuelectenerg-400	324	2	means	mean	VERB
fuelectenerg-400	324	3	that	that	SCONJ
fuelectenerg-400	324	4	in	in	ADP
fuelectenerg-400	324	5	the	the	DET
fuelectenerg-400	324	6	absence	absence	NOUN
fuelectenerg-400	324	7	of	of	ADP
fuelectenerg-400	324	8	knowledge	knowledge	NOUN
fuelectenerg-400	324	9	of	of	ADP
fuelectenerg-400	324	10	the	the	DET
fuelectenerg-400	324	11	tiling	tiling	NOUN
fuelectenerg-400	324	12	pattern	pattern	NOUN
fuelectenerg-400	324	13	,	,	PUNCT
fuelectenerg-400	324	14	the	the	DET
fuelectenerg-400	324	15	colored	colored	ADJ
fuelectenerg-400	324	16	tiling	tile	VERB
fuelectenerg-400	324	17	in	in	ADP
fuelectenerg-400	324	18	figure	figure	NOUN
fuelectenerg-400	324	19	6(a	6(a	NUM
fuelectenerg-400	324	20	)	)	PUNCT
fuelectenerg-400	324	21	is	be	AUX
fuelectenerg-400	324	22	not	not	PART
fuelectenerg-400	324	23	uniquely	uniquely	ADV
fuelectenerg-400	324	24	decodable	decodable	ADJ
fuelectenerg-400	324	25	.	.	PUNCT
fuelectenerg-400	325	1	in	in	ADP
fuelectenerg-400	325	2	particular	particular	ADJ
fuelectenerg-400	325	3	,	,	PUNCT
fuelectenerg-400	325	4	the	the	DET
fuelectenerg-400	325	5	two	two	NUM
fuelectenerg-400	325	6	tilings	tiling	NOUN
fuelectenerg-400	325	7	of	of	ADP
fuelectenerg-400	325	8	the	the	DET
fuelectenerg-400	325	9	(	(	PUNCT
fuelectenerg-400	325	10	1	1	NUM
fuelectenerg-400	325	11	,	,	PUNCT
fuelectenerg-400	325	12	1	1	NUM
fuelectenerg-400	325	13	,	,	PUNCT
fuelectenerg-400	325	14	1	1	X
fuelectenerg-400	325	15	)	)	PUNCT
fuelectenerg-400	325	16	hexagon	hexagon	NOUN
fuelectenerg-400	325	17	formed	form	VERB
fuelectenerg-400	325	18	at	at	ADP
fuelectenerg-400	325	19	the	the	DET
fuelectenerg-400	325	20	bottom	bottom	NOUN
fuelectenerg-400	325	21	of	of	ADP
fuelectenerg-400	325	22	the	the	DET
fuelectenerg-400	325	23	larger	large	ADJ
fuelectenerg-400	325	24	hexagon	hexagon	NOUN
fuelectenerg-400	325	25	(	(	PUNCT
fuelectenerg-400	325	26	marked	mark	VERB
fuelectenerg-400	325	27	with	with	ADP
fuelectenerg-400	325	28	bold	bold	ADJ
fuelectenerg-400	325	29	edges	edge	NOUN
fuelectenerg-400	325	30	)	)	PUNCT
fuelectenerg-400	325	31	can	can	AUX
fuelectenerg-400	325	32	not	not	PART
fuelectenerg-400	325	33	be	be	AUX
fuelectenerg-400	325	34	identified	identify	VERB
fuelectenerg-400	325	35	uniquely	uniquely	ADV
fuelectenerg-400	325	36	.	.	PUNCT
fuelectenerg-400	326	1	we	we	PRON
fuelectenerg-400	326	2	denote	denote	VERB
fuelectenerg-400	326	3	the	the	DET
fuelectenerg-400	326	4	(	(	PUNCT
fuelectenerg-400	326	5	1	1	NUM
fuelectenerg-400	326	6	,	,	PUNCT
fuelectenerg-400	326	7	1	1	NUM
fuelectenerg-400	326	8	,	,	PUNCT
fuelectenerg-400	326	9	1	1	X
fuelectenerg-400	326	10	)	)	PUNCT
fuelectenerg-400	326	11	hexagon	hexagon	NOUN
fuelectenerg-400	326	12	formed	form	VERB
fuelectenerg-400	326	13	in	in	ADP
fuelectenerg-400	326	14	fig	fig	NOUN
fuelectenerg-400	326	15	.	.	PUNCT
fuelectenerg-400	327	1	6(b	6(b	NUM
fuelectenerg-400	327	2	)	)	PUNCT
fuelectenerg-400	327	3	and	and	CCONJ
fuelectenerg-400	327	4	fig	fig	NOUN
fuelectenerg-400	327	5	.	.	PUNCT
fuelectenerg-400	328	1	6(c	6(c	NUM
fuelectenerg-400	328	2	)	)	PUNCT
fuelectenerg-400	328	3	as	as	ADP
fuelectenerg-400	328	4	type1	type1	NOUN
fuelectenerg-400	328	5	and	and	CCONJ
fuelectenerg-400	328	6	type-2	type-2	NUM
fuelectenerg-400	328	7	hexagon	hexagon	NOUN
fuelectenerg-400	328	8	,	,	PUNCT
fuelectenerg-400	328	9	respectively	respectively	ADV
fuelectenerg-400	328	10	.	.	PUNCT
fuelectenerg-400	329	1	to	to	PART
fuelectenerg-400	329	2	distinguish	distinguish	VERB
fuelectenerg-400	329	3	the	the	DET
fuelectenerg-400	329	4	two	two	NUM
fuelectenerg-400	329	5	hexagons	hexagon	NOUN
fuelectenerg-400	329	6	,	,	PUNCT
fuelectenerg-400	329	7	we	we	PRON
fuelectenerg-400	329	8	apply	apply	VERB
fuelectenerg-400	329	9	the	the	DET
fuelectenerg-400	329	10	following	follow	VERB
fuelectenerg-400	329	11	rule	rule	NOUN
fuelectenerg-400	329	12	:	:	PUNCT
fuelectenerg-400	329	13	whenever	whenever	SCONJ
fuelectenerg-400	329	14	a	a	DET
fuelectenerg-400	329	15	type-1	type-1	PROPN
fuelectenerg-400	329	16	hexagon	hexagon	NOUN
fuelectenerg-400	329	17	is	be	AUX
fuelectenerg-400	329	18	encountered	encounter	VERB
fuelectenerg-400	329	19	,	,	PUNCT
fuelectenerg-400	329	20	the	the	DET
fuelectenerg-400	329	21	vertical	vertical	ADJ
fuelectenerg-400	329	22	lozenges	lozenge	NOUN
fuelectenerg-400	329	23	of	of	ADP
fuelectenerg-400	329	24	different	different	ADJ
fuelectenerg-400	329	25	orientation	orientation	NOUN
fuelectenerg-400	329	26	,	,	PUNCT
fuelectenerg-400	329	27	i.e.	i.e.	X
fuelectenerg-400	329	28	,	,	PUNCT
fuelectenerg-400	329	29	type	type	NOUN
fuelectenerg-400	329	30	-	-	PUNCT
fuelectenerg-400	329	31	b	b	NOUN
fuelectenerg-400	329	32	and	and	CCONJ
fuelectenerg-400	329	33	type	type	NOUN
fuelectenerg-400	329	34	-	-	PUNCT
fuelectenerg-400	329	35	c	c	NOUN
fuelectenerg-400	329	36	lozenges	lozenge	NOUN
fuelectenerg-400	329	37	constituting	constitute	VERB
fuelectenerg-400	329	38	528	528	NUM
fuelectenerg-400	329	39	b.	b.	NOUN
fuelectenerg-400	329	40	vasic	vasic	NOUN
fuelectenerg-400	329	41	,	,	PUNCT
fuelectenerg-400	329	42	a.	a.	PROPN
fuelectenerg-400	329	43	r.	r.	PROPN
fuelectenerg-400	329	44	krishnan	krishnan	PROPN
fuelectenerg-400	329	45	lozenge	lozenge	PROPN
fuelectenerg-400	329	46	tiling	tile	VERB
fuelectenerg-400	329	47	constrained	constrained	ADJ
fuelectenerg-400	329	48	codes	code	NOUN
fuelectenerg-400	329	49	529	529	NUM
fuelectenerg-400	329	50	528	528	NUM
fuelectenerg-400	329	51	a.	a.	NOUN
fuelectenerg-400	329	52	r.	r.	PROPN
fuelectenerg-400	329	53	krishnanan	krishnanan	PROPN
fuelectenerg-400	329	54	and	and	CCONJ
fuelectenerg-400	329	55	b.	b.	PROPN
fuelectenerg-400	329	56	vasić	vasić	PROPN
fuelectenerg-400	329	57	above	above	ADV
fuelectenerg-400	329	58	.	.	PUNCT
fuelectenerg-400	330	1	the	the	DET
fuelectenerg-400	330	2	young	young	PROPN
fuelectenerg-400	330	3	’s	’s	PART
fuelectenerg-400	330	4	solid	solid	ADJ
fuelectenerg-400	330	5	diagram	diagram	NOUN
fuelectenerg-400	330	6	construction	construction	NOUN
fuelectenerg-400	330	7	is	be	AUX
fuelectenerg-400	330	8	also	also	ADV
fuelectenerg-400	330	9	apparent	apparent	ADJ
fuelectenerg-400	330	10	if	if	SCONJ
fuelectenerg-400	330	11	the	the	DET
fuelectenerg-400	330	12	tiled	tile	VERB
fuelectenerg-400	330	13	(	(	PUNCT
fuelectenerg-400	330	14	2	2	NUM
fuelectenerg-400	330	15	,	,	PUNCT
fuelectenerg-400	330	16	3	3	NUM
fuelectenerg-400	330	17	,	,	PUNCT
fuelectenerg-400	330	18	4	4	X
fuelectenerg-400	330	19	)	)	PUNCT
fuelectenerg-400	330	20	hexagon	hexagon	NOUN
fuelectenerg-400	330	21	is	be	AUX
fuelectenerg-400	330	22	visualized	visualize	VERB
fuelectenerg-400	330	23	as	as	ADP
fuelectenerg-400	330	24	a	a	DET
fuelectenerg-400	330	25	2	2	NUM
fuelectenerg-400	330	26	×	×	NOUN
fuelectenerg-400	330	27	3	3	NUM
fuelectenerg-400	330	28	×	×	NOUN
fuelectenerg-400	330	29	4	4	NUM
fuelectenerg-400	330	30	box	box	NOUN
fuelectenerg-400	330	31	.	.	PUNCT
fuelectenerg-400	331	1	for	for	ADP
fuelectenerg-400	331	2	ease	ease	NOUN
fuelectenerg-400	331	3	of	of	ADP
fuelectenerg-400	331	4	visualization	visualization	NOUN
fuelectenerg-400	331	5	,	,	PUNCT
fuelectenerg-400	331	6	the	the	DET
fuelectenerg-400	331	7	top	top	ADJ
fuelectenerg-400	331	8	face	face	NOUN
fuelectenerg-400	331	9	of	of	ADP
fuelectenerg-400	331	10	the	the	DET
fuelectenerg-400	331	11	topmost	topmost	PROPN
fuelectenerg-400	331	12	box	box	NOUN
fuelectenerg-400	331	13	is	be	AUX
fuelectenerg-400	331	14	colored	color	VERB
fuelectenerg-400	331	15	black	black	ADJ
fuelectenerg-400	331	16	.	.	PUNCT
fuelectenerg-400	332	1	the	the	DET
fuelectenerg-400	332	2	relationship	relationship	NOUN
fuelectenerg-400	332	3	between	between	ADP
fuelectenerg-400	332	4	lozenge	lozenge	NOUN
fuelectenerg-400	332	5	tiling	tile	VERB
fuelectenerg-400	332	6	and	and	CCONJ
fuelectenerg-400	332	7	boxed	boxed	ADJ
fuelectenerg-400	332	8	plane	plane	NOUN
fuelectenerg-400	332	9	partition	partition	NOUN
fuelectenerg-400	332	10	is	be	AUX
fuelectenerg-400	332	11	given	give	VERB
fuelectenerg-400	332	12	by	by	ADP
fuelectenerg-400	332	13	the	the	DET
fuelectenerg-400	332	14	theorem	theorem	NOUN
fuelectenerg-400	332	15	1	1	NUM
fuelectenerg-400	332	16	in	in	ADP
fuelectenerg-400	332	17	[	[	X
fuelectenerg-400	332	18	18	18	NUM
fuelectenerg-400	332	19	]	]	PUNCT
fuelectenerg-400	332	20	.	.	PUNCT
fuelectenerg-400	333	1	lemma	lemma	PROPN
fuelectenerg-400	333	2	1	1	NUM
fuelectenerg-400	333	3	the	the	DET
fuelectenerg-400	333	4	number	number	NOUN
fuelectenerg-400	333	5	of	of	ADP
fuelectenerg-400	333	6	boxed	boxed	ADJ
fuelectenerg-400	333	7	plane	plane	NOUN
fuelectenerg-400	333	8	partitions	partition	NOUN
fuelectenerg-400	333	9	fitting	fit	VERB
fuelectenerg-400	333	10	inside	inside	ADP
fuelectenerg-400	333	11	a	a	DET
fuelectenerg-400	333	12	a	a	DET
fuelectenerg-400	333	13	×	×	NOUN
fuelectenerg-400	333	14	b	b	PROPN
fuelectenerg-400	333	15	×	×	PROPN
fuelectenerg-400	333	16	c	c	PROPN
fuelectenerg-400	333	17	box	box	PROPN
fuelectenerg-400	333	18	is	be	AUX
fuelectenerg-400	333	19	equal	equal	ADJ
fuelectenerg-400	333	20	to	to	ADP
fuelectenerg-400	333	21	the	the	DET
fuelectenerg-400	333	22	number	number	NOUN
fuelectenerg-400	333	23	of	of	ADP
fuelectenerg-400	333	24	lozenge	lozenge	ADJ
fuelectenerg-400	333	25	tilings	tiling	NOUN
fuelectenerg-400	333	26	of	of	ADP
fuelectenerg-400	333	27	an	an	DET
fuelectenerg-400	333	28	(	(	PUNCT
fuelectenerg-400	333	29	a	a	PROPN
fuelectenerg-400	333	30	,	,	PUNCT
fuelectenerg-400	333	31	b	b	NOUN
fuelectenerg-400	333	32	,	,	PUNCT
fuelectenerg-400	333	33	c	c	NOUN
fuelectenerg-400	333	34	)	)	PUNCT
fuelectenerg-400	333	35	hexagon	hexagon	NOUN
fuelectenerg-400	333	36	.	.	PUNCT
fuelectenerg-400	334	1	proof	proof	NOUN
fuelectenerg-400	334	2	:	:	PUNCT
fuelectenerg-400	334	3	the	the	DET
fuelectenerg-400	334	4	proof	proof	NOUN
fuelectenerg-400	334	5	is	be	AUX
fuelectenerg-400	334	6	based	base	VERB
fuelectenerg-400	334	7	on	on	ADP
fuelectenerg-400	334	8	macmahon	macmahon	PROPN
fuelectenerg-400	335	1	[	[	X
fuelectenerg-400	335	2	16	16	NUM
fuelectenerg-400	335	3	]	]	PUNCT
fuelectenerg-400	335	4	formula	formula	NOUN
fuelectenerg-400	335	5	.	.	PUNCT
fuelectenerg-400	336	1	4.2	4.2	NUM
fuelectenerg-400	336	2	bounds	bound	NOUN
fuelectenerg-400	336	3	on	on	ADP
fuelectenerg-400	336	4	ct	ct	NUM
fuelectenerg-400	336	5	by	by	ADP
fuelectenerg-400	336	6	lemma	lemma	PROPN
fuelectenerg-400	336	7	1	1	NUM
fuelectenerg-400	336	8	,	,	PUNCT
fuelectenerg-400	336	9	the	the	DET
fuelectenerg-400	336	10	number	number	NOUN
fuelectenerg-400	336	11	of	of	ADP
fuelectenerg-400	336	12	lozenge	lozenge	NOUN
fuelectenerg-400	336	13	tiling	tiling	NOUN
fuelectenerg-400	336	14	of	of	ADP
fuelectenerg-400	336	15	any	any	DET
fuelectenerg-400	336	16	(	(	PUNCT
fuelectenerg-400	336	17	a	a	PRON
fuelectenerg-400	336	18	,	,	PUNCT
fuelectenerg-400	336	19	b	b	NOUN
fuelectenerg-400	336	20	,	,	PUNCT
fuelectenerg-400	336	21	c	c	NOUN
fuelectenerg-400	336	22	)	)	PUNCT
fuelectenerg-400	336	23	hexagon	hexagon	NOUN
fuelectenerg-400	336	24	is	be	AUX
fuelectenerg-400	336	25	equal	equal	ADJ
fuelectenerg-400	336	26	to	to	ADP
fuelectenerg-400	336	27	the	the	DET
fuelectenerg-400	336	28	number	number	NOUN
fuelectenerg-400	336	29	of	of	ADP
fuelectenerg-400	336	30	boxed	boxed	ADJ
fuelectenerg-400	336	31	partitions	partition	NOUN
fuelectenerg-400	336	32	fitting	fitting	ADJ
fuelectenerg-400	336	33	inside	inside	ADP
fuelectenerg-400	336	34	an	an	DET
fuelectenerg-400	336	35	a×b×c	a×b×c	PROPN
fuelectenerg-400	336	36	box	box	NOUN
fuelectenerg-400	336	37	.	.	PUNCT
fuelectenerg-400	337	1	macmahon	macmahon	PROPN
fuelectenerg-400	338	1	[	[	X
fuelectenerg-400	338	2	16	16	NUM
fuelectenerg-400	338	3	]	]	PUNCT
fuelectenerg-400	338	4	found	find	VERB
fuelectenerg-400	338	5	the	the	DET
fuelectenerg-400	338	6	number	number	NOUN
fuelectenerg-400	338	7	of	of	ADP
fuelectenerg-400	338	8	such	such	ADJ
fuelectenerg-400	338	9	partitions	partition	NOUN
fuelectenerg-400	338	10	,	,	PUNCT
fuelectenerg-400	338	11	n(a	n(a	PROPN
fuelectenerg-400	338	12	,	,	PUNCT
fuelectenerg-400	338	13	b	b	NOUN
fuelectenerg-400	338	14	,	,	PUNCT
fuelectenerg-400	338	15	c	c	NOUN
fuelectenerg-400	338	16	)	)	PUNCT
fuelectenerg-400	338	17	,	,	PUNCT
fuelectenerg-400	338	18	to	to	PART
fuelectenerg-400	338	19	be	be	AUX
fuelectenerg-400	338	20	n(a	n(a	PROPN
fuelectenerg-400	338	21	,	,	PUNCT
fuelectenerg-400	338	22	b	b	NOUN
fuelectenerg-400	338	23	,	,	PUNCT
fuelectenerg-400	338	24	c	c	NOUN
fuelectenerg-400	338	25	)	)	PUNCT
fuelectenerg-400	338	26	=	=	PRON
fuelectenerg-400	338	27	∏a	∏a	VERB
fuelectenerg-400	338	28	i=1(c+	i=1(c+	PROPN
fuelectenerg-400	338	29	i)b/(i)b	i)b/(i)b	PROPN
fuelectenerg-400	338	30	where	where	SCONJ
fuelectenerg-400	338	31	(	(	PUNCT
fuelectenerg-400	338	32	i)n	i)n	VERB
fuelectenerg-400	338	33	:	:	PUNCT
fuelectenerg-400	338	34	=	=	SYM
fuelectenerg-400	338	35	i(i	i(i	PROPN
fuelectenerg-400	338	36	+	+	CCONJ
fuelectenerg-400	338	37	1)(i	1)(i	NUM
fuelectenerg-400	338	38	+	+	CCONJ
fuelectenerg-400	338	39	2	2	NUM
fuelectenerg-400	338	40	)	)	PUNCT
fuelectenerg-400	338	41	.	.	PUNCT
fuelectenerg-400	338	42	.	.	PUNCT
fuelectenerg-400	339	1	.	.	PUNCT
fuelectenerg-400	340	1	(	(	PUNCT
fuelectenerg-400	340	2	i	i	PRON
fuelectenerg-400	340	3	+	+	CCONJ
fuelectenerg-400	340	4	n	n	CCONJ
fuelectenerg-400	340	5	−	−	PROPN
fuelectenerg-400	340	6	1	1	NUM
fuelectenerg-400	340	7	)	)	PUNCT
fuelectenerg-400	340	8	is	be	AUX
fuelectenerg-400	340	9	the	the	DET
fuelectenerg-400	340	10	rising	rise	VERB
fuelectenerg-400	340	11	factorial	factorial	NOUN
fuelectenerg-400	340	12	.	.	PUNCT
fuelectenerg-400	341	1	for	for	ADP
fuelectenerg-400	341	2	an	an	DET
fuelectenerg-400	341	3	equilateral	equilateral	ADJ
fuelectenerg-400	341	4	hexagon	hexagon	NOUN
fuelectenerg-400	341	5	,	,	PUNCT
fuelectenerg-400	341	6	we	we	PRON
fuelectenerg-400	341	7	were	be	AUX
fuelectenerg-400	341	8	able	able	ADJ
fuelectenerg-400	341	9	to	to	PART
fuelectenerg-400	341	10	find	find	VERB
fuelectenerg-400	341	11	the	the	DET
fuelectenerg-400	341	12	capacity	capacity	NOUN
fuelectenerg-400	341	13	of	of	ADP
fuelectenerg-400	341	14	tiling	tile	VERB
fuelectenerg-400	341	15	(	(	PUNCT
fuelectenerg-400	341	16	without	without	ADP
fuelectenerg-400	341	17	coloring	color	VERB
fuelectenerg-400	341	18	)	)	PUNCT
fuelectenerg-400	341	19	in	in	ADP
fuelectenerg-400	341	20	a	a	DET
fuelectenerg-400	341	21	closed	closed	ADJ
fuelectenerg-400	341	22	form	form	NOUN
fuelectenerg-400	341	23	.	.	PUNCT
fuelectenerg-400	342	1	it	it	PRON
fuelectenerg-400	342	2	is	be	AUX
fuelectenerg-400	342	3	given	give	VERB
fuelectenerg-400	342	4	by	by	ADP
fuelectenerg-400	342	5	theorem	theorem	NOUN
fuelectenerg-400	342	6	1	1	NUM
fuelectenerg-400	342	7	.	.	PUNCT
fuelectenerg-400	342	8	theorem	theorem	VERB
fuelectenerg-400	342	9	1	1	NUM
fuelectenerg-400	342	10	the	the	DET
fuelectenerg-400	342	11	capacity	capacity	NOUN
fuelectenerg-400	342	12	of	of	ADP
fuelectenerg-400	342	13	the	the	DET
fuelectenerg-400	342	14	lozenge	lozenge	NOUN
fuelectenerg-400	342	15	tiling	tile	VERB
fuelectenerg-400	342	16	for	for	ADP
fuelectenerg-400	342	17	an	an	DET
fuelectenerg-400	342	18	equilateral	equilateral	ADJ
fuelectenerg-400	342	19	hexagon	hexagon	NOUN
fuelectenerg-400	342	20	is	be	AUX
fuelectenerg-400	343	1	ct	ct	NOUN
fuelectenerg-400	343	2	=	=	SYM
fuelectenerg-400	343	3	3	3	NUM
fuelectenerg-400	343	4	4	4	NUM
fuelectenerg-400	343	5	log2	log2	NOUN
fuelectenerg-400	343	6	3	3	NUM
fuelectenerg-400	343	7	−	−	NOUN
fuelectenerg-400	343	8	1	1	NUM
fuelectenerg-400	343	9	.	.	PUNCT
fuelectenerg-400	343	10	proof	proof	NOUN
fuelectenerg-400	343	11	:	:	PUNCT
fuelectenerg-400	343	12	the	the	DET
fuelectenerg-400	343	13	proof	proof	NOUN
fuelectenerg-400	343	14	follows	follow	VERB
fuelectenerg-400	343	15	from	from	ADP
fuelectenerg-400	343	16	lemma	lemma	PROPN
fuelectenerg-400	343	17	1	1	NUM
fuelectenerg-400	343	18	as	as	SCONJ
fuelectenerg-400	343	19	given	give	VERB
fuelectenerg-400	343	20	in	in	ADP
fuelectenerg-400	343	21	appendix	appendix	ADJ
fuelectenerg-400	343	22	7	7	NUM
fuelectenerg-400	343	23	note	note	NOUN
fuelectenerg-400	343	24	that	that	PRON
fuelectenerg-400	343	25	closed	close	VERB
fuelectenerg-400	343	26	forms	form	NOUN
fuelectenerg-400	343	27	solutions	solution	NOUN
fuelectenerg-400	343	28	for	for	ADP
fuelectenerg-400	343	29	the	the	DET
fuelectenerg-400	343	30	capacity	capacity	NOUN
fuelectenerg-400	343	31	such	such	ADJ
fuelectenerg-400	343	32	as	as	ADP
fuelectenerg-400	343	33	one	one	NUM
fuelectenerg-400	343	34	given	give	VERB
fuelectenerg-400	343	35	by	by	ADP
fuelectenerg-400	343	36	the	the	DET
fuelectenerg-400	343	37	above	above	ADJ
fuelectenerg-400	343	38	theorem	theorem	NOUN
fuelectenerg-400	343	39	are	be	AUX
fuelectenerg-400	343	40	quite	quite	ADV
fuelectenerg-400	343	41	rare	rare	ADJ
fuelectenerg-400	343	42	in	in	ADP
fuelectenerg-400	343	43	problems	problem	NOUN
fuelectenerg-400	343	44	involving	involve	VERB
fuelectenerg-400	343	45	2d	2d	NUM
fuelectenerg-400	343	46	constraints	constraint	NOUN
fuelectenerg-400	343	47	.	.	PUNCT
fuelectenerg-400	344	1	4.3	4.3	NUM
fuelectenerg-400	344	2	bounds	bound	NOUN
fuelectenerg-400	344	3	on	on	ADP
fuelectenerg-400	344	4	cc	cc	ADP
fuelectenerg-400	344	5	the	the	DET
fuelectenerg-400	344	6	capacity	capacity	NOUN
fuelectenerg-400	344	7	of	of	ADP
fuelectenerg-400	344	8	the	the	DET
fuelectenerg-400	344	9	coloring	coloring	NOUN
fuelectenerg-400	344	10	problem	problem	NOUN
fuelectenerg-400	344	11	,	,	PUNCT
fuelectenerg-400	344	12	cc	cc	NOUN
fuelectenerg-400	344	13	,	,	PUNCT
fuelectenerg-400	344	14	can	can	AUX
fuelectenerg-400	344	15	be	be	AUX
fuelectenerg-400	344	16	estimated	estimate	VERB
fuelectenerg-400	344	17	by	by	ADP
fuelectenerg-400	344	18	counting	count	VERB
fuelectenerg-400	344	19	the	the	DET
fuelectenerg-400	344	20	number	number	NOUN
fuelectenerg-400	344	21	of	of	ADP
fuelectenerg-400	344	22	ways	way	NOUN
fuelectenerg-400	344	23	the	the	DET
fuelectenerg-400	344	24	lozenges	lozenge	NOUN
fuelectenerg-400	344	25	constituting	constitute	VERB
fuelectenerg-400	344	26	a	a	DET
fuelectenerg-400	344	27	lozenge	lozenge	NOUN
fuelectenerg-400	344	28	tiling	tiling	NOUN
fuelectenerg-400	344	29	can	can	AUX
fuelectenerg-400	344	30	be	be	AUX
fuelectenerg-400	344	31	colored	color	VERB
fuelectenerg-400	344	32	.	.	PUNCT
fuelectenerg-400	345	1	given	give	VERB
fuelectenerg-400	345	2	a	a	DET
fuelectenerg-400	345	3	lozenge	lozenge	NOUN
fuelectenerg-400	345	4	tiling	tiling	NOUN
fuelectenerg-400	345	5	of	of	ADP
fuelectenerg-400	345	6	an	an	DET
fuelectenerg-400	345	7	(	(	PUNCT
fuelectenerg-400	345	8	n	n	X
fuelectenerg-400	345	9	,	,	PUNCT
fuelectenerg-400	345	10	n	n	CCONJ
fuelectenerg-400	345	11	,	,	PUNCT
fuelectenerg-400	345	12	n	n	CCONJ
fuelectenerg-400	345	13	)	)	PUNCT
fuelectenerg-400	345	14	hexagon	hexagon	PROPN
fuelectenerg-400	345	15	,	,	PUNCT
fuelectenerg-400	345	16	h	h	NOUN
fuelectenerg-400	345	17	,	,	PUNCT
fuelectenerg-400	345	18	the	the	DET
fuelectenerg-400	345	19	coloring	coloring	NOUN
fuelectenerg-400	345	20	of	of	ADP
fuelectenerg-400	345	21	the	the	DET
fuelectenerg-400	345	22	lozenges	lozenge	NOUN
fuelectenerg-400	345	23	can	can	AUX
fuelectenerg-400	345	24	not	not	PART
fuelectenerg-400	345	25	be	be	AUX
fuelectenerg-400	345	26	done	do	VERB
fuelectenerg-400	345	27	arbitrarily	arbitrarily	ADV
fuelectenerg-400	345	28	.	.	PUNCT
fuelectenerg-400	346	1	to	to	PART
fuelectenerg-400	346	2	explain	explain	VERB
fuelectenerg-400	346	3	this	this	PRON
fuelectenerg-400	346	4	,	,	PUNCT
fuelectenerg-400	346	5	we	we	PRON
fuelectenerg-400	346	6	consider	consider	VERB
fuelectenerg-400	346	7	a	a	DET
fuelectenerg-400	346	8	colored	colored	ADJ
fuelectenerg-400	346	9	lozenge	lozenge	NOUN
fuelectenerg-400	346	10	tiling	tiling	NOUN
fuelectenerg-400	346	11	of	of	ADP
fuelectenerg-400	346	12	the	the	DET
fuelectenerg-400	346	13	(	(	PUNCT
fuelectenerg-400	346	14	2	2	NUM
fuelectenerg-400	346	15	,	,	PUNCT
fuelectenerg-400	346	16	1	1	NUM
fuelectenerg-400	346	17	,	,	PUNCT
fuelectenerg-400	346	18	1	1	NUM
fuelectenerg-400	346	19	)	)	PUNCT
fuelectenerg-400	346	20	hexagon	hexagon	NOUN
fuelectenerg-400	346	21	which	which	PRON
fuelectenerg-400	346	22	is	be	AUX
fuelectenerg-400	346	23	shown	show	VERB
fuelectenerg-400	346	24	in	in	ADP
fuelectenerg-400	346	25	figure	figure	NOUN
fuelectenerg-400	346	26	6	6	NUM
fuelectenerg-400	346	27	.	.	PUNCT
fuelectenerg-400	346	28	figure	figure	NOUN
fuelectenerg-400	346	29	6(a	6(a	NUM
fuelectenerg-400	346	30	)	)	PUNCT
fuelectenerg-400	346	31	shows	show	VERB
fuelectenerg-400	346	32	the	the	DET
fuelectenerg-400	346	33	colored	colored	ADJ
fuelectenerg-400	346	34	lozenge	lozenge	NOUN
fuelectenerg-400	346	35	tiling	tile	VERB
fuelectenerg-400	346	36	without	without	ADP
fuelectenerg-400	346	37	any	any	DET
fuelectenerg-400	346	38	boundaries	boundary	NOUN
fuelectenerg-400	346	39	.	.	PUNCT
fuelectenerg-400	347	1	in	in	ADP
fuelectenerg-400	347	2	the	the	DET
fuelectenerg-400	347	3	absence	absence	NOUN
fuelectenerg-400	347	4	of	of	ADP
fuelectenerg-400	347	5	the	the	DET
fuelectenerg-400	347	6	tiling	tile	VERB
fuelectenerg-400	347	7	information	information	NOUN
fuelectenerg-400	347	8	,	,	PUNCT
fuelectenerg-400	347	9	the	the	DET
fuelectenerg-400	347	10	decoder	decoder	NOUN
fuelectenerg-400	347	11	would	would	AUX
fuelectenerg-400	347	12	not	not	PART
fuelectenerg-400	347	13	be	be	AUX
fuelectenerg-400	347	14	able	able	ADJ
fuelectenerg-400	347	15	to	to	PART
fuelectenerg-400	347	16	decode	decode	VERB
fuelectenerg-400	347	17	this	this	DET
fuelectenerg-400	347	18	tiling	tile	VERB
fuelectenerg-400	347	19	correctly	correctly	ADV
fuelectenerg-400	347	20	.	.	PUNCT
fuelectenerg-400	348	1	figures	figure	NOUN
fuelectenerg-400	348	2	6(b	6(b	NUM
fuelectenerg-400	348	3	)	)	PUNCT
fuelectenerg-400	348	4	and	and	CCONJ
fuelectenerg-400	348	5	6(c	6(c	NUM
fuelectenerg-400	348	6	)	)	PUNCT
fuelectenerg-400	348	7	show	show	VERB
fuelectenerg-400	348	8	two	two	NUM
fuelectenerg-400	348	9	possible	possible	ADJ
fuelectenerg-400	348	10	lozenge	lozenge	NOUN
fuelectenerg-400	348	11	tilings	tiling	NOUN
fuelectenerg-400	348	12	this	this	PRON
fuelectenerg-400	348	13	can	can	AUX
fuelectenerg-400	348	14	be	be	AUX
fuelectenerg-400	348	15	decoded	decode	VERB
fuelectenerg-400	348	16	to	to	ADP
fuelectenerg-400	348	17	.	.	PUNCT
fuelectenerg-400	349	1	this	this	PRON
fuelectenerg-400	349	2	means	mean	VERB
fuelectenerg-400	349	3	that	that	SCONJ
fuelectenerg-400	349	4	in	in	ADP
fuelectenerg-400	349	5	the	the	DET
fuelectenerg-400	349	6	absence	absence	NOUN
fuelectenerg-400	349	7	of	of	ADP
fuelectenerg-400	349	8	knowledge	knowledge	NOUN
fuelectenerg-400	349	9	of	of	ADP
fuelectenerg-400	349	10	the	the	DET
fuelectenerg-400	349	11	tiling	tiling	NOUN
fuelectenerg-400	349	12	pattern	pattern	NOUN
fuelectenerg-400	349	13	,	,	PUNCT
fuelectenerg-400	349	14	the	the	DET
fuelectenerg-400	349	15	colored	colored	ADJ
fuelectenerg-400	349	16	tiling	tile	VERB
fuelectenerg-400	349	17	in	in	ADP
fuelectenerg-400	349	18	figure	figure	NOUN
fuelectenerg-400	349	19	6(a	6(a	NUM
fuelectenerg-400	349	20	)	)	PUNCT
fuelectenerg-400	349	21	is	be	AUX
fuelectenerg-400	349	22	not	not	PART
fuelectenerg-400	349	23	uniquely	uniquely	ADV
fuelectenerg-400	349	24	decodable	decodable	ADJ
fuelectenerg-400	349	25	.	.	PUNCT
fuelectenerg-400	350	1	in	in	ADP
fuelectenerg-400	350	2	particular	particular	ADJ
fuelectenerg-400	350	3	,	,	PUNCT
fuelectenerg-400	350	4	the	the	DET
fuelectenerg-400	350	5	two	two	NUM
fuelectenerg-400	350	6	tilings	tiling	NOUN
fuelectenerg-400	350	7	of	of	ADP
fuelectenerg-400	350	8	the	the	DET
fuelectenerg-400	350	9	(	(	PUNCT
fuelectenerg-400	350	10	1	1	NUM
fuelectenerg-400	350	11	,	,	PUNCT
fuelectenerg-400	350	12	1	1	NUM
fuelectenerg-400	350	13	,	,	PUNCT
fuelectenerg-400	350	14	1	1	X
fuelectenerg-400	350	15	)	)	PUNCT
fuelectenerg-400	350	16	hexagon	hexagon	NOUN
fuelectenerg-400	350	17	formed	form	VERB
fuelectenerg-400	350	18	at	at	ADP
fuelectenerg-400	350	19	the	the	DET
fuelectenerg-400	350	20	bottom	bottom	NOUN
fuelectenerg-400	350	21	of	of	ADP
fuelectenerg-400	350	22	the	the	DET
fuelectenerg-400	350	23	larger	large	ADJ
fuelectenerg-400	350	24	hexagon	hexagon	NOUN
fuelectenerg-400	350	25	(	(	PUNCT
fuelectenerg-400	350	26	marked	mark	VERB
fuelectenerg-400	350	27	with	with	ADP
fuelectenerg-400	350	28	bold	bold	ADJ
fuelectenerg-400	350	29	edges	edge	NOUN
fuelectenerg-400	350	30	)	)	PUNCT
fuelectenerg-400	350	31	can	can	AUX
fuelectenerg-400	350	32	not	not	PART
fuelectenerg-400	350	33	be	be	AUX
fuelectenerg-400	350	34	identified	identify	VERB
fuelectenerg-400	350	35	uniquely	uniquely	ADV
fuelectenerg-400	350	36	.	.	PUNCT
fuelectenerg-400	351	1	we	we	PRON
fuelectenerg-400	351	2	denote	denote	VERB
fuelectenerg-400	351	3	the	the	DET
fuelectenerg-400	351	4	(	(	PUNCT
fuelectenerg-400	351	5	1	1	NUM
fuelectenerg-400	351	6	,	,	PUNCT
fuelectenerg-400	351	7	1	1	NUM
fuelectenerg-400	351	8	,	,	PUNCT
fuelectenerg-400	351	9	1	1	X
fuelectenerg-400	351	10	)	)	PUNCT
fuelectenerg-400	351	11	hexagon	hexagon	NOUN
fuelectenerg-400	351	12	formed	form	VERB
fuelectenerg-400	351	13	in	in	ADP
fuelectenerg-400	351	14	fig	fig	NOUN
fuelectenerg-400	351	15	.	.	PUNCT
fuelectenerg-400	352	1	6(b	6(b	NUM
fuelectenerg-400	352	2	)	)	PUNCT
fuelectenerg-400	352	3	and	and	CCONJ
fuelectenerg-400	352	4	fig	fig	NOUN
fuelectenerg-400	352	5	.	.	PUNCT
fuelectenerg-400	353	1	6(c	6(c	NUM
fuelectenerg-400	353	2	)	)	PUNCT
fuelectenerg-400	353	3	as	as	ADP
fuelectenerg-400	353	4	type1	type1	NOUN
fuelectenerg-400	353	5	and	and	CCONJ
fuelectenerg-400	353	6	type-2	type-2	NUM
fuelectenerg-400	353	7	hexagon	hexagon	NOUN
fuelectenerg-400	353	8	,	,	PUNCT
fuelectenerg-400	353	9	respectively	respectively	ADV
fuelectenerg-400	353	10	.	.	PUNCT
fuelectenerg-400	354	1	to	to	PART
fuelectenerg-400	354	2	distinguish	distinguish	VERB
fuelectenerg-400	354	3	the	the	DET
fuelectenerg-400	354	4	two	two	NUM
fuelectenerg-400	354	5	hexagons	hexagon	NOUN
fuelectenerg-400	354	6	,	,	PUNCT
fuelectenerg-400	354	7	we	we	PRON
fuelectenerg-400	354	8	apply	apply	VERB
fuelectenerg-400	354	9	the	the	DET
fuelectenerg-400	354	10	following	follow	VERB
fuelectenerg-400	354	11	rule	rule	NOUN
fuelectenerg-400	354	12	:	:	PUNCT
fuelectenerg-400	354	13	whenever	whenever	SCONJ
fuelectenerg-400	354	14	a	a	DET
fuelectenerg-400	354	15	type-1	type-1	PROPN
fuelectenerg-400	354	16	hexagon	hexagon	NOUN
fuelectenerg-400	354	17	is	be	AUX
fuelectenerg-400	354	18	encountered	encounter	VERB
fuelectenerg-400	354	19	,	,	PUNCT
fuelectenerg-400	354	20	the	the	DET
fuelectenerg-400	354	21	vertical	vertical	ADJ
fuelectenerg-400	354	22	lozenges	lozenge	NOUN
fuelectenerg-400	354	23	of	of	ADP
fuelectenerg-400	354	24	different	different	ADJ
fuelectenerg-400	354	25	orientation	orientation	NOUN
fuelectenerg-400	354	26	,	,	PUNCT
fuelectenerg-400	354	27	i.e.	i.e.	X
fuelectenerg-400	354	28	,	,	PUNCT
fuelectenerg-400	354	29	type	type	NOUN
fuelectenerg-400	354	30	-	-	PUNCT
fuelectenerg-400	354	31	b	b	NOUN
fuelectenerg-400	354	32	and	and	CCONJ
fuelectenerg-400	354	33	type	type	NOUN
fuelectenerg-400	354	34	-	-	PUNCT
fuelectenerg-400	354	35	c	c	NOUN
fuelectenerg-400	354	36	lozenges	lozenge	NOUN
fuelectenerg-400	354	37	constituting	constitute	VERB
fuelectenerg-400	354	38	detection	detection	NOUN
fuelectenerg-400	354	39	and	and	CCONJ
fuelectenerg-400	354	40	coding	code	VERB
fuelectenerg-400	354	41	for	for	ADP
fuelectenerg-400	354	42	tdmr	tdmr	NOUN
fuelectenerg-400	354	43	channel	channel	PROPN
fuelectenerg-400	354	44	529	529	NUM
fuelectenerg-400	354	45	(	(	PUNCT
fuelectenerg-400	354	46	a	a	NOUN
fuelectenerg-400	354	47	)	)	PUNCT
fuelectenerg-400	354	48	(	(	PUNCT
fuelectenerg-400	354	49	b	b	X
fuelectenerg-400	354	50	)	)	PUNCT
fuelectenerg-400	354	51	(	(	PUNCT
fuelectenerg-400	354	52	c	c	X
fuelectenerg-400	354	53	)	)	PUNCT
fuelectenerg-400	354	54	fig	fig	NOUN
fuelectenerg-400	354	55	.	.	PUNCT
fuelectenerg-400	355	1	6	6	NUM
fuelectenerg-400	355	2	.	.	X
fuelectenerg-400	355	3	figure	figure	NOUN
fuelectenerg-400	355	4	(	(	PUNCT
fuelectenerg-400	355	5	a	a	PRON
fuelectenerg-400	355	6	)	)	PUNCT
fuelectenerg-400	355	7	shows	show	VERB
fuelectenerg-400	355	8	a	a	DET
fuelectenerg-400	355	9	colored	colored	ADJ
fuelectenerg-400	355	10	lozenge	lozenge	NOUN
fuelectenerg-400	355	11	tiling	tile	VERB
fuelectenerg-400	355	12	for	for	ADP
fuelectenerg-400	355	13	a	a	DET
fuelectenerg-400	355	14	(	(	PUNCT
fuelectenerg-400	355	15	2	2	NUM
fuelectenerg-400	355	16	,	,	PUNCT
fuelectenerg-400	355	17	1	1	NUM
fuelectenerg-400	355	18	,	,	PUNCT
fuelectenerg-400	355	19	1	1	NUM
fuelectenerg-400	355	20	,	,	PUNCT
fuelectenerg-400	355	21	)	)	PUNCT
fuelectenerg-400	355	22	hexagon	hexagon	NOUN
fuelectenerg-400	355	23	.	.	PUNCT
fuelectenerg-400	356	1	in	in	ADP
fuelectenerg-400	356	2	the	the	DET
fuelectenerg-400	356	3	absence	absence	NOUN
fuelectenerg-400	356	4	of	of	ADP
fuelectenerg-400	356	5	tiling	tile	VERB
fuelectenerg-400	356	6	information	information	NOUN
fuelectenerg-400	356	7	,	,	PUNCT
fuelectenerg-400	356	8	the	the	DET
fuelectenerg-400	356	9	colored	colored	ADJ
fuelectenerg-400	356	10	tiling	tile	VERB
fuelectenerg-400	356	11	in	in	ADP
fuelectenerg-400	356	12	figure	figure	NOUN
fuelectenerg-400	356	13	(	(	PUNCT
fuelectenerg-400	356	14	a	a	X
fuelectenerg-400	356	15	)	)	PUNCT
fuelectenerg-400	356	16	can	can	AUX
fuelectenerg-400	356	17	be	be	AUX
fuelectenerg-400	356	18	decoded	decode	VERB
fuelectenerg-400	356	19	to	to	ADP
fuelectenerg-400	356	20	either	either	PRON
fuelectenerg-400	356	21	of	of	ADP
fuelectenerg-400	356	22	the	the	DET
fuelectenerg-400	356	23	colored	colored	ADJ
fuelectenerg-400	356	24	tilings	tiling	NOUN
fuelectenerg-400	356	25	shown	show	VERB
fuelectenerg-400	356	26	in	in	ADP
fuelectenerg-400	356	27	figures	figure	NOUN
fuelectenerg-400	356	28	(	(	PUNCT
fuelectenerg-400	356	29	b	b	NOUN
fuelectenerg-400	356	30	)	)	PUNCT
fuelectenerg-400	356	31	and	and	CCONJ
fuelectenerg-400	356	32	(	(	PUNCT
fuelectenerg-400	356	33	c	c	X
fuelectenerg-400	356	34	)	)	PUNCT
fuelectenerg-400	356	35	it	it	PRON
fuelectenerg-400	356	36	are	be	AUX
fuelectenerg-400	356	37	colored	color	VERB
fuelectenerg-400	356	38	differently	differently	ADV
fuelectenerg-400	356	39	.	.	PUNCT
fuelectenerg-400	357	1	one	one	NUM
fuelectenerg-400	357	2	such	such	ADJ
fuelectenerg-400	357	3	coloring	coloring	NOUN
fuelectenerg-400	357	4	scheme	scheme	NOUN
fuelectenerg-400	357	5	is	be	AUX
fuelectenerg-400	357	6	shown	show	VERB
fuelectenerg-400	357	7	in	in	ADP
fuelectenerg-400	357	8	fig	fig	NOUN
fuelectenerg-400	357	9	.	.	PUNCT
fuelectenerg-400	358	1	7	7	NUM
fuelectenerg-400	358	2	,	,	PUNCT
fuelectenerg-400	358	3	where	where	SCONJ
fuelectenerg-400	358	4	type	type	NOUN
fuelectenerg-400	358	5	-	-	PUNCT
fuelectenerg-400	358	6	b	b	NOUN
fuelectenerg-400	358	7	prototiles	prototile	NOUN
fuelectenerg-400	358	8	are	be	AUX
fuelectenerg-400	358	9	always	always	ADV
fuelectenerg-400	358	10	colored	color	VERB
fuelectenerg-400	358	11	black	black	ADJ
fuelectenerg-400	358	12	,	,	PUNCT
fuelectenerg-400	358	13	and	and	CCONJ
fuelectenerg-400	358	14	type	type	NOUN
fuelectenerg-400	358	15	-	-	PUNCT
fuelectenerg-400	358	16	c	c	NOUN
fuelectenerg-400	358	17	prototiles	prototile	NOUN
fuelectenerg-400	358	18	are	be	AUX
fuelectenerg-400	358	19	always	always	ADV
fuelectenerg-400	358	20	colored	color	VERB
fuelectenerg-400	358	21	white	white	ADJ
fuelectenerg-400	358	22	.	.	PUNCT
fuelectenerg-400	359	1	by	by	ADP
fuelectenerg-400	359	2	using	use	VERB
fuelectenerg-400	359	3	this	this	DET
fuelectenerg-400	359	4	coloring	coloring	NOUN
fuelectenerg-400	359	5	scheme	scheme	NOUN
fuelectenerg-400	359	6	,	,	PUNCT
fuelectenerg-400	359	7	no	no	DET
fuelectenerg-400	359	8	information	information	NOUN
fuelectenerg-400	359	9	is	be	AUX
fuelectenerg-400	359	10	stored	store	VERB
fuelectenerg-400	359	11	in	in	ADP
fuelectenerg-400	359	12	the	the	DET
fuelectenerg-400	359	13	vertical	vertical	ADJ
fuelectenerg-400	359	14	lozenges	lozenge	NOUN
fuelectenerg-400	359	15	of	of	ADP
fuelectenerg-400	359	16	the	the	DET
fuelectenerg-400	359	17	type-1	type-1	PROPN
fuelectenerg-400	359	18	hexagon	hexagon	NOUN
fuelectenerg-400	359	19	.	.	PUNCT
fuelectenerg-400	360	1	we	we	PRON
fuelectenerg-400	360	2	refer	refer	VERB
fuelectenerg-400	360	3	to	to	ADP
fuelectenerg-400	360	4	this	this	DET
fuelectenerg-400	360	5	coloring	coloring	NOUN
fuelectenerg-400	360	6	scheme	scheme	NOUN
fuelectenerg-400	360	7	as	as	ADP
fuelectenerg-400	360	8	fixed	fix	VERB
fuelectenerg-400	360	9	-	-	PUNCT
fuelectenerg-400	360	10	color	color	NOUN
fuelectenerg-400	360	11	vertical	vertical	ADJ
fuelectenerg-400	360	12	lozenges	lozenge	NOUN
fuelectenerg-400	360	13	(	(	PUNCT
fuelectenerg-400	360	14	fcvl	fcvl	PROPN
fuelectenerg-400	360	15	)	)	PUNCT
fuelectenerg-400	360	16	coloring	coloring	NOUN
fuelectenerg-400	360	17	.	.	PUNCT
fuelectenerg-400	361	1	the	the	DET
fuelectenerg-400	361	2	fcvl	fcvl	NOUN
fuelectenerg-400	361	3	coloring	color	VERB
fuelectenerg-400	361	4	constraint	constraint	NOUN
fuelectenerg-400	361	5	reduces	reduce	VERB
fuelectenerg-400	361	6	the	the	DET
fuelectenerg-400	361	7	number	number	NOUN
fuelectenerg-400	361	8	of	of	ADP
fuelectenerg-400	361	9	ways	way	NOUN
fuelectenerg-400	361	10	of	of	ADP
fuelectenerg-400	361	11	coloring	color	VERB
fuelectenerg-400	361	12	for	for	ADP
fuelectenerg-400	361	13	each	each	DET
fuelectenerg-400	361	14	tiling	tiling	NOUN
fuelectenerg-400	361	15	.	.	PUNCT
fuelectenerg-400	362	1	this	this	DET
fuelectenerg-400	362	2	reduction	reduction	NOUN
fuelectenerg-400	362	3	depends	depend	VERB
fuelectenerg-400	362	4	on	on	ADP
fuelectenerg-400	362	5	the	the	DET
fuelectenerg-400	362	6	number	number	NOUN
fuelectenerg-400	362	7	of	of	ADP
fuelectenerg-400	362	8	type-1	type-1	PROPN
fuelectenerg-400	362	9	hexagons	hexagon	NOUN
fuelectenerg-400	362	10	formed	form	VERB
fuelectenerg-400	362	11	in	in	ADP
fuelectenerg-400	362	12	a	a	DET
fuelectenerg-400	362	13	tiling	tiling	NOUN
fuelectenerg-400	362	14	.	.	PUNCT
fuelectenerg-400	363	1	the	the	DET
fuelectenerg-400	363	2	capacity	capacity	NOUN
fuelectenerg-400	363	3	can	can	AUX
fuelectenerg-400	363	4	be	be	AUX
fuelectenerg-400	363	5	bounded	bound	VERB
fuelectenerg-400	363	6	by	by	ADP
fuelectenerg-400	363	7	calculating	calculate	VERB
fuelectenerg-400	363	8	the	the	DET
fuelectenerg-400	363	9	number	number	NOUN
fuelectenerg-400	363	10	of	of	ADP
fuelectenerg-400	363	11	type-1	type-1	PROPN
fuelectenerg-400	363	12	hexagons	hexagon	NOUN
fuelectenerg-400	363	13	formed	form	VERB
fuelectenerg-400	363	14	for	for	ADP
fuelectenerg-400	363	15	every	every	DET
fuelectenerg-400	363	16	tiling	tiling	NOUN
fuelectenerg-400	363	17	.	.	PUNCT
fuelectenerg-400	364	1	fig	fig	NOUN
fuelectenerg-400	364	2	.	.	PUNCT
fuelectenerg-400	365	1	7	7	X
fuelectenerg-400	365	2	.	.	X
fuelectenerg-400	365	3	the	the	DET
fuelectenerg-400	365	4	coloring	coloring	NOUN
fuelectenerg-400	365	5	scheme	scheme	NOUN
fuelectenerg-400	365	6	adopted	adopt	VERB
fuelectenerg-400	365	7	for	for	ADP
fuelectenerg-400	365	8	type-1	type-1	PROPN
fuelectenerg-400	365	9	hexagon	hexagon	NOUN
fuelectenerg-400	365	10	.	.	PUNCT
fuelectenerg-400	366	1	the	the	DET
fuelectenerg-400	366	2	coloring	coloring	NOUN
fuelectenerg-400	366	3	capacity	capacity	NOUN
fuelectenerg-400	366	4	,	,	PUNCT
fuelectenerg-400	366	5	cc	cc	VERB
fuelectenerg-400	366	6	,	,	PUNCT
fuelectenerg-400	366	7	can	can	AUX
fuelectenerg-400	366	8	be	be	AUX
fuelectenerg-400	366	9	estimated	estimate	VERB
fuelectenerg-400	366	10	by	by	ADP
fuelectenerg-400	366	11	counting	count	VERB
fuelectenerg-400	366	12	the	the	DET
fuelectenerg-400	366	13	number	number	NOUN
fuelectenerg-400	366	14	of	of	ADP
fuelectenerg-400	366	15	ways	way	NOUN
fuelectenerg-400	366	16	the	the	DET
fuelectenerg-400	366	17	lozenges	lozenge	NOUN
fuelectenerg-400	366	18	constituting	constitute	VERB
fuelectenerg-400	366	19	a	a	DET
fuelectenerg-400	366	20	lozenge	lozenge	NOUN
fuelectenerg-400	366	21	tiling	tiling	NOUN
fuelectenerg-400	366	22	can	can	AUX
fuelectenerg-400	366	23	be	be	AUX
fuelectenerg-400	366	24	colored	color	VERB
fuelectenerg-400	366	25	.	.	PUNCT
fuelectenerg-400	367	1	given	give	VERB
fuelectenerg-400	367	2	a	a	DET
fuelectenerg-400	367	3	lozenge	lozenge	NOUN
fuelectenerg-400	367	4	tiling	tiling	NOUN
fuelectenerg-400	367	5	of	of	ADP
fuelectenerg-400	367	6	an	an	DET
fuelectenerg-400	367	7	(	(	PUNCT
fuelectenerg-400	367	8	n	n	X
fuelectenerg-400	367	9	,	,	PUNCT
fuelectenerg-400	367	10	n	n	CCONJ
fuelectenerg-400	367	11	,	,	PUNCT
fuelectenerg-400	367	12	n	n	CCONJ
fuelectenerg-400	367	13	)	)	PUNCT
fuelectenerg-400	367	14	hexagon	hexagon	PROPN
fuelectenerg-400	367	15	,	,	PUNCT
fuelectenerg-400	367	16	h	h	NOUN
fuelectenerg-400	367	17	,	,	PUNCT
fuelectenerg-400	367	18	the	the	DET
fuelectenerg-400	367	19	coloring	coloring	NOUN
fuelectenerg-400	367	20	of	of	ADP
fuelectenerg-400	367	21	the	the	DET
fuelectenerg-400	367	22	lozenges	lozenge	NOUN
fuelectenerg-400	367	23	can	can	AUX
fuelectenerg-400	367	24	not	not	PART
fuelectenerg-400	367	25	be	be	AUX
fuelectenerg-400	367	26	done	do	VERB
fuelectenerg-400	367	27	arbitrarily	arbitrarily	ADV
fuelectenerg-400	367	28	.	.	PUNCT
fuelectenerg-400	368	1	theorem	theorem	NOUN
fuelectenerg-400	368	2	2	2	NUM
fuelectenerg-400	368	3	for	for	ADP
fuelectenerg-400	368	4	the	the	DET
fuelectenerg-400	368	5	coloring	coloring	NOUN
fuelectenerg-400	368	6	of	of	ADP
fuelectenerg-400	368	7	a	a	DET
fuelectenerg-400	368	8	lozenge	lozenge	NOUN
fuelectenerg-400	368	9	tiling	tiling	NOUN
fuelectenerg-400	368	10	of	of	ADP
fuelectenerg-400	368	11	an	an	DET
fuelectenerg-400	368	12	(	(	PUNCT
fuelectenerg-400	368	13	n	n	X
fuelectenerg-400	368	14	,	,	PUNCT
fuelectenerg-400	368	15	n	n	CCONJ
fuelectenerg-400	368	16	,	,	PUNCT
fuelectenerg-400	368	17	n	n	CCONJ
fuelectenerg-400	368	18	)	)	PUNCT
fuelectenerg-400	368	19	hexagon	hexagon	PROPN
fuelectenerg-400	368	20	h	h	PROPN
fuelectenerg-400	368	21	,	,	PUNCT
fuelectenerg-400	368	22	the	the	DET
fuelectenerg-400	368	23	capacity	capacity	NOUN
fuelectenerg-400	368	24	cc	cc	X
fuelectenerg-400	368	25	≥	≥	PROPN
fuelectenerg-400	368	26	1	1	NUM
fuelectenerg-400	368	27	3	3	NUM
fuelectenerg-400	368	28	.	.	PUNCT
fuelectenerg-400	369	1	proof	proof	NOUN
fuelectenerg-400	369	2	:	:	PUNCT
fuelectenerg-400	369	3	the	the	DET
fuelectenerg-400	369	4	proof	proof	NOUN
fuelectenerg-400	369	5	is	be	AUX
fuelectenerg-400	369	6	based	base	VERB
fuelectenerg-400	369	7	on	on	ADP
fuelectenerg-400	369	8	the	the	DET
fuelectenerg-400	369	9	equivalence	equivalence	NOUN
fuelectenerg-400	369	10	between	between	ADP
fuelectenerg-400	369	11	tilings	tiling	NOUN
fuelectenerg-400	369	12	and	and	CCONJ
fuelectenerg-400	369	13	boxed	boxed	ADJ
fuelectenerg-400	369	14	plane	plane	NOUN
fuelectenerg-400	369	15	partitions	partition	NOUN
fuelectenerg-400	369	16	and	and	CCONJ
fuelectenerg-400	369	17	lemma	lemma	PROPN
fuelectenerg-400	369	18	1	1	NUM
fuelectenerg-400	369	19	it	it	PRON
fuelectenerg-400	369	20	is	be	AUX
fuelectenerg-400	369	21	given	give	VERB
fuelectenerg-400	369	22	in	in	ADP
fuelectenerg-400	369	23	appendix	appendix	NOUN
fuelectenerg-400	369	24	8	8	NUM
fuelectenerg-400	369	25	.	.	PUNCT
fuelectenerg-400	370	1	note	note	VERB
fuelectenerg-400	370	2	that	that	SCONJ
fuelectenerg-400	370	3	the	the	DET
fuelectenerg-400	370	4	above	above	ADV
fuelectenerg-400	370	5	bound	bind	VERB
fuelectenerg-400	370	6	on	on	ADP
fuelectenerg-400	370	7	cc	cc	PROPN
fuelectenerg-400	370	8	may	may	AUX
fuelectenerg-400	370	9	be	be	AUX
fuelectenerg-400	370	10	strengthen	strengthen	VERB
fuelectenerg-400	370	11	at	at	ADP
fuelectenerg-400	370	12	the	the	DET
fuelectenerg-400	370	13	expense	expense	NOUN
fuelectenerg-400	370	14	of	of	ADP
fuelectenerg-400	370	15	much	much	ADV
fuelectenerg-400	370	16	harder	hard	ADJ
fuelectenerg-400	370	17	combinatorial	combinatorial	ADJ
fuelectenerg-400	370	18	argument	argument	NOUN
fuelectenerg-400	370	19	considering	consider	VERB
fuelectenerg-400	370	20	colors	color	NOUN
fuelectenerg-400	370	21	of	of	ADP
fuelectenerg-400	370	22	tiles	tile	NOUN
fuelectenerg-400	370	23	.	.	PUNCT
fuelectenerg-400	371	1	528	528	NUM
fuelectenerg-400	371	2	b.	b.	PROPN
fuelectenerg-400	371	3	vasic	vasic	PROPN
fuelectenerg-400	371	4	,	,	PUNCT
fuelectenerg-400	371	5	a.	a.	PROPN
fuelectenerg-400	371	6	r.	r.	PROPN
fuelectenerg-400	371	7	krishnan	krishnan	PROPN
fuelectenerg-400	371	8	lozenge	lozenge	PROPN
fuelectenerg-400	371	9	tiling	tile	VERB
fuelectenerg-400	371	10	constrained	constrained	ADJ
fuelectenerg-400	371	11	codes	code	NOUN
fuelectenerg-400	371	12	529	529	NUM
fuelectenerg-400	371	13	530	530	NUM
fuelectenerg-400	371	14	a.	a.	NOUN
fuelectenerg-400	371	15	r.	r.	PROPN
fuelectenerg-400	371	16	krishnanan	krishnanan	PROPN
fuelectenerg-400	371	17	and	and	CCONJ
fuelectenerg-400	371	18	b.	b.	PROPN
fuelectenerg-400	371	19	vasić	vasić	PROPN
fuelectenerg-400	371	20	5	5	NUM
fuelectenerg-400	371	21	encoding	encode	VERB
fuelectenerg-400	371	22	and	and	CCONJ
fuelectenerg-400	371	23	decoding	decode	VERB
fuelectenerg-400	371	24	lozenge	lozenge	NOUN
fuelectenerg-400	371	25	codes	code	NOUN
fuelectenerg-400	371	26	we	we	PRON
fuelectenerg-400	371	27	refer	refer	VERB
fuelectenerg-400	371	28	to	to	ADP
fuelectenerg-400	371	29	the	the	DET
fuelectenerg-400	371	30	assignment	assignment	NOUN
fuelectenerg-400	371	31	of	of	ADP
fuelectenerg-400	371	32	a	a	DET
fuelectenerg-400	371	33	distinct	distinct	ADJ
fuelectenerg-400	371	34	element	element	NOUN
fuelectenerg-400	371	35	from	from	ADP
fuelectenerg-400	371	36	the	the	DET
fuelectenerg-400	371	37	set	set	NOUN
fuelectenerg-400	371	38	of	of	ADP
fuelectenerg-400	371	39	integers	integer	NOUN
fuelectenerg-400	371	40	to	to	ADP
fuelectenerg-400	371	41	an	an	DET
fuelectenerg-400	371	42	element	element	NOUN
fuelectenerg-400	371	43	of	of	ADP
fuelectenerg-400	371	44	the	the	DET
fuelectenerg-400	371	45	set	set	NOUN
fuelectenerg-400	371	46	of	of	ADP
fuelectenerg-400	371	47	all	all	DET
fuelectenerg-400	371	48	possible	possible	ADJ
fuelectenerg-400	371	49	colored	colored	ADJ
fuelectenerg-400	371	50	tilings	tiling	NOUN
fuelectenerg-400	371	51	as	as	ADP
fuelectenerg-400	371	52	encoding	encoding	NOUN
fuelectenerg-400	371	53	of	of	ADP
fuelectenerg-400	371	54	colored	colored	ADJ
fuelectenerg-400	371	55	tilings	tiling	NOUN
fuelectenerg-400	371	56	.	.	PUNCT
fuelectenerg-400	372	1	again	again	ADV
fuelectenerg-400	372	2	,	,	PUNCT
fuelectenerg-400	372	3	we	we	PRON
fuelectenerg-400	372	4	divide	divide	VERB
fuelectenerg-400	372	5	the	the	DET
fuelectenerg-400	372	6	problem	problem	NOUN
fuelectenerg-400	372	7	into	into	ADP
fuelectenerg-400	372	8	two	two	NUM
fuelectenerg-400	372	9	separate	separate	ADJ
fuelectenerg-400	372	10	problems	problem	NOUN
fuelectenerg-400	372	11	:	:	PUNCT
fuelectenerg-400	372	12	the	the	DET
fuelectenerg-400	372	13	encoding	encoding	NOUN
fuelectenerg-400	372	14	of	of	ADP
fuelectenerg-400	372	15	tilings	tiling	NOUN
fuelectenerg-400	372	16	and	and	CCONJ
fuelectenerg-400	372	17	the	the	DET
fuelectenerg-400	372	18	coloring	coloring	NOUN
fuelectenerg-400	372	19	of	of	ADP
fuelectenerg-400	372	20	tiles	tile	NOUN
fuelectenerg-400	372	21	.	.	PUNCT
fuelectenerg-400	373	1	to	to	PART
fuelectenerg-400	373	2	facilitate	facilitate	VERB
fuelectenerg-400	373	3	this	this	PRON
fuelectenerg-400	373	4	,	,	PUNCT
fuelectenerg-400	373	5	we	we	PRON
fuelectenerg-400	373	6	assume	assume	VERB
fuelectenerg-400	373	7	that	that	SCONJ
fuelectenerg-400	373	8	the	the	DET
fuelectenerg-400	373	9	fcvl	fcvl	NOUN
fuelectenerg-400	373	10	coloring	coloring	NOUN
fuelectenerg-400	373	11	constraint	constraint	NOUN
fuelectenerg-400	373	12	is	be	AUX
fuelectenerg-400	373	13	imposed	impose	VERB
fuelectenerg-400	373	14	.	.	PUNCT
fuelectenerg-400	374	1	the	the	DET
fuelectenerg-400	374	2	first	first	ADJ
fuelectenerg-400	374	3	step	step	NOUN
fuelectenerg-400	374	4	of	of	ADP
fuelectenerg-400	374	5	the	the	DET
fuelectenerg-400	374	6	encoding	encoding	NOUN
fuelectenerg-400	374	7	process	process	NOUN
fuelectenerg-400	374	8	is	be	AUX
fuelectenerg-400	374	9	the	the	DET
fuelectenerg-400	374	10	encoding	encoding	NOUN
fuelectenerg-400	374	11	of	of	ADP
fuelectenerg-400	374	12	tilings	tiling	NOUN
fuelectenerg-400	374	13	for	for	ADP
fuelectenerg-400	374	14	which	which	PRON
fuelectenerg-400	374	15	we	we	PRON
fuelectenerg-400	374	16	seek	seek	VERB
fuelectenerg-400	374	17	a	a	DET
fuelectenerg-400	374	18	bijective	bijective	ADJ
fuelectenerg-400	374	19	assignment	assignment	NOUN
fuelectenerg-400	374	20	between	between	ADP
fuelectenerg-400	374	21	the	the	DET
fuelectenerg-400	374	22	set	set	NOUN
fuelectenerg-400	374	23	of	of	ADP
fuelectenerg-400	374	24	integers	integer	NOUN
fuelectenerg-400	374	25	and	and	CCONJ
fuelectenerg-400	374	26	the	the	DET
fuelectenerg-400	374	27	set	set	NOUN
fuelectenerg-400	374	28	of	of	ADP
fuelectenerg-400	374	29	all	all	DET
fuelectenerg-400	374	30	tilings	tiling	NOUN
fuelectenerg-400	374	31	.	.	PUNCT
fuelectenerg-400	375	1	the	the	DET
fuelectenerg-400	375	2	second	second	ADJ
fuelectenerg-400	375	3	step	step	NOUN
fuelectenerg-400	375	4	is	be	AUX
fuelectenerg-400	375	5	the	the	DET
fuelectenerg-400	375	6	coloring	coloring	NOUN
fuelectenerg-400	375	7	of	of	ADP
fuelectenerg-400	375	8	the	the	DET
fuelectenerg-400	375	9	tiling	tiling	NOUN
fuelectenerg-400	375	10	.	.	PUNCT
fuelectenerg-400	376	1	the	the	DET
fuelectenerg-400	376	2	second	second	ADJ
fuelectenerg-400	376	3	step	step	NOUN
fuelectenerg-400	376	4	is	be	AUX
fuelectenerg-400	376	5	trivial	trivial	ADJ
fuelectenerg-400	376	6	since	since	SCONJ
fuelectenerg-400	376	7	for	for	ADP
fuelectenerg-400	376	8	the	the	DET
fuelectenerg-400	376	9	fcvl	fcvl	NOUN
fuelectenerg-400	376	10	coloring	coloring	NOUN
fuelectenerg-400	376	11	,	,	PUNCT
fuelectenerg-400	376	12	n2	n2	ADJ
fuelectenerg-400	376	13	horizontal	horizontal	ADJ
fuelectenerg-400	376	14	prototiles	prototile	NOUN
fuelectenerg-400	376	15	,	,	PUNCT
fuelectenerg-400	376	16	which	which	PRON
fuelectenerg-400	376	17	is	be	AUX
fuelectenerg-400	376	18	the	the	DET
fuelectenerg-400	376	19	third	third	ADJ
fuelectenerg-400	376	20	of	of	ADP
fuelectenerg-400	376	21	all	all	DET
fuelectenerg-400	376	22	prototiles	prototile	NOUN
fuelectenerg-400	376	23	in	in	ADP
fuelectenerg-400	376	24	a	a	DET
fuelectenerg-400	376	25	(	(	PUNCT
fuelectenerg-400	376	26	n	n	X
fuelectenerg-400	376	27	,	,	PUNCT
fuelectenerg-400	376	28	n	n	CCONJ
fuelectenerg-400	376	29	,	,	PUNCT
fuelectenerg-400	376	30	n	n	CCONJ
fuelectenerg-400	376	31	)	)	PUNCT
fuelectenerg-400	376	32	hexagon	hexagon	NOUN
fuelectenerg-400	376	33	,	,	PUNCT
fuelectenerg-400	376	34	can	can	AUX
fuelectenerg-400	376	35	be	be	AUX
fuelectenerg-400	376	36	colored	color	VERB
fuelectenerg-400	376	37	independently	independently	ADV
fuelectenerg-400	376	38	.	.	PUNCT
fuelectenerg-400	377	1	thus	thus	ADV
fuelectenerg-400	377	2	we	we	PRON
fuelectenerg-400	377	3	focus	focus	VERB
fuelectenerg-400	377	4	on	on	ADP
fuelectenerg-400	377	5	the	the	DET
fuelectenerg-400	377	6	first	first	ADJ
fuelectenerg-400	377	7	step	step	NOUN
fuelectenerg-400	377	8	of	of	ADP
fuelectenerg-400	377	9	an	an	DET
fuelectenerg-400	377	10	encoding	encoding	NOUN
fuelectenerg-400	377	11	algorithm	algorithm	NOUN
fuelectenerg-400	377	12	.	.	PUNCT
fuelectenerg-400	378	1	before	before	ADP
fuelectenerg-400	378	2	discussing	discuss	VERB
fuelectenerg-400	378	3	the	the	DET
fuelectenerg-400	378	4	proposed	propose	VERB
fuelectenerg-400	378	5	encoding	encoding	NOUN
fuelectenerg-400	378	6	algorithm	algorithm	NOUN
fuelectenerg-400	378	7	we	we	PRON
fuelectenerg-400	378	8	give	give	VERB
fuelectenerg-400	378	9	an	an	DET
fuelectenerg-400	378	10	intuition	intuition	NOUN
fuelectenerg-400	378	11	behind	behind	ADP
fuelectenerg-400	378	12	our	our	PRON
fuelectenerg-400	378	13	approach	approach	NOUN
fuelectenerg-400	378	14	.	.	PUNCT
fuelectenerg-400	379	1	we	we	PRON
fuelectenerg-400	379	2	begin	begin	VERB
fuelectenerg-400	379	3	by	by	ADP
fuelectenerg-400	379	4	recalling	recall	VERB
fuelectenerg-400	379	5	that	that	SCONJ
fuelectenerg-400	379	6	there	there	PRON
fuelectenerg-400	379	7	is	be	VERB
fuelectenerg-400	379	8	a	a	DET
fuelectenerg-400	379	9	unique	unique	ADJ
fuelectenerg-400	379	10	boxed	box	VERB
fuelectenerg-400	379	11	plane	plane	NOUN
fuelectenerg-400	379	12	partition	partition	NOUN
fuelectenerg-400	379	13	corresponding	correspond	VERB
fuelectenerg-400	379	14	to	to	ADP
fuelectenerg-400	379	15	any	any	DET
fuelectenerg-400	379	16	lozenge	lozenge	NOUN
fuelectenerg-400	379	17	tiling	tiling	NOUN
fuelectenerg-400	379	18	.	.	PUNCT
fuelectenerg-400	380	1	consider	consider	VERB
fuelectenerg-400	380	2	an	an	DET
fuelectenerg-400	380	3	(	(	PUNCT
fuelectenerg-400	380	4	a	a	PROPN
fuelectenerg-400	380	5	,	,	PUNCT
fuelectenerg-400	380	6	b	b	NOUN
fuelectenerg-400	380	7	,	,	PUNCT
fuelectenerg-400	380	8	c	c	NOUN
fuelectenerg-400	380	9	)	)	PUNCT
fuelectenerg-400	380	10	hexagon	hexagon	PROPN
fuelectenerg-400	380	11	tiled	tile	VERB
fuelectenerg-400	380	12	with	with	ADP
fuelectenerg-400	380	13	equilateral	equilateral	ADJ
fuelectenerg-400	380	14	triangles	triangle	NOUN
fuelectenerg-400	380	15	with	with	ADP
fuelectenerg-400	380	16	unit	unit	NOUN
fuelectenerg-400	380	17	side	side	NOUN
fuelectenerg-400	380	18	-	-	PUNCT
fuelectenerg-400	380	19	lengths	length	NOUN
fuelectenerg-400	380	20	.	.	PUNCT
fuelectenerg-400	381	1	an	an	DET
fuelectenerg-400	381	2	alternative	alternative	ADJ
fuelectenerg-400	381	3	way	way	NOUN
fuelectenerg-400	381	4	to	to	PART
fuelectenerg-400	381	5	unambiguously	unambiguously	ADV
fuelectenerg-400	381	6	specify	specify	VERB
fuelectenerg-400	381	7	a	a	DET
fuelectenerg-400	381	8	boxed	box	VERB
fuelectenerg-400	381	9	plane	plane	NOUN
fuelectenerg-400	381	10	partition	partition	NOUN
fuelectenerg-400	381	11	is	be	AUX
fuelectenerg-400	381	12	to	to	PART
fuelectenerg-400	381	13	traverse	traverse	VERB
fuelectenerg-400	381	14	a	a	DET
fuelectenerg-400	381	15	paths	path	NOUN
fuelectenerg-400	381	16	covering	cover	VERB
fuelectenerg-400	381	17	only	only	ADV
fuelectenerg-400	381	18	vertical	vertical	ADJ
fuelectenerg-400	381	19	prototiles	prototile	NOUN
fuelectenerg-400	381	20	as	as	SCONJ
fuelectenerg-400	381	21	illustrated	illustrate	VERB
fuelectenerg-400	381	22	in	in	ADP
fuelectenerg-400	381	23	fig	fig	NOUN
fuelectenerg-400	381	24	.	.	PUNCT
fuelectenerg-400	382	1	8(d	8(d	NUM
fuelectenerg-400	382	2	)	)	PUNCT
fuelectenerg-400	382	3	for	for	ADP
fuelectenerg-400	382	4	the	the	DET
fuelectenerg-400	382	5	case	case	NOUN
fuelectenerg-400	382	6	of	of	ADP
fuelectenerg-400	382	7	the	the	DET
fuelectenerg-400	382	8	(	(	PUNCT
fuelectenerg-400	382	9	3	3	NUM
fuelectenerg-400	382	10	,	,	PUNCT
fuelectenerg-400	382	11	3	3	NUM
fuelectenerg-400	382	12	,	,	PUNCT
fuelectenerg-400	382	13	3	3	X
fuelectenerg-400	382	14	)	)	PUNCT
fuelectenerg-400	382	15	hexagon	hexagon	NOUN
fuelectenerg-400	382	16	.	.	PUNCT
fuelectenerg-400	383	1	we	we	PRON
fuelectenerg-400	383	2	refer	refer	VERB
fuelectenerg-400	383	3	to	to	ADP
fuelectenerg-400	383	4	these	these	DET
fuelectenerg-400	383	5	paths	path	NOUN
fuelectenerg-400	383	6	as	as	ADP
fuelectenerg-400	383	7	routings	routing	NOUN
fuelectenerg-400	383	8	.	.	PUNCT
fuelectenerg-400	384	1	each	each	DET
fuelectenerg-400	384	2	section	section	NOUN
fuelectenerg-400	384	3	of	of	ADP
fuelectenerg-400	384	4	the	the	DET
fuelectenerg-400	384	5	path	path	NOUN
fuelectenerg-400	384	6	corresponds	correspond	VERB
fuelectenerg-400	384	7	to	to	ADP
fuelectenerg-400	384	8	one	one	NUM
fuelectenerg-400	384	9	type	type	NOUN
fuelectenerg-400	384	10	-	-	PUNCT
fuelectenerg-400	384	11	b	b	NOUN
fuelectenerg-400	384	12	or	or	CCONJ
fuelectenerg-400	384	13	type	type	NOUN
fuelectenerg-400	384	14	-	-	PUNCT
fuelectenerg-400	384	15	c	c	NOUN
fuelectenerg-400	384	16	lozenge	lozenge	NOUN
fuelectenerg-400	384	17	and	and	CCONJ
fuelectenerg-400	384	18	it	it	PRON
fuelectenerg-400	384	19	is	be	AUX
fuelectenerg-400	384	20	drawn	draw	VERB
fuelectenerg-400	384	21	as	as	ADP
fuelectenerg-400	384	22	a	a	DET
fuelectenerg-400	384	23	line	line	NOUN
fuelectenerg-400	384	24	segment	segment	NOUN
fuelectenerg-400	384	25	of	of	ADP
fuelectenerg-400	384	26	”	"	PUNCT
fuelectenerg-400	384	27	northeast	northeast	NOUN
fuelectenerg-400	384	28	”	"	PUNCT
fuelectenerg-400	384	29	or	or	CCONJ
fuelectenerg-400	384	30	”	"	PUNCT
fuelectenerg-400	384	31	souteast	souteast	ADJ
fuelectenerg-400	384	32	”	"	PUNCT
fuelectenerg-400	384	33	orientation	orientation	NOUN
fuelectenerg-400	384	34	in	in	ADP
fuelectenerg-400	384	35	fig	fig	NOUN
fuelectenerg-400	384	36	.	.	PUNCT
fuelectenerg-400	385	1	8(d	8(d	NUM
fuelectenerg-400	385	2	)	)	PUNCT
fuelectenerg-400	385	3	.	.	PUNCT
fuelectenerg-400	386	1	a	a	DET
fuelectenerg-400	386	2	collection	collection	NOUN
fuelectenerg-400	386	3	of	of	ADP
fuelectenerg-400	386	4	n	n	DET
fuelectenerg-400	386	5	such	such	ADJ
fuelectenerg-400	386	6	paths	path	NOUN
fuelectenerg-400	386	7	determines	determine	VERB
fuelectenerg-400	386	8	the	the	DET
fuelectenerg-400	386	9	tiling	tiling	NOUN
fuelectenerg-400	386	10	.	.	PUNCT
fuelectenerg-400	387	1	note	note	NOUN
fuelectenerg-400	387	2	,	,	PUNCT
fuelectenerg-400	387	3	however	however	ADV
fuelectenerg-400	387	4	,	,	PUNCT
fuelectenerg-400	387	5	that	that	SCONJ
fuelectenerg-400	387	6	the	the	DET
fuelectenerg-400	387	7	n	n	PROPN
fuelectenerg-400	387	8	paths	path	NOUN
fuelectenerg-400	387	9	in	in	ADP
fuelectenerg-400	387	10	a	a	DET
fuelectenerg-400	387	11	collection	collection	NOUN
fuelectenerg-400	387	12	can	can	AUX
fuelectenerg-400	387	13	not	not	PART
fuelectenerg-400	387	14	be	be	AUX
fuelectenerg-400	387	15	chosen	choose	VERB
fuelectenerg-400	387	16	arbitrarily	arbitrarily	ADV
fuelectenerg-400	387	17	.	.	PUNCT
fuelectenerg-400	388	1	this	this	PRON
fuelectenerg-400	388	2	is	be	AUX
fuelectenerg-400	388	3	simply	simply	ADV
fuelectenerg-400	388	4	because	because	SCONJ
fuelectenerg-400	388	5	we	we	PRON
fuelectenerg-400	388	6	do	do	AUX
fuelectenerg-400	388	7	not	not	PART
fuelectenerg-400	388	8	allow	allow	VERB
fuelectenerg-400	388	9	that	that	SCONJ
fuelectenerg-400	388	10	a	a	DET
fuelectenerg-400	388	11	box	box	NOUN
fuelectenerg-400	388	12	at	at	ADP
fuelectenerg-400	388	13	any	any	DET
fuelectenerg-400	388	14	level	level	NOUN
fuelectenerg-400	388	15	“	"	PUNCT
fuelectenerg-400	388	16	levitates	levitate	NOUN
fuelectenerg-400	388	17	”	"	PUNCT
fuelectenerg-400	388	18	without	without	ADP
fuelectenerg-400	388	19	being	be	AUX
fuelectenerg-400	388	20	supported	support	VERB
fuelectenerg-400	388	21	by	by	ADP
fuelectenerg-400	388	22	boxes	box	NOUN
fuelectenerg-400	388	23	the	the	DET
fuelectenerg-400	388	24	beneath	beneath	ADP
fuelectenerg-400	388	25	it	it	PRON
fuelectenerg-400	388	26	.	.	PUNCT
fuelectenerg-400	389	1	we	we	PRON
fuelectenerg-400	389	2	describe	describe	VERB
fuelectenerg-400	389	3	this	this	DET
fuelectenerg-400	389	4	requirement	requirement	NOUN
fuelectenerg-400	389	5	though	though	SCONJ
fuelectenerg-400	389	6	combinatorial	combinatorial	ADJ
fuelectenerg-400	389	7	objects	object	NOUN
fuelectenerg-400	389	8	known	know	VERB
fuelectenerg-400	389	9	as	as	ADP
fuelectenerg-400	389	10	mountain	mountain	NOUN
fuelectenerg-400	389	11	ranges	range	NOUN
fuelectenerg-400	389	12	illustrated	illustrate	VERB
fuelectenerg-400	389	13	in	in	ADP
fuelectenerg-400	389	14	fig	fig	NOUN
fuelectenerg-400	389	15	.	.	PUNCT
fuelectenerg-400	389	16	8(c	8(c	NUM
fuelectenerg-400	389	17	)	)	PUNCT
fuelectenerg-400	389	18	.	.	PUNCT
fuelectenerg-400	390	1	each	each	DET
fuelectenerg-400	390	2	path	path	NOUN
fuelectenerg-400	390	3	correspond	correspond	VERB
fuelectenerg-400	390	4	to	to	ADP
fuelectenerg-400	390	5	one	one	NUM
fuelectenerg-400	390	6	mountain	mountain	NOUN
fuelectenerg-400	390	7	range	range	NOUN
fuelectenerg-400	390	8	,	,	PUNCT
fuelectenerg-400	390	9	but	but	CCONJ
fuelectenerg-400	390	10	“	"	PUNCT
fuelectenerg-400	390	11	lower	low	ADJ
fuelectenerg-400	390	12	”	"	PUNCT
fuelectenerg-400	390	13	paths	path	NOUN
fuelectenerg-400	390	14	can	can	AUX
fuelectenerg-400	390	15	not	not	PART
fuelectenerg-400	390	16	have	have	VERB
fuelectenerg-400	390	17	mountain	mountain	NOUN
fuelectenerg-400	390	18	ranges	range	NOUN
fuelectenerg-400	390	19	higher	higher	ADV
fuelectenerg-400	390	20	than	than	ADP
fuelectenerg-400	390	21	“	"	PUNCT
fuelectenerg-400	390	22	upper	upper	ADJ
fuelectenerg-400	390	23	”	"	PUNCT
fuelectenerg-400	390	24	paths	path	NOUN
fuelectenerg-400	390	25	.	.	PUNCT
fuelectenerg-400	391	1	we	we	PRON
fuelectenerg-400	391	2	formalize	formalize	VERB
fuelectenerg-400	391	3	this	this	DET
fuelectenerg-400	391	4	concept	concept	NOUN
fuelectenerg-400	391	5	through	through	ADP
fuelectenerg-400	391	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	391	7	ordering	ordering	NOUN
fuelectenerg-400	391	8	and	and	CCONJ
fuelectenerg-400	391	9	ranking	ranking	NOUN
fuelectenerg-400	391	10	of	of	ADP
fuelectenerg-400	391	11	mountain	mountain	NOUN
fuelectenerg-400	391	12	ranges	range	NOUN
fuelectenerg-400	391	13	.	.	PUNCT
fuelectenerg-400	392	1	a	a	DET
fuelectenerg-400	392	2	collection	collection	NOUN
fuelectenerg-400	392	3	of	of	ADP
fuelectenerg-400	392	4	n	n	DET
fuelectenerg-400	392	5	nondecreasing	nondecrease	VERB
fuelectenerg-400	392	6	mountain	mountain	NOUN
fuelectenerg-400	392	7	ranges	range	NOUN
fuelectenerg-400	392	8	represent	represent	VERB
fuelectenerg-400	392	9	an	an	DET
fuelectenerg-400	392	10	instance	instance	NOUN
fuelectenerg-400	392	11	of	of	ADP
fuelectenerg-400	392	12	a	a	DET
fuelectenerg-400	392	13	tiling	tiling	NOUN
fuelectenerg-400	392	14	.	.	PUNCT
fuelectenerg-400	393	1	the	the	DET
fuelectenerg-400	393	2	set	set	NOUN
fuelectenerg-400	393	3	of	of	ADP
fuelectenerg-400	393	4	all	all	DET
fuelectenerg-400	393	5	such	such	ADJ
fuelectenerg-400	393	6	collections	collection	NOUN
fuelectenerg-400	393	7	represent	represent	VERB
fuelectenerg-400	393	8	the	the	DET
fuelectenerg-400	393	9	set	set	NOUN
fuelectenerg-400	393	10	of	of	ADP
fuelectenerg-400	393	11	all	all	DET
fuelectenerg-400	393	12	tilings	tiling	NOUN
fuelectenerg-400	393	13	.	.	PUNCT
fuelectenerg-400	394	1	to	to	PART
fuelectenerg-400	394	2	perform	perform	VERB
fuelectenerg-400	394	3	encoding	encode	VERB
fuelectenerg-400	394	4	and	and	CCONJ
fuelectenerg-400	394	5	decoding	decode	VERB
fuelectenerg-400	394	6	we	we	PRON
fuelectenerg-400	394	7	need	need	VERB
fuelectenerg-400	394	8	to	to	PART
fuelectenerg-400	394	9	enumerate	enumerate	VERB
fuelectenerg-400	394	10	mountain	mountain	NOUN
fuelectenerg-400	394	11	ranges	range	NOUN
fuelectenerg-400	394	12	and	and	CCONJ
fuelectenerg-400	394	13	enumerate	enumerate	VERB
fuelectenerg-400	394	14	collection	collection	NOUN
fuelectenerg-400	394	15	of	of	ADP
fuelectenerg-400	394	16	mountain	mountain	NOUN
fuelectenerg-400	394	17	ranges	range	NOUN
fuelectenerg-400	394	18	.	.	PUNCT
fuelectenerg-400	395	1	thus	thus	ADV
fuelectenerg-400	395	2	the	the	DET
fuelectenerg-400	395	3	encoding	encoding	NOUN
fuelectenerg-400	395	4	procedure	procedure	NOUN
fuelectenerg-400	395	5	involves	involve	VERB
fuelectenerg-400	395	6	the	the	DET
fuelectenerg-400	395	7	step	step	NOUN
fuelectenerg-400	395	8	of	of	ADP
fuelectenerg-400	395	9	converting	convert	VERB
fuelectenerg-400	395	10	an	an	DET
fuelectenerg-400	395	11	integer	integer	NOUN
fuelectenerg-400	395	12	to	to	ADP
fuelectenerg-400	395	13	a	a	DET
fuelectenerg-400	395	14	routing	routing	NOUN
fuelectenerg-400	395	15	on	on	ADP
fuelectenerg-400	395	16	a	a	DET
fuelectenerg-400	395	17	graph	graph	NOUN
fuelectenerg-400	395	18	,	,	PUNCT
fuelectenerg-400	395	19	which	which	PRON
fuelectenerg-400	395	20	is	be	AUX
fuelectenerg-400	395	21	represented	represent	VERB
fuelectenerg-400	395	22	by	by	ADP
fuelectenerg-400	395	23	a	a	DET
fuelectenerg-400	395	24	set	set	NOUN
fuelectenerg-400	395	25	of	of	ADP
fuelectenerg-400	395	26	constant	constant	ADJ
fuelectenerg-400	395	27	-	-	PUNCT
fuelectenerg-400	395	28	weight	weight	NOUN
fuelectenerg-400	395	29	sequences	sequence	NOUN
fuelectenerg-400	395	30	and	and	CCONJ
fuelectenerg-400	395	31	then	then	ADV
fuelectenerg-400	395	32	converting	convert	VERB
fuelectenerg-400	395	33	it	it	PRON
fuelectenerg-400	395	34	to	to	ADP
fuelectenerg-400	395	35	a	a	DET
fuelectenerg-400	395	36	tiling	tiling	NOUN
fuelectenerg-400	395	37	.	.	PUNCT
fuelectenerg-400	396	1	in	in	ADP
fuelectenerg-400	396	2	the	the	DET
fuelectenerg-400	396	3	following	follow	VERB
fuelectenerg-400	396	4	subsections	subsection	NOUN
fuelectenerg-400	396	5	we	we	PRON
fuelectenerg-400	396	6	introduce	introduce	VERB
fuelectenerg-400	396	7	rigorously	rigorously	ADV
fuelectenerg-400	396	8	the	the	DET
fuelectenerg-400	396	9	combinatorial	combinatorial	ADJ
fuelectenerg-400	396	10	objects	object	NOUN
fuelectenerg-400	396	11	given	give	VERB
fuelectenerg-400	396	12	in	in	ADP
fuelectenerg-400	396	13	the	the	DET
fuelectenerg-400	396	14	above	above	ADJ
fuelectenerg-400	396	15	intuitive	intuitive	ADJ
fuelectenerg-400	396	16	explanation	explanation	NOUN
fuelectenerg-400	396	17	.	.	PUNCT
fuelectenerg-400	397	1	before	before	ADP
fuelectenerg-400	397	2	discussing	discuss	VERB
fuelectenerg-400	397	3	the	the	DET
fuelectenerg-400	397	4	details	detail	NOUN
fuelectenerg-400	397	5	of	of	ADP
fuelectenerg-400	397	6	the	the	DET
fuelectenerg-400	397	7	proposed	propose	VERB
fuelectenerg-400	397	8	algorithm	algorithm	NOUN
fuelectenerg-400	397	9	,	,	PUNCT
fuelectenerg-400	397	10	we	we	PRON
fuelectenerg-400	397	11	describe	describe	VERB
fuelectenerg-400	397	12	the	the	DET
fuelectenerg-400	397	13	problem	problem	NOUN
fuelectenerg-400	397	14	of	of	ADP
fuelectenerg-400	397	15	enumeration	enumeration	NOUN
fuelectenerg-400	397	16	of	of	ADP
fuelectenerg-400	397	17	the	the	DET
fuelectenerg-400	397	18	routings	routing	NOUN
fuelectenerg-400	397	19	on	on	ADP
fuelectenerg-400	397	20	a	a	DET
fuelectenerg-400	397	21	graph	graph	NOUN
fuelectenerg-400	397	22	.	.	PUNCT
fuelectenerg-400	398	1	5.1	5.1	NUM
fuelectenerg-400	398	2	routings	routing	NOUN
fuelectenerg-400	398	3	on	on	ADP
fuelectenerg-400	398	4	a	a	DET
fuelectenerg-400	398	5	graph	graph	NOUN
fuelectenerg-400	398	6	recall	recall	NOUN
fuelectenerg-400	398	7	that	that	SCONJ
fuelectenerg-400	398	8	the	the	DET
fuelectenerg-400	398	9	idea	idea	NOUN
fuelectenerg-400	398	10	is	be	AUX
fuelectenerg-400	398	11	to	to	PART
fuelectenerg-400	398	12	use	use	VERB
fuelectenerg-400	398	13	the	the	DET
fuelectenerg-400	398	14	bijection	bijection	NOUN
fuelectenerg-400	398	15	between	between	ADP
fuelectenerg-400	398	16	tiling	tile	VERB
fuelectenerg-400	398	17	and	and	CCONJ
fuelectenerg-400	398	18	routings	routing	NOUN
fuelectenerg-400	398	19	on	on	ADP
fuelectenerg-400	398	20	a	a	DET
fuelectenerg-400	398	21	graph	graph	NOUN
fuelectenerg-400	398	22	.	.	PUNCT
fuelectenerg-400	398	23	consider	consider	VERB
fuelectenerg-400	398	24	an	an	DET
fuelectenerg-400	398	25	(	(	PUNCT
fuelectenerg-400	398	26	a	a	PROPN
fuelectenerg-400	398	27	,	,	PUNCT
fuelectenerg-400	398	28	b	b	NOUN
fuelectenerg-400	398	29	,	,	PUNCT
fuelectenerg-400	398	30	c	c	NOUN
fuelectenerg-400	398	31	)	)	PUNCT
fuelectenerg-400	398	32	hexagon	hexagon	PROPN
fuelectenerg-400	398	33	h	h	PROPN
fuelectenerg-400	398	34	tiled	tile	VERB
fuelectenerg-400	398	35	with	with	ADP
fuelectenerg-400	398	36	equilateral	equilateral	ADJ
fuelectenerg-400	398	37	triangles	triangle	NOUN
fuelectenerg-400	398	38	with	with	ADP
fuelectenerg-400	398	39	unit	unit	NOUN
fuelectenerg-400	398	40	side	side	NOUN
fuelectenerg-400	398	41	-	-	PUNCT
fuelectenerg-400	398	42	lengths	length	NOUN
fuelectenerg-400	398	43	.	.	PUNCT
fuelectenerg-400	399	1	for	for	ADP
fuelectenerg-400	399	2	this	this	DET
fuelectenerg-400	399	3	tiling	tiling	NOUN
fuelectenerg-400	399	4	,	,	PUNCT
fuelectenerg-400	399	5	an	an	DET
fuelectenerg-400	399	6	associated	associate	VERB
fuelectenerg-400	399	7	graph	graph	NOUN
fuelectenerg-400	399	8	g	g	PROPN
fuelectenerg-400	399	9	can	can	AUX
fuelectenerg-400	399	10	be	be	AUX
fuelectenerg-400	399	11	constructed	construct	VERB
fuelectenerg-400	399	12	530	530	NUM
fuelectenerg-400	399	13	b.	b.	PROPN
fuelectenerg-400	399	14	vasic	vasic	NOUN
fuelectenerg-400	399	15	,	,	PUNCT
fuelectenerg-400	399	16	a.	a.	PROPN
fuelectenerg-400	399	17	r.	r.	PROPN
fuelectenerg-400	399	18	krishnan	krishnan	PROPN
fuelectenerg-400	399	19	lozenge	lozenge	PROPN
fuelectenerg-400	399	20	tiling	tile	VERB
fuelectenerg-400	399	21	constrained	constrained	ADJ
fuelectenerg-400	399	22	codes	code	NOUN
fuelectenerg-400	399	23	531	531	NUM
fuelectenerg-400	399	24	530	530	NUM
fuelectenerg-400	399	25	a.	a.	NOUN
fuelectenerg-400	399	26	r.	r.	PROPN
fuelectenerg-400	399	27	krishnanan	krishnanan	PROPN
fuelectenerg-400	399	28	and	and	CCONJ
fuelectenerg-400	399	29	b.	b.	PROPN
fuelectenerg-400	399	30	vasić	vasić	PROPN
fuelectenerg-400	399	31	5	5	NUM
fuelectenerg-400	399	32	encoding	encode	VERB
fuelectenerg-400	399	33	and	and	CCONJ
fuelectenerg-400	399	34	decoding	decode	VERB
fuelectenerg-400	399	35	lozenge	lozenge	NOUN
fuelectenerg-400	399	36	codes	code	NOUN
fuelectenerg-400	399	37	we	we	PRON
fuelectenerg-400	399	38	refer	refer	VERB
fuelectenerg-400	399	39	to	to	ADP
fuelectenerg-400	399	40	the	the	DET
fuelectenerg-400	399	41	assignment	assignment	NOUN
fuelectenerg-400	399	42	of	of	ADP
fuelectenerg-400	399	43	a	a	DET
fuelectenerg-400	399	44	distinct	distinct	ADJ
fuelectenerg-400	399	45	element	element	NOUN
fuelectenerg-400	399	46	from	from	ADP
fuelectenerg-400	399	47	the	the	DET
fuelectenerg-400	399	48	set	set	NOUN
fuelectenerg-400	399	49	of	of	ADP
fuelectenerg-400	399	50	integers	integer	NOUN
fuelectenerg-400	399	51	to	to	ADP
fuelectenerg-400	399	52	an	an	DET
fuelectenerg-400	399	53	element	element	NOUN
fuelectenerg-400	399	54	of	of	ADP
fuelectenerg-400	399	55	the	the	DET
fuelectenerg-400	399	56	set	set	NOUN
fuelectenerg-400	399	57	of	of	ADP
fuelectenerg-400	399	58	all	all	DET
fuelectenerg-400	399	59	possible	possible	ADJ
fuelectenerg-400	399	60	colored	colored	ADJ
fuelectenerg-400	399	61	tilings	tiling	NOUN
fuelectenerg-400	399	62	as	as	ADP
fuelectenerg-400	399	63	encoding	encoding	NOUN
fuelectenerg-400	399	64	of	of	ADP
fuelectenerg-400	399	65	colored	colored	ADJ
fuelectenerg-400	399	66	tilings	tiling	NOUN
fuelectenerg-400	399	67	.	.	PUNCT
fuelectenerg-400	400	1	again	again	ADV
fuelectenerg-400	400	2	,	,	PUNCT
fuelectenerg-400	400	3	we	we	PRON
fuelectenerg-400	400	4	divide	divide	VERB
fuelectenerg-400	400	5	the	the	DET
fuelectenerg-400	400	6	problem	problem	NOUN
fuelectenerg-400	400	7	into	into	ADP
fuelectenerg-400	400	8	two	two	NUM
fuelectenerg-400	400	9	separate	separate	ADJ
fuelectenerg-400	400	10	problems	problem	NOUN
fuelectenerg-400	400	11	:	:	PUNCT
fuelectenerg-400	400	12	the	the	DET
fuelectenerg-400	400	13	encoding	encoding	NOUN
fuelectenerg-400	400	14	of	of	ADP
fuelectenerg-400	400	15	tilings	tiling	NOUN
fuelectenerg-400	400	16	and	and	CCONJ
fuelectenerg-400	400	17	the	the	DET
fuelectenerg-400	400	18	coloring	coloring	NOUN
fuelectenerg-400	400	19	of	of	ADP
fuelectenerg-400	400	20	tiles	tile	NOUN
fuelectenerg-400	400	21	.	.	PUNCT
fuelectenerg-400	401	1	to	to	PART
fuelectenerg-400	401	2	facilitate	facilitate	VERB
fuelectenerg-400	401	3	this	this	PRON
fuelectenerg-400	401	4	,	,	PUNCT
fuelectenerg-400	401	5	we	we	PRON
fuelectenerg-400	401	6	assume	assume	VERB
fuelectenerg-400	401	7	that	that	SCONJ
fuelectenerg-400	401	8	the	the	DET
fuelectenerg-400	401	9	fcvl	fcvl	NOUN
fuelectenerg-400	401	10	coloring	coloring	NOUN
fuelectenerg-400	401	11	constraint	constraint	NOUN
fuelectenerg-400	401	12	is	be	AUX
fuelectenerg-400	401	13	imposed	impose	VERB
fuelectenerg-400	401	14	.	.	PUNCT
fuelectenerg-400	402	1	the	the	DET
fuelectenerg-400	402	2	first	first	ADJ
fuelectenerg-400	402	3	step	step	NOUN
fuelectenerg-400	402	4	of	of	ADP
fuelectenerg-400	402	5	the	the	DET
fuelectenerg-400	402	6	encoding	encoding	NOUN
fuelectenerg-400	402	7	process	process	NOUN
fuelectenerg-400	402	8	is	be	AUX
fuelectenerg-400	402	9	the	the	DET
fuelectenerg-400	402	10	encoding	encoding	NOUN
fuelectenerg-400	402	11	of	of	ADP
fuelectenerg-400	402	12	tilings	tiling	NOUN
fuelectenerg-400	402	13	for	for	ADP
fuelectenerg-400	402	14	which	which	PRON
fuelectenerg-400	402	15	we	we	PRON
fuelectenerg-400	402	16	seek	seek	VERB
fuelectenerg-400	402	17	a	a	DET
fuelectenerg-400	402	18	bijective	bijective	ADJ
fuelectenerg-400	402	19	assignment	assignment	NOUN
fuelectenerg-400	402	20	between	between	ADP
fuelectenerg-400	402	21	the	the	DET
fuelectenerg-400	402	22	set	set	NOUN
fuelectenerg-400	402	23	of	of	ADP
fuelectenerg-400	402	24	integers	integer	NOUN
fuelectenerg-400	402	25	and	and	CCONJ
fuelectenerg-400	402	26	the	the	DET
fuelectenerg-400	402	27	set	set	NOUN
fuelectenerg-400	402	28	of	of	ADP
fuelectenerg-400	402	29	all	all	DET
fuelectenerg-400	402	30	tilings	tiling	NOUN
fuelectenerg-400	402	31	.	.	PUNCT
fuelectenerg-400	403	1	the	the	DET
fuelectenerg-400	403	2	second	second	ADJ
fuelectenerg-400	403	3	step	step	NOUN
fuelectenerg-400	403	4	is	be	AUX
fuelectenerg-400	403	5	the	the	DET
fuelectenerg-400	403	6	coloring	coloring	NOUN
fuelectenerg-400	403	7	of	of	ADP
fuelectenerg-400	403	8	the	the	DET
fuelectenerg-400	403	9	tiling	tiling	NOUN
fuelectenerg-400	403	10	.	.	PUNCT
fuelectenerg-400	404	1	the	the	DET
fuelectenerg-400	404	2	second	second	ADJ
fuelectenerg-400	404	3	step	step	NOUN
fuelectenerg-400	404	4	is	be	AUX
fuelectenerg-400	404	5	trivial	trivial	ADJ
fuelectenerg-400	404	6	since	since	SCONJ
fuelectenerg-400	404	7	for	for	ADP
fuelectenerg-400	404	8	the	the	DET
fuelectenerg-400	404	9	fcvl	fcvl	NOUN
fuelectenerg-400	404	10	coloring	coloring	NOUN
fuelectenerg-400	404	11	,	,	PUNCT
fuelectenerg-400	404	12	n2	n2	ADJ
fuelectenerg-400	404	13	horizontal	horizontal	ADJ
fuelectenerg-400	404	14	prototiles	prototile	NOUN
fuelectenerg-400	404	15	,	,	PUNCT
fuelectenerg-400	404	16	which	which	PRON
fuelectenerg-400	404	17	is	be	AUX
fuelectenerg-400	404	18	the	the	DET
fuelectenerg-400	404	19	third	third	ADJ
fuelectenerg-400	404	20	of	of	ADP
fuelectenerg-400	404	21	all	all	DET
fuelectenerg-400	404	22	prototiles	prototile	NOUN
fuelectenerg-400	404	23	in	in	ADP
fuelectenerg-400	404	24	a	a	DET
fuelectenerg-400	404	25	(	(	PUNCT
fuelectenerg-400	404	26	n	n	X
fuelectenerg-400	404	27	,	,	PUNCT
fuelectenerg-400	404	28	n	n	CCONJ
fuelectenerg-400	404	29	,	,	PUNCT
fuelectenerg-400	404	30	n	n	CCONJ
fuelectenerg-400	404	31	)	)	PUNCT
fuelectenerg-400	404	32	hexagon	hexagon	NOUN
fuelectenerg-400	404	33	,	,	PUNCT
fuelectenerg-400	404	34	can	can	AUX
fuelectenerg-400	404	35	be	be	AUX
fuelectenerg-400	404	36	colored	color	VERB
fuelectenerg-400	404	37	independently	independently	ADV
fuelectenerg-400	404	38	.	.	PUNCT
fuelectenerg-400	405	1	thus	thus	ADV
fuelectenerg-400	405	2	we	we	PRON
fuelectenerg-400	405	3	focus	focus	VERB
fuelectenerg-400	405	4	on	on	ADP
fuelectenerg-400	405	5	the	the	DET
fuelectenerg-400	405	6	first	first	ADJ
fuelectenerg-400	405	7	step	step	NOUN
fuelectenerg-400	405	8	of	of	ADP
fuelectenerg-400	405	9	an	an	DET
fuelectenerg-400	405	10	encoding	encoding	NOUN
fuelectenerg-400	405	11	algorithm	algorithm	NOUN
fuelectenerg-400	405	12	.	.	PUNCT
fuelectenerg-400	406	1	before	before	ADP
fuelectenerg-400	406	2	discussing	discuss	VERB
fuelectenerg-400	406	3	the	the	DET
fuelectenerg-400	406	4	proposed	propose	VERB
fuelectenerg-400	406	5	encoding	encoding	NOUN
fuelectenerg-400	406	6	algorithm	algorithm	NOUN
fuelectenerg-400	406	7	we	we	PRON
fuelectenerg-400	406	8	give	give	VERB
fuelectenerg-400	406	9	an	an	DET
fuelectenerg-400	406	10	intuition	intuition	NOUN
fuelectenerg-400	406	11	behind	behind	ADP
fuelectenerg-400	406	12	our	our	PRON
fuelectenerg-400	406	13	approach	approach	NOUN
fuelectenerg-400	406	14	.	.	PUNCT
fuelectenerg-400	407	1	we	we	PRON
fuelectenerg-400	407	2	begin	begin	VERB
fuelectenerg-400	407	3	by	by	ADP
fuelectenerg-400	407	4	recalling	recall	VERB
fuelectenerg-400	407	5	that	that	SCONJ
fuelectenerg-400	407	6	there	there	PRON
fuelectenerg-400	407	7	is	be	VERB
fuelectenerg-400	407	8	a	a	DET
fuelectenerg-400	407	9	unique	unique	ADJ
fuelectenerg-400	407	10	boxed	box	VERB
fuelectenerg-400	407	11	plane	plane	NOUN
fuelectenerg-400	407	12	partition	partition	NOUN
fuelectenerg-400	407	13	corresponding	correspond	VERB
fuelectenerg-400	407	14	to	to	ADP
fuelectenerg-400	407	15	any	any	DET
fuelectenerg-400	407	16	lozenge	lozenge	NOUN
fuelectenerg-400	407	17	tiling	tiling	NOUN
fuelectenerg-400	407	18	.	.	PUNCT
fuelectenerg-400	408	1	consider	consider	VERB
fuelectenerg-400	408	2	an	an	DET
fuelectenerg-400	408	3	(	(	PUNCT
fuelectenerg-400	408	4	a	a	PROPN
fuelectenerg-400	408	5	,	,	PUNCT
fuelectenerg-400	408	6	b	b	NOUN
fuelectenerg-400	408	7	,	,	PUNCT
fuelectenerg-400	408	8	c	c	NOUN
fuelectenerg-400	408	9	)	)	PUNCT
fuelectenerg-400	408	10	hexagon	hexagon	PROPN
fuelectenerg-400	408	11	tiled	tile	VERB
fuelectenerg-400	408	12	with	with	ADP
fuelectenerg-400	408	13	equilateral	equilateral	ADJ
fuelectenerg-400	408	14	triangles	triangle	NOUN
fuelectenerg-400	408	15	with	with	ADP
fuelectenerg-400	408	16	unit	unit	NOUN
fuelectenerg-400	408	17	side	side	NOUN
fuelectenerg-400	408	18	-	-	PUNCT
fuelectenerg-400	408	19	lengths	length	NOUN
fuelectenerg-400	408	20	.	.	PUNCT
fuelectenerg-400	409	1	an	an	DET
fuelectenerg-400	409	2	alternative	alternative	ADJ
fuelectenerg-400	409	3	way	way	NOUN
fuelectenerg-400	409	4	to	to	PART
fuelectenerg-400	409	5	unambiguously	unambiguously	ADV
fuelectenerg-400	409	6	specify	specify	VERB
fuelectenerg-400	409	7	a	a	DET
fuelectenerg-400	409	8	boxed	box	VERB
fuelectenerg-400	409	9	plane	plane	NOUN
fuelectenerg-400	409	10	partition	partition	NOUN
fuelectenerg-400	409	11	is	be	AUX
fuelectenerg-400	409	12	to	to	PART
fuelectenerg-400	409	13	traverse	traverse	VERB
fuelectenerg-400	409	14	a	a	DET
fuelectenerg-400	409	15	paths	path	NOUN
fuelectenerg-400	409	16	covering	cover	VERB
fuelectenerg-400	409	17	only	only	ADV
fuelectenerg-400	409	18	vertical	vertical	ADJ
fuelectenerg-400	409	19	prototiles	prototile	NOUN
fuelectenerg-400	409	20	as	as	SCONJ
fuelectenerg-400	409	21	illustrated	illustrate	VERB
fuelectenerg-400	409	22	in	in	ADP
fuelectenerg-400	409	23	fig	fig	NOUN
fuelectenerg-400	409	24	.	.	PUNCT
fuelectenerg-400	410	1	8(d	8(d	NUM
fuelectenerg-400	410	2	)	)	PUNCT
fuelectenerg-400	410	3	for	for	ADP
fuelectenerg-400	410	4	the	the	DET
fuelectenerg-400	410	5	case	case	NOUN
fuelectenerg-400	410	6	of	of	ADP
fuelectenerg-400	410	7	the	the	DET
fuelectenerg-400	410	8	(	(	PUNCT
fuelectenerg-400	410	9	3	3	NUM
fuelectenerg-400	410	10	,	,	PUNCT
fuelectenerg-400	410	11	3	3	NUM
fuelectenerg-400	410	12	,	,	PUNCT
fuelectenerg-400	410	13	3	3	X
fuelectenerg-400	410	14	)	)	PUNCT
fuelectenerg-400	410	15	hexagon	hexagon	NOUN
fuelectenerg-400	410	16	.	.	PUNCT
fuelectenerg-400	411	1	we	we	PRON
fuelectenerg-400	411	2	refer	refer	VERB
fuelectenerg-400	411	3	to	to	ADP
fuelectenerg-400	411	4	these	these	DET
fuelectenerg-400	411	5	paths	path	NOUN
fuelectenerg-400	411	6	as	as	ADP
fuelectenerg-400	411	7	routings	routing	NOUN
fuelectenerg-400	411	8	.	.	PUNCT
fuelectenerg-400	412	1	each	each	DET
fuelectenerg-400	412	2	section	section	NOUN
fuelectenerg-400	412	3	of	of	ADP
fuelectenerg-400	412	4	the	the	DET
fuelectenerg-400	412	5	path	path	NOUN
fuelectenerg-400	412	6	corresponds	correspond	VERB
fuelectenerg-400	412	7	to	to	ADP
fuelectenerg-400	412	8	one	one	NUM
fuelectenerg-400	412	9	type	type	NOUN
fuelectenerg-400	412	10	-	-	PUNCT
fuelectenerg-400	412	11	b	b	NOUN
fuelectenerg-400	412	12	or	or	CCONJ
fuelectenerg-400	412	13	type	type	NOUN
fuelectenerg-400	412	14	-	-	PUNCT
fuelectenerg-400	412	15	c	c	NOUN
fuelectenerg-400	412	16	lozenge	lozenge	NOUN
fuelectenerg-400	412	17	and	and	CCONJ
fuelectenerg-400	412	18	it	it	PRON
fuelectenerg-400	412	19	is	be	AUX
fuelectenerg-400	412	20	drawn	draw	VERB
fuelectenerg-400	412	21	as	as	ADP
fuelectenerg-400	412	22	a	a	DET
fuelectenerg-400	412	23	line	line	NOUN
fuelectenerg-400	412	24	segment	segment	NOUN
fuelectenerg-400	412	25	of	of	ADP
fuelectenerg-400	412	26	”	"	PUNCT
fuelectenerg-400	412	27	northeast	northeast	NOUN
fuelectenerg-400	412	28	”	"	PUNCT
fuelectenerg-400	412	29	or	or	CCONJ
fuelectenerg-400	412	30	”	"	PUNCT
fuelectenerg-400	412	31	souteast	souteast	ADJ
fuelectenerg-400	412	32	”	"	PUNCT
fuelectenerg-400	412	33	orientation	orientation	NOUN
fuelectenerg-400	412	34	in	in	ADP
fuelectenerg-400	412	35	fig	fig	NOUN
fuelectenerg-400	412	36	.	.	PUNCT
fuelectenerg-400	413	1	8(d	8(d	NUM
fuelectenerg-400	413	2	)	)	PUNCT
fuelectenerg-400	413	3	.	.	PUNCT
fuelectenerg-400	414	1	a	a	DET
fuelectenerg-400	414	2	collection	collection	NOUN
fuelectenerg-400	414	3	of	of	ADP
fuelectenerg-400	414	4	n	n	DET
fuelectenerg-400	414	5	such	such	ADJ
fuelectenerg-400	414	6	paths	path	NOUN
fuelectenerg-400	414	7	determines	determine	VERB
fuelectenerg-400	414	8	the	the	DET
fuelectenerg-400	414	9	tiling	tiling	NOUN
fuelectenerg-400	414	10	.	.	PUNCT
fuelectenerg-400	415	1	note	note	NOUN
fuelectenerg-400	415	2	,	,	PUNCT
fuelectenerg-400	415	3	however	however	ADV
fuelectenerg-400	415	4	,	,	PUNCT
fuelectenerg-400	415	5	that	that	SCONJ
fuelectenerg-400	415	6	the	the	DET
fuelectenerg-400	415	7	n	n	PROPN
fuelectenerg-400	415	8	paths	path	NOUN
fuelectenerg-400	415	9	in	in	ADP
fuelectenerg-400	415	10	a	a	DET
fuelectenerg-400	415	11	collection	collection	NOUN
fuelectenerg-400	415	12	can	can	AUX
fuelectenerg-400	415	13	not	not	PART
fuelectenerg-400	415	14	be	be	AUX
fuelectenerg-400	415	15	chosen	choose	VERB
fuelectenerg-400	415	16	arbitrarily	arbitrarily	ADV
fuelectenerg-400	415	17	.	.	PUNCT
fuelectenerg-400	416	1	this	this	PRON
fuelectenerg-400	416	2	is	be	AUX
fuelectenerg-400	416	3	simply	simply	ADV
fuelectenerg-400	416	4	because	because	SCONJ
fuelectenerg-400	416	5	we	we	PRON
fuelectenerg-400	416	6	do	do	AUX
fuelectenerg-400	416	7	not	not	PART
fuelectenerg-400	416	8	allow	allow	VERB
fuelectenerg-400	416	9	that	that	SCONJ
fuelectenerg-400	416	10	a	a	DET
fuelectenerg-400	416	11	box	box	NOUN
fuelectenerg-400	416	12	at	at	ADP
fuelectenerg-400	416	13	any	any	DET
fuelectenerg-400	416	14	level	level	NOUN
fuelectenerg-400	416	15	“	"	PUNCT
fuelectenerg-400	416	16	levitates	levitate	NOUN
fuelectenerg-400	416	17	”	"	PUNCT
fuelectenerg-400	416	18	without	without	ADP
fuelectenerg-400	416	19	being	be	AUX
fuelectenerg-400	416	20	supported	support	VERB
fuelectenerg-400	416	21	by	by	ADP
fuelectenerg-400	416	22	boxes	box	NOUN
fuelectenerg-400	416	23	the	the	DET
fuelectenerg-400	416	24	beneath	beneath	ADP
fuelectenerg-400	416	25	it	it	PRON
fuelectenerg-400	416	26	.	.	PUNCT
fuelectenerg-400	417	1	we	we	PRON
fuelectenerg-400	417	2	describe	describe	VERB
fuelectenerg-400	417	3	this	this	DET
fuelectenerg-400	417	4	requirement	requirement	NOUN
fuelectenerg-400	417	5	though	though	SCONJ
fuelectenerg-400	417	6	combinatorial	combinatorial	ADJ
fuelectenerg-400	417	7	objects	object	NOUN
fuelectenerg-400	417	8	known	know	VERB
fuelectenerg-400	417	9	as	as	ADP
fuelectenerg-400	417	10	mountain	mountain	NOUN
fuelectenerg-400	417	11	ranges	range	NOUN
fuelectenerg-400	417	12	illustrated	illustrate	VERB
fuelectenerg-400	417	13	in	in	ADP
fuelectenerg-400	417	14	fig	fig	NOUN
fuelectenerg-400	417	15	.	.	PUNCT
fuelectenerg-400	417	16	8(c	8(c	NUM
fuelectenerg-400	417	17	)	)	PUNCT
fuelectenerg-400	417	18	.	.	PUNCT
fuelectenerg-400	418	1	each	each	DET
fuelectenerg-400	418	2	path	path	NOUN
fuelectenerg-400	418	3	correspond	correspond	VERB
fuelectenerg-400	418	4	to	to	ADP
fuelectenerg-400	418	5	one	one	NUM
fuelectenerg-400	418	6	mountain	mountain	NOUN
fuelectenerg-400	418	7	range	range	NOUN
fuelectenerg-400	418	8	,	,	PUNCT
fuelectenerg-400	418	9	but	but	CCONJ
fuelectenerg-400	418	10	“	"	PUNCT
fuelectenerg-400	418	11	lower	low	ADJ
fuelectenerg-400	418	12	”	"	PUNCT
fuelectenerg-400	418	13	paths	path	NOUN
fuelectenerg-400	418	14	can	can	AUX
fuelectenerg-400	418	15	not	not	PART
fuelectenerg-400	418	16	have	have	VERB
fuelectenerg-400	418	17	mountain	mountain	NOUN
fuelectenerg-400	418	18	ranges	range	NOUN
fuelectenerg-400	418	19	higher	higher	ADV
fuelectenerg-400	418	20	than	than	ADP
fuelectenerg-400	418	21	“	"	PUNCT
fuelectenerg-400	418	22	upper	upper	ADJ
fuelectenerg-400	418	23	”	"	PUNCT
fuelectenerg-400	418	24	paths	path	NOUN
fuelectenerg-400	418	25	.	.	PUNCT
fuelectenerg-400	419	1	we	we	PRON
fuelectenerg-400	419	2	formalize	formalize	VERB
fuelectenerg-400	419	3	this	this	DET
fuelectenerg-400	419	4	concept	concept	NOUN
fuelectenerg-400	419	5	through	through	ADP
fuelectenerg-400	419	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	419	7	ordering	ordering	NOUN
fuelectenerg-400	419	8	and	and	CCONJ
fuelectenerg-400	419	9	ranking	ranking	NOUN
fuelectenerg-400	419	10	of	of	ADP
fuelectenerg-400	419	11	mountain	mountain	NOUN
fuelectenerg-400	419	12	ranges	range	NOUN
fuelectenerg-400	419	13	.	.	PUNCT
fuelectenerg-400	420	1	a	a	DET
fuelectenerg-400	420	2	collection	collection	NOUN
fuelectenerg-400	420	3	of	of	ADP
fuelectenerg-400	420	4	n	n	DET
fuelectenerg-400	420	5	nondecreasing	nondecrease	VERB
fuelectenerg-400	420	6	mountain	mountain	NOUN
fuelectenerg-400	420	7	ranges	range	NOUN
fuelectenerg-400	420	8	represent	represent	VERB
fuelectenerg-400	420	9	an	an	DET
fuelectenerg-400	420	10	instance	instance	NOUN
fuelectenerg-400	420	11	of	of	ADP
fuelectenerg-400	420	12	a	a	DET
fuelectenerg-400	420	13	tiling	tiling	NOUN
fuelectenerg-400	420	14	.	.	PUNCT
fuelectenerg-400	421	1	the	the	DET
fuelectenerg-400	421	2	set	set	NOUN
fuelectenerg-400	421	3	of	of	ADP
fuelectenerg-400	421	4	all	all	DET
fuelectenerg-400	421	5	such	such	ADJ
fuelectenerg-400	421	6	collections	collection	NOUN
fuelectenerg-400	421	7	represent	represent	VERB
fuelectenerg-400	421	8	the	the	DET
fuelectenerg-400	421	9	set	set	NOUN
fuelectenerg-400	421	10	of	of	ADP
fuelectenerg-400	421	11	all	all	DET
fuelectenerg-400	421	12	tilings	tiling	NOUN
fuelectenerg-400	421	13	.	.	PUNCT
fuelectenerg-400	422	1	to	to	PART
fuelectenerg-400	422	2	perform	perform	VERB
fuelectenerg-400	422	3	encoding	encode	VERB
fuelectenerg-400	422	4	and	and	CCONJ
fuelectenerg-400	422	5	decoding	decode	VERB
fuelectenerg-400	422	6	we	we	PRON
fuelectenerg-400	422	7	need	need	VERB
fuelectenerg-400	422	8	to	to	PART
fuelectenerg-400	422	9	enumerate	enumerate	VERB
fuelectenerg-400	422	10	mountain	mountain	NOUN
fuelectenerg-400	422	11	ranges	range	NOUN
fuelectenerg-400	422	12	and	and	CCONJ
fuelectenerg-400	422	13	enumerate	enumerate	VERB
fuelectenerg-400	422	14	collection	collection	NOUN
fuelectenerg-400	422	15	of	of	ADP
fuelectenerg-400	422	16	mountain	mountain	NOUN
fuelectenerg-400	422	17	ranges	range	NOUN
fuelectenerg-400	422	18	.	.	PUNCT
fuelectenerg-400	423	1	thus	thus	ADV
fuelectenerg-400	423	2	the	the	DET
fuelectenerg-400	423	3	encoding	encoding	NOUN
fuelectenerg-400	423	4	procedure	procedure	NOUN
fuelectenerg-400	423	5	involves	involve	VERB
fuelectenerg-400	423	6	the	the	DET
fuelectenerg-400	423	7	step	step	NOUN
fuelectenerg-400	423	8	of	of	ADP
fuelectenerg-400	423	9	converting	convert	VERB
fuelectenerg-400	423	10	an	an	DET
fuelectenerg-400	423	11	integer	integer	NOUN
fuelectenerg-400	423	12	to	to	ADP
fuelectenerg-400	423	13	a	a	DET
fuelectenerg-400	423	14	routing	routing	NOUN
fuelectenerg-400	423	15	on	on	ADP
fuelectenerg-400	423	16	a	a	DET
fuelectenerg-400	423	17	graph	graph	NOUN
fuelectenerg-400	423	18	,	,	PUNCT
fuelectenerg-400	423	19	which	which	PRON
fuelectenerg-400	423	20	is	be	AUX
fuelectenerg-400	423	21	represented	represent	VERB
fuelectenerg-400	423	22	by	by	ADP
fuelectenerg-400	423	23	a	a	DET
fuelectenerg-400	423	24	set	set	NOUN
fuelectenerg-400	423	25	of	of	ADP
fuelectenerg-400	423	26	constant	constant	ADJ
fuelectenerg-400	423	27	-	-	PUNCT
fuelectenerg-400	423	28	weight	weight	NOUN
fuelectenerg-400	423	29	sequences	sequence	NOUN
fuelectenerg-400	423	30	and	and	CCONJ
fuelectenerg-400	423	31	then	then	ADV
fuelectenerg-400	423	32	converting	convert	VERB
fuelectenerg-400	423	33	it	it	PRON
fuelectenerg-400	423	34	to	to	ADP
fuelectenerg-400	423	35	a	a	DET
fuelectenerg-400	423	36	tiling	tiling	NOUN
fuelectenerg-400	423	37	.	.	PUNCT
fuelectenerg-400	424	1	in	in	ADP
fuelectenerg-400	424	2	the	the	DET
fuelectenerg-400	424	3	following	follow	VERB
fuelectenerg-400	424	4	subsections	subsection	NOUN
fuelectenerg-400	424	5	we	we	PRON
fuelectenerg-400	424	6	introduce	introduce	VERB
fuelectenerg-400	424	7	rigorously	rigorously	ADV
fuelectenerg-400	424	8	the	the	DET
fuelectenerg-400	424	9	combinatorial	combinatorial	ADJ
fuelectenerg-400	424	10	objects	object	NOUN
fuelectenerg-400	424	11	given	give	VERB
fuelectenerg-400	424	12	in	in	ADP
fuelectenerg-400	424	13	the	the	DET
fuelectenerg-400	424	14	above	above	ADJ
fuelectenerg-400	424	15	intuitive	intuitive	ADJ
fuelectenerg-400	424	16	explanation	explanation	NOUN
fuelectenerg-400	424	17	.	.	PUNCT
fuelectenerg-400	425	1	before	before	ADP
fuelectenerg-400	425	2	discussing	discuss	VERB
fuelectenerg-400	425	3	the	the	DET
fuelectenerg-400	425	4	details	detail	NOUN
fuelectenerg-400	425	5	of	of	ADP
fuelectenerg-400	425	6	the	the	DET
fuelectenerg-400	425	7	proposed	propose	VERB
fuelectenerg-400	425	8	algorithm	algorithm	NOUN
fuelectenerg-400	425	9	,	,	PUNCT
fuelectenerg-400	425	10	we	we	PRON
fuelectenerg-400	425	11	describe	describe	VERB
fuelectenerg-400	425	12	the	the	DET
fuelectenerg-400	425	13	problem	problem	NOUN
fuelectenerg-400	425	14	of	of	ADP
fuelectenerg-400	425	15	enumeration	enumeration	NOUN
fuelectenerg-400	425	16	of	of	ADP
fuelectenerg-400	425	17	the	the	DET
fuelectenerg-400	425	18	routings	routing	NOUN
fuelectenerg-400	425	19	on	on	ADP
fuelectenerg-400	425	20	a	a	DET
fuelectenerg-400	425	21	graph	graph	NOUN
fuelectenerg-400	425	22	.	.	PUNCT
fuelectenerg-400	426	1	5.1	5.1	NUM
fuelectenerg-400	426	2	routings	routing	NOUN
fuelectenerg-400	426	3	on	on	ADP
fuelectenerg-400	426	4	a	a	DET
fuelectenerg-400	426	5	graph	graph	NOUN
fuelectenerg-400	426	6	recall	recall	NOUN
fuelectenerg-400	426	7	that	that	SCONJ
fuelectenerg-400	426	8	the	the	DET
fuelectenerg-400	426	9	idea	idea	NOUN
fuelectenerg-400	426	10	is	be	AUX
fuelectenerg-400	426	11	to	to	PART
fuelectenerg-400	426	12	use	use	VERB
fuelectenerg-400	426	13	the	the	DET
fuelectenerg-400	426	14	bijection	bijection	NOUN
fuelectenerg-400	426	15	between	between	ADP
fuelectenerg-400	426	16	tiling	tile	VERB
fuelectenerg-400	426	17	and	and	CCONJ
fuelectenerg-400	426	18	routings	routing	NOUN
fuelectenerg-400	426	19	on	on	ADP
fuelectenerg-400	426	20	a	a	DET
fuelectenerg-400	426	21	graph	graph	NOUN
fuelectenerg-400	426	22	.	.	PUNCT
fuelectenerg-400	426	23	consider	consider	VERB
fuelectenerg-400	426	24	an	an	DET
fuelectenerg-400	426	25	(	(	PUNCT
fuelectenerg-400	426	26	a	a	PROPN
fuelectenerg-400	426	27	,	,	PUNCT
fuelectenerg-400	426	28	b	b	NOUN
fuelectenerg-400	426	29	,	,	PUNCT
fuelectenerg-400	426	30	c	c	NOUN
fuelectenerg-400	426	31	)	)	PUNCT
fuelectenerg-400	426	32	hexagon	hexagon	PROPN
fuelectenerg-400	426	33	h	h	PROPN
fuelectenerg-400	426	34	tiled	tile	VERB
fuelectenerg-400	426	35	with	with	ADP
fuelectenerg-400	426	36	equilateral	equilateral	ADJ
fuelectenerg-400	426	37	triangles	triangle	NOUN
fuelectenerg-400	426	38	with	with	ADP
fuelectenerg-400	426	39	unit	unit	NOUN
fuelectenerg-400	426	40	side	side	NOUN
fuelectenerg-400	426	41	-	-	PUNCT
fuelectenerg-400	426	42	lengths	length	NOUN
fuelectenerg-400	426	43	.	.	PUNCT
fuelectenerg-400	427	1	for	for	ADP
fuelectenerg-400	427	2	this	this	DET
fuelectenerg-400	427	3	tiling	tiling	NOUN
fuelectenerg-400	427	4	,	,	PUNCT
fuelectenerg-400	427	5	an	an	DET
fuelectenerg-400	427	6	associated	associate	VERB
fuelectenerg-400	427	7	graph	graph	NOUN
fuelectenerg-400	427	8	g	g	PROPN
fuelectenerg-400	427	9	can	can	AUX
fuelectenerg-400	427	10	be	be	AUX
fuelectenerg-400	427	11	constructed	construct	VERB
fuelectenerg-400	427	12	detection	detection	NOUN
fuelectenerg-400	427	13	and	and	CCONJ
fuelectenerg-400	427	14	coding	code	VERB
fuelectenerg-400	427	15	for	for	ADP
fuelectenerg-400	427	16	tdmr	tdmr	NOUN
fuelectenerg-400	427	17	channel	channel	NOUN
fuelectenerg-400	427	18	531	531	NUM
fuelectenerg-400	427	19	as	as	SCONJ
fuelectenerg-400	427	20	follows	follow	VERB
fuelectenerg-400	427	21	.	.	PUNCT
fuelectenerg-400	428	1	the	the	DET
fuelectenerg-400	428	2	vertices	vertex	NOUN
fuelectenerg-400	428	3	of	of	ADP
fuelectenerg-400	428	4	g	g	PROPN
fuelectenerg-400	428	5	are	be	AUX
fuelectenerg-400	428	6	the	the	DET
fuelectenerg-400	428	7	mid	mid	NOUN
fuelectenerg-400	428	8	-	-	NOUN
fuelectenerg-400	428	9	points	point	NOUN
fuelectenerg-400	428	10	of	of	ADP
fuelectenerg-400	428	11	the	the	DET
fuelectenerg-400	428	12	vertical	vertical	ADJ
fuelectenerg-400	428	13	sides	side	NOUN
fuelectenerg-400	428	14	in	in	ADP
fuelectenerg-400	428	15	the	the	DET
fuelectenerg-400	428	16	tiling	tiling	NOUN
fuelectenerg-400	428	17	of	of	ADP
fuelectenerg-400	428	18	h.	h.	PROPN
fuelectenerg-400	428	19	two	two	NUM
fuelectenerg-400	428	20	vertices	vertex	NOUN
fuelectenerg-400	428	21	of	of	ADP
fuelectenerg-400	428	22	g	g	NOUN
fuelectenerg-400	428	23	are	be	AUX
fuelectenerg-400	428	24	connected	connect	VERB
fuelectenerg-400	428	25	if	if	SCONJ
fuelectenerg-400	428	26	their	their	PRON
fuelectenerg-400	428	27	corresponding	correspond	VERB
fuelectenerg-400	428	28	sides	side	NOUN
fuelectenerg-400	428	29	lie	lie	VERB
fuelectenerg-400	428	30	on	on	ADP
fuelectenerg-400	428	31	adjacent	adjacent	ADJ
fuelectenerg-400	428	32	triangles	triangle	NOUN
fuelectenerg-400	428	33	.	.	PUNCT
fuelectenerg-400	429	1	fig	fig	NOUN
fuelectenerg-400	429	2	.	.	PUNCT
fuelectenerg-400	430	1	8	8	NUM
fuelectenerg-400	430	2	shows	show	VERB
fuelectenerg-400	430	3	a	a	DET
fuelectenerg-400	430	4	(	(	PUNCT
fuelectenerg-400	430	5	3	3	NUM
fuelectenerg-400	430	6	,	,	PUNCT
fuelectenerg-400	430	7	3	3	NUM
fuelectenerg-400	430	8	,	,	PUNCT
fuelectenerg-400	430	9	3	3	X
fuelectenerg-400	430	10	)	)	PUNCT
fuelectenerg-400	430	11	hexagon	hexagon	NOUN
fuelectenerg-400	430	12	(	(	PUNCT
fuelectenerg-400	430	13	fig	fig	NOUN
fuelectenerg-400	430	14	.	.	PUNCT
fuelectenerg-400	431	1	8(a	8(a	NUM
fuelectenerg-400	431	2	)	)	PUNCT
fuelectenerg-400	431	3	)	)	PUNCT
fuelectenerg-400	432	1	and	and	CCONJ
fuelectenerg-400	432	2	its	its	PRON
fuelectenerg-400	432	3	corresponding	corresponding	ADJ
fuelectenerg-400	432	4	graph	graph	NOUN
fuelectenerg-400	432	5	(	(	PUNCT
fuelectenerg-400	432	6	fig	fig	NOUN
fuelectenerg-400	432	7	.	.	PUNCT
fuelectenerg-400	432	8	8(b	8(b	NUM
fuelectenerg-400	432	9	)	)	PUNCT
fuelectenerg-400	432	10	)	)	PUNCT
fuelectenerg-400	432	11	.	.	PUNCT
fuelectenerg-400	433	1	the	the	DET
fuelectenerg-400	433	2	leftmost	leftmost	ADJ
fuelectenerg-400	433	3	nodes	node	NOUN
fuelectenerg-400	433	4	of	of	ADP
fuelectenerg-400	433	5	g	g	NOUN
fuelectenerg-400	433	6	are	be	AUX
fuelectenerg-400	433	7	designated	designate	VERB
fuelectenerg-400	433	8	as	as	ADP
fuelectenerg-400	433	9	sources	source	NOUN
fuelectenerg-400	433	10	and	and	CCONJ
fuelectenerg-400	433	11	the	the	DET
fuelectenerg-400	433	12	rightmost	rightmost	NOUN
fuelectenerg-400	433	13	nodes	node	NOUN
fuelectenerg-400	433	14	as	as	ADP
fuelectenerg-400	433	15	drains	drain	NOUN
fuelectenerg-400	433	16	.	.	PUNCT
fuelectenerg-400	434	1	notice	notice	VERB
fuelectenerg-400	434	2	that	that	SCONJ
fuelectenerg-400	434	3	the	the	DET
fuelectenerg-400	434	4	number	number	NOUN
fuelectenerg-400	434	5	of	of	ADP
fuelectenerg-400	434	6	sources	source	NOUN
fuelectenerg-400	434	7	is	be	AUX
fuelectenerg-400	434	8	equal	equal	ADJ
fuelectenerg-400	434	9	to	to	ADP
fuelectenerg-400	434	10	the	the	DET
fuelectenerg-400	434	11	number	number	NOUN
fuelectenerg-400	434	12	of	of	ADP
fuelectenerg-400	434	13	drains	drain	NOUN
fuelectenerg-400	434	14	.	.	PUNCT
fuelectenerg-400	435	1	traversing	traverse	VERB
fuelectenerg-400	435	2	the	the	DET
fuelectenerg-400	435	3	sources	source	NOUN
fuelectenerg-400	435	4	(	(	PUNCT
fuelectenerg-400	435	5	drains	drain	NOUN
fuelectenerg-400	435	6	respectively	respectively	ADV
fuelectenerg-400	435	7	)	)	PUNCT
fuelectenerg-400	435	8	from	from	ADP
fuelectenerg-400	435	9	top	top	NOUN
fuelectenerg-400	435	10	to	to	ADP
fuelectenerg-400	435	11	bottom	bottom	NOUN
fuelectenerg-400	435	12	,	,	PUNCT
fuelectenerg-400	435	13	each	each	PRON
fuelectenerg-400	435	14	of	of	ADP
fuelectenerg-400	435	15	the	the	DET
fuelectenerg-400	435	16	sources	source	NOUN
fuelectenerg-400	435	17	is	be	AUX
fuelectenerg-400	435	18	denoted	denote	VERB
fuelectenerg-400	435	19	as	as	ADP
fuelectenerg-400	435	20	s1	s1	NOUN
fuelectenerg-400	435	21	,	,	PUNCT
fuelectenerg-400	435	22	s2	s2	NOUN
fuelectenerg-400	435	23	,	,	PUNCT
fuelectenerg-400	435	24	.	.	PUNCT
fuelectenerg-400	435	25	.	.	PUNCT
fuelectenerg-400	436	1	.	.	PUNCT
fuelectenerg-400	437	1	,	,	PUNCT
fuelectenerg-400	437	2	sc	sc	PROPN
fuelectenerg-400	437	3	(	(	PUNCT
fuelectenerg-400	437	4	t1	t1	PROPN
fuelectenerg-400	437	5	,	,	PUNCT
fuelectenerg-400	437	6	t2	t2	NOUN
fuelectenerg-400	437	7	,	,	PUNCT
fuelectenerg-400	437	8	.	.	PUNCT
fuelectenerg-400	437	9	.	.	PUNCT
fuelectenerg-400	438	1	.	.	PUNCT
fuelectenerg-400	439	1	,	,	PUNCT
fuelectenerg-400	439	2	tc	tc	NUM
fuelectenerg-400	439	3	respectively	respectively	ADV
fuelectenerg-400	439	4	)	)	PUNCT
fuelectenerg-400	439	5	.	.	PUNCT
fuelectenerg-400	440	1	now	now	ADV
fuelectenerg-400	440	2	,	,	PUNCT
fuelectenerg-400	440	3	the	the	DET
fuelectenerg-400	440	4	routings	routing	NOUN
fuelectenerg-400	440	5	on	on	ADP
fuelectenerg-400	440	6	the	the	DET
fuelectenerg-400	440	7	graph	graph	NOUN
fuelectenerg-400	440	8	g	g	PROPN
fuelectenerg-400	440	9	is	be	AUX
fuelectenerg-400	440	10	the	the	DET
fuelectenerg-400	440	11	set	set	NOUN
fuelectenerg-400	440	12	of	of	ADP
fuelectenerg-400	440	13	c	c	PROPN
fuelectenerg-400	440	14	shortest	short	ADJ
fuelectenerg-400	440	15	nonintersecting	nonintersecting	NOUN
fuelectenerg-400	440	16	paths	path	NOUN
fuelectenerg-400	440	17	from	from	ADP
fuelectenerg-400	440	18	si	si	PROPN
fuelectenerg-400	440	19	to	to	ADP
fuelectenerg-400	440	20	ti	ti	PROPN
fuelectenerg-400	440	21	for	for	ADP
fuelectenerg-400	440	22	each	each	DET
fuelectenerg-400	440	23	i.	i.	NOUN
fuelectenerg-400	440	24	the	the	DET
fuelectenerg-400	440	25	routings	routing	NOUN
fuelectenerg-400	440	26	on	on	ADP
fuelectenerg-400	440	27	the	the	DET
fuelectenerg-400	440	28	graph	graph	NOUN
fuelectenerg-400	440	29	g	g	NOUN
fuelectenerg-400	440	30	are	be	AUX
fuelectenerg-400	440	31	associated	associate	VERB
fuelectenerg-400	440	32	to	to	ADP
fuelectenerg-400	440	33	the	the	DET
fuelectenerg-400	440	34	tilings	tiling	NOUN
fuelectenerg-400	440	35	of	of	ADP
fuelectenerg-400	440	36	h	h	NOUN
fuelectenerg-400	440	37	with	with	ADP
fuelectenerg-400	440	38	lozenges	lozenge	NOUN
fuelectenerg-400	440	39	by	by	ADP
fuelectenerg-400	440	40	the	the	DET
fuelectenerg-400	440	41	following	follow	VERB
fuelectenerg-400	440	42	theorem	theorem	VERB
fuelectenerg-400	440	43	.	.	PUNCT
fuelectenerg-400	441	1	(	(	PUNCT
fuelectenerg-400	441	2	a	a	X
fuelectenerg-400	441	3	)	)	PUNCT
fuelectenerg-400	441	4	(	(	PUNCT
fuelectenerg-400	441	5	b	b	X
fuelectenerg-400	441	6	)	)	PUNCT
fuelectenerg-400	441	7	(	(	PUNCT
fuelectenerg-400	441	8	c	c	X
fuelectenerg-400	441	9	)	)	PUNCT
fuelectenerg-400	441	10	(	(	PUNCT
fuelectenerg-400	441	11	d	d	X
fuelectenerg-400	441	12	)	)	PUNCT
fuelectenerg-400	441	13	fig	fig	NOUN
fuelectenerg-400	441	14	.	.	PUNCT
fuelectenerg-400	442	1	8	8	NUM
fuelectenerg-400	442	2	.	.	PUNCT
fuelectenerg-400	443	1	(	(	PUNCT
fuelectenerg-400	443	2	a	a	X
fuelectenerg-400	443	3	)	)	PUNCT
fuelectenerg-400	443	4	a	a	DET
fuelectenerg-400	443	5	(	(	PUNCT
fuelectenerg-400	443	6	3,3,3	3,3,3	NOUN
fuelectenerg-400	443	7	)	)	PUNCT
fuelectenerg-400	443	8	hexagon	hexagon	PROPN
fuelectenerg-400	443	9	h	h	PROPN
fuelectenerg-400	443	10	tiled	tile	VERB
fuelectenerg-400	443	11	with	with	ADP
fuelectenerg-400	443	12	equilateral	equilateral	ADJ
fuelectenerg-400	443	13	triangles	triangle	NOUN
fuelectenerg-400	443	14	of	of	ADP
fuelectenerg-400	443	15	unit	unit	NOUN
fuelectenerg-400	443	16	side	side	NOUN
fuelectenerg-400	443	17	.	.	PUNCT
fuelectenerg-400	444	1	(	(	PUNCT
fuelectenerg-400	444	2	b	b	X
fuelectenerg-400	444	3	)	)	PUNCT
fuelectenerg-400	444	4	the	the	DET
fuelectenerg-400	444	5	graph	graph	NOUN
fuelectenerg-400	444	6	g	g	PROPN
fuelectenerg-400	444	7	associated	associate	VERB
fuelectenerg-400	444	8	with	with	ADP
fuelectenerg-400	444	9	h.	h.	PROPN
fuelectenerg-400	444	10	(	(	PUNCT
fuelectenerg-400	444	11	c	c	NOUN
fuelectenerg-400	444	12	)	)	PUNCT
fuelectenerg-400	444	13	example	example	NOUN
fuelectenerg-400	444	14	of	of	ADP
fuelectenerg-400	444	15	a	a	DET
fuelectenerg-400	444	16	routing	routing	NOUN
fuelectenerg-400	444	17	on	on	ADP
fuelectenerg-400	444	18	the	the	DET
fuelectenerg-400	444	19	graph	graph	NOUN
fuelectenerg-400	444	20	associated	associate	VERB
fuelectenerg-400	444	21	with	with	ADP
fuelectenerg-400	444	22	a	a	DET
fuelectenerg-400	444	23	(	(	PUNCT
fuelectenerg-400	444	24	3,3,3	3,3,3	NOUN
fuelectenerg-400	444	25	)	)	PUNCT
fuelectenerg-400	444	26	hexagon	hexagon	NOUN
fuelectenerg-400	444	27	.	.	PUNCT
fuelectenerg-400	445	1	(	(	PUNCT
fuelectenerg-400	445	2	d	d	X
fuelectenerg-400	445	3	)	)	PUNCT
fuelectenerg-400	445	4	the	the	DET
fuelectenerg-400	445	5	corresponding	corresponding	ADJ
fuelectenerg-400	445	6	tiling	tiling	NOUN
fuelectenerg-400	445	7	on	on	ADP
fuelectenerg-400	445	8	the	the	DET
fuelectenerg-400	445	9	hexagon	hexagon	PROPN
fuelectenerg-400	445	10	.	.	PUNCT
fuelectenerg-400	446	1	theorem	theorem	VERB
fuelectenerg-400	446	2	3	3	NUM
fuelectenerg-400	446	3	the	the	DET
fuelectenerg-400	446	4	lozenge	lozenge	NOUN
fuelectenerg-400	446	5	tilings	tiling	NOUN
fuelectenerg-400	446	6	on	on	ADP
fuelectenerg-400	446	7	h	h	NOUN
fuelectenerg-400	446	8	corresponds	correspond	NOUN
fuelectenerg-400	446	9	bijectively	bijectively	ADV
fuelectenerg-400	446	10	to	to	ADP
fuelectenerg-400	446	11	the	the	DET
fuelectenerg-400	446	12	set	set	NOUN
fuelectenerg-400	446	13	of	of	ADP
fuelectenerg-400	446	14	routings	routing	NOUN
fuelectenerg-400	446	15	on	on	ADP
fuelectenerg-400	446	16	the	the	DET
fuelectenerg-400	446	17	associated	associated	ADJ
fuelectenerg-400	446	18	graph	graph	NOUN
fuelectenerg-400	446	19	g.	g.	NOUN
fuelectenerg-400	446	20	proof	proof	NOUN
fuelectenerg-400	446	21	:	:	PUNCT
fuelectenerg-400	446	22	to	to	PART
fuelectenerg-400	446	23	prove	prove	VERB
fuelectenerg-400	446	24	this	this	PRON
fuelectenerg-400	446	25	we	we	PRON
fuelectenerg-400	446	26	make	make	VERB
fuelectenerg-400	446	27	use	use	NOUN
fuelectenerg-400	446	28	of	of	ADP
fuelectenerg-400	446	29	the	the	DET
fuelectenerg-400	446	30	theorem	theorem	NOUN
fuelectenerg-400	446	31	1	1	NUM
fuelectenerg-400	446	32	in	in	ADP
fuelectenerg-400	446	33	[	[	X
fuelectenerg-400	446	34	21	21	NUM
fuelectenerg-400	446	35	]	]	PUNCT
fuelectenerg-400	446	36	.	.	PUNCT
fuelectenerg-400	447	1	figures	figure	NOUN
fuelectenerg-400	447	2	8(c	8(c	NUM
fuelectenerg-400	447	3	)	)	PUNCT
fuelectenerg-400	447	4	and	and	CCONJ
fuelectenerg-400	447	5	8(d	8(d	NUM
fuelectenerg-400	447	6	)	)	PUNCT
fuelectenerg-400	447	7	show	show	VERB
fuelectenerg-400	447	8	an	an	DET
fuelectenerg-400	447	9	example	example	NOUN
fuelectenerg-400	447	10	of	of	ADP
fuelectenerg-400	447	11	the	the	DET
fuelectenerg-400	447	12	relationship	relationship	NOUN
fuelectenerg-400	447	13	between	between	ADP
fuelectenerg-400	447	14	lozenge	lozenge	NOUN
fuelectenerg-400	447	15	tiling	tile	VERB
fuelectenerg-400	447	16	on	on	ADP
fuelectenerg-400	447	17	h	h	NOUN
fuelectenerg-400	447	18	and	and	CCONJ
fuelectenerg-400	447	19	a	a	DET
fuelectenerg-400	447	20	given	give	VERB
fuelectenerg-400	447	21	lattice	lattice	NOUN
fuelectenerg-400	447	22	routing	routing	NOUN
fuelectenerg-400	447	23	on	on	ADP
fuelectenerg-400	447	24	g.	g.	PROPN
fuelectenerg-400	447	25	fig	fig	PROPN
fuelectenerg-400	447	26	.	.	PUNCT
fuelectenerg-400	448	1	8(c	8(c	NUM
fuelectenerg-400	448	2	)	)	PUNCT
fuelectenerg-400	448	3	shows	show	VERB
fuelectenerg-400	448	4	a	a	DET
fuelectenerg-400	448	5	routing	routing	NOUN
fuelectenerg-400	448	6	on	on	ADP
fuelectenerg-400	448	7	a	a	DET
fuelectenerg-400	448	8	graph	graph	NOUN
fuelectenerg-400	448	9	associated	associate	VERB
fuelectenerg-400	448	10	with	with	ADP
fuelectenerg-400	448	11	a	a	DET
fuelectenerg-400	448	12	(	(	PUNCT
fuelectenerg-400	448	13	3	3	NUM
fuelectenerg-400	448	14	,	,	PUNCT
fuelectenerg-400	448	15	3	3	NUM
fuelectenerg-400	448	16	,	,	PUNCT
fuelectenerg-400	448	17	3	3	X
fuelectenerg-400	448	18	)	)	PUNCT
fuelectenerg-400	448	19	hexagon	hexagon	NOUN
fuelectenerg-400	448	20	(	(	PUNCT
fuelectenerg-400	448	21	marked	mark	VERB
fuelectenerg-400	448	22	in	in	ADP
fuelectenerg-400	448	23	bold	bold	ADJ
fuelectenerg-400	448	24	)	)	PUNCT
fuelectenerg-400	448	25	.	.	PUNCT
fuelectenerg-400	449	1	fig	fig	NOUN
fuelectenerg-400	449	2	.	.	PUNCT
fuelectenerg-400	450	1	8(d	8(d	NUM
fuelectenerg-400	450	2	)	)	PUNCT
fuelectenerg-400	450	3	shows	show	VERB
fuelectenerg-400	450	4	the	the	DET
fuelectenerg-400	450	5	corresponding	corresponding	ADJ
fuelectenerg-400	450	6	tiling	tiling	NOUN
fuelectenerg-400	450	7	on	on	ADP
fuelectenerg-400	450	8	the	the	DET
fuelectenerg-400	450	9	hexagon	hexagon	NOUN
fuelectenerg-400	450	10	.	.	PUNCT
fuelectenerg-400	451	1	the	the	DET
fuelectenerg-400	451	2	routing	routing	NOUN
fuelectenerg-400	451	3	overlaid	overlay	VERB
fuelectenerg-400	451	4	on	on	ADP
fuelectenerg-400	451	5	the	the	DET
fuelectenerg-400	451	6	hexagon	hexagon	NOUN
fuelectenerg-400	451	7	illustrates	illustrate	VERB
fuelectenerg-400	451	8	how	how	SCONJ
fuelectenerg-400	451	9	the	the	DET
fuelectenerg-400	451	10	tiling	tiling	NOUN
fuelectenerg-400	451	11	can	can	AUX
fuelectenerg-400	451	12	be	be	AUX
fuelectenerg-400	451	13	generated	generate	VERB
fuelectenerg-400	451	14	from	from	ADP
fuelectenerg-400	451	15	the	the	DET
fuelectenerg-400	451	16	routing	routing	NOUN
fuelectenerg-400	451	17	.	.	PUNCT
fuelectenerg-400	452	1	it	it	PRON
fuelectenerg-400	452	2	can	can	AUX
fuelectenerg-400	452	3	be	be	AUX
fuelectenerg-400	452	4	seen	see	VERB
fuelectenerg-400	452	5	that	that	SCONJ
fuelectenerg-400	452	6	each	each	PRON
fuelectenerg-400	452	7	of	of	ADP
fuelectenerg-400	452	8	the	the	DET
fuelectenerg-400	452	9	a	a	DET
fuelectenerg-400	452	10	paths	path	NOUN
fuelectenerg-400	452	11	of	of	ADP
fuelectenerg-400	452	12	the	the	DET
fuelectenerg-400	452	13	routing	routing	NOUN
fuelectenerg-400	452	14	has	have	VERB
fuelectenerg-400	452	15	a+	a+	PRON
fuelectenerg-400	452	16	b	b	NUM
fuelectenerg-400	452	17	moves	move	NOUN
fuelectenerg-400	452	18	with	with	ADP
fuelectenerg-400	452	19	b	b	X
fuelectenerg-400	452	20	“	"	PUNCT
fuelectenerg-400	452	21	northeast	northeast	ADJ
fuelectenerg-400	452	22	(	(	PUNCT
fuelectenerg-400	452	23	ne	ne	NOUN
fuelectenerg-400	452	24	)	)	PUNCT
fuelectenerg-400	452	25	moves	move	NOUN
fuelectenerg-400	452	26	”	"	PUNCT
fuelectenerg-400	452	27	and	and	CCONJ
fuelectenerg-400	452	28	c	c	NOUN
fuelectenerg-400	452	29	“	"	PUNCT
fuelectenerg-400	452	30	southeast	southeast	ADJ
fuelectenerg-400	452	31	(	(	PUNCT
fuelectenerg-400	452	32	se	se	ADJ
fuelectenerg-400	452	33	)	)	PUNCT
fuelectenerg-400	452	34	moves	move	NOUN
fuelectenerg-400	452	35	”	"	PUNCT
fuelectenerg-400	452	36	between	between	ADP
fuelectenerg-400	452	37	nodes	node	NOUN
fuelectenerg-400	452	38	.	.	PUNCT
fuelectenerg-400	453	1	by	by	ADP
fuelectenerg-400	453	2	mapping	map	VERB
fuelectenerg-400	453	3	the	the	DET
fuelectenerg-400	453	4	ne	ne	PROPN
fuelectenerg-400	453	5	move	move	NOUN
fuelectenerg-400	453	6	to	to	ADP
fuelectenerg-400	453	7	“	"	PUNCT
fuelectenerg-400	453	8	1	1	NUM
fuelectenerg-400	453	9	”	"	PUNCT
fuelectenerg-400	453	10	and	and	CCONJ
fuelectenerg-400	453	11	the	the	DET
fuelectenerg-400	453	12	se	se	PROPN
fuelectenerg-400	453	13	move	move	VERB
fuelectenerg-400	453	14	to	to	ADP
fuelectenerg-400	453	15	“	"	PUNCT
fuelectenerg-400	453	16	0	0	NUM
fuelectenerg-400	453	17	”	"	PUNCT
fuelectenerg-400	453	18	,	,	PUNCT
fuelectenerg-400	453	19	each	each	DET
fuelectenerg-400	453	20	routing	routing	NOUN
fuelectenerg-400	453	21	can	can	AUX
fuelectenerg-400	453	22	be	be	AUX
fuelectenerg-400	453	23	represented	represent	VERB
fuelectenerg-400	453	24	as	as	ADP
fuelectenerg-400	453	25	an	an	DET
fuelectenerg-400	453	26	ordered	order	VERB
fuelectenerg-400	453	27	collection	collection	NOUN
fuelectenerg-400	453	28	of	of	ADP
fuelectenerg-400	453	29	constant	constant	ADJ
fuelectenerg-400	453	30	weight	weight	NOUN
fuelectenerg-400	453	31	sequences	sequence	NOUN
fuelectenerg-400	453	32	.	.	PUNCT
fuelectenerg-400	454	1	thus	thus	ADV
fuelectenerg-400	454	2	the	the	DET
fuelectenerg-400	454	3	problem	problem	NOUN
fuelectenerg-400	454	4	reduces	reduce	VERB
fuelectenerg-400	454	5	to	to	ADP
fuelectenerg-400	454	6	coding	code	VERB
fuelectenerg-400	454	7	of	of	ADP
fuelectenerg-400	454	8	constant	constant	ADJ
fuelectenerg-400	454	9	weight	weight	NOUN
fuelectenerg-400	454	10	sequences	sequence	NOUN
fuelectenerg-400	454	11	.	.	PUNCT
fuelectenerg-400	455	1	we	we	PRON
fuelectenerg-400	455	2	now	now	ADV
fuelectenerg-400	455	3	describe	describe	VERB
fuelectenerg-400	455	4	the	the	DET
fuelectenerg-400	455	5	encoding	encoding	NOUN
fuelectenerg-400	455	6	.	.	PUNCT
fuelectenerg-400	456	1	let	let	VERB
fuelectenerg-400	456	2	r	r	NOUN
fuelectenerg-400	456	3	be	be	AUX
fuelectenerg-400	456	4	the	the	DET
fuelectenerg-400	456	5	ordered	order	VERB
fuelectenerg-400	456	6	set	set	NOUN
fuelectenerg-400	456	7	of	of	ADP
fuelectenerg-400	456	8	routings	routing	NOUN
fuelectenerg-400	456	9	on	on	ADP
fuelectenerg-400	456	10	the	the	DET
fuelectenerg-400	456	11	graph	graph	NOUN
fuelectenerg-400	456	12	g.	g.	PROPN
fuelectenerg-400	456	13	the	the	DET
fuelectenerg-400	456	14	ith	ith	PROPN
fuelectenerg-400	456	15	element	element	NOUN
fuelectenerg-400	456	16	of	of	ADP
fuelectenerg-400	456	17	r	r	PROPN
fuelectenerg-400	456	18	,	,	PUNCT
fuelectenerg-400	456	19	ri	ri	PROPN
fuelectenerg-400	456	20	,	,	PUNCT
fuelectenerg-400	456	21	is	be	AUX
fuelectenerg-400	456	22	an	an	DET
fuelectenerg-400	456	23	ordered	order	VERB
fuelectenerg-400	456	24	collection	collection	NOUN
fuelectenerg-400	456	25	of	of	ADP
fuelectenerg-400	456	26	a	a	DET
fuelectenerg-400	456	27	constant	constant	ADJ
fuelectenerg-400	456	28	weight	weight	NOUN
fuelectenerg-400	456	29	sequences	sequence	NOUN
fuelectenerg-400	456	30	of	of	ADP
fuelectenerg-400	456	31	length	length	NOUN
fuelectenerg-400	457	1	a	a	DET
fuelectenerg-400	457	2	+	+	NOUN
fuelectenerg-400	457	3	b	b	NOUN
fuelectenerg-400	457	4	and	and	CCONJ
fuelectenerg-400	457	5	weight	weight	NOUN
fuelectenerg-400	457	6	b.	b.	PROPN
fuelectenerg-400	458	1	we	we	PRON
fuelectenerg-400	458	2	denote	denote	VERB
fuelectenerg-400	458	3	the	the	DET
fuelectenerg-400	458	4	ordered	ordered	ADJ
fuelectenerg-400	458	5	set	set	NOUN
fuelectenerg-400	458	6	of	of	ADP
fuelectenerg-400	458	7	all	all	DET
fuelectenerg-400	458	8	sequences	sequence	NOUN
fuelectenerg-400	458	9	with	with	ADP
fuelectenerg-400	458	10	length	length	NOUN
fuelectenerg-400	458	11	n	n	PROPN
fuelectenerg-400	458	12	and	and	CCONJ
fuelectenerg-400	458	13	weight	weight	NOUN
fuelectenerg-400	458	14	k	k	PROPN
fuelectenerg-400	458	15	as	as	ADP
fuelectenerg-400	458	16	d(n	d(n	NOUN
fuelectenerg-400	458	17	,	,	PUNCT
fuelectenerg-400	458	18	k	k	NOUN
fuelectenerg-400	458	19	)	)	PUNCT
fuelectenerg-400	458	20	.	.	PUNCT
fuelectenerg-400	459	1	hence	hence	ADV
fuelectenerg-400	459	2	,	,	PUNCT
fuelectenerg-400	459	3	each	each	DET
fuelectenerg-400	459	4	element	element	NOUN
fuelectenerg-400	459	5	of	of	ADP
fuelectenerg-400	459	6	ri	ri	PROPN
fuelectenerg-400	459	7	is	be	AUX
fuelectenerg-400	459	8	a	a	DET
fuelectenerg-400	459	9	member	member	NOUN
fuelectenerg-400	459	10	of	of	ADP
fuelectenerg-400	459	11	d(a+b	d(a+b	PROPN
fuelectenerg-400	459	12	,	,	PUNCT
fuelectenerg-400	459	13	b	b	NOUN
fuelectenerg-400	459	14	)	)	PUNCT
fuelectenerg-400	459	15	.	.	PUNCT
fuelectenerg-400	460	1	the	the	DET
fuelectenerg-400	460	2	encoding	encoding	NOUN
fuelectenerg-400	460	3	process	process	NOUN
fuelectenerg-400	460	4	consists	consist	VERB
fuelectenerg-400	460	5	of	of	ADP
fuelectenerg-400	460	6	assigning	assign	VERB
fuelectenerg-400	460	7	to	to	ADP
fuelectenerg-400	460	8	the	the	DET
fuelectenerg-400	460	9	number	number	NOUN
fuelectenerg-400	460	10	i	i	PRON
fuelectenerg-400	460	11	,	,	PUNCT
fuelectenerg-400	460	12	0	0	NUM
fuelectenerg-400	460	13	≤	≤	NUM
fuelectenerg-400	460	14	i	i	PRON
fuelectenerg-400	460	15	≤	≤	NUM
fuelectenerg-400	460	16	|r|	|r|	PROPN
fuelectenerg-400	460	17	,	,	PUNCT
fuelectenerg-400	460	18	the	the	DET
fuelectenerg-400	460	19	ith	ith	PROPN
fuelectenerg-400	460	20	element	element	NOUN
fuelectenerg-400	460	21	of	of	ADP
fuelectenerg-400	460	22	r	r	PROPN
fuelectenerg-400	460	23	,	,	PUNCT
fuelectenerg-400	460	24	ri	ri	PROPN
fuelectenerg-400	460	25	.	.	PUNCT
fuelectenerg-400	461	1	in	in	ADP
fuelectenerg-400	461	2	order	order	NOUN
fuelectenerg-400	461	3	to	to	PART
fuelectenerg-400	461	4	perform	perform	VERB
fuelectenerg-400	461	5	this	this	DET
fuelectenerg-400	461	6	operation	operation	NOUN
fuelectenerg-400	461	7	without	without	ADP
fuelectenerg-400	461	8	physically	physically	ADV
fuelectenerg-400	461	9	storing	store	VERB
fuelectenerg-400	461	10	r	r	NOUN
fuelectenerg-400	461	11	,	,	PUNCT
fuelectenerg-400	461	12	algorithms	algorithm	NOUN
fuelectenerg-400	461	13	which	which	PRON
fuelectenerg-400	461	14	directly	directly	ADV
fuelectenerg-400	461	15	map	map	VERB
fuelectenerg-400	461	16	an	an	DET
fuelectenerg-400	461	17	integer	integer	NOUN
fuelectenerg-400	461	18	i	i	PRON
fuelectenerg-400	461	19	to	to	ADP
fuelectenerg-400	461	20	a	a	DET
fuelectenerg-400	461	21	distinct	distinct	NOUN
fuelectenerg-400	461	22	ordered	order	VERB
fuelectenerg-400	461	23	530	530	NUM
fuelectenerg-400	461	24	b.	b.	PROPN
fuelectenerg-400	461	25	vasic	vasic	PROPN
fuelectenerg-400	461	26	,	,	PUNCT
fuelectenerg-400	461	27	a.	a.	PROPN
fuelectenerg-400	461	28	r.	r.	PROPN
fuelectenerg-400	461	29	krishnan	krishnan	PROPN
fuelectenerg-400	461	30	lozenge	lozenge	PROPN
fuelectenerg-400	461	31	tiling	tile	VERB
fuelectenerg-400	461	32	constrained	constrained	ADJ
fuelectenerg-400	461	33	codes	code	NOUN
fuelectenerg-400	461	34	531	531	NUM
fuelectenerg-400	461	35	532	532	NUM
fuelectenerg-400	461	36	a.	a.	NOUN
fuelectenerg-400	461	37	r.	r.	PROPN
fuelectenerg-400	461	38	krishnanan	krishnanan	PROPN
fuelectenerg-400	461	39	and	and	CCONJ
fuelectenerg-400	461	40	b.	b.	PROPN
fuelectenerg-400	461	41	vasić	vasić	PROPN
fuelectenerg-400	461	42	sets	set	VERB
fuelectenerg-400	461	43	in	in	ADP
fuelectenerg-400	461	44	r	r	NOUN
fuelectenerg-400	461	45	have	have	AUX
fuelectenerg-400	461	46	been	be	AUX
fuelectenerg-400	461	47	designed	design	VERB
fuelectenerg-400	461	48	.	.	PUNCT
fuelectenerg-400	462	1	to	to	PART
fuelectenerg-400	462	2	explain	explain	VERB
fuelectenerg-400	462	3	this	this	PRON
fuelectenerg-400	462	4	,	,	PUNCT
fuelectenerg-400	462	5	we	we	PRON
fuelectenerg-400	462	6	consider	consider	VERB
fuelectenerg-400	462	7	the	the	DET
fuelectenerg-400	462	8	following	following	NOUN
fuelectenerg-400	462	9	:	:	PUNCT
fuelectenerg-400	462	10	let	let	VERB
fuelectenerg-400	462	11	ri	ri	VERB
fuelectenerg-400	462	12	=	=	PUNCT
fuelectenerg-400	462	13	{	{	PUNCT
fuelectenerg-400	462	14	di	di	NOUN
fuelectenerg-400	462	15	,	,	PUNCT
fuelectenerg-400	462	16	i	i	NOUN
fuelectenerg-400	462	17	=	=	NOUN
fuelectenerg-400	462	18	1	1	NUM
fuelectenerg-400	462	19	,	,	PUNCT
fuelectenerg-400	462	20	2	2	NUM
fuelectenerg-400	462	21	,	,	PUNCT
fuelectenerg-400	462	22	.	.	PUNCT
fuelectenerg-400	462	23	.	.	PUNCT
fuelectenerg-400	463	1	.	.	PUNCT
fuelectenerg-400	464	1	,	,	PUNCT
fuelectenerg-400	464	2	c|di	c|di	PUNCT
fuelectenerg-400	465	1	∈	∈	PROPN
fuelectenerg-400	465	2	d(a+b	d(a+b	PRON
fuelectenerg-400	465	3	,	,	PUNCT
fuelectenerg-400	465	4	b	b	NOUN
fuelectenerg-400	465	5	)	)	PUNCT
fuelectenerg-400	465	6	}	}	PUNCT
fuelectenerg-400	465	7	.	.	PUNCT
fuelectenerg-400	466	1	there	there	PRON
fuelectenerg-400	466	2	exists	exist	VERB
fuelectenerg-400	466	3	an	an	DET
fuelectenerg-400	466	4	ordering	ordering	NOUN
fuelectenerg-400	466	5	of	of	ADP
fuelectenerg-400	466	6	elements	element	NOUN
fuelectenerg-400	466	7	of	of	ADP
fuelectenerg-400	466	8	d(a+b	d(a+b	NOUN
fuelectenerg-400	466	9	,	,	PUNCT
fuelectenerg-400	466	10	b	b	NOUN
fuelectenerg-400	466	11	)	)	PUNCT
fuelectenerg-400	466	12	such	such	ADJ
fuelectenerg-400	466	13	that	that	SCONJ
fuelectenerg-400	466	14	∀i	∀i	NOUN
fuelectenerg-400	466	15	,	,	PUNCT
fuelectenerg-400	466	16	j	j	PROPN
fuelectenerg-400	466	17	1	1	NUM
fuelectenerg-400	466	18	≤	≤	PUNCT
fuelectenerg-400	466	19	i	i	PROPN
fuelectenerg-400	466	20	,	,	PUNCT
fuelectenerg-400	466	21	j	j	PROPN
fuelectenerg-400	466	22	≤	≤	PROPN
fuelectenerg-400	466	23	c	c	X
fuelectenerg-400	466	24	,	,	PUNCT
fuelectenerg-400	466	25	if	if	SCONJ
fuelectenerg-400	466	26	i	i	PRON
fuelectenerg-400	466	27	<	<	X
fuelectenerg-400	466	28	j	j	PROPN
fuelectenerg-400	466	29	,	,	PUNCT
fuelectenerg-400	466	30	then	then	ADV
fuelectenerg-400	466	31	rank(di	rank(di	VERB
fuelectenerg-400	466	32	)	)	PUNCT
fuelectenerg-400	466	33	≤	≤	NOUN
fuelectenerg-400	466	34	rank(dj	rank(dj	NOUN
fuelectenerg-400	466	35	)	)	PUNCT
fuelectenerg-400	466	36	where	where	SCONJ
fuelectenerg-400	466	37	rank	rank	NOUN
fuelectenerg-400	466	38	(	(	PUNCT
fuelectenerg-400	466	39	.	.	PUNCT
fuelectenerg-400	466	40	)	)	PUNCT
fuelectenerg-400	466	41	denotes	denote	VERB
fuelectenerg-400	466	42	the	the	DET
fuelectenerg-400	466	43	rank	rank	NOUN
fuelectenerg-400	466	44	of	of	ADP
fuelectenerg-400	466	45	an	an	DET
fuelectenerg-400	466	46	element	element	NOUN
fuelectenerg-400	466	47	in	in	ADP
fuelectenerg-400	466	48	the	the	DET
fuelectenerg-400	466	49	ordered	order	VERB
fuelectenerg-400	466	50	set	set	NOUN
fuelectenerg-400	466	51	.	.	PUNCT
fuelectenerg-400	467	1	hence	hence	ADV
fuelectenerg-400	467	2	,	,	PUNCT
fuelectenerg-400	467	3	instead	instead	ADV
fuelectenerg-400	467	4	of	of	ADP
fuelectenerg-400	467	5	storing	store	VERB
fuelectenerg-400	467	6	individual	individual	ADJ
fuelectenerg-400	467	7	sequences	sequence	NOUN
fuelectenerg-400	467	8	,	,	PUNCT
fuelectenerg-400	467	9	ri	ri	PROPN
fuelectenerg-400	467	10	can	can	AUX
fuelectenerg-400	467	11	be	be	AUX
fuelectenerg-400	467	12	represented	represent	VERB
fuelectenerg-400	467	13	using	use	VERB
fuelectenerg-400	467	14	the	the	DET
fuelectenerg-400	467	15	ranks	rank	NOUN
fuelectenerg-400	467	16	of	of	ADP
fuelectenerg-400	467	17	di	di	NOUN
fuelectenerg-400	467	18	as	as	ADP
fuelectenerg-400	467	19	ri	ri	NOUN
fuelectenerg-400	467	20	=	=	PUNCT
fuelectenerg-400	467	21	{	{	PUNCT
fuelectenerg-400	467	22	rank(di	rank(di	NOUN
fuelectenerg-400	467	23	)	)	PUNCT
fuelectenerg-400	467	24	,	,	PUNCT
fuelectenerg-400	467	25	i	i	PRON
fuelectenerg-400	467	26	=	=	NOUN
fuelectenerg-400	467	27	1	1	NUM
fuelectenerg-400	467	28	,	,	PUNCT
fuelectenerg-400	467	29	2	2	NUM
fuelectenerg-400	467	30	,	,	PUNCT
fuelectenerg-400	467	31	.	.	PUNCT
fuelectenerg-400	467	32	.	.	PUNCT
fuelectenerg-400	467	33	.	.	PUNCT
fuelectenerg-400	468	1	c|	c|	PROPN
fuelectenerg-400	468	2	di	di	PROPN
fuelectenerg-400	468	3	∈	∈	PROPN
fuelectenerg-400	468	4	d(a+b	d(a+b	PROPN
fuelectenerg-400	468	5	,	,	PUNCT
fuelectenerg-400	468	6	b	b	NOUN
fuelectenerg-400	468	7	)	)	PUNCT
fuelectenerg-400	468	8	}	}	PUNCT
fuelectenerg-400	468	9	(	(	PUNCT
fuelectenerg-400	468	10	we	we	PRON
fuelectenerg-400	468	11	will	will	AUX
fuelectenerg-400	468	12	later	later	ADV
fuelectenerg-400	468	13	show	show	VERB
fuelectenerg-400	468	14	that	that	SCONJ
fuelectenerg-400	468	15	this	this	PRON
fuelectenerg-400	468	16	can	can	AUX
fuelectenerg-400	468	17	be	be	AUX
fuelectenerg-400	468	18	further	far	ADV
fuelectenerg-400	468	19	simplified	simplify	VERB
fuelectenerg-400	468	20	by	by	ADP
fuelectenerg-400	468	21	the	the	DET
fuelectenerg-400	468	22	use	use	NOUN
fuelectenerg-400	468	23	of	of	ADP
fuelectenerg-400	468	24	non	non	ADJ
fuelectenerg-400	468	25	-	-	ADJ
fuelectenerg-400	468	26	decreasing	decrease	VERB
fuelectenerg-400	468	27	strings	string	NOUN
fuelectenerg-400	468	28	.	.	PUNCT
fuelectenerg-400	469	1	this	this	PRON
fuelectenerg-400	469	2	will	will	AUX
fuelectenerg-400	469	3	be	be	AUX
fuelectenerg-400	469	4	dealt	deal	VERB
fuelectenerg-400	469	5	with	with	ADP
fuelectenerg-400	469	6	in	in	ADP
fuelectenerg-400	469	7	detail	detail	NOUN
fuelectenerg-400	469	8	in	in	ADP
fuelectenerg-400	469	9	section	section	NOUN
fuelectenerg-400	469	10	5.3	5.3	NUM
fuelectenerg-400	469	11	)	)	PUNCT
fuelectenerg-400	469	12	.	.	PUNCT
fuelectenerg-400	470	1	we	we	PRON
fuelectenerg-400	470	2	refer	refer	VERB
fuelectenerg-400	470	3	to	to	ADP
fuelectenerg-400	470	4	this	this	PRON
fuelectenerg-400	470	5	as	as	ADP
fuelectenerg-400	470	6	the	the	DET
fuelectenerg-400	470	7	rank	rank	NOUN
fuelectenerg-400	470	8	-	-	PUNCT
fuelectenerg-400	470	9	based	base	VERB
fuelectenerg-400	470	10	representation	representation	NOUN
fuelectenerg-400	470	11	.	.	PUNCT
fuelectenerg-400	471	1	we	we	PRON
fuelectenerg-400	471	2	now	now	ADV
fuelectenerg-400	471	3	describe	describe	VERB
fuelectenerg-400	471	4	the	the	DET
fuelectenerg-400	471	5	reverse	reverse	ADJ
fuelectenerg-400	471	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	471	7	ordering	ordering	NOUN
fuelectenerg-400	471	8	of	of	ADP
fuelectenerg-400	471	9	constant	constant	ADJ
fuelectenerg-400	471	10	weight	weight	NOUN
fuelectenerg-400	471	11	sequences	sequence	NOUN
fuelectenerg-400	471	12	which	which	PRON
fuelectenerg-400	471	13	is	be	AUX
fuelectenerg-400	471	14	one	one	NUM
fuelectenerg-400	471	15	such	such	ADJ
fuelectenerg-400	471	16	ordering	ordering	NOUN
fuelectenerg-400	471	17	of	of	ADP
fuelectenerg-400	471	18	sequences	sequence	NOUN
fuelectenerg-400	471	19	.	.	PUNCT
fuelectenerg-400	472	1	5.2	5.2	NUM
fuelectenerg-400	472	2	reverse	reverse	VERB
fuelectenerg-400	472	3	lexicographical	lexicographical	ADJ
fuelectenerg-400	472	4	ordering	ordering	NOUN
fuelectenerg-400	472	5	of	of	ADP
fuelectenerg-400	472	6	constant	constant	ADJ
fuelectenerg-400	472	7	weight	weight	NOUN
fuelectenerg-400	472	8	sequences	sequence	NOUN
fuelectenerg-400	472	9	in	in	ADP
fuelectenerg-400	472	10	this	this	DET
fuelectenerg-400	472	11	section	section	NOUN
fuelectenerg-400	472	12	,	,	PUNCT
fuelectenerg-400	472	13	methods	method	NOUN
fuelectenerg-400	472	14	to	to	PART
fuelectenerg-400	472	15	obtain	obtain	VERB
fuelectenerg-400	472	16	a	a	DET
fuelectenerg-400	472	17	bijective	bijective	ADJ
fuelectenerg-400	472	18	mapping	mapping	NOUN
fuelectenerg-400	472	19	between	between	ADP
fuelectenerg-400	472	20	members	member	NOUN
fuelectenerg-400	472	21	of	of	ADP
fuelectenerg-400	472	22	d(n	d(n	PROPN
fuelectenerg-400	472	23	,	,	PUNCT
fuelectenerg-400	472	24	k	k	NOUN
fuelectenerg-400	472	25	)	)	PUNCT
fuelectenerg-400	472	26	and	and	CCONJ
fuelectenerg-400	472	27	integers	integer	NOUN
fuelectenerg-400	472	28	will	will	AUX
fuelectenerg-400	472	29	be	be	AUX
fuelectenerg-400	472	30	developed	develop	VERB
fuelectenerg-400	472	31	.	.	PUNCT
fuelectenerg-400	473	1	firstly	firstly	ADV
fuelectenerg-400	473	2	,	,	PUNCT
fuelectenerg-400	473	3	we	we	PRON
fuelectenerg-400	473	4	note	note	VERB
fuelectenerg-400	473	5	that	that	SCONJ
fuelectenerg-400	473	6	the	the	DET
fuelectenerg-400	473	7	size	size	NOUN
fuelectenerg-400	473	8	of	of	ADP
fuelectenerg-400	473	9	d(n	d(n	PROPN
fuelectenerg-400	473	10	,	,	PUNCT
fuelectenerg-400	473	11	k	k	NOUN
fuelectenerg-400	473	12	)	)	PUNCT
fuelectenerg-400	473	13	,	,	PUNCT
fuelectenerg-400	473	14	∣∣d(n	∣∣d(n	PROPN
fuelectenerg-400	473	15	,	,	PUNCT
fuelectenerg-400	473	16	k	k	NOUN
fuelectenerg-400	473	17	)	)	PUNCT
fuelectenerg-400	473	18	∣∣	∣∣	NUM
fuelectenerg-400	473	19	,	,	PUNCT
fuelectenerg-400	473	20	is	be	AUX
fuelectenerg-400	473	21	(	(	PUNCT
fuelectenerg-400	473	22	n	n	X
fuelectenerg-400	473	23	k	k	PROPN
fuelectenerg-400	473	24	)	)	PUNCT
fuelectenerg-400	473	25	.	.	PUNCT
fuelectenerg-400	474	1	also	also	ADV
fuelectenerg-400	474	2	,	,	PUNCT
fuelectenerg-400	474	3	note	note	VERB
fuelectenerg-400	474	4	that	that	SCONJ
fuelectenerg-400	474	5	each	each	DET
fuelectenerg-400	474	6	n	n	CCONJ
fuelectenerg-400	474	7	-	-	PUNCT
fuelectenerg-400	474	8	bit	bit	NOUN
fuelectenerg-400	474	9	sequence	sequence	NOUN
fuelectenerg-400	474	10	has	have	VERB
fuelectenerg-400	474	11	a	a	DET
fuelectenerg-400	474	12	decimal	decimal	ADJ
fuelectenerg-400	474	13	equivalent	equivalent	NOUN
fuelectenerg-400	474	14	between	between	ADP
fuelectenerg-400	474	15	0	0	NUM
fuelectenerg-400	474	16	and	and	CCONJ
fuelectenerg-400	474	17	2n	2n	NUM
fuelectenerg-400	475	1	−	−	NOUN
fuelectenerg-400	475	2	1	1	X
fuelectenerg-400	475	3	.	.	PUNCT
fuelectenerg-400	476	1	let	let	VERB
fuelectenerg-400	476	2	the	the	DET
fuelectenerg-400	476	3	decimal	decimal	ADJ
fuelectenerg-400	476	4	equivalent	equivalent	NOUN
fuelectenerg-400	476	5	be	be	AUX
fuelectenerg-400	476	6	denoted	denote	VERB
fuelectenerg-400	476	7	as	as	ADP
fuelectenerg-400	476	8	de	de	PROPN
fuelectenerg-400	476	9	(	(	PUNCT
fuelectenerg-400	476	10	.	.	PUNCT
fuelectenerg-400	476	11	)	)	PUNCT
fuelectenerg-400	476	12	.	.	PUNCT
fuelectenerg-400	477	1	the	the	DET
fuelectenerg-400	477	2	lexicographical	lexicographical	ADJ
fuelectenerg-400	477	3	ordering	ordering	NOUN
fuelectenerg-400	477	4	of	of	ADP
fuelectenerg-400	477	5	the	the	DET
fuelectenerg-400	477	6	sequences	sequence	NOUN
fuelectenerg-400	477	7	is	be	AUX
fuelectenerg-400	477	8	the	the	DET
fuelectenerg-400	477	9	arrangement	arrangement	NOUN
fuelectenerg-400	477	10	of	of	ADP
fuelectenerg-400	477	11	all	all	DET
fuelectenerg-400	477	12	the	the	DET
fuelectenerg-400	477	13	sequences	sequence	NOUN
fuelectenerg-400	477	14	in	in	ADP
fuelectenerg-400	477	15	the	the	DET
fuelectenerg-400	477	16	ascending	ascend	VERB
fuelectenerg-400	477	17	order	order	NOUN
fuelectenerg-400	477	18	of	of	ADP
fuelectenerg-400	477	19	their	their	PRON
fuelectenerg-400	477	20	decimal	decimal	ADJ
fuelectenerg-400	477	21	equivalent	equivalent	NOUN
fuelectenerg-400	477	22	.	.	PUNCT
fuelectenerg-400	478	1	the	the	DET
fuelectenerg-400	478	2	reverse	reverse	ADJ
fuelectenerg-400	478	3	lexicographical	lexicographical	ADJ
fuelectenerg-400	478	4	ordering	ordering	NOUN
fuelectenerg-400	478	5	can	can	AUX
fuelectenerg-400	478	6	be	be	AUX
fuelectenerg-400	478	7	defined	define	VERB
fuelectenerg-400	478	8	analogously	analogously	ADV
fuelectenerg-400	478	9	.	.	PUNCT
fuelectenerg-400	479	1	in	in	ADP
fuelectenerg-400	479	2	our	our	PRON
fuelectenerg-400	479	3	description	description	NOUN
fuelectenerg-400	479	4	,	,	PUNCT
fuelectenerg-400	479	5	we	we	PRON
fuelectenerg-400	479	6	use	use	VERB
fuelectenerg-400	479	7	the	the	DET
fuelectenerg-400	479	8	reverse	reverse	ADJ
fuelectenerg-400	479	9	lexicographical	lexicographical	ADJ
fuelectenerg-400	479	10	ordering	ordering	NOUN
fuelectenerg-400	479	11	.	.	PUNCT
fuelectenerg-400	480	1	table	table	NOUN
fuelectenerg-400	480	2	1	1	NUM
fuelectenerg-400	480	3	shows	show	VERB
fuelectenerg-400	480	4	the	the	DET
fuelectenerg-400	480	5	reverse	reverse	ADJ
fuelectenerg-400	480	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	480	7	ordering	ordering	NOUN
fuelectenerg-400	480	8	for	for	ADP
fuelectenerg-400	480	9	d(4,2	d(4,2	NOUN
fuelectenerg-400	480	10	)	)	PUNCT
fuelectenerg-400	480	11	.	.	PUNCT
fuelectenerg-400	481	1	the	the	DET
fuelectenerg-400	481	2	first	first	ADJ
fuelectenerg-400	481	3	column	column	NOUN
fuelectenerg-400	481	4	is	be	AUX
fuelectenerg-400	481	5	the	the	DET
fuelectenerg-400	481	6	rank	rank	NOUN
fuelectenerg-400	481	7	which	which	PRON
fuelectenerg-400	481	8	gives	give	VERB
fuelectenerg-400	481	9	the	the	DET
fuelectenerg-400	481	10	position	position	NOUN
fuelectenerg-400	481	11	of	of	ADP
fuelectenerg-400	481	12	the	the	DET
fuelectenerg-400	481	13	sequence	sequence	NOUN
fuelectenerg-400	481	14	in	in	ADP
fuelectenerg-400	481	15	the	the	DET
fuelectenerg-400	481	16	reverse	reverse	NOUN
fuelectenerg-400	481	17	lexicographically	lexicographically	ADV
fuelectenerg-400	481	18	ordered	order	VERB
fuelectenerg-400	481	19	set	set	NOUN
fuelectenerg-400	481	20	.	.	PUNCT
fuelectenerg-400	482	1	again	again	ADV
fuelectenerg-400	482	2	,	,	PUNCT
fuelectenerg-400	482	3	we	we	PRON
fuelectenerg-400	482	4	use	use	VERB
fuelectenerg-400	482	5	rank	rank	NOUN
fuelectenerg-400	482	6	(	(	PUNCT
fuelectenerg-400	482	7	.	.	PUNCT
fuelectenerg-400	482	8	)	)	PUNCT
fuelectenerg-400	482	9	to	to	PART
fuelectenerg-400	482	10	denote	denote	VERB
fuelectenerg-400	482	11	the	the	DET
fuelectenerg-400	482	12	rank	rank	NOUN
fuelectenerg-400	482	13	of	of	ADP
fuelectenerg-400	482	14	a	a	DET
fuelectenerg-400	482	15	particular	particular	ADJ
fuelectenerg-400	482	16	element	element	NOUN
fuelectenerg-400	482	17	.	.	PUNCT
fuelectenerg-400	483	1	it	it	PRON
fuelectenerg-400	483	2	is	be	AUX
fuelectenerg-400	483	3	easily	easily	ADV
fuelectenerg-400	483	4	seen	see	VERB
fuelectenerg-400	483	5	that	that	SCONJ
fuelectenerg-400	483	6	if	if	SCONJ
fuelectenerg-400	483	7	de(a	de(a	NOUN
fuelectenerg-400	483	8	)	)	PUNCT
fuelectenerg-400	483	9	≥	≥	NOUN
fuelectenerg-400	483	10	de(b	de(b	PUNCT
fuelectenerg-400	483	11	)	)	PUNCT
fuelectenerg-400	483	12	,	,	PUNCT
fuelectenerg-400	483	13	then	then	ADV
fuelectenerg-400	483	14	rank(a	rank(a	NOUN
fuelectenerg-400	483	15	)	)	PUNCT
fuelectenerg-400	483	16	≤	≤	NUM
fuelectenerg-400	483	17	rank(b	rank(b	NOUN
fuelectenerg-400	483	18	)	)	PUNCT
fuelectenerg-400	483	19	.	.	PUNCT
fuelectenerg-400	484	1	next	next	ADV
fuelectenerg-400	484	2	,	,	PUNCT
fuelectenerg-400	484	3	we	we	PRON
fuelectenerg-400	484	4	consider	consider	VERB
fuelectenerg-400	484	5	the	the	DET
fuelectenerg-400	484	6	transformation	transformation	NOUN
fuelectenerg-400	484	7	of	of	ADP
fuelectenerg-400	484	8	the	the	DET
fuelectenerg-400	484	9	members	member	NOUN
fuelectenerg-400	484	10	of	of	ADP
fuelectenerg-400	484	11	d(n	d(n	PROPN
fuelectenerg-400	484	12	,	,	PUNCT
fuelectenerg-400	484	13	k	k	NOUN
fuelectenerg-400	484	14	)	)	PUNCT
fuelectenerg-400	484	15	,	,	PUNCT
fuelectenerg-400	484	16	to	to	ADP
fuelectenerg-400	484	17	paths	path	NOUN
fuelectenerg-400	484	18	in	in	ADP
fuelectenerg-400	484	19	a	a	DET
fuelectenerg-400	484	20	cartesian	cartesian	ADJ
fuelectenerg-400	484	21	plane	plane	NOUN
fuelectenerg-400	484	22	.	.	PUNCT
fuelectenerg-400	485	1	we	we	PRON
fuelectenerg-400	485	2	refer	refer	VERB
fuelectenerg-400	485	3	to	to	ADP
fuelectenerg-400	485	4	these	these	DET
fuelectenerg-400	485	5	paths	path	NOUN
fuelectenerg-400	485	6	as	as	SCONJ
fuelectenerg-400	485	7	mountain	mountain	NOUN
fuelectenerg-400	485	8	ranges	range	NOUN
fuelectenerg-400	485	9	(	(	PUNCT
fuelectenerg-400	485	10	similar	similar	ADJ
fuelectenerg-400	485	11	to	to	ADP
fuelectenerg-400	485	12	the	the	DET
fuelectenerg-400	485	13	catalan	catalan	NOUN
fuelectenerg-400	485	14	mountain	mountain	NOUN
fuelectenerg-400	485	15	ranges	range	VERB
fuelectenerg-400	486	1	[	[	X
fuelectenerg-400	486	2	22	22	NUM
fuelectenerg-400	486	3	]	]	PUNCT
fuelectenerg-400	486	4	)	)	PUNCT
fuelectenerg-400	486	5	.	.	PUNCT
fuelectenerg-400	487	1	let	let	VERB
fuelectenerg-400	487	2	b	b	X
fuelectenerg-400	487	3	be	be	AUX
fuelectenerg-400	487	4	a	a	DET
fuelectenerg-400	487	5	member	member	NOUN
fuelectenerg-400	487	6	of	of	ADP
fuelectenerg-400	487	7	d(n	d(n	PROPN
fuelectenerg-400	487	8	,	,	PUNCT
fuelectenerg-400	487	9	k	k	NOUN
fuelectenerg-400	487	10	)	)	PUNCT
fuelectenerg-400	487	11	.	.	PUNCT
fuelectenerg-400	488	1	the	the	DET
fuelectenerg-400	488	2	mountain	mountain	NOUN
fuelectenerg-400	488	3	range	range	NOUN
fuelectenerg-400	488	4	mountain	mountain	NOUN
fuelectenerg-400	488	5	(	(	PUNCT
fuelectenerg-400	488	6	.	.	PUNCT
fuelectenerg-400	488	7	)	)	PUNCT
fuelectenerg-400	489	1	corresponding	correspond	VERB
fuelectenerg-400	489	2	to	to	ADP
fuelectenerg-400	489	3	b	b	NOUN
fuelectenerg-400	489	4	can	can	AUX
fuelectenerg-400	489	5	be	be	AUX
fuelectenerg-400	489	6	calculated	calculate	VERB
fuelectenerg-400	489	7	as	as	SCONJ
fuelectenerg-400	489	8	follows	follow	VERB
fuelectenerg-400	489	9	:	:	PUNCT
fuelectenerg-400	489	10	the	the	DET
fuelectenerg-400	489	11	mount	mount	PROPN
fuelectenerg-400	489	12	ranges	range	VERB
fuelectenerg-400	489	13	can	can	AUX
fuelectenerg-400	489	14	also	also	ADV
fuelectenerg-400	489	15	be	be	AUX
fuelectenerg-400	489	16	represented	represent	VERB
fuelectenerg-400	489	17	by	by	ADP
fuelectenerg-400	489	18	the	the	DET
fuelectenerg-400	489	19	n	n	CCONJ
fuelectenerg-400	489	20	-	-	PUNCT
fuelectenerg-400	489	21	tuple	tuple	NOUN
fuelectenerg-400	489	22	containing	contain	VERB
fuelectenerg-400	489	23	y	y	PROPN
fuelectenerg-400	489	24	coordinates	coordinate	NOUN
fuelectenerg-400	489	25	of	of	ADP
fuelectenerg-400	489	26	points	point	NOUN
fuelectenerg-400	489	27	traced	trace	VERB
fuelectenerg-400	489	28	by	by	ADP
fuelectenerg-400	489	29	the	the	DET
fuelectenerg-400	489	30	sequence	sequence	NOUN
fuelectenerg-400	489	31	,	,	PUNCT
fuelectenerg-400	489	32	denoted	denote	VERB
fuelectenerg-400	489	33	by	by	ADP
fuelectenerg-400	489	34	y.	y.	PROPN
fuelectenerg-400	489	35	figure	figure	NOUN
fuelectenerg-400	489	36	9	9	NUM
fuelectenerg-400	489	37	shows	show	VERB
fuelectenerg-400	489	38	the	the	DET
fuelectenerg-400	489	39	table	table	NOUN
fuelectenerg-400	489	40	1	1	NUM
fuelectenerg-400	489	41	.	.	PUNCT
fuelectenerg-400	490	1	ordering	ordering	NOUN
fuelectenerg-400	490	2	of	of	ADP
fuelectenerg-400	490	3	elements	element	NOUN
fuelectenerg-400	490	4	in	in	ADP
fuelectenerg-400	490	5	d(4,2	d(4,2	NOUN
fuelectenerg-400	490	6	)	)	PUNCT
fuelectenerg-400	490	7	.	.	PUNCT
fuelectenerg-400	491	1	rank	rank	PROPN
fuelectenerg-400	491	2	string	string	PROPN
fuelectenerg-400	491	3	decimal	decimal	PROPN
fuelectenerg-400	491	4	equivalent	equivalent	NOUN
fuelectenerg-400	491	5	0	0	NUM
fuelectenerg-400	491	6	1100	1100	NUM
fuelectenerg-400	491	7	12	12	NUM
fuelectenerg-400	491	8	1	1	NUM
fuelectenerg-400	491	9	1010	1010	NUM
fuelectenerg-400	491	10	10	10	NUM
fuelectenerg-400	491	11	2	2	NUM
fuelectenerg-400	491	12	1001	1001	NUM
fuelectenerg-400	491	13	9	9	NUM
fuelectenerg-400	491	14	3	3	NUM
fuelectenerg-400	491	15	0110	0110	NUM
fuelectenerg-400	491	16	6	6	NUM
fuelectenerg-400	491	17	4	4	NUM
fuelectenerg-400	491	18	0101	0101	NUM
fuelectenerg-400	491	19	5	5	NUM
fuelectenerg-400	491	20	5	5	NUM
fuelectenerg-400	491	21	0011	0011	NUM
fuelectenerg-400	491	22	3	3	NUM
fuelectenerg-400	491	23	detection	detection	NOUN
fuelectenerg-400	491	24	and	and	CCONJ
fuelectenerg-400	491	25	coding	code	VERB
fuelectenerg-400	491	26	for	for	ADP
fuelectenerg-400	491	27	tdmr	tdmr	NOUN
fuelectenerg-400	491	28	channel	channel	NOUN
fuelectenerg-400	491	29	533	533	NUM
fuelectenerg-400	491	30	algorithm	algorithm	NOUN
fuelectenerg-400	491	31	1	1	NUM
fuelectenerg-400	491	32	the	the	DET
fuelectenerg-400	491	33	mount	mount	PROPN
fuelectenerg-400	491	34	range	range	PROPN
fuelectenerg-400	491	35	algorithm	algorithm	PROPN
fuelectenerg-400	491	36	start	start	VERB
fuelectenerg-400	491	37	from	from	ADP
fuelectenerg-400	491	38	(	(	PUNCT
fuelectenerg-400	491	39	x	x	SYM
fuelectenerg-400	491	40	=	=	SYM
fuelectenerg-400	491	41	0	0	NUM
fuelectenerg-400	491	42	,	,	PUNCT
fuelectenerg-400	491	43	y	y	PROPN
fuelectenerg-400	491	44	=	=	NOUN
fuelectenerg-400	491	45	0	0	NUM
fuelectenerg-400	491	46	)	)	PUNCT
fuelectenerg-400	491	47	for	for	ADP
fuelectenerg-400	491	48	i	i	PRON
fuelectenerg-400	491	49	=	=	NOUN
fuelectenerg-400	491	50	1	1	NUM
fuelectenerg-400	491	51	to	to	PART
fuelectenerg-400	491	52	n	n	PRON
fuelectenerg-400	491	53	do	do	VERB
fuelectenerg-400	491	54	if	if	SCONJ
fuelectenerg-400	491	55	b(i	b(i	VERB
fuelectenerg-400	491	56	)	)	PUNCT
fuelectenerg-400	491	57	=	=	SYM
fuelectenerg-400	491	58	1	1	NUM
fuelectenerg-400	491	59	then	then	ADV
fuelectenerg-400	491	60	move	move	VERB
fuelectenerg-400	491	61	to	to	ADP
fuelectenerg-400	491	62	(	(	PUNCT
fuelectenerg-400	491	63	x	x	SYM
fuelectenerg-400	491	64	+	+	NUM
fuelectenerg-400	491	65	1	1	NUM
fuelectenerg-400	491	66	,	,	PUNCT
fuelectenerg-400	491	67	y	y	PROPN
fuelectenerg-400	491	68	+	+	NOUN
fuelectenerg-400	491	69	1	1	X
fuelectenerg-400	491	70	)	)	PUNCT
fuelectenerg-400	491	71	else	else	ADV
fuelectenerg-400	491	72	move	move	VERB
fuelectenerg-400	491	73	to	to	ADP
fuelectenerg-400	491	74	(	(	PUNCT
fuelectenerg-400	491	75	x	x	SYM
fuelectenerg-400	492	1	+	+	NUM
fuelectenerg-400	492	2	1	1	NUM
fuelectenerg-400	492	3	,	,	PUNCT
fuelectenerg-400	492	4	y	y	PROPN
fuelectenerg-400	492	5	−	−	PROPN
fuelectenerg-400	492	6	1	1	X
fuelectenerg-400	492	7	)	)	PUNCT
fuelectenerg-400	492	8	end	end	NOUN
fuelectenerg-400	492	9	if	if	SCONJ
fuelectenerg-400	492	10	end	end	NOUN
fuelectenerg-400	492	11	for	for	ADP
fuelectenerg-400	492	12	output	output	NOUN
fuelectenerg-400	492	13	the	the	DET
fuelectenerg-400	492	14	mount	mount	PROPN
fuelectenerg-400	492	15	range	range	PROPN
fuelectenerg-400	492	16	mountain	mountain	NOUN
fuelectenerg-400	492	17	(	(	PUNCT
fuelectenerg-400	492	18	.	.	PUNCT
fuelectenerg-400	492	19	)	)	PUNCT
fuelectenerg-400	493	1	fig	fig	NOUN
fuelectenerg-400	493	2	.	.	PUNCT
fuelectenerg-400	494	1	9	9	X
fuelectenerg-400	494	2	.	.	X
fuelectenerg-400	494	3	mountain	mountain	NOUN
fuelectenerg-400	494	4	range	range	NOUN
fuelectenerg-400	494	5	corresponding	correspond	VERB
fuelectenerg-400	494	6	to	to	ADP
fuelectenerg-400	494	7	the	the	DET
fuelectenerg-400	494	8	string	string	NOUN
fuelectenerg-400	494	9	100101	100101	NUM
fuelectenerg-400	494	10	,	,	PUNCT
fuelectenerg-400	494	11	mountain(100101	mountain(100101	PROPN
fuelectenerg-400	494	12	)	)	PUNCT
fuelectenerg-400	494	13	mountain	mountain	NOUN
fuelectenerg-400	494	14	range	range	NOUN
fuelectenerg-400	494	15	corresponding	correspond	VERB
fuelectenerg-400	494	16	to	to	ADP
fuelectenerg-400	494	17	the	the	DET
fuelectenerg-400	494	18	sequence	sequence	NOUN
fuelectenerg-400	494	19	100101	100101	NUM
fuelectenerg-400	494	20	,	,	PUNCT
fuelectenerg-400	494	21	a	a	DET
fuelectenerg-400	494	22	member	member	NOUN
fuelectenerg-400	494	23	of	of	ADP
fuelectenerg-400	494	24	d(6,3	d(6,3	NOUN
fuelectenerg-400	494	25	)	)	PUNCT
fuelectenerg-400	494	26	.	.	PUNCT
fuelectenerg-400	495	1	we	we	PRON
fuelectenerg-400	495	2	now	now	ADV
fuelectenerg-400	495	3	establish	establish	VERB
fuelectenerg-400	495	4	a	a	DET
fuelectenerg-400	495	5	relation	relation	NOUN
fuelectenerg-400	495	6	between	between	ADP
fuelectenerg-400	495	7	the	the	DET
fuelectenerg-400	495	8	lexicographical	lexicographical	ADJ
fuelectenerg-400	495	9	ranking	ranking	NOUN
fuelectenerg-400	495	10	and	and	CCONJ
fuelectenerg-400	495	11	the	the	DET
fuelectenerg-400	495	12	containment	containment	NOUN
fuelectenerg-400	495	13	of	of	ADP
fuelectenerg-400	495	14	mountain	mountain	NOUN
fuelectenerg-400	495	15	ranges	range	VERB
fuelectenerg-400	495	16	within	within	ADP
fuelectenerg-400	495	17	one	one	NUM
fuelectenerg-400	495	18	another	another	DET
fuelectenerg-400	495	19	.	.	PUNCT
fuelectenerg-400	496	1	for	for	ADP
fuelectenerg-400	496	2	any	any	DET
fuelectenerg-400	496	3	a	a	PRON
fuelectenerg-400	496	4	,	,	PUNCT
fuelectenerg-400	496	5	b	b	PROPN
fuelectenerg-400	496	6	∈	∈	PROPN
fuelectenerg-400	496	7	d(n	d(n	PROPN
fuelectenerg-400	496	8	,	,	PUNCT
fuelectenerg-400	496	9	k	k	NOUN
fuelectenerg-400	496	10	)	)	PUNCT
fuelectenerg-400	496	11	,	,	PUNCT
fuelectenerg-400	496	12	mountain(a	mountain(a	PROPN
fuelectenerg-400	496	13	)	)	PUNCT
fuelectenerg-400	496	14	is	be	AUX
fuelectenerg-400	496	15	said	say	VERB
fuelectenerg-400	496	16	to	to	PART
fuelectenerg-400	496	17	be	be	AUX
fuelectenerg-400	496	18	contained	contain	VERB
fuelectenerg-400	496	19	within	within	ADP
fuelectenerg-400	496	20	mountain(b	mountain(b	NOUN
fuelectenerg-400	496	21	)	)	PUNCT
fuelectenerg-400	496	22	(	(	PUNCT
fuelectenerg-400	496	23	denoted	denote	VERB
fuelectenerg-400	496	24	as	as	ADP
fuelectenerg-400	496	25	mountain(a	mountain(a	NOUN
fuelectenerg-400	496	26	)	)	PUNCT
fuelectenerg-400	496	27	⊂	⊂	PROPN
fuelectenerg-400	496	28	mountain(b	mountain(b	PROPN
fuelectenerg-400	496	29	)	)	PUNCT
fuelectenerg-400	496	30	)	)	PUNCT
fuelectenerg-400	496	31	if	if	SCONJ
fuelectenerg-400	496	32	each	each	DET
fuelectenerg-400	496	33	element	element	NOUN
fuelectenerg-400	496	34	of	of	ADP
fuelectenerg-400	496	35	the	the	DET
fuelectenerg-400	496	36	n	n	CCONJ
fuelectenerg-400	496	37	-	-	PUNCT
fuelectenerg-400	496	38	tuple	tuple	NOUN
fuelectenerg-400	496	39	corresponding	corresponding	NOUN
fuelectenerg-400	496	40	to	to	ADP
fuelectenerg-400	496	41	a	a	PRON
fuelectenerg-400	496	42	,	,	PUNCT
fuelectenerg-400	496	43	ya	ya	PROPN
fuelectenerg-400	496	44	is	be	AUX
fuelectenerg-400	496	45	never	never	ADV
fuelectenerg-400	496	46	more	more	ADJ
fuelectenerg-400	496	47	than	than	ADP
fuelectenerg-400	496	48	the	the	DET
fuelectenerg-400	496	49	corresponding	corresponding	ADJ
fuelectenerg-400	496	50	element	element	NOUN
fuelectenerg-400	496	51	of	of	ADP
fuelectenerg-400	496	52	the	the	DET
fuelectenerg-400	496	53	n	n	CCONJ
fuelectenerg-400	496	54	-	-	PUNCT
fuelectenerg-400	496	55	tuple	tuple	NOUN
fuelectenerg-400	496	56	corresponding	corresponding	NOUN
fuelectenerg-400	496	57	to	to	ADP
fuelectenerg-400	496	58	b	b	PROPN
fuelectenerg-400	496	59	,	,	PUNCT
fuelectenerg-400	496	60	yb	yb	PROPN
fuelectenerg-400	496	61	.	.	PROPN
fuelectenerg-400	497	1	for	for	ADP
fuelectenerg-400	497	2	instance	instance	NOUN
fuelectenerg-400	497	3	,	,	PUNCT
fuelectenerg-400	497	4	the	the	DET
fuelectenerg-400	497	5	mountain	mountain	NOUN
fuelectenerg-400	497	6	range	range	NOUN
fuelectenerg-400	497	7	mountain(1010	mountain(1010	PROPN
fuelectenerg-400	497	8	)	)	PUNCT
fuelectenerg-400	497	9	is	be	AUX
fuelectenerg-400	497	10	contained	contain	VERB
fuelectenerg-400	497	11	in	in	ADP
fuelectenerg-400	497	12	mountain(1100	mountain(1100	PROPN
fuelectenerg-400	497	13	)	)	PUNCT
fuelectenerg-400	497	14	.	.	PUNCT
fuelectenerg-400	498	1	the	the	DET
fuelectenerg-400	498	2	following	follow	VERB
fuelectenerg-400	498	3	theorem	theorem	NOUN
fuelectenerg-400	498	4	relates	relate	VERB
fuelectenerg-400	498	5	the	the	DET
fuelectenerg-400	498	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	498	7	ranking	ranking	NOUN
fuelectenerg-400	498	8	to	to	PART
fuelectenerg-400	498	9	containment	containment	VERB
fuelectenerg-400	498	10	.	.	PUNCT
fuelectenerg-400	499	1	theorem	theorem	VERB
fuelectenerg-400	499	2	4	4	NUM
fuelectenerg-400	499	3	for	for	ADP
fuelectenerg-400	499	4	any	any	DET
fuelectenerg-400	499	5	a	a	NOUN
fuelectenerg-400	499	6	,	,	PUNCT
fuelectenerg-400	499	7	b	b	PROPN
fuelectenerg-400	499	8	∈	∈	PROPN
fuelectenerg-400	499	9	d(n	d(n	PROPN
fuelectenerg-400	499	10	,	,	PUNCT
fuelectenerg-400	499	11	k	k	NOUN
fuelectenerg-400	499	12	)	)	PUNCT
fuelectenerg-400	499	13	,	,	PUNCT
fuelectenerg-400	499	14	if	if	SCONJ
fuelectenerg-400	499	15	mountain(a	mountain(a	NOUN
fuelectenerg-400	499	16	)	)	PUNCT
fuelectenerg-400	499	17	⊂	⊂	PROPN
fuelectenerg-400	499	18	mountain(b	mountain(b	PROPN
fuelectenerg-400	499	19	)	)	PUNCT
fuelectenerg-400	499	20	,	,	PUNCT
fuelectenerg-400	499	21	then	then	ADV
fuelectenerg-400	499	22	rank(a	rank(a	NOUN
fuelectenerg-400	499	23	)	)	PUNCT
fuelectenerg-400	499	24	≥	≥	NOUN
fuelectenerg-400	499	25	rank(b	rank(b	NOUN
fuelectenerg-400	499	26	)	)	PUNCT
fuelectenerg-400	499	27	proof	proof	NOUN
fuelectenerg-400	499	28	:	:	PUNCT
fuelectenerg-400	499	29	the	the	DET
fuelectenerg-400	499	30	proof	proof	NOUN
fuelectenerg-400	499	31	is	be	AUX
fuelectenerg-400	499	32	given	give	VERB
fuelectenerg-400	499	33	in	in	ADP
fuelectenerg-400	499	34	appendix	appendix	NOUN
fuelectenerg-400	499	35	9	9	NUM
fuelectenerg-400	499	36	the	the	DET
fuelectenerg-400	499	37	converse	converse	NOUN
fuelectenerg-400	499	38	is	be	AUX
fuelectenerg-400	499	39	not	not	PART
fuelectenerg-400	499	40	true	true	ADJ
fuelectenerg-400	499	41	.	.	PUNCT
fuelectenerg-400	500	1	one	one	NUM
fuelectenerg-400	500	2	counter	counter	NOUN
fuelectenerg-400	500	3	-	-	NOUN
fuelectenerg-400	500	4	example	example	NOUN
fuelectenerg-400	500	5	in	in	ADP
fuelectenerg-400	500	6	d(4,2	d(4,2	PROPN
fuelectenerg-400	500	7	)	)	PUNCT
fuelectenerg-400	500	8	is	be	AUX
fuelectenerg-400	500	9	1001	1001	NUM
fuelectenerg-400	500	10	and	and	CCONJ
fuelectenerg-400	500	11	0110	0110	NUM
fuelectenerg-400	500	12	.	.	PUNCT
fuelectenerg-400	501	1	it	it	PRON
fuelectenerg-400	501	2	is	be	AUX
fuelectenerg-400	501	3	easily	easily	ADV
fuelectenerg-400	501	4	seen	see	VERB
fuelectenerg-400	501	5	that	that	SCONJ
fuelectenerg-400	501	6	an	an	DET
fuelectenerg-400	501	7	ordered	order	VERB
fuelectenerg-400	501	8	set	set	NOUN
fuelectenerg-400	501	9	{	{	PUNCT
fuelectenerg-400	501	10	di	di	NOUN
fuelectenerg-400	501	11	,	,	PUNCT
fuelectenerg-400	501	12	i	i	NOUN
fuelectenerg-400	501	13	=	=	NOUN
fuelectenerg-400	501	14	1	1	NUM
fuelectenerg-400	501	15	,	,	PUNCT
fuelectenerg-400	501	16	2	2	NUM
fuelectenerg-400	501	17	,	,	PUNCT
fuelectenerg-400	501	18	.	.	PUNCT
fuelectenerg-400	501	19	.	.	PUNCT
fuelectenerg-400	501	20	.	.	PUNCT
fuelectenerg-400	502	1	,	,	PUNCT
fuelectenerg-400	502	2	a|di	a|di	NOUN
fuelectenerg-400	502	3	∈	∈	PROPN
fuelectenerg-400	502	4	d(a+b	d(a+b	PRON
fuelectenerg-400	502	5	,	,	PUNCT
fuelectenerg-400	502	6	b	b	NOUN
fuelectenerg-400	502	7	)	)	PUNCT
fuelectenerg-400	502	8	}	}	PUNCT
fuelectenerg-400	502	9	such	such	ADJ
fuelectenerg-400	502	10	that	that	DET
fuelectenerg-400	502	11	mountain(di	mountain(di	NOUN
fuelectenerg-400	502	12	)	)	PUNCT
fuelectenerg-400	502	13	⊂	⊂	PROPN
fuelectenerg-400	502	14	mountain(di+1	mountain(di+1	PROPN
fuelectenerg-400	502	15	)	)	PUNCT
fuelectenerg-400	502	16	for	for	ADP
fuelectenerg-400	502	17	all	all	DET
fuelectenerg-400	502	18	i	i	PRON
fuelectenerg-400	502	19	,	,	PUNCT
fuelectenerg-400	502	20	is	be	AUX
fuelectenerg-400	502	21	a	a	DET
fuelectenerg-400	502	22	member	member	NOUN
fuelectenerg-400	502	23	of	of	ADP
fuelectenerg-400	502	24	r	r	NOUN
fuelectenerg-400	502	25	and	and	CCONJ
fuelectenerg-400	502	26	hence	hence	ADV
fuelectenerg-400	502	27	corresponds	correspond	VERB
fuelectenerg-400	502	28	to	to	ADP
fuelectenerg-400	502	29	a	a	DET
fuelectenerg-400	502	30	valid	valid	ADJ
fuelectenerg-400	502	31	tiling	tiling	NOUN
fuelectenerg-400	502	32	.	.	PUNCT
fuelectenerg-400	503	1	this	this	PRON
fuelectenerg-400	503	2	implies	imply	VERB
fuelectenerg-400	503	3	that	that	SCONJ
fuelectenerg-400	503	4	the	the	DET
fuelectenerg-400	503	5	rank	rank	NOUN
fuelectenerg-400	503	6	-	-	PUNCT
fuelectenerg-400	503	7	based	base	VERB
fuelectenerg-400	503	8	representation	representation	NOUN
fuelectenerg-400	503	9	of	of	ADP
fuelectenerg-400	503	10	ri	ri	PROPN
fuelectenerg-400	503	11	is	be	AUX
fuelectenerg-400	503	12	a	a	DET
fuelectenerg-400	503	13	string	string	NOUN
fuelectenerg-400	503	14	of	of	ADP
fuelectenerg-400	503	15	integers	integer	NOUN
fuelectenerg-400	503	16	in	in	ADP
fuelectenerg-400	503	17	which	which	PRON
fuelectenerg-400	503	18	the	the	DET
fuelectenerg-400	503	19	integers	integer	NOUN
fuelectenerg-400	503	20	are	be	AUX
fuelectenerg-400	503	21	non	non	ADJ
fuelectenerg-400	503	22	-	-	ADJ
fuelectenerg-400	503	23	decreasing	decrease	VERB
fuelectenerg-400	503	24	.	.	PUNCT
fuelectenerg-400	504	1	we	we	PRON
fuelectenerg-400	504	2	now	now	ADV
fuelectenerg-400	504	3	address	address	VERB
fuelectenerg-400	504	4	ranking	ranking	NOUN
fuelectenerg-400	504	5	and	and	CCONJ
fuelectenerg-400	504	6	unranking	unranking	NOUN
fuelectenerg-400	504	7	of	of	ADP
fuelectenerg-400	504	8	members	member	NOUN
fuelectenerg-400	504	9	.	.	PUNCT
fuelectenerg-400	505	1	ranking	ranking	PROPN
fuelectenerg-400	505	2	,	,	PUNCT
fuelectenerg-400	505	3	denoted	denote	VERB
fuelectenerg-400	505	4	by	by	ADP
fuelectenerg-400	505	5	rank	rank	NOUN
fuelectenerg-400	505	6	refers	refer	VERB
fuelectenerg-400	505	7	to	to	ADP
fuelectenerg-400	505	8	the	the	DET
fuelectenerg-400	505	9	process	process	NOUN
fuelectenerg-400	505	10	mapping	mapping	NOUN
fuelectenerg-400	505	11	of	of	ADP
fuelectenerg-400	505	12	a	a	DET
fuelectenerg-400	505	13	member	member	NOUN
fuelectenerg-400	505	14	of	of	ADP
fuelectenerg-400	505	15	an	an	DET
fuelectenerg-400	505	16	ordered	order	VERB
fuelectenerg-400	505	17	set	set	NOUN
fuelectenerg-400	505	18	to	to	ADP
fuelectenerg-400	505	19	a	a	DET
fuelectenerg-400	505	20	distinct	distinct	ADJ
fuelectenerg-400	505	21	integer	integer	NOUN
fuelectenerg-400	505	22	.	.	PUNCT
fuelectenerg-400	506	1	unranking	unranking	NOUN
fuelectenerg-400	506	2	is	be	AUX
fuelectenerg-400	506	3	its	its	PRON
fuelectenerg-400	506	4	inverse	inverse	NOUN
fuelectenerg-400	506	5	operation	operation	NOUN
fuelectenerg-400	506	6	.	.	PUNCT
fuelectenerg-400	507	1	we	we	PRON
fuelectenerg-400	507	2	use	use	VERB
fuelectenerg-400	507	3	ranking	rank	VERB
fuelectenerg-400	507	4	and	and	CCONJ
fuelectenerg-400	507	5	unranking	unranking	ADJ
fuelectenerg-400	507	6	algorithms	algorithm	NOUN
fuelectenerg-400	507	7	on	on	ADP
fuelectenerg-400	507	8	the	the	DET
fuelectenerg-400	507	9	reverse	reverse	NOUN
fuelectenerg-400	507	10	lexicographically	lexicographically	ADV
fuelectenerg-400	507	11	ordered	order	VERB
fuelectenerg-400	507	12	set	set	NOUN
fuelectenerg-400	507	13	d(n	d(n	PROPN
fuelectenerg-400	507	14	,	,	PUNCT
fuelectenerg-400	507	15	k	k	NOUN
fuelectenerg-400	507	16	)	)	PUNCT
fuelectenerg-400	507	17	for	for	ADP
fuelectenerg-400	507	18	encoding	encode	VERB
fuelectenerg-400	507	19	data	datum	NOUN
fuelectenerg-400	507	20	532	532	NUM
fuelectenerg-400	507	21	b.	b.	PROPN
fuelectenerg-400	507	22	vasic	vasic	PROPN
fuelectenerg-400	507	23	,	,	PUNCT
fuelectenerg-400	508	1	a.	a.	PROPN
fuelectenerg-400	508	2	r.	r.	PROPN
fuelectenerg-400	508	3	krishnan	krishnan	PROPN
fuelectenerg-400	508	4	lozenge	lozenge	PROPN
fuelectenerg-400	508	5	tiling	tile	VERB
fuelectenerg-400	508	6	constrained	constrained	ADJ
fuelectenerg-400	508	7	codes	code	NOUN
fuelectenerg-400	508	8	533	533	NUM
fuelectenerg-400	508	9	532	532	NUM
fuelectenerg-400	508	10	a.	a.	NOUN
fuelectenerg-400	508	11	r.	r.	PROPN
fuelectenerg-400	508	12	krishnanan	krishnanan	PROPN
fuelectenerg-400	508	13	and	and	CCONJ
fuelectenerg-400	508	14	b.	b.	PROPN
fuelectenerg-400	508	15	vasić	vasić	PROPN
fuelectenerg-400	508	16	sets	set	VERB
fuelectenerg-400	508	17	in	in	ADP
fuelectenerg-400	508	18	r	r	NOUN
fuelectenerg-400	508	19	have	have	AUX
fuelectenerg-400	508	20	been	be	AUX
fuelectenerg-400	508	21	designed	design	VERB
fuelectenerg-400	508	22	.	.	PUNCT
fuelectenerg-400	509	1	to	to	PART
fuelectenerg-400	509	2	explain	explain	VERB
fuelectenerg-400	509	3	this	this	PRON
fuelectenerg-400	509	4	,	,	PUNCT
fuelectenerg-400	509	5	we	we	PRON
fuelectenerg-400	509	6	consider	consider	VERB
fuelectenerg-400	509	7	the	the	DET
fuelectenerg-400	509	8	following	following	NOUN
fuelectenerg-400	509	9	:	:	PUNCT
fuelectenerg-400	509	10	let	let	VERB
fuelectenerg-400	509	11	ri	ri	VERB
fuelectenerg-400	509	12	=	=	PUNCT
fuelectenerg-400	509	13	{	{	PUNCT
fuelectenerg-400	509	14	di	di	NOUN
fuelectenerg-400	509	15	,	,	PUNCT
fuelectenerg-400	509	16	i	i	NOUN
fuelectenerg-400	509	17	=	=	NOUN
fuelectenerg-400	509	18	1	1	NUM
fuelectenerg-400	509	19	,	,	PUNCT
fuelectenerg-400	509	20	2	2	NUM
fuelectenerg-400	509	21	,	,	PUNCT
fuelectenerg-400	509	22	.	.	PUNCT
fuelectenerg-400	509	23	.	.	PUNCT
fuelectenerg-400	510	1	.	.	PUNCT
fuelectenerg-400	511	1	,	,	PUNCT
fuelectenerg-400	511	2	c|di	c|di	PUNCT
fuelectenerg-400	512	1	∈	∈	PROPN
fuelectenerg-400	512	2	d(a+b	d(a+b	PRON
fuelectenerg-400	512	3	,	,	PUNCT
fuelectenerg-400	512	4	b	b	NOUN
fuelectenerg-400	512	5	)	)	PUNCT
fuelectenerg-400	512	6	}	}	PUNCT
fuelectenerg-400	512	7	.	.	PUNCT
fuelectenerg-400	513	1	there	there	PRON
fuelectenerg-400	513	2	exists	exist	VERB
fuelectenerg-400	513	3	an	an	DET
fuelectenerg-400	513	4	ordering	ordering	NOUN
fuelectenerg-400	513	5	of	of	ADP
fuelectenerg-400	513	6	elements	element	NOUN
fuelectenerg-400	513	7	of	of	ADP
fuelectenerg-400	513	8	d(a+b	d(a+b	NOUN
fuelectenerg-400	513	9	,	,	PUNCT
fuelectenerg-400	513	10	b	b	NOUN
fuelectenerg-400	513	11	)	)	PUNCT
fuelectenerg-400	513	12	such	such	ADJ
fuelectenerg-400	513	13	that	that	SCONJ
fuelectenerg-400	513	14	∀i	∀i	NOUN
fuelectenerg-400	513	15	,	,	PUNCT
fuelectenerg-400	513	16	j	j	PROPN
fuelectenerg-400	513	17	1	1	NUM
fuelectenerg-400	513	18	≤	≤	PUNCT
fuelectenerg-400	513	19	i	i	PROPN
fuelectenerg-400	513	20	,	,	PUNCT
fuelectenerg-400	513	21	j	j	PROPN
fuelectenerg-400	513	22	≤	≤	PROPN
fuelectenerg-400	513	23	c	c	X
fuelectenerg-400	513	24	,	,	PUNCT
fuelectenerg-400	513	25	if	if	SCONJ
fuelectenerg-400	513	26	i	i	PRON
fuelectenerg-400	513	27	<	<	X
fuelectenerg-400	513	28	j	j	PROPN
fuelectenerg-400	513	29	,	,	PUNCT
fuelectenerg-400	513	30	then	then	ADV
fuelectenerg-400	513	31	rank(di	rank(di	VERB
fuelectenerg-400	513	32	)	)	PUNCT
fuelectenerg-400	513	33	≤	≤	NOUN
fuelectenerg-400	513	34	rank(dj	rank(dj	NOUN
fuelectenerg-400	513	35	)	)	PUNCT
fuelectenerg-400	513	36	where	where	SCONJ
fuelectenerg-400	513	37	rank	rank	NOUN
fuelectenerg-400	513	38	(	(	PUNCT
fuelectenerg-400	513	39	.	.	PUNCT
fuelectenerg-400	513	40	)	)	PUNCT
fuelectenerg-400	513	41	denotes	denote	VERB
fuelectenerg-400	513	42	the	the	DET
fuelectenerg-400	513	43	rank	rank	NOUN
fuelectenerg-400	513	44	of	of	ADP
fuelectenerg-400	513	45	an	an	DET
fuelectenerg-400	513	46	element	element	NOUN
fuelectenerg-400	513	47	in	in	ADP
fuelectenerg-400	513	48	the	the	DET
fuelectenerg-400	513	49	ordered	order	VERB
fuelectenerg-400	513	50	set	set	NOUN
fuelectenerg-400	513	51	.	.	PUNCT
fuelectenerg-400	514	1	hence	hence	ADV
fuelectenerg-400	514	2	,	,	PUNCT
fuelectenerg-400	514	3	instead	instead	ADV
fuelectenerg-400	514	4	of	of	ADP
fuelectenerg-400	514	5	storing	store	VERB
fuelectenerg-400	514	6	individual	individual	ADJ
fuelectenerg-400	514	7	sequences	sequence	NOUN
fuelectenerg-400	514	8	,	,	PUNCT
fuelectenerg-400	514	9	ri	ri	PROPN
fuelectenerg-400	514	10	can	can	AUX
fuelectenerg-400	514	11	be	be	AUX
fuelectenerg-400	514	12	represented	represent	VERB
fuelectenerg-400	514	13	using	use	VERB
fuelectenerg-400	514	14	the	the	DET
fuelectenerg-400	514	15	ranks	rank	NOUN
fuelectenerg-400	514	16	of	of	ADP
fuelectenerg-400	514	17	di	di	NOUN
fuelectenerg-400	514	18	as	as	ADP
fuelectenerg-400	514	19	ri	ri	NOUN
fuelectenerg-400	514	20	=	=	PUNCT
fuelectenerg-400	514	21	{	{	PUNCT
fuelectenerg-400	514	22	rank(di	rank(di	NOUN
fuelectenerg-400	514	23	)	)	PUNCT
fuelectenerg-400	514	24	,	,	PUNCT
fuelectenerg-400	514	25	i	i	PRON
fuelectenerg-400	514	26	=	=	NOUN
fuelectenerg-400	514	27	1	1	NUM
fuelectenerg-400	514	28	,	,	PUNCT
fuelectenerg-400	514	29	2	2	NUM
fuelectenerg-400	514	30	,	,	PUNCT
fuelectenerg-400	514	31	.	.	PUNCT
fuelectenerg-400	514	32	.	.	PUNCT
fuelectenerg-400	514	33	.	.	PUNCT
fuelectenerg-400	515	1	c|	c|	PROPN
fuelectenerg-400	515	2	di	di	PROPN
fuelectenerg-400	515	3	∈	∈	PROPN
fuelectenerg-400	515	4	d(a+b	d(a+b	PROPN
fuelectenerg-400	515	5	,	,	PUNCT
fuelectenerg-400	515	6	b	b	NOUN
fuelectenerg-400	515	7	)	)	PUNCT
fuelectenerg-400	515	8	}	}	PUNCT
fuelectenerg-400	515	9	(	(	PUNCT
fuelectenerg-400	515	10	we	we	PRON
fuelectenerg-400	515	11	will	will	AUX
fuelectenerg-400	515	12	later	later	ADV
fuelectenerg-400	515	13	show	show	VERB
fuelectenerg-400	515	14	that	that	SCONJ
fuelectenerg-400	515	15	this	this	PRON
fuelectenerg-400	515	16	can	can	AUX
fuelectenerg-400	515	17	be	be	AUX
fuelectenerg-400	515	18	further	far	ADV
fuelectenerg-400	515	19	simplified	simplify	VERB
fuelectenerg-400	515	20	by	by	ADP
fuelectenerg-400	515	21	the	the	DET
fuelectenerg-400	515	22	use	use	NOUN
fuelectenerg-400	515	23	of	of	ADP
fuelectenerg-400	515	24	non	non	ADJ
fuelectenerg-400	515	25	-	-	ADJ
fuelectenerg-400	515	26	decreasing	decrease	VERB
fuelectenerg-400	515	27	strings	string	NOUN
fuelectenerg-400	515	28	.	.	PUNCT
fuelectenerg-400	516	1	this	this	PRON
fuelectenerg-400	516	2	will	will	AUX
fuelectenerg-400	516	3	be	be	AUX
fuelectenerg-400	516	4	dealt	deal	VERB
fuelectenerg-400	516	5	with	with	ADP
fuelectenerg-400	516	6	in	in	ADP
fuelectenerg-400	516	7	detail	detail	NOUN
fuelectenerg-400	516	8	in	in	ADP
fuelectenerg-400	516	9	section	section	NOUN
fuelectenerg-400	516	10	5.3	5.3	NUM
fuelectenerg-400	516	11	)	)	PUNCT
fuelectenerg-400	516	12	.	.	PUNCT
fuelectenerg-400	517	1	we	we	PRON
fuelectenerg-400	517	2	refer	refer	VERB
fuelectenerg-400	517	3	to	to	ADP
fuelectenerg-400	517	4	this	this	PRON
fuelectenerg-400	517	5	as	as	ADP
fuelectenerg-400	517	6	the	the	DET
fuelectenerg-400	517	7	rank	rank	NOUN
fuelectenerg-400	517	8	-	-	PUNCT
fuelectenerg-400	517	9	based	base	VERB
fuelectenerg-400	517	10	representation	representation	NOUN
fuelectenerg-400	517	11	.	.	PUNCT
fuelectenerg-400	518	1	we	we	PRON
fuelectenerg-400	518	2	now	now	ADV
fuelectenerg-400	518	3	describe	describe	VERB
fuelectenerg-400	518	4	the	the	DET
fuelectenerg-400	518	5	reverse	reverse	ADJ
fuelectenerg-400	518	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	518	7	ordering	ordering	NOUN
fuelectenerg-400	518	8	of	of	ADP
fuelectenerg-400	518	9	constant	constant	ADJ
fuelectenerg-400	518	10	weight	weight	NOUN
fuelectenerg-400	518	11	sequences	sequence	NOUN
fuelectenerg-400	518	12	which	which	PRON
fuelectenerg-400	518	13	is	be	AUX
fuelectenerg-400	518	14	one	one	NUM
fuelectenerg-400	518	15	such	such	ADJ
fuelectenerg-400	518	16	ordering	ordering	NOUN
fuelectenerg-400	518	17	of	of	ADP
fuelectenerg-400	518	18	sequences	sequence	NOUN
fuelectenerg-400	518	19	.	.	PUNCT
fuelectenerg-400	519	1	5.2	5.2	NUM
fuelectenerg-400	519	2	reverse	reverse	VERB
fuelectenerg-400	519	3	lexicographical	lexicographical	ADJ
fuelectenerg-400	519	4	ordering	ordering	NOUN
fuelectenerg-400	519	5	of	of	ADP
fuelectenerg-400	519	6	constant	constant	ADJ
fuelectenerg-400	519	7	weight	weight	NOUN
fuelectenerg-400	519	8	sequences	sequence	NOUN
fuelectenerg-400	519	9	in	in	ADP
fuelectenerg-400	519	10	this	this	DET
fuelectenerg-400	519	11	section	section	NOUN
fuelectenerg-400	519	12	,	,	PUNCT
fuelectenerg-400	519	13	methods	method	NOUN
fuelectenerg-400	519	14	to	to	PART
fuelectenerg-400	519	15	obtain	obtain	VERB
fuelectenerg-400	519	16	a	a	DET
fuelectenerg-400	519	17	bijective	bijective	ADJ
fuelectenerg-400	519	18	mapping	mapping	NOUN
fuelectenerg-400	519	19	between	between	ADP
fuelectenerg-400	519	20	members	member	NOUN
fuelectenerg-400	519	21	of	of	ADP
fuelectenerg-400	519	22	d(n	d(n	PROPN
fuelectenerg-400	519	23	,	,	PUNCT
fuelectenerg-400	519	24	k	k	NOUN
fuelectenerg-400	519	25	)	)	PUNCT
fuelectenerg-400	519	26	and	and	CCONJ
fuelectenerg-400	519	27	integers	integer	NOUN
fuelectenerg-400	519	28	will	will	AUX
fuelectenerg-400	519	29	be	be	AUX
fuelectenerg-400	519	30	developed	develop	VERB
fuelectenerg-400	519	31	.	.	PUNCT
fuelectenerg-400	520	1	firstly	firstly	ADV
fuelectenerg-400	520	2	,	,	PUNCT
fuelectenerg-400	520	3	we	we	PRON
fuelectenerg-400	520	4	note	note	VERB
fuelectenerg-400	520	5	that	that	SCONJ
fuelectenerg-400	520	6	the	the	DET
fuelectenerg-400	520	7	size	size	NOUN
fuelectenerg-400	520	8	of	of	ADP
fuelectenerg-400	520	9	d(n	d(n	PROPN
fuelectenerg-400	520	10	,	,	PUNCT
fuelectenerg-400	520	11	k	k	NOUN
fuelectenerg-400	520	12	)	)	PUNCT
fuelectenerg-400	520	13	,	,	PUNCT
fuelectenerg-400	520	14	∣∣d(n	∣∣d(n	PROPN
fuelectenerg-400	520	15	,	,	PUNCT
fuelectenerg-400	520	16	k	k	NOUN
fuelectenerg-400	520	17	)	)	PUNCT
fuelectenerg-400	520	18	∣∣	∣∣	NUM
fuelectenerg-400	520	19	,	,	PUNCT
fuelectenerg-400	520	20	is	be	AUX
fuelectenerg-400	520	21	(	(	PUNCT
fuelectenerg-400	520	22	n	n	X
fuelectenerg-400	520	23	k	k	PROPN
fuelectenerg-400	520	24	)	)	PUNCT
fuelectenerg-400	520	25	.	.	PUNCT
fuelectenerg-400	521	1	also	also	ADV
fuelectenerg-400	521	2	,	,	PUNCT
fuelectenerg-400	521	3	note	note	VERB
fuelectenerg-400	521	4	that	that	SCONJ
fuelectenerg-400	521	5	each	each	DET
fuelectenerg-400	521	6	n	n	CCONJ
fuelectenerg-400	521	7	-	-	PUNCT
fuelectenerg-400	521	8	bit	bit	NOUN
fuelectenerg-400	521	9	sequence	sequence	NOUN
fuelectenerg-400	521	10	has	have	VERB
fuelectenerg-400	521	11	a	a	DET
fuelectenerg-400	521	12	decimal	decimal	ADJ
fuelectenerg-400	521	13	equivalent	equivalent	NOUN
fuelectenerg-400	521	14	between	between	ADP
fuelectenerg-400	521	15	0	0	NUM
fuelectenerg-400	521	16	and	and	CCONJ
fuelectenerg-400	521	17	2n	2n	NUM
fuelectenerg-400	522	1	−	−	NOUN
fuelectenerg-400	522	2	1	1	X
fuelectenerg-400	522	3	.	.	PUNCT
fuelectenerg-400	523	1	let	let	VERB
fuelectenerg-400	523	2	the	the	DET
fuelectenerg-400	523	3	decimal	decimal	ADJ
fuelectenerg-400	523	4	equivalent	equivalent	NOUN
fuelectenerg-400	523	5	be	be	AUX
fuelectenerg-400	523	6	denoted	denote	VERB
fuelectenerg-400	523	7	as	as	ADP
fuelectenerg-400	523	8	de	de	PROPN
fuelectenerg-400	523	9	(	(	PUNCT
fuelectenerg-400	523	10	.	.	PUNCT
fuelectenerg-400	523	11	)	)	PUNCT
fuelectenerg-400	523	12	.	.	PUNCT
fuelectenerg-400	524	1	the	the	DET
fuelectenerg-400	524	2	lexicographical	lexicographical	ADJ
fuelectenerg-400	524	3	ordering	ordering	NOUN
fuelectenerg-400	524	4	of	of	ADP
fuelectenerg-400	524	5	the	the	DET
fuelectenerg-400	524	6	sequences	sequence	NOUN
fuelectenerg-400	524	7	is	be	AUX
fuelectenerg-400	524	8	the	the	DET
fuelectenerg-400	524	9	arrangement	arrangement	NOUN
fuelectenerg-400	524	10	of	of	ADP
fuelectenerg-400	524	11	all	all	DET
fuelectenerg-400	524	12	the	the	DET
fuelectenerg-400	524	13	sequences	sequence	NOUN
fuelectenerg-400	524	14	in	in	ADP
fuelectenerg-400	524	15	the	the	DET
fuelectenerg-400	524	16	ascending	ascend	VERB
fuelectenerg-400	524	17	order	order	NOUN
fuelectenerg-400	524	18	of	of	ADP
fuelectenerg-400	524	19	their	their	PRON
fuelectenerg-400	524	20	decimal	decimal	ADJ
fuelectenerg-400	524	21	equivalent	equivalent	NOUN
fuelectenerg-400	524	22	.	.	PUNCT
fuelectenerg-400	525	1	the	the	DET
fuelectenerg-400	525	2	reverse	reverse	ADJ
fuelectenerg-400	525	3	lexicographical	lexicographical	ADJ
fuelectenerg-400	525	4	ordering	ordering	NOUN
fuelectenerg-400	525	5	can	can	AUX
fuelectenerg-400	525	6	be	be	AUX
fuelectenerg-400	525	7	defined	define	VERB
fuelectenerg-400	525	8	analogously	analogously	ADV
fuelectenerg-400	525	9	.	.	PUNCT
fuelectenerg-400	526	1	in	in	ADP
fuelectenerg-400	526	2	our	our	PRON
fuelectenerg-400	526	3	description	description	NOUN
fuelectenerg-400	526	4	,	,	PUNCT
fuelectenerg-400	526	5	we	we	PRON
fuelectenerg-400	526	6	use	use	VERB
fuelectenerg-400	526	7	the	the	DET
fuelectenerg-400	526	8	reverse	reverse	ADJ
fuelectenerg-400	526	9	lexicographical	lexicographical	ADJ
fuelectenerg-400	526	10	ordering	ordering	NOUN
fuelectenerg-400	526	11	.	.	PUNCT
fuelectenerg-400	527	1	table	table	NOUN
fuelectenerg-400	527	2	1	1	NUM
fuelectenerg-400	527	3	shows	show	VERB
fuelectenerg-400	527	4	the	the	DET
fuelectenerg-400	527	5	reverse	reverse	ADJ
fuelectenerg-400	527	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	527	7	ordering	ordering	NOUN
fuelectenerg-400	527	8	for	for	ADP
fuelectenerg-400	527	9	d(4,2	d(4,2	NOUN
fuelectenerg-400	527	10	)	)	PUNCT
fuelectenerg-400	527	11	.	.	PUNCT
fuelectenerg-400	528	1	the	the	DET
fuelectenerg-400	528	2	first	first	ADJ
fuelectenerg-400	528	3	column	column	NOUN
fuelectenerg-400	528	4	is	be	AUX
fuelectenerg-400	528	5	the	the	DET
fuelectenerg-400	528	6	rank	rank	NOUN
fuelectenerg-400	528	7	which	which	PRON
fuelectenerg-400	528	8	gives	give	VERB
fuelectenerg-400	528	9	the	the	DET
fuelectenerg-400	528	10	position	position	NOUN
fuelectenerg-400	528	11	of	of	ADP
fuelectenerg-400	528	12	the	the	DET
fuelectenerg-400	528	13	sequence	sequence	NOUN
fuelectenerg-400	528	14	in	in	ADP
fuelectenerg-400	528	15	the	the	DET
fuelectenerg-400	528	16	reverse	reverse	NOUN
fuelectenerg-400	528	17	lexicographically	lexicographically	ADV
fuelectenerg-400	528	18	ordered	order	VERB
fuelectenerg-400	528	19	set	set	NOUN
fuelectenerg-400	528	20	.	.	PUNCT
fuelectenerg-400	529	1	again	again	ADV
fuelectenerg-400	529	2	,	,	PUNCT
fuelectenerg-400	529	3	we	we	PRON
fuelectenerg-400	529	4	use	use	VERB
fuelectenerg-400	529	5	rank	rank	NOUN
fuelectenerg-400	529	6	(	(	PUNCT
fuelectenerg-400	529	7	.	.	PUNCT
fuelectenerg-400	529	8	)	)	PUNCT
fuelectenerg-400	529	9	to	to	PART
fuelectenerg-400	529	10	denote	denote	VERB
fuelectenerg-400	529	11	the	the	DET
fuelectenerg-400	529	12	rank	rank	NOUN
fuelectenerg-400	529	13	of	of	ADP
fuelectenerg-400	529	14	a	a	DET
fuelectenerg-400	529	15	particular	particular	ADJ
fuelectenerg-400	529	16	element	element	NOUN
fuelectenerg-400	529	17	.	.	PUNCT
fuelectenerg-400	530	1	it	it	PRON
fuelectenerg-400	530	2	is	be	AUX
fuelectenerg-400	530	3	easily	easily	ADV
fuelectenerg-400	530	4	seen	see	VERB
fuelectenerg-400	530	5	that	that	SCONJ
fuelectenerg-400	530	6	if	if	SCONJ
fuelectenerg-400	530	7	de(a	de(a	NOUN
fuelectenerg-400	530	8	)	)	PUNCT
fuelectenerg-400	530	9	≥	≥	NOUN
fuelectenerg-400	530	10	de(b	de(b	PUNCT
fuelectenerg-400	530	11	)	)	PUNCT
fuelectenerg-400	530	12	,	,	PUNCT
fuelectenerg-400	530	13	then	then	ADV
fuelectenerg-400	530	14	rank(a	rank(a	NOUN
fuelectenerg-400	530	15	)	)	PUNCT
fuelectenerg-400	530	16	≤	≤	NUM
fuelectenerg-400	530	17	rank(b	rank(b	NOUN
fuelectenerg-400	530	18	)	)	PUNCT
fuelectenerg-400	530	19	.	.	PUNCT
fuelectenerg-400	531	1	next	next	ADV
fuelectenerg-400	531	2	,	,	PUNCT
fuelectenerg-400	531	3	we	we	PRON
fuelectenerg-400	531	4	consider	consider	VERB
fuelectenerg-400	531	5	the	the	DET
fuelectenerg-400	531	6	transformation	transformation	NOUN
fuelectenerg-400	531	7	of	of	ADP
fuelectenerg-400	531	8	the	the	DET
fuelectenerg-400	531	9	members	member	NOUN
fuelectenerg-400	531	10	of	of	ADP
fuelectenerg-400	531	11	d(n	d(n	PROPN
fuelectenerg-400	531	12	,	,	PUNCT
fuelectenerg-400	531	13	k	k	NOUN
fuelectenerg-400	531	14	)	)	PUNCT
fuelectenerg-400	531	15	,	,	PUNCT
fuelectenerg-400	531	16	to	to	ADP
fuelectenerg-400	531	17	paths	path	NOUN
fuelectenerg-400	531	18	in	in	ADP
fuelectenerg-400	531	19	a	a	DET
fuelectenerg-400	531	20	cartesian	cartesian	ADJ
fuelectenerg-400	531	21	plane	plane	NOUN
fuelectenerg-400	531	22	.	.	PUNCT
fuelectenerg-400	532	1	we	we	PRON
fuelectenerg-400	532	2	refer	refer	VERB
fuelectenerg-400	532	3	to	to	ADP
fuelectenerg-400	532	4	these	these	DET
fuelectenerg-400	532	5	paths	path	NOUN
fuelectenerg-400	532	6	as	as	SCONJ
fuelectenerg-400	532	7	mountain	mountain	NOUN
fuelectenerg-400	532	8	ranges	range	NOUN
fuelectenerg-400	532	9	(	(	PUNCT
fuelectenerg-400	532	10	similar	similar	ADJ
fuelectenerg-400	532	11	to	to	ADP
fuelectenerg-400	532	12	the	the	DET
fuelectenerg-400	532	13	catalan	catalan	NOUN
fuelectenerg-400	532	14	mountain	mountain	NOUN
fuelectenerg-400	532	15	ranges	range	VERB
fuelectenerg-400	533	1	[	[	X
fuelectenerg-400	533	2	22	22	NUM
fuelectenerg-400	533	3	]	]	PUNCT
fuelectenerg-400	533	4	)	)	PUNCT
fuelectenerg-400	533	5	.	.	PUNCT
fuelectenerg-400	534	1	let	let	VERB
fuelectenerg-400	534	2	b	b	X
fuelectenerg-400	534	3	be	be	AUX
fuelectenerg-400	534	4	a	a	DET
fuelectenerg-400	534	5	member	member	NOUN
fuelectenerg-400	534	6	of	of	ADP
fuelectenerg-400	534	7	d(n	d(n	PROPN
fuelectenerg-400	534	8	,	,	PUNCT
fuelectenerg-400	534	9	k	k	NOUN
fuelectenerg-400	534	10	)	)	PUNCT
fuelectenerg-400	534	11	.	.	PUNCT
fuelectenerg-400	535	1	the	the	DET
fuelectenerg-400	535	2	mountain	mountain	NOUN
fuelectenerg-400	535	3	range	range	NOUN
fuelectenerg-400	535	4	mountain	mountain	NOUN
fuelectenerg-400	535	5	(	(	PUNCT
fuelectenerg-400	535	6	.	.	PUNCT
fuelectenerg-400	535	7	)	)	PUNCT
fuelectenerg-400	536	1	corresponding	correspond	VERB
fuelectenerg-400	536	2	to	to	ADP
fuelectenerg-400	536	3	b	b	NOUN
fuelectenerg-400	536	4	can	can	AUX
fuelectenerg-400	536	5	be	be	AUX
fuelectenerg-400	536	6	calculated	calculate	VERB
fuelectenerg-400	536	7	as	as	SCONJ
fuelectenerg-400	536	8	follows	follow	VERB
fuelectenerg-400	536	9	:	:	PUNCT
fuelectenerg-400	536	10	the	the	DET
fuelectenerg-400	536	11	mount	mount	PROPN
fuelectenerg-400	536	12	ranges	range	VERB
fuelectenerg-400	536	13	can	can	AUX
fuelectenerg-400	536	14	also	also	ADV
fuelectenerg-400	536	15	be	be	AUX
fuelectenerg-400	536	16	represented	represent	VERB
fuelectenerg-400	536	17	by	by	ADP
fuelectenerg-400	536	18	the	the	DET
fuelectenerg-400	536	19	n	n	CCONJ
fuelectenerg-400	536	20	-	-	PUNCT
fuelectenerg-400	536	21	tuple	tuple	NOUN
fuelectenerg-400	536	22	containing	contain	VERB
fuelectenerg-400	536	23	y	y	PROPN
fuelectenerg-400	536	24	coordinates	coordinate	NOUN
fuelectenerg-400	536	25	of	of	ADP
fuelectenerg-400	536	26	points	point	NOUN
fuelectenerg-400	536	27	traced	trace	VERB
fuelectenerg-400	536	28	by	by	ADP
fuelectenerg-400	536	29	the	the	DET
fuelectenerg-400	536	30	sequence	sequence	NOUN
fuelectenerg-400	536	31	,	,	PUNCT
fuelectenerg-400	536	32	denoted	denote	VERB
fuelectenerg-400	536	33	by	by	ADP
fuelectenerg-400	536	34	y.	y.	PROPN
fuelectenerg-400	536	35	figure	figure	NOUN
fuelectenerg-400	536	36	9	9	NUM
fuelectenerg-400	536	37	shows	show	VERB
fuelectenerg-400	536	38	the	the	DET
fuelectenerg-400	536	39	table	table	NOUN
fuelectenerg-400	536	40	1	1	NUM
fuelectenerg-400	536	41	.	.	PUNCT
fuelectenerg-400	537	1	ordering	ordering	NOUN
fuelectenerg-400	537	2	of	of	ADP
fuelectenerg-400	537	3	elements	element	NOUN
fuelectenerg-400	537	4	in	in	ADP
fuelectenerg-400	537	5	d(4,2	d(4,2	NOUN
fuelectenerg-400	537	6	)	)	PUNCT
fuelectenerg-400	537	7	.	.	PUNCT
fuelectenerg-400	538	1	rank	rank	PROPN
fuelectenerg-400	538	2	string	string	PROPN
fuelectenerg-400	538	3	decimal	decimal	PROPN
fuelectenerg-400	538	4	equivalent	equivalent	NOUN
fuelectenerg-400	538	5	0	0	NUM
fuelectenerg-400	538	6	1100	1100	NUM
fuelectenerg-400	538	7	12	12	NUM
fuelectenerg-400	538	8	1	1	NUM
fuelectenerg-400	538	9	1010	1010	NUM
fuelectenerg-400	538	10	10	10	NUM
fuelectenerg-400	538	11	2	2	NUM
fuelectenerg-400	538	12	1001	1001	NUM
fuelectenerg-400	538	13	9	9	NUM
fuelectenerg-400	538	14	3	3	NUM
fuelectenerg-400	538	15	0110	0110	NUM
fuelectenerg-400	538	16	6	6	NUM
fuelectenerg-400	538	17	4	4	NUM
fuelectenerg-400	538	18	0101	0101	NUM
fuelectenerg-400	538	19	5	5	NUM
fuelectenerg-400	538	20	5	5	NUM
fuelectenerg-400	538	21	0011	0011	NUM
fuelectenerg-400	538	22	3	3	NUM
fuelectenerg-400	538	23	detection	detection	NOUN
fuelectenerg-400	538	24	and	and	CCONJ
fuelectenerg-400	538	25	coding	code	VERB
fuelectenerg-400	538	26	for	for	ADP
fuelectenerg-400	538	27	tdmr	tdmr	NOUN
fuelectenerg-400	538	28	channel	channel	NOUN
fuelectenerg-400	538	29	533	533	NUM
fuelectenerg-400	538	30	algorithm	algorithm	NOUN
fuelectenerg-400	538	31	1	1	NUM
fuelectenerg-400	538	32	the	the	DET
fuelectenerg-400	538	33	mount	mount	PROPN
fuelectenerg-400	538	34	range	range	PROPN
fuelectenerg-400	538	35	algorithm	algorithm	PROPN
fuelectenerg-400	538	36	start	start	VERB
fuelectenerg-400	538	37	from	from	ADP
fuelectenerg-400	538	38	(	(	PUNCT
fuelectenerg-400	538	39	x	x	SYM
fuelectenerg-400	538	40	=	=	SYM
fuelectenerg-400	538	41	0	0	NUM
fuelectenerg-400	538	42	,	,	PUNCT
fuelectenerg-400	538	43	y	y	PROPN
fuelectenerg-400	538	44	=	=	NOUN
fuelectenerg-400	538	45	0	0	NUM
fuelectenerg-400	538	46	)	)	PUNCT
fuelectenerg-400	538	47	for	for	ADP
fuelectenerg-400	538	48	i	i	PRON
fuelectenerg-400	538	49	=	=	NOUN
fuelectenerg-400	538	50	1	1	NUM
fuelectenerg-400	538	51	to	to	PART
fuelectenerg-400	538	52	n	n	PRON
fuelectenerg-400	538	53	do	do	VERB
fuelectenerg-400	538	54	if	if	SCONJ
fuelectenerg-400	538	55	b(i	b(i	VERB
fuelectenerg-400	538	56	)	)	PUNCT
fuelectenerg-400	538	57	=	=	SYM
fuelectenerg-400	538	58	1	1	NUM
fuelectenerg-400	538	59	then	then	ADV
fuelectenerg-400	538	60	move	move	VERB
fuelectenerg-400	538	61	to	to	ADP
fuelectenerg-400	538	62	(	(	PUNCT
fuelectenerg-400	538	63	x	x	SYM
fuelectenerg-400	538	64	+	+	NUM
fuelectenerg-400	538	65	1	1	NUM
fuelectenerg-400	538	66	,	,	PUNCT
fuelectenerg-400	538	67	y	y	PROPN
fuelectenerg-400	538	68	+	+	NOUN
fuelectenerg-400	538	69	1	1	X
fuelectenerg-400	538	70	)	)	PUNCT
fuelectenerg-400	538	71	else	else	ADV
fuelectenerg-400	538	72	move	move	VERB
fuelectenerg-400	538	73	to	to	ADP
fuelectenerg-400	538	74	(	(	PUNCT
fuelectenerg-400	538	75	x	x	SYM
fuelectenerg-400	539	1	+	+	NUM
fuelectenerg-400	539	2	1	1	NUM
fuelectenerg-400	539	3	,	,	PUNCT
fuelectenerg-400	539	4	y	y	PROPN
fuelectenerg-400	539	5	−	−	PROPN
fuelectenerg-400	539	6	1	1	X
fuelectenerg-400	539	7	)	)	PUNCT
fuelectenerg-400	539	8	end	end	NOUN
fuelectenerg-400	539	9	if	if	SCONJ
fuelectenerg-400	539	10	end	end	NOUN
fuelectenerg-400	539	11	for	for	ADP
fuelectenerg-400	539	12	output	output	NOUN
fuelectenerg-400	539	13	the	the	DET
fuelectenerg-400	539	14	mount	mount	PROPN
fuelectenerg-400	539	15	range	range	PROPN
fuelectenerg-400	539	16	mountain	mountain	NOUN
fuelectenerg-400	539	17	(	(	PUNCT
fuelectenerg-400	539	18	.	.	PUNCT
fuelectenerg-400	539	19	)	)	PUNCT
fuelectenerg-400	540	1	fig	fig	NOUN
fuelectenerg-400	540	2	.	.	PUNCT
fuelectenerg-400	541	1	9	9	X
fuelectenerg-400	541	2	.	.	X
fuelectenerg-400	541	3	mountain	mountain	NOUN
fuelectenerg-400	541	4	range	range	NOUN
fuelectenerg-400	541	5	corresponding	correspond	VERB
fuelectenerg-400	541	6	to	to	ADP
fuelectenerg-400	541	7	the	the	DET
fuelectenerg-400	541	8	string	string	NOUN
fuelectenerg-400	541	9	100101	100101	NUM
fuelectenerg-400	541	10	,	,	PUNCT
fuelectenerg-400	541	11	mountain(100101	mountain(100101	PROPN
fuelectenerg-400	541	12	)	)	PUNCT
fuelectenerg-400	541	13	mountain	mountain	NOUN
fuelectenerg-400	541	14	range	range	NOUN
fuelectenerg-400	541	15	corresponding	correspond	VERB
fuelectenerg-400	541	16	to	to	ADP
fuelectenerg-400	541	17	the	the	DET
fuelectenerg-400	541	18	sequence	sequence	NOUN
fuelectenerg-400	541	19	100101	100101	NUM
fuelectenerg-400	541	20	,	,	PUNCT
fuelectenerg-400	541	21	a	a	DET
fuelectenerg-400	541	22	member	member	NOUN
fuelectenerg-400	541	23	of	of	ADP
fuelectenerg-400	541	24	d(6,3	d(6,3	NOUN
fuelectenerg-400	541	25	)	)	PUNCT
fuelectenerg-400	541	26	.	.	PUNCT
fuelectenerg-400	542	1	we	we	PRON
fuelectenerg-400	542	2	now	now	ADV
fuelectenerg-400	542	3	establish	establish	VERB
fuelectenerg-400	542	4	a	a	DET
fuelectenerg-400	542	5	relation	relation	NOUN
fuelectenerg-400	542	6	between	between	ADP
fuelectenerg-400	542	7	the	the	DET
fuelectenerg-400	542	8	lexicographical	lexicographical	ADJ
fuelectenerg-400	542	9	ranking	ranking	NOUN
fuelectenerg-400	542	10	and	and	CCONJ
fuelectenerg-400	542	11	the	the	DET
fuelectenerg-400	542	12	containment	containment	NOUN
fuelectenerg-400	542	13	of	of	ADP
fuelectenerg-400	542	14	mountain	mountain	NOUN
fuelectenerg-400	542	15	ranges	range	VERB
fuelectenerg-400	542	16	within	within	ADP
fuelectenerg-400	542	17	one	one	NUM
fuelectenerg-400	542	18	another	another	DET
fuelectenerg-400	542	19	.	.	PUNCT
fuelectenerg-400	543	1	for	for	ADP
fuelectenerg-400	543	2	any	any	DET
fuelectenerg-400	543	3	a	a	PRON
fuelectenerg-400	543	4	,	,	PUNCT
fuelectenerg-400	543	5	b	b	PROPN
fuelectenerg-400	543	6	∈	∈	PROPN
fuelectenerg-400	543	7	d(n	d(n	PROPN
fuelectenerg-400	543	8	,	,	PUNCT
fuelectenerg-400	543	9	k	k	NOUN
fuelectenerg-400	543	10	)	)	PUNCT
fuelectenerg-400	543	11	,	,	PUNCT
fuelectenerg-400	543	12	mountain(a	mountain(a	PROPN
fuelectenerg-400	543	13	)	)	PUNCT
fuelectenerg-400	543	14	is	be	AUX
fuelectenerg-400	543	15	said	say	VERB
fuelectenerg-400	543	16	to	to	PART
fuelectenerg-400	543	17	be	be	AUX
fuelectenerg-400	543	18	contained	contain	VERB
fuelectenerg-400	543	19	within	within	ADP
fuelectenerg-400	543	20	mountain(b	mountain(b	NOUN
fuelectenerg-400	543	21	)	)	PUNCT
fuelectenerg-400	543	22	(	(	PUNCT
fuelectenerg-400	543	23	denoted	denote	VERB
fuelectenerg-400	543	24	as	as	ADP
fuelectenerg-400	543	25	mountain(a	mountain(a	NOUN
fuelectenerg-400	543	26	)	)	PUNCT
fuelectenerg-400	543	27	⊂	⊂	PROPN
fuelectenerg-400	543	28	mountain(b	mountain(b	PROPN
fuelectenerg-400	543	29	)	)	PUNCT
fuelectenerg-400	543	30	)	)	PUNCT
fuelectenerg-400	543	31	if	if	SCONJ
fuelectenerg-400	543	32	each	each	DET
fuelectenerg-400	543	33	element	element	NOUN
fuelectenerg-400	543	34	of	of	ADP
fuelectenerg-400	543	35	the	the	DET
fuelectenerg-400	543	36	n	n	CCONJ
fuelectenerg-400	543	37	-	-	PUNCT
fuelectenerg-400	543	38	tuple	tuple	NOUN
fuelectenerg-400	543	39	corresponding	corresponding	NOUN
fuelectenerg-400	543	40	to	to	ADP
fuelectenerg-400	543	41	a	a	PRON
fuelectenerg-400	543	42	,	,	PUNCT
fuelectenerg-400	543	43	ya	ya	PROPN
fuelectenerg-400	543	44	is	be	AUX
fuelectenerg-400	543	45	never	never	ADV
fuelectenerg-400	543	46	more	more	ADJ
fuelectenerg-400	543	47	than	than	ADP
fuelectenerg-400	543	48	the	the	DET
fuelectenerg-400	543	49	corresponding	corresponding	ADJ
fuelectenerg-400	543	50	element	element	NOUN
fuelectenerg-400	543	51	of	of	ADP
fuelectenerg-400	543	52	the	the	DET
fuelectenerg-400	543	53	n	n	CCONJ
fuelectenerg-400	543	54	-	-	PUNCT
fuelectenerg-400	543	55	tuple	tuple	NOUN
fuelectenerg-400	543	56	corresponding	corresponding	NOUN
fuelectenerg-400	543	57	to	to	ADP
fuelectenerg-400	543	58	b	b	PROPN
fuelectenerg-400	543	59	,	,	PUNCT
fuelectenerg-400	543	60	yb	yb	PROPN
fuelectenerg-400	543	61	.	.	PROPN
fuelectenerg-400	544	1	for	for	ADP
fuelectenerg-400	544	2	instance	instance	NOUN
fuelectenerg-400	544	3	,	,	PUNCT
fuelectenerg-400	544	4	the	the	DET
fuelectenerg-400	544	5	mountain	mountain	NOUN
fuelectenerg-400	544	6	range	range	NOUN
fuelectenerg-400	544	7	mountain(1010	mountain(1010	PROPN
fuelectenerg-400	544	8	)	)	PUNCT
fuelectenerg-400	544	9	is	be	AUX
fuelectenerg-400	544	10	contained	contain	VERB
fuelectenerg-400	544	11	in	in	ADP
fuelectenerg-400	544	12	mountain(1100	mountain(1100	PROPN
fuelectenerg-400	544	13	)	)	PUNCT
fuelectenerg-400	544	14	.	.	PUNCT
fuelectenerg-400	545	1	the	the	DET
fuelectenerg-400	545	2	following	follow	VERB
fuelectenerg-400	545	3	theorem	theorem	NOUN
fuelectenerg-400	545	4	relates	relate	VERB
fuelectenerg-400	545	5	the	the	DET
fuelectenerg-400	545	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	545	7	ranking	ranking	NOUN
fuelectenerg-400	545	8	to	to	PART
fuelectenerg-400	545	9	containment	containment	VERB
fuelectenerg-400	545	10	.	.	PUNCT
fuelectenerg-400	546	1	theorem	theorem	VERB
fuelectenerg-400	546	2	4	4	NUM
fuelectenerg-400	546	3	for	for	ADP
fuelectenerg-400	546	4	any	any	DET
fuelectenerg-400	546	5	a	a	NOUN
fuelectenerg-400	546	6	,	,	PUNCT
fuelectenerg-400	546	7	b	b	PROPN
fuelectenerg-400	546	8	∈	∈	PROPN
fuelectenerg-400	546	9	d(n	d(n	PROPN
fuelectenerg-400	546	10	,	,	PUNCT
fuelectenerg-400	546	11	k	k	NOUN
fuelectenerg-400	546	12	)	)	PUNCT
fuelectenerg-400	546	13	,	,	PUNCT
fuelectenerg-400	546	14	if	if	SCONJ
fuelectenerg-400	546	15	mountain(a	mountain(a	NOUN
fuelectenerg-400	546	16	)	)	PUNCT
fuelectenerg-400	546	17	⊂	⊂	PROPN
fuelectenerg-400	546	18	mountain(b	mountain(b	PROPN
fuelectenerg-400	546	19	)	)	PUNCT
fuelectenerg-400	546	20	,	,	PUNCT
fuelectenerg-400	546	21	then	then	ADV
fuelectenerg-400	546	22	rank(a	rank(a	NOUN
fuelectenerg-400	546	23	)	)	PUNCT
fuelectenerg-400	546	24	≥	≥	NOUN
fuelectenerg-400	546	25	rank(b	rank(b	NOUN
fuelectenerg-400	546	26	)	)	PUNCT
fuelectenerg-400	546	27	proof	proof	NOUN
fuelectenerg-400	546	28	:	:	PUNCT
fuelectenerg-400	546	29	the	the	DET
fuelectenerg-400	546	30	proof	proof	NOUN
fuelectenerg-400	546	31	is	be	AUX
fuelectenerg-400	546	32	given	give	VERB
fuelectenerg-400	546	33	in	in	ADP
fuelectenerg-400	546	34	appendix	appendix	NOUN
fuelectenerg-400	546	35	9	9	NUM
fuelectenerg-400	546	36	the	the	DET
fuelectenerg-400	546	37	converse	converse	NOUN
fuelectenerg-400	546	38	is	be	AUX
fuelectenerg-400	546	39	not	not	PART
fuelectenerg-400	546	40	true	true	ADJ
fuelectenerg-400	546	41	.	.	PUNCT
fuelectenerg-400	547	1	one	one	NUM
fuelectenerg-400	547	2	counter	counter	NOUN
fuelectenerg-400	547	3	-	-	NOUN
fuelectenerg-400	547	4	example	example	NOUN
fuelectenerg-400	547	5	in	in	ADP
fuelectenerg-400	547	6	d(4,2	d(4,2	PROPN
fuelectenerg-400	547	7	)	)	PUNCT
fuelectenerg-400	547	8	is	be	AUX
fuelectenerg-400	547	9	1001	1001	NUM
fuelectenerg-400	547	10	and	and	CCONJ
fuelectenerg-400	547	11	0110	0110	NUM
fuelectenerg-400	547	12	.	.	PUNCT
fuelectenerg-400	548	1	it	it	PRON
fuelectenerg-400	548	2	is	be	AUX
fuelectenerg-400	548	3	easily	easily	ADV
fuelectenerg-400	548	4	seen	see	VERB
fuelectenerg-400	548	5	that	that	SCONJ
fuelectenerg-400	548	6	an	an	DET
fuelectenerg-400	548	7	ordered	order	VERB
fuelectenerg-400	548	8	set	set	NOUN
fuelectenerg-400	548	9	{	{	PUNCT
fuelectenerg-400	548	10	di	di	NOUN
fuelectenerg-400	548	11	,	,	PUNCT
fuelectenerg-400	548	12	i	i	NOUN
fuelectenerg-400	548	13	=	=	NOUN
fuelectenerg-400	548	14	1	1	NUM
fuelectenerg-400	548	15	,	,	PUNCT
fuelectenerg-400	548	16	2	2	NUM
fuelectenerg-400	548	17	,	,	PUNCT
fuelectenerg-400	548	18	.	.	PUNCT
fuelectenerg-400	548	19	.	.	PUNCT
fuelectenerg-400	548	20	.	.	PUNCT
fuelectenerg-400	549	1	,	,	PUNCT
fuelectenerg-400	549	2	a|di	a|di	NOUN
fuelectenerg-400	549	3	∈	∈	PROPN
fuelectenerg-400	549	4	d(a+b	d(a+b	PRON
fuelectenerg-400	549	5	,	,	PUNCT
fuelectenerg-400	549	6	b	b	NOUN
fuelectenerg-400	549	7	)	)	PUNCT
fuelectenerg-400	549	8	}	}	PUNCT
fuelectenerg-400	549	9	such	such	ADJ
fuelectenerg-400	549	10	that	that	DET
fuelectenerg-400	549	11	mountain(di	mountain(di	NOUN
fuelectenerg-400	549	12	)	)	PUNCT
fuelectenerg-400	549	13	⊂	⊂	PROPN
fuelectenerg-400	549	14	mountain(di+1	mountain(di+1	PROPN
fuelectenerg-400	549	15	)	)	PUNCT
fuelectenerg-400	549	16	for	for	ADP
fuelectenerg-400	549	17	all	all	DET
fuelectenerg-400	549	18	i	i	PRON
fuelectenerg-400	549	19	,	,	PUNCT
fuelectenerg-400	549	20	is	be	AUX
fuelectenerg-400	549	21	a	a	DET
fuelectenerg-400	549	22	member	member	NOUN
fuelectenerg-400	549	23	of	of	ADP
fuelectenerg-400	549	24	r	r	NOUN
fuelectenerg-400	549	25	and	and	CCONJ
fuelectenerg-400	549	26	hence	hence	ADV
fuelectenerg-400	549	27	corresponds	correspond	VERB
fuelectenerg-400	549	28	to	to	ADP
fuelectenerg-400	549	29	a	a	DET
fuelectenerg-400	549	30	valid	valid	ADJ
fuelectenerg-400	549	31	tiling	tiling	NOUN
fuelectenerg-400	549	32	.	.	PUNCT
fuelectenerg-400	550	1	this	this	PRON
fuelectenerg-400	550	2	implies	imply	VERB
fuelectenerg-400	550	3	that	that	SCONJ
fuelectenerg-400	550	4	the	the	DET
fuelectenerg-400	550	5	rank	rank	NOUN
fuelectenerg-400	550	6	-	-	PUNCT
fuelectenerg-400	550	7	based	base	VERB
fuelectenerg-400	550	8	representation	representation	NOUN
fuelectenerg-400	550	9	of	of	ADP
fuelectenerg-400	550	10	ri	ri	PROPN
fuelectenerg-400	550	11	is	be	AUX
fuelectenerg-400	550	12	a	a	DET
fuelectenerg-400	550	13	string	string	NOUN
fuelectenerg-400	550	14	of	of	ADP
fuelectenerg-400	550	15	integers	integer	NOUN
fuelectenerg-400	550	16	in	in	ADP
fuelectenerg-400	550	17	which	which	PRON
fuelectenerg-400	550	18	the	the	DET
fuelectenerg-400	550	19	integers	integer	NOUN
fuelectenerg-400	550	20	are	be	AUX
fuelectenerg-400	550	21	non	non	ADJ
fuelectenerg-400	550	22	-	-	ADJ
fuelectenerg-400	550	23	decreasing	decrease	VERB
fuelectenerg-400	550	24	.	.	PUNCT
fuelectenerg-400	551	1	we	we	PRON
fuelectenerg-400	551	2	now	now	ADV
fuelectenerg-400	551	3	address	address	VERB
fuelectenerg-400	551	4	ranking	ranking	NOUN
fuelectenerg-400	551	5	and	and	CCONJ
fuelectenerg-400	551	6	unranking	unranking	NOUN
fuelectenerg-400	551	7	of	of	ADP
fuelectenerg-400	551	8	members	member	NOUN
fuelectenerg-400	551	9	.	.	PUNCT
fuelectenerg-400	552	1	ranking	ranking	PROPN
fuelectenerg-400	552	2	,	,	PUNCT
fuelectenerg-400	552	3	denoted	denote	VERB
fuelectenerg-400	552	4	by	by	ADP
fuelectenerg-400	552	5	rank	rank	NOUN
fuelectenerg-400	552	6	refers	refer	VERB
fuelectenerg-400	552	7	to	to	ADP
fuelectenerg-400	552	8	the	the	DET
fuelectenerg-400	552	9	process	process	NOUN
fuelectenerg-400	552	10	mapping	mapping	NOUN
fuelectenerg-400	552	11	of	of	ADP
fuelectenerg-400	552	12	a	a	DET
fuelectenerg-400	552	13	member	member	NOUN
fuelectenerg-400	552	14	of	of	ADP
fuelectenerg-400	552	15	an	an	DET
fuelectenerg-400	552	16	ordered	order	VERB
fuelectenerg-400	552	17	set	set	NOUN
fuelectenerg-400	552	18	to	to	ADP
fuelectenerg-400	552	19	a	a	DET
fuelectenerg-400	552	20	distinct	distinct	ADJ
fuelectenerg-400	552	21	integer	integer	NOUN
fuelectenerg-400	552	22	.	.	PUNCT
fuelectenerg-400	553	1	unranking	unranking	NOUN
fuelectenerg-400	553	2	is	be	AUX
fuelectenerg-400	553	3	its	its	PRON
fuelectenerg-400	553	4	inverse	inverse	NOUN
fuelectenerg-400	553	5	operation	operation	NOUN
fuelectenerg-400	553	6	.	.	PUNCT
fuelectenerg-400	554	1	we	we	PRON
fuelectenerg-400	554	2	use	use	VERB
fuelectenerg-400	554	3	ranking	rank	VERB
fuelectenerg-400	554	4	and	and	CCONJ
fuelectenerg-400	554	5	unranking	unranking	ADJ
fuelectenerg-400	554	6	algorithms	algorithm	NOUN
fuelectenerg-400	554	7	on	on	ADP
fuelectenerg-400	554	8	the	the	DET
fuelectenerg-400	554	9	reverse	reverse	NOUN
fuelectenerg-400	554	10	lexicographically	lexicographically	ADV
fuelectenerg-400	554	11	ordered	order	VERB
fuelectenerg-400	554	12	set	set	NOUN
fuelectenerg-400	554	13	d(n	d(n	PROPN
fuelectenerg-400	554	14	,	,	PUNCT
fuelectenerg-400	554	15	k	k	NOUN
fuelectenerg-400	554	16	)	)	PUNCT
fuelectenerg-400	554	17	for	for	ADP
fuelectenerg-400	554	18	encoding	encode	VERB
fuelectenerg-400	554	19	data	datum	NOUN
fuelectenerg-400	554	20	532	532	NUM
fuelectenerg-400	554	21	b.	b.	PROPN
fuelectenerg-400	554	22	vasic	vasic	PROPN
fuelectenerg-400	554	23	,	,	PUNCT
fuelectenerg-400	554	24	a.	a.	PROPN
fuelectenerg-400	554	25	r.	r.	PROPN
fuelectenerg-400	554	26	krishnan	krishnan	PROPN
fuelectenerg-400	554	27	lozenge	lozenge	PROPN
fuelectenerg-400	554	28	tiling	tile	VERB
fuelectenerg-400	554	29	constrained	constrained	ADJ
fuelectenerg-400	554	30	codes	code	NOUN
fuelectenerg-400	554	31	533	533	NUM
fuelectenerg-400	554	32	534	534	NUM
fuelectenerg-400	554	33	a.	a.	NOUN
fuelectenerg-400	554	34	r.	r.	PROPN
fuelectenerg-400	554	35	krishnanan	krishnanan	PROPN
fuelectenerg-400	554	36	and	and	CCONJ
fuelectenerg-400	554	37	b.	b.	PROPN
fuelectenerg-400	554	38	vasić	vasić	PROPN
fuelectenerg-400	554	39	fig	fig	PROPN
fuelectenerg-400	554	40	.	.	PUNCT
fuelectenerg-400	555	1	10	10	NUM
fuelectenerg-400	555	2	.	.	X
fuelectenerg-400	555	3	ranking	rank	VERB
fuelectenerg-400	555	4	of	of	ADP
fuelectenerg-400	555	5	string	string	NOUN
fuelectenerg-400	555	6	110010	110010	NUM
fuelectenerg-400	555	7	.	.	PUNCT
fuelectenerg-400	556	1	vertex	vertex	NOUN
fuelectenerg-400	556	2	labels	label	NOUN
fuelectenerg-400	556	3	denote	denote	VERB
fuelectenerg-400	556	4	the	the	DET
fuelectenerg-400	556	5	number	number	NOUN
fuelectenerg-400	556	6	of	of	ADP
fuelectenerg-400	556	7	possible	possible	ADJ
fuelectenerg-400	556	8	sequences	sequence	NOUN
fuelectenerg-400	556	9	from	from	ADP
fuelectenerg-400	556	10	the	the	DET
fuelectenerg-400	556	11	corresponding	correspond	VERB
fuelectenerg-400	556	12	node	node	NOUN
fuelectenerg-400	556	13	to	to	ADP
fuelectenerg-400	556	14	a	a	DET
fuelectenerg-400	556	15	drain	drain	NOUN
fuelectenerg-400	556	16	.	.	PUNCT
fuelectenerg-400	557	1	the	the	DET
fuelectenerg-400	557	2	edge	edge	NOUN
fuelectenerg-400	557	3	labels	label	NOUN
fuelectenerg-400	557	4	on	on	ADP
fuelectenerg-400	557	5	the	the	DET
fuelectenerg-400	557	6	mountain	mountain	NOUN
fuelectenerg-400	557	7	range	range	NOUN
fuelectenerg-400	557	8	,	,	PUNCT
fuelectenerg-400	557	9	shown	show	VERB
fuelectenerg-400	557	10	as	as	ADP
fuelectenerg-400	557	11	a	a	DET
fuelectenerg-400	557	12	bold	bold	ADJ
fuelectenerg-400	557	13	path	path	NOUN
fuelectenerg-400	557	14	,	,	PUNCT
fuelectenerg-400	557	15	correspond	correspond	VERB
fuelectenerg-400	557	16	to	to	ADP
fuelectenerg-400	557	17	intermediate	intermediate	ADJ
fuelectenerg-400	557	18	steps	step	NOUN
fuelectenerg-400	557	19	of	of	ADP
fuelectenerg-400	557	20	rank	rank	NOUN
fuelectenerg-400	557	21	computation	computation	NOUN
fuelectenerg-400	557	22	.	.	PUNCT
fuelectenerg-400	558	1	to	to	ADP
fuelectenerg-400	558	2	tilings	tiling	NOUN
fuelectenerg-400	558	3	.	.	PUNCT
fuelectenerg-400	559	1	ranking	ranking	ADJ
fuelectenerg-400	559	2	and	and	CCONJ
fuelectenerg-400	559	3	unranking	unranking	ADJ
fuelectenerg-400	559	4	algorithms	algorithm	NOUN
fuelectenerg-400	559	5	for	for	ADP
fuelectenerg-400	559	6	this	this	DET
fuelectenerg-400	559	7	set	set	NOUN
fuelectenerg-400	559	8	are	be	AUX
fuelectenerg-400	559	9	available	available	ADJ
fuelectenerg-400	559	10	[	[	X
fuelectenerg-400	559	11	23,24	23,24	NUM
fuelectenerg-400	559	12	]	]	PUNCT
fuelectenerg-400	559	13	.	.	PUNCT
fuelectenerg-400	560	1	we	we	PRON
fuelectenerg-400	560	2	have	have	AUX
fuelectenerg-400	560	3	designed	design	VERB
fuelectenerg-400	560	4	algorithms	algorithm	NOUN
fuelectenerg-400	560	5	using	use	VERB
fuelectenerg-400	560	6	methods	method	NOUN
fuelectenerg-400	560	7	similar	similar	ADJ
fuelectenerg-400	560	8	to	to	ADP
fuelectenerg-400	560	9	[	[	X
fuelectenerg-400	560	10	22	22	NUM
fuelectenerg-400	560	11	]	]	PUNCT
fuelectenerg-400	560	12	.	.	PUNCT
fuelectenerg-400	561	1	to	to	PART
fuelectenerg-400	561	2	perform	perform	VERB
fuelectenerg-400	561	3	the	the	DET
fuelectenerg-400	561	4	ranking	ranking	NOUN
fuelectenerg-400	561	5	,	,	PUNCT
fuelectenerg-400	561	6	first	first	ADV
fuelectenerg-400	561	7	the	the	DET
fuelectenerg-400	561	8	number	number	NOUN
fuelectenerg-400	561	9	of	of	ADP
fuelectenerg-400	561	10	paths	path	NOUN
fuelectenerg-400	561	11	passing	pass	VERB
fuelectenerg-400	561	12	through	through	ADP
fuelectenerg-400	561	13	every	every	DET
fuelectenerg-400	561	14	node	node	NOUN
fuelectenerg-400	561	15	(	(	PUNCT
fuelectenerg-400	561	16	x	x	NOUN
fuelectenerg-400	561	17	,	,	PUNCT
fuelectenerg-400	561	18	y	y	NOUN
fuelectenerg-400	561	19	)	)	PUNCT
fuelectenerg-400	561	20	in	in	ADP
fuelectenerg-400	561	21	g	g	NOUN
fuelectenerg-400	561	22	,	,	PUNCT
fuelectenerg-400	561	23	n(x	n(x	PROPN
fuelectenerg-400	561	24	,	,	PUNCT
fuelectenerg-400	561	25	y	y	NOUN
fuelectenerg-400	561	26	)	)	PUNCT
fuelectenerg-400	561	27	is	be	AUX
fuelectenerg-400	561	28	calculated	calculate	VERB
fuelectenerg-400	561	29	.	.	PUNCT
fuelectenerg-400	562	1	the	the	DET
fuelectenerg-400	562	2	rank	rank	NOUN
fuelectenerg-400	562	3	is	be	AUX
fuelectenerg-400	562	4	calculated	calculate	VERB
fuelectenerg-400	562	5	by	by	ADP
fuelectenerg-400	562	6	starting	start	VERB
fuelectenerg-400	562	7	with	with	ADP
fuelectenerg-400	562	8	an	an	DET
fuelectenerg-400	562	9	initial	initial	ADJ
fuelectenerg-400	562	10	estimate	estimate	NOUN
fuelectenerg-400	562	11	of	of	ADP
fuelectenerg-400	562	12	rank	rank	NOUN
fuelectenerg-400	562	13	(=	(=	NOUN
fuelectenerg-400	562	14	0	0	NUM
fuelectenerg-400	562	15	)	)	PUNCT
fuelectenerg-400	562	16	and	and	CCONJ
fuelectenerg-400	562	17	then	then	ADV
fuelectenerg-400	562	18	refining	refine	VERB
fuelectenerg-400	562	19	the	the	DET
fuelectenerg-400	562	20	estimate	estimate	NOUN
fuelectenerg-400	562	21	as	as	SCONJ
fuelectenerg-400	562	22	the	the	DET
fuelectenerg-400	562	23	sequence	sequence	NOUN
fuelectenerg-400	562	24	is	be	AUX
fuelectenerg-400	562	25	parsed	parse	VERB
fuelectenerg-400	562	26	bit	bit	NOUN
fuelectenerg-400	562	27	by	by	ADP
fuelectenerg-400	562	28	bit	bit	NOUN
fuelectenerg-400	562	29	.	.	PUNCT
fuelectenerg-400	563	1	from	from	ADP
fuelectenerg-400	563	2	any	any	DET
fuelectenerg-400	563	3	node	node	NOUN
fuelectenerg-400	563	4	(	(	PUNCT
fuelectenerg-400	563	5	x	x	NOUN
fuelectenerg-400	563	6	,	,	PUNCT
fuelectenerg-400	563	7	y	y	PROPN
fuelectenerg-400	563	8	)	)	PUNCT
fuelectenerg-400	563	9	,	,	PUNCT
fuelectenerg-400	563	10	if	if	SCONJ
fuelectenerg-400	563	11	the	the	DET
fuelectenerg-400	563	12	next	next	ADJ
fuelectenerg-400	563	13	bit	bit	NOUN
fuelectenerg-400	563	14	is	be	AUX
fuelectenerg-400	563	15	0	0	NUM
fuelectenerg-400	563	16	,	,	PUNCT
fuelectenerg-400	563	17	the	the	DET
fuelectenerg-400	563	18	corresponding	corresponding	ADJ
fuelectenerg-400	563	19	point	point	NOUN
fuelectenerg-400	563	20	in	in	ADP
fuelectenerg-400	563	21	the	the	DET
fuelectenerg-400	563	22	cartesian	cartesian	ADJ
fuelectenerg-400	563	23	plane	plane	NOUN
fuelectenerg-400	563	24	is	be	AUX
fuelectenerg-400	563	25	(	(	PUNCT
fuelectenerg-400	563	26	x	x	SYM
fuelectenerg-400	563	27	+	+	NUM
fuelectenerg-400	563	28	1	1	NUM
fuelectenerg-400	563	29	,	,	PUNCT
fuelectenerg-400	563	30	y	y	PROPN
fuelectenerg-400	563	31	−	−	PROPN
fuelectenerg-400	563	32	1	1	NUM
fuelectenerg-400	563	33	)	)	PUNCT
fuelectenerg-400	563	34	.	.	PUNCT
fuelectenerg-400	564	1	this	this	PRON
fuelectenerg-400	564	2	implies	imply	VERB
fuelectenerg-400	564	3	that	that	SCONJ
fuelectenerg-400	564	4	all	all	DET
fuelectenerg-400	564	5	sequences	sequence	NOUN
fuelectenerg-400	564	6	which	which	PRON
fuelectenerg-400	564	7	start	start	VERB
fuelectenerg-400	564	8	from	from	ADP
fuelectenerg-400	564	9	the	the	DET
fuelectenerg-400	564	10	node	node	NOUN
fuelectenerg-400	564	11	(	(	PUNCT
fuelectenerg-400	564	12	x+1	x+1	PROPN
fuelectenerg-400	564	13	,	,	PUNCT
fuelectenerg-400	564	14	y+1	y+1	NUM
fuelectenerg-400	564	15	)	)	PUNCT
fuelectenerg-400	564	16	have	have	VERB
fuelectenerg-400	564	17	a	a	DET
fuelectenerg-400	564	18	lower	low	ADJ
fuelectenerg-400	564	19	rank	rank	NOUN
fuelectenerg-400	564	20	.	.	PUNCT
fuelectenerg-400	565	1	thus	thus	ADV
fuelectenerg-400	565	2	,	,	PUNCT
fuelectenerg-400	565	3	given	give	VERB
fuelectenerg-400	565	4	that	that	SCONJ
fuelectenerg-400	565	5	the	the	DET
fuelectenerg-400	565	6	current	current	ADJ
fuelectenerg-400	565	7	estimate	estimate	NOUN
fuelectenerg-400	565	8	is	be	AUX
fuelectenerg-400	565	9	e	e	NOUN
fuelectenerg-400	565	10	,	,	PUNCT
fuelectenerg-400	565	11	the	the	DET
fuelectenerg-400	565	12	rank	rank	NOUN
fuelectenerg-400	565	13	of	of	ADP
fuelectenerg-400	565	14	this	this	DET
fuelectenerg-400	565	15	sequence	sequence	NOUN
fuelectenerg-400	565	16	is	be	AUX
fuelectenerg-400	565	17	greater	great	ADJ
fuelectenerg-400	565	18	than	than	ADP
fuelectenerg-400	565	19	e	e	NOUN
fuelectenerg-400	565	20	+	+	CCONJ
fuelectenerg-400	565	21	n(x+1,y+1	n(x+1,y+1	NOUN
fuelectenerg-400	565	22	)	)	PUNCT
fuelectenerg-400	565	23	.	.	PUNCT
fuelectenerg-400	566	1	hence	hence	ADV
fuelectenerg-400	566	2	the	the	DET
fuelectenerg-400	566	3	estimate	estimate	NOUN
fuelectenerg-400	566	4	can	can	AUX
fuelectenerg-400	566	5	be	be	AUX
fuelectenerg-400	566	6	refined	refine	VERB
fuelectenerg-400	566	7	by	by	ADP
fuelectenerg-400	566	8	adding	add	VERB
fuelectenerg-400	566	9	the	the	DET
fuelectenerg-400	566	10	number	number	NOUN
fuelectenerg-400	566	11	to	to	ADP
fuelectenerg-400	566	12	the	the	DET
fuelectenerg-400	566	13	current	current	ADJ
fuelectenerg-400	566	14	estimate	estimate	NOUN
fuelectenerg-400	566	15	.	.	PUNCT
fuelectenerg-400	567	1	this	this	DET
fuelectenerg-400	567	2	process	process	NOUN
fuelectenerg-400	567	3	is	be	AUX
fuelectenerg-400	567	4	continued	continue	VERB
fuelectenerg-400	567	5	till	till	SCONJ
fuelectenerg-400	567	6	all	all	DET
fuelectenerg-400	567	7	the	the	DET
fuelectenerg-400	567	8	bits	bit	NOUN
fuelectenerg-400	567	9	are	be	AUX
fuelectenerg-400	567	10	parsed	parse	VERB
fuelectenerg-400	567	11	.	.	PUNCT
fuelectenerg-400	568	1	the	the	DET
fuelectenerg-400	568	2	final	final	ADJ
fuelectenerg-400	568	3	estimate	estimate	NOUN
fuelectenerg-400	568	4	is	be	AUX
fuelectenerg-400	568	5	the	the	DET
fuelectenerg-400	568	6	rank	rank	NOUN
fuelectenerg-400	568	7	of	of	ADP
fuelectenerg-400	568	8	the	the	DET
fuelectenerg-400	568	9	sequence	sequence	NOUN
fuelectenerg-400	568	10	.	.	PUNCT
fuelectenerg-400	569	1	figure	figure	NOUN
fuelectenerg-400	569	2	10	10	NUM
fuelectenerg-400	569	3	shows	show	NOUN
fuelectenerg-400	569	4	flow	flow	NOUN
fuelectenerg-400	569	5	of	of	ADP
fuelectenerg-400	569	6	the	the	DET
fuelectenerg-400	569	7	algorithm	algorithm	NOUN
fuelectenerg-400	569	8	for	for	ADP
fuelectenerg-400	569	9	the	the	DET
fuelectenerg-400	569	10	sequence	sequence	NOUN
fuelectenerg-400	569	11	110010	110010	NUM
fuelectenerg-400	569	12	,	,	PUNCT
fuelectenerg-400	569	13	a	a	DET
fuelectenerg-400	569	14	member	member	NOUN
fuelectenerg-400	569	15	of	of	ADP
fuelectenerg-400	569	16	d(6,3	d(6,3	NOUN
fuelectenerg-400	569	17	)	)	PUNCT
fuelectenerg-400	569	18	.	.	PUNCT
fuelectenerg-400	570	1	the	the	DET
fuelectenerg-400	570	2	number	number	NOUN
fuelectenerg-400	570	3	of	of	ADP
fuelectenerg-400	570	4	sequences	sequence	NOUN
fuelectenerg-400	570	5	passing	pass	VERB
fuelectenerg-400	570	6	through	through	ADP
fuelectenerg-400	570	7	every	every	DET
fuelectenerg-400	570	8	node	node	NOUN
fuelectenerg-400	570	9	is	be	AUX
fuelectenerg-400	570	10	marked	mark	VERB
fuelectenerg-400	570	11	next	next	ADV
fuelectenerg-400	570	12	to	to	ADP
fuelectenerg-400	570	13	the	the	DET
fuelectenerg-400	570	14	node	node	NOUN
fuelectenerg-400	570	15	.	.	PUNCT
fuelectenerg-400	571	1	the	the	DET
fuelectenerg-400	571	2	refinement	refinement	NOUN
fuelectenerg-400	571	3	of	of	ADP
fuelectenerg-400	571	4	the	the	DET
fuelectenerg-400	571	5	rank	rank	NOUN
fuelectenerg-400	571	6	at	at	ADP
fuelectenerg-400	571	7	every	every	DET
fuelectenerg-400	571	8	bit	bit	NOUN
fuelectenerg-400	571	9	is	be	AUX
fuelectenerg-400	571	10	shown	show	VERB
fuelectenerg-400	571	11	in	in	ADP
fuelectenerg-400	571	12	the	the	DET
fuelectenerg-400	571	13	figure	figure	NOUN
fuelectenerg-400	571	14	.	.	PUNCT
fuelectenerg-400	572	1	at	at	ADP
fuelectenerg-400	572	2	the	the	DET
fuelectenerg-400	572	3	last	last	ADJ
fuelectenerg-400	572	4	bit	bit	NOUN
fuelectenerg-400	572	5	,	,	PUNCT
fuelectenerg-400	572	6	the	the	DET
fuelectenerg-400	572	7	rank	rank	NOUN
fuelectenerg-400	572	8	is	be	AUX
fuelectenerg-400	572	9	calculated	calculate	VERB
fuelectenerg-400	572	10	as	as	ADP
fuelectenerg-400	572	11	2	2	NUM
fuelectenerg-400	572	12	.	.	NOUN
fuelectenerg-400	572	13	similar	similar	ADJ
fuelectenerg-400	572	14	approach	approach	NOUN
fuelectenerg-400	572	15	can	can	AUX
fuelectenerg-400	572	16	be	be	AUX
fuelectenerg-400	572	17	used	use	VERB
fuelectenerg-400	572	18	to	to	PART
fuelectenerg-400	572	19	unrank	unrank	VERB
fuelectenerg-400	572	20	an	an	DET
fuelectenerg-400	572	21	integer	integer	NOUN
fuelectenerg-400	572	22	.	.	PUNCT
fuelectenerg-400	573	1	through	through	ADP
fuelectenerg-400	573	2	the	the	DET
fuelectenerg-400	573	3	rest	rest	NOUN
fuelectenerg-400	573	4	of	of	ADP
fuelectenerg-400	573	5	this	this	DET
fuelectenerg-400	573	6	document	document	NOUN
fuelectenerg-400	573	7	,	,	PUNCT
fuelectenerg-400	573	8	the	the	DET
fuelectenerg-400	573	9	ranking	ranking	NOUN
fuelectenerg-400	573	10	and	and	CCONJ
fuelectenerg-400	573	11	unranking	unranking	NOUN
fuelectenerg-400	573	12	on	on	ADP
fuelectenerg-400	573	13	this	this	DET
fuelectenerg-400	573	14	set	set	NOUN
fuelectenerg-400	573	15	will	will	AUX
fuelectenerg-400	573	16	be	be	AUX
fuelectenerg-400	573	17	denoted	denote	VERB
fuelectenerg-400	573	18	rd	rd	NOUN
fuelectenerg-400	573	19	and	and	CCONJ
fuelectenerg-400	573	20	r−1	r−1	PROPN
fuelectenerg-400	573	21	d	d	PROPN
fuelectenerg-400	573	22	respectively	respectively	ADV
fuelectenerg-400	573	23	.	.	PUNCT
fuelectenerg-400	574	1	it	it	PRON
fuelectenerg-400	574	2	was	be	AUX
fuelectenerg-400	574	3	earlier	early	ADV
fuelectenerg-400	574	4	stated	state	VERB
fuelectenerg-400	574	5	that	that	SCONJ
fuelectenerg-400	574	6	ri	ri	PROPN
fuelectenerg-400	574	7	can	can	AUX
fuelectenerg-400	574	8	be	be	AUX
fuelectenerg-400	574	9	represented	represent	VERB
fuelectenerg-400	574	10	as	as	ADP
fuelectenerg-400	574	11	ri	ri	NOUN
fuelectenerg-400	574	12	=	=	PUNCT
fuelectenerg-400	574	13	{	{	PUNCT
fuelectenerg-400	574	14	rank(di	rank(di	NOUN
fuelectenerg-400	574	15	)	)	PUNCT
fuelectenerg-400	574	16	,	,	PUNCT
fuelectenerg-400	575	1	i	i	PRON
fuelectenerg-400	575	2	=	=	NOUN
fuelectenerg-400	575	3	1	1	NUM
fuelectenerg-400	575	4	,	,	PUNCT
fuelectenerg-400	575	5	2	2	NUM
fuelectenerg-400	575	6	,	,	PUNCT
fuelectenerg-400	575	7	.	.	PUNCT
fuelectenerg-400	575	8	.	.	PUNCT
fuelectenerg-400	575	9	.	.	PUNCT
fuelectenerg-400	576	1	,	,	PUNCT
fuelectenerg-400	576	2	c	c	X
fuelectenerg-400	576	3	}	}	PUNCT
fuelectenerg-400	576	4	.	.	PUNCT
fuelectenerg-400	577	1	we	we	PRON
fuelectenerg-400	577	2	note	note	VERB
fuelectenerg-400	577	3	that	that	SCONJ
fuelectenerg-400	577	4	the	the	DET
fuelectenerg-400	577	5	rank	rank	NOUN
fuelectenerg-400	577	6	of	of	ADP
fuelectenerg-400	577	7	each	each	DET
fuelectenerg-400	577	8	dsi	dsi	NOUN
fuelectenerg-400	577	9	is	be	AUX
fuelectenerg-400	577	10	between	between	ADP
fuelectenerg-400	577	11	0	0	NUM
fuelectenerg-400	577	12	and	and	CCONJ
fuelectenerg-400	577	13	(	(	PUNCT
fuelectenerg-400	577	14	a+b	a+b	NUM
fuelectenerg-400	577	15	b	b	NOUN
fuelectenerg-400	577	16	)	)	PUNCT
fuelectenerg-400	577	17	−1	−1	NOUN
fuelectenerg-400	577	18	.	.	PUNCT
fuelectenerg-400	578	1	also	also	ADV
fuelectenerg-400	578	2	,	,	PUNCT
fuelectenerg-400	578	3	we	we	PRON
fuelectenerg-400	578	4	noted	note	VERB
fuelectenerg-400	578	5	that	that	SCONJ
fuelectenerg-400	578	6	for	for	ADP
fuelectenerg-400	578	7	all	all	DET
fuelectenerg-400	578	8	di	di	NOUN
fuelectenerg-400	578	9	,	,	PUNCT
fuelectenerg-400	578	10	dj	dj	ADP
fuelectenerg-400	578	11	such	such	ADJ
fuelectenerg-400	578	12	that	that	SCONJ
fuelectenerg-400	578	13	i	i	PRON
fuelectenerg-400	578	14	<	<	X
fuelectenerg-400	578	15	j	j	PROPN
fuelectenerg-400	578	16	,	,	PUNCT
fuelectenerg-400	578	17	rank(di	rank(di	NOUN
fuelectenerg-400	578	18	)	)	PUNCT
fuelectenerg-400	578	19	≤	≤	NOUN
fuelectenerg-400	578	20	rank(dj	rank(dj	NOUN
fuelectenerg-400	578	21	)	)	PUNCT
fuelectenerg-400	578	22	.	.	PUNCT
fuelectenerg-400	579	1	now	now	ADV
fuelectenerg-400	579	2	,	,	PUNCT
fuelectenerg-400	579	3	we	we	PRON
fuelectenerg-400	579	4	consider	consider	VERB
fuelectenerg-400	579	5	the	the	DET
fuelectenerg-400	579	6	rankbased	rankbase	VERB
fuelectenerg-400	579	7	representation	representation	NOUN
fuelectenerg-400	579	8	which	which	PRON
fuelectenerg-400	579	9	is	be	AUX
fuelectenerg-400	579	10	the	the	DET
fuelectenerg-400	579	11	ordered	order	VERB
fuelectenerg-400	579	12	set	set	NOUN
fuelectenerg-400	579	13	{	{	PUNCT
fuelectenerg-400	579	14	rank(di	rank(di	NOUN
fuelectenerg-400	579	15	)	)	PUNCT
fuelectenerg-400	579	16	,	,	PUNCT
fuelectenerg-400	579	17	i	i	PRON
fuelectenerg-400	579	18	=	=	NOUN
fuelectenerg-400	579	19	1	1	NUM
fuelectenerg-400	579	20	,	,	PUNCT
fuelectenerg-400	579	21	2	2	NUM
fuelectenerg-400	579	22	,	,	PUNCT
fuelectenerg-400	579	23	.	.	PUNCT
fuelectenerg-400	579	24	.	.	PUNCT
fuelectenerg-400	579	25	.	.	PUNCT
fuelectenerg-400	580	1	,	,	PUNCT
fuelectenerg-400	580	2	a|di	a|di	NOUN
fuelectenerg-400	580	3	∈	∈	PROPN
fuelectenerg-400	580	4	d(a+b	d(a+b	PRON
fuelectenerg-400	580	5	,	,	PUNCT
fuelectenerg-400	580	6	b	b	NOUN
fuelectenerg-400	580	7	)	)	PUNCT
fuelectenerg-400	580	8	}	}	PUNCT
fuelectenerg-400	580	9	.	.	PUNCT
fuelectenerg-400	581	1	this	this	DET
fuelectenerg-400	581	2	set	set	NOUN
fuelectenerg-400	581	3	can	can	AUX
fuelectenerg-400	581	4	be	be	AUX
fuelectenerg-400	581	5	expressed	express	VERB
fuelectenerg-400	581	6	as	as	ADP
fuelectenerg-400	581	7	a	a	DET
fuelectenerg-400	581	8	non	non	ADJ
fuelectenerg-400	581	9	-	-	ADJ
fuelectenerg-400	581	10	decreasing	decrease	VERB
fuelectenerg-400	581	11	string	string	NOUN
fuelectenerg-400	581	12	of	of	ADP
fuelectenerg-400	581	13	length	length	NOUN
fuelectenerg-400	581	14	c	c	NOUN
fuelectenerg-400	581	15	with	with	ADP
fuelectenerg-400	581	16	members	member	NOUN
fuelectenerg-400	581	17	of	of	ADP
fuelectenerg-400	581	18	the	the	DET
fuelectenerg-400	581	19	set	set	NOUN
fuelectenerg-400	581	20	{	{	PUNCT
fuelectenerg-400	581	21	1	1	NUM
fuelectenerg-400	581	22	,	,	PUNCT
fuelectenerg-400	581	23	2	2	NUM
fuelectenerg-400	581	24	,	,	PUNCT
fuelectenerg-400	581	25	.	.	PUNCT
fuelectenerg-400	581	26	.	.	PUNCT
fuelectenerg-400	582	1	.	.	PUNCT
fuelectenerg-400	583	1	,	,	PUNCT
fuelectenerg-400	583	2	(	(	PUNCT
fuelectenerg-400	583	3	a+b	a+b	NUM
fuelectenerg-400	583	4	b	b	NOUN
fuelectenerg-400	583	5	)	)	PUNCT
fuelectenerg-400	583	6	}	}	PUNCT
fuelectenerg-400	583	7	.	.	PUNCT
fuelectenerg-400	584	1	we	we	PRON
fuelectenerg-400	584	2	can	can	AUX
fuelectenerg-400	584	3	further	far	ADV
fuelectenerg-400	584	4	reduce	reduce	VERB
fuelectenerg-400	584	5	the	the	DET
fuelectenerg-400	584	6	complexity	complexity	NOUN
fuelectenerg-400	584	7	of	of	ADP
fuelectenerg-400	584	8	representation	representation	NOUN
fuelectenerg-400	584	9	of	of	ADP
fuelectenerg-400	584	10	elements	element	NOUN
fuelectenerg-400	584	11	of	of	ADP
fuelectenerg-400	584	12	r	r	NOUN
fuelectenerg-400	584	13	if	if	SCONJ
fuelectenerg-400	584	14	the	the	DET
fuelectenerg-400	584	15	non	non	ADJ
fuelectenerg-400	584	16	-	-	ADJ
fuelectenerg-400	584	17	decreasing	decrease	VERB
fuelectenerg-400	584	18	strings	string	NOUN
fuelectenerg-400	584	19	can	can	AUX
fuelectenerg-400	584	20	be	be	AUX
fuelectenerg-400	584	21	ordered	order	VERB
fuelectenerg-400	584	22	.	.	PUNCT
fuelectenerg-400	585	1	section	section	NOUN
fuelectenerg-400	585	2	5.3	5.3	NUM
fuelectenerg-400	585	3	deals	deal	NOUN
fuelectenerg-400	585	4	with	with	ADP
fuelectenerg-400	585	5	this	this	PRON
fuelectenerg-400	585	6	.	.	PUNCT
fuelectenerg-400	586	1	5.3	5.3	NUM
fuelectenerg-400	586	2	lexicographical	lexicographical	ADJ
fuelectenerg-400	586	3	ordering	ordering	NOUN
fuelectenerg-400	586	4	of	of	ADP
fuelectenerg-400	586	5	non	non	ADJ
fuelectenerg-400	586	6	-	-	ADJ
fuelectenerg-400	586	7	decreasing	decrease	VERB
fuelectenerg-400	586	8	strings	string	NOUN
fuelectenerg-400	586	9	this	this	DET
fuelectenerg-400	586	10	section	section	NOUN
fuelectenerg-400	586	11	deals	deal	VERB
fuelectenerg-400	586	12	with	with	ADP
fuelectenerg-400	586	13	the	the	DET
fuelectenerg-400	586	14	lexicographical	lexicographical	ADJ
fuelectenerg-400	586	15	ordering	ordering	NOUN
fuelectenerg-400	586	16	in	in	ADP
fuelectenerg-400	586	17	the	the	DET
fuelectenerg-400	586	18	set	set	NOUN
fuelectenerg-400	586	19	of	of	ADP
fuelectenerg-400	586	20	non	non	ADJ
fuelectenerg-400	586	21	-	-	ADJ
fuelectenerg-400	586	22	decreasing	decrease	VERB
fuelectenerg-400	586	23	strings	string	NOUN
fuelectenerg-400	586	24	of	of	ADP
fuelectenerg-400	586	25	length	length	NOUN
fuelectenerg-400	586	26	n	n	PRON
fuelectenerg-400	586	27	consisting	consist	VERB
fuelectenerg-400	586	28	of	of	ADP
fuelectenerg-400	586	29	members	member	NOUN
fuelectenerg-400	586	30	of	of	ADP
fuelectenerg-400	586	31	the	the	DET
fuelectenerg-400	586	32	set	set	NOUN
fuelectenerg-400	586	33	n	n	NOUN
fuelectenerg-400	586	34	=	=	SYM
fuelectenerg-400	586	35	{	{	PUNCT
fuelectenerg-400	586	36	1	1	NUM
fuelectenerg-400	586	37	,	,	PUNCT
fuelectenerg-400	586	38	2	2	NUM
fuelectenerg-400	586	39	,	,	PUNCT
fuelectenerg-400	586	40	3	3	NUM
fuelectenerg-400	586	41	,	,	PUNCT
fuelectenerg-400	586	42	...	...	PUNCT
fuelectenerg-400	586	43	,	,	PUNCT
fuelectenerg-400	586	44	n	n	CCONJ
fuelectenerg-400	586	45	}	}	PUNCT
fuelectenerg-400	586	46	.	.	PUNCT
fuelectenerg-400	587	1	this	this	DET
fuelectenerg-400	587	2	detection	detection	NOUN
fuelectenerg-400	587	3	and	and	CCONJ
fuelectenerg-400	587	4	coding	code	VERB
fuelectenerg-400	587	5	for	for	ADP
fuelectenerg-400	587	6	tdmr	tdmr	NOUN
fuelectenerg-400	587	7	channel	channel	NOUN
fuelectenerg-400	587	8	535	535	NUM
fuelectenerg-400	587	9	set	set	NOUN
fuelectenerg-400	587	10	is	be	AUX
fuelectenerg-400	587	11	denoted	denote	VERB
fuelectenerg-400	587	12	sn	sn	PROPN
fuelectenerg-400	587	13	n	n	NOUN
fuelectenerg-400	587	14	and	and	CCONJ
fuelectenerg-400	587	15	is	be	AUX
fuelectenerg-400	587	16	defined	define	VERB
fuelectenerg-400	587	17	as	as	ADP
fuelectenerg-400	587	18	the	the	DET
fuelectenerg-400	587	19	set	set	NOUN
fuelectenerg-400	587	20	of	of	ADP
fuelectenerg-400	587	21	all	all	DET
fuelectenerg-400	587	22	strings	string	NOUN
fuelectenerg-400	587	23	,	,	PUNCT
fuelectenerg-400	587	24	d	d	NOUN
fuelectenerg-400	587	25	of	of	ADP
fuelectenerg-400	587	26	length	length	NOUN
fuelectenerg-400	587	27	n	n	PRON
fuelectenerg-400	587	28	such	such	ADJ
fuelectenerg-400	587	29	that	that	PRON
fuelectenerg-400	587	30	for	for	ADP
fuelectenerg-400	587	31	all	all	DET
fuelectenerg-400	587	32	i	i	PRON
fuelectenerg-400	587	33	,	,	PUNCT
fuelectenerg-400	587	34	1	1	NUM
fuelectenerg-400	587	35	≤	≤	NUM
fuelectenerg-400	587	36	i	i	X
fuelectenerg-400	587	37	≤	≤	PROPN
fuelectenerg-400	587	38	n−1	n−1	PROPN
fuelectenerg-400	587	39	,	,	PUNCT
fuelectenerg-400	587	40	d(i	d(i	PROPN
fuelectenerg-400	587	41	)	)	PUNCT
fuelectenerg-400	587	42	,	,	PUNCT
fuelectenerg-400	587	43	d(i+1	d(i+1	NOUN
fuelectenerg-400	587	44	)	)	PUNCT
fuelectenerg-400	587	45	∈	∈	PROPN
fuelectenerg-400	587	46	n	n	PROPN
fuelectenerg-400	587	47	and	and	CCONJ
fuelectenerg-400	587	48	d(i	d(i	PROPN
fuelectenerg-400	587	49	)	)	PUNCT
fuelectenerg-400	587	50	≤	≤	NUM
fuelectenerg-400	587	51	d(i+1	d(i+1	NOUN
fuelectenerg-400	587	52	)	)	PUNCT
fuelectenerg-400	587	53	.	.	PUNCT
fuelectenerg-400	588	1	the	the	DET
fuelectenerg-400	588	2	set	set	VERB
fuelectenerg-400	588	3	sn	sn	PROPN
fuelectenerg-400	588	4	n	n	VERB
fuelectenerg-400	588	5	is	be	AUX
fuelectenerg-400	588	6	said	say	VERB
fuelectenerg-400	588	7	to	to	PART
fuelectenerg-400	588	8	be	be	AUX
fuelectenerg-400	588	9	lexicographically	lexicographically	ADV
fuelectenerg-400	588	10	ordered	order	VERB
fuelectenerg-400	588	11	if	if	SCONJ
fuelectenerg-400	588	12	for	for	ADP
fuelectenerg-400	588	13	any	any	DET
fuelectenerg-400	588	14	d1	d1	NOUN
fuelectenerg-400	588	15	,	,	PUNCT
fuelectenerg-400	588	16	d2	d2	PROPN
fuelectenerg-400	588	17	∈	∈	PROPN
fuelectenerg-400	588	18	sn	sn	PROPN
fuelectenerg-400	588	19	n	n	PROPN
fuelectenerg-400	588	20	,	,	PUNCT
fuelectenerg-400	588	21	d1(i	d1(i	NOUN
fuelectenerg-400	588	22	)	)	PUNCT
fuelectenerg-400	588	23	≤	≤	NUM
fuelectenerg-400	588	24	d2(i	d2(i	PROPN
fuelectenerg-400	588	25	)	)	PUNCT
fuelectenerg-400	588	26	∀i	∀i	NOUN
fuelectenerg-400	588	27	⇔	⇔	X
fuelectenerg-400	588	28	rank(d1	rank(d1	X
fuelectenerg-400	588	29	)	)	PUNCT
fuelectenerg-400	588	30	≤	≤	NUM
fuelectenerg-400	588	31	rank(d2	rank(d2	NOUN
fuelectenerg-400	588	32	)	)	PUNCT
fuelectenerg-400	588	33	,	,	PUNCT
fuelectenerg-400	588	34	where	where	SCONJ
fuelectenerg-400	588	35	,	,	PUNCT
fuelectenerg-400	588	36	as	as	ADP
fuelectenerg-400	588	37	before	before	ADV
fuelectenerg-400	588	38	,	,	PUNCT
fuelectenerg-400	588	39	rank	rank	NOUN
fuelectenerg-400	588	40	of	of	ADP
fuelectenerg-400	588	41	a	a	DET
fuelectenerg-400	588	42	member	member	NOUN
fuelectenerg-400	588	43	is	be	AUX
fuelectenerg-400	588	44	the	the	DET
fuelectenerg-400	588	45	position	position	NOUN
fuelectenerg-400	588	46	of	of	ADP
fuelectenerg-400	588	47	the	the	DET
fuelectenerg-400	588	48	member	member	NOUN
fuelectenerg-400	588	49	in	in	ADP
fuelectenerg-400	588	50	the	the	DET
fuelectenerg-400	588	51	ordered	order	VERB
fuelectenerg-400	588	52	set	set	NOUN
fuelectenerg-400	588	53	.	.	PUNCT
fuelectenerg-400	589	1	table	table	NOUN
fuelectenerg-400	589	2	2	2	NUM
fuelectenerg-400	589	3	shows	show	VERB
fuelectenerg-400	589	4	the	the	DET
fuelectenerg-400	589	5	set	set	ADJ
fuelectenerg-400	589	6	s2	s2	NOUN
fuelectenerg-400	589	7	3	3	NUM
fuelectenerg-400	589	8	along	along	ADP
fuelectenerg-400	589	9	with	with	ADP
fuelectenerg-400	589	10	the	the	DET
fuelectenerg-400	589	11	rank	rank	NOUN
fuelectenerg-400	589	12	of	of	ADP
fuelectenerg-400	589	13	each	each	DET
fuelectenerg-400	589	14	element	element	NOUN
fuelectenerg-400	589	15	.	.	PUNCT
fuelectenerg-400	590	1	table	table	NOUN
fuelectenerg-400	590	2	2	2	NUM
fuelectenerg-400	590	3	.	.	PUNCT
fuelectenerg-400	591	1	ordering	ordering	NOUN
fuelectenerg-400	591	2	of	of	ADP
fuelectenerg-400	591	3	elements	element	NOUN
fuelectenerg-400	591	4	in	in	ADP
fuelectenerg-400	591	5	s2	s2	PROPN
fuelectenerg-400	591	6	3	3	NUM
fuelectenerg-400	591	7	.	.	PUNCT
fuelectenerg-400	592	1	rank	rank	PROPN
fuelectenerg-400	592	2	string	string	NOUN
fuelectenerg-400	592	3	0	0	NUM
fuelectenerg-400	592	4	111	111	NUM
fuelectenerg-400	592	5	1	1	NUM
fuelectenerg-400	592	6	112	112	NUM
fuelectenerg-400	592	7	2	2	NUM
fuelectenerg-400	592	8	122	122	NUM
fuelectenerg-400	592	9	3	3	NUM
fuelectenerg-400	592	10	222	222	NUM
fuelectenerg-400	592	11	to	to	PART
fuelectenerg-400	592	12	calculate	calculate	VERB
fuelectenerg-400	592	13	the	the	DET
fuelectenerg-400	592	14	size	size	NOUN
fuelectenerg-400	592	15	of	of	ADP
fuelectenerg-400	592	16	sn	sn	PROPN
fuelectenerg-400	593	1	n	n	CCONJ
fuelectenerg-400	593	2	we	we	PRON
fuelectenerg-400	593	3	analyze	analyze	VERB
fuelectenerg-400	593	4	the	the	DET
fuelectenerg-400	593	5	construction	construction	NOUN
fuelectenerg-400	593	6	of	of	ADP
fuelectenerg-400	593	7	strings	string	NOUN
fuelectenerg-400	593	8	of	of	ADP
fuelectenerg-400	593	9	length	length	NOUN
fuelectenerg-400	593	10	k	k	NOUN
fuelectenerg-400	593	11	using	use	VERB
fuelectenerg-400	593	12	strings	string	NOUN
fuelectenerg-400	593	13	of	of	ADP
fuelectenerg-400	593	14	length	length	NOUN
fuelectenerg-400	593	15	k	k	PROPN
fuelectenerg-400	594	1	−	−	PROPN
fuelectenerg-400	594	2	1	1	NUM
fuelectenerg-400	594	3	for	for	ADP
fuelectenerg-400	594	4	k	k	PROPN
fuelectenerg-400	594	5	<	<	X
fuelectenerg-400	594	6	n.	n.	PROPN
fuelectenerg-400	594	7	consider	consider	VERB
fuelectenerg-400	594	8	a	a	DET
fuelectenerg-400	594	9	number	number	NOUN
fuelectenerg-400	594	10	i	i	PRON
fuelectenerg-400	594	11	such	such	ADJ
fuelectenerg-400	594	12	that	that	SCONJ
fuelectenerg-400	594	13	1	1	NUM
fuelectenerg-400	594	14	<	<	X
fuelectenerg-400	594	15	i	i	PROPN
fuelectenerg-400	594	16	≤	≤	ADJ
fuelectenerg-400	594	17	n	n	ADV
fuelectenerg-400	594	18	.	.	PUNCT
fuelectenerg-400	595	1	the	the	DET
fuelectenerg-400	595	2	number	number	NOUN
fuelectenerg-400	595	3	of	of	ADP
fuelectenerg-400	595	4	strings	string	NOUN
fuelectenerg-400	595	5	of	of	ADP
fuelectenerg-400	595	6	length	length	NOUN
fuelectenerg-400	595	7	k	k	PROPN
fuelectenerg-400	595	8	ending	end	VERB
fuelectenerg-400	595	9	in	in	ADP
fuelectenerg-400	595	10	i	i	PROPN
fuelectenerg-400	595	11	,	,	PUNCT
fuelectenerg-400	595	12	n	n	CCONJ
fuelectenerg-400	595	13	i	i	PRON
fuelectenerg-400	595	14	k	k	PROPN
fuelectenerg-400	595	15	is	be	AUX
fuelectenerg-400	595	16	equal	equal	ADJ
fuelectenerg-400	595	17	to	to	ADP
fuelectenerg-400	595	18	the	the	DET
fuelectenerg-400	595	19	number	number	NOUN
fuelectenerg-400	595	20	of	of	ADP
fuelectenerg-400	595	21	strings	string	NOUN
fuelectenerg-400	595	22	of	of	ADP
fuelectenerg-400	595	23	length	length	NOUN
fuelectenerg-400	595	24	(	(	PUNCT
fuelectenerg-400	595	25	k−1	k−1	PROPN
fuelectenerg-400	595	26	)	)	PUNCT
fuelectenerg-400	595	27	ending	end	VERB
fuelectenerg-400	595	28	in	in	ADP
fuelectenerg-400	595	29	digits	digit	NOUN
fuelectenerg-400	595	30	less	less	ADJ
fuelectenerg-400	595	31	than	than	ADP
fuelectenerg-400	595	32	or	or	CCONJ
fuelectenerg-400	595	33	equal	equal	ADJ
fuelectenerg-400	595	34	to	to	ADP
fuelectenerg-400	595	35	i.	i.	NOUN
fuelectenerg-400	595	36	that	that	PRON
fuelectenerg-400	595	37	is	be	AUX
fuelectenerg-400	595	38	,	,	PUNCT
fuelectenerg-400	595	39	n	n	CCONJ
fuelectenerg-400	596	1	i	i	NOUN
fuelectenerg-400	596	2	k	k	NOUN
fuelectenerg-400	597	1	=	=	PUNCT
fuelectenerg-400	597	2	i∑	i∑	PROPN
fuelectenerg-400	597	3	j=1	j=1	PROPN
fuelectenerg-400	597	4	n	n	NUM
fuelectenerg-400	597	5	j	j	PROPN
fuelectenerg-400	597	6	k−1	k−1	PROPN
fuelectenerg-400	597	7	(	(	PUNCT
fuelectenerg-400	597	8	n	n	NOUN
fuelectenerg-400	597	9	i	i	PROPN
fuelectenerg-400	597	10	1	1	NUM
fuelectenerg-400	597	11	=	=	SYM
fuelectenerg-400	597	12	1	1	NUM
fuelectenerg-400	597	13	,	,	PUNCT
fuelectenerg-400	597	14	n1	n1	PROPN
fuelectenerg-400	597	15	k	k	NOUN
fuelectenerg-400	597	16	=	=	SYM
fuelectenerg-400	597	17	1	1	X
fuelectenerg-400	597	18	)	)	PUNCT
fuelectenerg-400	597	19	=	=	NOUN
fuelectenerg-400	597	20	i−1∑	i−1∑	NUM
fuelectenerg-400	597	21	j=1	j=1	PROPN
fuelectenerg-400	597	22	n	n	NUM
fuelectenerg-400	597	23	j	j	PROPN
fuelectenerg-400	597	24	k−1	k−1	PROPN
fuelectenerg-400	598	1	+	+	CCONJ
fuelectenerg-400	598	2	n	n	PROPN
fuelectenerg-400	599	1	i	i	PRON
fuelectenerg-400	599	2	k−1	k−1	PROPN
fuelectenerg-400	599	3	=	=	PUNCT
fuelectenerg-400	599	4	n	n	PROPN
fuelectenerg-400	600	1	i−1	i−1	PROPN
fuelectenerg-400	600	2	k	k	PROPN
fuelectenerg-400	601	1	+	+	CCONJ
fuelectenerg-400	601	2	n	n	CCONJ
fuelectenerg-400	602	1	i	i	PRON
fuelectenerg-400	602	2	k−1	k−1	PROPN
fuelectenerg-400	602	3	(	(	PUNCT
fuelectenerg-400	602	4	6	6	NUM
fuelectenerg-400	602	5	)	)	PUNCT
fuelectenerg-400	602	6	this	this	PRON
fuelectenerg-400	602	7	yields	yield	VERB
fuelectenerg-400	602	8	the	the	DET
fuelectenerg-400	602	9	recursive	recursive	ADJ
fuelectenerg-400	602	10	relation	relation	NOUN
fuelectenerg-400	603	1	n	n	PRON
fuelectenerg-400	604	1	i	i	NOUN
fuelectenerg-400	604	2	k	k	NOUN
fuelectenerg-400	604	3	=	=	PUNCT
fuelectenerg-400	604	4	n	n	PROPN
fuelectenerg-400	605	1	i−1	i−1	PROPN
fuelectenerg-400	605	2	k	k	PROPN
fuelectenerg-400	606	1	+	+	CCONJ
fuelectenerg-400	606	2	n	n	CCONJ
fuelectenerg-400	607	1	i	i	PRON
fuelectenerg-400	607	2	k−1	k−1	PROPN
fuelectenerg-400	607	3	(	(	PUNCT
fuelectenerg-400	607	4	n	n	NOUN
fuelectenerg-400	607	5	i	i	PROPN
fuelectenerg-400	607	6	1	1	NUM
fuelectenerg-400	607	7	=	=	SYM
fuelectenerg-400	607	8	1	1	NUM
fuelectenerg-400	607	9	,	,	PUNCT
fuelectenerg-400	607	10	n1	n1	PROPN
fuelectenerg-400	607	11	k	k	NOUN
fuelectenerg-400	608	1	=	=	SYM
fuelectenerg-400	609	1	1	1	X
fuelectenerg-400	609	2	)	)	PUNCT
fuelectenerg-400	609	3	(	(	PUNCT
fuelectenerg-400	609	4	7	7	X
fuelectenerg-400	609	5	)	)	PUNCT
fuelectenerg-400	609	6	the	the	DET
fuelectenerg-400	609	7	generating	generate	VERB
fuelectenerg-400	609	8	function	function	NOUN
fuelectenerg-400	609	9	for	for	ADP
fuelectenerg-400	609	10	this	this	DET
fuelectenerg-400	609	11	recursion	recursion	NOUN
fuelectenerg-400	609	12	is	be	AUX
fuelectenerg-400	609	13	given	give	VERB
fuelectenerg-400	609	14	by	by	ADP
fuelectenerg-400	609	15	bi(x	bi(x	NUM
fuelectenerg-400	609	16	)	)	PUNCT
fuelectenerg-400	610	1	=	=	SYM
fuelectenerg-400	610	2	x	x	SYM
fuelectenerg-400	610	3	(	(	PUNCT
fuelectenerg-400	610	4	1−x)i	1−x)i	NUM
fuelectenerg-400	610	5	.	.	PUNCT
fuelectenerg-400	611	1	the	the	DET
fuelectenerg-400	611	2	coefficient	coefficient	NOUN
fuelectenerg-400	611	3	of	of	ADP
fuelectenerg-400	611	4	xk	xk	PROPN
fuelectenerg-400	611	5	in	in	ADP
fuelectenerg-400	611	6	bi(x	bi(x	NUM
fuelectenerg-400	611	7	)	)	PUNCT
fuelectenerg-400	611	8	gives	give	VERB
fuelectenerg-400	611	9	the	the	DET
fuelectenerg-400	611	10	total	total	ADJ
fuelectenerg-400	611	11	number	number	NOUN
fuelectenerg-400	611	12	of	of	ADP
fuelectenerg-400	611	13	sequences	sequence	NOUN
fuelectenerg-400	611	14	of	of	ADP
fuelectenerg-400	611	15	length	length	NOUN
fuelectenerg-400	611	16	k	k	PROPN
fuelectenerg-400	611	17	ending	end	VERB
fuelectenerg-400	611	18	in	in	ADP
fuelectenerg-400	611	19	i.	i.	NOUN
fuelectenerg-400	611	20	since	since	SCONJ
fuelectenerg-400	611	21	only	only	ADV
fuelectenerg-400	611	22	the	the	DET
fuelectenerg-400	611	23	members	member	NOUN
fuelectenerg-400	611	24	of	of	ADP
fuelectenerg-400	611	25	sn	sn	PROPN
fuelectenerg-400	611	26	n	n	PRON
fuelectenerg-400	611	27	can	can	AUX
fuelectenerg-400	611	28	be	be	AUX
fuelectenerg-400	611	29	used	use	VERB
fuelectenerg-400	611	30	to	to	PART
fuelectenerg-400	611	31	make	make	VERB
fuelectenerg-400	611	32	sequences	sequence	NOUN
fuelectenerg-400	611	33	of	of	ADP
fuelectenerg-400	611	34	length	length	NOUN
fuelectenerg-400	612	1	n	n	PROPN
fuelectenerg-400	612	2	+	+	NOUN
fuelectenerg-400	612	3	1	1	NUM
fuelectenerg-400	612	4	ending	end	VERB
fuelectenerg-400	612	5	in	in	ADP
fuelectenerg-400	612	6	n	n	PROPN
fuelectenerg-400	612	7	,	,	PUNCT
fuelectenerg-400	612	8	we	we	PRON
fuelectenerg-400	612	9	have	have	VERB
fuelectenerg-400	612	10	∣∣sn	∣∣sn	PROPN
fuelectenerg-400	612	11	n	n	PART
fuelectenerg-400	612	12	∣∣	∣∣	X
fuelectenerg-400	612	13	=	=	SYM
fuelectenerg-400	612	14	nn	nn	PROPN
fuelectenerg-400	612	15	n+1	n+1	PROPN
fuelectenerg-400	612	16	.	.	PUNCT
fuelectenerg-400	613	1	by	by	ADP
fuelectenerg-400	613	2	using	use	VERB
fuelectenerg-400	613	3	the	the	DET
fuelectenerg-400	613	4	generating	generate	VERB
fuelectenerg-400	613	5	function	function	NOUN
fuelectenerg-400	613	6	,	,	PUNCT
fuelectenerg-400	613	7	this	this	PRON
fuelectenerg-400	613	8	is	be	AUX
fuelectenerg-400	613	9	evaluated	evaluate	VERB
fuelectenerg-400	613	10	as	as	ADP
fuelectenerg-400	613	11	(	(	PUNCT
fuelectenerg-400	613	12	n+n−1	n+n−1	ADJ
fuelectenerg-400	613	13	n	n	ADJ
fuelectenerg-400	613	14	)	)	PUNCT
fuelectenerg-400	613	15	.	.	PUNCT
fuelectenerg-400	614	1	the	the	DET
fuelectenerg-400	614	2	ranking	rank	VERB
fuelectenerg-400	614	3	algorithm	algorithm	NOUN
fuelectenerg-400	614	4	for	for	ADP
fuelectenerg-400	614	5	the	the	DET
fuelectenerg-400	614	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	614	7	ordering	ordering	NOUN
fuelectenerg-400	614	8	of	of	ADP
fuelectenerg-400	614	9	members	member	NOUN
fuelectenerg-400	614	10	involves	involve	VERB
fuelectenerg-400	614	11	mapping	map	VERB
fuelectenerg-400	614	12	an	an	DET
fuelectenerg-400	614	13	integer	integer	NOUN
fuelectenerg-400	614	14	between	between	ADP
fuelectenerg-400	614	15	0	0	NUM
fuelectenerg-400	614	16	and	and	CCONJ
fuelectenerg-400	614	17	(	(	PUNCT
fuelectenerg-400	614	18	n+n−1	n+n−1	ADJ
fuelectenerg-400	614	19	n	n	ADJ
fuelectenerg-400	614	20	)	)	PUNCT
fuelectenerg-400	614	21	−	−	ADP
fuelectenerg-400	614	22	1	1	NUM
fuelectenerg-400	614	23	to	to	ADP
fuelectenerg-400	614	24	a	a	DET
fuelectenerg-400	614	25	sequence	sequence	NOUN
fuelectenerg-400	614	26	in	in	ADP
fuelectenerg-400	614	27	sn	sn	PROPN
fuelectenerg-400	614	28	n	n	PROPN
fuelectenerg-400	614	29	.	.	PUNCT
fuelectenerg-400	615	1	as	as	SCONJ
fuelectenerg-400	615	2	in	in	ADP
fuelectenerg-400	615	3	the	the	DET
fuelectenerg-400	615	4	previous	previous	ADJ
fuelectenerg-400	615	5	case	case	NOUN
fuelectenerg-400	615	6	,	,	PUNCT
fuelectenerg-400	615	7	the	the	DET
fuelectenerg-400	615	8	ranking	ranking	ADJ
fuelectenerg-400	615	9	algorithm	algorithm	NOUN
fuelectenerg-400	615	10	starts	start	VERB
fuelectenerg-400	615	11	with	with	ADP
fuelectenerg-400	615	12	an	an	DET
fuelectenerg-400	615	13	initial	initial	ADJ
fuelectenerg-400	615	14	estimate	estimate	NOUN
fuelectenerg-400	615	15	(	(	PUNCT
fuelectenerg-400	615	16	e0	e0	PROPN
fuelectenerg-400	615	17	=	=	PUNCT
fuelectenerg-400	615	18	(	(	PUNCT
fuelectenerg-400	615	19	n+n−1	n+n−1	PROPN
fuelectenerg-400	615	20	n	n	ADJ
fuelectenerg-400	615	21	)	)	PUNCT
fuelectenerg-400	615	22	−	−	PROPN
fuelectenerg-400	615	23	1	1	NUM
fuelectenerg-400	615	24	)	)	PUNCT
fuelectenerg-400	615	25	and	and	CCONJ
fuelectenerg-400	615	26	refines	refine	VERB
fuelectenerg-400	615	27	its	its	PRON
fuelectenerg-400	615	28	estimate	estimate	NOUN
fuelectenerg-400	615	29	as	as	SCONJ
fuelectenerg-400	615	30	the	the	DET
fuelectenerg-400	615	31	string	string	NOUN
fuelectenerg-400	615	32	is	be	AUX
fuelectenerg-400	615	33	parsed	parse	VERB
fuelectenerg-400	615	34	digit	digit	NOUN
fuelectenerg-400	615	35	by	by	ADP
fuelectenerg-400	615	36	digit	digit	NOUN
fuelectenerg-400	615	37	.	.	PUNCT
fuelectenerg-400	616	1	given	give	VERB
fuelectenerg-400	616	2	the	the	DET
fuelectenerg-400	616	3	estimate	estimate	NOUN
fuelectenerg-400	616	4	of	of	ADP
fuelectenerg-400	616	5	the	the	DET
fuelectenerg-400	616	6	rank	rank	NOUN
fuelectenerg-400	616	7	at	at	ADP
fuelectenerg-400	616	8	the	the	DET
fuelectenerg-400	616	9	(	(	PUNCT
fuelectenerg-400	616	10	b	b	X
fuelectenerg-400	616	11	−	−	PROPN
fuelectenerg-400	616	12	1)th	1)th	NOUN
fuelectenerg-400	616	13	digit	digit	NOUN
fuelectenerg-400	616	14	,	,	PUNCT
fuelectenerg-400	616	15	eb−1	eb−1	PROPN
fuelectenerg-400	616	16	,	,	PUNCT
fuelectenerg-400	616	17	and	and	CCONJ
fuelectenerg-400	616	18	that	that	SCONJ
fuelectenerg-400	616	19	the	the	DET
fuelectenerg-400	616	20	bth	bth	NOUN
fuelectenerg-400	616	21	digit	digit	NOUN
fuelectenerg-400	616	22	is	be	AUX
fuelectenerg-400	616	23	d(b	d(b	PROPN
fuelectenerg-400	616	24	)	)	PUNCT
fuelectenerg-400	616	25	,	,	PUNCT
fuelectenerg-400	616	26	the	the	DET
fuelectenerg-400	616	27	following	follow	VERB
fuelectenerg-400	616	28	conclusion	conclusion	NOUN
fuelectenerg-400	616	29	can	can	AUX
fuelectenerg-400	616	30	be	be	AUX
fuelectenerg-400	616	31	drawn	draw	VERB
fuelectenerg-400	616	32	about	about	ADP
fuelectenerg-400	616	33	the	the	DET
fuelectenerg-400	616	34	rank	rank	NOUN
fuelectenerg-400	616	35	.	.	PUNCT
fuelectenerg-400	617	1	the	the	DET
fuelectenerg-400	617	2	rank	rank	NOUN
fuelectenerg-400	617	3	is	be	AUX
fuelectenerg-400	617	4	less	less	ADJ
fuelectenerg-400	617	5	than	than	ADP
fuelectenerg-400	617	6	or	or	CCONJ
fuelectenerg-400	617	7	equal	equal	ADJ
fuelectenerg-400	617	8	to	to	ADP
fuelectenerg-400	617	9	eb−1	eb−1	PROPN
fuelectenerg-400	617	10	−	−	PROPN
fuelectenerg-400	617	11	(	(	PUNCT
fuelectenerg-400	617	12	n	n	CCONJ
fuelectenerg-400	617	13	′+b′−1	′+b′−1	PROPN
fuelectenerg-400	617	14	b′	b′	NUM
fuelectenerg-400	617	15	)	)	PUNCT
fuelectenerg-400	617	16	where	where	SCONJ
fuelectenerg-400	617	17	n	n	ADV
fuelectenerg-400	617	18	′	′	NUM
fuelectenerg-400	617	19	=	=	PUNCT
fuelectenerg-400	617	20	n	n	PRON
fuelectenerg-400	617	21	−	−	PROPN
fuelectenerg-400	617	22	d(b	d(b	PROPN
fuelectenerg-400	617	23	)	)	PUNCT
fuelectenerg-400	617	24	and	and	CCONJ
fuelectenerg-400	617	25	534	534	NUM
fuelectenerg-400	617	26	b.	b.	PROPN
fuelectenerg-400	617	27	vasic	vasic	PROPN
fuelectenerg-400	617	28	,	,	PUNCT
fuelectenerg-400	617	29	a.	a.	PROPN
fuelectenerg-400	617	30	r.	r.	PROPN
fuelectenerg-400	617	31	krishnan	krishnan	PROPN
fuelectenerg-400	617	32	lozenge	lozenge	PROPN
fuelectenerg-400	617	33	tiling	tile	VERB
fuelectenerg-400	617	34	constrained	constrained	ADJ
fuelectenerg-400	617	35	codes	code	NOUN
fuelectenerg-400	617	36	535	535	NUM
fuelectenerg-400	617	37	534	534	NUM
fuelectenerg-400	617	38	a.	a.	NOUN
fuelectenerg-400	617	39	r.	r.	PROPN
fuelectenerg-400	617	40	krishnanan	krishnanan	PROPN
fuelectenerg-400	617	41	and	and	CCONJ
fuelectenerg-400	617	42	b.	b.	PROPN
fuelectenerg-400	617	43	vasić	vasić	PROPN
fuelectenerg-400	617	44	fig	fig	PROPN
fuelectenerg-400	617	45	.	.	PUNCT
fuelectenerg-400	618	1	10	10	NUM
fuelectenerg-400	618	2	.	.	X
fuelectenerg-400	618	3	ranking	rank	VERB
fuelectenerg-400	618	4	of	of	ADP
fuelectenerg-400	618	5	string	string	NOUN
fuelectenerg-400	618	6	110010	110010	NUM
fuelectenerg-400	618	7	.	.	PUNCT
fuelectenerg-400	619	1	vertex	vertex	NOUN
fuelectenerg-400	619	2	labels	label	NOUN
fuelectenerg-400	619	3	denote	denote	VERB
fuelectenerg-400	619	4	the	the	DET
fuelectenerg-400	619	5	number	number	NOUN
fuelectenerg-400	619	6	of	of	ADP
fuelectenerg-400	619	7	possible	possible	ADJ
fuelectenerg-400	619	8	sequences	sequence	NOUN
fuelectenerg-400	619	9	from	from	ADP
fuelectenerg-400	619	10	the	the	DET
fuelectenerg-400	619	11	corresponding	correspond	VERB
fuelectenerg-400	619	12	node	node	NOUN
fuelectenerg-400	619	13	to	to	ADP
fuelectenerg-400	619	14	a	a	DET
fuelectenerg-400	619	15	drain	drain	NOUN
fuelectenerg-400	619	16	.	.	PUNCT
fuelectenerg-400	620	1	the	the	DET
fuelectenerg-400	620	2	edge	edge	NOUN
fuelectenerg-400	620	3	labels	label	NOUN
fuelectenerg-400	620	4	on	on	ADP
fuelectenerg-400	620	5	the	the	DET
fuelectenerg-400	620	6	mountain	mountain	NOUN
fuelectenerg-400	620	7	range	range	NOUN
fuelectenerg-400	620	8	,	,	PUNCT
fuelectenerg-400	620	9	shown	show	VERB
fuelectenerg-400	620	10	as	as	ADP
fuelectenerg-400	620	11	a	a	DET
fuelectenerg-400	620	12	bold	bold	ADJ
fuelectenerg-400	620	13	path	path	NOUN
fuelectenerg-400	620	14	,	,	PUNCT
fuelectenerg-400	620	15	correspond	correspond	VERB
fuelectenerg-400	620	16	to	to	ADP
fuelectenerg-400	620	17	intermediate	intermediate	ADJ
fuelectenerg-400	620	18	steps	step	NOUN
fuelectenerg-400	620	19	of	of	ADP
fuelectenerg-400	620	20	rank	rank	NOUN
fuelectenerg-400	620	21	computation	computation	NOUN
fuelectenerg-400	620	22	.	.	PUNCT
fuelectenerg-400	621	1	to	to	ADP
fuelectenerg-400	621	2	tilings	tiling	NOUN
fuelectenerg-400	621	3	.	.	PUNCT
fuelectenerg-400	622	1	ranking	ranking	ADJ
fuelectenerg-400	622	2	and	and	CCONJ
fuelectenerg-400	622	3	unranking	unranking	ADJ
fuelectenerg-400	622	4	algorithms	algorithm	NOUN
fuelectenerg-400	622	5	for	for	ADP
fuelectenerg-400	622	6	this	this	DET
fuelectenerg-400	622	7	set	set	NOUN
fuelectenerg-400	622	8	are	be	AUX
fuelectenerg-400	622	9	available	available	ADJ
fuelectenerg-400	622	10	[	[	X
fuelectenerg-400	622	11	23,24	23,24	NUM
fuelectenerg-400	622	12	]	]	PUNCT
fuelectenerg-400	622	13	.	.	PUNCT
fuelectenerg-400	623	1	we	we	PRON
fuelectenerg-400	623	2	have	have	AUX
fuelectenerg-400	623	3	designed	design	VERB
fuelectenerg-400	623	4	algorithms	algorithm	NOUN
fuelectenerg-400	623	5	using	use	VERB
fuelectenerg-400	623	6	methods	method	NOUN
fuelectenerg-400	623	7	similar	similar	ADJ
fuelectenerg-400	623	8	to	to	ADP
fuelectenerg-400	623	9	[	[	X
fuelectenerg-400	623	10	22	22	NUM
fuelectenerg-400	623	11	]	]	PUNCT
fuelectenerg-400	623	12	.	.	PUNCT
fuelectenerg-400	624	1	to	to	PART
fuelectenerg-400	624	2	perform	perform	VERB
fuelectenerg-400	624	3	the	the	DET
fuelectenerg-400	624	4	ranking	ranking	NOUN
fuelectenerg-400	624	5	,	,	PUNCT
fuelectenerg-400	624	6	first	first	ADV
fuelectenerg-400	624	7	the	the	DET
fuelectenerg-400	624	8	number	number	NOUN
fuelectenerg-400	624	9	of	of	ADP
fuelectenerg-400	624	10	paths	path	NOUN
fuelectenerg-400	624	11	passing	pass	VERB
fuelectenerg-400	624	12	through	through	ADP
fuelectenerg-400	624	13	every	every	DET
fuelectenerg-400	624	14	node	node	NOUN
fuelectenerg-400	624	15	(	(	PUNCT
fuelectenerg-400	624	16	x	x	NOUN
fuelectenerg-400	624	17	,	,	PUNCT
fuelectenerg-400	624	18	y	y	NOUN
fuelectenerg-400	624	19	)	)	PUNCT
fuelectenerg-400	624	20	in	in	ADP
fuelectenerg-400	624	21	g	g	NOUN
fuelectenerg-400	624	22	,	,	PUNCT
fuelectenerg-400	624	23	n(x	n(x	PROPN
fuelectenerg-400	624	24	,	,	PUNCT
fuelectenerg-400	624	25	y	y	NOUN
fuelectenerg-400	624	26	)	)	PUNCT
fuelectenerg-400	624	27	is	be	AUX
fuelectenerg-400	624	28	calculated	calculate	VERB
fuelectenerg-400	624	29	.	.	PUNCT
fuelectenerg-400	625	1	the	the	DET
fuelectenerg-400	625	2	rank	rank	NOUN
fuelectenerg-400	625	3	is	be	AUX
fuelectenerg-400	625	4	calculated	calculate	VERB
fuelectenerg-400	625	5	by	by	ADP
fuelectenerg-400	625	6	starting	start	VERB
fuelectenerg-400	625	7	with	with	ADP
fuelectenerg-400	625	8	an	an	DET
fuelectenerg-400	625	9	initial	initial	ADJ
fuelectenerg-400	625	10	estimate	estimate	NOUN
fuelectenerg-400	625	11	of	of	ADP
fuelectenerg-400	625	12	rank	rank	NOUN
fuelectenerg-400	625	13	(=	(=	NOUN
fuelectenerg-400	625	14	0	0	NUM
fuelectenerg-400	625	15	)	)	PUNCT
fuelectenerg-400	625	16	and	and	CCONJ
fuelectenerg-400	625	17	then	then	ADV
fuelectenerg-400	625	18	refining	refine	VERB
fuelectenerg-400	625	19	the	the	DET
fuelectenerg-400	625	20	estimate	estimate	NOUN
fuelectenerg-400	625	21	as	as	SCONJ
fuelectenerg-400	625	22	the	the	DET
fuelectenerg-400	625	23	sequence	sequence	NOUN
fuelectenerg-400	625	24	is	be	AUX
fuelectenerg-400	625	25	parsed	parse	VERB
fuelectenerg-400	625	26	bit	bit	NOUN
fuelectenerg-400	625	27	by	by	ADP
fuelectenerg-400	625	28	bit	bit	NOUN
fuelectenerg-400	625	29	.	.	PUNCT
fuelectenerg-400	626	1	from	from	ADP
fuelectenerg-400	626	2	any	any	DET
fuelectenerg-400	626	3	node	node	NOUN
fuelectenerg-400	626	4	(	(	PUNCT
fuelectenerg-400	626	5	x	x	NOUN
fuelectenerg-400	626	6	,	,	PUNCT
fuelectenerg-400	626	7	y	y	PROPN
fuelectenerg-400	626	8	)	)	PUNCT
fuelectenerg-400	626	9	,	,	PUNCT
fuelectenerg-400	626	10	if	if	SCONJ
fuelectenerg-400	626	11	the	the	DET
fuelectenerg-400	626	12	next	next	ADJ
fuelectenerg-400	626	13	bit	bit	NOUN
fuelectenerg-400	626	14	is	be	AUX
fuelectenerg-400	626	15	0	0	NUM
fuelectenerg-400	626	16	,	,	PUNCT
fuelectenerg-400	626	17	the	the	DET
fuelectenerg-400	626	18	corresponding	corresponding	ADJ
fuelectenerg-400	626	19	point	point	NOUN
fuelectenerg-400	626	20	in	in	ADP
fuelectenerg-400	626	21	the	the	DET
fuelectenerg-400	626	22	cartesian	cartesian	ADJ
fuelectenerg-400	626	23	plane	plane	NOUN
fuelectenerg-400	626	24	is	be	AUX
fuelectenerg-400	626	25	(	(	PUNCT
fuelectenerg-400	626	26	x	x	SYM
fuelectenerg-400	626	27	+	+	NUM
fuelectenerg-400	626	28	1	1	NUM
fuelectenerg-400	626	29	,	,	PUNCT
fuelectenerg-400	626	30	y	y	PROPN
fuelectenerg-400	626	31	−	−	PROPN
fuelectenerg-400	626	32	1	1	NUM
fuelectenerg-400	626	33	)	)	PUNCT
fuelectenerg-400	626	34	.	.	PUNCT
fuelectenerg-400	627	1	this	this	PRON
fuelectenerg-400	627	2	implies	imply	VERB
fuelectenerg-400	627	3	that	that	SCONJ
fuelectenerg-400	627	4	all	all	DET
fuelectenerg-400	627	5	sequences	sequence	NOUN
fuelectenerg-400	627	6	which	which	PRON
fuelectenerg-400	627	7	start	start	VERB
fuelectenerg-400	627	8	from	from	ADP
fuelectenerg-400	627	9	the	the	DET
fuelectenerg-400	627	10	node	node	NOUN
fuelectenerg-400	627	11	(	(	PUNCT
fuelectenerg-400	627	12	x+1	x+1	PROPN
fuelectenerg-400	627	13	,	,	PUNCT
fuelectenerg-400	627	14	y+1	y+1	NUM
fuelectenerg-400	627	15	)	)	PUNCT
fuelectenerg-400	627	16	have	have	VERB
fuelectenerg-400	627	17	a	a	DET
fuelectenerg-400	627	18	lower	low	ADJ
fuelectenerg-400	627	19	rank	rank	NOUN
fuelectenerg-400	627	20	.	.	PUNCT
fuelectenerg-400	628	1	thus	thus	ADV
fuelectenerg-400	628	2	,	,	PUNCT
fuelectenerg-400	628	3	given	give	VERB
fuelectenerg-400	628	4	that	that	SCONJ
fuelectenerg-400	628	5	the	the	DET
fuelectenerg-400	628	6	current	current	ADJ
fuelectenerg-400	628	7	estimate	estimate	NOUN
fuelectenerg-400	628	8	is	be	AUX
fuelectenerg-400	628	9	e	e	NOUN
fuelectenerg-400	628	10	,	,	PUNCT
fuelectenerg-400	628	11	the	the	DET
fuelectenerg-400	628	12	rank	rank	NOUN
fuelectenerg-400	628	13	of	of	ADP
fuelectenerg-400	628	14	this	this	DET
fuelectenerg-400	628	15	sequence	sequence	NOUN
fuelectenerg-400	628	16	is	be	AUX
fuelectenerg-400	628	17	greater	great	ADJ
fuelectenerg-400	628	18	than	than	ADP
fuelectenerg-400	628	19	e	e	NOUN
fuelectenerg-400	628	20	+	+	CCONJ
fuelectenerg-400	628	21	n(x+1,y+1	n(x+1,y+1	NOUN
fuelectenerg-400	628	22	)	)	PUNCT
fuelectenerg-400	628	23	.	.	PUNCT
fuelectenerg-400	629	1	hence	hence	ADV
fuelectenerg-400	629	2	the	the	DET
fuelectenerg-400	629	3	estimate	estimate	NOUN
fuelectenerg-400	629	4	can	can	AUX
fuelectenerg-400	629	5	be	be	AUX
fuelectenerg-400	629	6	refined	refine	VERB
fuelectenerg-400	629	7	by	by	ADP
fuelectenerg-400	629	8	adding	add	VERB
fuelectenerg-400	629	9	the	the	DET
fuelectenerg-400	629	10	number	number	NOUN
fuelectenerg-400	629	11	to	to	ADP
fuelectenerg-400	629	12	the	the	DET
fuelectenerg-400	629	13	current	current	ADJ
fuelectenerg-400	629	14	estimate	estimate	NOUN
fuelectenerg-400	629	15	.	.	PUNCT
fuelectenerg-400	630	1	this	this	DET
fuelectenerg-400	630	2	process	process	NOUN
fuelectenerg-400	630	3	is	be	AUX
fuelectenerg-400	630	4	continued	continue	VERB
fuelectenerg-400	630	5	till	till	SCONJ
fuelectenerg-400	630	6	all	all	DET
fuelectenerg-400	630	7	the	the	DET
fuelectenerg-400	630	8	bits	bit	NOUN
fuelectenerg-400	630	9	are	be	AUX
fuelectenerg-400	630	10	parsed	parse	VERB
fuelectenerg-400	630	11	.	.	PUNCT
fuelectenerg-400	631	1	the	the	DET
fuelectenerg-400	631	2	final	final	ADJ
fuelectenerg-400	631	3	estimate	estimate	NOUN
fuelectenerg-400	631	4	is	be	AUX
fuelectenerg-400	631	5	the	the	DET
fuelectenerg-400	631	6	rank	rank	NOUN
fuelectenerg-400	631	7	of	of	ADP
fuelectenerg-400	631	8	the	the	DET
fuelectenerg-400	631	9	sequence	sequence	NOUN
fuelectenerg-400	631	10	.	.	PUNCT
fuelectenerg-400	632	1	figure	figure	NOUN
fuelectenerg-400	632	2	10	10	NUM
fuelectenerg-400	632	3	shows	show	NOUN
fuelectenerg-400	632	4	flow	flow	NOUN
fuelectenerg-400	632	5	of	of	ADP
fuelectenerg-400	632	6	the	the	DET
fuelectenerg-400	632	7	algorithm	algorithm	NOUN
fuelectenerg-400	632	8	for	for	ADP
fuelectenerg-400	632	9	the	the	DET
fuelectenerg-400	632	10	sequence	sequence	NOUN
fuelectenerg-400	632	11	110010	110010	NUM
fuelectenerg-400	632	12	,	,	PUNCT
fuelectenerg-400	632	13	a	a	DET
fuelectenerg-400	632	14	member	member	NOUN
fuelectenerg-400	632	15	of	of	ADP
fuelectenerg-400	632	16	d(6,3	d(6,3	NOUN
fuelectenerg-400	632	17	)	)	PUNCT
fuelectenerg-400	632	18	.	.	PUNCT
fuelectenerg-400	633	1	the	the	DET
fuelectenerg-400	633	2	number	number	NOUN
fuelectenerg-400	633	3	of	of	ADP
fuelectenerg-400	633	4	sequences	sequence	NOUN
fuelectenerg-400	633	5	passing	pass	VERB
fuelectenerg-400	633	6	through	through	ADP
fuelectenerg-400	633	7	every	every	DET
fuelectenerg-400	633	8	node	node	NOUN
fuelectenerg-400	633	9	is	be	AUX
fuelectenerg-400	633	10	marked	mark	VERB
fuelectenerg-400	633	11	next	next	ADV
fuelectenerg-400	633	12	to	to	ADP
fuelectenerg-400	633	13	the	the	DET
fuelectenerg-400	633	14	node	node	NOUN
fuelectenerg-400	633	15	.	.	PUNCT
fuelectenerg-400	634	1	the	the	DET
fuelectenerg-400	634	2	refinement	refinement	NOUN
fuelectenerg-400	634	3	of	of	ADP
fuelectenerg-400	634	4	the	the	DET
fuelectenerg-400	634	5	rank	rank	NOUN
fuelectenerg-400	634	6	at	at	ADP
fuelectenerg-400	634	7	every	every	DET
fuelectenerg-400	634	8	bit	bit	NOUN
fuelectenerg-400	634	9	is	be	AUX
fuelectenerg-400	634	10	shown	show	VERB
fuelectenerg-400	634	11	in	in	ADP
fuelectenerg-400	634	12	the	the	DET
fuelectenerg-400	634	13	figure	figure	NOUN
fuelectenerg-400	634	14	.	.	PUNCT
fuelectenerg-400	635	1	at	at	ADP
fuelectenerg-400	635	2	the	the	DET
fuelectenerg-400	635	3	last	last	ADJ
fuelectenerg-400	635	4	bit	bit	NOUN
fuelectenerg-400	635	5	,	,	PUNCT
fuelectenerg-400	635	6	the	the	DET
fuelectenerg-400	635	7	rank	rank	NOUN
fuelectenerg-400	635	8	is	be	AUX
fuelectenerg-400	635	9	calculated	calculate	VERB
fuelectenerg-400	635	10	as	as	ADP
fuelectenerg-400	635	11	2	2	NUM
fuelectenerg-400	635	12	.	.	NOUN
fuelectenerg-400	635	13	similar	similar	ADJ
fuelectenerg-400	635	14	approach	approach	NOUN
fuelectenerg-400	635	15	can	can	AUX
fuelectenerg-400	635	16	be	be	AUX
fuelectenerg-400	635	17	used	use	VERB
fuelectenerg-400	635	18	to	to	PART
fuelectenerg-400	635	19	unrank	unrank	VERB
fuelectenerg-400	635	20	an	an	DET
fuelectenerg-400	635	21	integer	integer	NOUN
fuelectenerg-400	635	22	.	.	PUNCT
fuelectenerg-400	636	1	through	through	ADP
fuelectenerg-400	636	2	the	the	DET
fuelectenerg-400	636	3	rest	rest	NOUN
fuelectenerg-400	636	4	of	of	ADP
fuelectenerg-400	636	5	this	this	DET
fuelectenerg-400	636	6	document	document	NOUN
fuelectenerg-400	636	7	,	,	PUNCT
fuelectenerg-400	636	8	the	the	DET
fuelectenerg-400	636	9	ranking	ranking	NOUN
fuelectenerg-400	636	10	and	and	CCONJ
fuelectenerg-400	636	11	unranking	unranking	NOUN
fuelectenerg-400	636	12	on	on	ADP
fuelectenerg-400	636	13	this	this	DET
fuelectenerg-400	636	14	set	set	NOUN
fuelectenerg-400	636	15	will	will	AUX
fuelectenerg-400	636	16	be	be	AUX
fuelectenerg-400	636	17	denoted	denote	VERB
fuelectenerg-400	636	18	rd	rd	NOUN
fuelectenerg-400	636	19	and	and	CCONJ
fuelectenerg-400	636	20	r−1	r−1	PROPN
fuelectenerg-400	636	21	d	d	PROPN
fuelectenerg-400	636	22	respectively	respectively	ADV
fuelectenerg-400	636	23	.	.	PUNCT
fuelectenerg-400	637	1	it	it	PRON
fuelectenerg-400	637	2	was	be	AUX
fuelectenerg-400	637	3	earlier	early	ADV
fuelectenerg-400	637	4	stated	state	VERB
fuelectenerg-400	637	5	that	that	SCONJ
fuelectenerg-400	637	6	ri	ri	PROPN
fuelectenerg-400	637	7	can	can	AUX
fuelectenerg-400	637	8	be	be	AUX
fuelectenerg-400	637	9	represented	represent	VERB
fuelectenerg-400	637	10	as	as	ADP
fuelectenerg-400	637	11	ri	ri	NOUN
fuelectenerg-400	637	12	=	=	PUNCT
fuelectenerg-400	637	13	{	{	PUNCT
fuelectenerg-400	637	14	rank(di	rank(di	NOUN
fuelectenerg-400	637	15	)	)	PUNCT
fuelectenerg-400	637	16	,	,	PUNCT
fuelectenerg-400	638	1	i	i	PRON
fuelectenerg-400	638	2	=	=	NOUN
fuelectenerg-400	638	3	1	1	NUM
fuelectenerg-400	638	4	,	,	PUNCT
fuelectenerg-400	638	5	2	2	NUM
fuelectenerg-400	638	6	,	,	PUNCT
fuelectenerg-400	638	7	.	.	PUNCT
fuelectenerg-400	638	8	.	.	PUNCT
fuelectenerg-400	638	9	.	.	PUNCT
fuelectenerg-400	639	1	,	,	PUNCT
fuelectenerg-400	639	2	c	c	X
fuelectenerg-400	639	3	}	}	PUNCT
fuelectenerg-400	639	4	.	.	PUNCT
fuelectenerg-400	640	1	we	we	PRON
fuelectenerg-400	640	2	note	note	VERB
fuelectenerg-400	640	3	that	that	SCONJ
fuelectenerg-400	640	4	the	the	DET
fuelectenerg-400	640	5	rank	rank	NOUN
fuelectenerg-400	640	6	of	of	ADP
fuelectenerg-400	640	7	each	each	DET
fuelectenerg-400	640	8	dsi	dsi	NOUN
fuelectenerg-400	640	9	is	be	AUX
fuelectenerg-400	640	10	between	between	ADP
fuelectenerg-400	640	11	0	0	NUM
fuelectenerg-400	640	12	and	and	CCONJ
fuelectenerg-400	640	13	(	(	PUNCT
fuelectenerg-400	640	14	a+b	a+b	NUM
fuelectenerg-400	640	15	b	b	NOUN
fuelectenerg-400	640	16	)	)	PUNCT
fuelectenerg-400	640	17	−1	−1	NOUN
fuelectenerg-400	640	18	.	.	PUNCT
fuelectenerg-400	641	1	also	also	ADV
fuelectenerg-400	641	2	,	,	PUNCT
fuelectenerg-400	641	3	we	we	PRON
fuelectenerg-400	641	4	noted	note	VERB
fuelectenerg-400	641	5	that	that	SCONJ
fuelectenerg-400	641	6	for	for	ADP
fuelectenerg-400	641	7	all	all	DET
fuelectenerg-400	641	8	di	di	NOUN
fuelectenerg-400	641	9	,	,	PUNCT
fuelectenerg-400	641	10	dj	dj	ADP
fuelectenerg-400	641	11	such	such	ADJ
fuelectenerg-400	641	12	that	that	SCONJ
fuelectenerg-400	641	13	i	i	PRON
fuelectenerg-400	641	14	<	<	X
fuelectenerg-400	641	15	j	j	PROPN
fuelectenerg-400	641	16	,	,	PUNCT
fuelectenerg-400	641	17	rank(di	rank(di	NOUN
fuelectenerg-400	641	18	)	)	PUNCT
fuelectenerg-400	641	19	≤	≤	NOUN
fuelectenerg-400	641	20	rank(dj	rank(dj	NOUN
fuelectenerg-400	641	21	)	)	PUNCT
fuelectenerg-400	641	22	.	.	PUNCT
fuelectenerg-400	642	1	now	now	ADV
fuelectenerg-400	642	2	,	,	PUNCT
fuelectenerg-400	642	3	we	we	PRON
fuelectenerg-400	642	4	consider	consider	VERB
fuelectenerg-400	642	5	the	the	DET
fuelectenerg-400	642	6	rankbased	rankbase	VERB
fuelectenerg-400	642	7	representation	representation	NOUN
fuelectenerg-400	642	8	which	which	PRON
fuelectenerg-400	642	9	is	be	AUX
fuelectenerg-400	642	10	the	the	DET
fuelectenerg-400	642	11	ordered	order	VERB
fuelectenerg-400	642	12	set	set	NOUN
fuelectenerg-400	642	13	{	{	PUNCT
fuelectenerg-400	642	14	rank(di	rank(di	NOUN
fuelectenerg-400	642	15	)	)	PUNCT
fuelectenerg-400	642	16	,	,	PUNCT
fuelectenerg-400	642	17	i	i	PRON
fuelectenerg-400	642	18	=	=	NOUN
fuelectenerg-400	642	19	1	1	NUM
fuelectenerg-400	642	20	,	,	PUNCT
fuelectenerg-400	642	21	2	2	NUM
fuelectenerg-400	642	22	,	,	PUNCT
fuelectenerg-400	642	23	.	.	PUNCT
fuelectenerg-400	642	24	.	.	PUNCT
fuelectenerg-400	642	25	.	.	PUNCT
fuelectenerg-400	643	1	,	,	PUNCT
fuelectenerg-400	643	2	a|di	a|di	NOUN
fuelectenerg-400	643	3	∈	∈	PROPN
fuelectenerg-400	643	4	d(a+b	d(a+b	PRON
fuelectenerg-400	643	5	,	,	PUNCT
fuelectenerg-400	643	6	b	b	NOUN
fuelectenerg-400	643	7	)	)	PUNCT
fuelectenerg-400	643	8	}	}	PUNCT
fuelectenerg-400	643	9	.	.	PUNCT
fuelectenerg-400	644	1	this	this	DET
fuelectenerg-400	644	2	set	set	NOUN
fuelectenerg-400	644	3	can	can	AUX
fuelectenerg-400	644	4	be	be	AUX
fuelectenerg-400	644	5	expressed	express	VERB
fuelectenerg-400	644	6	as	as	ADP
fuelectenerg-400	644	7	a	a	DET
fuelectenerg-400	644	8	non	non	ADJ
fuelectenerg-400	644	9	-	-	ADJ
fuelectenerg-400	644	10	decreasing	decrease	VERB
fuelectenerg-400	644	11	string	string	NOUN
fuelectenerg-400	644	12	of	of	ADP
fuelectenerg-400	644	13	length	length	NOUN
fuelectenerg-400	644	14	c	c	NOUN
fuelectenerg-400	644	15	with	with	ADP
fuelectenerg-400	644	16	members	member	NOUN
fuelectenerg-400	644	17	of	of	ADP
fuelectenerg-400	644	18	the	the	DET
fuelectenerg-400	644	19	set	set	NOUN
fuelectenerg-400	644	20	{	{	PUNCT
fuelectenerg-400	644	21	1	1	NUM
fuelectenerg-400	644	22	,	,	PUNCT
fuelectenerg-400	644	23	2	2	NUM
fuelectenerg-400	644	24	,	,	PUNCT
fuelectenerg-400	644	25	.	.	PUNCT
fuelectenerg-400	644	26	.	.	PUNCT
fuelectenerg-400	645	1	.	.	PUNCT
fuelectenerg-400	646	1	,	,	PUNCT
fuelectenerg-400	646	2	(	(	PUNCT
fuelectenerg-400	646	3	a+b	a+b	NUM
fuelectenerg-400	646	4	b	b	NOUN
fuelectenerg-400	646	5	)	)	PUNCT
fuelectenerg-400	646	6	}	}	PUNCT
fuelectenerg-400	646	7	.	.	PUNCT
fuelectenerg-400	647	1	we	we	PRON
fuelectenerg-400	647	2	can	can	AUX
fuelectenerg-400	647	3	further	far	ADV
fuelectenerg-400	647	4	reduce	reduce	VERB
fuelectenerg-400	647	5	the	the	DET
fuelectenerg-400	647	6	complexity	complexity	NOUN
fuelectenerg-400	647	7	of	of	ADP
fuelectenerg-400	647	8	representation	representation	NOUN
fuelectenerg-400	647	9	of	of	ADP
fuelectenerg-400	647	10	elements	element	NOUN
fuelectenerg-400	647	11	of	of	ADP
fuelectenerg-400	647	12	r	r	NOUN
fuelectenerg-400	647	13	if	if	SCONJ
fuelectenerg-400	647	14	the	the	DET
fuelectenerg-400	647	15	non	non	ADJ
fuelectenerg-400	647	16	-	-	ADJ
fuelectenerg-400	647	17	decreasing	decrease	VERB
fuelectenerg-400	647	18	strings	string	NOUN
fuelectenerg-400	647	19	can	can	AUX
fuelectenerg-400	647	20	be	be	AUX
fuelectenerg-400	647	21	ordered	order	VERB
fuelectenerg-400	647	22	.	.	PUNCT
fuelectenerg-400	648	1	section	section	NOUN
fuelectenerg-400	648	2	5.3	5.3	NUM
fuelectenerg-400	648	3	deals	deal	NOUN
fuelectenerg-400	648	4	with	with	ADP
fuelectenerg-400	648	5	this	this	PRON
fuelectenerg-400	648	6	.	.	PUNCT
fuelectenerg-400	649	1	5.3	5.3	NUM
fuelectenerg-400	649	2	lexicographical	lexicographical	ADJ
fuelectenerg-400	649	3	ordering	ordering	NOUN
fuelectenerg-400	649	4	of	of	ADP
fuelectenerg-400	649	5	non	non	ADJ
fuelectenerg-400	649	6	-	-	ADJ
fuelectenerg-400	649	7	decreasing	decrease	VERB
fuelectenerg-400	649	8	strings	string	NOUN
fuelectenerg-400	649	9	this	this	DET
fuelectenerg-400	649	10	section	section	NOUN
fuelectenerg-400	649	11	deals	deal	VERB
fuelectenerg-400	649	12	with	with	ADP
fuelectenerg-400	649	13	the	the	DET
fuelectenerg-400	649	14	lexicographical	lexicographical	ADJ
fuelectenerg-400	649	15	ordering	ordering	NOUN
fuelectenerg-400	649	16	in	in	ADP
fuelectenerg-400	649	17	the	the	DET
fuelectenerg-400	649	18	set	set	NOUN
fuelectenerg-400	649	19	of	of	ADP
fuelectenerg-400	649	20	non	non	ADJ
fuelectenerg-400	649	21	-	-	ADJ
fuelectenerg-400	649	22	decreasing	decrease	VERB
fuelectenerg-400	649	23	strings	string	NOUN
fuelectenerg-400	649	24	of	of	ADP
fuelectenerg-400	649	25	length	length	NOUN
fuelectenerg-400	649	26	n	n	PRON
fuelectenerg-400	649	27	consisting	consist	VERB
fuelectenerg-400	649	28	of	of	ADP
fuelectenerg-400	649	29	members	member	NOUN
fuelectenerg-400	649	30	of	of	ADP
fuelectenerg-400	649	31	the	the	DET
fuelectenerg-400	649	32	set	set	NOUN
fuelectenerg-400	649	33	n	n	NOUN
fuelectenerg-400	649	34	=	=	SYM
fuelectenerg-400	649	35	{	{	PUNCT
fuelectenerg-400	649	36	1	1	NUM
fuelectenerg-400	649	37	,	,	PUNCT
fuelectenerg-400	649	38	2	2	NUM
fuelectenerg-400	649	39	,	,	PUNCT
fuelectenerg-400	649	40	3	3	NUM
fuelectenerg-400	649	41	,	,	PUNCT
fuelectenerg-400	649	42	...	...	PUNCT
fuelectenerg-400	649	43	,	,	PUNCT
fuelectenerg-400	649	44	n	n	CCONJ
fuelectenerg-400	649	45	}	}	PUNCT
fuelectenerg-400	649	46	.	.	PUNCT
fuelectenerg-400	650	1	this	this	DET
fuelectenerg-400	650	2	detection	detection	NOUN
fuelectenerg-400	650	3	and	and	CCONJ
fuelectenerg-400	650	4	coding	code	VERB
fuelectenerg-400	650	5	for	for	ADP
fuelectenerg-400	650	6	tdmr	tdmr	NOUN
fuelectenerg-400	650	7	channel	channel	NOUN
fuelectenerg-400	650	8	535	535	NUM
fuelectenerg-400	650	9	set	set	NOUN
fuelectenerg-400	650	10	is	be	AUX
fuelectenerg-400	650	11	denoted	denote	VERB
fuelectenerg-400	650	12	sn	sn	PROPN
fuelectenerg-400	650	13	n	n	NOUN
fuelectenerg-400	650	14	and	and	CCONJ
fuelectenerg-400	650	15	is	be	AUX
fuelectenerg-400	650	16	defined	define	VERB
fuelectenerg-400	650	17	as	as	ADP
fuelectenerg-400	650	18	the	the	DET
fuelectenerg-400	650	19	set	set	NOUN
fuelectenerg-400	650	20	of	of	ADP
fuelectenerg-400	650	21	all	all	DET
fuelectenerg-400	650	22	strings	string	NOUN
fuelectenerg-400	650	23	,	,	PUNCT
fuelectenerg-400	650	24	d	d	NOUN
fuelectenerg-400	650	25	of	of	ADP
fuelectenerg-400	650	26	length	length	NOUN
fuelectenerg-400	650	27	n	n	PRON
fuelectenerg-400	650	28	such	such	ADJ
fuelectenerg-400	650	29	that	that	PRON
fuelectenerg-400	650	30	for	for	ADP
fuelectenerg-400	650	31	all	all	DET
fuelectenerg-400	650	32	i	i	PRON
fuelectenerg-400	650	33	,	,	PUNCT
fuelectenerg-400	650	34	1	1	NUM
fuelectenerg-400	650	35	≤	≤	NUM
fuelectenerg-400	650	36	i	i	X
fuelectenerg-400	650	37	≤	≤	PROPN
fuelectenerg-400	650	38	n−1	n−1	PROPN
fuelectenerg-400	650	39	,	,	PUNCT
fuelectenerg-400	650	40	d(i	d(i	PROPN
fuelectenerg-400	650	41	)	)	PUNCT
fuelectenerg-400	650	42	,	,	PUNCT
fuelectenerg-400	650	43	d(i+1	d(i+1	NOUN
fuelectenerg-400	650	44	)	)	PUNCT
fuelectenerg-400	650	45	∈	∈	PROPN
fuelectenerg-400	650	46	n	n	PROPN
fuelectenerg-400	650	47	and	and	CCONJ
fuelectenerg-400	650	48	d(i	d(i	PROPN
fuelectenerg-400	650	49	)	)	PUNCT
fuelectenerg-400	650	50	≤	≤	NUM
fuelectenerg-400	650	51	d(i+1	d(i+1	NOUN
fuelectenerg-400	650	52	)	)	PUNCT
fuelectenerg-400	650	53	.	.	PUNCT
fuelectenerg-400	651	1	the	the	DET
fuelectenerg-400	651	2	set	set	VERB
fuelectenerg-400	651	3	sn	sn	PROPN
fuelectenerg-400	651	4	n	n	VERB
fuelectenerg-400	651	5	is	be	AUX
fuelectenerg-400	651	6	said	say	VERB
fuelectenerg-400	651	7	to	to	PART
fuelectenerg-400	651	8	be	be	AUX
fuelectenerg-400	651	9	lexicographically	lexicographically	ADV
fuelectenerg-400	651	10	ordered	order	VERB
fuelectenerg-400	651	11	if	if	SCONJ
fuelectenerg-400	651	12	for	for	ADP
fuelectenerg-400	651	13	any	any	DET
fuelectenerg-400	651	14	d1	d1	NOUN
fuelectenerg-400	651	15	,	,	PUNCT
fuelectenerg-400	651	16	d2	d2	PROPN
fuelectenerg-400	651	17	∈	∈	PROPN
fuelectenerg-400	651	18	sn	sn	PROPN
fuelectenerg-400	651	19	n	n	PROPN
fuelectenerg-400	651	20	,	,	PUNCT
fuelectenerg-400	651	21	d1(i	d1(i	NOUN
fuelectenerg-400	651	22	)	)	PUNCT
fuelectenerg-400	651	23	≤	≤	NUM
fuelectenerg-400	651	24	d2(i	d2(i	PROPN
fuelectenerg-400	651	25	)	)	PUNCT
fuelectenerg-400	651	26	∀i	∀i	NOUN
fuelectenerg-400	651	27	⇔	⇔	X
fuelectenerg-400	651	28	rank(d1	rank(d1	X
fuelectenerg-400	651	29	)	)	PUNCT
fuelectenerg-400	651	30	≤	≤	NUM
fuelectenerg-400	651	31	rank(d2	rank(d2	NOUN
fuelectenerg-400	651	32	)	)	PUNCT
fuelectenerg-400	651	33	,	,	PUNCT
fuelectenerg-400	651	34	where	where	SCONJ
fuelectenerg-400	651	35	,	,	PUNCT
fuelectenerg-400	651	36	as	as	ADP
fuelectenerg-400	651	37	before	before	ADV
fuelectenerg-400	651	38	,	,	PUNCT
fuelectenerg-400	651	39	rank	rank	NOUN
fuelectenerg-400	651	40	of	of	ADP
fuelectenerg-400	651	41	a	a	DET
fuelectenerg-400	651	42	member	member	NOUN
fuelectenerg-400	651	43	is	be	AUX
fuelectenerg-400	651	44	the	the	DET
fuelectenerg-400	651	45	position	position	NOUN
fuelectenerg-400	651	46	of	of	ADP
fuelectenerg-400	651	47	the	the	DET
fuelectenerg-400	651	48	member	member	NOUN
fuelectenerg-400	651	49	in	in	ADP
fuelectenerg-400	651	50	the	the	DET
fuelectenerg-400	651	51	ordered	order	VERB
fuelectenerg-400	651	52	set	set	NOUN
fuelectenerg-400	651	53	.	.	PUNCT
fuelectenerg-400	652	1	table	table	NOUN
fuelectenerg-400	652	2	2	2	NUM
fuelectenerg-400	652	3	shows	show	VERB
fuelectenerg-400	652	4	the	the	DET
fuelectenerg-400	652	5	set	set	ADJ
fuelectenerg-400	652	6	s2	s2	NOUN
fuelectenerg-400	652	7	3	3	NUM
fuelectenerg-400	652	8	along	along	ADP
fuelectenerg-400	652	9	with	with	ADP
fuelectenerg-400	652	10	the	the	DET
fuelectenerg-400	652	11	rank	rank	NOUN
fuelectenerg-400	652	12	of	of	ADP
fuelectenerg-400	652	13	each	each	DET
fuelectenerg-400	652	14	element	element	NOUN
fuelectenerg-400	652	15	.	.	PUNCT
fuelectenerg-400	653	1	table	table	NOUN
fuelectenerg-400	653	2	2	2	NUM
fuelectenerg-400	653	3	.	.	PUNCT
fuelectenerg-400	654	1	ordering	ordering	NOUN
fuelectenerg-400	654	2	of	of	ADP
fuelectenerg-400	654	3	elements	element	NOUN
fuelectenerg-400	654	4	in	in	ADP
fuelectenerg-400	654	5	s2	s2	PROPN
fuelectenerg-400	654	6	3	3	NUM
fuelectenerg-400	654	7	.	.	PUNCT
fuelectenerg-400	655	1	rank	rank	PROPN
fuelectenerg-400	655	2	string	string	NOUN
fuelectenerg-400	655	3	0	0	NUM
fuelectenerg-400	655	4	111	111	NUM
fuelectenerg-400	655	5	1	1	NUM
fuelectenerg-400	655	6	112	112	NUM
fuelectenerg-400	655	7	2	2	NUM
fuelectenerg-400	655	8	122	122	NUM
fuelectenerg-400	655	9	3	3	NUM
fuelectenerg-400	655	10	222	222	NUM
fuelectenerg-400	655	11	to	to	PART
fuelectenerg-400	655	12	calculate	calculate	VERB
fuelectenerg-400	655	13	the	the	DET
fuelectenerg-400	655	14	size	size	NOUN
fuelectenerg-400	655	15	of	of	ADP
fuelectenerg-400	655	16	sn	sn	PROPN
fuelectenerg-400	656	1	n	n	CCONJ
fuelectenerg-400	656	2	we	we	PRON
fuelectenerg-400	656	3	analyze	analyze	VERB
fuelectenerg-400	656	4	the	the	DET
fuelectenerg-400	656	5	construction	construction	NOUN
fuelectenerg-400	656	6	of	of	ADP
fuelectenerg-400	656	7	strings	string	NOUN
fuelectenerg-400	656	8	of	of	ADP
fuelectenerg-400	656	9	length	length	NOUN
fuelectenerg-400	656	10	k	k	NOUN
fuelectenerg-400	656	11	using	use	VERB
fuelectenerg-400	656	12	strings	string	NOUN
fuelectenerg-400	656	13	of	of	ADP
fuelectenerg-400	656	14	length	length	NOUN
fuelectenerg-400	656	15	k	k	PROPN
fuelectenerg-400	657	1	−	−	PROPN
fuelectenerg-400	657	2	1	1	NUM
fuelectenerg-400	657	3	for	for	ADP
fuelectenerg-400	657	4	k	k	PROPN
fuelectenerg-400	657	5	<	<	X
fuelectenerg-400	657	6	n.	n.	PROPN
fuelectenerg-400	657	7	consider	consider	VERB
fuelectenerg-400	657	8	a	a	DET
fuelectenerg-400	657	9	number	number	NOUN
fuelectenerg-400	657	10	i	i	PRON
fuelectenerg-400	657	11	such	such	ADJ
fuelectenerg-400	657	12	that	that	SCONJ
fuelectenerg-400	657	13	1	1	NUM
fuelectenerg-400	657	14	<	<	X
fuelectenerg-400	657	15	i	i	PROPN
fuelectenerg-400	657	16	≤	≤	ADJ
fuelectenerg-400	657	17	n	n	ADV
fuelectenerg-400	657	18	.	.	PUNCT
fuelectenerg-400	658	1	the	the	DET
fuelectenerg-400	658	2	number	number	NOUN
fuelectenerg-400	658	3	of	of	ADP
fuelectenerg-400	658	4	strings	string	NOUN
fuelectenerg-400	658	5	of	of	ADP
fuelectenerg-400	658	6	length	length	NOUN
fuelectenerg-400	658	7	k	k	PROPN
fuelectenerg-400	658	8	ending	end	VERB
fuelectenerg-400	658	9	in	in	ADP
fuelectenerg-400	658	10	i	i	PROPN
fuelectenerg-400	658	11	,	,	PUNCT
fuelectenerg-400	658	12	n	n	CCONJ
fuelectenerg-400	658	13	i	i	PRON
fuelectenerg-400	658	14	k	k	PROPN
fuelectenerg-400	658	15	is	be	AUX
fuelectenerg-400	658	16	equal	equal	ADJ
fuelectenerg-400	658	17	to	to	ADP
fuelectenerg-400	658	18	the	the	DET
fuelectenerg-400	658	19	number	number	NOUN
fuelectenerg-400	658	20	of	of	ADP
fuelectenerg-400	658	21	strings	string	NOUN
fuelectenerg-400	658	22	of	of	ADP
fuelectenerg-400	658	23	length	length	NOUN
fuelectenerg-400	658	24	(	(	PUNCT
fuelectenerg-400	658	25	k−1	k−1	PROPN
fuelectenerg-400	658	26	)	)	PUNCT
fuelectenerg-400	658	27	ending	end	VERB
fuelectenerg-400	658	28	in	in	ADP
fuelectenerg-400	658	29	digits	digit	NOUN
fuelectenerg-400	658	30	less	less	ADJ
fuelectenerg-400	658	31	than	than	ADP
fuelectenerg-400	658	32	or	or	CCONJ
fuelectenerg-400	658	33	equal	equal	ADJ
fuelectenerg-400	658	34	to	to	ADP
fuelectenerg-400	658	35	i.	i.	NOUN
fuelectenerg-400	658	36	that	that	PRON
fuelectenerg-400	658	37	is	be	AUX
fuelectenerg-400	658	38	,	,	PUNCT
fuelectenerg-400	658	39	n	n	CCONJ
fuelectenerg-400	659	1	i	i	NOUN
fuelectenerg-400	659	2	k	k	NOUN
fuelectenerg-400	660	1	=	=	PUNCT
fuelectenerg-400	660	2	i∑	i∑	PROPN
fuelectenerg-400	660	3	j=1	j=1	PROPN
fuelectenerg-400	660	4	n	n	NUM
fuelectenerg-400	660	5	j	j	PROPN
fuelectenerg-400	660	6	k−1	k−1	PROPN
fuelectenerg-400	660	7	(	(	PUNCT
fuelectenerg-400	660	8	n	n	NOUN
fuelectenerg-400	660	9	i	i	PROPN
fuelectenerg-400	660	10	1	1	NUM
fuelectenerg-400	660	11	=	=	SYM
fuelectenerg-400	660	12	1	1	NUM
fuelectenerg-400	660	13	,	,	PUNCT
fuelectenerg-400	660	14	n1	n1	PROPN
fuelectenerg-400	660	15	k	k	NOUN
fuelectenerg-400	660	16	=	=	SYM
fuelectenerg-400	660	17	1	1	X
fuelectenerg-400	660	18	)	)	PUNCT
fuelectenerg-400	660	19	=	=	NOUN
fuelectenerg-400	660	20	i−1∑	i−1∑	NUM
fuelectenerg-400	660	21	j=1	j=1	PROPN
fuelectenerg-400	660	22	n	n	NUM
fuelectenerg-400	660	23	j	j	PROPN
fuelectenerg-400	660	24	k−1	k−1	PROPN
fuelectenerg-400	661	1	+	+	CCONJ
fuelectenerg-400	661	2	n	n	PROPN
fuelectenerg-400	662	1	i	i	PRON
fuelectenerg-400	662	2	k−1	k−1	PROPN
fuelectenerg-400	662	3	=	=	PUNCT
fuelectenerg-400	662	4	n	n	PROPN
fuelectenerg-400	663	1	i−1	i−1	PROPN
fuelectenerg-400	663	2	k	k	PROPN
fuelectenerg-400	664	1	+	+	CCONJ
fuelectenerg-400	664	2	n	n	CCONJ
fuelectenerg-400	665	1	i	i	PRON
fuelectenerg-400	665	2	k−1	k−1	PROPN
fuelectenerg-400	665	3	(	(	PUNCT
fuelectenerg-400	665	4	6	6	NUM
fuelectenerg-400	665	5	)	)	PUNCT
fuelectenerg-400	665	6	this	this	PRON
fuelectenerg-400	665	7	yields	yield	VERB
fuelectenerg-400	665	8	the	the	DET
fuelectenerg-400	665	9	recursive	recursive	ADJ
fuelectenerg-400	665	10	relation	relation	NOUN
fuelectenerg-400	666	1	n	n	PRON
fuelectenerg-400	667	1	i	i	NOUN
fuelectenerg-400	667	2	k	k	NOUN
fuelectenerg-400	667	3	=	=	PUNCT
fuelectenerg-400	667	4	n	n	PROPN
fuelectenerg-400	668	1	i−1	i−1	PROPN
fuelectenerg-400	668	2	k	k	PROPN
fuelectenerg-400	669	1	+	+	CCONJ
fuelectenerg-400	669	2	n	n	CCONJ
fuelectenerg-400	670	1	i	i	PRON
fuelectenerg-400	670	2	k−1	k−1	PROPN
fuelectenerg-400	670	3	(	(	PUNCT
fuelectenerg-400	670	4	n	n	NOUN
fuelectenerg-400	670	5	i	i	PROPN
fuelectenerg-400	670	6	1	1	NUM
fuelectenerg-400	670	7	=	=	SYM
fuelectenerg-400	670	8	1	1	NUM
fuelectenerg-400	670	9	,	,	PUNCT
fuelectenerg-400	670	10	n1	n1	PROPN
fuelectenerg-400	670	11	k	k	NOUN
fuelectenerg-400	671	1	=	=	SYM
fuelectenerg-400	672	1	1	1	X
fuelectenerg-400	672	2	)	)	PUNCT
fuelectenerg-400	672	3	(	(	PUNCT
fuelectenerg-400	672	4	7	7	X
fuelectenerg-400	672	5	)	)	PUNCT
fuelectenerg-400	672	6	the	the	DET
fuelectenerg-400	672	7	generating	generate	VERB
fuelectenerg-400	672	8	function	function	NOUN
fuelectenerg-400	672	9	for	for	ADP
fuelectenerg-400	672	10	this	this	DET
fuelectenerg-400	672	11	recursion	recursion	NOUN
fuelectenerg-400	672	12	is	be	AUX
fuelectenerg-400	672	13	given	give	VERB
fuelectenerg-400	672	14	by	by	ADP
fuelectenerg-400	672	15	bi(x	bi(x	NUM
fuelectenerg-400	672	16	)	)	PUNCT
fuelectenerg-400	673	1	=	=	SYM
fuelectenerg-400	673	2	x	x	SYM
fuelectenerg-400	673	3	(	(	PUNCT
fuelectenerg-400	673	4	1−x)i	1−x)i	NUM
fuelectenerg-400	673	5	.	.	PUNCT
fuelectenerg-400	674	1	the	the	DET
fuelectenerg-400	674	2	coefficient	coefficient	NOUN
fuelectenerg-400	674	3	of	of	ADP
fuelectenerg-400	674	4	xk	xk	PROPN
fuelectenerg-400	674	5	in	in	ADP
fuelectenerg-400	674	6	bi(x	bi(x	NUM
fuelectenerg-400	674	7	)	)	PUNCT
fuelectenerg-400	674	8	gives	give	VERB
fuelectenerg-400	674	9	the	the	DET
fuelectenerg-400	674	10	total	total	ADJ
fuelectenerg-400	674	11	number	number	NOUN
fuelectenerg-400	674	12	of	of	ADP
fuelectenerg-400	674	13	sequences	sequence	NOUN
fuelectenerg-400	674	14	of	of	ADP
fuelectenerg-400	674	15	length	length	NOUN
fuelectenerg-400	674	16	k	k	PROPN
fuelectenerg-400	674	17	ending	end	VERB
fuelectenerg-400	674	18	in	in	ADP
fuelectenerg-400	674	19	i.	i.	NOUN
fuelectenerg-400	674	20	since	since	SCONJ
fuelectenerg-400	674	21	only	only	ADV
fuelectenerg-400	674	22	the	the	DET
fuelectenerg-400	674	23	members	member	NOUN
fuelectenerg-400	674	24	of	of	ADP
fuelectenerg-400	674	25	sn	sn	PROPN
fuelectenerg-400	674	26	n	n	PRON
fuelectenerg-400	674	27	can	can	AUX
fuelectenerg-400	674	28	be	be	AUX
fuelectenerg-400	674	29	used	use	VERB
fuelectenerg-400	674	30	to	to	PART
fuelectenerg-400	674	31	make	make	VERB
fuelectenerg-400	674	32	sequences	sequence	NOUN
fuelectenerg-400	674	33	of	of	ADP
fuelectenerg-400	674	34	length	length	NOUN
fuelectenerg-400	675	1	n	n	PROPN
fuelectenerg-400	675	2	+	+	NOUN
fuelectenerg-400	675	3	1	1	NUM
fuelectenerg-400	675	4	ending	end	VERB
fuelectenerg-400	675	5	in	in	ADP
fuelectenerg-400	675	6	n	n	PROPN
fuelectenerg-400	675	7	,	,	PUNCT
fuelectenerg-400	675	8	we	we	PRON
fuelectenerg-400	675	9	have	have	VERB
fuelectenerg-400	675	10	∣∣sn	∣∣sn	PROPN
fuelectenerg-400	675	11	n	n	PART
fuelectenerg-400	675	12	∣∣	∣∣	X
fuelectenerg-400	675	13	=	=	SYM
fuelectenerg-400	675	14	nn	nn	PROPN
fuelectenerg-400	675	15	n+1	n+1	PROPN
fuelectenerg-400	675	16	.	.	PUNCT
fuelectenerg-400	676	1	by	by	ADP
fuelectenerg-400	676	2	using	use	VERB
fuelectenerg-400	676	3	the	the	DET
fuelectenerg-400	676	4	generating	generate	VERB
fuelectenerg-400	676	5	function	function	NOUN
fuelectenerg-400	676	6	,	,	PUNCT
fuelectenerg-400	676	7	this	this	PRON
fuelectenerg-400	676	8	is	be	AUX
fuelectenerg-400	676	9	evaluated	evaluate	VERB
fuelectenerg-400	676	10	as	as	ADP
fuelectenerg-400	676	11	(	(	PUNCT
fuelectenerg-400	676	12	n+n−1	n+n−1	ADJ
fuelectenerg-400	676	13	n	n	ADJ
fuelectenerg-400	676	14	)	)	PUNCT
fuelectenerg-400	676	15	.	.	PUNCT
fuelectenerg-400	677	1	the	the	DET
fuelectenerg-400	677	2	ranking	rank	VERB
fuelectenerg-400	677	3	algorithm	algorithm	NOUN
fuelectenerg-400	677	4	for	for	ADP
fuelectenerg-400	677	5	the	the	DET
fuelectenerg-400	677	6	lexicographical	lexicographical	ADJ
fuelectenerg-400	677	7	ordering	ordering	NOUN
fuelectenerg-400	677	8	of	of	ADP
fuelectenerg-400	677	9	members	member	NOUN
fuelectenerg-400	677	10	involves	involve	VERB
fuelectenerg-400	677	11	mapping	map	VERB
fuelectenerg-400	677	12	an	an	DET
fuelectenerg-400	677	13	integer	integer	NOUN
fuelectenerg-400	677	14	between	between	ADP
fuelectenerg-400	677	15	0	0	NUM
fuelectenerg-400	677	16	and	and	CCONJ
fuelectenerg-400	677	17	(	(	PUNCT
fuelectenerg-400	677	18	n+n−1	n+n−1	ADJ
fuelectenerg-400	677	19	n	n	ADJ
fuelectenerg-400	677	20	)	)	PUNCT
fuelectenerg-400	677	21	−	−	ADP
fuelectenerg-400	677	22	1	1	NUM
fuelectenerg-400	677	23	to	to	ADP
fuelectenerg-400	677	24	a	a	DET
fuelectenerg-400	677	25	sequence	sequence	NOUN
fuelectenerg-400	677	26	in	in	ADP
fuelectenerg-400	677	27	sn	sn	PROPN
fuelectenerg-400	677	28	n	n	PROPN
fuelectenerg-400	677	29	.	.	PUNCT
fuelectenerg-400	678	1	as	as	SCONJ
fuelectenerg-400	678	2	in	in	ADP
fuelectenerg-400	678	3	the	the	DET
fuelectenerg-400	678	4	previous	previous	ADJ
fuelectenerg-400	678	5	case	case	NOUN
fuelectenerg-400	678	6	,	,	PUNCT
fuelectenerg-400	678	7	the	the	DET
fuelectenerg-400	678	8	ranking	ranking	ADJ
fuelectenerg-400	678	9	algorithm	algorithm	NOUN
fuelectenerg-400	678	10	starts	start	VERB
fuelectenerg-400	678	11	with	with	ADP
fuelectenerg-400	678	12	an	an	DET
fuelectenerg-400	678	13	initial	initial	ADJ
fuelectenerg-400	678	14	estimate	estimate	NOUN
fuelectenerg-400	678	15	(	(	PUNCT
fuelectenerg-400	678	16	e0	e0	PROPN
fuelectenerg-400	678	17	=	=	PUNCT
fuelectenerg-400	678	18	(	(	PUNCT
fuelectenerg-400	678	19	n+n−1	n+n−1	PROPN
fuelectenerg-400	678	20	n	n	ADJ
fuelectenerg-400	678	21	)	)	PUNCT
fuelectenerg-400	678	22	−	−	PROPN
fuelectenerg-400	678	23	1	1	NUM
fuelectenerg-400	678	24	)	)	PUNCT
fuelectenerg-400	678	25	and	and	CCONJ
fuelectenerg-400	678	26	refines	refine	VERB
fuelectenerg-400	678	27	its	its	PRON
fuelectenerg-400	678	28	estimate	estimate	NOUN
fuelectenerg-400	678	29	as	as	SCONJ
fuelectenerg-400	678	30	the	the	DET
fuelectenerg-400	678	31	string	string	NOUN
fuelectenerg-400	678	32	is	be	AUX
fuelectenerg-400	678	33	parsed	parse	VERB
fuelectenerg-400	678	34	digit	digit	NOUN
fuelectenerg-400	678	35	by	by	ADP
fuelectenerg-400	678	36	digit	digit	NOUN
fuelectenerg-400	678	37	.	.	PUNCT
fuelectenerg-400	679	1	given	give	VERB
fuelectenerg-400	679	2	the	the	DET
fuelectenerg-400	679	3	estimate	estimate	NOUN
fuelectenerg-400	679	4	of	of	ADP
fuelectenerg-400	679	5	the	the	DET
fuelectenerg-400	679	6	rank	rank	NOUN
fuelectenerg-400	679	7	at	at	ADP
fuelectenerg-400	679	8	the	the	DET
fuelectenerg-400	679	9	(	(	PUNCT
fuelectenerg-400	679	10	b	b	X
fuelectenerg-400	679	11	−	−	PROPN
fuelectenerg-400	679	12	1)th	1)th	NOUN
fuelectenerg-400	679	13	digit	digit	NOUN
fuelectenerg-400	679	14	,	,	PUNCT
fuelectenerg-400	679	15	eb−1	eb−1	PROPN
fuelectenerg-400	679	16	,	,	PUNCT
fuelectenerg-400	679	17	and	and	CCONJ
fuelectenerg-400	679	18	that	that	SCONJ
fuelectenerg-400	679	19	the	the	DET
fuelectenerg-400	679	20	bth	bth	NOUN
fuelectenerg-400	679	21	digit	digit	NOUN
fuelectenerg-400	679	22	is	be	AUX
fuelectenerg-400	679	23	d(b	d(b	PROPN
fuelectenerg-400	679	24	)	)	PUNCT
fuelectenerg-400	679	25	,	,	PUNCT
fuelectenerg-400	679	26	the	the	DET
fuelectenerg-400	679	27	following	follow	VERB
fuelectenerg-400	679	28	conclusion	conclusion	NOUN
fuelectenerg-400	679	29	can	can	AUX
fuelectenerg-400	679	30	be	be	AUX
fuelectenerg-400	679	31	drawn	draw	VERB
fuelectenerg-400	679	32	about	about	ADP
fuelectenerg-400	679	33	the	the	DET
fuelectenerg-400	679	34	rank	rank	NOUN
fuelectenerg-400	679	35	.	.	PUNCT
fuelectenerg-400	680	1	the	the	DET
fuelectenerg-400	680	2	rank	rank	NOUN
fuelectenerg-400	680	3	is	be	AUX
fuelectenerg-400	680	4	less	less	ADJ
fuelectenerg-400	680	5	than	than	ADP
fuelectenerg-400	680	6	or	or	CCONJ
fuelectenerg-400	680	7	equal	equal	ADJ
fuelectenerg-400	680	8	to	to	ADP
fuelectenerg-400	680	9	eb−1	eb−1	PROPN
fuelectenerg-400	680	10	−	−	PROPN
fuelectenerg-400	680	11	(	(	PUNCT
fuelectenerg-400	680	12	n	n	CCONJ
fuelectenerg-400	680	13	′+b′−1	′+b′−1	PROPN
fuelectenerg-400	680	14	b′	b′	NUM
fuelectenerg-400	680	15	)	)	PUNCT
fuelectenerg-400	680	16	where	where	SCONJ
fuelectenerg-400	680	17	n	n	ADV
fuelectenerg-400	680	18	′	′	NUM
fuelectenerg-400	680	19	=	=	PUNCT
fuelectenerg-400	680	20	n	n	PRON
fuelectenerg-400	680	21	−	−	PROPN
fuelectenerg-400	680	22	d(b	d(b	PROPN
fuelectenerg-400	680	23	)	)	PUNCT
fuelectenerg-400	680	24	and	and	CCONJ
fuelectenerg-400	680	25	534	534	NUM
fuelectenerg-400	680	26	b.	b.	PROPN
fuelectenerg-400	680	27	vasic	vasic	PROPN
fuelectenerg-400	680	28	,	,	PUNCT
fuelectenerg-400	680	29	a.	a.	PROPN
fuelectenerg-400	680	30	r.	r.	PROPN
fuelectenerg-400	680	31	krishnan	krishnan	PROPN
fuelectenerg-400	680	32	lozenge	lozenge	PROPN
fuelectenerg-400	680	33	tiling	tile	VERB
fuelectenerg-400	680	34	constrained	constrained	ADJ
fuelectenerg-400	680	35	codes	code	NOUN
fuelectenerg-400	680	36	535	535	NUM
fuelectenerg-400	680	37	536	536	NUM
fuelectenerg-400	680	38	a.	a.	NOUN
fuelectenerg-400	680	39	r.	r.	PROPN
fuelectenerg-400	680	40	krishnanan	krishnanan	PROPN
fuelectenerg-400	680	41	and	and	CCONJ
fuelectenerg-400	680	42	b.	b.	PROPN
fuelectenerg-400	680	43	vasić	vasić	PROPN
fuelectenerg-400	680	44	b′	b′	NUM
fuelectenerg-400	681	1	=	=	NOUN
fuelectenerg-400	682	1	n	n	PRON
fuelectenerg-400	682	2	−	−	PROPN
fuelectenerg-400	682	3	b	b	PROPN
fuelectenerg-400	682	4	+	+	CCONJ
fuelectenerg-400	682	5	1	1	NUM
fuelectenerg-400	682	6	.	.	X
fuelectenerg-400	683	1	n	n	NOUN
fuelectenerg-400	683	2	′	′	NOUN
fuelectenerg-400	683	3	gives	give	VERB
fuelectenerg-400	683	4	the	the	DET
fuelectenerg-400	683	5	total	total	ADJ
fuelectenerg-400	683	6	number	number	NOUN
fuelectenerg-400	683	7	of	of	ADP
fuelectenerg-400	683	8	members	member	NOUN
fuelectenerg-400	683	9	of	of	ADP
fuelectenerg-400	683	10	n	n	X
fuelectenerg-400	683	11	greater	great	ADJ
fuelectenerg-400	683	12	than	than	ADP
fuelectenerg-400	683	13	d(b	d(b	PROPN
fuelectenerg-400	683	14	)	)	PUNCT
fuelectenerg-400	683	15	and	and	CCONJ
fuelectenerg-400	683	16	b′	b′	NOUN
fuelectenerg-400	683	17	gives	give	VERB
fuelectenerg-400	683	18	the	the	DET
fuelectenerg-400	683	19	total	total	ADJ
fuelectenerg-400	683	20	number	number	NOUN
fuelectenerg-400	683	21	of	of	ADP
fuelectenerg-400	683	22	available	available	ADJ
fuelectenerg-400	683	23	digits	digit	NOUN
fuelectenerg-400	683	24	including	include	VERB
fuelectenerg-400	683	25	the	the	DET
fuelectenerg-400	683	26	current	current	ADJ
fuelectenerg-400	683	27	digit	digit	NOUN
fuelectenerg-400	683	28	.	.	PUNCT
fuelectenerg-400	684	1	the	the	DET
fuelectenerg-400	684	2	second	second	ADJ
fuelectenerg-400	684	3	term	term	NOUN
fuelectenerg-400	684	4	in	in	ADP
fuelectenerg-400	684	5	the	the	DET
fuelectenerg-400	684	6	refined	refined	ADJ
fuelectenerg-400	684	7	estimate	estimate	NOUN
fuelectenerg-400	684	8	is	be	AUX
fuelectenerg-400	684	9	the	the	DET
fuelectenerg-400	684	10	total	total	ADJ
fuelectenerg-400	684	11	number	number	NOUN
fuelectenerg-400	684	12	of	of	ADP
fuelectenerg-400	684	13	strings	string	NOUN
fuelectenerg-400	684	14	of	of	ADP
fuelectenerg-400	684	15	length	length	NOUN
fuelectenerg-400	684	16	b′	b′	NOUN
fuelectenerg-400	684	17	that	that	PRON
fuelectenerg-400	684	18	can	can	AUX
fuelectenerg-400	684	19	be	be	AUX
fuelectenerg-400	684	20	generated	generate	VERB
fuelectenerg-400	684	21	using	use	VERB
fuelectenerg-400	684	22	the	the	DET
fuelectenerg-400	684	23	members	member	NOUN
fuelectenerg-400	684	24	of	of	ADP
fuelectenerg-400	684	25	n	n	X
fuelectenerg-400	684	26	larger	large	ADJ
fuelectenerg-400	684	27	than	than	ADP
fuelectenerg-400	684	28	d.	d.	PROPN
fuelectenerg-400	684	29	the	the	DET
fuelectenerg-400	684	30	strings	string	NOUN
fuelectenerg-400	684	31	having	have	VERB
fuelectenerg-400	684	32	these	these	DET
fuelectenerg-400	684	33	substrings	substring	NOUN
fuelectenerg-400	684	34	will	will	AUX
fuelectenerg-400	684	35	have	have	VERB
fuelectenerg-400	684	36	a	a	DET
fuelectenerg-400	684	37	higher	high	ADJ
fuelectenerg-400	684	38	ranking	ranking	NOUN
fuelectenerg-400	684	39	.	.	PUNCT
fuelectenerg-400	684	40	table	table	NOUN
fuelectenerg-400	684	41	3	3	NUM
fuelectenerg-400	684	42	shows	show	VERB
fuelectenerg-400	684	43	the	the	DET
fuelectenerg-400	684	44	progression	progression	NOUN
fuelectenerg-400	684	45	of	of	ADP
fuelectenerg-400	684	46	the	the	DET
fuelectenerg-400	684	47	algorithm	algorithm	NOUN
fuelectenerg-400	684	48	for	for	ADP
fuelectenerg-400	684	49	the	the	DET
fuelectenerg-400	684	50	member	member	NOUN
fuelectenerg-400	684	51	112	112	NUM
fuelectenerg-400	684	52	,	,	PUNCT
fuelectenerg-400	684	53	a	a	DET
fuelectenerg-400	684	54	member	member	NOUN
fuelectenerg-400	684	55	of	of	ADP
fuelectenerg-400	684	56	the	the	DET
fuelectenerg-400	684	57	set	set	ADJ
fuelectenerg-400	684	58	s2	s2	NOUN
fuelectenerg-400	684	59	3	3	NUM
fuelectenerg-400	684	60	.	.	PUNCT
fuelectenerg-400	685	1	at	at	ADP
fuelectenerg-400	685	2	each	each	DET
fuelectenerg-400	685	3	step	step	NOUN
fuelectenerg-400	685	4	,	,	PUNCT
fuelectenerg-400	685	5	the	the	DET
fuelectenerg-400	685	6	strings	string	NOUN
fuelectenerg-400	685	7	which	which	PRON
fuelectenerg-400	685	8	are	be	AUX
fuelectenerg-400	685	9	eliminated	eliminate	VERB
fuelectenerg-400	685	10	are	be	AUX
fuelectenerg-400	685	11	shown	show	VERB
fuelectenerg-400	685	12	in	in	ADP
fuelectenerg-400	685	13	parentheses	parenthesis	NOUN
fuelectenerg-400	685	14	.	.	PUNCT
fuelectenerg-400	686	1	table	table	NOUN
fuelectenerg-400	686	2	3	3	NUM
fuelectenerg-400	686	3	.	.	PUNCT
fuelectenerg-400	687	1	progression	progression	NOUN
fuelectenerg-400	687	2	of	of	ADP
fuelectenerg-400	687	3	the	the	DET
fuelectenerg-400	687	4	ranking	ranking	ADJ
fuelectenerg-400	687	5	algorithm	algorithm	NOUN
fuelectenerg-400	687	6	for	for	ADP
fuelectenerg-400	687	7	an	an	DET
fuelectenerg-400	687	8	example	example	NOUN
fuelectenerg-400	687	9	.	.	PUNCT
fuelectenerg-400	688	1	b	b	X
fuelectenerg-400	688	2	db	db	PROPN
fuelectenerg-400	688	3	eb	eb	PROPN
fuelectenerg-400	688	4	3	3	NUM
fuelectenerg-400	688	5	1	1	NUM
fuelectenerg-400	688	6	1	1	NUM
fuelectenerg-400	688	7	3	3	NUM
fuelectenerg-400	688	8	−	−	NOUN
fuelectenerg-400	688	9	1	1	NUM
fuelectenerg-400	688	10	=	=	SYM
fuelectenerg-400	688	11	2	2	NUM
fuelectenerg-400	688	12	(	(	PUNCT
fuelectenerg-400	688	13	222	222	NUM
fuelectenerg-400	688	14	)	)	PUNCT
fuelectenerg-400	688	15	2	2	NUM
fuelectenerg-400	688	16	1	1	NUM
fuelectenerg-400	688	17	2	2	NUM
fuelectenerg-400	688	18	−	−	NOUN
fuelectenerg-400	688	19	1	1	NUM
fuelectenerg-400	688	20	=	=	SYM
fuelectenerg-400	688	21	1	1	NUM
fuelectenerg-400	688	22	(	(	PUNCT
fuelectenerg-400	688	23	122	122	NUM
fuelectenerg-400	688	24	)	)	PUNCT
fuelectenerg-400	688	25	3	3	NUM
fuelectenerg-400	688	26	2	2	NUM
fuelectenerg-400	688	27	1	1	NUM
fuelectenerg-400	688	28	the	the	DET
fuelectenerg-400	688	29	unranking	unranking	NOUN
fuelectenerg-400	688	30	of	of	ADP
fuelectenerg-400	688	31	an	an	DET
fuelectenerg-400	688	32	integer	integer	NOUN
fuelectenerg-400	688	33	can	can	AUX
fuelectenerg-400	688	34	be	be	AUX
fuelectenerg-400	688	35	achieved	achieve	VERB
fuelectenerg-400	688	36	by	by	ADP
fuelectenerg-400	688	37	using	use	VERB
fuelectenerg-400	688	38	a	a	DET
fuelectenerg-400	688	39	similar	similar	ADJ
fuelectenerg-400	688	40	approach	approach	NOUN
fuelectenerg-400	688	41	.	.	PUNCT
fuelectenerg-400	689	1	through	through	ADP
fuelectenerg-400	689	2	the	the	DET
fuelectenerg-400	689	3	rest	rest	NOUN
fuelectenerg-400	689	4	of	of	ADP
fuelectenerg-400	689	5	this	this	DET
fuelectenerg-400	689	6	document	document	NOUN
fuelectenerg-400	689	7	,	,	PUNCT
fuelectenerg-400	689	8	the	the	DET
fuelectenerg-400	689	9	ranking	ranking	NOUN
fuelectenerg-400	689	10	and	and	CCONJ
fuelectenerg-400	689	11	unranking	unranking	NOUN
fuelectenerg-400	689	12	on	on	ADP
fuelectenerg-400	689	13	this	this	DET
fuelectenerg-400	689	14	set	set	NOUN
fuelectenerg-400	689	15	will	will	AUX
fuelectenerg-400	689	16	be	be	AUX
fuelectenerg-400	689	17	denoted	denote	VERB
fuelectenerg-400	689	18	rs	rs	ADV
fuelectenerg-400	689	19	and	and	CCONJ
fuelectenerg-400	689	20	r−1	r−1	PROPN
fuelectenerg-400	689	21	s	s	VERB
fuelectenerg-400	689	22	respectively	respectively	ADV
fuelectenerg-400	689	23	.	.	PUNCT
fuelectenerg-400	690	1	5.4	5.4	NUM
fuelectenerg-400	690	2	encoding	encoding	NOUN
fuelectenerg-400	690	3	by	by	ADP
fuelectenerg-400	690	4	routing	route	VERB
fuelectenerg-400	690	5	given	give	VERB
fuelectenerg-400	690	6	the	the	DET
fuelectenerg-400	690	7	lattice	lattice	NOUN
fuelectenerg-400	690	8	h	h	PROPN
fuelectenerg-400	690	9	of	of	ADP
fuelectenerg-400	690	10	dimension	dimension	NOUN
fuelectenerg-400	690	11	(	(	PUNCT
fuelectenerg-400	690	12	a	a	DET
fuelectenerg-400	690	13	,	,	PUNCT
fuelectenerg-400	690	14	b	b	NOUN
fuelectenerg-400	690	15	,	,	PUNCT
fuelectenerg-400	690	16	c	c	NOUN
fuelectenerg-400	690	17	)	)	PUNCT
fuelectenerg-400	690	18	,	,	PUNCT
fuelectenerg-400	690	19	the	the	DET
fuelectenerg-400	690	20	set	set	NOUN
fuelectenerg-400	690	21	of	of	ADP
fuelectenerg-400	690	22	valid	valid	ADJ
fuelectenerg-400	690	23	routings	routing	NOUN
fuelectenerg-400	690	24	,	,	PUNCT
fuelectenerg-400	690	25	r	r	NOUN
fuelectenerg-400	690	26	,	,	PUNCT
fuelectenerg-400	690	27	on	on	ADP
fuelectenerg-400	690	28	g	g	NOUN
fuelectenerg-400	690	29	consists	consist	VERB
fuelectenerg-400	690	30	of	of	ADP
fuelectenerg-400	690	31	ordered	order	VERB
fuelectenerg-400	690	32	sets	set	NOUN
fuelectenerg-400	690	33	of	of	ADP
fuelectenerg-400	690	34	size	size	NOUN
fuelectenerg-400	690	35	a	a	DET
fuelectenerg-400	690	36	consisting	consisting	NOUN
fuelectenerg-400	690	37	of	of	ADP
fuelectenerg-400	690	38	members	member	NOUN
fuelectenerg-400	690	39	of	of	ADP
fuelectenerg-400	690	40	the	the	DET
fuelectenerg-400	690	41	set	set	NOUN
fuelectenerg-400	690	42	d(a+b	d(a+b	X
fuelectenerg-400	690	43	,	,	PUNCT
fuelectenerg-400	690	44	b	b	NOUN
fuelectenerg-400	690	45	)	)	PUNCT
fuelectenerg-400	690	46	.	.	PUNCT
fuelectenerg-400	691	1	also	also	ADV
fuelectenerg-400	691	2	,	,	PUNCT
fuelectenerg-400	691	3	the	the	DET
fuelectenerg-400	691	4	ordered	order	VERB
fuelectenerg-400	691	5	sets	set	NOUN
fuelectenerg-400	691	6	will	will	AUX
fuelectenerg-400	691	7	be	be	AUX
fuelectenerg-400	691	8	in	in	ADP
fuelectenerg-400	691	9	non	non	ADJ
fuelectenerg-400	691	10	-	-	ADJ
fuelectenerg-400	691	11	decreasing	decrease	VERB
fuelectenerg-400	691	12	order	order	NOUN
fuelectenerg-400	691	13	of	of	ADP
fuelectenerg-400	691	14	rank	rank	NOUN
fuelectenerg-400	691	15	.	.	PUNCT
fuelectenerg-400	692	1	hence	hence	ADV
fuelectenerg-400	692	2	,	,	PUNCT
fuelectenerg-400	692	3	these	these	PRON
fuelectenerg-400	692	4	will	will	AUX
fuelectenerg-400	692	5	correspond	correspond	VERB
fuelectenerg-400	692	6	to	to	ADP
fuelectenerg-400	692	7	a	a	DET
fuelectenerg-400	692	8	non	non	ADJ
fuelectenerg-400	692	9	-	-	ADJ
fuelectenerg-400	692	10	decreasing	decrease	VERB
fuelectenerg-400	692	11	string	string	NOUN
fuelectenerg-400	692	12	of	of	ADP
fuelectenerg-400	692	13	length	length	NOUN
fuelectenerg-400	692	14	a	a	PRON
fuelectenerg-400	692	15	with	with	ADP
fuelectenerg-400	692	16	members	member	NOUN
fuelectenerg-400	692	17	from	from	ADP
fuelectenerg-400	692	18	the	the	DET
fuelectenerg-400	692	19	set	set	NOUN
fuelectenerg-400	692	20	{	{	PUNCT
fuelectenerg-400	692	21	1	1	NUM
fuelectenerg-400	692	22	,	,	PUNCT
fuelectenerg-400	692	23	2	2	NUM
fuelectenerg-400	692	24	,	,	PUNCT
fuelectenerg-400	692	25	3	3	NUM
fuelectenerg-400	692	26	,	,	PUNCT
fuelectenerg-400	692	27	...	...	PUNCT
fuelectenerg-400	692	28	,	,	PUNCT
fuelectenerg-400	692	29	∣∣d(a+b	∣∣d(a+b	PROPN
fuelectenerg-400	692	30	,	,	PUNCT
fuelectenerg-400	692	31	b	b	NOUN
fuelectenerg-400	692	32	)	)	PUNCT
fuelectenerg-400	692	33	∣∣	∣∣	NUM
fuelectenerg-400	692	34	}	}	PUNCT
fuelectenerg-400	692	35	.	.	PUNCT
fuelectenerg-400	693	1	this	this	DET
fuelectenerg-400	693	2	set	set	NOUN
fuelectenerg-400	693	3	is	be	AUX
fuelectenerg-400	693	4	s|d(a+b	s|d(a+b	NOUN
fuelectenerg-400	693	5	,	,	PUNCT
fuelectenerg-400	693	6	b)|	b)|	NOUN
fuelectenerg-400	693	7	c	c	PROPN
fuelectenerg-400	693	8	.	.	PUNCT
fuelectenerg-400	694	1	hence	hence	ADV
fuelectenerg-400	694	2	,	,	PUNCT
fuelectenerg-400	694	3	we	we	PRON
fuelectenerg-400	694	4	have	have	AUX
fuelectenerg-400	694	5	established	establish	VERB
fuelectenerg-400	694	6	a	a	DET
fuelectenerg-400	694	7	transitive	transitive	ADJ
fuelectenerg-400	694	8	relationship	relationship	NOUN
fuelectenerg-400	694	9	between	between	ADP
fuelectenerg-400	694	10	r	r	NOUN
fuelectenerg-400	694	11	and	and	CCONJ
fuelectenerg-400	694	12	s|d(a+b	s|d(a+b	NOUN
fuelectenerg-400	694	13	,	,	PUNCT
fuelectenerg-400	694	14	b)|	b)|	NOUN
fuelectenerg-400	694	15	c	c	PROPN
fuelectenerg-400	694	16	.	.	PUNCT
fuelectenerg-400	695	1	however	however	ADV
fuelectenerg-400	695	2	,	,	PUNCT
fuelectenerg-400	695	3	all	all	DET
fuelectenerg-400	695	4	the	the	DET
fuelectenerg-400	695	5	sequences	sequence	NOUN
fuelectenerg-400	695	6	in	in	ADP
fuelectenerg-400	695	7	this	this	DET
fuelectenerg-400	695	8	set	set	NOUN
fuelectenerg-400	695	9	do	do	AUX
fuelectenerg-400	695	10	not	not	PART
fuelectenerg-400	695	11	correspond	correspond	VERB
fuelectenerg-400	695	12	to	to	ADP
fuelectenerg-400	695	13	valid	valid	ADJ
fuelectenerg-400	695	14	tilings	tiling	NOUN
fuelectenerg-400	695	15	(	(	PUNCT
fuelectenerg-400	695	16	as	as	SCONJ
fuelectenerg-400	695	17	the	the	DET
fuelectenerg-400	695	18	converse	converse	NOUN
fuelectenerg-400	695	19	of	of	ADP
fuelectenerg-400	695	20	theorem	theorem	NOUN
fuelectenerg-400	695	21	4	4	NUM
fuelectenerg-400	695	22	is	be	AUX
fuelectenerg-400	695	23	not	not	PART
fuelectenerg-400	695	24	true	true	ADJ
fuelectenerg-400	695	25	)	)	PUNCT
fuelectenerg-400	695	26	.	.	PUNCT
fuelectenerg-400	696	1	hence	hence	ADV
fuelectenerg-400	696	2	,	,	PUNCT
fuelectenerg-400	696	3	we	we	PRON
fuelectenerg-400	696	4	generate	generate	VERB
fuelectenerg-400	696	5	a	a	DET
fuelectenerg-400	696	6	look	look	VERB
fuelectenerg-400	696	7	-	-	PUNCT
fuelectenerg-400	696	8	up	up	ADP
fuelectenerg-400	696	9	table	table	NOUN
fuelectenerg-400	696	10	(	(	PUNCT
fuelectenerg-400	696	11	lut	lut	PROPN
fuelectenerg-400	696	12	)	)	PUNCT
fuelectenerg-400	696	13	to	to	PART
fuelectenerg-400	696	14	map	map	VERB
fuelectenerg-400	696	15	the	the	DET
fuelectenerg-400	696	16	integers	integer	NOUN
fuelectenerg-400	696	17	in	in	ADP
fuelectenerg-400	696	18	[	[	X
fuelectenerg-400	696	19	0	0	NUM
fuelectenerg-400	696	20	,	,	PUNCT
fuelectenerg-400	696	21	|r|	|r|	NOUN
fuelectenerg-400	696	22	−	−	NOUN
fuelectenerg-400	696	23	1	1	NUM
fuelectenerg-400	696	24	]	]	PUNCT
fuelectenerg-400	696	25	to	to	ADP
fuelectenerg-400	696	26	the	the	DET
fuelectenerg-400	696	27	ranks	rank	NOUN
fuelectenerg-400	696	28	of	of	ADP
fuelectenerg-400	696	29	members	member	NOUN
fuelectenerg-400	696	30	of	of	ADP
fuelectenerg-400	696	31	sd(a+b	sd(a+b	PROPN
fuelectenerg-400	696	32	,	,	PUNCT
fuelectenerg-400	696	33	b	b	NOUN
fuelectenerg-400	696	34	)	)	PUNCT
fuelectenerg-400	696	35	c	c	NOUN
fuelectenerg-400	696	36	corresponding	correspond	VERB
fuelectenerg-400	696	37	to	to	ADP
fuelectenerg-400	696	38	valid	valid	ADJ
fuelectenerg-400	696	39	tilings	tiling	NOUN
fuelectenerg-400	696	40	.	.	PUNCT
fuelectenerg-400	697	1	the	the	DET
fuelectenerg-400	697	2	encoding	encoding	NOUN
fuelectenerg-400	697	3	process	process	NOUN
fuelectenerg-400	697	4	is	be	AUX
fuelectenerg-400	697	5	given	give	VERB
fuelectenerg-400	697	6	by	by	ADP
fuelectenerg-400	697	7	algorithm	algorithm	NOUN
fuelectenerg-400	697	8	2	2	NUM
fuelectenerg-400	697	9	.	.	PUNCT
fuelectenerg-400	698	1	the	the	DET
fuelectenerg-400	698	2	ranking	ranking	ADJ
fuelectenerg-400	698	3	algorithms	algorithm	NOUN
fuelectenerg-400	698	4	,	,	PUNCT
fuelectenerg-400	698	5	along	along	ADP
fuelectenerg-400	698	6	with	with	ADP
fuelectenerg-400	698	7	the	the	DET
fuelectenerg-400	698	8	lut	lut	PROPN
fuelectenerg-400	698	9	,	,	PUNCT
fuelectenerg-400	698	10	can	can	AUX
fuelectenerg-400	698	11	be	be	AUX
fuelectenerg-400	698	12	used	use	VERB
fuelectenerg-400	698	13	to	to	PART
fuelectenerg-400	698	14	map	map	VERB
fuelectenerg-400	698	15	a	a	DET
fuelectenerg-400	698	16	tiling	tiling	NOUN
fuelectenerg-400	698	17	to	to	ADP
fuelectenerg-400	698	18	a	a	DET
fuelectenerg-400	698	19	digit	digit	NOUN
fuelectenerg-400	698	20	in	in	ADP
fuelectenerg-400	698	21	[	[	X
fuelectenerg-400	698	22	0	0	NUM
fuelectenerg-400	698	23	,	,	PUNCT
fuelectenerg-400	698	24	|r|	|r|	NOUN
fuelectenerg-400	699	1	−	−	NOUN
fuelectenerg-400	699	2	1	1	NUM
fuelectenerg-400	699	3	]	]	PUNCT
fuelectenerg-400	699	4	.	.	PUNCT
fuelectenerg-400	700	1	6	6	NUM
fuelectenerg-400	700	2	conclusion	conclusion	NOUN
fuelectenerg-400	700	3	in	in	ADP
fuelectenerg-400	700	4	this	this	DET
fuelectenerg-400	700	5	paper	paper	NOUN
fuelectenerg-400	700	6	we	we	PRON
fuelectenerg-400	700	7	first	first	ADV
fuelectenerg-400	700	8	introduced	introduce	VERB
fuelectenerg-400	700	9	a	a	DET
fuelectenerg-400	700	10	class	class	NOUN
fuelectenerg-400	700	11	of	of	ADP
fuelectenerg-400	700	12	two	two	NUM
fuelectenerg-400	700	13	dimensional	dimensional	ADJ
fuelectenerg-400	700	14	constraints	constraint	NOUN
fuelectenerg-400	700	15	we	we	PRON
fuelectenerg-400	700	16	call	call	VERB
fuelectenerg-400	700	17	segregation	segregation	NOUN
fuelectenerg-400	700	18	constraints	constraint	NOUN
fuelectenerg-400	700	19	.	.	PUNCT
fuelectenerg-400	701	1	in	in	ADP
fuelectenerg-400	701	2	contrast	contrast	NOUN
fuelectenerg-400	701	3	to	to	ADP
fuelectenerg-400	701	4	isolation	isolation	NOUN
fuelectenerg-400	701	5	runlength	runlength	NOUN
fuelectenerg-400	701	6	constraints	constraint	NOUN
fuelectenerg-400	701	7	considered	consider	VERB
fuelectenerg-400	701	8	in	in	ADP
fuelectenerg-400	701	9	literature	literature	NOUN
fuelectenerg-400	701	10	,	,	PUNCT
fuelectenerg-400	701	11	we	we	PRON
fuelectenerg-400	701	12	limit	limit	VERB
fuelectenerg-400	701	13	the	the	DET
fuelectenerg-400	701	14	minimal	minimal	ADJ
fuelectenerg-400	701	15	number	number	NOUN
fuelectenerg-400	701	16	of	of	ADP
fuelectenerg-400	701	17	neighboring	neighboring	NOUN
fuelectenerg-400	701	18	or	or	CCONJ
fuelectenerg-400	701	19	touching	touching	ADJ
fuelectenerg-400	701	20	tiles	tile	NOUN
fuelectenerg-400	701	21	536	536	NUM
fuelectenerg-400	701	22	b.	b.	PROPN
fuelectenerg-400	701	23	vasic	vasic	PROPN
fuelectenerg-400	701	24	,	,	PUNCT
fuelectenerg-400	701	25	a.	a.	PROPN
fuelectenerg-400	701	26	r.	r.	PROPN
fuelectenerg-400	701	27	krishnan	krishnan	PROPN
fuelectenerg-400	701	28	lozenge	lozenge	PROPN
fuelectenerg-400	701	29	tiling	tile	VERB
fuelectenerg-400	701	30	constrained	constrained	ADJ
fuelectenerg-400	701	31	codes	code	NOUN
fuelectenerg-400	701	32	537	537	NUM
fuelectenerg-400	701	33	536	536	NUM
fuelectenerg-400	701	34	a.	a.	NOUN
fuelectenerg-400	701	35	r.	r.	PROPN
fuelectenerg-400	701	36	krishnanan	krishnanan	PROPN
fuelectenerg-400	701	37	and	and	CCONJ
fuelectenerg-400	701	38	b.	b.	PROPN
fuelectenerg-400	701	39	vasić	vasić	PROPN
fuelectenerg-400	701	40	b′	b′	NUM
fuelectenerg-400	701	41	=	=	NOUN
fuelectenerg-400	701	42	n	n	PRON
fuelectenerg-400	701	43	−	−	PROPN
fuelectenerg-400	701	44	b	b	PROPN
fuelectenerg-400	701	45	+	+	CCONJ
fuelectenerg-400	701	46	1	1	NUM
fuelectenerg-400	701	47	.	.	X
fuelectenerg-400	702	1	n	n	NOUN
fuelectenerg-400	702	2	′	′	NOUN
fuelectenerg-400	702	3	gives	give	VERB
fuelectenerg-400	702	4	the	the	DET
fuelectenerg-400	702	5	total	total	ADJ
fuelectenerg-400	702	6	number	number	NOUN
fuelectenerg-400	702	7	of	of	ADP
fuelectenerg-400	702	8	members	member	NOUN
fuelectenerg-400	702	9	of	of	ADP
fuelectenerg-400	702	10	n	n	X
fuelectenerg-400	702	11	greater	great	ADJ
fuelectenerg-400	702	12	than	than	ADP
fuelectenerg-400	702	13	d(b	d(b	PROPN
fuelectenerg-400	702	14	)	)	PUNCT
fuelectenerg-400	702	15	and	and	CCONJ
fuelectenerg-400	702	16	b′	b′	NOUN
fuelectenerg-400	702	17	gives	give	VERB
fuelectenerg-400	702	18	the	the	DET
fuelectenerg-400	702	19	total	total	ADJ
fuelectenerg-400	702	20	number	number	NOUN
fuelectenerg-400	702	21	of	of	ADP
fuelectenerg-400	702	22	available	available	ADJ
fuelectenerg-400	702	23	digits	digit	NOUN
fuelectenerg-400	702	24	including	include	VERB
fuelectenerg-400	702	25	the	the	DET
fuelectenerg-400	702	26	current	current	ADJ
fuelectenerg-400	702	27	digit	digit	NOUN
fuelectenerg-400	702	28	.	.	PUNCT
fuelectenerg-400	703	1	the	the	DET
fuelectenerg-400	703	2	second	second	ADJ
fuelectenerg-400	703	3	term	term	NOUN
fuelectenerg-400	703	4	in	in	ADP
fuelectenerg-400	703	5	the	the	DET
fuelectenerg-400	703	6	refined	refined	ADJ
fuelectenerg-400	703	7	estimate	estimate	NOUN
fuelectenerg-400	703	8	is	be	AUX
fuelectenerg-400	703	9	the	the	DET
fuelectenerg-400	703	10	total	total	ADJ
fuelectenerg-400	703	11	number	number	NOUN
fuelectenerg-400	703	12	of	of	ADP
fuelectenerg-400	703	13	strings	string	NOUN
fuelectenerg-400	703	14	of	of	ADP
fuelectenerg-400	703	15	length	length	NOUN
fuelectenerg-400	703	16	b′	b′	NOUN
fuelectenerg-400	703	17	that	that	PRON
fuelectenerg-400	703	18	can	can	AUX
fuelectenerg-400	703	19	be	be	AUX
fuelectenerg-400	703	20	generated	generate	VERB
fuelectenerg-400	703	21	using	use	VERB
fuelectenerg-400	703	22	the	the	DET
fuelectenerg-400	703	23	members	member	NOUN
fuelectenerg-400	703	24	of	of	ADP
fuelectenerg-400	703	25	n	n	X
fuelectenerg-400	703	26	larger	large	ADJ
fuelectenerg-400	703	27	than	than	ADP
fuelectenerg-400	703	28	d.	d.	PROPN
fuelectenerg-400	703	29	the	the	DET
fuelectenerg-400	703	30	strings	string	NOUN
fuelectenerg-400	703	31	having	have	VERB
fuelectenerg-400	703	32	these	these	DET
fuelectenerg-400	703	33	substrings	substring	NOUN
fuelectenerg-400	703	34	will	will	AUX
fuelectenerg-400	703	35	have	have	VERB
fuelectenerg-400	703	36	a	a	DET
fuelectenerg-400	703	37	higher	high	ADJ
fuelectenerg-400	703	38	ranking	ranking	NOUN
fuelectenerg-400	703	39	.	.	PUNCT
fuelectenerg-400	703	40	table	table	NOUN
fuelectenerg-400	703	41	3	3	NUM
fuelectenerg-400	703	42	shows	show	VERB
fuelectenerg-400	703	43	the	the	DET
fuelectenerg-400	703	44	progression	progression	NOUN
fuelectenerg-400	703	45	of	of	ADP
fuelectenerg-400	703	46	the	the	DET
fuelectenerg-400	703	47	algorithm	algorithm	NOUN
fuelectenerg-400	703	48	for	for	ADP
fuelectenerg-400	703	49	the	the	DET
fuelectenerg-400	703	50	member	member	NOUN
fuelectenerg-400	703	51	112	112	NUM
fuelectenerg-400	703	52	,	,	PUNCT
fuelectenerg-400	703	53	a	a	DET
fuelectenerg-400	703	54	member	member	NOUN
fuelectenerg-400	703	55	of	of	ADP
fuelectenerg-400	703	56	the	the	DET
fuelectenerg-400	703	57	set	set	ADJ
fuelectenerg-400	703	58	s2	s2	NOUN
fuelectenerg-400	703	59	3	3	NUM
fuelectenerg-400	703	60	.	.	PUNCT
fuelectenerg-400	704	1	at	at	ADP
fuelectenerg-400	704	2	each	each	DET
fuelectenerg-400	704	3	step	step	NOUN
fuelectenerg-400	704	4	,	,	PUNCT
fuelectenerg-400	704	5	the	the	DET
fuelectenerg-400	704	6	strings	string	NOUN
fuelectenerg-400	704	7	which	which	PRON
fuelectenerg-400	704	8	are	be	AUX
fuelectenerg-400	704	9	eliminated	eliminate	VERB
fuelectenerg-400	704	10	are	be	AUX
fuelectenerg-400	704	11	shown	show	VERB
fuelectenerg-400	704	12	in	in	ADP
fuelectenerg-400	704	13	parentheses	parenthesis	NOUN
fuelectenerg-400	704	14	.	.	PUNCT
fuelectenerg-400	705	1	table	table	NOUN
fuelectenerg-400	705	2	3	3	NUM
fuelectenerg-400	705	3	.	.	PUNCT
fuelectenerg-400	706	1	progression	progression	NOUN
fuelectenerg-400	706	2	of	of	ADP
fuelectenerg-400	706	3	the	the	DET
fuelectenerg-400	706	4	ranking	ranking	ADJ
fuelectenerg-400	706	5	algorithm	algorithm	NOUN
fuelectenerg-400	706	6	for	for	ADP
fuelectenerg-400	706	7	an	an	DET
fuelectenerg-400	706	8	example	example	NOUN
fuelectenerg-400	706	9	.	.	PUNCT
fuelectenerg-400	707	1	b	b	X
fuelectenerg-400	707	2	db	db	PROPN
fuelectenerg-400	707	3	eb	eb	PROPN
fuelectenerg-400	707	4	3	3	NUM
fuelectenerg-400	707	5	1	1	NUM
fuelectenerg-400	707	6	1	1	NUM
fuelectenerg-400	707	7	3	3	NUM
fuelectenerg-400	707	8	−	−	NOUN
fuelectenerg-400	707	9	1	1	NUM
fuelectenerg-400	707	10	=	=	SYM
fuelectenerg-400	707	11	2	2	NUM
fuelectenerg-400	707	12	(	(	PUNCT
fuelectenerg-400	707	13	222	222	NUM
fuelectenerg-400	707	14	)	)	PUNCT
fuelectenerg-400	707	15	2	2	NUM
fuelectenerg-400	707	16	1	1	NUM
fuelectenerg-400	707	17	2	2	NUM
fuelectenerg-400	707	18	−	−	NOUN
fuelectenerg-400	707	19	1	1	NUM
fuelectenerg-400	707	20	=	=	SYM
fuelectenerg-400	707	21	1	1	NUM
fuelectenerg-400	707	22	(	(	PUNCT
fuelectenerg-400	707	23	122	122	NUM
fuelectenerg-400	707	24	)	)	PUNCT
fuelectenerg-400	707	25	3	3	NUM
fuelectenerg-400	707	26	2	2	NUM
fuelectenerg-400	707	27	1	1	NUM
fuelectenerg-400	707	28	the	the	DET
fuelectenerg-400	707	29	unranking	unranking	NOUN
fuelectenerg-400	707	30	of	of	ADP
fuelectenerg-400	707	31	an	an	DET
fuelectenerg-400	707	32	integer	integer	NOUN
fuelectenerg-400	707	33	can	can	AUX
fuelectenerg-400	707	34	be	be	AUX
fuelectenerg-400	707	35	achieved	achieve	VERB
fuelectenerg-400	707	36	by	by	ADP
fuelectenerg-400	707	37	using	use	VERB
fuelectenerg-400	707	38	a	a	DET
fuelectenerg-400	707	39	similar	similar	ADJ
fuelectenerg-400	707	40	approach	approach	NOUN
fuelectenerg-400	707	41	.	.	PUNCT
fuelectenerg-400	708	1	through	through	ADP
fuelectenerg-400	708	2	the	the	DET
fuelectenerg-400	708	3	rest	rest	NOUN
fuelectenerg-400	708	4	of	of	ADP
fuelectenerg-400	708	5	this	this	DET
fuelectenerg-400	708	6	document	document	NOUN
fuelectenerg-400	708	7	,	,	PUNCT
fuelectenerg-400	708	8	the	the	DET
fuelectenerg-400	708	9	ranking	ranking	NOUN
fuelectenerg-400	708	10	and	and	CCONJ
fuelectenerg-400	708	11	unranking	unranking	NOUN
fuelectenerg-400	708	12	on	on	ADP
fuelectenerg-400	708	13	this	this	DET
fuelectenerg-400	708	14	set	set	NOUN
fuelectenerg-400	708	15	will	will	AUX
fuelectenerg-400	708	16	be	be	AUX
fuelectenerg-400	708	17	denoted	denote	VERB
fuelectenerg-400	708	18	rs	rs	ADV
fuelectenerg-400	708	19	and	and	CCONJ
fuelectenerg-400	708	20	r−1	r−1	PROPN
fuelectenerg-400	708	21	s	s	VERB
fuelectenerg-400	708	22	respectively	respectively	ADV
fuelectenerg-400	708	23	.	.	PUNCT
fuelectenerg-400	709	1	5.4	5.4	NUM
fuelectenerg-400	709	2	encoding	encoding	NOUN
fuelectenerg-400	709	3	by	by	ADP
fuelectenerg-400	709	4	routing	route	VERB
fuelectenerg-400	709	5	given	give	VERB
fuelectenerg-400	709	6	the	the	DET
fuelectenerg-400	709	7	lattice	lattice	NOUN
fuelectenerg-400	709	8	h	h	PROPN
fuelectenerg-400	709	9	of	of	ADP
fuelectenerg-400	709	10	dimension	dimension	NOUN
fuelectenerg-400	709	11	(	(	PUNCT
fuelectenerg-400	709	12	a	a	DET
fuelectenerg-400	709	13	,	,	PUNCT
fuelectenerg-400	709	14	b	b	NOUN
fuelectenerg-400	709	15	,	,	PUNCT
fuelectenerg-400	709	16	c	c	NOUN
fuelectenerg-400	709	17	)	)	PUNCT
fuelectenerg-400	709	18	,	,	PUNCT
fuelectenerg-400	709	19	the	the	DET
fuelectenerg-400	709	20	set	set	NOUN
fuelectenerg-400	709	21	of	of	ADP
fuelectenerg-400	709	22	valid	valid	ADJ
fuelectenerg-400	709	23	routings	routing	NOUN
fuelectenerg-400	709	24	,	,	PUNCT
fuelectenerg-400	709	25	r	r	NOUN
fuelectenerg-400	709	26	,	,	PUNCT
fuelectenerg-400	709	27	on	on	ADP
fuelectenerg-400	709	28	g	g	NOUN
fuelectenerg-400	709	29	consists	consist	VERB
fuelectenerg-400	709	30	of	of	ADP
fuelectenerg-400	709	31	ordered	order	VERB
fuelectenerg-400	709	32	sets	set	NOUN
fuelectenerg-400	709	33	of	of	ADP
fuelectenerg-400	709	34	size	size	NOUN
fuelectenerg-400	709	35	a	a	DET
fuelectenerg-400	709	36	consisting	consisting	NOUN
fuelectenerg-400	709	37	of	of	ADP
fuelectenerg-400	709	38	members	member	NOUN
fuelectenerg-400	709	39	of	of	ADP
fuelectenerg-400	709	40	the	the	DET
fuelectenerg-400	709	41	set	set	NOUN
fuelectenerg-400	709	42	d(a+b	d(a+b	X
fuelectenerg-400	709	43	,	,	PUNCT
fuelectenerg-400	709	44	b	b	NOUN
fuelectenerg-400	709	45	)	)	PUNCT
fuelectenerg-400	709	46	.	.	PUNCT
fuelectenerg-400	710	1	also	also	ADV
fuelectenerg-400	710	2	,	,	PUNCT
fuelectenerg-400	710	3	the	the	DET
fuelectenerg-400	710	4	ordered	order	VERB
fuelectenerg-400	710	5	sets	set	NOUN
fuelectenerg-400	710	6	will	will	AUX
fuelectenerg-400	710	7	be	be	AUX
fuelectenerg-400	710	8	in	in	ADP
fuelectenerg-400	710	9	non	non	ADJ
fuelectenerg-400	710	10	-	-	ADJ
fuelectenerg-400	710	11	decreasing	decrease	VERB
fuelectenerg-400	710	12	order	order	NOUN
fuelectenerg-400	710	13	of	of	ADP
fuelectenerg-400	710	14	rank	rank	NOUN
fuelectenerg-400	710	15	.	.	PUNCT
fuelectenerg-400	711	1	hence	hence	ADV
fuelectenerg-400	711	2	,	,	PUNCT
fuelectenerg-400	711	3	these	these	PRON
fuelectenerg-400	711	4	will	will	AUX
fuelectenerg-400	711	5	correspond	correspond	VERB
fuelectenerg-400	711	6	to	to	ADP
fuelectenerg-400	711	7	a	a	DET
fuelectenerg-400	711	8	non	non	ADJ
fuelectenerg-400	711	9	-	-	ADJ
fuelectenerg-400	711	10	decreasing	decrease	VERB
fuelectenerg-400	711	11	string	string	NOUN
fuelectenerg-400	711	12	of	of	ADP
fuelectenerg-400	711	13	length	length	NOUN
fuelectenerg-400	711	14	a	a	PRON
fuelectenerg-400	711	15	with	with	ADP
fuelectenerg-400	711	16	members	member	NOUN
fuelectenerg-400	711	17	from	from	ADP
fuelectenerg-400	711	18	the	the	DET
fuelectenerg-400	711	19	set	set	NOUN
fuelectenerg-400	711	20	{	{	PUNCT
fuelectenerg-400	711	21	1	1	NUM
fuelectenerg-400	711	22	,	,	PUNCT
fuelectenerg-400	711	23	2	2	NUM
fuelectenerg-400	711	24	,	,	PUNCT
fuelectenerg-400	711	25	3	3	NUM
fuelectenerg-400	711	26	,	,	PUNCT
fuelectenerg-400	711	27	...	...	PUNCT
fuelectenerg-400	711	28	,	,	PUNCT
fuelectenerg-400	711	29	∣∣d(a+b	∣∣d(a+b	PROPN
fuelectenerg-400	711	30	,	,	PUNCT
fuelectenerg-400	711	31	b	b	NOUN
fuelectenerg-400	711	32	)	)	PUNCT
fuelectenerg-400	711	33	∣∣	∣∣	NUM
fuelectenerg-400	711	34	}	}	PUNCT
fuelectenerg-400	711	35	.	.	PUNCT
fuelectenerg-400	712	1	this	this	DET
fuelectenerg-400	712	2	set	set	NOUN
fuelectenerg-400	712	3	is	be	AUX
fuelectenerg-400	712	4	s|d(a+b	s|d(a+b	NOUN
fuelectenerg-400	712	5	,	,	PUNCT
fuelectenerg-400	712	6	b)|	b)|	NOUN
fuelectenerg-400	712	7	c	c	PROPN
fuelectenerg-400	712	8	.	.	PUNCT
fuelectenerg-400	713	1	hence	hence	ADV
fuelectenerg-400	713	2	,	,	PUNCT
fuelectenerg-400	713	3	we	we	PRON
fuelectenerg-400	713	4	have	have	AUX
fuelectenerg-400	713	5	established	establish	VERB
fuelectenerg-400	713	6	a	a	DET
fuelectenerg-400	713	7	transitive	transitive	ADJ
fuelectenerg-400	713	8	relationship	relationship	NOUN
fuelectenerg-400	713	9	between	between	ADP
fuelectenerg-400	713	10	r	r	NOUN
fuelectenerg-400	713	11	and	and	CCONJ
fuelectenerg-400	713	12	s|d(a+b	s|d(a+b	NOUN
fuelectenerg-400	713	13	,	,	PUNCT
fuelectenerg-400	713	14	b)|	b)|	NOUN
fuelectenerg-400	713	15	c	c	PROPN
fuelectenerg-400	713	16	.	.	PUNCT
fuelectenerg-400	714	1	however	however	ADV
fuelectenerg-400	714	2	,	,	PUNCT
fuelectenerg-400	714	3	all	all	DET
fuelectenerg-400	714	4	the	the	DET
fuelectenerg-400	714	5	sequences	sequence	NOUN
fuelectenerg-400	714	6	in	in	ADP
fuelectenerg-400	714	7	this	this	DET
fuelectenerg-400	714	8	set	set	NOUN
fuelectenerg-400	714	9	do	do	AUX
fuelectenerg-400	714	10	not	not	PART
fuelectenerg-400	714	11	correspond	correspond	VERB
fuelectenerg-400	714	12	to	to	ADP
fuelectenerg-400	714	13	valid	valid	ADJ
fuelectenerg-400	714	14	tilings	tiling	NOUN
fuelectenerg-400	714	15	(	(	PUNCT
fuelectenerg-400	714	16	as	as	SCONJ
fuelectenerg-400	714	17	the	the	DET
fuelectenerg-400	714	18	converse	converse	NOUN
fuelectenerg-400	714	19	of	of	ADP
fuelectenerg-400	714	20	theorem	theorem	NOUN
fuelectenerg-400	714	21	4	4	NUM
fuelectenerg-400	714	22	is	be	AUX
fuelectenerg-400	714	23	not	not	PART
fuelectenerg-400	714	24	true	true	ADJ
fuelectenerg-400	714	25	)	)	PUNCT
fuelectenerg-400	714	26	.	.	PUNCT
fuelectenerg-400	715	1	hence	hence	ADV
fuelectenerg-400	715	2	,	,	PUNCT
fuelectenerg-400	715	3	we	we	PRON
fuelectenerg-400	715	4	generate	generate	VERB
fuelectenerg-400	715	5	a	a	DET
fuelectenerg-400	715	6	look	look	VERB
fuelectenerg-400	715	7	-	-	PUNCT
fuelectenerg-400	715	8	up	up	ADP
fuelectenerg-400	715	9	table	table	NOUN
fuelectenerg-400	715	10	(	(	PUNCT
fuelectenerg-400	715	11	lut	lut	PROPN
fuelectenerg-400	715	12	)	)	PUNCT
fuelectenerg-400	715	13	to	to	PART
fuelectenerg-400	715	14	map	map	VERB
fuelectenerg-400	715	15	the	the	DET
fuelectenerg-400	715	16	integers	integer	NOUN
fuelectenerg-400	715	17	in	in	ADP
fuelectenerg-400	715	18	[	[	X
fuelectenerg-400	715	19	0	0	NUM
fuelectenerg-400	715	20	,	,	PUNCT
fuelectenerg-400	715	21	|r|	|r|	NOUN
fuelectenerg-400	715	22	−	−	NOUN
fuelectenerg-400	715	23	1	1	NUM
fuelectenerg-400	715	24	]	]	PUNCT
fuelectenerg-400	715	25	to	to	ADP
fuelectenerg-400	715	26	the	the	DET
fuelectenerg-400	715	27	ranks	rank	NOUN
fuelectenerg-400	715	28	of	of	ADP
fuelectenerg-400	715	29	members	member	NOUN
fuelectenerg-400	715	30	of	of	ADP
fuelectenerg-400	715	31	sd(a+b	sd(a+b	PROPN
fuelectenerg-400	715	32	,	,	PUNCT
fuelectenerg-400	715	33	b	b	NOUN
fuelectenerg-400	715	34	)	)	PUNCT
fuelectenerg-400	715	35	c	c	NOUN
fuelectenerg-400	715	36	corresponding	correspond	VERB
fuelectenerg-400	715	37	to	to	ADP
fuelectenerg-400	715	38	valid	valid	ADJ
fuelectenerg-400	715	39	tilings	tiling	NOUN
fuelectenerg-400	715	40	.	.	PUNCT
fuelectenerg-400	716	1	the	the	DET
fuelectenerg-400	716	2	encoding	encoding	NOUN
fuelectenerg-400	716	3	process	process	NOUN
fuelectenerg-400	716	4	is	be	AUX
fuelectenerg-400	716	5	given	give	VERB
fuelectenerg-400	716	6	by	by	ADP
fuelectenerg-400	716	7	algorithm	algorithm	NOUN
fuelectenerg-400	716	8	2	2	NUM
fuelectenerg-400	716	9	.	.	PUNCT
fuelectenerg-400	717	1	the	the	DET
fuelectenerg-400	717	2	ranking	ranking	ADJ
fuelectenerg-400	717	3	algorithms	algorithm	NOUN
fuelectenerg-400	717	4	,	,	PUNCT
fuelectenerg-400	717	5	along	along	ADP
fuelectenerg-400	717	6	with	with	ADP
fuelectenerg-400	717	7	the	the	DET
fuelectenerg-400	717	8	lut	lut	PROPN
fuelectenerg-400	717	9	,	,	PUNCT
fuelectenerg-400	717	10	can	can	AUX
fuelectenerg-400	717	11	be	be	AUX
fuelectenerg-400	717	12	used	use	VERB
fuelectenerg-400	717	13	to	to	PART
fuelectenerg-400	717	14	map	map	VERB
fuelectenerg-400	717	15	a	a	DET
fuelectenerg-400	717	16	tiling	tiling	NOUN
fuelectenerg-400	717	17	to	to	ADP
fuelectenerg-400	717	18	a	a	DET
fuelectenerg-400	717	19	digit	digit	NOUN
fuelectenerg-400	717	20	in	in	ADP
fuelectenerg-400	717	21	[	[	X
fuelectenerg-400	717	22	0	0	NUM
fuelectenerg-400	717	23	,	,	PUNCT
fuelectenerg-400	717	24	|r|	|r|	NOUN
fuelectenerg-400	718	1	−	−	NOUN
fuelectenerg-400	718	2	1	1	NUM
fuelectenerg-400	718	3	]	]	PUNCT
fuelectenerg-400	718	4	.	.	PUNCT
fuelectenerg-400	719	1	6	6	NUM
fuelectenerg-400	719	2	conclusion	conclusion	NOUN
fuelectenerg-400	719	3	in	in	ADP
fuelectenerg-400	719	4	this	this	DET
fuelectenerg-400	719	5	paper	paper	NOUN
fuelectenerg-400	719	6	we	we	PRON
fuelectenerg-400	719	7	first	first	ADV
fuelectenerg-400	719	8	introduced	introduce	VERB
fuelectenerg-400	719	9	a	a	DET
fuelectenerg-400	719	10	class	class	NOUN
fuelectenerg-400	719	11	of	of	ADP
fuelectenerg-400	719	12	two	two	NUM
fuelectenerg-400	719	13	dimensional	dimensional	ADJ
fuelectenerg-400	719	14	constraints	constraint	NOUN
fuelectenerg-400	719	15	we	we	PRON
fuelectenerg-400	719	16	call	call	VERB
fuelectenerg-400	719	17	segregation	segregation	NOUN
fuelectenerg-400	719	18	constraints	constraint	NOUN
fuelectenerg-400	719	19	.	.	PUNCT
fuelectenerg-400	720	1	in	in	ADP
fuelectenerg-400	720	2	contrast	contrast	NOUN
fuelectenerg-400	720	3	to	to	ADP
fuelectenerg-400	720	4	isolation	isolation	NOUN
fuelectenerg-400	720	5	runlength	runlength	NOUN
fuelectenerg-400	720	6	constraints	constraint	NOUN
fuelectenerg-400	720	7	considered	consider	VERB
fuelectenerg-400	720	8	in	in	ADP
fuelectenerg-400	720	9	literature	literature	NOUN
fuelectenerg-400	720	10	,	,	PUNCT
fuelectenerg-400	720	11	we	we	PRON
fuelectenerg-400	720	12	limit	limit	VERB
fuelectenerg-400	720	13	the	the	DET
fuelectenerg-400	720	14	minimal	minimal	ADJ
fuelectenerg-400	720	15	number	number	NOUN
fuelectenerg-400	720	16	of	of	ADP
fuelectenerg-400	720	17	neighboring	neighboring	NOUN
fuelectenerg-400	720	18	or	or	CCONJ
fuelectenerg-400	720	19	touching	touching	ADJ
fuelectenerg-400	720	20	tiles	tile	NOUN
fuelectenerg-400	720	21	detection	detection	NOUN
fuelectenerg-400	720	22	and	and	CCONJ
fuelectenerg-400	720	23	coding	code	VERB
fuelectenerg-400	720	24	for	for	ADP
fuelectenerg-400	720	25	tdmr	tdmr	NOUN
fuelectenerg-400	720	26	channel	channel	NOUN
fuelectenerg-400	720	27	537	537	NUM
fuelectenerg-400	720	28	algorithm	algorithm	NOUN
fuelectenerg-400	720	29	2	2	NUM
fuelectenerg-400	720	30	the	the	DET
fuelectenerg-400	720	31	encoding	encoding	NOUN
fuelectenerg-400	720	32	algorithm	algorithm	NOUN
fuelectenerg-400	720	33	use	use	VERB
fuelectenerg-400	720	34	the	the	DET
fuelectenerg-400	720	35	lookup	lookup	NOUN
fuelectenerg-400	720	36	table	table	NOUN
fuelectenerg-400	720	37	(	(	PUNCT
fuelectenerg-400	720	38	lut	lut	PROPN
fuelectenerg-400	720	39	)	)	PUNCT
fuelectenerg-400	720	40	to	to	PART
fuelectenerg-400	720	41	find	find	VERB
fuelectenerg-400	720	42	the	the	DET
fuelectenerg-400	720	43	rank	rank	NOUN
fuelectenerg-400	720	44	of	of	ADP
fuelectenerg-400	720	45	the	the	DET
fuelectenerg-400	720	46	corresponding	corresponding	ADJ
fuelectenerg-400	720	47	string	string	NOUN
fuelectenerg-400	720	48	in	in	ADP
fuelectenerg-400	720	49	s|d(a+b	s|d(a+b	PROPN
fuelectenerg-400	720	50	,	,	PUNCT
fuelectenerg-400	720	51	b)|	b)|	NOUN
fuelectenerg-400	720	52	c	c	NOUN
fuelectenerg-400	720	53	use	use	VERB
fuelectenerg-400	720	54	the	the	DET
fuelectenerg-400	720	55	r−1	r−1	PROPN
fuelectenerg-400	720	56	s	s	VERB
fuelectenerg-400	720	57	to	to	PART
fuelectenerg-400	720	58	find	find	VERB
fuelectenerg-400	720	59	the	the	DET
fuelectenerg-400	720	60	string	string	NOUN
fuelectenerg-400	720	61	si	si	X
fuelectenerg-400	720	62	in	in	ADP
fuelectenerg-400	720	63	the	the	DET
fuelectenerg-400	720	64	set	set	PROPN
fuelectenerg-400	720	65	sd(a+b	sd(a+b	PROPN
fuelectenerg-400	720	66	,	,	PUNCT
fuelectenerg-400	720	67	b	b	NOUN
fuelectenerg-400	720	68	)	)	PUNCT
fuelectenerg-400	720	69	c	c	NOUN
fuelectenerg-400	720	70	.	.	PUNCT
fuelectenerg-400	721	1	each	each	DET
fuelectenerg-400	721	2	digit	digit	NOUN
fuelectenerg-400	721	3	in	in	ADP
fuelectenerg-400	721	4	si	si	NOUN
fuelectenerg-400	721	5	,	,	PUNCT
fuelectenerg-400	721	6	si(j	si(j	NOUN
fuelectenerg-400	721	7	)	)	PUNCT
fuelectenerg-400	721	8	,	,	PUNCT
fuelectenerg-400	721	9	corresponds	correspond	VERB
fuelectenerg-400	721	10	to	to	ADP
fuelectenerg-400	721	11	the	the	DET
fuelectenerg-400	721	12	rank	rank	NOUN
fuelectenerg-400	721	13	of	of	ADP
fuelectenerg-400	721	14	a	a	DET
fuelectenerg-400	721	15	sequence	sequence	NOUN
fuelectenerg-400	721	16	in	in	ADP
fuelectenerg-400	721	17	d(a+b	d(a+b	NOUN
fuelectenerg-400	721	18	,	,	PUNCT
fuelectenerg-400	721	19	b	b	NOUN
fuelectenerg-400	721	20	)	)	PUNCT
fuelectenerg-400	721	21	.	.	PUNCT
fuelectenerg-400	722	1	for	for	ADP
fuelectenerg-400	722	2	all	all	DET
fuelectenerg-400	722	3	si(j	si(j	NOUN
fuelectenerg-400	722	4	)	)	PUNCT
fuelectenerg-400	722	5	do	do	AUX
fuelectenerg-400	722	6	use	use	VERB
fuelectenerg-400	722	7	the	the	DET
fuelectenerg-400	722	8	r−1	r−1	PROPN
fuelectenerg-400	722	9	d	d	NOUN
fuelectenerg-400	722	10	to	to	PART
fuelectenerg-400	722	11	find	find	VERB
fuelectenerg-400	722	12	the	the	DET
fuelectenerg-400	722	13	sequence	sequence	NOUN
fuelectenerg-400	722	14	corresponding	correspond	VERB
fuelectenerg-400	722	15	to	to	ADP
fuelectenerg-400	722	16	the	the	DET
fuelectenerg-400	722	17	rank	rank	NOUN
fuelectenerg-400	722	18	si(j	si(j	PUNCT
fuelectenerg-400	722	19	)	)	PUNCT
fuelectenerg-400	722	20	.	.	PUNCT
fuelectenerg-400	723	1	end	end	NOUN
fuelectenerg-400	723	2	for	for	ADP
fuelectenerg-400	723	3	assemble	assemble	VERB
fuelectenerg-400	723	4	the	the	DET
fuelectenerg-400	723	5	sequences	sequence	NOUN
fuelectenerg-400	723	6	to	to	PART
fuelectenerg-400	723	7	find	find	VERB
fuelectenerg-400	723	8	the	the	DET
fuelectenerg-400	723	9	ordered	order	VERB
fuelectenerg-400	723	10	set	set	NOUN
fuelectenerg-400	723	11	in	in	ADP
fuelectenerg-400	723	12	r.	r.	PROPN
fuelectenerg-400	723	13	of	of	ADP
fuelectenerg-400	723	14	the	the	DET
fuelectenerg-400	723	15	same	same	ADJ
fuelectenerg-400	723	16	color	color	NOUN
fuelectenerg-400	723	17	and	and	CCONJ
fuelectenerg-400	723	18	restrict	restrict	VERB
fuelectenerg-400	723	19	the	the	DET
fuelectenerg-400	723	20	shape	shape	NOUN
fuelectenerg-400	723	21	of	of	ADP
fuelectenerg-400	723	22	equaly	equaly	NOUN
fuelectenerg-400	723	23	-	-	PUNCT
fuelectenerg-400	723	24	colored	colored	ADJ
fuelectenerg-400	723	25	regions	region	NOUN
fuelectenerg-400	723	26	.	.	PUNCT
fuelectenerg-400	724	1	for	for	ADP
fuelectenerg-400	724	2	most	most	ADJ
fuelectenerg-400	724	3	twodimensional	twodimensional	ADJ
fuelectenerg-400	724	4	recording	recording	NOUN
fuelectenerg-400	724	5	systems	system	NOUN
fuelectenerg-400	724	6	such	such	ADJ
fuelectenerg-400	724	7	constraints	constraint	NOUN
fuelectenerg-400	724	8	are	be	AUX
fuelectenerg-400	724	9	more	more	ADV
fuelectenerg-400	724	10	natural	natural	ADJ
fuelectenerg-400	724	11	than	than	ADP
fuelectenerg-400	724	12	isolation	isolation	NOUN
fuelectenerg-400	724	13	constraints	constraint	NOUN
fuelectenerg-400	724	14	.	.	PUNCT
fuelectenerg-400	725	1	the	the	DET
fuelectenerg-400	725	2	reason	reason	NOUN
fuelectenerg-400	725	3	is	be	AUX
fuelectenerg-400	725	4	that	that	SCONJ
fuelectenerg-400	725	5	in	in	ADP
fuelectenerg-400	725	6	high	high	ADJ
fuelectenerg-400	725	7	density	density	NOUN
fuelectenerg-400	725	8	recording	recording	NOUN
fuelectenerg-400	725	9	systems	system	NOUN
fuelectenerg-400	725	10	recorded	record	VERB
fuelectenerg-400	725	11	pattern	pattern	NOUN
fuelectenerg-400	725	12	features	feature	NOUN
fuelectenerg-400	725	13	(	(	PUNCT
fuelectenerg-400	725	14	areas	area	NOUN
fuelectenerg-400	725	15	of	of	ADP
fuelectenerg-400	725	16	same	same	ADJ
fuelectenerg-400	725	17	physical	physical	ADJ
fuelectenerg-400	725	18	properties	property	NOUN
fuelectenerg-400	725	19	)	)	PUNCT
fuelectenerg-400	725	20	are	be	AUX
fuelectenerg-400	725	21	smaller	small	ADJ
fuelectenerg-400	725	22	than	than	ADP
fuelectenerg-400	725	23	what	what	PRON
fuelectenerg-400	725	24	can	can	AUX
fuelectenerg-400	725	25	be	be	AUX
fuelectenerg-400	725	26	reliably	reliably	ADV
fuelectenerg-400	725	27	distinguished	distinguish	VERB
fuelectenerg-400	725	28	by	by	ADP
fuelectenerg-400	725	29	a	a	DET
fuelectenerg-400	725	30	reading	reading	NOUN
fuelectenerg-400	725	31	device	device	NOUN
fuelectenerg-400	725	32	.	.	PUNCT
fuelectenerg-400	726	1	for	for	ADP
fuelectenerg-400	726	2	a	a	DET
fuelectenerg-400	726	3	particular	particular	ADJ
fuelectenerg-400	726	4	constraint	constraint	NOUN
fuelectenerg-400	726	5	on	on	ADP
fuelectenerg-400	726	6	a	a	DET
fuelectenerg-400	726	7	triangular	triangular	NOUN
fuelectenerg-400	726	8	lattice	lattice	NOUN
fuelectenerg-400	726	9	called	call	VERB
fuelectenerg-400	726	10	the	the	DET
fuelectenerg-400	726	11	no	no	ADV
fuelectenerg-400	726	12	-	-	PUNCT
fuelectenerg-400	726	13	isolated	isolate	VERB
fuelectenerg-400	726	14	bit	bit	NOUN
fuelectenerg-400	726	15	constraint	constraint	NOUN
fuelectenerg-400	726	16	we	we	PRON
fuelectenerg-400	726	17	introduced	introduce	VERB
fuelectenerg-400	726	18	a	a	DET
fuelectenerg-400	726	19	method	method	NOUN
fuelectenerg-400	726	20	for	for	ADP
fuelectenerg-400	726	21	encoding	encode	VERB
fuelectenerg-400	726	22	and	and	CCONJ
fuelectenerg-400	726	23	decoding	decode	VERB
fuelectenerg-400	726	24	.	.	PUNCT
fuelectenerg-400	727	1	future	future	ADJ
fuelectenerg-400	727	2	work	work	NOUN
fuelectenerg-400	727	3	include	include	VERB
fuelectenerg-400	727	4	studying	study	VERB
fuelectenerg-400	727	5	the	the	DET
fuelectenerg-400	727	6	effect	effect	NOUN
fuelectenerg-400	727	7	of	of	ADP
fuelectenerg-400	727	8	lozenge	lozenge	ADJ
fuelectenerg-400	727	9	constraints	constraint	NOUN
fuelectenerg-400	727	10	on	on	ADP
fuelectenerg-400	727	11	a	a	DET
fuelectenerg-400	727	12	tdmr	tdmr	NOUN
fuelectenerg-400	727	13	detector	detector	NOUN
fuelectenerg-400	727	14	performance	performance	NOUN
fuelectenerg-400	727	15	in	in	ADP
fuelectenerg-400	727	16	the	the	DET
fuelectenerg-400	727	17	spirit	spirit	NOUN
fuelectenerg-400	727	18	of	of	ADP
fuelectenerg-400	727	19	what	what	PRON
fuelectenerg-400	727	20	we	we	PRON
fuelectenerg-400	727	21	have	have	AUX
fuelectenerg-400	727	22	done	do	VERB
fuelectenerg-400	727	23	for	for	ADP
fuelectenerg-400	727	24	the	the	DET
fuelectenerg-400	727	25	square	square	ADJ
fuelectenerg-400	727	26	lattice	lattice	NOUN
fuelectenerg-400	728	1	[	[	X
fuelectenerg-400	728	2	25	25	NUM
fuelectenerg-400	728	3	]	]	PUNCT
fuelectenerg-400	728	4	.	.	PUNCT
fuelectenerg-400	729	1	acknowledgment	acknowledgment	NOUN
fuelectenerg-400	729	2	this	this	DET
fuelectenerg-400	729	3	work	work	NOUN
fuelectenerg-400	729	4	was	be	AUX
fuelectenerg-400	729	5	supported	support	VERB
fuelectenerg-400	729	6	by	by	ADP
fuelectenerg-400	729	7	the	the	DET
fuelectenerg-400	729	8	national	national	PROPN
fuelectenerg-400	729	9	science	science	PROPN
fuelectenerg-400	729	10	foundation	foundation	PROPN
fuelectenerg-400	729	11	under	under	ADP
fuelectenerg-400	729	12	grant	grant	NOUN
fuelectenerg-400	729	13	ccf-0963726	ccf-0963726	NOUN
fuelectenerg-400	729	14	and	and	CCONJ
fuelectenerg-400	729	15	ccf-1314147	ccf-1314147	NOUN
fuelectenerg-400	729	16	.	.	PUNCT
fuelectenerg-400	730	1	the	the	DET
fuelectenerg-400	730	2	work	work	NOUN
fuelectenerg-400	730	3	of	of	ADP
fuelectenerg-400	730	4	a.	a.	PROPN
fuelectenerg-400	730	5	r.	r.	PROPN
fuelectenerg-400	730	6	krishnan	krishnan	PROPN
fuelectenerg-400	730	7	was	be	AUX
fuelectenerg-400	730	8	performed	perform	VERB
fuelectenerg-400	730	9	when	when	SCONJ
fuelectenerg-400	730	10	he	he	PRON
fuelectenerg-400	730	11	was	be	AUX
fuelectenerg-400	730	12	with	with	ADP
fuelectenerg-400	730	13	the	the	DET
fuelectenerg-400	730	14	department	department	NOUN
fuelectenerg-400	730	15	of	of	ADP
fuelectenerg-400	730	16	electrical	electrical	ADJ
fuelectenerg-400	730	17	and	and	CCONJ
fuelectenerg-400	730	18	computer	computer	NOUN
fuelectenerg-400	730	19	engineering	engineering	NOUN
fuelectenerg-400	730	20	,	,	PUNCT
fuelectenerg-400	730	21	university	university	PROPN
fuelectenerg-400	730	22	of	of	ADP
fuelectenerg-400	730	23	arizona	arizona	PROPN
fuelectenerg-400	730	24	,	,	PUNCT
fuelectenerg-400	730	25	tucson	tucson	PROPN
fuelectenerg-400	730	26	,	,	PUNCT
fuelectenerg-400	730	27	az	az	PROPN
fuelectenerg-400	730	28	,	,	PUNCT
fuelectenerg-400	730	29	usa	usa	PROPN
fuelectenerg-400	730	30	.	.	PUNCT
fuelectenerg-400	731	1	the	the	DET
fuelectenerg-400	731	2	authors	author	NOUN
fuelectenerg-400	731	3	would	would	AUX
fuelectenerg-400	731	4	like	like	VERB
fuelectenerg-400	731	5	to	to	PART
fuelectenerg-400	731	6	thank	thank	VERB
fuelectenerg-400	731	7	seyed	seyed	PROPN
fuelectenerg-400	731	8	mehrdad	mehrdad	PROPN
fuelectenerg-400	731	9	khatami	khatami	PROPN
fuelectenerg-400	731	10	for	for	ADP
fuelectenerg-400	731	11	his	his	PRON
fuelectenerg-400	731	12	help	help	NOUN
fuelectenerg-400	731	13	and	and	CCONJ
fuelectenerg-400	731	14	fruitful	fruitful	ADJ
fuelectenerg-400	731	15	discussions	discussion	NOUN
fuelectenerg-400	731	16	.	.	PUNCT
fuelectenerg-400	732	1	7	7	NUM
fuelectenerg-400	732	2	appendix	appendix	X
fuelectenerg-400	732	3	proof:[proof	proof:[proof	NOUN
fuelectenerg-400	732	4	of	of	ADP
fuelectenerg-400	732	5	theorem	theorem	NOUN
fuelectenerg-400	732	6	1	1	NUM
fuelectenerg-400	732	7	]	]	PUNCT
fuelectenerg-400	732	8	in	in	ADP
fuelectenerg-400	732	9	this	this	DET
fuelectenerg-400	732	10	appendix	appendix	NOUN
fuelectenerg-400	732	11	we	we	PRON
fuelectenerg-400	732	12	prove	prove	VERB
fuelectenerg-400	732	13	the	the	DET
fuelectenerg-400	732	14	theorem	theorem	NOUN
fuelectenerg-400	732	15	8	8	NUM
fuelectenerg-400	732	16	.	.	PUNCT
fuelectenerg-400	733	1	macmahon	macmahon	PROPN
fuelectenerg-400	733	2	formula	formula	NOUN
fuelectenerg-400	733	3	[	[	X
fuelectenerg-400	733	4	16	16	NUM
fuelectenerg-400	733	5	]	]	PUNCT
fuelectenerg-400	733	6	gives	give	VERB
fuelectenerg-400	733	7	the	the	DET
fuelectenerg-400	733	8	number	number	NOUN
fuelectenerg-400	733	9	n(a	n(a	PROPN
fuelectenerg-400	733	10	,	,	PUNCT
fuelectenerg-400	733	11	b	b	NOUN
fuelectenerg-400	733	12	,	,	PUNCT
fuelectenerg-400	733	13	c	c	NOUN
fuelectenerg-400	733	14	)	)	PUNCT
fuelectenerg-400	733	15	of	of	ADP
fuelectenerg-400	733	16	restricted	restrict	VERB
fuelectenerg-400	733	17	plane	plane	NOUN
fuelectenerg-400	733	18	partitions	partition	NOUN
fuelectenerg-400	733	19	in	in	ADP
fuelectenerg-400	733	20	the	the	DET
fuelectenerg-400	733	21	form	form	NOUN
fuelectenerg-400	733	22	n(a	n(a	PROPN
fuelectenerg-400	733	23	,	,	PUNCT
fuelectenerg-400	733	24	b	b	NOUN
fuelectenerg-400	733	25	,	,	PUNCT
fuelectenerg-400	733	26	c	c	NOUN
fuelectenerg-400	733	27	)	)	PUNCT
fuelectenerg-400	734	1	=	=	SYM
fuelectenerg-400	735	1	a∏	a∏	PROPN
fuelectenerg-400	735	2	i=1	i=1	PROPN
fuelectenerg-400	736	1	b∏	b∏	PROPN
fuelectenerg-400	736	2	j=1	j=1	NOUN
fuelectenerg-400	736	3	c∏	c∏	PROPN
fuelectenerg-400	736	4	k=1	k=1	PUNCT
fuelectenerg-400	737	1	i	i	PRON
fuelectenerg-400	737	2	+	+	NUM
fuelectenerg-400	737	3	j	j	PROPN
fuelectenerg-400	738	1	+	+	CCONJ
fuelectenerg-400	738	2	k	k	PROPN
fuelectenerg-400	739	1	−	−	PROPN
fuelectenerg-400	739	2	1	1	NUM
fuelectenerg-400	740	1	i	i	NOUN
fuelectenerg-400	740	2	+	+	NUM
fuelectenerg-400	740	3	j	j	PROPN
fuelectenerg-400	741	1	+	+	CCONJ
fuelectenerg-400	741	2	k	k	PROPN
fuelectenerg-400	742	1	−	−	PROPN
fuelectenerg-400	742	2	2	2	NUM
fuelectenerg-400	742	3	it	it	PRON
fuelectenerg-400	742	4	can	can	AUX
fuelectenerg-400	742	5	be	be	AUX
fuelectenerg-400	742	6	rewritten	rewrite	VERB
fuelectenerg-400	742	7	as	as	ADP
fuelectenerg-400	742	8	n(a	n(a	NOUN
fuelectenerg-400	742	9	,	,	PUNCT
fuelectenerg-400	742	10	b	b	NOUN
fuelectenerg-400	742	11	,	,	PUNCT
fuelectenerg-400	742	12	c	c	NOUN
fuelectenerg-400	742	13	)	)	PUNCT
fuelectenerg-400	742	14	=	=	SYM
fuelectenerg-400	743	1	a∏	a∏	NOUN
fuelectenerg-400	743	2	i=1	i=1	X
fuelectenerg-400	744	1	(	(	PUNCT
fuelectenerg-400	744	2	c	c	X
fuelectenerg-400	744	3	+	+	X
fuelectenerg-400	744	4	i)b	i)b	ADJ
fuelectenerg-400	744	5	(	(	PUNCT
fuelectenerg-400	744	6	i)b	i)b	ADJ
fuelectenerg-400	744	7	536	536	NUM
fuelectenerg-400	744	8	b.	b.	PROPN
fuelectenerg-400	744	9	vasic	vasic	PROPN
fuelectenerg-400	744	10	,	,	PUNCT
fuelectenerg-400	744	11	a.	a.	PROPN
fuelectenerg-400	744	12	r.	r.	PROPN
fuelectenerg-400	744	13	krishnan	krishnan	PROPN
fuelectenerg-400	744	14	lozenge	lozenge	PROPN
fuelectenerg-400	744	15	tiling	tile	VERB
fuelectenerg-400	744	16	constrained	constrained	ADJ
fuelectenerg-400	744	17	codes	code	NOUN
fuelectenerg-400	744	18	537	537	NUM
fuelectenerg-400	744	19	538	538	NUM
fuelectenerg-400	744	20	a.	a.	NOUN
fuelectenerg-400	744	21	r.	r.	PROPN
fuelectenerg-400	744	22	krishnanan	krishnanan	PROPN
fuelectenerg-400	744	23	and	and	CCONJ
fuelectenerg-400	744	24	b.	b.	PROPN
fuelectenerg-400	744	25	vasić	vasić	PROPN
fuelectenerg-400	745	1	where	where	SCONJ
fuelectenerg-400	745	2	(	(	PUNCT
fuelectenerg-400	745	3	i)n	i)n	VERB
fuelectenerg-400	745	4	:	:	PUNCT
fuelectenerg-400	745	5	=	=	SYM
fuelectenerg-400	745	6	i(i	i(i	PROPN
fuelectenerg-400	745	7	+	+	CCONJ
fuelectenerg-400	745	8	1)(i	1)(i	NUM
fuelectenerg-400	745	9	+	+	CCONJ
fuelectenerg-400	745	10	2)	2)	NUM
fuelectenerg-400	745	11	...	...	PUNCT
fuelectenerg-400	745	12	(i	(i	X
fuelectenerg-400	745	13	+	+	CCONJ
fuelectenerg-400	745	14	n	n	CCONJ
fuelectenerg-400	745	15	−	−	PROPN
fuelectenerg-400	745	16	1	1	NUM
fuelectenerg-400	745	17	)	)	PUNCT
fuelectenerg-400	745	18	is	be	AUX
fuelectenerg-400	745	19	the	the	DET
fuelectenerg-400	745	20	rising	rise	VERB
fuelectenerg-400	745	21	factorial	factorial	NOUN
fuelectenerg-400	745	22	.	.	PUNCT
fuelectenerg-400	746	1	since	since	SCONJ
fuelectenerg-400	746	2	(	(	PUNCT
fuelectenerg-400	746	3	i)n	i)n	NOUN
fuelectenerg-400	746	4	=	=	SYM
fuelectenerg-400	746	5	(	(	PUNCT
fuelectenerg-400	746	6	i	i	PRON
fuelectenerg-400	746	7	+	+	CCONJ
fuelectenerg-400	746	8	n	n	CCONJ
fuelectenerg-400	746	9	−	−	NUM
fuelectenerg-400	746	10	1)!/(a	1)!/(a	NUM
fuelectenerg-400	746	11	−	−	NOUN
fuelectenerg-400	746	12	1	1	NUM
fuelectenerg-400	746	13	)	)	PUNCT
fuelectenerg-400	746	14	!	!	PUNCT
fuelectenerg-400	746	15	,	,	PUNCT
fuelectenerg-400	746	16	we	we	PRON
fuelectenerg-400	746	17	have	have	VERB
fuelectenerg-400	746	18	a∏	a∏	PROPN
fuelectenerg-400	746	19	i=1	i=1	PROPN
fuelectenerg-400	747	1	(	(	PUNCT
fuelectenerg-400	747	2	c	c	NOUN
fuelectenerg-400	747	3	+	+	X
fuelectenerg-400	747	4	i)b	i)b	ADJ
fuelectenerg-400	747	5	(	(	PUNCT
fuelectenerg-400	747	6	i)b	i)b	ADJ
fuelectenerg-400	747	7	=	=	PUNCT
fuelectenerg-400	747	8	a∏	a∏	NOUN
fuelectenerg-400	747	9	i=1	i=1	X
fuelectenerg-400	748	1	(	(	PUNCT
fuelectenerg-400	748	2	c	c	X
fuelectenerg-400	748	3	+	+	NOUN
fuelectenerg-400	749	1	i	i	PRON
fuelectenerg-400	749	2	+	+	CCONJ
fuelectenerg-400	749	3	b	b	X
fuelectenerg-400	749	4	−	−	PROPN
fuelectenerg-400	749	5	1)!(i	1)!(i	NOUN
fuelectenerg-400	749	6	−	−	PROPN
fuelectenerg-400	749	7	1	1	NUM
fuelectenerg-400	749	8	)	)	PUNCT
fuelectenerg-400	749	9	!	!	PUNCT
fuelectenerg-400	750	1	(	(	PUNCT
fuelectenerg-400	750	2	c	c	X
fuelectenerg-400	751	1	+	+	CCONJ
fuelectenerg-400	752	1	i	i	PRON
fuelectenerg-400	752	2	−	−	PROPN
fuelectenerg-400	753	1	1)!(i	1)!(i	PROPN
fuelectenerg-400	754	1	+	+	CCONJ
fuelectenerg-400	754	2	b	b	X
fuelectenerg-400	754	3	−	−	NOUN
fuelectenerg-400	754	4	1	1	NUM
fuelectenerg-400	754	5	)	)	PUNCT
fuelectenerg-400	754	6	!	!	PUNCT
fuelectenerg-400	755	1	each	each	DET
fuelectenerg-400	755	2	product	product	NOUN
fuelectenerg-400	755	3	of	of	ADP
fuelectenerg-400	755	4	factorials	factorial	NOUN
fuelectenerg-400	755	5	in	in	ADP
fuelectenerg-400	755	6	7	7	NUM
fuelectenerg-400	755	7	is	be	AUX
fuelectenerg-400	755	8	of	of	ADP
fuelectenerg-400	755	9	the	the	DET
fuelectenerg-400	755	10	form	form	NOUN
fuelectenerg-400	755	11	∏a	∏a	VERB
fuelectenerg-400	755	12	i=1	i=1	PROPN
fuelectenerg-400	755	13	(	(	PUNCT
fuelectenerg-400	755	14	d	d	X
fuelectenerg-400	756	1	+	+	CCONJ
fuelectenerg-400	756	2	i	i	PRON
fuelectenerg-400	756	3	−	−	NOUN
fuelectenerg-400	756	4	1	1	NUM
fuelectenerg-400	756	5	)	)	PUNCT
fuelectenerg-400	756	6	!	!	PUNCT
fuelectenerg-400	757	1	and	and	CCONJ
fuelectenerg-400	757	2	can	can	AUX
fuelectenerg-400	757	3	be	be	AUX
fuelectenerg-400	757	4	written	write	VERB
fuelectenerg-400	757	5	as	as	ADP
fuelectenerg-400	757	6	a∏	a∏	PROPN
fuelectenerg-400	757	7	i=1	i=1	PROPN
fuelectenerg-400	758	1	(	(	PUNCT
fuelectenerg-400	758	2	d	d	X
fuelectenerg-400	758	3	+	+	CCONJ
fuelectenerg-400	759	1	i	i	PRON
fuelectenerg-400	759	2	−	−	NOUN
fuelectenerg-400	759	3	1	1	NUM
fuelectenerg-400	759	4	)	)	PUNCT
fuelectenerg-400	759	5	!	!	PUNCT
fuelectenerg-400	760	1	=	=	PUNCT
fuelectenerg-400	760	2	∏d+a−1	∏d+a−1	PROPN
fuelectenerg-400	760	3	i=1	i=1	PROPN
fuelectenerg-400	760	4	i!∏d−1	i!∏d−1	PROPN
fuelectenerg-400	760	5	i=1	i=1	PROPN
fuelectenerg-400	761	1	i	i	PROPN
fuelectenerg-400	761	2	!	!	PUNCT
fuelectenerg-400	762	1	the	the	DET
fuelectenerg-400	762	2	superfactorials	superfactorial	NOUN
fuelectenerg-400	762	3	∏a	∏a	VERB
fuelectenerg-400	762	4	i=1	i=1	PROPN
fuelectenerg-400	763	1	i	i	PRON
fuelectenerg-400	763	2	!	!	PUNCT
fuelectenerg-400	764	1	in	in	ADP
fuelectenerg-400	764	2	7	7	NUM
fuelectenerg-400	764	3	can	can	AUX
fuelectenerg-400	764	4	be	be	AUX
fuelectenerg-400	764	5	expressed	express	VERB
fuelectenerg-400	764	6	as	as	ADP
fuelectenerg-400	764	7	∏n−1	∏n−1	PROPN
fuelectenerg-400	764	8	i=1	i=1	PROPN
fuelectenerg-400	764	9	i	i	PRON
fuelectenerg-400	764	10	!	!	PUNCT
fuelectenerg-400	765	1	=	=	PUNCT
fuelectenerg-400	765	2	g(n	g(n	PROPN
fuelectenerg-400	765	3	+	+	CCONJ
fuelectenerg-400	765	4	1	1	NUM
fuelectenerg-400	765	5	)	)	PUNCT
fuelectenerg-400	765	6	.	.	PUNCT
fuelectenerg-400	766	1	therefore	therefore	ADV
fuelectenerg-400	766	2	we	we	PRON
fuelectenerg-400	766	3	obtain	obtain	VERB
fuelectenerg-400	766	4	n(a	n(a	NOUN
fuelectenerg-400	766	5	,	,	PUNCT
fuelectenerg-400	766	6	b	b	NOUN
fuelectenerg-400	766	7	,	,	PUNCT
fuelectenerg-400	766	8	c	c	NOUN
fuelectenerg-400	766	9	)	)	PUNCT
fuelectenerg-400	766	10	=	=	PUNCT
fuelectenerg-400	767	1	a∏	a∏	NOUN
fuelectenerg-400	767	2	i=1	i=1	X
fuelectenerg-400	767	3	g(a	g(a	PROPN
fuelectenerg-400	768	1	+	+	NUM
fuelectenerg-400	768	2	b	b	PROPN
fuelectenerg-400	768	3	+	+	NUM
fuelectenerg-400	768	4	c	c	NOUN
fuelectenerg-400	768	5	+	+	CCONJ
fuelectenerg-400	768	6	1)g(a	1)g(a	NUM
fuelectenerg-400	769	1	+	+	SYM
fuelectenerg-400	769	2	1)g(b	1)g(b	NUM
fuelectenerg-400	770	1	+	+	CCONJ
fuelectenerg-400	770	2	1)g(c	1)g(c	NUM
fuelectenerg-400	770	3	+	+	CCONJ
fuelectenerg-400	770	4	1	1	NUM
fuelectenerg-400	770	5	)	)	PUNCT
fuelectenerg-400	770	6	g(a	g(a	PROPN
fuelectenerg-400	771	1	+	+	CCONJ
fuelectenerg-400	771	2	b	b	PROPN
fuelectenerg-400	771	3	+	+	NUM
fuelectenerg-400	771	4	1)g(a	1)g(a	NUM
fuelectenerg-400	771	5	+	+	CCONJ
fuelectenerg-400	771	6	c	c	NOUN
fuelectenerg-400	771	7	+	+	SYM
fuelectenerg-400	771	8	1)g(b	1)g(b	NUM
fuelectenerg-400	772	1	+	+	CCONJ
fuelectenerg-400	772	2	c	c	NOUN
fuelectenerg-400	772	3	+	+	NOUN
fuelectenerg-400	772	4	1	1	NUM
fuelectenerg-400	772	5	)	)	PUNCT
fuelectenerg-400	772	6	(	(	PUNCT
fuelectenerg-400	772	7	8)	8)	NUM
fuelectenerg-400	772	8	where	where	SCONJ
fuelectenerg-400	772	9	in	in	ADP
fuelectenerg-400	772	10	eq	eq	NOUN
fuelectenerg-400	772	11	.	.	PROPN
fuelectenerg-400	772	12	8	8	NUM
fuelectenerg-400	772	13	g	g	NOUN
fuelectenerg-400	772	14	denotes	denote	VERB
fuelectenerg-400	772	15	the	the	DET
fuelectenerg-400	772	16	barnes	barnes	PROPN
fuelectenerg-400	772	17	g	g	NOUN
fuelectenerg-400	772	18	-	-	PUNCT
fuelectenerg-400	772	19	function	function	NOUN
fuelectenerg-400	772	20	[	[	X
fuelectenerg-400	772	21	26	26	NUM
fuelectenerg-400	772	22	]	]	PUNCT
fuelectenerg-400	772	23	defined	define	VERB
fuelectenerg-400	772	24	by	by	ADP
fuelectenerg-400	772	25	g(d	g(d	PROPN
fuelectenerg-400	772	26	+	+	CCONJ
fuelectenerg-400	772	27	1	1	X
fuelectenerg-400	772	28	)	)	PUNCT
fuelectenerg-400	772	29	=	=	NOUN
fuelectenerg-400	772	30	(	(	PUNCT
fuelectenerg-400	772	31	2π	2π	NOUN
fuelectenerg-400	772	32	)	)	PUNCT
fuelectenerg-400	772	33	d	d	NOUN
fuelectenerg-400	772	34	2	2	NUM
fuelectenerg-400	772	35	e−	e−	PROPN
fuelectenerg-400	772	36	1	1	NUM
fuelectenerg-400	772	37	2	2	NUM
fuelectenerg-400	772	38	(	(	PUNCT
fuelectenerg-400	772	39	d(d+1)+γd2	d(d+1)+γd2	PROPN
fuelectenerg-400	772	40	)	)	PUNCT
fuelectenerg-400	772	41	·	·	PUNCT
fuelectenerg-400	772	42	·	·	PUNCT
fuelectenerg-400	773	1	+	+	X
fuelectenerg-400	773	2	∞∏	∞∏	X
fuelectenerg-400	773	3	i=1	i=1	X
fuelectenerg-400	773	4	(	(	PUNCT
fuelectenerg-400	773	5	(	(	PUNCT
fuelectenerg-400	773	6	1	1	NUM
fuelectenerg-400	773	7	+	+	CCONJ
fuelectenerg-400	773	8	d	d	NOUN
fuelectenerg-400	773	9	i	i	NOUN
fuelectenerg-400	773	10	)	)	PUNCT
fuelectenerg-400	773	11	i	i	PRON
fuelectenerg-400	773	12	e−d+d2/(2i	e−d+d2/(2i	PROPN
fuelectenerg-400	773	13	)	)	PUNCT
fuelectenerg-400	773	14	)	)	PUNCT
fuelectenerg-400	773	15	for	for	ADP
fuelectenerg-400	773	16	a	a	DET
fuelectenerg-400	773	17	regular	regular	ADJ
fuelectenerg-400	773	18	hexagon	hexagon	NOUN
fuelectenerg-400	773	19	with	with	ADP
fuelectenerg-400	773	20	a	a	DET
fuelectenerg-400	773	21	=	=	SYM
fuelectenerg-400	773	22	b	b	NOUN
fuelectenerg-400	773	23	=	=	SYM
fuelectenerg-400	773	24	c	c	NOUN
fuelectenerg-400	773	25	=	=	PUNCT
fuelectenerg-400	773	26	n	n	CCONJ
fuelectenerg-400	773	27	we	we	PRON
fuelectenerg-400	773	28	have	have	VERB
fuelectenerg-400	773	29	n(n	n(n	NOUN
fuelectenerg-400	773	30	,	,	PUNCT
fuelectenerg-400	773	31	n	n	CCONJ
fuelectenerg-400	773	32	,	,	PUNCT
fuelectenerg-400	773	33	n	n	CCONJ
fuelectenerg-400	773	34	)	)	PUNCT
fuelectenerg-400	774	1	=	=	PUNCT
fuelectenerg-400	774	2	a∏	a∏	NOUN
fuelectenerg-400	774	3	i=1	i=1	VERB
fuelectenerg-400	774	4	g(3n	g(3n	ADJ
fuelectenerg-400	775	1	+	+	NOUN
fuelectenerg-400	775	2	1	1	X
fuelectenerg-400	775	3	)	)	PUNCT
fuelectenerg-400	775	4	(	(	PUNCT
fuelectenerg-400	775	5	g(n	g(n	PROPN
fuelectenerg-400	775	6	+	+	CCONJ
fuelectenerg-400	775	7	1))3	1))3	NUM
fuelectenerg-400	775	8	g(2n	g(2n	VERB
fuelectenerg-400	775	9	+	+	X
fuelectenerg-400	776	1	1)3	1)3	NUM
fuelectenerg-400	776	2	(	(	PUNCT
fuelectenerg-400	776	3	9	9	NUM
fuelectenerg-400	776	4	)	)	PUNCT
fuelectenerg-400	776	5	using	use	VERB
fuelectenerg-400	776	6	the	the	DET
fuelectenerg-400	776	7	asymptotic	asymptotic	NOUN
fuelectenerg-400	776	8	of	of	ADP
fuelectenerg-400	776	9	g(d	g(d	PROPN
fuelectenerg-400	776	10	+	+	CCONJ
fuelectenerg-400	776	11	1	1	X
fuelectenerg-400	776	12	)	)	PUNCT
fuelectenerg-400	776	13	lng(d	lng(d	PROPN
fuelectenerg-400	777	1	+	+	NOUN
fuelectenerg-400	777	2	1)˜z2	1)˜z2	PROPN
fuelectenerg-400	777	3	(	(	PUNCT
fuelectenerg-400	777	4	1	1	NUM
fuelectenerg-400	777	5	2	2	NUM
fuelectenerg-400	777	6	ln	ln	NOUN
fuelectenerg-400	777	7	z	z	NOUN
fuelectenerg-400	777	8	−	−	NOUN
fuelectenerg-400	777	9	3	3	NUM
fuelectenerg-400	777	10	4	4	NUM
fuelectenerg-400	777	11	)	)	PUNCT
fuelectenerg-400	778	1	+	+	CCONJ
fuelectenerg-400	778	2	1	1	NUM
fuelectenerg-400	778	3	2	2	NUM
fuelectenerg-400	778	4	ln(2π)z	ln(2π)z	NOUN
fuelectenerg-400	778	5	−	−	NOUN
fuelectenerg-400	778	6	−	−	NUM
fuelectenerg-400	778	7	1	1	NUM
fuelectenerg-400	778	8	12	12	NUM
fuelectenerg-400	778	9	ln	ln	ADJ
fuelectenerg-400	778	10	z	z	NOUN
fuelectenerg-400	778	11	+	+	NUM
fuelectenerg-400	778	12	ξ	ξ	X
fuelectenerg-400	778	13	′	′	NUM
fuelectenerg-400	778	14	(	(	PUNCT
fuelectenerg-400	778	15	−1)o	−1)o	NOUN
fuelectenerg-400	778	16	(	(	PUNCT
fuelectenerg-400	778	17	1	1	NUM
fuelectenerg-400	778	18	2	2	NUM
fuelectenerg-400	778	19	)	)	PUNCT
fuelectenerg-400	778	20	we	we	PRON
fuelectenerg-400	778	21	obtain	obtain	VERB
fuelectenerg-400	778	22	lnn(n	lnn(n	PROPN
fuelectenerg-400	778	23	,	,	PUNCT
fuelectenerg-400	778	24	n	n	CCONJ
fuelectenerg-400	778	25	,	,	PUNCT
fuelectenerg-400	778	26	n	n	CCONJ
fuelectenerg-400	778	27	)	)	PUNCT
fuelectenerg-400	778	28	∼	∼	NOUN
fuelectenerg-400	778	29	lng(3n	lng(3n	NOUN
fuelectenerg-400	778	30	+	+	CCONJ
fuelectenerg-400	778	31	1	1	X
fuelectenerg-400	778	32	)	)	PUNCT
fuelectenerg-400	778	33	+	+	CCONJ
fuelectenerg-400	778	34	3	3	NUM
fuelectenerg-400	778	35	ln	ln	PROPN
fuelectenerg-400	778	36	g(n	g(n	PROPN
fuelectenerg-400	778	37	+	+	CCONJ
fuelectenerg-400	778	38	1	1	X
fuelectenerg-400	778	39	)	)	PUNCT
fuelectenerg-400	778	40	−	−	ADP
fuelectenerg-400	778	41	−3	−3	NOUN
fuelectenerg-400	778	42	lng(2n	lng(2n	NOUN
fuelectenerg-400	778	43	+	+	NOUN
fuelectenerg-400	778	44	1	1	X
fuelectenerg-400	778	45	)	)	PUNCT
fuelectenerg-400	778	46	∼	∼	NOUN
fuelectenerg-400	778	47	n2	n2	NOUN
fuelectenerg-400	778	48	(	(	PUNCT
fuelectenerg-400	778	49	9	9	NUM
fuelectenerg-400	778	50	2	2	NUM
fuelectenerg-400	778	51	ln	ln	NOUN
fuelectenerg-400	778	52	3	3	NUM
fuelectenerg-400	778	53	−	−	PROPN
fuelectenerg-400	778	54	6	6	NUM
fuelectenerg-400	778	55	ln	ln	NOUN
fuelectenerg-400	778	56	2	2	NUM
fuelectenerg-400	778	57	)	)	PUNCT
fuelectenerg-400	778	58	+	+	PUNCT
fuelectenerg-400	779	1	+	+	ADP
fuelectenerg-400	779	2	n	n	VERB
fuelectenerg-400	779	3	ln	ln	ADJ
fuelectenerg-400	779	4	2π	2π	PROPN
fuelectenerg-400	779	5	−	−	NOUN
fuelectenerg-400	779	6	1	1	NUM
fuelectenerg-400	779	7	12	12	NUM
fuelectenerg-400	779	8	lnn	lnn	NOUN
fuelectenerg-400	779	9	−	−	NOUN
fuelectenerg-400	779	10	1	1	NUM
fuelectenerg-400	779	11	12	12	NUM
fuelectenerg-400	779	12	ln	ln	NOUN
fuelectenerg-400	779	13	3	3	NUM
fuelectenerg-400	779	14	2	2	NUM
fuelectenerg-400	779	15	by	by	ADP
fuelectenerg-400	779	16	changing	change	VERB
fuelectenerg-400	779	17	the	the	DET
fuelectenerg-400	779	18	base	base	NOUN
fuelectenerg-400	779	19	of	of	ADP
fuelectenerg-400	779	20	the	the	DET
fuelectenerg-400	779	21	logarithm	logarithm	NOUN
fuelectenerg-400	779	22	we	we	PRON
fuelectenerg-400	779	23	obtain	obtain	VERB
fuelectenerg-400	779	24	log2	log2	PROPN
fuelectenerg-400	779	25	n(n	n(n	PROPN
fuelectenerg-400	779	26	,	,	PUNCT
fuelectenerg-400	779	27	n	n	CCONJ
fuelectenerg-400	779	28	,	,	PUNCT
fuelectenerg-400	779	29	n	n	CCONJ
fuelectenerg-400	779	30	)	)	PUNCT
fuelectenerg-400	779	31	∼	∼	NOUN
fuelectenerg-400	779	32	n2	n2	NOUN
fuelectenerg-400	779	33	(	(	PUNCT
fuelectenerg-400	779	34	9	9	NUM
fuelectenerg-400	779	35	2	2	NUM
fuelectenerg-400	779	36	log2	log2	NOUN
fuelectenerg-400	779	37	3	3	NUM
fuelectenerg-400	779	38	−	−	NOUN
fuelectenerg-400	779	39	6	6	NUM
fuelectenerg-400	779	40	)	)	PUNCT
fuelectenerg-400	779	41	(	(	PUNCT
fuelectenerg-400	779	42	10	10	NUM
fuelectenerg-400	779	43	)	)	PUNCT
fuelectenerg-400	779	44	detection	detection	NOUN
fuelectenerg-400	779	45	and	and	CCONJ
fuelectenerg-400	779	46	coding	code	VERB
fuelectenerg-400	779	47	for	for	ADP
fuelectenerg-400	779	48	tdmr	tdmr	NOUN
fuelectenerg-400	779	49	channel	channel	NOUN
fuelectenerg-400	779	50	539	539	NUM
fuelectenerg-400	779	51	the	the	DET
fuelectenerg-400	779	52	area	area	NOUN
fuelectenerg-400	779	53	of	of	ADP
fuelectenerg-400	779	54	the	the	DET
fuelectenerg-400	779	55	hexagon	hexagon	NOUN
fuelectenerg-400	779	56	with	with	ADP
fuelectenerg-400	779	57	sides	side	NOUN
fuelectenerg-400	779	58	a	a	DET
fuelectenerg-400	779	59	,	,	PUNCT
fuelectenerg-400	779	60	b	b	NOUN
fuelectenerg-400	779	61	and	and	CCONJ
fuelectenerg-400	779	62	c	c	PROPN
fuelectenerg-400	779	63	is	be	AUX
fuelectenerg-400	779	64	a(a	a(a	PROPN
fuelectenerg-400	779	65	,	,	PUNCT
fuelectenerg-400	779	66	b	b	X
fuelectenerg-400	779	67	,	,	PUNCT
fuelectenerg-400	779	68	c	c	NOUN
fuelectenerg-400	779	69	)	)	PUNCT
fuelectenerg-400	779	70	=	=	SYM
fuelectenerg-400	780	1	2(ab	2(ab	PROPN
fuelectenerg-400	781	1	+	+	CCONJ
fuelectenerg-400	781	2	ac	ac	PROPN
fuelectenerg-400	781	3	+	+	CCONJ
fuelectenerg-400	781	4	bc	bc	PROPN
fuelectenerg-400	781	5	)	)	PUNCT
fuelectenerg-400	781	6	√	√	ADV
fuelectenerg-400	781	7	3	3	NUM
fuelectenerg-400	781	8	4	4	NUM
fuelectenerg-400	781	9	.	.	PUNCT
fuelectenerg-400	782	1	for	for	ADP
fuelectenerg-400	782	2	a	a	DET
fuelectenerg-400	782	3	regular	regular	ADJ
fuelectenerg-400	782	4	hexagon	hexagon	NOUN
fuelectenerg-400	782	5	a(n	a(n	PROPN
fuelectenerg-400	782	6	,	,	PUNCT
fuelectenerg-400	782	7	n	n	CCONJ
fuelectenerg-400	782	8	,	,	PUNCT
fuelectenerg-400	782	9	n	n	CCONJ
fuelectenerg-400	782	10	)	)	PUNCT
fuelectenerg-400	782	11	=	=	SYM
fuelectenerg-400	782	12	2	2	NUM
fuelectenerg-400	782	13	√	√	NUM
fuelectenerg-400	782	14	3	3	NUM
fuelectenerg-400	782	15	2	2	NUM
fuelectenerg-400	782	16	n2	n2	NOUN
fuelectenerg-400	782	17	,	,	PUNCT
fuelectenerg-400	782	18	so	so	SCONJ
fuelectenerg-400	782	19	that	that	SCONJ
fuelectenerg-400	782	20	finally	finally	ADV
fuelectenerg-400	782	21	the	the	DET
fuelectenerg-400	782	22	density	density	NOUN
fuelectenerg-400	782	23	is	be	AUX
fuelectenerg-400	782	24	d	d	NOUN
fuelectenerg-400	782	25	=	=	SYM
fuelectenerg-400	782	26	lim	lim	PROPN
fuelectenerg-400	782	27	n→∞	n→∞	NUM
fuelectenerg-400	782	28	log2	log2	PROPN
fuelectenerg-400	782	29	n(n	n(n	PROPN
fuelectenerg-400	782	30	,	,	PUNCT
fuelectenerg-400	782	31	n	n	CCONJ
fuelectenerg-400	782	32	,	,	PUNCT
fuelectenerg-400	782	33	n	n	CCONJ
fuelectenerg-400	782	34	)	)	PUNCT
fuelectenerg-400	782	35	a(n	a(n	ADV
fuelectenerg-400	782	36	,	,	PUNCT
fuelectenerg-400	782	37	n	n	CCONJ
fuelectenerg-400	782	38	,	,	PUNCT
fuelectenerg-400	782	39	n	n	CCONJ
fuelectenerg-400	782	40	)	)	PUNCT
fuelectenerg-400	782	41	=	=	VERB
fuelectenerg-400	782	42	lim	lim	PROPN
fuelectenerg-400	782	43	n→∞	n→∞	NUM
fuelectenerg-400	782	44	n2	n2	NOUN
fuelectenerg-400	782	45	(	(	PUNCT
fuelectenerg-400	782	46	9	9	NUM
fuelectenerg-400	782	47	2	2	NUM
fuelectenerg-400	782	48	log2	log2	NOUN
fuelectenerg-400	782	49	3	3	NUM
fuelectenerg-400	782	50	−	−	NOUN
fuelectenerg-400	782	51	6	6	NUM
fuelectenerg-400	782	52	)	)	PUNCT
fuelectenerg-400	782	53	2	2	NUM
fuelectenerg-400	782	54	√	√	NUM
fuelectenerg-400	782	55	3	3	NUM
fuelectenerg-400	782	56	2	2	NUM
fuelectenerg-400	782	57	n2	n2	NOUN
fuelectenerg-400	782	58	=	=	SYM
fuelectenerg-400	783	1	√	√	ADP
fuelectenerg-400	783	2	3(log2	3(log2	NUM
fuelectenerg-400	783	3	3	3	NUM
fuelectenerg-400	783	4	−	−	NOUN
fuelectenerg-400	783	5	4	4	NUM
fuelectenerg-400	783	6	3	3	NUM
fuelectenerg-400	783	7	)	)	PUNCT
fuelectenerg-400	783	8	8	8	NUM
fuelectenerg-400	783	9	proof:[proof	proof:[proof	NOUN
fuelectenerg-400	783	10	of	of	ADP
fuelectenerg-400	783	11	theorem	theorem	NOUN
fuelectenerg-400	783	12	2	2	NUM
fuelectenerg-400	783	13	]	]	PUNCT
fuelectenerg-400	783	14	consider	consider	VERB
fuelectenerg-400	783	15	the	the	DET
fuelectenerg-400	783	16	equivalence	equivalence	NOUN
fuelectenerg-400	783	17	between	between	ADP
fuelectenerg-400	783	18	tilings	tiling	NOUN
fuelectenerg-400	783	19	and	and	CCONJ
fuelectenerg-400	783	20	boxed	boxed	ADJ
fuelectenerg-400	783	21	plane	plane	NOUN
fuelectenerg-400	783	22	partitions	partition	NOUN
fuelectenerg-400	783	23	.	.	PUNCT
fuelectenerg-400	784	1	it	it	PRON
fuelectenerg-400	784	2	can	can	AUX
fuelectenerg-400	784	3	be	be	AUX
fuelectenerg-400	784	4	seen	see	VERB
fuelectenerg-400	784	5	that	that	SCONJ
fuelectenerg-400	784	6	each	each	DET
fuelectenerg-400	784	7	box	box	NOUN
fuelectenerg-400	784	8	in	in	ADP
fuelectenerg-400	784	9	the	the	DET
fuelectenerg-400	784	10	young	young	PROPN
fuelectenerg-400	784	11	’s	’s	PART
fuelectenerg-400	784	12	solid	solid	ADJ
fuelectenerg-400	784	13	diagram	diagram	NOUN
fuelectenerg-400	784	14	of	of	ADP
fuelectenerg-400	784	15	an	an	DET
fuelectenerg-400	784	16	(	(	PUNCT
fuelectenerg-400	784	17	a	a	PROPN
fuelectenerg-400	784	18	,	,	PUNCT
fuelectenerg-400	784	19	b	b	NOUN
fuelectenerg-400	784	20	,	,	PUNCT
fuelectenerg-400	784	21	c	c	NOUN
fuelectenerg-400	784	22	)	)	PUNCT
fuelectenerg-400	784	23	hexagon	hexagon	NOUN
fuelectenerg-400	784	24	with	with	ADP
fuelectenerg-400	784	25	3	3	NUM
fuelectenerg-400	784	26	visible	visible	ADJ
fuelectenerg-400	784	27	faces	face	NOUN
fuelectenerg-400	784	28	corresponds	correspond	VERB
fuelectenerg-400	784	29	to	to	ADP
fuelectenerg-400	784	30	a	a	DET
fuelectenerg-400	784	31	type-1	type-1	PROPN
fuelectenerg-400	784	32	hexagon	hexagon	NOUN
fuelectenerg-400	784	33	.	.	PUNCT
fuelectenerg-400	785	1	to	to	PART
fuelectenerg-400	785	2	find	find	VERB
fuelectenerg-400	785	3	the	the	DET
fuelectenerg-400	785	4	maximum	maximum	ADJ
fuelectenerg-400	785	5	number	number	NOUN
fuelectenerg-400	785	6	of	of	ADP
fuelectenerg-400	785	7	type-1	type-1	PROPN
fuelectenerg-400	785	8	hexagon	hexagon	VERB
fuelectenerg-400	785	9	in	in	ADP
fuelectenerg-400	785	10	h	h	NOUN
fuelectenerg-400	785	11	,	,	PUNCT
fuelectenerg-400	785	12	the	the	DET
fuelectenerg-400	785	13	young	young	PROPN
fuelectenerg-400	785	14	’s	’s	PART
fuelectenerg-400	785	15	solid	solid	ADJ
fuelectenerg-400	785	16	diagram	diagram	NOUN
fuelectenerg-400	785	17	corresponding	correspond	VERB
fuelectenerg-400	785	18	to	to	ADP
fuelectenerg-400	785	19	an	an	DET
fuelectenerg-400	785	20	n×	n×	PRON
fuelectenerg-400	785	21	n×	n×	PROPN
fuelectenerg-400	785	22	n	n	PROPN
fuelectenerg-400	785	23	box	box	PROPN
fuelectenerg-400	785	24	with	with	ADP
fuelectenerg-400	785	25	the	the	DET
fuelectenerg-400	785	26	maximum	maximum	ADJ
fuelectenerg-400	785	27	number	number	NOUN
fuelectenerg-400	785	28	of	of	ADP
fuelectenerg-400	785	29	visible	visible	ADJ
fuelectenerg-400	785	30	boxes	box	NOUN
fuelectenerg-400	785	31	is	be	AUX
fuelectenerg-400	785	32	constructed	construct	VERB
fuelectenerg-400	785	33	.	.	PUNCT
fuelectenerg-400	786	1	this	this	PRON
fuelectenerg-400	786	2	can	can	AUX
fuelectenerg-400	786	3	be	be	AUX
fuelectenerg-400	786	4	constructed	construct	VERB
fuelectenerg-400	786	5	as	as	SCONJ
fuelectenerg-400	786	6	follows	follow	VERB
fuelectenerg-400	786	7	:	:	PUNCT
fuelectenerg-400	786	8	start	start	VERB
fuelectenerg-400	786	9	at	at	ADP
fuelectenerg-400	786	10	(	(	PUNCT
fuelectenerg-400	786	11	x	x	NOUN
fuelectenerg-400	786	12	,	,	PUNCT
fuelectenerg-400	786	13	y	y	NOUN
fuelectenerg-400	786	14	)	)	PUNCT
fuelectenerg-400	786	15	=	=	SYM
fuelectenerg-400	787	1	(	(	PUNCT
fuelectenerg-400	787	2	0	0	NUM
fuelectenerg-400	787	3	,	,	PUNCT
fuelectenerg-400	787	4	0	0	NUM
fuelectenerg-400	787	5	)	)	PUNCT
fuelectenerg-400	787	6	of	of	ADP
fuelectenerg-400	787	7	the	the	DET
fuelectenerg-400	787	8	n	n	NUM
fuelectenerg-400	787	9	×	×	NOUN
fuelectenerg-400	787	10	n	n	CCONJ
fuelectenerg-400	787	11	×	×	PROPN
fuelectenerg-400	787	12	n	n	CCONJ
fuelectenerg-400	787	13	box	box	NOUN
fuelectenerg-400	787	14	and	and	CCONJ
fuelectenerg-400	787	15	stack	stack	VERB
fuelectenerg-400	787	16	n	n	PRON
fuelectenerg-400	787	17	boxes	box	NOUN
fuelectenerg-400	787	18	.	.	PUNCT
fuelectenerg-400	788	1	now	now	ADV
fuelectenerg-400	788	2	,	,	PUNCT
fuelectenerg-400	788	3	at	at	ADP
fuelectenerg-400	788	4	(	(	PUNCT
fuelectenerg-400	788	5	x	x	NOUN
fuelectenerg-400	788	6	,	,	PUNCT
fuelectenerg-400	788	7	y	y	NOUN
fuelectenerg-400	788	8	)	)	PUNCT
fuelectenerg-400	788	9	=	=	PUNCT
fuelectenerg-400	788	10	(	(	PUNCT
fuelectenerg-400	788	11	1	1	NUM
fuelectenerg-400	788	12	,	,	PUNCT
fuelectenerg-400	788	13	0	0	NUM
fuelectenerg-400	788	14	)	)	PUNCT
fuelectenerg-400	788	15	,	,	PUNCT
fuelectenerg-400	788	16	stack	stack	VERB
fuelectenerg-400	788	17	n	n	PRON
fuelectenerg-400	788	18	−	−	NUM
fuelectenerg-400	788	19	1	1	NUM
fuelectenerg-400	788	20	boxes	box	NOUN
fuelectenerg-400	788	21	.	.	PUNCT
fuelectenerg-400	789	1	step	step	NOUN
fuelectenerg-400	789	2	in	in	ADP
fuelectenerg-400	789	3	the	the	DET
fuelectenerg-400	789	4	x	x	NOUN
fuelectenerg-400	789	5	direction	direction	NOUN
fuelectenerg-400	789	6	reducing	reduce	VERB
fuelectenerg-400	789	7	the	the	DET
fuelectenerg-400	789	8	number	number	NOUN
fuelectenerg-400	789	9	of	of	ADP
fuelectenerg-400	789	10	boxes	box	NOUN
fuelectenerg-400	789	11	stacked	stack	VERB
fuelectenerg-400	789	12	by	by	ADP
fuelectenerg-400	789	13	1	1	NUM
fuelectenerg-400	789	14	at	at	ADP
fuelectenerg-400	789	15	each	each	DET
fuelectenerg-400	789	16	step	step	NOUN
fuelectenerg-400	789	17	.	.	PUNCT
fuelectenerg-400	790	1	this	this	PRON
fuelectenerg-400	790	2	is	be	AUX
fuelectenerg-400	790	3	continued	continue	VERB
fuelectenerg-400	790	4	till	till	SCONJ
fuelectenerg-400	790	5	(	(	PUNCT
fuelectenerg-400	790	6	x	x	NOUN
fuelectenerg-400	790	7	,	,	PUNCT
fuelectenerg-400	790	8	y	y	NOUN
fuelectenerg-400	790	9	)	)	PUNCT
fuelectenerg-400	790	10	=	=	SYM
fuelectenerg-400	790	11	(	(	PUNCT
fuelectenerg-400	790	12	n−1	n−1	PROPN
fuelectenerg-400	790	13	,	,	PUNCT
fuelectenerg-400	790	14	0	0	NUM
fuelectenerg-400	790	15	)	)	PUNCT
fuelectenerg-400	790	16	where	where	SCONJ
fuelectenerg-400	790	17	1	1	NUM
fuelectenerg-400	790	18	box	box	NOUN
fuelectenerg-400	790	19	is	be	AUX
fuelectenerg-400	790	20	stacked	stack	VERB
fuelectenerg-400	790	21	.	.	PUNCT
fuelectenerg-400	791	1	next	next	ADV
fuelectenerg-400	791	2	,	,	PUNCT
fuelectenerg-400	791	3	start	start	VERB
fuelectenerg-400	791	4	at	at	ADP
fuelectenerg-400	791	5	(	(	PUNCT
fuelectenerg-400	791	6	x	x	NOUN
fuelectenerg-400	791	7	,	,	PUNCT
fuelectenerg-400	791	8	y	y	NOUN
fuelectenerg-400	791	9	)	)	PUNCT
fuelectenerg-400	791	10	=	=	SYM
fuelectenerg-400	792	1	(	(	PUNCT
fuelectenerg-400	792	2	0	0	NUM
fuelectenerg-400	792	3	,	,	PUNCT
fuelectenerg-400	792	4	1	1	NUM
fuelectenerg-400	792	5	)	)	PUNCT
fuelectenerg-400	793	1	and	and	CCONJ
fuelectenerg-400	793	2	stack	stack	VERB
fuelectenerg-400	793	3	n	n	CCONJ
fuelectenerg-400	793	4	−	−	NUM
fuelectenerg-400	793	5	1	1	NUM
fuelectenerg-400	793	6	boxes	box	NOUN
fuelectenerg-400	793	7	.	.	PUNCT
fuelectenerg-400	794	1	continue	continue	VERB
fuelectenerg-400	794	2	the	the	DET
fuelectenerg-400	794	3	same	same	ADJ
fuelectenerg-400	794	4	process	process	NOUN
fuelectenerg-400	794	5	till	till	SCONJ
fuelectenerg-400	794	6	(	(	PUNCT
fuelectenerg-400	794	7	x	x	NOUN
fuelectenerg-400	794	8	,	,	PUNCT
fuelectenerg-400	794	9	y	y	NOUN
fuelectenerg-400	794	10	)	)	PUNCT
fuelectenerg-400	794	11	=	=	PUNCT
fuelectenerg-400	794	12	(	(	PUNCT
fuelectenerg-400	794	13	n−	n−	NOUN
fuelectenerg-400	794	14	2	2	NUM
fuelectenerg-400	794	15	,	,	PUNCT
fuelectenerg-400	794	16	1	1	NUM
fuelectenerg-400	794	17	)	)	PUNCT
fuelectenerg-400	794	18	is	be	AUX
fuelectenerg-400	794	19	reached	reach	VERB
fuelectenerg-400	794	20	where	where	SCONJ
fuelectenerg-400	794	21	1	1	NUM
fuelectenerg-400	794	22	box	box	NOUN
fuelectenerg-400	794	23	is	be	AUX
fuelectenerg-400	794	24	stacked	stack	VERB
fuelectenerg-400	794	25	.	.	PUNCT
fuelectenerg-400	795	1	this	this	DET
fuelectenerg-400	795	2	process	process	NOUN
fuelectenerg-400	795	3	is	be	AUX
fuelectenerg-400	795	4	continued	continue	VERB
fuelectenerg-400	795	5	till	till	SCONJ
fuelectenerg-400	795	6	(	(	PUNCT
fuelectenerg-400	795	7	x	x	NOUN
fuelectenerg-400	795	8	,	,	PUNCT
fuelectenerg-400	795	9	y	y	NOUN
fuelectenerg-400	795	10	)	)	PUNCT
fuelectenerg-400	795	11	=	=	PUNCT
fuelectenerg-400	795	12	(	(	PUNCT
fuelectenerg-400	795	13	n	n	CCONJ
fuelectenerg-400	795	14	−	−	PROPN
fuelectenerg-400	795	15	1	1	NUM
fuelectenerg-400	795	16	,	,	PUNCT
fuelectenerg-400	795	17	0	0	NUM
fuelectenerg-400	795	18	)	)	PUNCT
fuelectenerg-400	795	19	is	be	AUX
fuelectenerg-400	795	20	reached	reach	VERB
fuelectenerg-400	795	21	where	where	SCONJ
fuelectenerg-400	795	22	1	1	NUM
fuelectenerg-400	795	23	box	box	NOUN
fuelectenerg-400	795	24	is	be	AUX
fuelectenerg-400	795	25	stacked	stack	VERB
fuelectenerg-400	795	26	.	.	PUNCT
fuelectenerg-400	796	1	this	this	PRON
fuelectenerg-400	796	2	corresponds	correspond	VERB
fuelectenerg-400	796	3	to	to	ADP
fuelectenerg-400	796	4	the	the	DET
fuelectenerg-400	796	5	young	young	ADJ
fuelectenerg-400	796	6	’s	’s	PART
fuelectenerg-400	796	7	solid	solid	ADJ
fuelectenerg-400	796	8	diagram	diagram	NOUN
fuelectenerg-400	796	9	with	with	ADP
fuelectenerg-400	796	10	the	the	DET
fuelectenerg-400	796	11	maximum	maximum	ADJ
fuelectenerg-400	796	12	number	number	NOUN
fuelectenerg-400	796	13	of	of	ADP
fuelectenerg-400	796	14	visible	visible	ADJ
fuelectenerg-400	796	15	boxes	box	NOUN
fuelectenerg-400	796	16	.	.	PUNCT
fuelectenerg-400	797	1	the	the	DET
fuelectenerg-400	797	2	boxed	box	VERB
fuelectenerg-400	797	3	plane	plane	NOUN
fuelectenerg-400	797	4	partition	partition	NOUN
fuelectenerg-400	797	5	corresponding	correspond	VERB
fuelectenerg-400	797	6	to	to	ADP
fuelectenerg-400	797	7	this	this	DET
fuelectenerg-400	797	8	young	young	PROPN
fuelectenerg-400	797	9	’s	’s	PART
fuelectenerg-400	797	10	diagram	diagram	NOUN
fuelectenerg-400	797	11	is	be	AUX
fuelectenerg-400	797	12	given	give	VERB
fuelectenerg-400	797	13	by	by	ADP
fuelectenerg-400	797	14	:	:	PUNCT
fuelectenerg-400	797	15	π	π	NOUN
fuelectenerg-400	797	16	=	=	PUNCT
fuelectenerg-400	797	17			VERB
fuelectenerg-400	797	18			PROPN
fuelectenerg-400	797	19	n	n	CCONJ
fuelectenerg-400	797	20	n	n	CCONJ
fuelectenerg-400	797	21	−	−	PROPN
fuelectenerg-400	797	22	1	1	NUM
fuelectenerg-400	797	23	.	.	PUNCT
fuelectenerg-400	797	24	.	.	PUNCT
fuelectenerg-400	797	25	.	.	PUNCT
fuelectenerg-400	798	1	3	3	NUM
fuelectenerg-400	798	2	2	2	NUM
fuelectenerg-400	798	3	1	1	NUM
fuelectenerg-400	798	4	n	n	NUM
fuelectenerg-400	798	5	−	−	NUM
fuelectenerg-400	798	6	1	1	NUM
fuelectenerg-400	798	7	n	n	CCONJ
fuelectenerg-400	798	8	−	−	PROPN
fuelectenerg-400	798	9	2	2	NUM
fuelectenerg-400	798	10	.	.	PUNCT
fuelectenerg-400	798	11	.	.	PUNCT
fuelectenerg-400	798	12	.	.	PUNCT
fuelectenerg-400	799	1	2	2	NUM
fuelectenerg-400	799	2	1	1	NUM
fuelectenerg-400	799	3	0	0	NUM
fuelectenerg-400	799	4	n	n	CCONJ
fuelectenerg-400	799	5	−	−	NUM
fuelectenerg-400	799	6	2	2	NUM
fuelectenerg-400	799	7	n	n	NOUN
fuelectenerg-400	799	8	−	−	PROPN
fuelectenerg-400	799	9	3	3	NUM
fuelectenerg-400	799	10	.	.	PUNCT
fuelectenerg-400	799	11	.	.	PUNCT
fuelectenerg-400	799	12	.	.	PUNCT
fuelectenerg-400	800	1	1	1	NUM
fuelectenerg-400	800	2	0	0	NUM
fuelectenerg-400	800	3	0	0	NUM
fuelectenerg-400	800	4	...	...	PUNCT
fuelectenerg-400	800	5	...	...	PUNCT
fuelectenerg-400	801	1	1	1	NUM
fuelectenerg-400	801	2	0	0	NUM
fuelectenerg-400	801	3	.	.	PUNCT
fuelectenerg-400	801	4	.	.	PUNCT
fuelectenerg-400	801	5	.	.	PUNCT
fuelectenerg-400	801	6	0	0	PUNCT
fuelectenerg-400	802	1			X
fuelectenerg-400	803	1			NOUN
fuelectenerg-400	803	2	as	as	ADP
fuelectenerg-400	803	3	an	an	DET
fuelectenerg-400	803	4	example	example	NOUN
fuelectenerg-400	803	5	,	,	PUNCT
fuelectenerg-400	803	6	figure	figure	NOUN
fuelectenerg-400	803	7	11	11	NUM
fuelectenerg-400	803	8	shows	show	VERB
fuelectenerg-400	803	9	the	the	DET
fuelectenerg-400	803	10	lozenge	lozenge	NOUN
fuelectenerg-400	803	11	tiling	tiling	NOUN
fuelectenerg-400	803	12	of	of	ADP
fuelectenerg-400	803	13	a	a	DET
fuelectenerg-400	803	14	(	(	PUNCT
fuelectenerg-400	803	15	4	4	NUM
fuelectenerg-400	803	16	,	,	PUNCT
fuelectenerg-400	803	17	4	4	NUM
fuelectenerg-400	803	18	,	,	PUNCT
fuelectenerg-400	803	19	4	4	X
fuelectenerg-400	803	20	)	)	PUNCT
fuelectenerg-400	803	21	hexagon	hexagon	NOUN
fuelectenerg-400	803	22	with	with	ADP
fuelectenerg-400	803	23	the	the	DET
fuelectenerg-400	803	24	maximum	maximum	ADJ
fuelectenerg-400	803	25	number	number	NOUN
fuelectenerg-400	803	26	of	of	ADP
fuelectenerg-400	803	27	type-1	type-1	PROPN
fuelectenerg-400	803	28	hexagons	hexagon	NOUN
fuelectenerg-400	803	29	.	.	PUNCT
fuelectenerg-400	804	1	alternatively	alternatively	ADV
fuelectenerg-400	804	2	,	,	PUNCT
fuelectenerg-400	804	3	it	it	PRON
fuelectenerg-400	804	4	can	can	AUX
fuelectenerg-400	804	5	be	be	AUX
fuelectenerg-400	804	6	visualized	visualize	VERB
fuelectenerg-400	804	7	as	as	ADP
fuelectenerg-400	804	8	a	a	DET
fuelectenerg-400	804	9	the	the	DET
fuelectenerg-400	804	10	young	young	ADJ
fuelectenerg-400	804	11	’s	’s	PART
fuelectenerg-400	804	12	solid	solid	ADJ
fuelectenerg-400	804	13	diagram	diagram	NOUN
fuelectenerg-400	804	14	corresponding	correspond	VERB
fuelectenerg-400	804	15	to	to	ADP
fuelectenerg-400	804	16	a	a	DET
fuelectenerg-400	804	17	4	4	NUM
fuelectenerg-400	804	18	×	×	NOUN
fuelectenerg-400	804	19	4	4	NUM
fuelectenerg-400	804	20	×	×	NOUN
fuelectenerg-400	804	21	4	4	NUM
fuelectenerg-400	804	22	box	box	NOUN
fuelectenerg-400	804	23	.	.	PUNCT
fuelectenerg-400	805	1	the	the	DET
fuelectenerg-400	805	2	number	number	NOUN
fuelectenerg-400	805	3	of	of	ADP
fuelectenerg-400	805	4	visible	visible	ADJ
fuelectenerg-400	805	5	boxes	box	NOUN
fuelectenerg-400	805	6	is	be	AUX
fuelectenerg-400	805	7	equal	equal	ADJ
fuelectenerg-400	805	8	to	to	ADP
fuelectenerg-400	805	9	the	the	DET
fuelectenerg-400	805	10	number	number	NOUN
fuelectenerg-400	805	11	of	of	ADP
fuelectenerg-400	805	12	non	non	ADJ
fuelectenerg-400	805	13	-	-	ADJ
fuelectenerg-400	805	14	zero	zero	NUM
fuelectenerg-400	805	15	entries	entry	NOUN
fuelectenerg-400	805	16	in	in	ADP
fuelectenerg-400	805	17	π	π	PROPN
fuelectenerg-400	805	18	.	.	PUNCT
fuelectenerg-400	806	1	this	this	PRON
fuelectenerg-400	806	2	is	be	AUX
fuelectenerg-400	806	3	equal	equal	ADJ
fuelectenerg-400	806	4	to	to	ADP
fuelectenerg-400	806	5	n(n+1	n(n+1	NOUN
fuelectenerg-400	806	6	)	)	PUNCT
fuelectenerg-400	806	7	2	2	NUM
fuelectenerg-400	806	8	.	.	PUNCT
fuelectenerg-400	807	1	this	this	PRON
fuelectenerg-400	807	2	is	be	AUX
fuelectenerg-400	807	3	equal	equal	ADJ
fuelectenerg-400	807	4	to	to	ADP
fuelectenerg-400	807	5	the	the	DET
fuelectenerg-400	807	6	number	number	NOUN
fuelectenerg-400	807	7	of	of	ADP
fuelectenerg-400	807	8	type-1	type-1	PROPN
fuelectenerg-400	807	9	hexagons	hexagon	NOUN
fuelectenerg-400	807	10	formed	form	VERB
fuelectenerg-400	807	11	in	in	ADP
fuelectenerg-400	807	12	h.	h.	PROPN
fuelectenerg-400	807	13	the	the	DET
fuelectenerg-400	807	14	number	number	NOUN
fuelectenerg-400	807	15	of	of	ADP
fuelectenerg-400	807	16	lozenges	lozenge	NOUN
fuelectenerg-400	807	17	where	where	SCONJ
fuelectenerg-400	807	18	no	no	DET
fuelectenerg-400	807	19	information	information	NOUN
fuelectenerg-400	807	20	is	be	AUX
fuelectenerg-400	807	21	stored	store	VERB
fuelectenerg-400	807	22	is	be	AUX
fuelectenerg-400	807	23	twice	twice	DET
fuelectenerg-400	807	24	the	the	DET
fuelectenerg-400	807	25	number	number	NOUN
fuelectenerg-400	807	26	of	of	ADP
fuelectenerg-400	807	27	such	such	ADJ
fuelectenerg-400	807	28	hexagons	hexagon	NOUN
fuelectenerg-400	807	29	.	.	PUNCT
fuelectenerg-400	808	1	by	by	ADP
fuelectenerg-400	808	2	subtracting	subtract	VERB
fuelectenerg-400	808	3	this	this	PRON
fuelectenerg-400	808	4	from	from	ADP
fuelectenerg-400	808	5	the	the	DET
fuelectenerg-400	808	6	total	total	ADJ
fuelectenerg-400	808	7	number	number	NOUN
fuelectenerg-400	808	8	of	of	ADP
fuelectenerg-400	808	9	lozenges	lozenge	NOUN
fuelectenerg-400	808	10	in	in	ADP
fuelectenerg-400	808	11	h	h	NOUN
fuelectenerg-400	808	12	,	,	PUNCT
fuelectenerg-400	808	13	the	the	DET
fuelectenerg-400	808	14	number	number	NOUN
fuelectenerg-400	808	15	of	of	ADP
fuelectenerg-400	808	16	bits	bit	NOUN
fuelectenerg-400	808	17	that	that	PRON
fuelectenerg-400	808	18	can	can	AUX
fuelectenerg-400	808	19	be	be	AUX
fuelectenerg-400	808	20	stored	store	VERB
fuelectenerg-400	808	21	in	in	ADP
fuelectenerg-400	808	22	this	this	DET
fuelectenerg-400	808	23	region	region	NOUN
fuelectenerg-400	808	24	can	can	AUX
fuelectenerg-400	808	25	be	be	AUX
fuelectenerg-400	808	26	found	find	VERB
fuelectenerg-400	808	27	.	.	PUNCT
fuelectenerg-400	809	1	the	the	DET
fuelectenerg-400	809	2	total	total	ADJ
fuelectenerg-400	809	3	number	number	NOUN
fuelectenerg-400	809	4	of	of	ADP
fuelectenerg-400	809	5	lozenges	lozenge	NOUN
fuelectenerg-400	809	6	is	be	AUX
fuelectenerg-400	809	7	half	half	DET
fuelectenerg-400	809	8	the	the	DET
fuelectenerg-400	809	9	number	number	NOUN
fuelectenerg-400	809	10	of	of	ADP
fuelectenerg-400	809	11	equilateral	equilateral	ADJ
fuelectenerg-400	809	12	triangles	triangle	NOUN
fuelectenerg-400	809	13	tiling	tile	VERB
fuelectenerg-400	809	14	h.	h.	NOUN
fuelectenerg-400	809	15	by	by	ADP
fuelectenerg-400	809	16	calculating	calculate	VERB
fuelectenerg-400	809	17	the	the	DET
fuelectenerg-400	809	18	areas	area	NOUN
fuelectenerg-400	809	19	of	of	ADP
fuelectenerg-400	809	20	h	h	NOUN
fuelectenerg-400	809	21	and	and	CCONJ
fuelectenerg-400	809	22	a	a	DET
fuelectenerg-400	809	23	unit	unit	NOUN
fuelectenerg-400	809	24	triangle	triangle	NOUN
fuelectenerg-400	809	25	,	,	PUNCT
fuelectenerg-400	809	26	the	the	DET
fuelectenerg-400	809	27	number	number	NOUN
fuelectenerg-400	809	28	of	of	ADP
fuelectenerg-400	809	29	538	538	NUM
fuelectenerg-400	809	30	b.	b.	PROPN
fuelectenerg-400	809	31	vasic	vasic	NOUN
fuelectenerg-400	809	32	,	,	PUNCT
fuelectenerg-400	809	33	a.	a.	PROPN
fuelectenerg-400	809	34	r.	r.	PROPN
fuelectenerg-400	809	35	krishnan	krishnan	PROPN
fuelectenerg-400	809	36	lozenge	lozenge	PROPN
fuelectenerg-400	809	37	tiling	tile	VERB
fuelectenerg-400	809	38	constrained	constrained	ADJ
fuelectenerg-400	809	39	codes	code	NOUN
fuelectenerg-400	809	40	539	539	NUM
fuelectenerg-400	809	41	538	538	NUM
fuelectenerg-400	809	42	a.	a.	NOUN
fuelectenerg-400	809	43	r.	r.	PROPN
fuelectenerg-400	809	44	krishnanan	krishnanan	PROPN
fuelectenerg-400	809	45	and	and	CCONJ
fuelectenerg-400	809	46	b.	b.	PROPN
fuelectenerg-400	809	47	vasić	vasić	PROPN
fuelectenerg-400	810	1	where	where	SCONJ
fuelectenerg-400	810	2	(	(	PUNCT
fuelectenerg-400	810	3	i)n	i)n	VERB
fuelectenerg-400	810	4	:	:	PUNCT
fuelectenerg-400	810	5	=	=	SYM
fuelectenerg-400	810	6	i(i	i(i	PROPN
fuelectenerg-400	810	7	+	+	CCONJ
fuelectenerg-400	810	8	1)(i	1)(i	NUM
fuelectenerg-400	810	9	+	+	CCONJ
fuelectenerg-400	810	10	2)	2)	NUM
fuelectenerg-400	810	11	...	...	PUNCT
fuelectenerg-400	810	12	(i	(i	X
fuelectenerg-400	810	13	+	+	CCONJ
fuelectenerg-400	810	14	n	n	CCONJ
fuelectenerg-400	810	15	−	−	PROPN
fuelectenerg-400	810	16	1	1	NUM
fuelectenerg-400	810	17	)	)	PUNCT
fuelectenerg-400	810	18	is	be	AUX
fuelectenerg-400	810	19	the	the	DET
fuelectenerg-400	810	20	rising	rise	VERB
fuelectenerg-400	810	21	factorial	factorial	NOUN
fuelectenerg-400	810	22	.	.	PUNCT
fuelectenerg-400	811	1	since	since	SCONJ
fuelectenerg-400	811	2	(	(	PUNCT
fuelectenerg-400	811	3	i)n	i)n	NOUN
fuelectenerg-400	811	4	=	=	SYM
fuelectenerg-400	811	5	(	(	PUNCT
fuelectenerg-400	811	6	i	i	PRON
fuelectenerg-400	811	7	+	+	CCONJ
fuelectenerg-400	811	8	n	n	CCONJ
fuelectenerg-400	811	9	−	−	NUM
fuelectenerg-400	811	10	1)!/(a	1)!/(a	NUM
fuelectenerg-400	811	11	−	−	NOUN
fuelectenerg-400	811	12	1	1	NUM
fuelectenerg-400	811	13	)	)	PUNCT
fuelectenerg-400	811	14	!	!	PUNCT
fuelectenerg-400	811	15	,	,	PUNCT
fuelectenerg-400	811	16	we	we	PRON
fuelectenerg-400	811	17	have	have	VERB
fuelectenerg-400	811	18	a∏	a∏	PROPN
fuelectenerg-400	811	19	i=1	i=1	PROPN
fuelectenerg-400	812	1	(	(	PUNCT
fuelectenerg-400	812	2	c	c	NOUN
fuelectenerg-400	812	3	+	+	X
fuelectenerg-400	812	4	i)b	i)b	ADJ
fuelectenerg-400	812	5	(	(	PUNCT
fuelectenerg-400	812	6	i)b	i)b	ADJ
fuelectenerg-400	812	7	=	=	PUNCT
fuelectenerg-400	812	8	a∏	a∏	NOUN
fuelectenerg-400	812	9	i=1	i=1	X
fuelectenerg-400	813	1	(	(	PUNCT
fuelectenerg-400	813	2	c	c	X
fuelectenerg-400	813	3	+	+	NOUN
fuelectenerg-400	814	1	i	i	PRON
fuelectenerg-400	814	2	+	+	CCONJ
fuelectenerg-400	814	3	b	b	X
fuelectenerg-400	814	4	−	−	PROPN
fuelectenerg-400	814	5	1)!(i	1)!(i	NOUN
fuelectenerg-400	814	6	−	−	PROPN
fuelectenerg-400	814	7	1	1	NUM
fuelectenerg-400	814	8	)	)	PUNCT
fuelectenerg-400	814	9	!	!	PUNCT
fuelectenerg-400	815	1	(	(	PUNCT
fuelectenerg-400	815	2	c	c	X
fuelectenerg-400	816	1	+	+	CCONJ
fuelectenerg-400	817	1	i	i	PRON
fuelectenerg-400	817	2	−	−	PROPN
fuelectenerg-400	818	1	1)!(i	1)!(i	PROPN
fuelectenerg-400	819	1	+	+	CCONJ
fuelectenerg-400	819	2	b	b	X
fuelectenerg-400	819	3	−	−	NOUN
fuelectenerg-400	819	4	1	1	NUM
fuelectenerg-400	819	5	)	)	PUNCT
fuelectenerg-400	819	6	!	!	PUNCT
fuelectenerg-400	820	1	each	each	DET
fuelectenerg-400	820	2	product	product	NOUN
fuelectenerg-400	820	3	of	of	ADP
fuelectenerg-400	820	4	factorials	factorial	NOUN
fuelectenerg-400	820	5	in	in	ADP
fuelectenerg-400	820	6	7	7	NUM
fuelectenerg-400	820	7	is	be	AUX
fuelectenerg-400	820	8	of	of	ADP
fuelectenerg-400	820	9	the	the	DET
fuelectenerg-400	820	10	form	form	NOUN
fuelectenerg-400	820	11	∏a	∏a	VERB
fuelectenerg-400	820	12	i=1	i=1	PROPN
fuelectenerg-400	820	13	(	(	PUNCT
fuelectenerg-400	820	14	d	d	X
fuelectenerg-400	821	1	+	+	CCONJ
fuelectenerg-400	821	2	i	i	PRON
fuelectenerg-400	821	3	−	−	NOUN
fuelectenerg-400	821	4	1	1	NUM
fuelectenerg-400	821	5	)	)	PUNCT
fuelectenerg-400	821	6	!	!	PUNCT
fuelectenerg-400	822	1	and	and	CCONJ
fuelectenerg-400	822	2	can	can	AUX
fuelectenerg-400	822	3	be	be	AUX
fuelectenerg-400	822	4	written	write	VERB
fuelectenerg-400	822	5	as	as	ADP
fuelectenerg-400	822	6	a∏	a∏	PROPN
fuelectenerg-400	822	7	i=1	i=1	PROPN
fuelectenerg-400	823	1	(	(	PUNCT
fuelectenerg-400	823	2	d	d	X
fuelectenerg-400	823	3	+	+	CCONJ
fuelectenerg-400	824	1	i	i	PRON
fuelectenerg-400	824	2	−	−	NOUN
fuelectenerg-400	824	3	1	1	NUM
fuelectenerg-400	824	4	)	)	PUNCT
fuelectenerg-400	824	5	!	!	PUNCT
fuelectenerg-400	825	1	=	=	PUNCT
fuelectenerg-400	825	2	∏d+a−1	∏d+a−1	PROPN
fuelectenerg-400	825	3	i=1	i=1	PROPN
fuelectenerg-400	825	4	i!∏d−1	i!∏d−1	PROPN
fuelectenerg-400	825	5	i=1	i=1	PROPN
fuelectenerg-400	826	1	i	i	PROPN
fuelectenerg-400	826	2	!	!	PUNCT
fuelectenerg-400	827	1	the	the	DET
fuelectenerg-400	827	2	superfactorials	superfactorial	NOUN
fuelectenerg-400	827	3	∏a	∏a	VERB
fuelectenerg-400	827	4	i=1	i=1	PROPN
fuelectenerg-400	828	1	i	i	PRON
fuelectenerg-400	828	2	!	!	PUNCT
fuelectenerg-400	829	1	in	in	ADP
fuelectenerg-400	829	2	7	7	NUM
fuelectenerg-400	829	3	can	can	AUX
fuelectenerg-400	829	4	be	be	AUX
fuelectenerg-400	829	5	expressed	express	VERB
fuelectenerg-400	829	6	as	as	ADP
fuelectenerg-400	829	7	∏n−1	∏n−1	PROPN
fuelectenerg-400	829	8	i=1	i=1	PROPN
fuelectenerg-400	829	9	i	i	PRON
fuelectenerg-400	829	10	!	!	PUNCT
fuelectenerg-400	830	1	=	=	PUNCT
fuelectenerg-400	830	2	g(n	g(n	PROPN
fuelectenerg-400	830	3	+	+	CCONJ
fuelectenerg-400	830	4	1	1	NUM
fuelectenerg-400	830	5	)	)	PUNCT
fuelectenerg-400	830	6	.	.	PUNCT
fuelectenerg-400	831	1	therefore	therefore	ADV
fuelectenerg-400	831	2	we	we	PRON
fuelectenerg-400	831	3	obtain	obtain	VERB
fuelectenerg-400	831	4	n(a	n(a	NOUN
fuelectenerg-400	831	5	,	,	PUNCT
fuelectenerg-400	831	6	b	b	NOUN
fuelectenerg-400	831	7	,	,	PUNCT
fuelectenerg-400	831	8	c	c	NOUN
fuelectenerg-400	831	9	)	)	PUNCT
fuelectenerg-400	831	10	=	=	PUNCT
fuelectenerg-400	832	1	a∏	a∏	NOUN
fuelectenerg-400	832	2	i=1	i=1	X
fuelectenerg-400	832	3	g(a	g(a	PROPN
fuelectenerg-400	833	1	+	+	NUM
fuelectenerg-400	833	2	b	b	PROPN
fuelectenerg-400	833	3	+	+	NUM
fuelectenerg-400	833	4	c	c	NOUN
fuelectenerg-400	833	5	+	+	CCONJ
fuelectenerg-400	833	6	1)g(a	1)g(a	NUM
fuelectenerg-400	834	1	+	+	SYM
fuelectenerg-400	834	2	1)g(b	1)g(b	NUM
fuelectenerg-400	835	1	+	+	CCONJ
fuelectenerg-400	835	2	1)g(c	1)g(c	NUM
fuelectenerg-400	835	3	+	+	CCONJ
fuelectenerg-400	835	4	1	1	NUM
fuelectenerg-400	835	5	)	)	PUNCT
fuelectenerg-400	835	6	g(a	g(a	PROPN
fuelectenerg-400	836	1	+	+	CCONJ
fuelectenerg-400	836	2	b	b	PROPN
fuelectenerg-400	836	3	+	+	NUM
fuelectenerg-400	836	4	1)g(a	1)g(a	NUM
fuelectenerg-400	836	5	+	+	CCONJ
fuelectenerg-400	836	6	c	c	NOUN
fuelectenerg-400	836	7	+	+	SYM
fuelectenerg-400	836	8	1)g(b	1)g(b	NUM
fuelectenerg-400	837	1	+	+	CCONJ
fuelectenerg-400	837	2	c	c	NOUN
fuelectenerg-400	837	3	+	+	NOUN
fuelectenerg-400	837	4	1	1	NUM
fuelectenerg-400	837	5	)	)	PUNCT
fuelectenerg-400	837	6	(	(	PUNCT
fuelectenerg-400	837	7	8)	8)	NUM
fuelectenerg-400	837	8	where	where	SCONJ
fuelectenerg-400	837	9	in	in	ADP
fuelectenerg-400	837	10	eq	eq	NOUN
fuelectenerg-400	837	11	.	.	PROPN
fuelectenerg-400	837	12	8	8	NUM
fuelectenerg-400	837	13	g	g	NOUN
fuelectenerg-400	837	14	denotes	denote	VERB
fuelectenerg-400	837	15	the	the	DET
fuelectenerg-400	837	16	barnes	barnes	PROPN
fuelectenerg-400	837	17	g	g	NOUN
fuelectenerg-400	837	18	-	-	PUNCT
fuelectenerg-400	837	19	function	function	NOUN
fuelectenerg-400	837	20	[	[	X
fuelectenerg-400	837	21	26	26	NUM
fuelectenerg-400	837	22	]	]	PUNCT
fuelectenerg-400	837	23	defined	define	VERB
fuelectenerg-400	837	24	by	by	ADP
fuelectenerg-400	837	25	g(d	g(d	PROPN
fuelectenerg-400	837	26	+	+	CCONJ
fuelectenerg-400	837	27	1	1	X
fuelectenerg-400	837	28	)	)	PUNCT
fuelectenerg-400	837	29	=	=	NOUN
fuelectenerg-400	837	30	(	(	PUNCT
fuelectenerg-400	837	31	2π	2π	NOUN
fuelectenerg-400	837	32	)	)	PUNCT
fuelectenerg-400	837	33	d	d	NOUN
fuelectenerg-400	837	34	2	2	NUM
fuelectenerg-400	837	35	e−	e−	PROPN
fuelectenerg-400	837	36	1	1	NUM
fuelectenerg-400	837	37	2	2	NUM
fuelectenerg-400	837	38	(	(	PUNCT
fuelectenerg-400	837	39	d(d+1)+γd2	d(d+1)+γd2	PROPN
fuelectenerg-400	837	40	)	)	PUNCT
fuelectenerg-400	837	41	·	·	PUNCT
fuelectenerg-400	837	42	·	·	PUNCT
fuelectenerg-400	838	1	+	+	X
fuelectenerg-400	838	2	∞∏	∞∏	X
fuelectenerg-400	838	3	i=1	i=1	X
fuelectenerg-400	838	4	(	(	PUNCT
fuelectenerg-400	838	5	(	(	PUNCT
fuelectenerg-400	838	6	1	1	NUM
fuelectenerg-400	838	7	+	+	CCONJ
fuelectenerg-400	838	8	d	d	NOUN
fuelectenerg-400	838	9	i	i	NOUN
fuelectenerg-400	838	10	)	)	PUNCT
fuelectenerg-400	838	11	i	i	PRON
fuelectenerg-400	838	12	e−d+d2/(2i	e−d+d2/(2i	PROPN
fuelectenerg-400	838	13	)	)	PUNCT
fuelectenerg-400	838	14	)	)	PUNCT
fuelectenerg-400	838	15	for	for	ADP
fuelectenerg-400	838	16	a	a	DET
fuelectenerg-400	838	17	regular	regular	ADJ
fuelectenerg-400	838	18	hexagon	hexagon	NOUN
fuelectenerg-400	838	19	with	with	ADP
fuelectenerg-400	838	20	a	a	DET
fuelectenerg-400	838	21	=	=	SYM
fuelectenerg-400	838	22	b	b	NOUN
fuelectenerg-400	838	23	=	=	SYM
fuelectenerg-400	838	24	c	c	NOUN
fuelectenerg-400	838	25	=	=	PUNCT
fuelectenerg-400	838	26	n	n	CCONJ
fuelectenerg-400	838	27	we	we	PRON
fuelectenerg-400	838	28	have	have	VERB
fuelectenerg-400	838	29	n(n	n(n	NOUN
fuelectenerg-400	838	30	,	,	PUNCT
fuelectenerg-400	838	31	n	n	CCONJ
fuelectenerg-400	838	32	,	,	PUNCT
fuelectenerg-400	838	33	n	n	CCONJ
fuelectenerg-400	838	34	)	)	PUNCT
fuelectenerg-400	839	1	=	=	PUNCT
fuelectenerg-400	839	2	a∏	a∏	NOUN
fuelectenerg-400	839	3	i=1	i=1	VERB
fuelectenerg-400	839	4	g(3n	g(3n	ADJ
fuelectenerg-400	840	1	+	+	NOUN
fuelectenerg-400	840	2	1	1	X
fuelectenerg-400	840	3	)	)	PUNCT
fuelectenerg-400	840	4	(	(	PUNCT
fuelectenerg-400	840	5	g(n	g(n	PROPN
fuelectenerg-400	840	6	+	+	CCONJ
fuelectenerg-400	840	7	1))3	1))3	NUM
fuelectenerg-400	840	8	g(2n	g(2n	VERB
fuelectenerg-400	840	9	+	+	X
fuelectenerg-400	841	1	1)3	1)3	NUM
fuelectenerg-400	841	2	(	(	PUNCT
fuelectenerg-400	841	3	9	9	NUM
fuelectenerg-400	841	4	)	)	PUNCT
fuelectenerg-400	841	5	using	use	VERB
fuelectenerg-400	841	6	the	the	DET
fuelectenerg-400	841	7	asymptotic	asymptotic	NOUN
fuelectenerg-400	841	8	of	of	ADP
fuelectenerg-400	841	9	g(d	g(d	PROPN
fuelectenerg-400	841	10	+	+	CCONJ
fuelectenerg-400	841	11	1	1	X
fuelectenerg-400	841	12	)	)	PUNCT
fuelectenerg-400	841	13	lng(d	lng(d	PROPN
fuelectenerg-400	842	1	+	+	NOUN
fuelectenerg-400	842	2	1)˜z2	1)˜z2	PROPN
fuelectenerg-400	842	3	(	(	PUNCT
fuelectenerg-400	842	4	1	1	NUM
fuelectenerg-400	842	5	2	2	NUM
fuelectenerg-400	842	6	ln	ln	NOUN
fuelectenerg-400	842	7	z	z	NOUN
fuelectenerg-400	842	8	−	−	NOUN
fuelectenerg-400	842	9	3	3	NUM
fuelectenerg-400	842	10	4	4	NUM
fuelectenerg-400	842	11	)	)	PUNCT
fuelectenerg-400	843	1	+	+	CCONJ
fuelectenerg-400	843	2	1	1	NUM
fuelectenerg-400	843	3	2	2	NUM
fuelectenerg-400	843	4	ln(2π)z	ln(2π)z	NOUN
fuelectenerg-400	843	5	−	−	NOUN
fuelectenerg-400	843	6	−	−	NUM
fuelectenerg-400	843	7	1	1	NUM
fuelectenerg-400	843	8	12	12	NUM
fuelectenerg-400	843	9	ln	ln	ADJ
fuelectenerg-400	843	10	z	z	NOUN
fuelectenerg-400	843	11	+	+	NUM
fuelectenerg-400	843	12	ξ	ξ	X
fuelectenerg-400	843	13	′	′	NUM
fuelectenerg-400	843	14	(	(	PUNCT
fuelectenerg-400	843	15	−1)o	−1)o	NOUN
fuelectenerg-400	843	16	(	(	PUNCT
fuelectenerg-400	843	17	1	1	NUM
fuelectenerg-400	843	18	2	2	NUM
fuelectenerg-400	843	19	)	)	PUNCT
fuelectenerg-400	843	20	we	we	PRON
fuelectenerg-400	843	21	obtain	obtain	VERB
fuelectenerg-400	843	22	lnn(n	lnn(n	PROPN
fuelectenerg-400	843	23	,	,	PUNCT
fuelectenerg-400	843	24	n	n	CCONJ
fuelectenerg-400	843	25	,	,	PUNCT
fuelectenerg-400	843	26	n	n	CCONJ
fuelectenerg-400	843	27	)	)	PUNCT
fuelectenerg-400	843	28	∼	∼	NOUN
fuelectenerg-400	843	29	lng(3n	lng(3n	NOUN
fuelectenerg-400	843	30	+	+	CCONJ
fuelectenerg-400	843	31	1	1	X
fuelectenerg-400	843	32	)	)	PUNCT
fuelectenerg-400	843	33	+	+	CCONJ
fuelectenerg-400	843	34	3	3	NUM
fuelectenerg-400	843	35	ln	ln	PROPN
fuelectenerg-400	843	36	g(n	g(n	PROPN
fuelectenerg-400	843	37	+	+	CCONJ
fuelectenerg-400	843	38	1	1	X
fuelectenerg-400	843	39	)	)	PUNCT
fuelectenerg-400	843	40	−	−	ADP
fuelectenerg-400	843	41	−3	−3	NOUN
fuelectenerg-400	843	42	lng(2n	lng(2n	NOUN
fuelectenerg-400	843	43	+	+	NOUN
fuelectenerg-400	843	44	1	1	X
fuelectenerg-400	843	45	)	)	PUNCT
fuelectenerg-400	843	46	∼	∼	NOUN
fuelectenerg-400	843	47	n2	n2	NOUN
fuelectenerg-400	843	48	(	(	PUNCT
fuelectenerg-400	843	49	9	9	NUM
fuelectenerg-400	843	50	2	2	NUM
fuelectenerg-400	843	51	ln	ln	NOUN
fuelectenerg-400	843	52	3	3	NUM
fuelectenerg-400	843	53	−	−	PROPN
fuelectenerg-400	843	54	6	6	NUM
fuelectenerg-400	843	55	ln	ln	NOUN
fuelectenerg-400	843	56	2	2	NUM
fuelectenerg-400	843	57	)	)	PUNCT
fuelectenerg-400	843	58	+	+	PUNCT
fuelectenerg-400	844	1	+	+	ADP
fuelectenerg-400	844	2	n	n	VERB
fuelectenerg-400	844	3	ln	ln	ADJ
fuelectenerg-400	844	4	2π	2π	PROPN
fuelectenerg-400	844	5	−	−	NOUN
fuelectenerg-400	844	6	1	1	NUM
fuelectenerg-400	844	7	12	12	NUM
fuelectenerg-400	844	8	lnn	lnn	NOUN
fuelectenerg-400	844	9	−	−	NOUN
fuelectenerg-400	844	10	1	1	NUM
fuelectenerg-400	844	11	12	12	NUM
fuelectenerg-400	844	12	ln	ln	NOUN
fuelectenerg-400	844	13	3	3	NUM
fuelectenerg-400	844	14	2	2	NUM
fuelectenerg-400	844	15	by	by	ADP
fuelectenerg-400	844	16	changing	change	VERB
fuelectenerg-400	844	17	the	the	DET
fuelectenerg-400	844	18	base	base	NOUN
fuelectenerg-400	844	19	of	of	ADP
fuelectenerg-400	844	20	the	the	DET
fuelectenerg-400	844	21	logarithm	logarithm	NOUN
fuelectenerg-400	844	22	we	we	PRON
fuelectenerg-400	844	23	obtain	obtain	VERB
fuelectenerg-400	844	24	log2	log2	PROPN
fuelectenerg-400	844	25	n(n	n(n	PROPN
fuelectenerg-400	844	26	,	,	PUNCT
fuelectenerg-400	844	27	n	n	CCONJ
fuelectenerg-400	844	28	,	,	PUNCT
fuelectenerg-400	844	29	n	n	CCONJ
fuelectenerg-400	844	30	)	)	PUNCT
fuelectenerg-400	844	31	∼	∼	NOUN
fuelectenerg-400	844	32	n2	n2	NOUN
fuelectenerg-400	844	33	(	(	PUNCT
fuelectenerg-400	844	34	9	9	NUM
fuelectenerg-400	844	35	2	2	NUM
fuelectenerg-400	844	36	log2	log2	NOUN
fuelectenerg-400	844	37	3	3	NUM
fuelectenerg-400	844	38	−	−	NOUN
fuelectenerg-400	844	39	6	6	NUM
fuelectenerg-400	844	40	)	)	PUNCT
fuelectenerg-400	844	41	(	(	PUNCT
fuelectenerg-400	844	42	10	10	NUM
fuelectenerg-400	844	43	)	)	PUNCT
fuelectenerg-400	844	44	detection	detection	NOUN
fuelectenerg-400	844	45	and	and	CCONJ
fuelectenerg-400	844	46	coding	code	VERB
fuelectenerg-400	844	47	for	for	ADP
fuelectenerg-400	844	48	tdmr	tdmr	NOUN
fuelectenerg-400	844	49	channel	channel	NOUN
fuelectenerg-400	844	50	539	539	NUM
fuelectenerg-400	844	51	the	the	DET
fuelectenerg-400	844	52	area	area	NOUN
fuelectenerg-400	844	53	of	of	ADP
fuelectenerg-400	844	54	the	the	DET
fuelectenerg-400	844	55	hexagon	hexagon	NOUN
fuelectenerg-400	844	56	with	with	ADP
fuelectenerg-400	844	57	sides	side	NOUN
fuelectenerg-400	844	58	a	a	DET
fuelectenerg-400	844	59	,	,	PUNCT
fuelectenerg-400	844	60	b	b	NOUN
fuelectenerg-400	844	61	and	and	CCONJ
fuelectenerg-400	844	62	c	c	PROPN
fuelectenerg-400	844	63	is	be	AUX
fuelectenerg-400	844	64	a(a	a(a	PROPN
fuelectenerg-400	844	65	,	,	PUNCT
fuelectenerg-400	844	66	b	b	X
fuelectenerg-400	844	67	,	,	PUNCT
fuelectenerg-400	844	68	c	c	NOUN
fuelectenerg-400	844	69	)	)	PUNCT
fuelectenerg-400	844	70	=	=	SYM
fuelectenerg-400	845	1	2(ab	2(ab	PROPN
fuelectenerg-400	846	1	+	+	CCONJ
fuelectenerg-400	846	2	ac	ac	PROPN
fuelectenerg-400	846	3	+	+	CCONJ
fuelectenerg-400	846	4	bc	bc	PROPN
fuelectenerg-400	846	5	)	)	PUNCT
fuelectenerg-400	846	6	√	√	ADV
fuelectenerg-400	846	7	3	3	NUM
fuelectenerg-400	846	8	4	4	NUM
fuelectenerg-400	846	9	.	.	PUNCT
fuelectenerg-400	847	1	for	for	ADP
fuelectenerg-400	847	2	a	a	DET
fuelectenerg-400	847	3	regular	regular	ADJ
fuelectenerg-400	847	4	hexagon	hexagon	NOUN
fuelectenerg-400	847	5	a(n	a(n	PROPN
fuelectenerg-400	847	6	,	,	PUNCT
fuelectenerg-400	847	7	n	n	CCONJ
fuelectenerg-400	847	8	,	,	PUNCT
fuelectenerg-400	847	9	n	n	CCONJ
fuelectenerg-400	847	10	)	)	PUNCT
fuelectenerg-400	847	11	=	=	SYM
fuelectenerg-400	847	12	2	2	NUM
fuelectenerg-400	847	13	√	√	NUM
fuelectenerg-400	847	14	3	3	NUM
fuelectenerg-400	847	15	2	2	NUM
fuelectenerg-400	847	16	n2	n2	NOUN
fuelectenerg-400	847	17	,	,	PUNCT
fuelectenerg-400	847	18	so	so	SCONJ
fuelectenerg-400	847	19	that	that	SCONJ
fuelectenerg-400	847	20	finally	finally	ADV
fuelectenerg-400	847	21	the	the	DET
fuelectenerg-400	847	22	density	density	NOUN
fuelectenerg-400	847	23	is	be	AUX
fuelectenerg-400	847	24	d	d	NOUN
fuelectenerg-400	847	25	=	=	SYM
fuelectenerg-400	847	26	lim	lim	PROPN
fuelectenerg-400	847	27	n→∞	n→∞	NUM
fuelectenerg-400	847	28	log2	log2	PROPN
fuelectenerg-400	847	29	n(n	n(n	PROPN
fuelectenerg-400	847	30	,	,	PUNCT
fuelectenerg-400	847	31	n	n	CCONJ
fuelectenerg-400	847	32	,	,	PUNCT
fuelectenerg-400	847	33	n	n	CCONJ
fuelectenerg-400	847	34	)	)	PUNCT
fuelectenerg-400	847	35	a(n	a(n	ADV
fuelectenerg-400	847	36	,	,	PUNCT
fuelectenerg-400	847	37	n	n	CCONJ
fuelectenerg-400	847	38	,	,	PUNCT
fuelectenerg-400	847	39	n	n	CCONJ
fuelectenerg-400	847	40	)	)	PUNCT
fuelectenerg-400	847	41	=	=	VERB
fuelectenerg-400	847	42	lim	lim	PROPN
fuelectenerg-400	847	43	n→∞	n→∞	NUM
fuelectenerg-400	847	44	n2	n2	NOUN
fuelectenerg-400	847	45	(	(	PUNCT
fuelectenerg-400	847	46	9	9	NUM
fuelectenerg-400	847	47	2	2	NUM
fuelectenerg-400	847	48	log2	log2	NOUN
fuelectenerg-400	847	49	3	3	NUM
fuelectenerg-400	847	50	−	−	NOUN
fuelectenerg-400	847	51	6	6	NUM
fuelectenerg-400	847	52	)	)	PUNCT
fuelectenerg-400	847	53	2	2	NUM
fuelectenerg-400	847	54	√	√	NUM
fuelectenerg-400	847	55	3	3	NUM
fuelectenerg-400	847	56	2	2	NUM
fuelectenerg-400	847	57	n2	n2	NOUN
fuelectenerg-400	847	58	=	=	SYM
fuelectenerg-400	848	1	√	√	ADP
fuelectenerg-400	848	2	3(log2	3(log2	NUM
fuelectenerg-400	848	3	3	3	NUM
fuelectenerg-400	848	4	−	−	NOUN
fuelectenerg-400	848	5	4	4	NUM
fuelectenerg-400	848	6	3	3	NUM
fuelectenerg-400	848	7	)	)	PUNCT
fuelectenerg-400	848	8	8	8	NUM
fuelectenerg-400	848	9	proof:[proof	proof:[proof	NOUN
fuelectenerg-400	848	10	of	of	ADP
fuelectenerg-400	848	11	theorem	theorem	NOUN
fuelectenerg-400	848	12	2	2	NUM
fuelectenerg-400	848	13	]	]	PUNCT
fuelectenerg-400	848	14	consider	consider	VERB
fuelectenerg-400	848	15	the	the	DET
fuelectenerg-400	848	16	equivalence	equivalence	NOUN
fuelectenerg-400	848	17	between	between	ADP
fuelectenerg-400	848	18	tilings	tiling	NOUN
fuelectenerg-400	848	19	and	and	CCONJ
fuelectenerg-400	848	20	boxed	boxed	ADJ
fuelectenerg-400	848	21	plane	plane	NOUN
fuelectenerg-400	848	22	partitions	partition	NOUN
fuelectenerg-400	848	23	.	.	PUNCT
fuelectenerg-400	849	1	it	it	PRON
fuelectenerg-400	849	2	can	can	AUX
fuelectenerg-400	849	3	be	be	AUX
fuelectenerg-400	849	4	seen	see	VERB
fuelectenerg-400	849	5	that	that	SCONJ
fuelectenerg-400	849	6	each	each	DET
fuelectenerg-400	849	7	box	box	NOUN
fuelectenerg-400	849	8	in	in	ADP
fuelectenerg-400	849	9	the	the	DET
fuelectenerg-400	849	10	young	young	PROPN
fuelectenerg-400	849	11	’s	’s	PART
fuelectenerg-400	849	12	solid	solid	ADJ
fuelectenerg-400	849	13	diagram	diagram	NOUN
fuelectenerg-400	849	14	of	of	ADP
fuelectenerg-400	849	15	an	an	DET
fuelectenerg-400	849	16	(	(	PUNCT
fuelectenerg-400	849	17	a	a	PROPN
fuelectenerg-400	849	18	,	,	PUNCT
fuelectenerg-400	849	19	b	b	NOUN
fuelectenerg-400	849	20	,	,	PUNCT
fuelectenerg-400	849	21	c	c	NOUN
fuelectenerg-400	849	22	)	)	PUNCT
fuelectenerg-400	849	23	hexagon	hexagon	NOUN
fuelectenerg-400	849	24	with	with	ADP
fuelectenerg-400	849	25	3	3	NUM
fuelectenerg-400	849	26	visible	visible	ADJ
fuelectenerg-400	849	27	faces	face	NOUN
fuelectenerg-400	849	28	corresponds	correspond	VERB
fuelectenerg-400	849	29	to	to	ADP
fuelectenerg-400	849	30	a	a	DET
fuelectenerg-400	849	31	type-1	type-1	PROPN
fuelectenerg-400	849	32	hexagon	hexagon	NOUN
fuelectenerg-400	849	33	.	.	PUNCT
fuelectenerg-400	850	1	to	to	PART
fuelectenerg-400	850	2	find	find	VERB
fuelectenerg-400	850	3	the	the	DET
fuelectenerg-400	850	4	maximum	maximum	ADJ
fuelectenerg-400	850	5	number	number	NOUN
fuelectenerg-400	850	6	of	of	ADP
fuelectenerg-400	850	7	type-1	type-1	PROPN
fuelectenerg-400	850	8	hexagon	hexagon	VERB
fuelectenerg-400	850	9	in	in	ADP
fuelectenerg-400	850	10	h	h	NOUN
fuelectenerg-400	850	11	,	,	PUNCT
fuelectenerg-400	850	12	the	the	DET
fuelectenerg-400	850	13	young	young	PROPN
fuelectenerg-400	850	14	’s	’s	PART
fuelectenerg-400	850	15	solid	solid	ADJ
fuelectenerg-400	850	16	diagram	diagram	NOUN
fuelectenerg-400	850	17	corresponding	correspond	VERB
fuelectenerg-400	850	18	to	to	ADP
fuelectenerg-400	850	19	an	an	DET
fuelectenerg-400	850	20	n×	n×	PRON
fuelectenerg-400	850	21	n×	n×	PROPN
fuelectenerg-400	850	22	n	n	PROPN
fuelectenerg-400	850	23	box	box	PROPN
fuelectenerg-400	850	24	with	with	ADP
fuelectenerg-400	850	25	the	the	DET
fuelectenerg-400	850	26	maximum	maximum	ADJ
fuelectenerg-400	850	27	number	number	NOUN
fuelectenerg-400	850	28	of	of	ADP
fuelectenerg-400	850	29	visible	visible	ADJ
fuelectenerg-400	850	30	boxes	box	NOUN
fuelectenerg-400	850	31	is	be	AUX
fuelectenerg-400	850	32	constructed	construct	VERB
fuelectenerg-400	850	33	.	.	PUNCT
fuelectenerg-400	851	1	this	this	PRON
fuelectenerg-400	851	2	can	can	AUX
fuelectenerg-400	851	3	be	be	AUX
fuelectenerg-400	851	4	constructed	construct	VERB
fuelectenerg-400	851	5	as	as	SCONJ
fuelectenerg-400	851	6	follows	follow	VERB
fuelectenerg-400	851	7	:	:	PUNCT
fuelectenerg-400	851	8	start	start	VERB
fuelectenerg-400	851	9	at	at	ADP
fuelectenerg-400	851	10	(	(	PUNCT
fuelectenerg-400	851	11	x	x	NOUN
fuelectenerg-400	851	12	,	,	PUNCT
fuelectenerg-400	851	13	y	y	NOUN
fuelectenerg-400	851	14	)	)	PUNCT
fuelectenerg-400	851	15	=	=	SYM
fuelectenerg-400	852	1	(	(	PUNCT
fuelectenerg-400	852	2	0	0	NUM
fuelectenerg-400	852	3	,	,	PUNCT
fuelectenerg-400	852	4	0	0	NUM
fuelectenerg-400	852	5	)	)	PUNCT
fuelectenerg-400	852	6	of	of	ADP
fuelectenerg-400	852	7	the	the	DET
fuelectenerg-400	852	8	n	n	NUM
fuelectenerg-400	852	9	×	×	NOUN
fuelectenerg-400	852	10	n	n	CCONJ
fuelectenerg-400	852	11	×	×	PROPN
fuelectenerg-400	852	12	n	n	CCONJ
fuelectenerg-400	852	13	box	box	NOUN
fuelectenerg-400	852	14	and	and	CCONJ
fuelectenerg-400	852	15	stack	stack	VERB
fuelectenerg-400	852	16	n	n	PRON
fuelectenerg-400	852	17	boxes	box	NOUN
fuelectenerg-400	852	18	.	.	PUNCT
fuelectenerg-400	853	1	now	now	ADV
fuelectenerg-400	853	2	,	,	PUNCT
fuelectenerg-400	853	3	at	at	ADP
fuelectenerg-400	853	4	(	(	PUNCT
fuelectenerg-400	853	5	x	x	NOUN
fuelectenerg-400	853	6	,	,	PUNCT
fuelectenerg-400	853	7	y	y	NOUN
fuelectenerg-400	853	8	)	)	PUNCT
fuelectenerg-400	853	9	=	=	PUNCT
fuelectenerg-400	853	10	(	(	PUNCT
fuelectenerg-400	853	11	1	1	NUM
fuelectenerg-400	853	12	,	,	PUNCT
fuelectenerg-400	853	13	0	0	NUM
fuelectenerg-400	853	14	)	)	PUNCT
fuelectenerg-400	853	15	,	,	PUNCT
fuelectenerg-400	853	16	stack	stack	VERB
fuelectenerg-400	853	17	n	n	PRON
fuelectenerg-400	853	18	−	−	NUM
fuelectenerg-400	853	19	1	1	NUM
fuelectenerg-400	853	20	boxes	box	NOUN
fuelectenerg-400	853	21	.	.	PUNCT
fuelectenerg-400	854	1	step	step	NOUN
fuelectenerg-400	854	2	in	in	ADP
fuelectenerg-400	854	3	the	the	DET
fuelectenerg-400	854	4	x	x	NOUN
fuelectenerg-400	854	5	direction	direction	NOUN
fuelectenerg-400	854	6	reducing	reduce	VERB
fuelectenerg-400	854	7	the	the	DET
fuelectenerg-400	854	8	number	number	NOUN
fuelectenerg-400	854	9	of	of	ADP
fuelectenerg-400	854	10	boxes	box	NOUN
fuelectenerg-400	854	11	stacked	stack	VERB
fuelectenerg-400	854	12	by	by	ADP
fuelectenerg-400	854	13	1	1	NUM
fuelectenerg-400	854	14	at	at	ADP
fuelectenerg-400	854	15	each	each	DET
fuelectenerg-400	854	16	step	step	NOUN
fuelectenerg-400	854	17	.	.	PUNCT
fuelectenerg-400	855	1	this	this	PRON
fuelectenerg-400	855	2	is	be	AUX
fuelectenerg-400	855	3	continued	continue	VERB
fuelectenerg-400	855	4	till	till	SCONJ
fuelectenerg-400	855	5	(	(	PUNCT
fuelectenerg-400	855	6	x	x	NOUN
fuelectenerg-400	855	7	,	,	PUNCT
fuelectenerg-400	855	8	y	y	NOUN
fuelectenerg-400	855	9	)	)	PUNCT
fuelectenerg-400	855	10	=	=	SYM
fuelectenerg-400	855	11	(	(	PUNCT
fuelectenerg-400	855	12	n−1	n−1	PROPN
fuelectenerg-400	855	13	,	,	PUNCT
fuelectenerg-400	855	14	0	0	NUM
fuelectenerg-400	855	15	)	)	PUNCT
fuelectenerg-400	855	16	where	where	SCONJ
fuelectenerg-400	855	17	1	1	NUM
fuelectenerg-400	855	18	box	box	NOUN
fuelectenerg-400	855	19	is	be	AUX
fuelectenerg-400	855	20	stacked	stack	VERB
fuelectenerg-400	855	21	.	.	PUNCT
fuelectenerg-400	856	1	next	next	ADV
fuelectenerg-400	856	2	,	,	PUNCT
fuelectenerg-400	856	3	start	start	VERB
fuelectenerg-400	856	4	at	at	ADP
fuelectenerg-400	856	5	(	(	PUNCT
fuelectenerg-400	856	6	x	x	NOUN
fuelectenerg-400	856	7	,	,	PUNCT
fuelectenerg-400	856	8	y	y	NOUN
fuelectenerg-400	856	9	)	)	PUNCT
fuelectenerg-400	856	10	=	=	SYM
fuelectenerg-400	857	1	(	(	PUNCT
fuelectenerg-400	857	2	0	0	NUM
fuelectenerg-400	857	3	,	,	PUNCT
fuelectenerg-400	857	4	1	1	NUM
fuelectenerg-400	857	5	)	)	PUNCT
fuelectenerg-400	858	1	and	and	CCONJ
fuelectenerg-400	858	2	stack	stack	VERB
fuelectenerg-400	858	3	n	n	CCONJ
fuelectenerg-400	858	4	−	−	NUM
fuelectenerg-400	858	5	1	1	NUM
fuelectenerg-400	858	6	boxes	box	NOUN
fuelectenerg-400	858	7	.	.	PUNCT
fuelectenerg-400	859	1	continue	continue	VERB
fuelectenerg-400	859	2	the	the	DET
fuelectenerg-400	859	3	same	same	ADJ
fuelectenerg-400	859	4	process	process	NOUN
fuelectenerg-400	859	5	till	till	SCONJ
fuelectenerg-400	859	6	(	(	PUNCT
fuelectenerg-400	859	7	x	x	NOUN
fuelectenerg-400	859	8	,	,	PUNCT
fuelectenerg-400	859	9	y	y	NOUN
fuelectenerg-400	859	10	)	)	PUNCT
fuelectenerg-400	859	11	=	=	PUNCT
fuelectenerg-400	859	12	(	(	PUNCT
fuelectenerg-400	859	13	n−	n−	NOUN
fuelectenerg-400	859	14	2	2	NUM
fuelectenerg-400	859	15	,	,	PUNCT
fuelectenerg-400	859	16	1	1	NUM
fuelectenerg-400	859	17	)	)	PUNCT
fuelectenerg-400	859	18	is	be	AUX
fuelectenerg-400	859	19	reached	reach	VERB
fuelectenerg-400	859	20	where	where	SCONJ
fuelectenerg-400	859	21	1	1	NUM
fuelectenerg-400	859	22	box	box	NOUN
fuelectenerg-400	859	23	is	be	AUX
fuelectenerg-400	859	24	stacked	stack	VERB
fuelectenerg-400	859	25	.	.	PUNCT
fuelectenerg-400	860	1	this	this	DET
fuelectenerg-400	860	2	process	process	NOUN
fuelectenerg-400	860	3	is	be	AUX
fuelectenerg-400	860	4	continued	continue	VERB
fuelectenerg-400	860	5	till	till	SCONJ
fuelectenerg-400	860	6	(	(	PUNCT
fuelectenerg-400	860	7	x	x	NOUN
fuelectenerg-400	860	8	,	,	PUNCT
fuelectenerg-400	860	9	y	y	NOUN
fuelectenerg-400	860	10	)	)	PUNCT
fuelectenerg-400	860	11	=	=	PUNCT
fuelectenerg-400	860	12	(	(	PUNCT
fuelectenerg-400	860	13	n	n	CCONJ
fuelectenerg-400	860	14	−	−	PROPN
fuelectenerg-400	860	15	1	1	NUM
fuelectenerg-400	860	16	,	,	PUNCT
fuelectenerg-400	860	17	0	0	NUM
fuelectenerg-400	860	18	)	)	PUNCT
fuelectenerg-400	860	19	is	be	AUX
fuelectenerg-400	860	20	reached	reach	VERB
fuelectenerg-400	860	21	where	where	SCONJ
fuelectenerg-400	860	22	1	1	NUM
fuelectenerg-400	860	23	box	box	NOUN
fuelectenerg-400	860	24	is	be	AUX
fuelectenerg-400	860	25	stacked	stack	VERB
fuelectenerg-400	860	26	.	.	PUNCT
fuelectenerg-400	861	1	this	this	PRON
fuelectenerg-400	861	2	corresponds	correspond	VERB
fuelectenerg-400	861	3	to	to	ADP
fuelectenerg-400	861	4	the	the	DET
fuelectenerg-400	861	5	young	young	ADJ
fuelectenerg-400	861	6	’s	’s	PART
fuelectenerg-400	861	7	solid	solid	ADJ
fuelectenerg-400	861	8	diagram	diagram	NOUN
fuelectenerg-400	861	9	with	with	ADP
fuelectenerg-400	861	10	the	the	DET
fuelectenerg-400	861	11	maximum	maximum	ADJ
fuelectenerg-400	861	12	number	number	NOUN
fuelectenerg-400	861	13	of	of	ADP
fuelectenerg-400	861	14	visible	visible	ADJ
fuelectenerg-400	861	15	boxes	box	NOUN
fuelectenerg-400	861	16	.	.	PUNCT
fuelectenerg-400	862	1	the	the	DET
fuelectenerg-400	862	2	boxed	box	VERB
fuelectenerg-400	862	3	plane	plane	NOUN
fuelectenerg-400	862	4	partition	partition	NOUN
fuelectenerg-400	862	5	corresponding	correspond	VERB
fuelectenerg-400	862	6	to	to	ADP
fuelectenerg-400	862	7	this	this	DET
fuelectenerg-400	862	8	young	young	PROPN
fuelectenerg-400	862	9	’s	’s	PART
fuelectenerg-400	862	10	diagram	diagram	NOUN
fuelectenerg-400	862	11	is	be	AUX
fuelectenerg-400	862	12	given	give	VERB
fuelectenerg-400	862	13	by	by	ADP
fuelectenerg-400	862	14	:	:	PUNCT
fuelectenerg-400	862	15	π	π	NOUN
fuelectenerg-400	862	16	=	=	PUNCT
fuelectenerg-400	862	17			VERB
fuelectenerg-400	862	18			PROPN
fuelectenerg-400	862	19	n	n	CCONJ
fuelectenerg-400	862	20	n	n	CCONJ
fuelectenerg-400	862	21	−	−	PROPN
fuelectenerg-400	862	22	1	1	NUM
fuelectenerg-400	862	23	.	.	PUNCT
fuelectenerg-400	862	24	.	.	PUNCT
fuelectenerg-400	862	25	.	.	PUNCT
fuelectenerg-400	863	1	3	3	NUM
fuelectenerg-400	863	2	2	2	NUM
fuelectenerg-400	863	3	1	1	NUM
fuelectenerg-400	863	4	n	n	NUM
fuelectenerg-400	863	5	−	−	NUM
fuelectenerg-400	863	6	1	1	NUM
fuelectenerg-400	863	7	n	n	CCONJ
fuelectenerg-400	863	8	−	−	PROPN
fuelectenerg-400	863	9	2	2	NUM
fuelectenerg-400	863	10	.	.	PUNCT
fuelectenerg-400	863	11	.	.	PUNCT
fuelectenerg-400	863	12	.	.	PUNCT
fuelectenerg-400	864	1	2	2	NUM
fuelectenerg-400	864	2	1	1	NUM
fuelectenerg-400	864	3	0	0	NUM
fuelectenerg-400	864	4	n	n	CCONJ
fuelectenerg-400	864	5	−	−	NUM
fuelectenerg-400	864	6	2	2	NUM
fuelectenerg-400	864	7	n	n	NOUN
fuelectenerg-400	864	8	−	−	PROPN
fuelectenerg-400	864	9	3	3	NUM
fuelectenerg-400	864	10	.	.	PUNCT
fuelectenerg-400	864	11	.	.	PUNCT
fuelectenerg-400	864	12	.	.	PUNCT
fuelectenerg-400	865	1	1	1	NUM
fuelectenerg-400	865	2	0	0	NUM
fuelectenerg-400	865	3	0	0	NUM
fuelectenerg-400	865	4	...	...	PUNCT
fuelectenerg-400	865	5	...	...	PUNCT
fuelectenerg-400	866	1	1	1	NUM
fuelectenerg-400	866	2	0	0	NUM
fuelectenerg-400	866	3	.	.	PUNCT
fuelectenerg-400	866	4	.	.	PUNCT
fuelectenerg-400	866	5	.	.	PUNCT
fuelectenerg-400	866	6	0	0	PUNCT
fuelectenerg-400	867	1			X
fuelectenerg-400	868	1			NOUN
fuelectenerg-400	868	2	as	as	ADP
fuelectenerg-400	868	3	an	an	DET
fuelectenerg-400	868	4	example	example	NOUN
fuelectenerg-400	868	5	,	,	PUNCT
fuelectenerg-400	868	6	figure	figure	NOUN
fuelectenerg-400	868	7	11	11	NUM
fuelectenerg-400	868	8	shows	show	VERB
fuelectenerg-400	868	9	the	the	DET
fuelectenerg-400	868	10	lozenge	lozenge	NOUN
fuelectenerg-400	868	11	tiling	tiling	NOUN
fuelectenerg-400	868	12	of	of	ADP
fuelectenerg-400	868	13	a	a	DET
fuelectenerg-400	868	14	(	(	PUNCT
fuelectenerg-400	868	15	4	4	NUM
fuelectenerg-400	868	16	,	,	PUNCT
fuelectenerg-400	868	17	4	4	NUM
fuelectenerg-400	868	18	,	,	PUNCT
fuelectenerg-400	868	19	4	4	X
fuelectenerg-400	868	20	)	)	PUNCT
fuelectenerg-400	868	21	hexagon	hexagon	NOUN
fuelectenerg-400	868	22	with	with	ADP
fuelectenerg-400	868	23	the	the	DET
fuelectenerg-400	868	24	maximum	maximum	ADJ
fuelectenerg-400	868	25	number	number	NOUN
fuelectenerg-400	868	26	of	of	ADP
fuelectenerg-400	868	27	type-1	type-1	PROPN
fuelectenerg-400	868	28	hexagons	hexagon	NOUN
fuelectenerg-400	868	29	.	.	PUNCT
fuelectenerg-400	869	1	alternatively	alternatively	ADV
fuelectenerg-400	869	2	,	,	PUNCT
fuelectenerg-400	869	3	it	it	PRON
fuelectenerg-400	869	4	can	can	AUX
fuelectenerg-400	869	5	be	be	AUX
fuelectenerg-400	869	6	visualized	visualize	VERB
fuelectenerg-400	869	7	as	as	ADP
fuelectenerg-400	869	8	a	a	DET
fuelectenerg-400	869	9	the	the	DET
fuelectenerg-400	869	10	young	young	ADJ
fuelectenerg-400	869	11	’s	’s	PART
fuelectenerg-400	869	12	solid	solid	ADJ
fuelectenerg-400	869	13	diagram	diagram	NOUN
fuelectenerg-400	869	14	corresponding	correspond	VERB
fuelectenerg-400	869	15	to	to	ADP
fuelectenerg-400	869	16	a	a	DET
fuelectenerg-400	869	17	4	4	NUM
fuelectenerg-400	869	18	×	×	NOUN
fuelectenerg-400	869	19	4	4	NUM
fuelectenerg-400	869	20	×	×	NOUN
fuelectenerg-400	869	21	4	4	NUM
fuelectenerg-400	869	22	box	box	NOUN
fuelectenerg-400	869	23	.	.	PUNCT
fuelectenerg-400	870	1	the	the	DET
fuelectenerg-400	870	2	number	number	NOUN
fuelectenerg-400	870	3	of	of	ADP
fuelectenerg-400	870	4	visible	visible	ADJ
fuelectenerg-400	870	5	boxes	box	NOUN
fuelectenerg-400	870	6	is	be	AUX
fuelectenerg-400	870	7	equal	equal	ADJ
fuelectenerg-400	870	8	to	to	ADP
fuelectenerg-400	870	9	the	the	DET
fuelectenerg-400	870	10	number	number	NOUN
fuelectenerg-400	870	11	of	of	ADP
fuelectenerg-400	870	12	non	non	ADJ
fuelectenerg-400	870	13	-	-	ADJ
fuelectenerg-400	870	14	zero	zero	NUM
fuelectenerg-400	870	15	entries	entry	NOUN
fuelectenerg-400	870	16	in	in	ADP
fuelectenerg-400	870	17	π	π	PROPN
fuelectenerg-400	870	18	.	.	PUNCT
fuelectenerg-400	871	1	this	this	PRON
fuelectenerg-400	871	2	is	be	AUX
fuelectenerg-400	871	3	equal	equal	ADJ
fuelectenerg-400	871	4	to	to	ADP
fuelectenerg-400	871	5	n(n+1	n(n+1	NOUN
fuelectenerg-400	871	6	)	)	PUNCT
fuelectenerg-400	871	7	2	2	NUM
fuelectenerg-400	871	8	.	.	PUNCT
fuelectenerg-400	872	1	this	this	PRON
fuelectenerg-400	872	2	is	be	AUX
fuelectenerg-400	872	3	equal	equal	ADJ
fuelectenerg-400	872	4	to	to	ADP
fuelectenerg-400	872	5	the	the	DET
fuelectenerg-400	872	6	number	number	NOUN
fuelectenerg-400	872	7	of	of	ADP
fuelectenerg-400	872	8	type-1	type-1	PROPN
fuelectenerg-400	872	9	hexagons	hexagon	NOUN
fuelectenerg-400	872	10	formed	form	VERB
fuelectenerg-400	872	11	in	in	ADP
fuelectenerg-400	872	12	h.	h.	PROPN
fuelectenerg-400	872	13	the	the	DET
fuelectenerg-400	872	14	number	number	NOUN
fuelectenerg-400	872	15	of	of	ADP
fuelectenerg-400	872	16	lozenges	lozenge	NOUN
fuelectenerg-400	872	17	where	where	SCONJ
fuelectenerg-400	872	18	no	no	DET
fuelectenerg-400	872	19	information	information	NOUN
fuelectenerg-400	872	20	is	be	AUX
fuelectenerg-400	872	21	stored	store	VERB
fuelectenerg-400	872	22	is	be	AUX
fuelectenerg-400	872	23	twice	twice	DET
fuelectenerg-400	872	24	the	the	DET
fuelectenerg-400	872	25	number	number	NOUN
fuelectenerg-400	872	26	of	of	ADP
fuelectenerg-400	872	27	such	such	ADJ
fuelectenerg-400	872	28	hexagons	hexagon	NOUN
fuelectenerg-400	872	29	.	.	PUNCT
fuelectenerg-400	873	1	by	by	ADP
fuelectenerg-400	873	2	subtracting	subtract	VERB
fuelectenerg-400	873	3	this	this	PRON
fuelectenerg-400	873	4	from	from	ADP
fuelectenerg-400	873	5	the	the	DET
fuelectenerg-400	873	6	total	total	ADJ
fuelectenerg-400	873	7	number	number	NOUN
fuelectenerg-400	873	8	of	of	ADP
fuelectenerg-400	873	9	lozenges	lozenge	NOUN
fuelectenerg-400	873	10	in	in	ADP
fuelectenerg-400	873	11	h	h	NOUN
fuelectenerg-400	873	12	,	,	PUNCT
fuelectenerg-400	873	13	the	the	DET
fuelectenerg-400	873	14	number	number	NOUN
fuelectenerg-400	873	15	of	of	ADP
fuelectenerg-400	873	16	bits	bit	NOUN
fuelectenerg-400	873	17	that	that	PRON
fuelectenerg-400	873	18	can	can	AUX
fuelectenerg-400	873	19	be	be	AUX
fuelectenerg-400	873	20	stored	store	VERB
fuelectenerg-400	873	21	in	in	ADP
fuelectenerg-400	873	22	this	this	DET
fuelectenerg-400	873	23	region	region	NOUN
fuelectenerg-400	873	24	can	can	AUX
fuelectenerg-400	873	25	be	be	AUX
fuelectenerg-400	873	26	found	find	VERB
fuelectenerg-400	873	27	.	.	PUNCT
fuelectenerg-400	874	1	the	the	DET
fuelectenerg-400	874	2	total	total	ADJ
fuelectenerg-400	874	3	number	number	NOUN
fuelectenerg-400	874	4	of	of	ADP
fuelectenerg-400	874	5	lozenges	lozenge	NOUN
fuelectenerg-400	874	6	is	be	AUX
fuelectenerg-400	874	7	half	half	DET
fuelectenerg-400	874	8	the	the	DET
fuelectenerg-400	874	9	number	number	NOUN
fuelectenerg-400	874	10	of	of	ADP
fuelectenerg-400	874	11	equilateral	equilateral	ADJ
fuelectenerg-400	874	12	triangles	triangle	NOUN
fuelectenerg-400	874	13	tiling	tile	VERB
fuelectenerg-400	874	14	h.	h.	NOUN
fuelectenerg-400	874	15	by	by	ADP
fuelectenerg-400	874	16	calculating	calculate	VERB
fuelectenerg-400	874	17	the	the	DET
fuelectenerg-400	874	18	areas	area	NOUN
fuelectenerg-400	874	19	of	of	ADP
fuelectenerg-400	874	20	h	h	NOUN
fuelectenerg-400	874	21	and	and	CCONJ
fuelectenerg-400	874	22	a	a	DET
fuelectenerg-400	874	23	unit	unit	NOUN
fuelectenerg-400	874	24	triangle	triangle	NOUN
fuelectenerg-400	874	25	,	,	PUNCT
fuelectenerg-400	874	26	the	the	DET
fuelectenerg-400	874	27	number	number	NOUN
fuelectenerg-400	874	28	of	of	ADP
fuelectenerg-400	874	29	538	538	NUM
fuelectenerg-400	874	30	b.	b.	PROPN
fuelectenerg-400	874	31	vasic	vasic	NOUN
fuelectenerg-400	874	32	,	,	PUNCT
fuelectenerg-400	874	33	a.	a.	PROPN
fuelectenerg-400	874	34	r.	r.	PROPN
fuelectenerg-400	874	35	krishnan	krishnan	PROPN
fuelectenerg-400	874	36	lozenge	lozenge	PROPN
fuelectenerg-400	874	37	tiling	tile	VERB
fuelectenerg-400	874	38	constrained	constrained	ADJ
fuelectenerg-400	874	39	codes	code	NOUN
fuelectenerg-400	874	40	539	539	NUM
fuelectenerg-400	874	41	540	540	NUM
fuelectenerg-400	874	42	a.	a.	NOUN
fuelectenerg-400	874	43	r.	r.	PROPN
fuelectenerg-400	874	44	krishnanan	krishnanan	PROPN
fuelectenerg-400	874	45	and	and	CCONJ
fuelectenerg-400	874	46	b.	b.	PROPN
fuelectenerg-400	874	47	vasić	vasić	PROPN
fuelectenerg-400	874	48	fig	fig	PROPN
fuelectenerg-400	874	49	.	.	PUNCT
fuelectenerg-400	875	1	11	11	NUM
fuelectenerg-400	875	2	.	.	PUNCT
fuelectenerg-400	876	1	the	the	DET
fuelectenerg-400	876	2	lozenge	lozenge	NOUN
fuelectenerg-400	876	3	tiling	tiling	NOUN
fuelectenerg-400	876	4	of	of	ADP
fuelectenerg-400	876	5	a	a	DET
fuelectenerg-400	876	6	(	(	PUNCT
fuelectenerg-400	876	7	4	4	NUM
fuelectenerg-400	876	8	,	,	PUNCT
fuelectenerg-400	876	9	4	4	NUM
fuelectenerg-400	876	10	,	,	PUNCT
fuelectenerg-400	876	11	4	4	X
fuelectenerg-400	876	12	)	)	PUNCT
fuelectenerg-400	876	13	hexagon	hexagon	NOUN
fuelectenerg-400	876	14	with	with	ADP
fuelectenerg-400	876	15	maximum	maximum	ADJ
fuelectenerg-400	876	16	number	number	NOUN
fuelectenerg-400	876	17	of	of	ADP
fuelectenerg-400	876	18	type-1	type-1	PROPN
fuelectenerg-400	876	19	hexagons	hexagon	NOUN
fuelectenerg-400	876	20	.	.	PUNCT
fuelectenerg-400	877	1	it	it	PRON
fuelectenerg-400	877	2	can	can	AUX
fuelectenerg-400	877	3	also	also	ADV
fuelectenerg-400	877	4	be	be	AUX
fuelectenerg-400	877	5	visualized	visualize	VERB
fuelectenerg-400	877	6	as	as	ADP
fuelectenerg-400	877	7	the	the	DET
fuelectenerg-400	877	8	young	young	ADJ
fuelectenerg-400	877	9	’s	’s	PART
fuelectenerg-400	877	10	solid	solid	ADJ
fuelectenerg-400	877	11	diagram	diagram	NOUN
fuelectenerg-400	877	12	of	of	ADP
fuelectenerg-400	877	13	a	a	DET
fuelectenerg-400	877	14	4×4×4	4×4×4	NUM
fuelectenerg-400	877	15	box	box	NOUN
fuelectenerg-400	877	16	with	with	ADP
fuelectenerg-400	877	17	the	the	DET
fuelectenerg-400	877	18	maximum	maximum	ADJ
fuelectenerg-400	877	19	number	number	NOUN
fuelectenerg-400	877	20	of	of	ADP
fuelectenerg-400	877	21	visible	visible	ADJ
fuelectenerg-400	877	22	boxes	box	NOUN
fuelectenerg-400	877	23	.	.	PUNCT
fuelectenerg-400	878	1	triangles	triangle	NOUN
fuelectenerg-400	878	2	is	be	AUX
fuelectenerg-400	878	3	calculated	calculate	VERB
fuelectenerg-400	878	4	as	as	ADP
fuelectenerg-400	878	5	6n2	6n2	NUM
fuelectenerg-400	878	6	.	.	PUNCT
fuelectenerg-400	879	1	hence	hence	ADV
fuelectenerg-400	879	2	,	,	PUNCT
fuelectenerg-400	879	3	the	the	DET
fuelectenerg-400	879	4	number	number	NOUN
fuelectenerg-400	879	5	of	of	ADP
fuelectenerg-400	879	6	lozenges	lozenge	NOUN
fuelectenerg-400	879	7	is	be	AUX
fuelectenerg-400	879	8	3n2	3n2	NUM
fuelectenerg-400	879	9	.	.	PUNCT
fuelectenerg-400	880	1	since	since	SCONJ
fuelectenerg-400	880	2	for	for	ADP
fuelectenerg-400	880	3	any	any	DET
fuelectenerg-400	880	4	lozenge	lozenge	NOUN
fuelectenerg-400	880	5	tiling	tiling	NOUN
fuelectenerg-400	880	6	of	of	ADP
fuelectenerg-400	880	7	h	h	NOUN
fuelectenerg-400	880	8	,	,	PUNCT
fuelectenerg-400	880	9	the	the	DET
fuelectenerg-400	880	10	number	number	NOUN
fuelectenerg-400	880	11	of	of	ADP
fuelectenerg-400	880	12	type-1	type-1	PROPN
fuelectenerg-400	880	13	hexagons	hexagon	NOUN
fuelectenerg-400	880	14	is	be	AUX
fuelectenerg-400	880	15	always	always	ADV
fuelectenerg-400	880	16	less	less	ADJ
fuelectenerg-400	880	17	than	than	ADP
fuelectenerg-400	880	18	or	or	CCONJ
fuelectenerg-400	880	19	equal	equal	ADJ
fuelectenerg-400	880	20	to	to	ADP
fuelectenerg-400	880	21	n(n	n(n	PROPN
fuelectenerg-400	880	22	+	+	CCONJ
fuelectenerg-400	880	23	1	1	NUM
fuelectenerg-400	880	24	)	)	PUNCT
fuelectenerg-400	880	25	,	,	PUNCT
fuelectenerg-400	880	26	we	we	PRON
fuelectenerg-400	880	27	have	have	VERB
fuelectenerg-400	880	28	a	a	DET
fuelectenerg-400	880	29	lower	low	ADJ
fuelectenerg-400	880	30	bound	bind	VERB
fuelectenerg-400	880	31	on	on	ADP
fuelectenerg-400	880	32	the	the	DET
fuelectenerg-400	880	33	capacity	capacity	NOUN
fuelectenerg-400	880	34	cc	cc	NOUN
fuelectenerg-400	880	35	as	as	SCONJ
fuelectenerg-400	880	36	follows	follow	VERB
fuelectenerg-400	880	37	:	:	PUNCT
fuelectenerg-400	880	38	cc	cc	NOUN
fuelectenerg-400	880	39	≥	≥	PROPN
fuelectenerg-400	880	40	lim	lim	PROPN
fuelectenerg-400	880	41	n→∞	n→∞	X
fuelectenerg-400	880	42	3n2	3n2	NUM
fuelectenerg-400	880	43	−	−	PROPN
fuelectenerg-400	880	44	n(n	n(n	NOUN
fuelectenerg-400	880	45	+	+	CCONJ
fuelectenerg-400	880	46	1	1	NUM
fuelectenerg-400	880	47	)	)	PUNCT
fuelectenerg-400	880	48	6n2	6n2	NUM
fuelectenerg-400	881	1	=	=	SYM
fuelectenerg-400	881	2	1	1	NUM
fuelectenerg-400	881	3	3	3	NUM
fuelectenerg-400	881	4	(	(	PUNCT
fuelectenerg-400	881	5	11	11	NUM
fuelectenerg-400	881	6	)	)	PUNCT
fuelectenerg-400	881	7	9	9	NUM
fuelectenerg-400	881	8	proof:[proof	proof:[proof	NOUN
fuelectenerg-400	881	9	of	of	ADP
fuelectenerg-400	881	10	theorem	theorem	NOUN
fuelectenerg-400	881	11	3	3	NUM
fuelectenerg-400	881	12	]	]	PUNCT
fuelectenerg-400	881	13	if	if	SCONJ
fuelectenerg-400	881	14	mountain(a	mountain(a	NOUN
fuelectenerg-400	881	15	)	)	PUNCT
fuelectenerg-400	881	16	⊂	⊂	PROPN
fuelectenerg-400	881	17	mountain(b	mountain(b	PROPN
fuelectenerg-400	881	18	)	)	PUNCT
fuelectenerg-400	881	19	,	,	PUNCT
fuelectenerg-400	881	20	then	then	ADV
fuelectenerg-400	881	21	ya(i	ya(i	VERB
fuelectenerg-400	881	22	)	)	PUNCT
fuelectenerg-400	881	23	≤	≤	NOUN
fuelectenerg-400	881	24	yb(i	yb(i	NUM
fuelectenerg-400	881	25	)	)	PUNCT
fuelectenerg-400	881	26	for	for	ADP
fuelectenerg-400	881	27	all	all	DET
fuelectenerg-400	881	28	i.	i.	NOUN
fuelectenerg-400	881	29	it	it	PRON
fuelectenerg-400	881	30	is	be	AUX
fuelectenerg-400	881	31	enough	enough	ADJ
fuelectenerg-400	881	32	to	to	PART
fuelectenerg-400	881	33	prove	prove	VERB
fuelectenerg-400	881	34	that	that	SCONJ
fuelectenerg-400	881	35	if	if	SCONJ
fuelectenerg-400	881	36	ya(i	ya(i	NOUN
fuelectenerg-400	881	37	)	)	PUNCT
fuelectenerg-400	881	38	≤	≤	NOUN
fuelectenerg-400	881	39	yb(i	yb(i	NOUN
fuelectenerg-400	882	1	)	)	PUNCT
fuelectenerg-400	882	2	∀	∀	X
fuelectenerg-400	883	1	i	i	NOUN
fuelectenerg-400	883	2	=	=	NOUN
fuelectenerg-400	883	3	1	1	NUM
fuelectenerg-400	883	4	,	,	PUNCT
fuelectenerg-400	883	5	2	2	NUM
fuelectenerg-400	883	6	,	,	PUNCT
fuelectenerg-400	883	7	.	.	PUNCT
fuelectenerg-400	883	8	.	.	PUNCT
fuelectenerg-400	884	1	.	.	PUNCT
fuelectenerg-400	885	1	,	,	PUNCT
fuelectenerg-400	885	2	n	n	CCONJ
fuelectenerg-400	885	3	,	,	PUNCT
fuelectenerg-400	885	4	then	then	ADV
fuelectenerg-400	885	5	a	a	DET
fuelectenerg-400	885	6	≤	≤	PROPN
fuelectenerg-400	885	7	b.	b.	NOUN
fuelectenerg-400	886	1	in	in	ADP
fuelectenerg-400	886	2	order	order	NOUN
fuelectenerg-400	886	3	to	to	PART
fuelectenerg-400	886	4	do	do	AUX
fuelectenerg-400	886	5	this	this	PRON
fuelectenerg-400	886	6	,	,	PUNCT
fuelectenerg-400	886	7	reconstruct	reconstruct	VERB
fuelectenerg-400	886	8	the	the	DET
fuelectenerg-400	886	9	sequences	sequence	NOUN
fuelectenerg-400	886	10	a	a	PRON
fuelectenerg-400	886	11	and	and	CCONJ
fuelectenerg-400	886	12	b	b	NOUN
fuelectenerg-400	886	13	from	from	ADP
fuelectenerg-400	886	14	ya	ya	PRON
fuelectenerg-400	886	15	and	and	CCONJ
fuelectenerg-400	886	16	yb	yb	PROPN
fuelectenerg-400	886	17	.	.	PUNCT
fuelectenerg-400	887	1	let	let	VERB
fuelectenerg-400	887	2	t	t	PROPN
fuelectenerg-400	887	3	,	,	PUNCT
fuelectenerg-400	887	4	1	1	NUM
fuelectenerg-400	887	5	≤	≤	NUM
fuelectenerg-400	887	6	t	t	NOUN
fuelectenerg-400	887	7	≤	≤	NOUN
fuelectenerg-400	887	8	n	n	CCONJ
fuelectenerg-400	887	9	such	such	ADJ
fuelectenerg-400	887	10	that	that	SCONJ
fuelectenerg-400	887	11	∀i	∀i	NOUN
fuelectenerg-400	887	12	<	<	X
fuelectenerg-400	887	13	t	t	PROPN
fuelectenerg-400	887	14	,	,	PUNCT
fuelectenerg-400	887	15	ya(i	ya(i	PUNCT
fuelectenerg-400	887	16	)	)	PUNCT
fuelectenerg-400	887	17	=	=	NOUN
fuelectenerg-400	887	18	yb(i	yb(i	NUM
fuelectenerg-400	887	19	)	)	PUNCT
fuelectenerg-400	887	20	and	and	CCONJ
fuelectenerg-400	887	21	ya(t	ya(t	X
fuelectenerg-400	887	22	)	)	PUNCT
fuelectenerg-400	887	23	�	�	PROPN
fuelectenerg-400	887	24	=	=	SYM
fuelectenerg-400	887	25	yb(t	yb(t	NOUN
fuelectenerg-400	887	26	)	)	PUNCT
fuelectenerg-400	887	27	.	.	PUNCT
fuelectenerg-400	888	1	this	this	PRON
fuelectenerg-400	888	2	means	mean	VERB
fuelectenerg-400	888	3	that	that	SCONJ
fuelectenerg-400	888	4	the	the	DET
fuelectenerg-400	888	5	ith	ith	ADJ
fuelectenerg-400	888	6	term	term	NOUN
fuelectenerg-400	888	7	of	of	ADP
fuelectenerg-400	888	8	a	a	PRON
fuelectenerg-400	888	9	is	be	AUX
fuelectenerg-400	888	10	0	0	NUM
fuelectenerg-400	888	11	and	and	CCONJ
fuelectenerg-400	888	12	that	that	PRON
fuelectenerg-400	888	13	of	of	ADP
fuelectenerg-400	888	14	b	b	PROPN
fuelectenerg-400	888	15	is	be	AUX
fuelectenerg-400	888	16	1	1	NUM
fuelectenerg-400	888	17	(	(	PUNCT
fuelectenerg-400	888	18	to	to	PART
fuelectenerg-400	888	19	satisfy	satisfy	VERB
fuelectenerg-400	888	20	the	the	DET
fuelectenerg-400	888	21	inequality	inequality	NOUN
fuelectenerg-400	888	22	in	in	ADP
fuelectenerg-400	888	23	the	the	DET
fuelectenerg-400	888	24	terms	term	NOUN
fuelectenerg-400	888	25	of	of	ADP
fuelectenerg-400	888	26	ya	ya	PRON
fuelectenerg-400	888	27	and	and	CCONJ
fuelectenerg-400	888	28	yb	yb	PROPN
fuelectenerg-400	888	29	)	)	PUNCT
fuelectenerg-400	888	30	.	.	PUNCT
fuelectenerg-400	889	1	hence	hence	ADV
fuelectenerg-400	889	2	,	,	PUNCT
fuelectenerg-400	889	3	de(a	de(a	NOUN
fuelectenerg-400	889	4	)	)	PUNCT
fuelectenerg-400	889	5	≤	≤	NOUN
fuelectenerg-400	889	6	de(b	de(b	PUNCT
fuelectenerg-400	889	7	)	)	PUNCT
fuelectenerg-400	889	8	(	(	PUNCT
fuelectenerg-400	889	9	inequality	inequality	NOUN
fuelectenerg-400	889	10	occurs	occur	VERB
fuelectenerg-400	889	11	if	if	SCONJ
fuelectenerg-400	889	12	they	they	PRON
fuelectenerg-400	889	13	differ	differ	VERB
fuelectenerg-400	889	14	in	in	ADP
fuelectenerg-400	889	15	one	one	NUM
fuelectenerg-400	889	16	or	or	CCONJ
fuelectenerg-400	889	17	more	more	ADJ
fuelectenerg-400	889	18	bits	bit	NOUN
fuelectenerg-400	889	19	and	and	CCONJ
fuelectenerg-400	889	20	equality	equality	NOUN
fuelectenerg-400	889	21	occurs	occur	VERB
fuelectenerg-400	889	22	if	if	SCONJ
fuelectenerg-400	889	23	they	they	PRON
fuelectenerg-400	889	24	do	do	AUX
fuelectenerg-400	889	25	not	not	PART
fuelectenerg-400	889	26	differ	differ	VERB
fuelectenerg-400	889	27	)	)	PUNCT
fuelectenerg-400	889	28	.	.	PUNCT
fuelectenerg-400	890	1	hence	hence	ADV
fuelectenerg-400	890	2	rank(a	rank(a	NOUN
fuelectenerg-400	890	3	)	)	PUNCT
fuelectenerg-400	890	4	≥	≥	PROPN
fuelectenerg-400	890	5	rank(b)/	rank(b)/	VERB
fuelectenerg-400	890	6	references	reference	NOUN
fuelectenerg-400	890	7	[	[	X
fuelectenerg-400	890	8	1	1	NUM
fuelectenerg-400	890	9	]	]	PUNCT
fuelectenerg-400	890	10	b.	b.	PROPN
fuelectenerg-400	890	11	h.	h.	PROPN
fuelectenerg-400	890	12	marcus	marcus	PROPN
fuelectenerg-400	890	13	,	,	PUNCT
fuelectenerg-400	890	14	p.	p.	PROPN
fuelectenerg-400	890	15	h.	h.	PROPN
fuelectenerg-400	890	16	siegel	siegel	PROPN
fuelectenerg-400	890	17	,	,	PUNCT
fuelectenerg-400	890	18	and	and	CCONJ
fuelectenerg-400	890	19	j.	j.	PROPN
fuelectenerg-400	890	20	k.	k.	PROPN
fuelectenerg-400	890	21	wolf	wolf	PROPN
fuelectenerg-400	890	22	,	,	PUNCT
fuelectenerg-400	890	23	“	"	PUNCT
fuelectenerg-400	890	24	finite	finite	ADJ
fuelectenerg-400	890	25	-	-	ADJ
fuelectenerg-400	890	26	state	state	ADJ
fuelectenerg-400	890	27	modulation	modulation	NOUN
fuelectenerg-400	890	28	codes	code	NOUN
fuelectenerg-400	890	29	for	for	ADP
fuelectenerg-400	890	30	data	datum	NOUN
fuelectenerg-400	890	31	storage	storage	NOUN
fuelectenerg-400	890	32	,	,	PUNCT
fuelectenerg-400	890	33	”	"	PUNCT
fuelectenerg-400	890	34	ieee	ieee	NOUN
fuelectenerg-400	890	35	journal	journal	NOUN
fuelectenerg-400	890	36	of	of	ADP
fuelectenerg-400	890	37	selected	select	VERB
fuelectenerg-400	890	38	areas	area	NOUN
fuelectenerg-400	890	39	in	in	ADP
fuelectenerg-400	890	40	communication	communication	NOUN
fuelectenerg-400	890	41	,	,	PUNCT
fuelectenerg-400	890	42	vol	vol	NOUN
fuelectenerg-400	890	43	.	.	PROPN
fuelectenerg-400	891	1	10	10	NUM
fuelectenerg-400	891	2	,	,	PUNCT
fuelectenerg-400	891	3	no	no	INTJ
fuelectenerg-400	891	4	.	.	NOUN
fuelectenerg-400	891	5	1	1	NUM
fuelectenerg-400	891	6	,	,	PUNCT
fuelectenerg-400	891	7	pp	pp	ADJ
fuelectenerg-400	891	8	.	.	PUNCT
fuelectenerg-400	892	1	5–37	5–37	NOUN
fuelectenerg-400	892	2	,	,	PUNCT
fuelectenerg-400	892	3	1992	1992	NUM
fuelectenerg-400	892	4	.	.	PUNCT
fuelectenerg-400	893	1	[	[	X
fuelectenerg-400	893	2	2	2	X
fuelectenerg-400	893	3	]	]	PUNCT
fuelectenerg-400	893	4	j.	j.	PROPN
fuelectenerg-400	893	5	j.	j.	PROPN
fuelectenerg-400	893	6	ashley	ashley	PROPN
fuelectenerg-400	893	7	and	and	CCONJ
fuelectenerg-400	893	8	b.	b.	PROPN
fuelectenerg-400	893	9	h.	h.	PROPN
fuelectenerg-400	893	10	marcus	marcus	PROPN
fuelectenerg-400	893	11	,	,	PUNCT
fuelectenerg-400	893	12	“	"	PUNCT
fuelectenerg-400	893	13	two	two	NUM
fuelectenerg-400	893	14	-	-	PUNCT
fuelectenerg-400	893	15	dimensional	dimensional	ADJ
fuelectenerg-400	893	16	low	low	ADJ
fuelectenerg-400	893	17	-	-	PUNCT
fuelectenerg-400	893	18	pass	pass	NOUN
fuelectenerg-400	893	19	filtering	filter	VERB
fuelectenerg-400	893	20	codes	code	NOUN
fuelectenerg-400	893	21	,	,	PUNCT
fuelectenerg-400	893	22	”	"	PUNCT
fuelectenerg-400	893	23	ieee	ieee	NOUN
fuelectenerg-400	893	24	transactions	transaction	NOUN
fuelectenerg-400	893	25	on	on	ADP
fuelectenerg-400	893	26	communications	communication	NOUN
fuelectenerg-400	893	27	,	,	PUNCT
fuelectenerg-400	893	28	vol	vol	NOUN
fuelectenerg-400	893	29	.	.	PROPN
fuelectenerg-400	893	30	46	46	NUM
fuelectenerg-400	893	31	,	,	PUNCT
fuelectenerg-400	893	32	pp	pp	ADJ
fuelectenerg-400	893	33	.	.	PUNCT
fuelectenerg-400	894	1	724–727	724–727	NUM
fuelectenerg-400	894	2	,	,	PUNCT
fuelectenerg-400	894	3	jun	jun	PROPN
fuelectenerg-400	894	4	1998	1998	NUM
fuelectenerg-400	894	5	.	.	PUNCT
fuelectenerg-400	895	1	[	[	X
fuelectenerg-400	895	2	3	3	X
fuelectenerg-400	895	3	]	]	PUNCT
fuelectenerg-400	895	4	z.	z.	PROPN
fuelectenerg-400	895	5	nagy	nagy	PROPN
fuelectenerg-400	895	6	and	and	CCONJ
fuelectenerg-400	895	7	k.	k.	PROPN
fuelectenerg-400	895	8	zeger	zeger	PROPN
fuelectenerg-400	895	9	,	,	PUNCT
fuelectenerg-400	895	10	“	"	PUNCT
fuelectenerg-400	895	11	capacity	capacity	NOUN
fuelectenerg-400	895	12	bounds	bound	VERB
fuelectenerg-400	895	13	for	for	ADP
fuelectenerg-400	895	14	the	the	DET
fuelectenerg-400	895	15	hard	hard	ADJ
fuelectenerg-400	895	16	-	-	PUNCT
fuelectenerg-400	895	17	triangle	triangle	NOUN
fuelectenerg-400	895	18	model	model	NOUN
fuelectenerg-400	895	19	,	,	PUNCT
fuelectenerg-400	895	20	”	"	PUNCT
fuelectenerg-400	895	21	proceedings	proceeding	NOUN
fuelectenerg-400	895	22	of	of	ADP
fuelectenerg-400	895	23	international	international	ADJ
fuelectenerg-400	895	24	symposium	symposium	NOUN
fuelectenerg-400	895	25	on	on	ADP
fuelectenerg-400	895	26	information	information	NOUN
fuelectenerg-400	895	27	theory	theory	NOUN
fuelectenerg-400	895	28	2004	2004	NUM
fuelectenerg-400	895	29	,	,	PUNCT
fuelectenerg-400	895	30	p.	p.	NOUN
fuelectenerg-400	895	31	162	162	NUM
fuelectenerg-400	895	32	,	,	PUNCT
fuelectenerg-400	895	33	2004	2004	NUM
fuelectenerg-400	895	34	.	.	PUNCT
fuelectenerg-400	896	1	[	[	X
fuelectenerg-400	896	2	4	4	NUM
fuelectenerg-400	896	3	]	]	X
fuelectenerg-400	896	4	i.	i.	NOUN
fuelectenerg-400	896	5	demirkan	demirkan	PROPN
fuelectenerg-400	896	6	and	and	CCONJ
fuelectenerg-400	896	7	j.	j.	PROPN
fuelectenerg-400	896	8	k.	k.	PROPN
fuelectenerg-400	896	9	wolf	wolf	PROPN
fuelectenerg-400	896	10	,	,	PUNCT
fuelectenerg-400	896	11	“	"	PUNCT
fuelectenerg-400	896	12	block	block	NOUN
fuelectenerg-400	896	13	codes	code	NOUN
fuelectenerg-400	896	14	for	for	ADP
fuelectenerg-400	896	15	the	the	DET
fuelectenerg-400	896	16	hard	hard	ADJ
fuelectenerg-400	896	17	-	-	PUNCT
fuelectenerg-400	896	18	square	square	NOUN
fuelectenerg-400	896	19	model	model	NOUN
fuelectenerg-400	896	20	,	,	PUNCT
fuelectenerg-400	896	21	”	"	PUNCT
fuelectenerg-400	896	22	ieee	ieee	NOUN
fuelectenerg-400	896	23	transactions	transaction	NOUN
fuelectenerg-400	896	24	on	on	ADP
fuelectenerg-400	896	25	information	information	NOUN
fuelectenerg-400	896	26	theory	theory	NOUN
fuelectenerg-400	896	27	,	,	PUNCT
fuelectenerg-400	896	28	vol	vol	NOUN
fuelectenerg-400	896	29	.	.	PROPN
fuelectenerg-400	896	30	51	51	NUM
fuelectenerg-400	896	31	,	,	PUNCT
fuelectenerg-400	896	32	no	no	INTJ
fuelectenerg-400	896	33	.	.	NOUN
fuelectenerg-400	896	34	8	8	NUM
fuelectenerg-400	896	35	,	,	PUNCT
fuelectenerg-400	896	36	p.	p.	NOUN
fuelectenerg-400	896	37	2836	2836	NUM
fuelectenerg-400	896	38	,	,	PUNCT
fuelectenerg-400	896	39	aug	aug	PROPN
fuelectenerg-400	896	40	2005	2005	NUM
fuelectenerg-400	896	41	.	.	PUNCT
fuelectenerg-400	897	1	540	540	NUM
fuelectenerg-400	897	2	b.	b.	PROPN
fuelectenerg-400	897	3	vasic	vasic	PROPN
fuelectenerg-400	897	4	,	,	PUNCT
fuelectenerg-400	897	5	a.	a.	PROPN
fuelectenerg-400	897	6	r.	r.	PROPN
fuelectenerg-400	897	7	krishnan	krishnan	PROPN
fuelectenerg-400	897	8	lozenge	lozenge	PROPN
fuelectenerg-400	897	9	tiling	tile	VERB
fuelectenerg-400	897	10	constrained	constrained	ADJ
fuelectenerg-400	897	11	codes	code	NOUN
fuelectenerg-400	897	12	541	541	NUM
fuelectenerg-400	897	13	540	540	NUM
fuelectenerg-400	897	14	a.	a.	NOUN
fuelectenerg-400	897	15	r.	r.	PROPN
fuelectenerg-400	897	16	krishnanan	krishnanan	PROPN
fuelectenerg-400	897	17	and	and	CCONJ
fuelectenerg-400	897	18	b.	b.	PROPN
fuelectenerg-400	897	19	vasić	vasić	PROPN
fuelectenerg-400	897	20	fig	fig	PROPN
fuelectenerg-400	897	21	.	.	PUNCT
fuelectenerg-400	898	1	11	11	NUM
fuelectenerg-400	898	2	.	.	PUNCT
fuelectenerg-400	899	1	the	the	DET
fuelectenerg-400	899	2	lozenge	lozenge	NOUN
fuelectenerg-400	899	3	tiling	tiling	NOUN
fuelectenerg-400	899	4	of	of	ADP
fuelectenerg-400	899	5	a	a	DET
fuelectenerg-400	899	6	(	(	PUNCT
fuelectenerg-400	899	7	4	4	NUM
fuelectenerg-400	899	8	,	,	PUNCT
fuelectenerg-400	899	9	4	4	NUM
fuelectenerg-400	899	10	,	,	PUNCT
fuelectenerg-400	899	11	4	4	X
fuelectenerg-400	899	12	)	)	PUNCT
fuelectenerg-400	899	13	hexagon	hexagon	NOUN
fuelectenerg-400	899	14	with	with	ADP
fuelectenerg-400	899	15	maximum	maximum	ADJ
fuelectenerg-400	899	16	number	number	NOUN
fuelectenerg-400	899	17	of	of	ADP
fuelectenerg-400	899	18	type-1	type-1	PROPN
fuelectenerg-400	899	19	hexagons	hexagon	NOUN
fuelectenerg-400	899	20	.	.	PUNCT
fuelectenerg-400	900	1	it	it	PRON
fuelectenerg-400	900	2	can	can	AUX
fuelectenerg-400	900	3	also	also	ADV
fuelectenerg-400	900	4	be	be	AUX
fuelectenerg-400	900	5	visualized	visualize	VERB
fuelectenerg-400	900	6	as	as	ADP
fuelectenerg-400	900	7	the	the	DET
fuelectenerg-400	900	8	young	young	ADJ
fuelectenerg-400	900	9	’s	’s	PART
fuelectenerg-400	900	10	solid	solid	ADJ
fuelectenerg-400	900	11	diagram	diagram	NOUN
fuelectenerg-400	900	12	of	of	ADP
fuelectenerg-400	900	13	a	a	DET
fuelectenerg-400	900	14	4×4×4	4×4×4	NUM
fuelectenerg-400	900	15	box	box	NOUN
fuelectenerg-400	900	16	with	with	ADP
fuelectenerg-400	900	17	the	the	DET
fuelectenerg-400	900	18	maximum	maximum	ADJ
fuelectenerg-400	900	19	number	number	NOUN
fuelectenerg-400	900	20	of	of	ADP
fuelectenerg-400	900	21	visible	visible	ADJ
fuelectenerg-400	900	22	boxes	box	NOUN
fuelectenerg-400	900	23	.	.	PUNCT
fuelectenerg-400	901	1	triangles	triangle	NOUN
fuelectenerg-400	901	2	is	be	AUX
fuelectenerg-400	901	3	calculated	calculate	VERB
fuelectenerg-400	901	4	as	as	ADP
fuelectenerg-400	901	5	6n2	6n2	NUM
fuelectenerg-400	901	6	.	.	PUNCT
fuelectenerg-400	902	1	hence	hence	ADV
fuelectenerg-400	902	2	,	,	PUNCT
fuelectenerg-400	902	3	the	the	DET
fuelectenerg-400	902	4	number	number	NOUN
fuelectenerg-400	902	5	of	of	ADP
fuelectenerg-400	902	6	lozenges	lozenge	NOUN
fuelectenerg-400	902	7	is	be	AUX
fuelectenerg-400	902	8	3n2	3n2	NUM
fuelectenerg-400	902	9	.	.	PUNCT
fuelectenerg-400	903	1	since	since	SCONJ
fuelectenerg-400	903	2	for	for	ADP
fuelectenerg-400	903	3	any	any	DET
fuelectenerg-400	903	4	lozenge	lozenge	NOUN
fuelectenerg-400	903	5	tiling	tiling	NOUN
fuelectenerg-400	903	6	of	of	ADP
fuelectenerg-400	903	7	h	h	NOUN
fuelectenerg-400	903	8	,	,	PUNCT
fuelectenerg-400	903	9	the	the	DET
fuelectenerg-400	903	10	number	number	NOUN
fuelectenerg-400	903	11	of	of	ADP
fuelectenerg-400	903	12	type-1	type-1	PROPN
fuelectenerg-400	903	13	hexagons	hexagon	NOUN
fuelectenerg-400	903	14	is	be	AUX
fuelectenerg-400	903	15	always	always	ADV
fuelectenerg-400	903	16	less	less	ADJ
fuelectenerg-400	903	17	than	than	ADP
fuelectenerg-400	903	18	or	or	CCONJ
fuelectenerg-400	903	19	equal	equal	ADJ
fuelectenerg-400	903	20	to	to	ADP
fuelectenerg-400	903	21	n(n	n(n	PROPN
fuelectenerg-400	903	22	+	+	CCONJ
fuelectenerg-400	903	23	1	1	NUM
fuelectenerg-400	903	24	)	)	PUNCT
fuelectenerg-400	903	25	,	,	PUNCT
fuelectenerg-400	903	26	we	we	PRON
fuelectenerg-400	903	27	have	have	VERB
fuelectenerg-400	903	28	a	a	DET
fuelectenerg-400	903	29	lower	low	ADJ
fuelectenerg-400	903	30	bound	bind	VERB
fuelectenerg-400	903	31	on	on	ADP
fuelectenerg-400	903	32	the	the	DET
fuelectenerg-400	903	33	capacity	capacity	NOUN
fuelectenerg-400	903	34	cc	cc	NOUN
fuelectenerg-400	903	35	as	as	SCONJ
fuelectenerg-400	903	36	follows	follow	VERB
fuelectenerg-400	903	37	:	:	PUNCT
fuelectenerg-400	903	38	cc	cc	NOUN
fuelectenerg-400	903	39	≥	≥	PROPN
fuelectenerg-400	903	40	lim	lim	PROPN
fuelectenerg-400	903	41	n→∞	n→∞	X
fuelectenerg-400	903	42	3n2	3n2	NUM
fuelectenerg-400	903	43	−	−	PROPN
fuelectenerg-400	903	44	n(n	n(n	NOUN
fuelectenerg-400	903	45	+	+	CCONJ
fuelectenerg-400	903	46	1	1	NUM
fuelectenerg-400	903	47	)	)	PUNCT
fuelectenerg-400	903	48	6n2	6n2	NUM
fuelectenerg-400	904	1	=	=	SYM
fuelectenerg-400	904	2	1	1	NUM
fuelectenerg-400	904	3	3	3	NUM
fuelectenerg-400	904	4	(	(	PUNCT
fuelectenerg-400	904	5	11	11	NUM
fuelectenerg-400	904	6	)	)	PUNCT
fuelectenerg-400	904	7	9	9	NUM
fuelectenerg-400	904	8	proof:[proof	proof:[proof	NOUN
fuelectenerg-400	904	9	of	of	ADP
fuelectenerg-400	904	10	theorem	theorem	NOUN
fuelectenerg-400	904	11	3	3	NUM
fuelectenerg-400	904	12	]	]	PUNCT
fuelectenerg-400	904	13	if	if	SCONJ
fuelectenerg-400	904	14	mountain(a	mountain(a	NOUN
fuelectenerg-400	904	15	)	)	PUNCT
fuelectenerg-400	904	16	⊂	⊂	PROPN
fuelectenerg-400	904	17	mountain(b	mountain(b	PROPN
fuelectenerg-400	904	18	)	)	PUNCT
fuelectenerg-400	904	19	,	,	PUNCT
fuelectenerg-400	904	20	then	then	ADV
fuelectenerg-400	904	21	ya(i	ya(i	VERB
fuelectenerg-400	904	22	)	)	PUNCT
fuelectenerg-400	904	23	≤	≤	NOUN
fuelectenerg-400	904	24	yb(i	yb(i	NUM
fuelectenerg-400	904	25	)	)	PUNCT
fuelectenerg-400	904	26	for	for	ADP
fuelectenerg-400	904	27	all	all	DET
fuelectenerg-400	904	28	i.	i.	NOUN
fuelectenerg-400	904	29	it	it	PRON
fuelectenerg-400	904	30	is	be	AUX
fuelectenerg-400	904	31	enough	enough	ADJ
fuelectenerg-400	904	32	to	to	PART
fuelectenerg-400	904	33	prove	prove	VERB
fuelectenerg-400	904	34	that	that	SCONJ
fuelectenerg-400	904	35	if	if	SCONJ
fuelectenerg-400	904	36	ya(i	ya(i	NOUN
fuelectenerg-400	904	37	)	)	PUNCT
fuelectenerg-400	904	38	≤	≤	NOUN
fuelectenerg-400	904	39	yb(i	yb(i	NOUN
fuelectenerg-400	905	1	)	)	PUNCT
fuelectenerg-400	905	2	∀	∀	X
fuelectenerg-400	906	1	i	i	NOUN
fuelectenerg-400	906	2	=	=	NOUN
fuelectenerg-400	906	3	1	1	NUM
fuelectenerg-400	906	4	,	,	PUNCT
fuelectenerg-400	906	5	2	2	NUM
fuelectenerg-400	906	6	,	,	PUNCT
fuelectenerg-400	906	7	.	.	PUNCT
fuelectenerg-400	906	8	.	.	PUNCT
fuelectenerg-400	907	1	.	.	PUNCT
fuelectenerg-400	908	1	,	,	PUNCT
fuelectenerg-400	908	2	n	n	CCONJ
fuelectenerg-400	908	3	,	,	PUNCT
fuelectenerg-400	908	4	then	then	ADV
fuelectenerg-400	908	5	a	a	DET
fuelectenerg-400	908	6	≤	≤	PROPN
fuelectenerg-400	908	7	b.	b.	NOUN
fuelectenerg-400	909	1	in	in	ADP
fuelectenerg-400	909	2	order	order	NOUN
fuelectenerg-400	909	3	to	to	PART
fuelectenerg-400	909	4	do	do	AUX
fuelectenerg-400	909	5	this	this	PRON
fuelectenerg-400	909	6	,	,	PUNCT
fuelectenerg-400	909	7	reconstruct	reconstruct	VERB
fuelectenerg-400	909	8	the	the	DET
fuelectenerg-400	909	9	sequences	sequence	NOUN
fuelectenerg-400	909	10	a	a	PRON
fuelectenerg-400	909	11	and	and	CCONJ
fuelectenerg-400	909	12	b	b	NOUN
fuelectenerg-400	909	13	from	from	ADP
fuelectenerg-400	909	14	ya	ya	PRON
fuelectenerg-400	909	15	and	and	CCONJ
fuelectenerg-400	909	16	yb	yb	PROPN
fuelectenerg-400	909	17	.	.	PUNCT
fuelectenerg-400	910	1	let	let	VERB
fuelectenerg-400	910	2	t	t	PROPN
fuelectenerg-400	910	3	,	,	PUNCT
fuelectenerg-400	910	4	1	1	NUM
fuelectenerg-400	910	5	≤	≤	NUM
fuelectenerg-400	910	6	t	t	NOUN
fuelectenerg-400	910	7	≤	≤	NOUN
fuelectenerg-400	910	8	n	n	CCONJ
fuelectenerg-400	910	9	such	such	ADJ
fuelectenerg-400	910	10	that	that	SCONJ
fuelectenerg-400	910	11	∀i	∀i	NOUN
fuelectenerg-400	910	12	<	<	X
fuelectenerg-400	910	13	t	t	PROPN
fuelectenerg-400	910	14	,	,	PUNCT
fuelectenerg-400	910	15	ya(i	ya(i	PUNCT
fuelectenerg-400	910	16	)	)	PUNCT
fuelectenerg-400	910	17	=	=	NOUN
fuelectenerg-400	910	18	yb(i	yb(i	NUM
fuelectenerg-400	910	19	)	)	PUNCT
fuelectenerg-400	910	20	and	and	CCONJ
fuelectenerg-400	910	21	ya(t	ya(t	X
fuelectenerg-400	910	22	)	)	PUNCT
fuelectenerg-400	910	23	�	�	PROPN
fuelectenerg-400	910	24	=	=	SYM
fuelectenerg-400	910	25	yb(t	yb(t	NOUN
fuelectenerg-400	910	26	)	)	PUNCT
fuelectenerg-400	910	27	.	.	PUNCT
fuelectenerg-400	911	1	this	this	PRON
fuelectenerg-400	911	2	means	mean	VERB
fuelectenerg-400	911	3	that	that	SCONJ
fuelectenerg-400	911	4	the	the	DET
fuelectenerg-400	911	5	ith	ith	ADJ
fuelectenerg-400	911	6	term	term	NOUN
fuelectenerg-400	911	7	of	of	ADP
fuelectenerg-400	911	8	a	a	PRON
fuelectenerg-400	911	9	is	be	AUX
fuelectenerg-400	911	10	0	0	NUM
fuelectenerg-400	911	11	and	and	CCONJ
fuelectenerg-400	911	12	that	that	PRON
fuelectenerg-400	911	13	of	of	ADP
fuelectenerg-400	911	14	b	b	PROPN
fuelectenerg-400	911	15	is	be	AUX
fuelectenerg-400	911	16	1	1	NUM
fuelectenerg-400	911	17	(	(	PUNCT
fuelectenerg-400	911	18	to	to	PART
fuelectenerg-400	911	19	satisfy	satisfy	VERB
fuelectenerg-400	911	20	the	the	DET
fuelectenerg-400	911	21	inequality	inequality	NOUN
fuelectenerg-400	911	22	in	in	ADP
fuelectenerg-400	911	23	the	the	DET
fuelectenerg-400	911	24	terms	term	NOUN
fuelectenerg-400	911	25	of	of	ADP
fuelectenerg-400	911	26	ya	ya	PRON
fuelectenerg-400	911	27	and	and	CCONJ
fuelectenerg-400	911	28	yb	yb	PROPN
fuelectenerg-400	911	29	)	)	PUNCT
fuelectenerg-400	911	30	.	.	PUNCT
fuelectenerg-400	912	1	hence	hence	ADV
fuelectenerg-400	912	2	,	,	PUNCT
fuelectenerg-400	912	3	de(a	de(a	NOUN
fuelectenerg-400	912	4	)	)	PUNCT
fuelectenerg-400	912	5	≤	≤	NOUN
fuelectenerg-400	912	6	de(b	de(b	PUNCT
fuelectenerg-400	912	7	)	)	PUNCT
fuelectenerg-400	912	8	(	(	PUNCT
fuelectenerg-400	912	9	inequality	inequality	NOUN
fuelectenerg-400	912	10	occurs	occur	VERB
fuelectenerg-400	912	11	if	if	SCONJ
fuelectenerg-400	912	12	they	they	PRON
fuelectenerg-400	912	13	differ	differ	VERB
fuelectenerg-400	912	14	in	in	ADP
fuelectenerg-400	912	15	one	one	NUM
fuelectenerg-400	912	16	or	or	CCONJ
fuelectenerg-400	912	17	more	more	ADJ
fuelectenerg-400	912	18	bits	bit	NOUN
fuelectenerg-400	912	19	and	and	CCONJ
fuelectenerg-400	912	20	equality	equality	NOUN
fuelectenerg-400	912	21	occurs	occur	VERB
fuelectenerg-400	912	22	if	if	SCONJ
fuelectenerg-400	912	23	they	they	PRON
fuelectenerg-400	912	24	do	do	AUX
fuelectenerg-400	912	25	not	not	PART
fuelectenerg-400	912	26	differ	differ	VERB
fuelectenerg-400	912	27	)	)	PUNCT
fuelectenerg-400	912	28	.	.	PUNCT
fuelectenerg-400	913	1	hence	hence	ADV
fuelectenerg-400	913	2	rank(a	rank(a	NOUN
fuelectenerg-400	913	3	)	)	PUNCT
fuelectenerg-400	913	4	≥	≥	PROPN
fuelectenerg-400	913	5	rank(b)/	rank(b)/	VERB
fuelectenerg-400	913	6	references	reference	NOUN
fuelectenerg-400	913	7	[	[	X
fuelectenerg-400	913	8	1	1	NUM
fuelectenerg-400	913	9	]	]	PUNCT
fuelectenerg-400	913	10	b.	b.	PROPN
fuelectenerg-400	913	11	h.	h.	PROPN
fuelectenerg-400	913	12	marcus	marcus	PROPN
fuelectenerg-400	913	13	,	,	PUNCT
fuelectenerg-400	913	14	p.	p.	PROPN
fuelectenerg-400	913	15	h.	h.	PROPN
fuelectenerg-400	913	16	siegel	siegel	PROPN
fuelectenerg-400	913	17	,	,	PUNCT
fuelectenerg-400	913	18	and	and	CCONJ
fuelectenerg-400	913	19	j.	j.	PROPN
fuelectenerg-400	913	20	k.	k.	PROPN
fuelectenerg-400	913	21	wolf	wolf	PROPN
fuelectenerg-400	913	22	,	,	PUNCT
fuelectenerg-400	913	23	“	"	PUNCT
fuelectenerg-400	913	24	finite	finite	ADJ
fuelectenerg-400	913	25	-	-	ADJ
fuelectenerg-400	913	26	state	state	ADJ
fuelectenerg-400	913	27	modulation	modulation	NOUN
fuelectenerg-400	913	28	codes	code	NOUN
fuelectenerg-400	913	29	for	for	ADP
fuelectenerg-400	913	30	data	datum	NOUN
fuelectenerg-400	913	31	storage	storage	NOUN
fuelectenerg-400	913	32	,	,	PUNCT
fuelectenerg-400	913	33	”	"	PUNCT
fuelectenerg-400	913	34	ieee	ieee	NOUN
fuelectenerg-400	913	35	journal	journal	NOUN
fuelectenerg-400	913	36	of	of	ADP
fuelectenerg-400	913	37	selected	select	VERB
fuelectenerg-400	913	38	areas	area	NOUN
fuelectenerg-400	913	39	in	in	ADP
fuelectenerg-400	913	40	communication	communication	NOUN
fuelectenerg-400	913	41	,	,	PUNCT
fuelectenerg-400	913	42	vol	vol	NOUN
fuelectenerg-400	913	43	.	.	PROPN
fuelectenerg-400	914	1	10	10	NUM
fuelectenerg-400	914	2	,	,	PUNCT
fuelectenerg-400	914	3	no	no	INTJ
fuelectenerg-400	914	4	.	.	NOUN
fuelectenerg-400	914	5	1	1	NUM
fuelectenerg-400	914	6	,	,	PUNCT
fuelectenerg-400	914	7	pp	pp	ADJ
fuelectenerg-400	914	8	.	.	PUNCT
fuelectenerg-400	915	1	5–37	5–37	NOUN
fuelectenerg-400	915	2	,	,	PUNCT
fuelectenerg-400	915	3	1992	1992	NUM
fuelectenerg-400	915	4	.	.	PUNCT
fuelectenerg-400	916	1	[	[	X
fuelectenerg-400	916	2	2	2	X
fuelectenerg-400	916	3	]	]	PUNCT
fuelectenerg-400	916	4	j.	j.	PROPN
fuelectenerg-400	916	5	j.	j.	PROPN
fuelectenerg-400	916	6	ashley	ashley	PROPN
fuelectenerg-400	916	7	and	and	CCONJ
fuelectenerg-400	916	8	b.	b.	PROPN
fuelectenerg-400	916	9	h.	h.	PROPN
fuelectenerg-400	916	10	marcus	marcus	PROPN
fuelectenerg-400	916	11	,	,	PUNCT
fuelectenerg-400	916	12	“	"	PUNCT
fuelectenerg-400	916	13	two	two	NUM
fuelectenerg-400	916	14	-	-	PUNCT
fuelectenerg-400	916	15	dimensional	dimensional	ADJ
fuelectenerg-400	916	16	low	low	ADJ
fuelectenerg-400	916	17	-	-	PUNCT
fuelectenerg-400	916	18	pass	pass	NOUN
fuelectenerg-400	916	19	filtering	filter	VERB
fuelectenerg-400	916	20	codes	code	NOUN
fuelectenerg-400	916	21	,	,	PUNCT
fuelectenerg-400	916	22	”	"	PUNCT
fuelectenerg-400	916	23	ieee	ieee	NOUN
fuelectenerg-400	916	24	transactions	transaction	NOUN
fuelectenerg-400	916	25	on	on	ADP
fuelectenerg-400	916	26	communications	communication	NOUN
fuelectenerg-400	916	27	,	,	PUNCT
fuelectenerg-400	916	28	vol	vol	NOUN
fuelectenerg-400	916	29	.	.	PROPN
fuelectenerg-400	916	30	46	46	NUM
fuelectenerg-400	916	31	,	,	PUNCT
fuelectenerg-400	916	32	pp	pp	ADJ
fuelectenerg-400	916	33	.	.	PUNCT
fuelectenerg-400	917	1	724–727	724–727	NUM
fuelectenerg-400	917	2	,	,	PUNCT
fuelectenerg-400	917	3	jun	jun	PROPN
fuelectenerg-400	917	4	1998	1998	NUM
fuelectenerg-400	917	5	.	.	PUNCT
fuelectenerg-400	918	1	[	[	X
fuelectenerg-400	918	2	3	3	X
fuelectenerg-400	918	3	]	]	PUNCT
fuelectenerg-400	918	4	z.	z.	PROPN
fuelectenerg-400	918	5	nagy	nagy	PROPN
fuelectenerg-400	918	6	and	and	CCONJ
fuelectenerg-400	918	7	k.	k.	PROPN
fuelectenerg-400	918	8	zeger	zeger	PROPN
fuelectenerg-400	918	9	,	,	PUNCT
fuelectenerg-400	918	10	“	"	PUNCT
fuelectenerg-400	918	11	capacity	capacity	NOUN
fuelectenerg-400	918	12	bounds	bound	VERB
fuelectenerg-400	918	13	for	for	ADP
fuelectenerg-400	918	14	the	the	DET
fuelectenerg-400	918	15	hard	hard	ADJ
fuelectenerg-400	918	16	-	-	PUNCT
fuelectenerg-400	918	17	triangle	triangle	NOUN
fuelectenerg-400	918	18	model	model	NOUN
fuelectenerg-400	918	19	,	,	PUNCT
fuelectenerg-400	918	20	”	"	PUNCT
fuelectenerg-400	918	21	proceedings	proceeding	NOUN
fuelectenerg-400	918	22	of	of	ADP
fuelectenerg-400	918	23	international	international	ADJ
fuelectenerg-400	918	24	symposium	symposium	NOUN
fuelectenerg-400	918	25	on	on	ADP
fuelectenerg-400	918	26	information	information	NOUN
fuelectenerg-400	918	27	theory	theory	NOUN
fuelectenerg-400	918	28	2004	2004	NUM
fuelectenerg-400	918	29	,	,	PUNCT
fuelectenerg-400	918	30	p.	p.	NOUN
fuelectenerg-400	918	31	162	162	NUM
fuelectenerg-400	918	32	,	,	PUNCT
fuelectenerg-400	918	33	2004	2004	NUM
fuelectenerg-400	918	34	.	.	PUNCT
fuelectenerg-400	919	1	[	[	X
fuelectenerg-400	919	2	4	4	NUM
fuelectenerg-400	919	3	]	]	X
fuelectenerg-400	919	4	i.	i.	NOUN
fuelectenerg-400	919	5	demirkan	demirkan	PROPN
fuelectenerg-400	919	6	and	and	CCONJ
fuelectenerg-400	919	7	j.	j.	PROPN
fuelectenerg-400	919	8	k.	k.	PROPN
fuelectenerg-400	919	9	wolf	wolf	PROPN
fuelectenerg-400	919	10	,	,	PUNCT
fuelectenerg-400	919	11	“	"	PUNCT
fuelectenerg-400	919	12	block	block	NOUN
fuelectenerg-400	919	13	codes	code	NOUN
fuelectenerg-400	919	14	for	for	ADP
fuelectenerg-400	919	15	the	the	DET
fuelectenerg-400	919	16	hard	hard	ADJ
fuelectenerg-400	919	17	-	-	PUNCT
fuelectenerg-400	919	18	square	square	NOUN
fuelectenerg-400	919	19	model	model	NOUN
fuelectenerg-400	919	20	,	,	PUNCT
fuelectenerg-400	919	21	”	"	PUNCT
fuelectenerg-400	919	22	ieee	ieee	NOUN
fuelectenerg-400	919	23	transactions	transaction	NOUN
fuelectenerg-400	919	24	on	on	ADP
fuelectenerg-400	919	25	information	information	NOUN
fuelectenerg-400	919	26	theory	theory	NOUN
fuelectenerg-400	919	27	,	,	PUNCT
fuelectenerg-400	919	28	vol	vol	NOUN
fuelectenerg-400	919	29	.	.	PROPN
fuelectenerg-400	919	30	51	51	NUM
fuelectenerg-400	919	31	,	,	PUNCT
fuelectenerg-400	919	32	no	no	INTJ
fuelectenerg-400	919	33	.	.	NOUN
fuelectenerg-400	919	34	8	8	NUM
fuelectenerg-400	919	35	,	,	PUNCT
fuelectenerg-400	919	36	p.	p.	NOUN
fuelectenerg-400	919	37	2836	2836	NUM
fuelectenerg-400	919	38	,	,	PUNCT
fuelectenerg-400	919	39	aug	aug	PROPN
fuelectenerg-400	919	40	2005	2005	NUM
fuelectenerg-400	919	41	.	.	PUNCT
fuelectenerg-400	920	1	detection	detection	NOUN
fuelectenerg-400	920	2	and	and	CCONJ
fuelectenerg-400	920	3	coding	code	VERB
fuelectenerg-400	920	4	for	for	ADP
fuelectenerg-400	920	5	tdmr	tdmr	NOUN
fuelectenerg-400	920	6	channel	channel	NOUN
fuelectenerg-400	920	7	541	541	NUM
fuelectenerg-400	920	8	[	[	X
fuelectenerg-400	920	9	5	5	NUM
fuelectenerg-400	920	10	]	]	PUNCT
fuelectenerg-400	920	11	a.	a.	NOUN
fuelectenerg-400	920	12	kato	kato	PROPN
fuelectenerg-400	920	13	and	and	CCONJ
fuelectenerg-400	920	14	k.	k.	PROPN
fuelectenerg-400	920	15	zeger	zeger	PROPN
fuelectenerg-400	920	16	,	,	PUNCT
fuelectenerg-400	920	17	“	"	PUNCT
fuelectenerg-400	920	18	partial	partial	ADJ
fuelectenerg-400	920	19	characterization	characterization	NOUN
fuelectenerg-400	920	20	of	of	ADP
fuelectenerg-400	920	21	the	the	DET
fuelectenerg-400	920	22	positive	positive	ADJ
fuelectenerg-400	920	23	capacity	capacity	NOUN
fuelectenerg-400	920	24	region	region	NOUN
fuelectenerg-400	920	25	of	of	ADP
fuelectenerg-400	920	26	the	the	DET
fuelectenerg-400	920	27	two	two	NUM
fuelectenerg-400	920	28	-	-	PUNCT
fuelectenerg-400	920	29	dimensional	dimensional	ADJ
fuelectenerg-400	920	30	asymmetric	asymmetric	ADJ
fuelectenerg-400	920	31	run	run	NOUN
fuelectenerg-400	920	32	length	length	NOUN
fuelectenerg-400	920	33	constrained	constrain	VERB
fuelectenerg-400	920	34	channels	channel	NOUN
fuelectenerg-400	920	35	,	,	PUNCT
fuelectenerg-400	920	36	”	"	PUNCT
fuelectenerg-400	920	37	ieee	ieee	NOUN
fuelectenerg-400	920	38	transactions	transaction	NOUN
fuelectenerg-400	920	39	on	on	ADP
fuelectenerg-400	920	40	information	information	NOUN
fuelectenerg-400	920	41	theory	theory	NOUN
fuelectenerg-400	920	42	,	,	PUNCT
fuelectenerg-400	920	43	vol	vol	NOUN
fuelectenerg-400	920	44	.	.	PROPN
fuelectenerg-400	920	45	46	46	NUM
fuelectenerg-400	920	46	,	,	PUNCT
fuelectenerg-400	920	47	no	no	INTJ
fuelectenerg-400	920	48	.	.	NOUN
fuelectenerg-400	920	49	7	7	NUM
fuelectenerg-400	920	50	,	,	PUNCT
fuelectenerg-400	920	51	p.	p.	NOUN
fuelectenerg-400	920	52	2666	2666	NUM
fuelectenerg-400	920	53	,	,	PUNCT
fuelectenerg-400	920	54	nov	nov	PROPN
fuelectenerg-400	920	55	2000	2000	NUM
fuelectenerg-400	920	56	.	.	PUNCT
fuelectenerg-400	921	1	[	[	X
fuelectenerg-400	921	2	6	6	NUM
fuelectenerg-400	921	3	]	]	PUNCT
fuelectenerg-400	921	4	—	—	PUNCT
fuelectenerg-400	921	5	—	—	PUNCT
fuelectenerg-400	921	6	,	,	PUNCT
fuelectenerg-400	921	7	“	"	PUNCT
fuelectenerg-400	921	8	on	on	ADP
fuelectenerg-400	921	9	the	the	DET
fuelectenerg-400	921	10	capacity	capacity	NOUN
fuelectenerg-400	921	11	of	of	ADP
fuelectenerg-400	921	12	two	two	NUM
fuelectenerg-400	921	13	-	-	PUNCT
fuelectenerg-400	921	14	dimensional	dimensional	ADJ
fuelectenerg-400	921	15	run	run	NOUN
fuelectenerg-400	921	16	-	-	PUNCT
fuelectenerg-400	921	17	length	length	NOUN
fuelectenerg-400	921	18	constrained	constrain	VERB
fuelectenerg-400	921	19	channels	channel	NOUN
fuelectenerg-400	921	20	,	,	PUNCT
fuelectenerg-400	921	21	”	"	PUNCT
fuelectenerg-400	921	22	ieee	ieee	NOUN
fuelectenerg-400	921	23	transactions	transaction	NOUN
fuelectenerg-400	921	24	on	on	ADP
fuelectenerg-400	921	25	information	information	NOUN
fuelectenerg-400	921	26	theory	theory	NOUN
fuelectenerg-400	921	27	,	,	PUNCT
fuelectenerg-400	921	28	vol	vol	NOUN
fuelectenerg-400	921	29	.	.	PROPN
fuelectenerg-400	922	1	45	45	NUM
fuelectenerg-400	922	2	,	,	PUNCT
fuelectenerg-400	922	3	no	no	INTJ
fuelectenerg-400	922	4	.	.	NOUN
fuelectenerg-400	922	5	5	5	NUM
fuelectenerg-400	922	6	,	,	PUNCT
fuelectenerg-400	922	7	p.	p.	NOUN
fuelectenerg-400	922	8	1527	1527	NUM
fuelectenerg-400	922	9	,	,	PUNCT
fuelectenerg-400	922	10	july	july	PROPN
fuelectenerg-400	922	11	1999	1999	NUM
fuelectenerg-400	922	12	.	.	PUNCT
fuelectenerg-400	923	1	[	[	X
fuelectenerg-400	923	2	7	7	X
fuelectenerg-400	923	3	]	]	PUNCT
fuelectenerg-400	923	4	z.	z.	PROPN
fuelectenerg-400	923	5	nagy	nagy	PROPN
fuelectenerg-400	923	6	and	and	CCONJ
fuelectenerg-400	923	7	k.	k.	PROPN
fuelectenerg-400	923	8	zeger	zeger	PROPN
fuelectenerg-400	923	9	,	,	PUNCT
fuelectenerg-400	923	10	“	"	PUNCT
fuelectenerg-400	923	11	bit	bit	ADV
fuelectenerg-400	923	12	-	-	PUNCT
fuelectenerg-400	923	13	stuffing	stuff	VERB
fuelectenerg-400	923	14	algorithms	algorithm	NOUN
fuelectenerg-400	923	15	and	and	CCONJ
fuelectenerg-400	923	16	analysis	analysis	NOUN
fuelectenerg-400	923	17	for	for	ADP
fuelectenerg-400	923	18	run	run	NOUN
fuelectenerg-400	923	19	-	-	PUNCT
fuelectenerg-400	923	20	length	length	NOUN
fuelectenerg-400	923	21	constrained	constrain	VERB
fuelectenerg-400	923	22	channels	channel	NOUN
fuelectenerg-400	923	23	in	in	ADP
fuelectenerg-400	923	24	two	two	NUM
fuelectenerg-400	923	25	and	and	CCONJ
fuelectenerg-400	923	26	three	three	NUM
fuelectenerg-400	923	27	dimensions	dimension	NOUN
fuelectenerg-400	923	28	,	,	PUNCT
fuelectenerg-400	923	29	”	"	PUNCT
fuelectenerg-400	923	30	ieee	ieee	NOUN
fuelectenerg-400	923	31	transactions	transaction	NOUN
fuelectenerg-400	923	32	on	on	ADP
fuelectenerg-400	923	33	information	information	NOUN
fuelectenerg-400	923	34	theory	theory	NOUN
fuelectenerg-400	923	35	,	,	PUNCT
fuelectenerg-400	923	36	vol	vol	NOUN
fuelectenerg-400	923	37	.	.	PROPN
fuelectenerg-400	923	38	50	50	NUM
fuelectenerg-400	923	39	,	,	PUNCT
fuelectenerg-400	923	40	no	no	INTJ
fuelectenerg-400	923	41	.	.	NOUN
fuelectenerg-400	923	42	12	12	NUM
fuelectenerg-400	923	43	,	,	PUNCT
fuelectenerg-400	923	44	p.	p.	NOUN
fuelectenerg-400	923	45	3146	3146	NUM
fuelectenerg-400	923	46	,	,	PUNCT
fuelectenerg-400	923	47	dec	dec	PROPN
fuelectenerg-400	923	48	.	.	PROPN
fuelectenerg-400	923	49	2004	2004	NUM
fuelectenerg-400	923	50	.	.	PUNCT
fuelectenerg-400	924	1	[	[	X
fuelectenerg-400	924	2	8	8	NUM
fuelectenerg-400	924	3	]	]	PUNCT
fuelectenerg-400	924	4	p.	p.	NOUN
fuelectenerg-400	924	5	siegel	siegel	PROPN
fuelectenerg-400	924	6	and	and	CCONJ
fuelectenerg-400	924	7	j.	j.	PROPN
fuelectenerg-400	924	8	wolf	wolf	PROPN
fuelectenerg-400	924	9	,	,	PUNCT
fuelectenerg-400	924	10	“	"	PUNCT
fuelectenerg-400	924	11	bit	bit	ADV
fuelectenerg-400	924	12	-	-	PUNCT
fuelectenerg-400	924	13	stuffing	stuff	VERB
fuelectenerg-400	924	14	bounds	bound	NOUN
fuelectenerg-400	924	15	on	on	ADP
fuelectenerg-400	924	16	the	the	DET
fuelectenerg-400	924	17	capacity	capacity	NOUN
fuelectenerg-400	924	18	of	of	ADP
fuelectenerg-400	924	19	2	2	NUM
fuelectenerg-400	924	20	-	-	PUNCT
fuelectenerg-400	924	21	dimensional	dimensional	ADJ
fuelectenerg-400	924	22	constrained	constrain	VERB
fuelectenerg-400	924	23	arrays	array	NOUN
fuelectenerg-400	924	24	,	,	PUNCT
fuelectenerg-400	924	25	”	"	PUNCT
fuelectenerg-400	924	26	in	in	ADP
fuelectenerg-400	924	27	international	international	ADJ
fuelectenerg-400	924	28	symposium	symposium	NOUN
fuelectenerg-400	924	29	on	on	ADP
fuelectenerg-400	924	30	information	information	NOUN
fuelectenerg-400	924	31	theory	theory	NOUN
fuelectenerg-400	924	32	,	,	PUNCT
fuelectenerg-400	924	33	august	august	PROPN
fuelectenerg-400	924	34	16	16	NUM
fuelectenerg-400	924	35	august	august	PROPN
fuelectenerg-400	924	36	21	21	NUM
fuelectenerg-400	924	37	1998	1998	NUM
fuelectenerg-400	924	38	,	,	PUNCT
fuelectenerg-400	924	39	p.	p.	NOUN
fuelectenerg-400	924	40	323	323	NUM
fuelectenerg-400	924	41	.	.	PUNCT
fuelectenerg-400	925	1	[	[	X
fuelectenerg-400	925	2	9	9	NUM
fuelectenerg-400	925	3	]	]	PUNCT
fuelectenerg-400	925	4	z.	z.	PROPN
fuelectenerg-400	925	5	nagy	nagy	PROPN
fuelectenerg-400	925	6	and	and	CCONJ
fuelectenerg-400	925	7	k.	k.	PROPN
fuelectenerg-400	925	8	zeger	zeger	PROPN
fuelectenerg-400	925	9	,	,	PUNCT
fuelectenerg-400	925	10	“	"	PUNCT
fuelectenerg-400	925	11	asymptotic	asymptotic	ADJ
fuelectenerg-400	925	12	capacity	capacity	NOUN
fuelectenerg-400	925	13	of	of	ADP
fuelectenerg-400	925	14	two	two	NUM
fuelectenerg-400	925	15	-	-	PUNCT
fuelectenerg-400	925	16	dimensional	dimensional	ADJ
fuelectenerg-400	925	17	channels	channel	NOUN
fuelectenerg-400	925	18	with	with	ADP
fuelectenerg-400	925	19	checkerboard	checkerboard	NOUN
fuelectenerg-400	925	20	constraints	constraint	NOUN
fuelectenerg-400	925	21	,	,	PUNCT
fuelectenerg-400	925	22	”	"	PUNCT
fuelectenerg-400	925	23	ieee	ieee	NOUN
fuelectenerg-400	925	24	transactions	transaction	NOUN
fuelectenerg-400	925	25	on	on	ADP
fuelectenerg-400	925	26	information	information	NOUN
fuelectenerg-400	925	27	theory	theory	NOUN
fuelectenerg-400	925	28	,	,	PUNCT
fuelectenerg-400	925	29	vol	vol	NOUN
fuelectenerg-400	925	30	.	.	PROPN
fuelectenerg-400	925	31	49	49	NUM
fuelectenerg-400	925	32	,	,	PUNCT
fuelectenerg-400	925	33	no	no	INTJ
fuelectenerg-400	925	34	.	.	NOUN
fuelectenerg-400	925	35	9	9	NUM
fuelectenerg-400	925	36	,	,	PUNCT
fuelectenerg-400	925	37	p.	p.	NOUN
fuelectenerg-400	925	38	2115	2115	NUM
fuelectenerg-400	925	39	,	,	PUNCT
fuelectenerg-400	925	40	2003	2003	NUM
fuelectenerg-400	925	41	.	.	PUNCT
fuelectenerg-400	926	1	[	[	X
fuelectenerg-400	926	2	10	10	NUM
fuelectenerg-400	926	3	]	]	PUNCT
fuelectenerg-400	926	4	t.	t.	NOUN
fuelectenerg-400	926	5	etzion	etzion	PROPN
fuelectenerg-400	926	6	and	and	CCONJ
fuelectenerg-400	926	7	k.	k.	PROPN
fuelectenerg-400	926	8	g.	g.	PROPN
fuelectenerg-400	926	9	paterson	paterson	PROPN
fuelectenerg-400	926	10	,	,	PUNCT
fuelectenerg-400	926	11	“	"	PUNCT
fuelectenerg-400	926	12	zero	zero	NUM
fuelectenerg-400	926	13	/	/	SYM
fuelectenerg-400	926	14	positive	positive	ADJ
fuelectenerg-400	926	15	capacities	capacity	NOUN
fuelectenerg-400	926	16	of	of	ADP
fuelectenerg-400	926	17	two	two	NUM
fuelectenerg-400	926	18	-	-	PUNCT
fuelectenerg-400	926	19	dimensional	dimensional	ADJ
fuelectenerg-400	926	20	runlength	runlength	NOUN
fuelectenerg-400	926	21	constrained	constrain	VERB
fuelectenerg-400	926	22	arrays	array	NOUN
fuelectenerg-400	926	23	,	,	PUNCT
fuelectenerg-400	926	24	”	"	PUNCT
fuelectenerg-400	926	25	in	in	ADP
fuelectenerg-400	926	26	in	in	ADP
fuelectenerg-400	926	27	proc	proc	NOUN
fuelectenerg-400	926	28	.	.	PUNCT
fuelectenerg-400	927	1	2001	2001	NUM
fuelectenerg-400	927	2	ieee	ieee	PROPN
fuelectenerg-400	927	3	intl	intl	PROPN
fuelectenerg-400	927	4	.	.	PUNCT
fuelectenerg-400	928	1	symp	symp	PROPN
fuelectenerg-400	928	2	.	.	PUNCT
fuelectenerg-400	929	1	on	on	ADP
fuelectenerg-400	929	2	inform	inform	NOUN
fuelectenerg-400	929	3	.	.	PUNCT
fuelectenerg-400	930	1	theory	theory	NOUN
fuelectenerg-400	930	2	,	,	PUNCT
fuelectenerg-400	930	3	2004	2004	NUM
fuelectenerg-400	930	4	,	,	PUNCT
fuelectenerg-400	930	5	p.	p.	NOUN
fuelectenerg-400	930	6	269	269	NUM
fuelectenerg-400	930	7	.	.	PUNCT
fuelectenerg-400	931	1	[	[	X
fuelectenerg-400	931	2	11	11	NUM
fuelectenerg-400	931	3	]	]	PUNCT
fuelectenerg-400	931	4	s.	s.	PROPN
fuelectenerg-400	931	5	khatami	khatami	PROPN
fuelectenerg-400	931	6	and	and	CCONJ
fuelectenerg-400	931	7	b.	b.	PROPN
fuelectenerg-400	931	8	vasic	vasic	PROPN
fuelectenerg-400	931	9	,	,	PUNCT
fuelectenerg-400	931	10	“	"	PUNCT
fuelectenerg-400	931	11	generalized	generalized	ADJ
fuelectenerg-400	931	12	belief	belief	NOUN
fuelectenerg-400	931	13	propagation	propagation	NOUN
fuelectenerg-400	931	14	detector	detector	NOUN
fuelectenerg-400	931	15	for	for	ADP
fuelectenerg-400	931	16	tdmr	tdmr	NOUN
fuelectenerg-400	931	17	microcell	microcell	NOUN
fuelectenerg-400	931	18	model	model	NOUN
fuelectenerg-400	931	19	,	,	PUNCT
fuelectenerg-400	931	20	”	"	PUNCT
fuelectenerg-400	931	21	ieee	ieee	NOUN
fuelectenerg-400	931	22	transactions	transaction	NOUN
fuelectenerg-400	931	23	on	on	ADP
fuelectenerg-400	931	24	magnetics	magnetic	NOUN
fuelectenerg-400	931	25	,	,	PUNCT
fuelectenerg-400	931	26	vol	vol	NOUN
fuelectenerg-400	931	27	.	.	PROPN
fuelectenerg-400	931	28	45	45	NUM
fuelectenerg-400	931	29	,	,	PUNCT
fuelectenerg-400	931	30	no	no	INTJ
fuelectenerg-400	931	31	.	.	NOUN
fuelectenerg-400	931	32	10	10	NUM
fuelectenerg-400	931	33	,	,	PUNCT
fuelectenerg-400	931	34	p.	p.	NOUN
fuelectenerg-400	931	35	submitted	submit	VERB
fuelectenerg-400	931	36	,	,	PUNCT
fuelectenerg-400	931	37	october	october	PROPN
fuelectenerg-400	931	38	2012	2012	NUM
fuelectenerg-400	931	39	.	.	PUNCT
fuelectenerg-400	932	1	[	[	X
fuelectenerg-400	932	2	12	12	NUM
fuelectenerg-400	932	3	]	]	PUNCT
fuelectenerg-400	932	4	a.	a.	NOUN
fuelectenerg-400	932	5	krishnan	krishnan	PROPN
fuelectenerg-400	932	6	,	,	PUNCT
fuelectenerg-400	932	7	r.	r.	PROPN
fuelectenerg-400	932	8	radhakrishnan	radhakrishnan	PROPN
fuelectenerg-400	932	9	,	,	PUNCT
fuelectenerg-400	932	10	b.	b.	PROPN
fuelectenerg-400	932	11	vasic	vasic	PROPN
fuelectenerg-400	932	12	,	,	PUNCT
fuelectenerg-400	932	13	a.	a.	PROPN
fuelectenerg-400	932	14	kavcic	kavcic	PROPN
fuelectenerg-400	932	15	,	,	PUNCT
fuelectenerg-400	932	16	w.	w.	PROPN
fuelectenerg-400	932	17	ryan	ryan	PROPN
fuelectenerg-400	932	18	,	,	PUNCT
fuelectenerg-400	932	19	and	and	CCONJ
fuelectenerg-400	932	20	f.	f.	PROPN
fuelectenerg-400	932	21	erden	erden	PROPN
fuelectenerg-400	932	22	,	,	PUNCT
fuelectenerg-400	932	23	“	"	PUNCT
fuelectenerg-400	932	24	2	2	NUM
fuelectenerg-400	932	25	-	-	PUNCT
fuelectenerg-400	932	26	d	d	NOUN
fuelectenerg-400	932	27	magnetic	magnetic	ADJ
fuelectenerg-400	932	28	recording	recording	NOUN
fuelectenerg-400	932	29	:	:	PUNCT
fuelectenerg-400	932	30	read	read	VERB
fuelectenerg-400	932	31	channel	channel	NOUN
fuelectenerg-400	932	32	modeling	modeling	NOUN
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fuelectenerg-400	932	34	detection	detection	NOUN
fuelectenerg-400	932	35	,	,	PUNCT
fuelectenerg-400	932	36	”	"	PUNCT
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fuelectenerg-400	932	38	trans	tran	NOUN
fuelectenerg-400	932	39	.	.	PUNCT
fuelectenerg-400	933	1	on	on	ADP
fuelectenerg-400	933	2	magn	magn	PROPN
fuelectenerg-400	933	3	.	.	PROPN
fuelectenerg-400	933	4	,	,	PUNCT
fuelectenerg-400	933	5	vol	vol	NOUN
fuelectenerg-400	933	6	.	.	PROPN
fuelectenerg-400	934	1	45	45	NUM
fuelectenerg-400	934	2	,	,	PUNCT
fuelectenerg-400	934	3	no	no	INTJ
fuelectenerg-400	934	4	.	.	NOUN
fuelectenerg-400	934	5	10	10	NUM
fuelectenerg-400	934	6	,	,	PUNCT
fuelectenerg-400	934	7	pp	pp	ADJ
fuelectenerg-400	934	8	.	.	PUNCT
fuelectenerg-400	935	1	3830	3830	NUM
fuelectenerg-400	935	2	–	–	PUNCT
fuelectenerg-400	935	3	3836	3836	NUM
fuelectenerg-400	935	4	,	,	PUNCT
fuelectenerg-400	935	5	oct	oct	PROPN
fuelectenerg-400	935	6	.	.	PROPN
fuelectenerg-400	935	7	2009	2009	NUM
fuelectenerg-400	935	8	.	.	PUNCT
fuelectenerg-400	936	1	[	[	X
fuelectenerg-400	936	2	13	13	NUM
fuelectenerg-400	936	3	]	]	PUNCT
fuelectenerg-400	936	4	l.	l.	PROPN
fuelectenerg-400	936	5	pan	pan	PROPN
fuelectenerg-400	936	6	,	,	PUNCT
fuelectenerg-400	936	7	w.	w.	PROPN
fuelectenerg-400	936	8	e.	e.	PROPN
fuelectenerg-400	936	9	ryan	ryan	PROPN
fuelectenerg-400	936	10	,	,	PUNCT
fuelectenerg-400	936	11	r.	r.	PROPN
fuelectenerg-400	936	12	wood	wood	PROPN
fuelectenerg-400	936	13	,	,	PUNCT
fuelectenerg-400	936	14	and	and	CCONJ
fuelectenerg-400	936	15	b.	b.	PROPN
fuelectenerg-400	936	16	vasic	vasic	PROPN
fuelectenerg-400	936	17	,	,	PUNCT
fuelectenerg-400	936	18	“	"	PUNCT
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fuelectenerg-400	936	28	,	,	PUNCT
fuelectenerg-400	936	29	”	"	PUNCT
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fuelectenerg-400	936	31	trans	trans	PROPN
fuelectenerg-400	936	32	.	.	PUNCT
fuelectenerg-400	937	1	magn	magn	PROPN
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fuelectenerg-400	937	3	,	,	PUNCT
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fuelectenerg-400	937	5	.	.	PROPN
fuelectenerg-400	938	1	47	47	NUM
fuelectenerg-400	938	2	,	,	PUNCT
fuelectenerg-400	938	3	no	no	INTJ
fuelectenerg-400	938	4	.	.	NOUN
fuelectenerg-400	938	5	6	6	NUM
fuelectenerg-400	938	6	,	,	PUNCT
fuelectenerg-400	938	7	pp	pp	ADJ
fuelectenerg-400	938	8	.	.	PUNCT
fuelectenerg-400	939	1	1705–1711	1705–1711	NUM
fuelectenerg-400	939	2	,	,	PUNCT
fuelectenerg-400	939	3	jun	jun	PROPN
fuelectenerg-400	939	4	.	.	PROPN
fuelectenerg-400	939	5	2011	2011	NUM
fuelectenerg-400	939	6	.	.	PUNCT
fuelectenerg-400	940	1	[	[	X
fuelectenerg-400	940	2	14	14	NUM
fuelectenerg-400	940	3	]	]	PUNCT
fuelectenerg-400	940	4	r.	r.	PROPN
fuelectenerg-400	940	5	j.	j.	PROPN
fuelectenerg-400	940	6	baxter	baxter	PROPN
fuelectenerg-400	940	7	,	,	PUNCT
fuelectenerg-400	940	8	“	"	PUNCT
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fuelectenerg-400	940	14	,	,	PUNCT
fuelectenerg-400	940	15	”	"	PUNCT
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fuelectenerg-400	940	17	of	of	ADP
fuelectenerg-400	940	18	physics	physics	PROPN
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fuelectenerg-400	940	20	:	:	PUNCT
fuelectenerg-400	940	21	mathematical	mathematical	ADJ
fuelectenerg-400	940	22	and	and	CCONJ
fuelectenerg-400	940	23	general	general	ADJ
fuelectenerg-400	940	24	,	,	PUNCT
fuelectenerg-400	940	25	vol	vol	NOUN
fuelectenerg-400	940	26	.	.	PROPN
fuelectenerg-400	940	27	13	13	NUM
fuelectenerg-400	940	28	,	,	PUNCT
fuelectenerg-400	940	29	no	no	INTJ
fuelectenerg-400	940	30	.	.	NOUN
fuelectenerg-400	940	31	3	3	NUM
fuelectenerg-400	940	32	,	,	PUNCT
fuelectenerg-400	940	33	p.	p.	NOUN
fuelectenerg-400	940	34	l61	l61	PROPN
fuelectenerg-400	940	35	,	,	PUNCT
fuelectenerg-400	940	36	1980	1980	NUM
fuelectenerg-400	940	37	.	.	PUNCT
fuelectenerg-400	941	1	[	[	X
fuelectenerg-400	941	2	online	online	X
fuelectenerg-400	941	3	]	]	X
fuelectenerg-400	941	4	.	.	PUNCT
fuelectenerg-400	942	1	available	available	ADJ
fuelectenerg-400	942	2	:	:	PUNCT
fuelectenerg-400	942	3	http://stacks.iop.org/0305-4470/13/i=3/a=007	http://stacks.iop.org/0305-4470/13/i=3/a=007	ADJ
fuelectenerg-400	942	4	[	[	X
fuelectenerg-400	942	5	15	15	NUM
fuelectenerg-400	942	6	]	]	X
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fuelectenerg-400	942	9	,	,	PUNCT
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fuelectenerg-400	942	11	radhakrishnan	radhakrishnan	PROPN
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fuelectenerg-400	942	13	and	and	CCONJ
fuelectenerg-400	942	14	b.	b.	PROPN
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fuelectenerg-400	942	16	,	,	PUNCT
fuelectenerg-400	942	17	“	"	PUNCT
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fuelectenerg-400	942	21	for	for	ADP
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fuelectenerg-400	942	23	in	in	ADP
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fuelectenerg-400	942	29	systems	system	NOUN
fuelectenerg-400	942	30	,	,	PUNCT
fuelectenerg-400	942	31	”	"	PUNCT
fuelectenerg-400	942	32	ieee	ieee	NOUN
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fuelectenerg-400	942	34	on	on	ADP
fuelectenerg-400	942	35	magnetics	magnetic	NOUN
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fuelectenerg-400	942	38	.	.	PROPN
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fuelectenerg-400	943	2	,	,	PUNCT
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fuelectenerg-400	943	4	.	.	NOUN
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fuelectenerg-400	943	7	pp	pp	ADJ
fuelectenerg-400	943	8	.	.	PUNCT
fuelectenerg-400	944	1	3679–3682	3679–3682	NUM
fuelectenerg-400	944	2	,	,	PUNCT
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fuelectenerg-400	944	5	.	.	PUNCT
fuelectenerg-400	945	1	[	[	X
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fuelectenerg-400	945	3	]	]	PUNCT
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fuelectenerg-400	945	5	a.	a.	PROPN
fuelectenerg-400	945	6	macmahon	macmahon	PROPN
fuelectenerg-400	945	7	,	,	PUNCT
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fuelectenerg-400	945	9	analysis	analysis	NOUN
fuelectenerg-400	945	10	(	(	PUNCT
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fuelectenerg-400	945	12	ii	ii	PROPN
fuelectenerg-400	945	13	)	)	PUNCT
fuelectenerg-400	945	14	,	,	PUNCT
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fuelectenerg-400	945	16	.	.	PUNCT
fuelectenerg-400	946	1	new	new	PROPN
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fuelectenerg-400	946	3	:	:	PUNCT
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fuelectenerg-400	946	6	company	company	NOUN
fuelectenerg-400	946	7	,	,	PUNCT
fuelectenerg-400	946	8	1990	1990	NUM
fuelectenerg-400	946	9	.	.	PUNCT
fuelectenerg-400	947	1	[	[	X
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fuelectenerg-400	947	3	]	]	X
fuelectenerg-400	947	4	h.	h.	PROPN
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fuelectenerg-400	947	6	,	,	PUNCT
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fuelectenerg-400	947	10	and	and	CCONJ
fuelectenerg-400	947	11	j.	j.	PROPN
fuelectenerg-400	947	12	propp	propp	PROPN
fuelectenerg-400	947	13	,	,	PUNCT
fuelectenerg-400	947	14	“	"	PUNCT
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fuelectenerg-400	947	23	,	,	PUNCT
fuelectenerg-400	947	24	”	"	PUNCT
fuelectenerg-400	947	25	new	new	PROPN
fuelectenerg-400	947	26	york	york	PROPN
fuelectenerg-400	947	27	journal	journal	PROPN
fuelectenerg-400	947	28	of	of	ADP
fuelectenerg-400	947	29	mathematics	mathematics	PROPN
fuelectenerg-400	947	30	,	,	PUNCT
fuelectenerg-400	947	31	vol	vol	NOUN
fuelectenerg-400	947	32	.	.	PROPN
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fuelectenerg-400	947	36	137	137	NUM
fuelectenerg-400	947	37	,	,	PUNCT
fuelectenerg-400	947	38	1998	1998	NUM
fuelectenerg-400	947	39	.	.	PUNCT
fuelectenerg-400	948	1	[	[	X
fuelectenerg-400	948	2	online	online	X
fuelectenerg-400	948	3	]	]	X
fuelectenerg-400	948	4	.	.	PUNCT
fuelectenerg-400	949	1	available	available	ADJ
fuelectenerg-400	949	2	:	:	PUNCT
fuelectenerg-400	949	3	http://www.citebase.org/abstract?id=oai:arxiv.org:math/9801059	http://www.citebase.org/abstract?id=oai:arxiv.org:math/9801059	PROPN
fuelectenerg-400	949	4	[	[	X
fuelectenerg-400	949	5	18	18	NUM
fuelectenerg-400	949	6	]	]	X
fuelectenerg-400	949	7	g.	g.	PROPN
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fuelectenerg-400	949	10	c.	c.	PROPN
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fuelectenerg-400	949	12	,	,	PUNCT
fuelectenerg-400	949	13	“	"	PUNCT
fuelectenerg-400	949	14	the	the	DET
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fuelectenerg-400	949	16	of	of	ADP
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fuelectenerg-400	949	18	,	,	PUNCT
fuelectenerg-400	949	19	”	"	PUNCT
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fuelectenerg-400	949	23	,	,	PUNCT
fuelectenerg-400	949	24	vol	vol	NOUN
fuelectenerg-400	949	25	.	.	PROPN
fuelectenerg-400	950	1	96	96	NUM
fuelectenerg-400	950	2	,	,	PUNCT
fuelectenerg-400	950	3	no	no	INTJ
fuelectenerg-400	950	4	.	.	NOUN
fuelectenerg-400	950	5	5	5	NUM
fuelectenerg-400	950	6	,	,	PUNCT
fuelectenerg-400	950	7	pp	pp	ADJ
fuelectenerg-400	950	8	.	.	PUNCT
fuelectenerg-400	951	1	429–431	429–431	NUM
fuelectenerg-400	951	2	,	,	PUNCT
fuelectenerg-400	951	3	1989	1989	NUM
fuelectenerg-400	951	4	.	.	PUNCT
fuelectenerg-400	952	1	[	[	X
fuelectenerg-400	952	2	19	19	NUM
fuelectenerg-400	952	3	]	]	PUNCT
fuelectenerg-400	952	4	p.	p.	PROPN
fuelectenerg-400	952	5	w.	w.	PROPN
fuelectenerg-400	952	6	kasteleyn	kasteleyn	PROPN
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fuelectenerg-400	952	8	“	"	PUNCT
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fuelectenerg-400	952	13	on	on	ADP
fuelectenerg-400	952	14	a	a	DET
fuelectenerg-400	952	15	lattice	lattice	NOUN
fuelectenerg-400	952	16	:	:	PUNCT
fuelectenerg-400	952	17	the	the	DET
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fuelectenerg-400	952	22	on	on	ADP
fuelectenerg-400	952	23	a	a	DET
fuelectenerg-400	952	24	quadratic	quadratic	ADJ
fuelectenerg-400	952	25	lattice	lattice	NOUN
fuelectenerg-400	952	26	,	,	PUNCT
fuelectenerg-400	952	27	”	"	PUNCT
fuelectenerg-400	952	28	physica	physica	NOUN
fuelectenerg-400	952	29	,	,	PUNCT
fuelectenerg-400	952	30	vol	vol	NOUN
fuelectenerg-400	952	31	.	.	PROPN
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fuelectenerg-400	952	33	,	,	PUNCT
fuelectenerg-400	952	34	pp	pp	ADJ
fuelectenerg-400	952	35	.	.	PUNCT
fuelectenerg-400	953	1	1209–1225	1209–1225	NUM
fuelectenerg-400	953	2	,	,	PUNCT
fuelectenerg-400	953	3	1961	1961	NUM
fuelectenerg-400	953	4	.	.	PUNCT
fuelectenerg-400	954	1	540	540	NUM
fuelectenerg-400	954	2	b.	b.	PROPN
fuelectenerg-400	954	3	vasic	vasic	PROPN
fuelectenerg-400	954	4	,	,	PUNCT
fuelectenerg-400	954	5	a.	a.	PROPN
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fuelectenerg-400	954	7	krishnan	krishnan	PROPN
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fuelectenerg-400	954	11	codes	code	NOUN
fuelectenerg-400	954	12	541	541	NUM
fuelectenerg-400	954	13	542	542	NUM
fuelectenerg-400	954	14	a.	a.	PROPN
fuelectenerg-400	954	15	r.	r.	PROPN
fuelectenerg-400	954	16	krishnanan	krishnanan	PROPN
fuelectenerg-400	954	17	and	and	CCONJ
fuelectenerg-400	954	18	b.	b.	PROPN
fuelectenerg-400	954	19	vasić	vasić	PROPN
fuelectenerg-400	955	1	[	[	X
fuelectenerg-400	955	2	20	20	NUM
fuelectenerg-400	955	3	]	]	PUNCT
fuelectenerg-400	955	4	s.	s.	PROPN
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fuelectenerg-400	955	6	and	and	CCONJ
fuelectenerg-400	955	7	e.	e.	PROPN
fuelectenerg-400	955	8	remila	remila	PROPN
fuelectenerg-400	955	9	,	,	PUNCT
fuelectenerg-400	955	10	“	"	PUNCT
fuelectenerg-400	955	11	an	an	DET
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fuelectenerg-400	955	14	to	to	PART
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fuelectenerg-400	955	17	,	,	PUNCT
fuelectenerg-400	955	18	”	"	PUNCT
fuelectenerg-400	955	19	journal	journal	NOUN
fuelectenerg-400	955	20	of	of	ADP
fuelectenerg-400	955	21	discrete	discrete	ADJ
fuelectenerg-400	955	22	algorithms	algorithm	NOUN
fuelectenerg-400	955	23	,	,	PUNCT
fuelectenerg-400	955	24	vol	vol	NOUN
fuelectenerg-400	955	25	.	.	PROPN
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fuelectenerg-400	955	27	,	,	PUNCT
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fuelectenerg-400	955	29	.	.	NOUN
fuelectenerg-400	955	30	1	1	NUM
fuelectenerg-400	955	31	,	,	PUNCT
fuelectenerg-400	955	32	pp	pp	ADJ
fuelectenerg-400	955	33	.	.	PUNCT
fuelectenerg-400	956	1	168	168	NUM
fuelectenerg-400	956	2	–	–	PUNCT
fuelectenerg-400	956	3	180	180	NUM
fuelectenerg-400	956	4	,	,	PUNCT
fuelectenerg-400	956	5	2006	2006	NUM
fuelectenerg-400	956	6	.	.	PUNCT
fuelectenerg-400	957	1	[	[	X
fuelectenerg-400	957	2	21	21	NUM
fuelectenerg-400	957	3	]	]	X
fuelectenerg-400	957	4	m.	m.	NOUN
fuelectenerg-400	957	5	luby	luby	PROPN
fuelectenerg-400	957	6	,	,	PUNCT
fuelectenerg-400	957	7	d.	d.	PROPN
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fuelectenerg-400	957	9	,	,	PUNCT
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fuelectenerg-400	957	11	a.	a.	NOUN
fuelectenerg-400	957	12	sinclair	sinclair	PROPN
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fuelectenerg-400	957	14	“	"	PUNCT
fuelectenerg-400	957	15	markov	markov	NOUN
fuelectenerg-400	957	16	chain	chain	NOUN
fuelectenerg-400	957	17	algorithms	algorithm	NOUN
fuelectenerg-400	957	18	for	for	ADP
fuelectenerg-400	957	19	planar	planar	ADJ
fuelectenerg-400	957	20	lattice	lattice	NOUN
fuelectenerg-400	957	21	structures	structure	NOUN
fuelectenerg-400	957	22	(	(	PUNCT
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fuelectenerg-400	957	24	abstract	abstract	NOUN
fuelectenerg-400	957	25	)	)	PUNCT
fuelectenerg-400	957	26	,	,	PUNCT
fuelectenerg-400	957	27	”	"	PUNCT
fuelectenerg-400	957	28	ieee	ieee	NOUN
fuelectenerg-400	957	29	symposium	symposium	NOUN
fuelectenerg-400	957	30	on	on	ADP
fuelectenerg-400	957	31	foundations	foundation	NOUN
fuelectenerg-400	957	32	of	of	ADP
fuelectenerg-400	957	33	computer	computer	NOUN
fuelectenerg-400	957	34	science	science	NOUN
fuelectenerg-400	957	35	,	,	PUNCT
fuelectenerg-400	957	36	pp	pp	ADJ
fuelectenerg-400	957	37	.	.	PUNCT
fuelectenerg-400	958	1	150–159	150–159	NUM
fuelectenerg-400	958	2	,	,	PUNCT
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fuelectenerg-400	958	4	.	.	PUNCT
fuelectenerg-400	959	1	[	[	X
fuelectenerg-400	959	2	online	online	X
fuelectenerg-400	959	3	]	]	X
fuelectenerg-400	959	4	.	.	PUNCT
fuelectenerg-400	960	1	available	available	ADJ
fuelectenerg-400	960	2	:	:	PUNCT
fuelectenerg-400	960	3	citeseer.ist.psu.edu/luby95markov.html	citeseer.ist.psu.edu/luby95markov.html	PROPN
fuelectenerg-400	961	1	[	[	X
fuelectenerg-400	961	2	22	22	NUM
fuelectenerg-400	961	3	]	]	X
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fuelectenerg-400	961	7	and	and	CCONJ
fuelectenerg-400	961	8	d.	d.	PROPN
fuelectenerg-400	961	9	r.	r.	PROPN
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fuelectenerg-400	961	11	,	,	PUNCT
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fuelectenerg-400	961	13	algorithms	algorithm	NOUN
fuelectenerg-400	961	14	:	:	PUNCT
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fuelectenerg-400	961	18	and	and	CCONJ
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fuelectenerg-400	961	20	.	.	PUNCT
fuelectenerg-400	962	1	crc	crc	PROPN
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fuelectenerg-400	962	3	,	,	PUNCT
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fuelectenerg-400	962	5	,	,	PUNCT
fuelectenerg-400	962	6	pp	pp	ADV
fuelectenerg-400	962	7	.	.	PUNCT
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fuelectenerg-400	963	2	.	.	PUNCT
fuelectenerg-400	964	1	[	[	X
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fuelectenerg-400	964	3	]	]	X
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fuelectenerg-400	964	13	,	,	PUNCT
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fuelectenerg-400	965	1	and	and	CCONJ
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fuelectenerg-400	965	3	,	,	PUNCT
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fuelectenerg-400	965	5	.	.	PROPN
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fuelectenerg-400	965	7	,	,	PUNCT
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fuelectenerg-400	965	9	n2	n2	NOUN
fuelectenerg-400	965	10	,	,	PUNCT
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fuelectenerg-400	966	1	[	[	X
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fuelectenerg-400	966	3	]	]	X
fuelectenerg-400	966	4	.	.	PUNCT
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fuelectenerg-400	967	2	:	:	PUNCT
fuelectenerg-400	968	1	http://www.citebase	http://www.citebase	PROPN
fuelectenerg-400	968	2	.	.	PUNCT
fuelectenerg-400	969	1	org	org	PROPN
fuelectenerg-400	969	2	/	/	SYM
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fuelectenerg-400	969	30	.	.	PUNCT
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fuelectenerg-400	970	2	,	,	PUNCT
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fuelectenerg-400	970	4	.	.	NOUN
fuelectenerg-400	970	5	1	1	NUM
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fuelectenerg-400	970	9	,	,	PUNCT
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fuelectenerg-400	971	7	b.	b.	PROPN
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fuelectenerg-400	971	9	,	,	PUNCT
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fuelectenerg-400	971	21	,	,	PUNCT
fuelectenerg-400	971	22	”	"	PUNCT
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fuelectenerg-400	971	25	.	.	PUNCT
fuelectenerg-400	972	1	ieee	ieee	PROPN
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fuelectenerg-400	973	5	,	,	PUNCT
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fuelectenerg-400	973	9	,	,	PUNCT
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fuelectenerg-400	973	11	.	.	PROPN
fuelectenerg-400	974	1	10–14	10–14	NUM
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fuelectenerg-400	974	3	.	.	PUNCT
fuelectenerg-400	975	1	[	[	X
fuelectenerg-400	975	2	26	26	NUM
fuelectenerg-400	975	3	]	]	X
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fuelectenerg-400	975	7	,	,	PUNCT
fuelectenerg-400	975	8	“	"	PUNCT
fuelectenerg-400	975	9	the	the	DET
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fuelectenerg-400	975	13	g	g	NOUN
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fuelectenerg-400	976	1	j.	j.	PROPN
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fuelectenerg-400	976	4	.	.	PUNCT
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fuelectenerg-400	976	6	,	,	PUNCT
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fuelectenerg-400	976	8	.	.	PROPN
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fuelectenerg-400	976	10	,	,	PUNCT
fuelectenerg-400	976	11	pp	pp	ADJ
fuelectenerg-400	976	12	.	.	PUNCT
fuelectenerg-400	977	1	264–314	264–314	NUM
fuelectenerg-400	977	2	,	,	PUNCT
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fuelectenerg-400	977	4	.	.	PUNCT
fuelectenerg-400	978	1	542	542	NUM
fuelectenerg-400	978	2	b.	b.	PROPN
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