id	sid	tid	token	lemma	pos
ejpam-3448	1	1	european	european	PROPN
ejpam-3448	1	2	journal	journal	PROPN
ejpam-3448	1	3	of	of	ADP
ejpam-3448	1	4	pure	pure	ADJ
ejpam-3448	1	5	and	and	CCONJ
ejpam-3448	1	6	applied	apply	VERB
ejpam-3448	1	7	mathematics	mathematic	NOUN
ejpam-3448	1	8	vol	vol	NOUN
ejpam-3448	1	9	.	.	PROPN
ejpam-3448	2	1	12	12	NUM
ejpam-3448	2	2	,	,	PUNCT
ejpam-3448	2	3	no	no	INTJ
ejpam-3448	2	4	.	.	NOUN
ejpam-3448	2	5	3	3	NUM
ejpam-3448	2	6	,	,	PUNCT
ejpam-3448	2	7	2019	2019	NUM
ejpam-3448	2	8	,	,	PUNCT
ejpam-3448	2	9	734	734	NUM
ejpam-3448	2	10	-	-	SYM
ejpam-3448	2	11	748	748	NUM
ejpam-3448	2	12	issn	issn	PROPN
ejpam-3448	2	13	1307	1307	NUM
ejpam-3448	2	14	-	-	SYM
ejpam-3448	2	15	5543	5543	NUM
ejpam-3448	2	16	–	–	PUNCT
ejpam-3448	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3448	2	18	published	publish	VERB
ejpam-3448	2	19	by	by	ADP
ejpam-3448	2	20	new	new	PROPN
ejpam-3448	2	21	york	york	PROPN
ejpam-3448	2	22	business	business	PROPN
ejpam-3448	2	23	global	global	PROPN
ejpam-3448	2	24	labelled	label	VERB
ejpam-3448	2	25	maximal	maximal	ADJ
ejpam-3448	2	26	tubings	tubing	NOUN
ejpam-3448	2	27	on	on	ADP
ejpam-3448	2	28	paths	path	NOUN
ejpam-3448	2	29	and	and	CCONJ
ejpam-3448	2	30	graph	graph	NOUN
ejpam-3448	2	31	associahedra	associahedra	PROPN
ejpam-3448	2	32	s.	s.	PROPN
ejpam-3448	2	33	kaan	kaan	PROPN
ejpam-3448	2	34	gürbüzer1	gürbüzer1	PROPN
ejpam-3448	2	35	,	,	PUNCT
ejpam-3448	2	36	bedia	bedia	NOUN
ejpam-3448	2	37	akyar2,∗	akyar2,∗	NOUN
ejpam-3448	2	38	1	1	NUM
ejpam-3448	2	39	department	department	NOUN
ejpam-3448	2	40	of	of	ADP
ejpam-3448	2	41	mathematics	mathematic	NOUN
ejpam-3448	2	42	,	,	PUNCT
ejpam-3448	2	43	dokuz	dokuz	PROPN
ejpam-3448	2	44	eylül	eylül	PROPN
ejpam-3448	2	45	university	university	NOUN
ejpam-3448	2	46	,	,	PUNCT
ejpam-3448	2	47	i̇zmir	i̇zmir	NOUN
ejpam-3448	2	48	,	,	PUNCT
ejpam-3448	2	49	turkey	turkey	PROPN
ejpam-3448	2	50	2	2	NUM
ejpam-3448	2	51	department	department	NOUN
ejpam-3448	2	52	of	of	ADP
ejpam-3448	2	53	mathematical	mathematical	ADJ
ejpam-3448	2	54	sciences	sciences	PROPN
ejpam-3448	2	55	,	,	PUNCT
ejpam-3448	2	56	aalborg	aalborg	PROPN
ejpam-3448	2	57	university	university	NOUN
ejpam-3448	2	58	,	,	PUNCT
ejpam-3448	2	59	aalborg	aalborg	PROPN
ejpam-3448	2	60	ø	ø	PROPN
ejpam-3448	2	61	,	,	PUNCT
ejpam-3448	2	62	denmark	denmark	NOUN
ejpam-3448	2	63	abstract	abstract	NOUN
ejpam-3448	2	64	.	.	PUNCT
ejpam-3448	3	1	we	we	PRON
ejpam-3448	3	2	determine	determine	VERB
ejpam-3448	3	3	the	the	DET
ejpam-3448	3	4	triangulation	triangulation	NOUN
ejpam-3448	3	5	of	of	ADP
ejpam-3448	3	6	a	a	DET
ejpam-3448	3	7	cyclohedron	cyclohedron	NOUN
ejpam-3448	3	8	compatible	compatible	ADJ
ejpam-3448	3	9	with	with	ADP
ejpam-3448	3	10	the	the	DET
ejpam-3448	3	11	tamari	tamari	ADJ
ejpam-3448	3	12	order	order	NOUN
ejpam-3448	3	13	on	on	ADP
ejpam-3448	3	14	its	its	PRON
ejpam-3448	3	15	faces	face	NOUN
ejpam-3448	3	16	.	.	PUNCT
ejpam-3448	4	1	we	we	PRON
ejpam-3448	4	2	define	define	VERB
ejpam-3448	4	3	a	a	DET
ejpam-3448	4	4	name	name	NOUN
ejpam-3448	4	5	of	of	ADP
ejpam-3448	4	6	a	a	DET
ejpam-3448	4	7	tubing	tubing	NOUN
ejpam-3448	4	8	on	on	ADP
ejpam-3448	4	9	a	a	DET
ejpam-3448	4	10	path	path	NOUN
ejpam-3448	4	11	and	and	CCONJ
ejpam-3448	4	12	a	a	DET
ejpam-3448	4	13	plumbing	plumbing	NOUN
ejpam-3448	4	14	leading	lead	VERB
ejpam-3448	4	15	us	we	PRON
ejpam-3448	4	16	to	to	PART
ejpam-3448	4	17	construct	construct	VERB
ejpam-3448	4	18	the	the	DET
ejpam-3448	4	19	dendriform	dendriform	NOUN
ejpam-3448	4	20	algebra	algebra	NOUN
ejpam-3448	4	21	of	of	ADP
ejpam-3448	4	22	the	the	DET
ejpam-3448	4	23	collection	collection	NOUN
ejpam-3448	4	24	of	of	ADP
ejpam-3448	4	25	maximal	maximal	ADJ
ejpam-3448	4	26	tubings	tubing	NOUN
ejpam-3448	4	27	on	on	ADP
ejpam-3448	4	28	paths	path	NOUN
ejpam-3448	4	29	.	.	PUNCT
ejpam-3448	5	1	moreover	moreover	ADV
ejpam-3448	5	2	,	,	PUNCT
ejpam-3448	5	3	we	we	PRON
ejpam-3448	5	4	give	give	VERB
ejpam-3448	5	5	an	an	DET
ejpam-3448	5	6	operad	operad	ADJ
ejpam-3448	5	7	structure	structure	NOUN
ejpam-3448	5	8	of	of	ADP
ejpam-3448	5	9	associahedra	associahedra	PROPN
ejpam-3448	5	10	and	and	CCONJ
ejpam-3448	5	11	a	a	DET
ejpam-3448	5	12	module	module	NOUN
ejpam-3448	5	13	structure	structure	NOUN
ejpam-3448	5	14	of	of	ADP
ejpam-3448	5	15	cyclohedra	cyclohedra	NOUN
ejpam-3448	5	16	via	via	ADP
ejpam-3448	5	17	tubings	tubing	NOUN
ejpam-3448	5	18	.	.	PUNCT
ejpam-3448	6	1	we	we	PRON
ejpam-3448	6	2	define	define	VERB
ejpam-3448	6	3	labelled	label	VERB
ejpam-3448	6	4	maximal	maximal	ADJ
ejpam-3448	6	5	tubings	tubing	NOUN
ejpam-3448	6	6	on	on	ADP
ejpam-3448	6	7	paths	path	NOUN
ejpam-3448	6	8	and	and	CCONJ
ejpam-3448	6	9	give	give	VERB
ejpam-3448	6	10	to	to	ADP
ejpam-3448	6	11	an	an	DET
ejpam-3448	6	12	application	application	NOUN
ejpam-3448	6	13	of	of	ADP
ejpam-3448	6	14	tubings	tubing	NOUN
ejpam-3448	6	15	in	in	ADP
ejpam-3448	6	16	homological	homological	ADJ
ejpam-3448	6	17	algebra	algebra	NOUN
ejpam-3448	6	18	.	.	PUNCT
ejpam-3448	7	1	2010	2010	NUM
ejpam-3448	7	2	mathematics	mathematic	NOUN
ejpam-3448	7	3	subject	subject	NOUN
ejpam-3448	7	4	classifications	classification	NOUN
ejpam-3448	7	5	:	:	PUNCT
ejpam-3448	7	6	51m20	51m20	NUM
ejpam-3448	7	7	,	,	PUNCT
ejpam-3448	7	8	13p20	13p20	NUM
ejpam-3448	7	9	key	key	ADJ
ejpam-3448	7	10	words	word	NOUN
ejpam-3448	7	11	and	and	CCONJ
ejpam-3448	7	12	phrases	phrase	NOUN
ejpam-3448	7	13	:	:	PUNCT
ejpam-3448	7	14	graph	graph	NOUN
ejpam-3448	7	15	associahedra	associahedra	PROPN
ejpam-3448	7	16	,	,	PUNCT
ejpam-3448	7	17	dendriform	dendriform	NOUN
ejpam-3448	7	18	algebra	algebra	NOUN
ejpam-3448	7	19	,	,	PUNCT
ejpam-3448	7	20	triangulation	triangulation	NOUN
ejpam-3448	7	21	,	,	PUNCT
ejpam-3448	7	22	realization	realization	NOUN
ejpam-3448	7	23	1	1	NUM
ejpam-3448	7	24	.	.	PUNCT
ejpam-3448	8	1	introduction	introduction	NOUN
ejpam-3448	8	2	stasheff	stasheff	NOUN
ejpam-3448	8	3	[	[	X
ejpam-3448	8	4	13	13	NUM
ejpam-3448	8	5	]	]	PUNCT
ejpam-3448	8	6	constructed	construct	VERB
ejpam-3448	8	7	the	the	DET
ejpam-3448	8	8	associahedron	associahedron	ADJ
ejpam-3448	8	9	kn	kn	PROPN
ejpam-3448	8	10	as	as	ADP
ejpam-3448	8	11	a	a	DET
ejpam-3448	8	12	space	space	NOUN
ejpam-3448	8	13	homeomorphic	homeomorphic	NOUN
ejpam-3448	8	14	to	to	ADP
ejpam-3448	8	15	an	an	DET
ejpam-3448	8	16	ndimensional	ndimensional	ADJ
ejpam-3448	8	17	unit	unit	NOUN
ejpam-3448	8	18	cube	cube	NOUN
ejpam-3448	8	19	,	,	PUNCT
ejpam-3448	8	20	where	where	SCONJ
ejpam-3448	8	21	kn	kn	PROPN
ejpam-3448	8	22	has	have	VERB
ejpam-3448	8	23	a	a	DET
ejpam-3448	8	24	convex	convex	NOUN
ejpam-3448	8	25	,	,	PUNCT
ejpam-3448	8	26	curvilinear	curvilinear	ADJ
ejpam-3448	8	27	form	form	NOUN
ejpam-3448	8	28	.	.	PUNCT
ejpam-3448	9	1	in	in	ADP
ejpam-3448	9	2	the	the	DET
ejpam-3448	9	3	nineties	ninety	NOUN
ejpam-3448	9	4	,	,	PUNCT
ejpam-3448	9	5	shnider	shnider	NOUN
ejpam-3448	9	6	and	and	CCONJ
ejpam-3448	9	7	sternberg	sternberg	PROPN
ejpam-3448	9	8	[	[	X
ejpam-3448	9	9	12	12	NUM
ejpam-3448	9	10	]	]	PUNCT
ejpam-3448	9	11	defined	define	VERB
ejpam-3448	9	12	the	the	DET
ejpam-3448	9	13	associahedron	associahedron	ADJ
ejpam-3448	9	14	kn	kn	PROPN
ejpam-3448	9	15	as	as	ADP
ejpam-3448	9	16	a	a	DET
ejpam-3448	9	17	truncation	truncation	NOUN
ejpam-3448	9	18	of	of	ADP
ejpam-3448	9	19	an	an	DET
ejpam-3448	9	20	n	n	NOUN
ejpam-3448	9	21	-	-	PUNCT
ejpam-3448	9	22	simplex	simplex	NOUN
ejpam-3448	9	23	in	in	ADP
ejpam-3448	9	24	rn+1	rn+1	PROPN
ejpam-3448	9	25	.	.	PUNCT
ejpam-3448	9	26	carr	carr	PROPN
ejpam-3448	9	27	and	and	CCONJ
ejpam-3448	9	28	devadoss	devadoss	ADJ
ejpam-3448	10	1	[	[	X
ejpam-3448	10	2	1	1	NUM
ejpam-3448	10	3	]	]	PUNCT
ejpam-3448	10	4	gave	give	VERB
ejpam-3448	10	5	an	an	DET
ejpam-3448	10	6	alternative	alternative	ADJ
ejpam-3448	10	7	definition	definition	NOUN
ejpam-3448	10	8	of	of	ADP
ejpam-3448	10	9	kn	kn	PROPN
ejpam-3448	10	10	with	with	ADP
ejpam-3448	10	11	respect	respect	NOUN
ejpam-3448	10	12	to	to	ADP
ejpam-3448	10	13	tubings	tubing	NOUN
ejpam-3448	10	14	to	to	PART
ejpam-3448	10	15	obtain	obtain	VERB
ejpam-3448	10	16	a	a	DET
ejpam-3448	10	17	family	family	NOUN
ejpam-3448	10	18	of	of	ADP
ejpam-3448	10	19	polytopes	polytope	NOUN
ejpam-3448	10	20	,	,	PUNCT
ejpam-3448	10	21	namely	namely	ADV
ejpam-3448	10	22	graph	graph	VERB
ejpam-3448	10	23	associahedron	associahedron	NOUN
ejpam-3448	10	24	.	.	PUNCT
ejpam-3448	11	1	given	give	VERB
ejpam-3448	11	2	any	any	DET
ejpam-3448	11	3	simple	simple	ADJ
ejpam-3448	11	4	finite	finite	NOUN
ejpam-3448	11	5	graph	graph	NOUN
ejpam-3448	11	6	,	,	PUNCT
ejpam-3448	11	7	devadoss	devadoss	ADJ
ejpam-3448	11	8	[	[	X
ejpam-3448	11	9	2	2	NUM
ejpam-3448	11	10	]	]	PUNCT
ejpam-3448	11	11	gave	give	VERB
ejpam-3448	11	12	a	a	DET
ejpam-3448	11	13	realization	realization	NOUN
ejpam-3448	11	14	of	of	ADP
ejpam-3448	11	15	its	its	PRON
ejpam-3448	11	16	corresponding	corresponding	ADJ
ejpam-3448	11	17	graph	graph	NOUN
ejpam-3448	11	18	associahedron	associahedron	NOUN
ejpam-3448	11	19	and	and	CCONJ
ejpam-3448	11	20	a	a	DET
ejpam-3448	11	21	geometric	geometric	ADJ
ejpam-3448	11	22	meaning	meaning	NOUN
ejpam-3448	11	23	of	of	ADP
ejpam-3448	11	24	every	every	DET
ejpam-3448	11	25	collection	collection	NOUN
ejpam-3448	11	26	of	of	ADP
ejpam-3448	11	27	tubings	tubing	NOUN
ejpam-3448	11	28	on	on	ADP
ejpam-3448	11	29	graphs	graph	NOUN
ejpam-3448	11	30	for	for	ADP
ejpam-3448	11	31	a	a	DET
ejpam-3448	11	32	chosen	choose	VERB
ejpam-3448	11	33	suitable	suitable	ADJ
ejpam-3448	11	34	algorithm	algorithm	NOUN
ejpam-3448	11	35	.	.	PUNCT
ejpam-3448	12	1	loday	loday	PROPN
ejpam-3448	12	2	[	[	X
ejpam-3448	12	3	6	6	NUM
ejpam-3448	12	4	]	]	PUNCT
ejpam-3448	12	5	gave	give	VERB
ejpam-3448	12	6	a	a	DET
ejpam-3448	12	7	simple	simple	ADJ
ejpam-3448	12	8	realization	realization	NOUN
ejpam-3448	12	9	of	of	ADP
ejpam-3448	12	10	an	an	DET
ejpam-3448	12	11	associahedron	associahedron	NOUN
ejpam-3448	12	12	by	by	ADP
ejpam-3448	12	13	taking	take	VERB
ejpam-3448	12	14	the	the	DET
ejpam-3448	12	15	convex	convex	NOUN
ejpam-3448	12	16	hull	hull	NOUN
ejpam-3448	12	17	of	of	ADP
ejpam-3448	12	18	the	the	DET
ejpam-3448	12	19	points	point	NOUN
ejpam-3448	12	20	corresponding	correspond	VERB
ejpam-3448	12	21	to	to	ADP
ejpam-3448	12	22	the	the	DET
ejpam-3448	12	23	set	set	NOUN
ejpam-3448	12	24	of	of	ADP
ejpam-3448	12	25	planar	planar	ADJ
ejpam-3448	12	26	binary	binary	ADJ
ejpam-3448	12	27	trees	tree	NOUN
ejpam-3448	12	28	.	.	PUNCT
ejpam-3448	13	1	in	in	ADP
ejpam-3448	13	2	addition	addition	NOUN
ejpam-3448	13	3	,	,	PUNCT
ejpam-3448	13	4	loday	loday	PROPN
ejpam-3448	13	5	[	[	X
ejpam-3448	13	6	4	4	X
ejpam-3448	13	7	]	]	PUNCT
ejpam-3448	13	8	constructed	construct	VERB
ejpam-3448	13	9	some	some	DET
ejpam-3448	13	10	operations	operation	NOUN
ejpam-3448	13	11	mainly	mainly	ADV
ejpam-3448	13	12	addition	addition	NOUN
ejpam-3448	13	13	and	and	CCONJ
ejpam-3448	13	14	multiplication	multiplication	NOUN
ejpam-3448	13	15	on	on	ADP
ejpam-3448	13	16	the	the	DET
ejpam-3448	13	17	set	set	NOUN
ejpam-3448	13	18	of	of	ADP
ejpam-3448	13	19	planar	planar	ADJ
ejpam-3448	13	20	binary	binary	ADJ
ejpam-3448	13	21	trees	tree	NOUN
ejpam-3448	13	22	and	and	CCONJ
ejpam-3448	13	23	also	also	ADV
ejpam-3448	13	24	some	some	DET
ejpam-3448	13	25	algebraic	algebraic	ADJ
ejpam-3448	13	26	structures	structure	NOUN
ejpam-3448	13	27	such	such	ADJ
ejpam-3448	13	28	as	as	ADP
ejpam-3448	13	29	dendriform	dendriform	NOUN
ejpam-3448	13	30	algebra	algebra	NOUN
ejpam-3448	13	31	of	of	ADP
ejpam-3448	13	32	planar	planar	ADJ
ejpam-3448	13	33	binary	binary	ADJ
ejpam-3448	13	34	trees	tree	NOUN
ejpam-3448	13	35	.	.	PUNCT
ejpam-3448	14	1	on	on	ADP
ejpam-3448	14	2	the	the	DET
ejpam-3448	14	3	other	other	ADJ
ejpam-3448	14	4	hand	hand	NOUN
ejpam-3448	14	5	,	,	PUNCT
ejpam-3448	14	6	forcey	forcey	NOUN
ejpam-3448	14	7	and	and	CCONJ
ejpam-3448	14	8	springfield	springfield	NOUN
ejpam-3448	15	1	[	[	X
ejpam-3448	15	2	3	3	X
ejpam-3448	15	3	]	]	PUNCT
ejpam-3448	15	4	constructed	construct	VERB
ejpam-3448	15	5	a	a	DET
ejpam-3448	15	6	module	module	NOUN
ejpam-3448	15	7	on	on	ADP
ejpam-3448	15	8	the	the	DET
ejpam-3448	15	9	vertices	vertex	NOUN
ejpam-3448	15	10	of	of	ADP
ejpam-3448	15	11	cyclohedron	cyclohedron	NOUN
ejpam-3448	15	12	via	via	ADP
ejpam-3448	15	13	tubings	tubing	NOUN
ejpam-3448	15	14	considering	consider	VERB
ejpam-3448	15	15	the	the	DET
ejpam-3448	15	16	relation	relation	NOUN
ejpam-3448	15	17	between	between	ADP
ejpam-3448	15	18	tubings	tubing	NOUN
ejpam-3448	15	19	and	and	CCONJ
ejpam-3448	15	20	trees	tree	NOUN
ejpam-3448	15	21	which	which	PRON
ejpam-3448	15	22	enables	enable	VERB
ejpam-3448	15	23	to	to	PART
ejpam-3448	15	24	give	give	VERB
ejpam-3448	15	25	a	a	DET
ejpam-3448	15	26	geometrical	geometrical	ADJ
ejpam-3448	15	27	view	view	NOUN
ejpam-3448	15	28	point	point	NOUN
ejpam-3448	15	29	for	for	ADP
ejpam-3448	15	30	graded	grade	VERB
ejpam-3448	15	31	algebras	algebra	NOUN
ejpam-3448	15	32	.	.	PUNCT
ejpam-3448	16	1	the	the	DET
ejpam-3448	16	2	product	product	NOUN
ejpam-3448	16	3	on	on	ADP
ejpam-3448	16	4	a	a	DET
ejpam-3448	16	5	graded	grade	VERB
ejpam-3448	16	6	algebra	algebra	NOUN
ejpam-3448	16	7	turns	turn	VERB
ejpam-3448	16	8	into	into	ADP
ejpam-3448	16	9	the	the	DET
ejpam-3448	16	10	one	one	NOUN
ejpam-3448	16	11	on	on	ADP
ejpam-3448	16	12	the	the	DET
ejpam-3448	16	13	vertices	vertex	NOUN
ejpam-3448	16	14	of	of	ADP
ejpam-3448	16	15	a	a	DET
ejpam-3448	16	16	sequence	sequence	NOUN
ejpam-3448	16	17	of	of	ADP
ejpam-3448	16	18	polytopes	polytope	NOUN
ejpam-3448	16	19	and	and	CCONJ
ejpam-3448	16	20	this	this	DET
ejpam-3448	16	21	product	product	NOUN
ejpam-3448	16	22	is	be	AUX
ejpam-3448	16	23	represented	represent	VERB
ejpam-3448	16	24	by	by	ADP
ejpam-3448	16	25	the	the	DET
ejpam-3448	16	26	∗corresponding	∗corresponde	VERB
ejpam-3448	16	27	author	author	NOUN
ejpam-3448	16	28	.	.	PUNCT
ejpam-3448	17	1	doi	doi	NOUN
ejpam-3448	17	2	:	:	PUNCT
ejpam-3448	17	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3448	https://doi.org/10.29020/nybg.ejpam.v12i3.3448	X
ejpam-3448	17	4	email	email	NOUN
ejpam-3448	17	5	addresses	address	NOUN
ejpam-3448	17	6	:	:	PUNCT
ejpam-3448	17	7	kaan.gurbuzer@deu.edu.tr	kaan.gurbuzer@deu.edu.tr	PROPN
ejpam-3448	17	8	(	(	PUNCT
ejpam-3448	17	9	s.	s.	PROPN
ejpam-3448	17	10	kaan	kaan	PROPN
ejpam-3448	17	11	gürbüzer	gürbüzer	PROPN
ejpam-3448	17	12	)	)	PUNCT
ejpam-3448	17	13	,	,	PUNCT
ejpam-3448	17	14	bedia@math.aau.dk	bedia@math.aau.dk	NOUN
ejpam-3448	17	15	(	(	PUNCT
ejpam-3448	17	16	bedia	bedia	NOUN
ejpam-3448	17	17	akyar	akyar	PROPN
ejpam-3448	17	18	)	)	PUNCT
ejpam-3448	17	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3448	18	1	734	734	NUM
ejpam-3448	18	2	c	c	NOUN
ejpam-3448	18	3	©	©	PROPN
ejpam-3448	18	4	2019	2019	NUM
ejpam-3448	18	5	ejpam	ejpam	NOUN
ejpam-3448	18	6	all	all	DET
ejpam-3448	18	7	rights	right	NOUN
ejpam-3448	18	8	reserved	reserve	VERB
ejpam-3448	18	9	.	.	PUNCT
ejpam-3448	19	1	s.	s.	PROPN
ejpam-3448	19	2	k.	k.	PROPN
ejpam-3448	19	3	gürbüzer	gürbüzer	PROPN
ejpam-3448	19	4	,	,	PUNCT
ejpam-3448	19	5	b.	b.	PROPN
ejpam-3448	19	6	akyar	akyar	PROPN
ejpam-3448	19	7	/	/	SYM
ejpam-3448	19	8	eur	eur	PROPN
ejpam-3448	19	9	.	.	PUNCT
ejpam-3448	20	1	j.	j.	PROPN
ejpam-3448	20	2	pure	pure	PROPN
ejpam-3448	20	3	appl	appl	PROPN
ejpam-3448	20	4	.	.	PROPN
ejpam-3448	20	5	math	math	PROPN
ejpam-3448	20	6	,	,	PUNCT
ejpam-3448	20	7	12	12	NUM
ejpam-3448	20	8	(	(	PUNCT
ejpam-3448	20	9	3	3	NUM
ejpam-3448	20	10	)	)	PUNCT
ejpam-3448	20	11	(	(	PUNCT
ejpam-3448	20	12	2019	2019	NUM
ejpam-3448	20	13	)	)	PUNCT
ejpam-3448	20	14	,	,	PUNCT
ejpam-3448	20	15	734	734	NUM
ejpam-3448	20	16	-	-	SYM
ejpam-3448	20	17	748	748	NUM
ejpam-3448	20	18	735	735	NUM
ejpam-3448	20	19	sum	sum	NOUN
ejpam-3448	20	20	of	of	ADP
ejpam-3448	20	21	the	the	DET
ejpam-3448	20	22	vertices	vertex	NOUN
ejpam-3448	20	23	in	in	ADP
ejpam-3448	20	24	higher	high	ADJ
ejpam-3448	20	25	dimensions	dimension	NOUN
ejpam-3448	20	26	.	.	PUNCT
ejpam-3448	21	1	since	since	SCONJ
ejpam-3448	21	2	there	there	PRON
ejpam-3448	21	3	exists	exist	VERB
ejpam-3448	21	4	a	a	DET
ejpam-3448	21	5	one	one	NUM
ejpam-3448	21	6	to	to	ADP
ejpam-3448	21	7	one	one	NUM
ejpam-3448	21	8	correspondence	correspondence	NOUN
ejpam-3448	21	9	between	between	ADP
ejpam-3448	21	10	the	the	DET
ejpam-3448	21	11	set	set	NOUN
ejpam-3448	21	12	of	of	ADP
ejpam-3448	21	13	planar	planar	ADJ
ejpam-3448	21	14	binary	binary	ADJ
ejpam-3448	21	15	trees	tree	NOUN
ejpam-3448	21	16	and	and	CCONJ
ejpam-3448	21	17	the	the	DET
ejpam-3448	21	18	vertices	vertex	NOUN
ejpam-3448	21	19	of	of	ADP
ejpam-3448	21	20	associahedra	associahedra	PROPN
ejpam-3448	21	21	,	,	PUNCT
ejpam-3448	21	22	the	the	DET
ejpam-3448	21	23	dendriform	dendriform	NOUN
ejpam-3448	21	24	algebra	algebra	NOUN
ejpam-3448	21	25	structure	structure	NOUN
ejpam-3448	21	26	can	can	AUX
ejpam-3448	21	27	also	also	ADV
ejpam-3448	21	28	be	be	AUX
ejpam-3448	21	29	considered	consider	VERB
ejpam-3448	21	30	on	on	ADP
ejpam-3448	21	31	the	the	DET
ejpam-3448	21	32	vertices	vertex	NOUN
ejpam-3448	21	33	of	of	ADP
ejpam-3448	21	34	associahedra	associahedra	PROPN
ejpam-3448	21	35	.	.	PROPN
ejpam-3448	22	1	through	through	ADP
ejpam-3448	22	2	the	the	DET
ejpam-3448	22	3	collection	collection	NOUN
ejpam-3448	22	4	of	of	ADP
ejpam-3448	22	5	planar	planar	ADJ
ejpam-3448	22	6	rooted	root	VERB
ejpam-3448	22	7	trees	tree	NOUN
ejpam-3448	22	8	,	,	PUNCT
ejpam-3448	22	9	markl	markl	PROPN
ejpam-3448	22	10	,	,	PUNCT
ejpam-3448	22	11	shnider	shnider	NOUN
ejpam-3448	22	12	and	and	CCONJ
ejpam-3448	22	13	stasheff	stasheff	NOUN
ejpam-3448	22	14	[	[	X
ejpam-3448	22	15	10	10	NUM
ejpam-3448	22	16	]	]	PUNCT
ejpam-3448	22	17	showed	show	VERB
ejpam-3448	22	18	that	that	SCONJ
ejpam-3448	22	19	the	the	DET
ejpam-3448	22	20	sequence	sequence	NOUN
ejpam-3448	22	21	{	{	PUNCT
ejpam-3448	22	22	kn}n≥0	kn}n≥0	PRON
ejpam-3448	22	23	has	have	VERB
ejpam-3448	22	24	an	an	DET
ejpam-3448	22	25	operad	operad	ADJ
ejpam-3448	22	26	which	which	PRON
ejpam-3448	22	27	is	be	AUX
ejpam-3448	22	28	as	as	ADP
ejpam-3448	22	29	an	an	DET
ejpam-3448	22	30	abstraction	abstraction	NOUN
ejpam-3448	22	31	of	of	ADP
ejpam-3448	22	32	a	a	DET
ejpam-3448	22	33	family	family	NOUN
ejpam-3448	22	34	of	of	ADP
ejpam-3448	22	35	composable	composable	ADJ
ejpam-3448	22	36	functions	function	NOUN
ejpam-3448	22	37	of	of	ADP
ejpam-3448	22	38	finitely	finitely	ADV
ejpam-3448	22	39	many	many	ADJ
ejpam-3448	22	40	variables	variable	NOUN
ejpam-3448	22	41	.	.	PUNCT
ejpam-3448	23	1	operads	operad	NOUN
ejpam-3448	23	2	generalize	generalize	VERB
ejpam-3448	23	3	various	various	ADJ
ejpam-3448	23	4	associativity	associativity	NOUN
ejpam-3448	23	5	properties	property	NOUN
ejpam-3448	23	6	that	that	PRON
ejpam-3448	23	7	are	be	AUX
ejpam-3448	23	8	already	already	ADV
ejpam-3448	23	9	observed	observe	VERB
ejpam-3448	23	10	by	by	ADP
ejpam-3448	23	11	modeling	model	VERB
ejpam-3448	23	12	computational	computational	ADJ
ejpam-3448	23	13	trees	tree	NOUN
ejpam-3448	23	14	within	within	ADP
ejpam-3448	23	15	algebra	algebra	PROPN
ejpam-3448	23	16	.	.	PUNCT
ejpam-3448	24	1	markl	markl	PROPN
ejpam-3448	25	1	[	[	X
ejpam-3448	25	2	8	8	NUM
ejpam-3448	25	3	]	]	PUNCT
ejpam-3448	25	4	constructed	construct	VERB
ejpam-3448	25	5	a	a	DET
ejpam-3448	25	6	module	module	NOUN
ejpam-3448	25	7	structure	structure	NOUN
ejpam-3448	25	8	over	over	ADP
ejpam-3448	25	9	an	an	DET
ejpam-3448	25	10	operad	operad	NOUN
ejpam-3448	25	11	and	and	CCONJ
ejpam-3448	25	12	in	in	ADP
ejpam-3448	25	13	[	[	X
ejpam-3448	25	14	9	9	NUM
ejpam-3448	25	15	]	]	PUNCT
ejpam-3448	25	16	,	,	PUNCT
ejpam-3448	25	17	he	he	PRON
ejpam-3448	25	18	showed	show	VERB
ejpam-3448	25	19	that	that	SCONJ
ejpam-3448	25	20	the	the	DET
ejpam-3448	25	21	sequence	sequence	NOUN
ejpam-3448	25	22	{	{	PUNCT
ejpam-3448	25	23	wn}n≥0	wn}n≥0	X
ejpam-3448	25	24	of	of	ADP
ejpam-3448	25	25	cyclohedra	cyclohedra	NOUN
ejpam-3448	25	26	was	be	AUX
ejpam-3448	25	27	not	not	PART
ejpam-3448	25	28	an	an	DET
ejpam-3448	25	29	operad	operad	NOUN
ejpam-3448	25	30	but	but	CCONJ
ejpam-3448	25	31	a	a	DET
ejpam-3448	25	32	module	module	NOUN
ejpam-3448	25	33	over	over	ADP
ejpam-3448	25	34	the	the	DET
ejpam-3448	25	35	operad	operad	ADJ
ejpam-3448	25	36	{	{	PUNCT
ejpam-3448	25	37	kn}n≥0	kn}n≥0	X
ejpam-3448	25	38	.	.	PUNCT
ejpam-3448	26	1	briefly	briefly	NOUN
ejpam-3448	26	2	,	,	PUNCT
ejpam-3448	26	3	this	this	DET
ejpam-3448	26	4	module	module	NOUN
ejpam-3448	26	5	structure	structure	NOUN
ejpam-3448	26	6	results	result	VERB
ejpam-3448	26	7	from	from	ADP
ejpam-3448	26	8	the	the	DET
ejpam-3448	26	9	indexes	index	NOUN
ejpam-3448	26	10	of	of	ADP
ejpam-3448	26	11	the	the	DET
ejpam-3448	26	12	faces	face	NOUN
ejpam-3448	26	13	of	of	ADP
ejpam-3448	26	14	the	the	DET
ejpam-3448	26	15	form	form	NOUN
ejpam-3448	26	16	wn−k	wn−k	NOUN
ejpam-3448	26	17	×kk−1	×kk−1	NOUN
ejpam-3448	26	18	for	for	ADP
ejpam-3448	26	19	n	n	DET
ejpam-3448	26	20	≥	≥	NOUN
ejpam-3448	26	21	k	k	X
ejpam-3448	26	22	≥	≥	NUM
ejpam-3448	26	23	1	1	NUM
ejpam-3448	26	24	and	and	CCONJ
ejpam-3448	26	25	it	it	PRON
ejpam-3448	26	26	enables	enable	VERB
ejpam-3448	26	27	us	we	PRON
ejpam-3448	26	28	to	to	PART
ejpam-3448	26	29	generalize	generalize	VERB
ejpam-3448	26	30	many	many	ADJ
ejpam-3448	26	31	types	type	NOUN
ejpam-3448	26	32	of	of	ADP
ejpam-3448	26	33	graph	graph	NOUN
ejpam-3448	26	34	associahedra	associahedra	PROPN
ejpam-3448	26	35	.	.	PUNCT
ejpam-3448	27	1	in	in	ADP
ejpam-3448	27	2	this	this	DET
ejpam-3448	27	3	paper	paper	NOUN
ejpam-3448	27	4	,	,	PUNCT
ejpam-3448	27	5	section	section	NOUN
ejpam-3448	27	6	2	2	NUM
ejpam-3448	27	7	contains	contain	VERB
ejpam-3448	27	8	an	an	DET
ejpam-3448	27	9	introduction	introduction	NOUN
ejpam-3448	27	10	on	on	ADP
ejpam-3448	27	11	graph	graph	NOUN
ejpam-3448	27	12	associahedra	associahedra	NOUN
ejpam-3448	27	13	from	from	ADP
ejpam-3448	27	14	devadoss	devadoss	ADJ
ejpam-3448	27	15	[	[	X
ejpam-3448	27	16	2	2	NUM
ejpam-3448	27	17	]	]	PUNCT
ejpam-3448	27	18	and	and	CCONJ
ejpam-3448	27	19	the	the	DET
ejpam-3448	27	20	combinatorial	combinatorial	ADJ
ejpam-3448	27	21	properties	property	NOUN
ejpam-3448	27	22	of	of	ADP
ejpam-3448	27	23	the	the	DET
ejpam-3448	27	24	faces	face	NOUN
ejpam-3448	27	25	of	of	ADP
ejpam-3448	27	26	a	a	DET
ejpam-3448	27	27	graph	graph	NOUN
ejpam-3448	27	28	associahedron	associahedron	NOUN
ejpam-3448	27	29	from	from	ADP
ejpam-3448	27	30	forcey	forcey	NOUN
ejpam-3448	27	31	and	and	CCONJ
ejpam-3448	27	32	springfield	springfield	NOUN
ejpam-3448	28	1	[	[	X
ejpam-3448	28	2	3	3	NUM
ejpam-3448	28	3	]	]	PUNCT
ejpam-3448	28	4	.	.	PUNCT
ejpam-3448	29	1	we	we	PRON
ejpam-3448	29	2	give	give	VERB
ejpam-3448	29	3	the	the	DET
ejpam-3448	29	4	triangulation	triangulation	NOUN
ejpam-3448	29	5	of	of	ADP
ejpam-3448	29	6	a	a	DET
ejpam-3448	29	7	cyclohedron	cyclohedron	NOUN
ejpam-3448	29	8	compatible	compatible	ADJ
ejpam-3448	29	9	with	with	ADP
ejpam-3448	29	10	the	the	DET
ejpam-3448	29	11	tamari	tamari	ADJ
ejpam-3448	29	12	order	order	NOUN
ejpam-3448	29	13	on	on	ADP
ejpam-3448	29	14	its	its	PRON
ejpam-3448	29	15	faces	face	NOUN
ejpam-3448	29	16	.	.	PUNCT
ejpam-3448	30	1	in	in	ADP
ejpam-3448	30	2	section	section	NOUN
ejpam-3448	30	3	3	3	NUM
ejpam-3448	30	4	,	,	PUNCT
ejpam-3448	30	5	we	we	PRON
ejpam-3448	30	6	define	define	VERB
ejpam-3448	30	7	a	a	DET
ejpam-3448	30	8	name	name	NOUN
ejpam-3448	30	9	of	of	ADP
ejpam-3448	30	10	a	a	DET
ejpam-3448	30	11	tubing	tubing	NOUN
ejpam-3448	30	12	on	on	ADP
ejpam-3448	30	13	a	a	DET
ejpam-3448	30	14	path	path	NOUN
ejpam-3448	30	15	as	as	ADP
ejpam-3448	30	16	a	a	DET
ejpam-3448	30	17	sequence	sequence	NOUN
ejpam-3448	30	18	of	of	ADP
ejpam-3448	30	19	positive	positive	ADJ
ejpam-3448	30	20	integers	integer	NOUN
ejpam-3448	30	21	and	and	CCONJ
ejpam-3448	30	22	establish	establish	VERB
ejpam-3448	30	23	some	some	DET
ejpam-3448	30	24	operations	operation	NOUN
ejpam-3448	30	25	on	on	ADP
ejpam-3448	30	26	tubings	tubing	NOUN
ejpam-3448	30	27	on	on	ADP
ejpam-3448	30	28	paths	path	NOUN
ejpam-3448	30	29	.	.	PUNCT
ejpam-3448	31	1	furthermore	furthermore	ADV
ejpam-3448	31	2	,	,	PUNCT
ejpam-3448	31	3	we	we	PRON
ejpam-3448	31	4	define	define	VERB
ejpam-3448	31	5	a	a	DET
ejpam-3448	31	6	plumbing	plumbing	NOUN
ejpam-3448	31	7	as	as	ADP
ejpam-3448	31	8	a	a	DET
ejpam-3448	31	9	collection	collection	NOUN
ejpam-3448	31	10	of	of	ADP
ejpam-3448	31	11	maximal	maximal	ADJ
ejpam-3448	31	12	tubings	tubing	NOUN
ejpam-3448	31	13	with	with	ADP
ejpam-3448	31	14	the	the	DET
ejpam-3448	31	15	sum	sum	NOUN
ejpam-3448	31	16	and	and	CCONJ
ejpam-3448	31	17	product	product	NOUN
ejpam-3448	31	18	operations	operation	NOUN
ejpam-3448	31	19	.	.	PUNCT
ejpam-3448	32	1	we	we	PRON
ejpam-3448	32	2	construct	construct	VERB
ejpam-3448	32	3	the	the	DET
ejpam-3448	32	4	dendriform	dendriform	NOUN
ejpam-3448	32	5	algebra	algebra	NOUN
ejpam-3448	32	6	of	of	ADP
ejpam-3448	32	7	the	the	DET
ejpam-3448	32	8	collection	collection	NOUN
ejpam-3448	32	9	of	of	ADP
ejpam-3448	32	10	maximal	maximal	ADJ
ejpam-3448	32	11	tubings	tubing	NOUN
ejpam-3448	32	12	on	on	ADP
ejpam-3448	32	13	paths	path	NOUN
ejpam-3448	32	14	together	together	ADV
ejpam-3448	32	15	with	with	ADP
ejpam-3448	32	16	the	the	DET
ejpam-3448	32	17	operations	operation	NOUN
ejpam-3448	32	18	via	via	ADP
ejpam-3448	32	19	names	name	NOUN
ejpam-3448	32	20	.	.	PUNCT
ejpam-3448	33	1	after	after	ADP
ejpam-3448	33	2	that	that	PRON
ejpam-3448	33	3	,	,	PUNCT
ejpam-3448	33	4	we	we	PRON
ejpam-3448	33	5	determine	determine	VERB
ejpam-3448	33	6	the	the	DET
ejpam-3448	33	7	operad	operad	ADJ
ejpam-3448	33	8	structure	structure	NOUN
ejpam-3448	33	9	of	of	ADP
ejpam-3448	33	10	the	the	DET
ejpam-3448	33	11	sequence	sequence	NOUN
ejpam-3448	33	12	{	{	PUNCT
ejpam-3448	33	13	kn}n≥0	kn}n≥0	NOUN
ejpam-3448	33	14	and	and	CCONJ
ejpam-3448	33	15	interpret	interpret	VERB
ejpam-3448	33	16	the	the	DET
ejpam-3448	33	17	module	module	NOUN
ejpam-3448	33	18	structure	structure	NOUN
ejpam-3448	33	19	of	of	ADP
ejpam-3448	33	20	the	the	DET
ejpam-3448	33	21	sequence	sequence	NOUN
ejpam-3448	33	22	{	{	PUNCT
ejpam-3448	33	23	wn}n≥0	wn}n≥0	ADP
ejpam-3448	33	24	defining	define	VERB
ejpam-3448	33	25	the	the	DET
ejpam-3448	33	26	comp	comp	NOUN
ejpam-3448	33	27	maps	map	NOUN
ejpam-3448	33	28	and	and	CCONJ
ejpam-3448	33	29	the	the	DET
ejpam-3448	33	30	cellular	cellular	ADJ
ejpam-3448	33	31	chain	chain	NOUN
ejpam-3448	33	32	complex	complex	NOUN
ejpam-3448	33	33	of	of	ADP
ejpam-3448	33	34	an	an	DET
ejpam-3448	33	35	associahedron	associahedron	NOUN
ejpam-3448	33	36	in	in	ADP
ejpam-3448	33	37	terms	term	NOUN
ejpam-3448	33	38	of	of	ADP
ejpam-3448	33	39	tubings	tubing	NOUN
ejpam-3448	33	40	.	.	PUNCT
ejpam-3448	34	1	in	in	ADP
ejpam-3448	34	2	last	last	ADJ
ejpam-3448	34	3	section	section	NOUN
ejpam-3448	34	4	,	,	PUNCT
ejpam-3448	34	5	as	as	ADP
ejpam-3448	34	6	an	an	DET
ejpam-3448	34	7	application	application	NOUN
ejpam-3448	34	8	,	,	PUNCT
ejpam-3448	34	9	we	we	PRON
ejpam-3448	34	10	construct	construct	VERB
ejpam-3448	34	11	the	the	DET
ejpam-3448	34	12	chain	chain	NOUN
ejpam-3448	34	13	complex	complex	NOUN
ejpam-3448	34	14	whose	whose	DET
ejpam-3448	34	15	boundary	boundary	ADJ
ejpam-3448	34	16	map	map	NOUN
ejpam-3448	34	17	is	be	AUX
ejpam-3448	34	18	defined	define	VERB
ejpam-3448	34	19	on	on	ADP
ejpam-3448	34	20	labelled	label	VERB
ejpam-3448	34	21	maximal	maximal	ADJ
ejpam-3448	34	22	tubings	tubing	NOUN
ejpam-3448	34	23	on	on	ADP
ejpam-3448	34	24	a	a	DET
ejpam-3448	34	25	path	path	NOUN
ejpam-3448	34	26	and	and	CCONJ
ejpam-3448	34	27	compute	compute	VERB
ejpam-3448	34	28	its	its	PRON
ejpam-3448	34	29	homology	homology	NOUN
ejpam-3448	34	30	groups	group	NOUN
ejpam-3448	34	31	.	.	PUNCT
ejpam-3448	35	1	2	2	X
ejpam-3448	35	2	.	.	X
ejpam-3448	35	3	graph	graph	NOUN
ejpam-3448	35	4	associahedron	associahedron	NOUN
ejpam-3448	35	5	for	for	ADP
ejpam-3448	35	6	a	a	DET
ejpam-3448	35	7	finite	finite	ADJ
ejpam-3448	35	8	simple	simple	ADJ
ejpam-3448	35	9	graph	graph	NOUN
ejpam-3448	35	10	g	g	PROPN
ejpam-3448	35	11	,	,	PUNCT
ejpam-3448	35	12	devadoss	devadoss	ADJ
ejpam-3448	35	13	[	[	X
ejpam-3448	35	14	2	2	NUM
ejpam-3448	35	15	]	]	PUNCT
ejpam-3448	35	16	defined	define	VERB
ejpam-3448	35	17	a	a	DET
ejpam-3448	35	18	tube	tube	NOUN
ejpam-3448	35	19	as	as	ADP
ejpam-3448	35	20	a	a	DET
ejpam-3448	35	21	proper	proper	ADJ
ejpam-3448	35	22	subset	subset	NOUN
ejpam-3448	35	23	of	of	ADP
ejpam-3448	35	24	nodes	node	NOUN
ejpam-3448	35	25	of	of	ADP
ejpam-3448	35	26	g	g	NOUN
ejpam-3448	35	27	whose	whose	DET
ejpam-3448	35	28	induced	induced	ADJ
ejpam-3448	35	29	graph	graph	NOUN
ejpam-3448	35	30	is	be	AUX
ejpam-3448	35	31	a	a	DET
ejpam-3448	35	32	connected	connected	ADJ
ejpam-3448	35	33	subgraph	subgraph	NOUN
ejpam-3448	35	34	of	of	ADP
ejpam-3448	35	35	g.	g.	PROPN
ejpam-3448	35	36	the	the	DET
ejpam-3448	35	37	graph	graph	NOUN
ejpam-3448	35	38	g	g	PROPN
ejpam-3448	35	39	itself	itself	PRON
ejpam-3448	35	40	is	be	AUX
ejpam-3448	35	41	called	call	VERB
ejpam-3448	35	42	the	the	DET
ejpam-3448	35	43	universal	universal	ADJ
ejpam-3448	35	44	tube	tube	NOUN
ejpam-3448	35	45	which	which	PRON
ejpam-3448	35	46	is	be	AUX
ejpam-3448	35	47	preferably	preferably	ADV
ejpam-3448	35	48	not	not	PART
ejpam-3448	35	49	drawn.there	drawn.there	PRON
ejpam-3448	35	50	are	be	VERB
ejpam-3448	35	51	different	different	ADJ
ejpam-3448	35	52	positions	position	NOUN
ejpam-3448	35	53	of	of	ADP
ejpam-3448	35	54	tubes	tube	NOUN
ejpam-3448	35	55	on	on	ADP
ejpam-3448	35	56	a	a	DET
ejpam-3448	35	57	graph	graph	NOUN
ejpam-3448	35	58	with	with	ADP
ejpam-3448	35	59	respect	respect	NOUN
ejpam-3448	35	60	to	to	ADP
ejpam-3448	35	61	each	each	DET
ejpam-3448	35	62	other	other	ADJ
ejpam-3448	35	63	.	.	PUNCT
ejpam-3448	36	1	in	in	ADP
ejpam-3448	36	2	particular	particular	ADJ
ejpam-3448	36	3	,	,	PUNCT
ejpam-3448	36	4	two	two	NUM
ejpam-3448	36	5	tubes	tube	NOUN
ejpam-3448	36	6	t1	t1	PROPN
ejpam-3448	36	7	,	,	PUNCT
ejpam-3448	36	8	t2	t2	PROPN
ejpam-3448	36	9	are	be	AUX
ejpam-3448	36	10	called	call	VERB
ejpam-3448	36	11	nested	nested	ADJ
ejpam-3448	36	12	if	if	SCONJ
ejpam-3448	36	13	t1	t1	PROPN
ejpam-3448	36	14	⊂	⊂	PROPN
ejpam-3448	36	15	t2	t2	PROPN
ejpam-3448	36	16	or	or	CCONJ
ejpam-3448	36	17	t2	t2	PROPN
ejpam-3448	36	18	⊂	⊂	PROPN
ejpam-3448	36	19	t1	t1	PROPN
ejpam-3448	36	20	;	;	PUNCT
ejpam-3448	36	21	intersecting	intersect	VERB
ejpam-3448	36	22	if	if	SCONJ
ejpam-3448	36	23	they	they	PRON
ejpam-3448	36	24	are	be	AUX
ejpam-3448	36	25	not	not	PART
ejpam-3448	36	26	nested	nest	VERB
ejpam-3448	36	27	and	and	CCONJ
ejpam-3448	36	28	t1	t1	NOUN
ejpam-3448	36	29	∩	∩	ADJ
ejpam-3448	36	30	t2	t2	PROPN
ejpam-3448	36	31	6=	6=	PUNCT
ejpam-3448	36	32	∅	∅	NOUN
ejpam-3448	36	33	;	;	PUNCT
ejpam-3448	36	34	adjacent	adjacent	ADJ
ejpam-3448	36	35	if	if	SCONJ
ejpam-3448	36	36	t1	t1	PROPN
ejpam-3448	36	37	,	,	PUNCT
ejpam-3448	36	38	t2	t2	NOUN
ejpam-3448	36	39	do	do	AUX
ejpam-3448	36	40	not	not	PART
ejpam-3448	36	41	intersect	intersect	VERB
ejpam-3448	36	42	and	and	CCONJ
ejpam-3448	36	43	t1	t1	PROPN
ejpam-3448	36	44	∪	∪	ADP
ejpam-3448	36	45	t2	t2	PROPN
ejpam-3448	36	46	is	be	AUX
ejpam-3448	36	47	again	again	ADV
ejpam-3448	36	48	a	a	DET
ejpam-3448	36	49	tube	tube	NOUN
ejpam-3448	36	50	;	;	PUNCT
ejpam-3448	36	51	compatible	compatible	ADJ
ejpam-3448	36	52	if	if	SCONJ
ejpam-3448	36	53	they	they	PRON
ejpam-3448	36	54	are	be	AUX
ejpam-3448	36	55	neither	neither	CCONJ
ejpam-3448	36	56	adjacent	adjacent	ADJ
ejpam-3448	36	57	nor	nor	CCONJ
ejpam-3448	36	58	intersect	intersect	ADJ
ejpam-3448	36	59	each	each	DET
ejpam-3448	36	60	other	other	ADJ
ejpam-3448	36	61	.	.	PUNCT
ejpam-3448	37	1	a	a	DET
ejpam-3448	37	2	set	set	NOUN
ejpam-3448	37	3	of	of	ADP
ejpam-3448	37	4	compatible	compatible	ADJ
ejpam-3448	37	5	tubes	tube	NOUN
ejpam-3448	37	6	is	be	AUX
ejpam-3448	37	7	called	call	VERB
ejpam-3448	37	8	a	a	DET
ejpam-3448	37	9	tubing	tubing	NOUN
ejpam-3448	37	10	and	and	CCONJ
ejpam-3448	37	11	it	it	PRON
ejpam-3448	37	12	is	be	AUX
ejpam-3448	37	13	assumed	assume	VERB
ejpam-3448	37	14	that	that	SCONJ
ejpam-3448	37	15	each	each	DET
ejpam-3448	37	16	tubing	tubing	NOUN
ejpam-3448	37	17	always	always	ADV
ejpam-3448	37	18	contains	contain	VERB
ejpam-3448	37	19	the	the	DET
ejpam-3448	37	20	universal	universal	ADJ
ejpam-3448	37	21	tube	tube	NOUN
ejpam-3448	37	22	.	.	PUNCT
ejpam-3448	38	1	if	if	SCONJ
ejpam-3448	38	2	a	a	DET
ejpam-3448	38	3	graph	graph	NOUN
ejpam-3448	38	4	g	g	NOUN
ejpam-3448	38	5	is	be	AUX
ejpam-3448	38	6	a	a	DET
ejpam-3448	38	7	disconnected	disconnected	ADJ
ejpam-3448	38	8	simple	simple	ADJ
ejpam-3448	38	9	graph	graph	NOUN
ejpam-3448	38	10	with	with	ADP
ejpam-3448	38	11	connected	connected	ADJ
ejpam-3448	38	12	components	component	NOUN
ejpam-3448	38	13	g1	g1	NOUN
ejpam-3448	38	14	,	,	PUNCT
ejpam-3448	38	15	.	.	PUNCT
ejpam-3448	38	16	.	.	PUNCT
ejpam-3448	39	1	.	.	PUNCT
ejpam-3448	40	1	,	,	PUNCT
ejpam-3448	40	2	gk	gk	INTJ
ejpam-3448	40	3	then	then	ADV
ejpam-3448	40	4	it	it	PRON
ejpam-3448	40	5	is	be	AUX
ejpam-3448	40	6	also	also	ADV
ejpam-3448	40	7	assumed	assume	VERB
ejpam-3448	40	8	that	that	SCONJ
ejpam-3448	40	9	a	a	DET
ejpam-3448	40	10	tubing	tubing	NOUN
ejpam-3448	40	11	does	do	AUX
ejpam-3448	40	12	not	not	PART
ejpam-3448	40	13	contain	contain	VERB
ejpam-3448	40	14	all	all	DET
ejpam-3448	40	15	the	the	DET
ejpam-3448	40	16	connected	connected	ADJ
ejpam-3448	40	17	components	component	NOUN
ejpam-3448	40	18	.	.	PUNCT
ejpam-3448	41	1	in	in	ADP
ejpam-3448	41	2	general	general	ADJ
ejpam-3448	41	3	,	,	PUNCT
ejpam-3448	41	4	a	a	DET
ejpam-3448	41	5	tubing	tubing	NOUN
ejpam-3448	41	6	on	on	ADP
ejpam-3448	41	7	a	a	DET
ejpam-3448	41	8	graph	graph	NOUN
ejpam-3448	41	9	with	with	ADP
ejpam-3448	41	10	n	n	NOUN
ejpam-3448	41	11	nodes	node	NOUN
ejpam-3448	41	12	is	be	AUX
ejpam-3448	41	13	called	call	VERB
ejpam-3448	41	14	k	k	ADJ
ejpam-3448	41	15	-	-	NOUN
ejpam-3448	41	16	tubing	tubing	NOUN
ejpam-3448	41	17	,	,	PUNCT
ejpam-3448	41	18	0	0	NUM
ejpam-3448	41	19	≤	≤	NUM
ejpam-3448	41	20	k	k	NOUN
ejpam-3448	41	21	≤	≤	NUM
ejpam-3448	41	22	n	n	CCONJ
ejpam-3448	41	23	−	−	PROPN
ejpam-3448	41	24	1	1	NUM
ejpam-3448	41	25	,	,	PUNCT
ejpam-3448	41	26	if	if	SCONJ
ejpam-3448	41	27	it	it	PRON
ejpam-3448	41	28	contains	contain	VERB
ejpam-3448	41	29	k	k	PROPN
ejpam-3448	41	30	tubes	tube	NOUN
ejpam-3448	41	31	and	and	CCONJ
ejpam-3448	41	32	universal	universal	ADJ
ejpam-3448	41	33	tube	tube	NOUN
ejpam-3448	41	34	.	.	PUNCT
ejpam-3448	42	1	especially	especially	ADV
ejpam-3448	42	2	,	,	PUNCT
ejpam-3448	42	3	(	(	PUNCT
ejpam-3448	42	4	n	n	CCONJ
ejpam-3448	42	5	−	−	PROPN
ejpam-3448	42	6	1)-tubings	1)-tubing	NOUN
ejpam-3448	42	7	are	be	AUX
ejpam-3448	42	8	called	call	VERB
ejpam-3448	42	9	the	the	DET
ejpam-3448	42	10	maximal	maximal	ADJ
ejpam-3448	42	11	tubings	tubing	NOUN
ejpam-3448	42	12	whose	whose	DET
ejpam-3448	42	13	collection	collection	NOUN
ejpam-3448	42	14	is	be	AUX
ejpam-3448	42	15	denoted	denote	VERB
ejpam-3448	42	16	by	by	ADP
ejpam-3448	42	17	mg	mg	PROPN
ejpam-3448	42	18	.	.	PUNCT
ejpam-3448	43	1	the	the	DET
ejpam-3448	43	2	set	set	NOUN
ejpam-3448	43	3	of	of	ADP
ejpam-3448	43	4	all	all	DET
ejpam-3448	43	5	tubings	tubing	NOUN
ejpam-3448	43	6	on	on	ADP
ejpam-3448	43	7	a	a	DET
ejpam-3448	43	8	graph	graph	NOUN
ejpam-3448	43	9	g	g	NOUN
ejpam-3448	43	10	is	be	AUX
ejpam-3448	43	11	denoted	denote	VERB
ejpam-3448	43	12	by	by	ADP
ejpam-3448	43	13	pg	pg	PROPN
ejpam-3448	43	14	.	.	PUNCT
ejpam-3448	44	1	this	this	DET
ejpam-3448	44	2	set	set	NOUN
ejpam-3448	44	3	becomes	become	VERB
ejpam-3448	44	4	a	a	DET
ejpam-3448	44	5	partial	partial	ADJ
ejpam-3448	44	6	ordered	order	VERB
ejpam-3448	44	7	set	set	NOUN
ejpam-3448	44	8	ordered	order	VERB
ejpam-3448	44	9	by	by	ADP
ejpam-3448	44	10	inclusion	inclusion	NOUN
ejpam-3448	44	11	such	such	ADJ
ejpam-3448	44	12	that	that	SCONJ
ejpam-3448	44	13	if	if	SCONJ
ejpam-3448	44	14	t1	t1	PROPN
ejpam-3448	44	15	,	,	PUNCT
ejpam-3448	44	16	t2	t2	PROPN
ejpam-3448	44	17	∈	∈	PROPN
ejpam-3448	44	18	pg	pg	NOUN
ejpam-3448	44	19	and	and	CCONJ
ejpam-3448	44	20	t1	t1	NOUN
ejpam-3448	44	21	can	can	AUX
ejpam-3448	44	22	be	be	AUX
ejpam-3448	44	23	obtained	obtain	VERB
ejpam-3448	44	24	by	by	ADP
ejpam-3448	44	25	deleting	delete	VERB
ejpam-3448	44	26	one	one	NUM
ejpam-3448	44	27	or	or	CCONJ
ejpam-3448	44	28	more	more	ADJ
ejpam-3448	44	29	tubes	tube	NOUN
ejpam-3448	44	30	in	in	ADP
ejpam-3448	44	31	t2	t2	NOUN
ejpam-3448	44	32	then	then	ADV
ejpam-3448	44	33	t2	t2	VERB
ejpam-3448	44	34	<	<	X
ejpam-3448	44	35	t1	t1	NOUN
ejpam-3448	44	36	.	.	PUNCT
ejpam-3448	45	1	in	in	ADP
ejpam-3448	45	2	[	[	X
ejpam-3448	45	3	2	2	NUM
ejpam-3448	45	4	]	]	PUNCT
ejpam-3448	45	5	,	,	PUNCT
ejpam-3448	45	6	devadoss	devadoss	PROPN
ejpam-3448	45	7	proved	prove	VERB
ejpam-3448	45	8	that	that	SCONJ
ejpam-3448	45	9	the	the	DET
ejpam-3448	45	10	poset	poset	NOUN
ejpam-3448	45	11	pg	pg	NOUN
ejpam-3448	45	12	admits	admit	VERB
ejpam-3448	45	13	a	a	DET
ejpam-3448	45	14	geometric	geometric	ADJ
ejpam-3448	45	15	realization	realization	NOUN
ejpam-3448	45	16	kg	kg	NOUN
ejpam-3448	45	17	,	,	PUNCT
ejpam-3448	45	18	that	that	ADV
ejpam-3448	45	19	is	is	ADV
ejpam-3448	45	20	,	,	PUNCT
ejpam-3448	45	21	a	a	DET
ejpam-3448	45	22	convex	convex	ADJ
ejpam-3448	45	23	polytope	polytope	NOUN
ejpam-3448	45	24	whose	whose	DET
ejpam-3448	45	25	face	face	NOUN
ejpam-3448	45	26	poset	poset	NOUN
ejpam-3448	45	27	is	be	AUX
ejpam-3448	45	28	isomorphic	isomorphic	ADJ
ejpam-3448	45	29	to	to	PART
ejpam-3448	45	30	pg	pg	VERB
ejpam-3448	45	31	.	.	PUNCT
ejpam-3448	46	1	the	the	DET
ejpam-3448	46	2	polytope	polytope	NOUN
ejpam-3448	46	3	kg	kg	PROPN
ejpam-3448	46	4	is	be	AUX
ejpam-3448	46	5	called	call	VERB
ejpam-3448	46	6	s.	s.	PROPN
ejpam-3448	46	7	k.	k.	PROPN
ejpam-3448	46	8	gürbüzer	gürbüzer	PROPN
ejpam-3448	46	9	,	,	PUNCT
ejpam-3448	46	10	b.	b.	PROPN
ejpam-3448	46	11	akyar	akyar	PROPN
ejpam-3448	46	12	/	/	SYM
ejpam-3448	46	13	eur	eur	PROPN
ejpam-3448	46	14	.	.	PUNCT
ejpam-3448	47	1	j.	j.	PROPN
ejpam-3448	47	2	pure	pure	PROPN
ejpam-3448	47	3	appl	appl	PROPN
ejpam-3448	47	4	.	.	PROPN
ejpam-3448	47	5	math	math	PROPN
ejpam-3448	47	6	,	,	PUNCT
ejpam-3448	47	7	12	12	NUM
ejpam-3448	47	8	(	(	PUNCT
ejpam-3448	47	9	3	3	NUM
ejpam-3448	47	10	)	)	PUNCT
ejpam-3448	47	11	(	(	PUNCT
ejpam-3448	47	12	2019	2019	NUM
ejpam-3448	47	13	)	)	PUNCT
ejpam-3448	47	14	,	,	PUNCT
ejpam-3448	47	15	734	734	NUM
ejpam-3448	47	16	-	-	SYM
ejpam-3448	47	17	748	748	NUM
ejpam-3448	47	18	736	736	NUM
ejpam-3448	47	19	nested	nested	ADJ
ejpam-3448	47	20	intersect	intersect	ADJ
ejpam-3448	47	21	adjacent	adjacent	ADJ
ejpam-3448	47	22	compatible	compatible	ADJ
ejpam-3448	47	23	figure	figure	NOUN
ejpam-3448	47	24	1	1	NUM
ejpam-3448	47	25	:	:	PUNCT
ejpam-3448	47	26	types	type	NOUN
ejpam-3448	47	27	of	of	ADP
ejpam-3448	47	28	tubes	tube	NOUN
ejpam-3448	47	29	the	the	DET
ejpam-3448	47	30	graph	graph	NOUN
ejpam-3448	47	31	associahedra	associahedra	NOUN
ejpam-3448	47	32	associated	associate	VERB
ejpam-3448	47	33	to	to	ADP
ejpam-3448	47	34	g.	g.	VERB
ejpam-3448	47	35	in	in	ADP
ejpam-3448	47	36	order	order	NOUN
ejpam-3448	47	37	to	to	PART
ejpam-3448	47	38	obtain	obtain	VERB
ejpam-3448	47	39	the	the	DET
ejpam-3448	47	40	geometric	geometric	ADJ
ejpam-3448	47	41	realization	realization	NOUN
ejpam-3448	47	42	kg	kg	NOUN
ejpam-3448	47	43	,	,	PUNCT
ejpam-3448	47	44	devadoss	devadoss	PROPN
ejpam-3448	47	45	produced	produce	VERB
ejpam-3448	47	46	a	a	DET
ejpam-3448	47	47	combinatorial	combinatorial	ADJ
ejpam-3448	47	48	way	way	NOUN
ejpam-3448	47	49	which	which	PRON
ejpam-3448	47	50	relates	relate	VERB
ejpam-3448	47	51	the	the	DET
ejpam-3448	47	52	tubings	tubing	NOUN
ejpam-3448	47	53	in	in	ADP
ejpam-3448	47	54	mg	mg	PROPN
ejpam-3448	47	55	with	with	ADP
ejpam-3448	47	56	the	the	DET
ejpam-3448	47	57	points	point	NOUN
ejpam-3448	47	58	in	in	ADP
ejpam-3448	47	59	space	space	NOUN
ejpam-3448	47	60	.	.	PUNCT
ejpam-3448	48	1	he	he	PRON
ejpam-3448	48	2	also	also	ADV
ejpam-3448	48	3	proved	prove	VERB
ejpam-3448	48	4	that	that	SCONJ
ejpam-3448	48	5	the	the	DET
ejpam-3448	48	6	convex	convex	PROPN
ejpam-3448	48	7	hull	hull	NOUN
ejpam-3448	48	8	of	of	ADP
ejpam-3448	48	9	these	these	DET
ejpam-3448	48	10	points	point	NOUN
ejpam-3448	48	11	yields	yield	VERB
ejpam-3448	48	12	the	the	DET
ejpam-3448	48	13	graph	graph	NOUN
ejpam-3448	48	14	associahedra	associahedra	X
ejpam-3448	48	15	kg	kg	PROPN
ejpam-3448	48	16	.	.	PUNCT
ejpam-3448	49	1	for	for	ADP
ejpam-3448	49	2	instance	instance	NOUN
ejpam-3448	49	3	,	,	PUNCT
ejpam-3448	49	4	the	the	DET
ejpam-3448	49	5	graph	graph	NOUN
ejpam-3448	49	6	associahedra	associahedra	PRON
ejpam-3448	49	7	kg	kg	PROPN
ejpam-3448	49	8	associated	associate	VERB
ejpam-3448	49	9	to	to	ADP
ejpam-3448	49	10	the	the	DET
ejpam-3448	49	11	graph	graph	NOUN
ejpam-3448	49	12	g	g	NOUN
ejpam-3448	49	13	with	with	ADP
ejpam-3448	49	14	n	n	ADP
ejpam-3448	49	15	disconnected	disconnected	ADJ
ejpam-3448	49	16	nodes	node	NOUN
ejpam-3448	49	17	is	be	AUX
ejpam-3448	49	18	a	a	DET
ejpam-3448	49	19	simplex	simplex	NOUN
ejpam-3448	49	20	∆n−1	∆n−1	PROPN
ejpam-3448	49	21	in	in	ADP
ejpam-3448	49	22	rn	rn	NOUN
ejpam-3448	49	23	given	give	VERB
ejpam-3448	49	24	in	in	ADP
ejpam-3448	49	25	terms	term	NOUN
ejpam-3448	49	26	of	of	ADP
ejpam-3448	49	27	barycentric	barycentric	ADJ
ejpam-3448	49	28	coordinates	coordinate	NOUN
ejpam-3448	49	29	.	.	PUNCT
ejpam-3448	50	1	from	from	ADP
ejpam-3448	50	2	another	another	DET
ejpam-3448	50	3	point	point	NOUN
ejpam-3448	50	4	of	of	ADP
ejpam-3448	50	5	view	view	NOUN
ejpam-3448	50	6	,	,	PUNCT
ejpam-3448	50	7	his	his	PRON
ejpam-3448	50	8	method	method	NOUN
ejpam-3448	50	9	creates	create	VERB
ejpam-3448	50	10	a	a	DET
ejpam-3448	50	11	system	system	NOUN
ejpam-3448	50	12	or	or	CCONJ
ejpam-3448	50	13	a	a	DET
ejpam-3448	50	14	set	set	NOUN
ejpam-3448	50	15	of	of	ADP
ejpam-3448	50	16	affine	affine	NOUN
ejpam-3448	50	17	hyperplanes	hyperplane	NOUN
ejpam-3448	50	18	to	to	PART
ejpam-3448	50	19	truncate	truncate	VERB
ejpam-3448	50	20	the	the	DET
ejpam-3448	50	21	standart	standart	NOUN
ejpam-3448	50	22	simplex	simplex	NOUN
ejpam-3448	50	23	.	.	PUNCT
ejpam-3448	51	1	it	it	PRON
ejpam-3448	51	2	is	be	AUX
ejpam-3448	51	3	easily	easily	ADV
ejpam-3448	51	4	seen	see	VERB
ejpam-3448	51	5	that	that	SCONJ
ejpam-3448	51	6	these	these	DET
ejpam-3448	51	7	hyperplanes	hyperplane	NOUN
ejpam-3448	51	8	appear	appear	VERB
ejpam-3448	51	9	by	by	ADP
ejpam-3448	51	10	adding	add	VERB
ejpam-3448	51	11	a	a	DET
ejpam-3448	51	12	new	new	ADJ
ejpam-3448	51	13	edge	edge	NOUN
ejpam-3448	51	14	between	between	ADP
ejpam-3448	51	15	two	two	NUM
ejpam-3448	51	16	nodes	node	NOUN
ejpam-3448	51	17	in	in	ADP
ejpam-3448	51	18	the	the	DET
ejpam-3448	51	19	graph	graph	NOUN
ejpam-3448	51	20	and	and	CCONJ
ejpam-3448	51	21	it	it	PRON
ejpam-3448	51	22	causes	cause	VERB
ejpam-3448	51	23	new	new	ADJ
ejpam-3448	51	24	truncations	truncation	NOUN
ejpam-3448	51	25	in	in	ADP
ejpam-3448	51	26	which	which	PRON
ejpam-3448	51	27	new	new	ADJ
ejpam-3448	51	28	faces	face	NOUN
ejpam-3448	51	29	appear	appear	VERB
ejpam-3448	51	30	.	.	PUNCT
ejpam-3448	52	1	a	a	DET
ejpam-3448	52	2	remarkable	remarkable	ADJ
ejpam-3448	52	3	feature	feature	NOUN
ejpam-3448	52	4	of	of	ADP
ejpam-3448	52	5	a	a	DET
ejpam-3448	52	6	graph	graph	NOUN
ejpam-3448	52	7	associahedra	associahedra	NOUN
ejpam-3448	52	8	is	be	AUX
ejpam-3448	52	9	that	that	SCONJ
ejpam-3448	52	10	the	the	DET
ejpam-3448	52	11	faces	face	NOUN
ejpam-3448	52	12	of	of	ADP
ejpam-3448	52	13	it	it	PRON
ejpam-3448	52	14	can	can	AUX
ejpam-3448	52	15	be	be	AUX
ejpam-3448	52	16	obtained	obtain	VERB
ejpam-3448	52	17	by	by	ADP
ejpam-3448	52	18	a	a	DET
ejpam-3448	52	19	product	product	NOUN
ejpam-3448	52	20	of	of	ADP
ejpam-3448	52	21	other	other	ADJ
ejpam-3448	52	22	two	two	NUM
ejpam-3448	52	23	graph	graph	NOUN
ejpam-3448	52	24	associahedra	associahedra	PROPN
ejpam-3448	52	25	.	.	PROPN
ejpam-3448	52	26	carr	carr	PROPN
ejpam-3448	52	27	and	and	CCONJ
ejpam-3448	52	28	devadoss	devadoss	PROPN
ejpam-3448	52	29	described	describe	VERB
ejpam-3448	52	30	the	the	DET
ejpam-3448	52	31	face	face	NOUN
ejpam-3448	52	32	structure	structure	NOUN
ejpam-3448	52	33	of	of	ADP
ejpam-3448	52	34	the	the	DET
ejpam-3448	52	35	graph	graph	NOUN
ejpam-3448	52	36	associahedra	associahedra	INTJ
ejpam-3448	52	37	kg	kg	PROPN
ejpam-3448	52	38	in	in	ADP
ejpam-3448	52	39	[	[	X
ejpam-3448	52	40	1	1	NUM
ejpam-3448	52	41	]	]	PUNCT
ejpam-3448	52	42	.	.	PUNCT
ejpam-3448	53	1	given	give	VERB
ejpam-3448	53	2	a	a	DET
ejpam-3448	53	3	graph	graph	NOUN
ejpam-3448	53	4	g	g	NOUN
ejpam-3448	53	5	and	and	CCONJ
ejpam-3448	53	6	a	a	DET
ejpam-3448	53	7	tube	tube	NOUN
ejpam-3448	53	8	t	t	NOUN
ejpam-3448	53	9	on	on	ADP
ejpam-3448	53	10	g	g	PROPN
ejpam-3448	53	11	,	,	PUNCT
ejpam-3448	53	12	they	they	PRON
ejpam-3448	53	13	defined	define	VERB
ejpam-3448	53	14	the	the	DET
ejpam-3448	53	15	reconnected	reconnected	ADJ
ejpam-3448	53	16	complement	complement	NOUN
ejpam-3448	53	17	graph	graph	NOUN
ejpam-3448	53	18	g∗(t	g∗(t	NOUN
ejpam-3448	53	19	)	)	PUNCT
ejpam-3448	53	20	of	of	ADP
ejpam-3448	53	21	t	t	PROPN
ejpam-3448	53	22	in	in	ADP
ejpam-3448	53	23	g	g	PROPN
ejpam-3448	53	24	as	as	SCONJ
ejpam-3448	53	25	follows	follow	VERB
ejpam-3448	53	26	:	:	PUNCT
ejpam-3448	53	27	•	•	ADV
ejpam-3448	53	28	let	let	VERB
ejpam-3448	53	29	v	v	PART
ejpam-3448	53	30	denote	denote	VERB
ejpam-3448	53	31	the	the	DET
ejpam-3448	53	32	set	set	NOUN
ejpam-3448	53	33	of	of	ADP
ejpam-3448	53	34	nodes	node	NOUN
ejpam-3448	53	35	of	of	ADP
ejpam-3448	53	36	g	g	NOUN
ejpam-3448	53	37	,	,	PUNCT
ejpam-3448	53	38	then	then	ADV
ejpam-3448	53	39	v	v	NOUN
ejpam-3448	53	40	\	\	PROPN
ejpam-3448	53	41	t	t	PROPN
ejpam-3448	53	42	is	be	AUX
ejpam-3448	53	43	the	the	DET
ejpam-3448	53	44	set	set	NOUN
ejpam-3448	53	45	of	of	ADP
ejpam-3448	53	46	nodes	node	NOUN
ejpam-3448	53	47	of	of	ADP
ejpam-3448	53	48	g∗(t	g∗(t	NOUN
ejpam-3448	53	49	)	)	PUNCT
ejpam-3448	53	50	.	.	PUNCT
ejpam-3448	54	1	•	•	NUM
ejpam-3448	54	2	let	let	VERB
ejpam-3448	54	3	v1	v1	NOUN
ejpam-3448	54	4	,	,	PUNCT
ejpam-3448	54	5	v2	v2	PROPN
ejpam-3448	54	6	∈	∈	PROPN
ejpam-3448	54	7	v	v	NOUN
ejpam-3448	54	8	\	\	NOUN
ejpam-3448	55	1	t.	t.	NOUN
ejpam-3448	55	2	there	there	PRON
ejpam-3448	55	3	is	be	VERB
ejpam-3448	55	4	an	an	DET
ejpam-3448	55	5	edge	edge	NOUN
ejpam-3448	55	6	between	between	ADP
ejpam-3448	55	7	v1	v1	NOUN
ejpam-3448	55	8	and	and	CCONJ
ejpam-3448	55	9	v2	v2	PROPN
ejpam-3448	55	10	if	if	SCONJ
ejpam-3448	55	11	either	either	CCONJ
ejpam-3448	55	12	{	{	PUNCT
ejpam-3448	55	13	v1	v1	NOUN
ejpam-3448	55	14	,	,	PUNCT
ejpam-3448	55	15	v2	v2	NOUN
ejpam-3448	55	16	}	}	PUNCT
ejpam-3448	55	17	or	or	CCONJ
ejpam-3448	55	18	{	{	PUNCT
ejpam-3448	55	19	v1	v1	NOUN
ejpam-3448	55	20	,	,	PUNCT
ejpam-3448	55	21	v2}∪	v2}∪	PROPN
ejpam-3448	55	22	t	t	PROPN
ejpam-3448	55	23	is	be	AUX
ejpam-3448	55	24	connected	connect	VERB
ejpam-3448	55	25	in	in	ADP
ejpam-3448	55	26	g.	g.	PROPN
ejpam-3448	55	27	theorem	theorem	PROPN
ejpam-3448	55	28	1	1	NUM
ejpam-3448	55	29	.	.	PUNCT
ejpam-3448	56	1	all	all	DET
ejpam-3448	56	2	facets	facet	NOUN
ejpam-3448	56	3	of	of	ADP
ejpam-3448	56	4	kg	kg	NOUN
ejpam-3448	56	5	correspond	correspond	VERB
ejpam-3448	56	6	to	to	ADP
ejpam-3448	56	7	the	the	DET
ejpam-3448	56	8	set	set	NOUN
ejpam-3448	56	9	of	of	ADP
ejpam-3448	56	10	1	1	NUM
ejpam-3448	56	11	-	-	PUNCT
ejpam-3448	56	12	tubings	tubing	NOUN
ejpam-3448	56	13	.	.	PUNCT
ejpam-3448	57	1	in	in	ADP
ejpam-3448	57	2	particular	particular	ADJ
ejpam-3448	57	3	,	,	PUNCT
ejpam-3448	57	4	a	a	DET
ejpam-3448	57	5	facet	facet	NOUN
ejpam-3448	57	6	associated	associate	VERB
ejpam-3448	57	7	to	to	ADP
ejpam-3448	57	8	a	a	DET
ejpam-3448	57	9	1	1	NUM
ejpam-3448	57	10	-	-	PUNCT
ejpam-3448	57	11	tubing	tubing	NOUN
ejpam-3448	57	12	t	t	NOUN
ejpam-3448	57	13	=	=	SYM
ejpam-3448	57	14	{	{	PUNCT
ejpam-3448	57	15	g	g	PROPN
ejpam-3448	57	16	,	,	PUNCT
ejpam-3448	57	17	t	t	PROPN
ejpam-3448	57	18	}	}	PUNCT
ejpam-3448	57	19	is	be	AUX
ejpam-3448	57	20	combinatorially	combinatorially	ADV
ejpam-3448	57	21	equivalent	equivalent	ADJ
ejpam-3448	57	22	to	to	ADP
ejpam-3448	57	23	kg(t)×kg∗(t	kg(t)×kg∗(t	NOUN
ejpam-3448	57	24	)	)	PUNCT
ejpam-3448	57	25	,	,	PUNCT
ejpam-3448	57	26	where	where	SCONJ
ejpam-3448	57	27	kg(t	kg(t	NOUN
ejpam-3448	57	28	)	)	PUNCT
ejpam-3448	57	29	and	and	CCONJ
ejpam-3448	57	30	kg∗(t	kg∗(t	NOUN
ejpam-3448	57	31	)	)	PUNCT
ejpam-3448	57	32	are	be	AUX
ejpam-3448	57	33	graph	graph	VERB
ejpam-3448	57	34	associahedra	associahedra	PRON
ejpam-3448	57	35	corresponding	correspond	VERB
ejpam-3448	57	36	to	to	ADP
ejpam-3448	57	37	the	the	DET
ejpam-3448	57	38	tube	tube	NOUN
ejpam-3448	57	39	t	t	NOUN
ejpam-3448	57	40	and	and	CCONJ
ejpam-3448	57	41	the	the	DET
ejpam-3448	57	42	reconnected	reconnecte	VERB
ejpam-3448	57	43	complement	complement	NOUN
ejpam-3448	57	44	of	of	ADP
ejpam-3448	57	45	t	t	PROPN
ejpam-3448	57	46	in	in	ADP
ejpam-3448	57	47	g	g	PROPN
ejpam-3448	57	48	,	,	PUNCT
ejpam-3448	57	49	respectively	respectively	ADV
ejpam-3448	57	50	.	.	PUNCT
ejpam-3448	58	1	one	one	NUM
ejpam-3448	58	2	of	of	ADP
ejpam-3448	58	3	the	the	DET
ejpam-3448	58	4	most	most	ADV
ejpam-3448	58	5	well	well	ADV
ejpam-3448	58	6	-	-	PUNCT
ejpam-3448	58	7	known	know	VERB
ejpam-3448	58	8	graph	graph	NOUN
ejpam-3448	58	9	associahedra	associahedra	NOUN
ejpam-3448	58	10	is	be	AUX
ejpam-3448	58	11	the	the	DET
ejpam-3448	58	12	stasheff	stasheff	PROPN
ejpam-3448	58	13	polytope	polytope	PROPN
ejpam-3448	58	14	kn−1	kn−1	PROPN
ejpam-3448	58	15	,	,	PUNCT
ejpam-3448	58	16	also	also	ADV
ejpam-3448	58	17	called	call	VERB
ejpam-3448	58	18	associahedron	associahedron	NOUN
ejpam-3448	58	19	.	.	PUNCT
ejpam-3448	59	1	it	it	PRON
ejpam-3448	59	2	becomes	become	VERB
ejpam-3448	59	3	the	the	DET
ejpam-3448	59	4	realization	realization	NOUN
ejpam-3448	59	5	of	of	ADP
ejpam-3448	59	6	the	the	DET
ejpam-3448	59	7	poset	poset	NOUN
ejpam-3448	59	8	pp(n	pp(n	PROPN
ejpam-3448	59	9	)	)	PUNCT
ejpam-3448	59	10	,	,	PUNCT
ejpam-3448	59	11	where	where	SCONJ
ejpam-3448	59	12	p(n	p(n	NOUN
ejpam-3448	59	13	)	)	PUNCT
ejpam-3448	59	14	denotes	denote	VERB
ejpam-3448	59	15	an	an	DET
ejpam-3448	59	16	n	n	NOUN
ejpam-3448	59	17	-	-	PUNCT
ejpam-3448	59	18	path	path	NOUN
ejpam-3448	59	19	which	which	PRON
ejpam-3448	59	20	has	have	VERB
ejpam-3448	59	21	n	n	PRON
ejpam-3448	59	22	nodes	node	NOUN
ejpam-3448	59	23	labeled	label	VERB
ejpam-3448	59	24	by	by	ADP
ejpam-3448	59	25	the	the	DET
ejpam-3448	59	26	set	set	NOUN
ejpam-3448	59	27	{	{	PUNCT
ejpam-3448	59	28	1	1	NUM
ejpam-3448	59	29	,	,	PUNCT
ejpam-3448	59	30	2	2	NUM
ejpam-3448	59	31	,	,	PUNCT
ejpam-3448	59	32	.	.	PUNCT
ejpam-3448	59	33	.	.	PUNCT
ejpam-3448	60	1	.	.	PUNCT
ejpam-3448	61	1	,	,	PUNCT
ejpam-3448	61	2	n	n	CCONJ
ejpam-3448	61	3	}	}	PUNCT
ejpam-3448	61	4	with	with	ADP
ejpam-3448	61	5	an	an	DET
ejpam-3448	61	6	increasing	increase	VERB
ejpam-3448	61	7	order	order	NOUN
ejpam-3448	61	8	.	.	PUNCT
ejpam-3448	62	1	the	the	DET
ejpam-3448	62	2	classical	classical	ADJ
ejpam-3448	62	3	definition	definition	NOUN
ejpam-3448	62	4	of	of	ADP
ejpam-3448	62	5	an	an	DET
ejpam-3448	62	6	associahedron	associahedron	ADJ
ejpam-3448	62	7	kn	kn	PROPN
ejpam-3448	62	8	is	be	AUX
ejpam-3448	62	9	that	that	SCONJ
ejpam-3448	62	10	it	it	PRON
ejpam-3448	62	11	is	be	AUX
ejpam-3448	62	12	an	an	DET
ejpam-3448	62	13	n	n	ADV
ejpam-3448	62	14	-	-	PUNCT
ejpam-3448	62	15	dimensional	dimensional	ADJ
ejpam-3448	62	16	cell	cell	NOUN
ejpam-3448	62	17	complex	complex	NOUN
ejpam-3448	62	18	whose	whose	DET
ejpam-3448	62	19	cells	cell	NOUN
ejpam-3448	62	20	are	be	AUX
ejpam-3448	62	21	indexed	index	VERB
ejpam-3448	62	22	by	by	ADP
ejpam-3448	62	23	the	the	DET
ejpam-3448	62	24	meaningful	meaningful	ADJ
ejpam-3448	62	25	bracketings	bracketing	NOUN
ejpam-3448	62	26	of	of	ADP
ejpam-3448	62	27	(	(	PUNCT
ejpam-3448	62	28	n	n	X
ejpam-3448	62	29	+	+	CCONJ
ejpam-3448	62	30	2	2	NUM
ejpam-3448	62	31	)	)	PUNCT
ejpam-3448	62	32	variables	variable	NOUN
ejpam-3448	62	33	1	1	NUM
ejpam-3448	62	34	,	,	PUNCT
ejpam-3448	62	35	.	.	PUNCT
ejpam-3448	62	36	.	.	PUNCT
ejpam-3448	63	1	.	.	PUNCT
ejpam-3448	64	1	,	,	PUNCT
ejpam-3448	64	2	n	n	PROPN
ejpam-3448	64	3	+	+	NOUN
ejpam-3448	64	4	2	2	X
ejpam-3448	64	5	.	.	X
ejpam-3448	65	1	this	this	DET
ejpam-3448	65	2	cell	cell	NOUN
ejpam-3448	65	3	complex	complex	NOUN
ejpam-3448	65	4	has	have	VERB
ejpam-3448	65	5	a	a	DET
ejpam-3448	65	6	relation	relation	NOUN
ejpam-3448	65	7	with	with	ADP
ejpam-3448	65	8	the	the	DET
ejpam-3448	65	9	set	set	NOUN
ejpam-3448	65	10	of	of	ADP
ejpam-3448	65	11	the	the	DET
ejpam-3448	65	12	planar	planar	ADJ
ejpam-3448	65	13	rooted	root	VERB
ejpam-3448	65	14	trees	tree	NOUN
ejpam-3448	65	15	,	,	PUNCT
ejpam-3448	65	16	tree(n	tree(n	NOUN
ejpam-3448	65	17	+	+	CCONJ
ejpam-3448	65	18	1	1	NUM
ejpam-3448	65	19	)	)	PUNCT
ejpam-3448	65	20	,	,	PUNCT
ejpam-3448	65	21	with	with	ADP
ejpam-3448	65	22	(	(	PUNCT
ejpam-3448	65	23	n	n	X
ejpam-3448	65	24	+	+	CCONJ
ejpam-3448	65	25	2	2	NUM
ejpam-3448	65	26	)	)	PUNCT
ejpam-3448	65	27	leaves	leave	NOUN
ejpam-3448	65	28	.	.	PUNCT
ejpam-3448	66	1	each	each	DET
ejpam-3448	66	2	k	k	ADJ
ejpam-3448	66	3	-	-	ADJ
ejpam-3448	66	4	dimensional	dimensional	ADJ
ejpam-3448	66	5	cell	cell	NOUN
ejpam-3448	66	6	can	can	AUX
ejpam-3448	66	7	be	be	AUX
ejpam-3448	66	8	indexed	index	VERB
ejpam-3448	66	9	by	by	ADP
ejpam-3448	66	10	a	a	DET
ejpam-3448	66	11	rooted	rooted	ADJ
ejpam-3448	66	12	tree	tree	NOUN
ejpam-3448	66	13	which	which	PRON
ejpam-3448	66	14	has	have	VERB
ejpam-3448	66	15	(	(	PUNCT
ejpam-3448	66	16	n	n	X
ejpam-3448	66	17	+	+	CCONJ
ejpam-3448	66	18	2	2	NUM
ejpam-3448	66	19	)	)	PUNCT
ejpam-3448	66	20	leaves	leave	NOUN
ejpam-3448	66	21	and	and	CCONJ
ejpam-3448	66	22	(	(	PUNCT
ejpam-3448	66	23	n	n	CCONJ
ejpam-3448	66	24	−	−	PROPN
ejpam-3448	66	25	k	k	NOUN
ejpam-3448	67	1	+	+	CCONJ
ejpam-3448	67	2	1	1	X
ejpam-3448	67	3	)	)	PUNCT
ejpam-3448	67	4	internal	internal	ADJ
ejpam-3448	67	5	vertices	vertex	NOUN
ejpam-3448	67	6	.	.	PUNCT
ejpam-3448	68	1	moreover	moreover	ADV
ejpam-3448	68	2	,	,	PUNCT
ejpam-3448	68	3	the	the	DET
ejpam-3448	68	4	vertices	vertex	NOUN
ejpam-3448	68	5	of	of	ADP
ejpam-3448	68	6	kn	kn	PROPN
ejpam-3448	68	7	can	can	AUX
ejpam-3448	68	8	be	be	AUX
ejpam-3448	68	9	indexed	index	VERB
ejpam-3448	68	10	by	by	ADP
ejpam-3448	68	11	the	the	DET
ejpam-3448	68	12	elements	element	NOUN
ejpam-3448	68	13	of	of	ADP
ejpam-3448	68	14	the	the	DET
ejpam-3448	68	15	set	set	NOUN
ejpam-3448	68	16	yn+1	yn+1	PROPN
ejpam-3448	68	17	of	of	ADP
ejpam-3448	68	18	planar	planar	ADJ
ejpam-3448	68	19	binary	binary	ADJ
ejpam-3448	68	20	rooted	rooted	ADJ
ejpam-3448	68	21	trees	tree	NOUN
ejpam-3448	68	22	.	.	PUNCT
ejpam-3448	69	1	in	in	ADP
ejpam-3448	69	2	[	[	X
ejpam-3448	69	3	3	3	NUM
ejpam-3448	69	4	]	]	PUNCT
ejpam-3448	69	5	,	,	PUNCT
ejpam-3448	69	6	forcey	forcey	PROPN
ejpam-3448	69	7	s.	s.	PROPN
ejpam-3448	69	8	k.	k.	PROPN
ejpam-3448	69	9	gürbüzer	gürbüzer	PROPN
ejpam-3448	69	10	,	,	PUNCT
ejpam-3448	69	11	b.	b.	PROPN
ejpam-3448	69	12	akyar	akyar	PROPN
ejpam-3448	69	13	/	/	SYM
ejpam-3448	69	14	eur	eur	PROPN
ejpam-3448	69	15	.	.	PUNCT
ejpam-3448	70	1	j.	j.	PROPN
ejpam-3448	70	2	pure	pure	PROPN
ejpam-3448	70	3	appl	appl	PROPN
ejpam-3448	70	4	.	.	PROPN
ejpam-3448	70	5	math	math	PROPN
ejpam-3448	70	6	,	,	PUNCT
ejpam-3448	70	7	12	12	NUM
ejpam-3448	70	8	(	(	PUNCT
ejpam-3448	70	9	3	3	NUM
ejpam-3448	70	10	)	)	PUNCT
ejpam-3448	70	11	(	(	PUNCT
ejpam-3448	70	12	2019	2019	NUM
ejpam-3448	70	13	)	)	PUNCT
ejpam-3448	70	14	,	,	PUNCT
ejpam-3448	70	15	734	734	NUM
ejpam-3448	70	16	-	-	SYM
ejpam-3448	70	17	748	748	NUM
ejpam-3448	70	18	737	737	NUM
ejpam-3448	70	19	and	and	CCONJ
ejpam-3448	70	20	springfield	springfield	PROPN
ejpam-3448	70	21	described	describe	VERB
ejpam-3448	70	22	a	a	DET
ejpam-3448	70	23	bijection	bijection	NOUN
ejpam-3448	70	24	between	between	ADP
ejpam-3448	70	25	the	the	DET
ejpam-3448	70	26	set	set	NOUN
ejpam-3448	70	27	of	of	ADP
ejpam-3448	70	28	planar	planar	ADJ
ejpam-3448	70	29	rooted	root	VERB
ejpam-3448	70	30	trees	tree	NOUN
ejpam-3448	70	31	tree(n	tree(n	PROPN
ejpam-3448	70	32	)	)	PUNCT
ejpam-3448	70	33	and	and	CCONJ
ejpam-3448	70	34	the	the	DET
ejpam-3448	70	35	set	set	NOUN
ejpam-3448	70	36	pp(n	pp(n	NUM
ejpam-3448	70	37	)	)	PUNCT
ejpam-3448	70	38	of	of	ADP
ejpam-3448	70	39	tubings	tubing	NOUN
ejpam-3448	70	40	on	on	ADP
ejpam-3448	70	41	an	an	DET
ejpam-3448	70	42	n	n	NOUN
ejpam-3448	70	43	-	-	PUNCT
ejpam-3448	70	44	path	path	NOUN
ejpam-3448	70	45	.	.	PUNCT
ejpam-3448	71	1	the	the	DET
ejpam-3448	71	2	constructions	construction	NOUN
ejpam-3448	71	3	of	of	ADP
ejpam-3448	71	4	an	an	DET
ejpam-3448	71	5	associahedron	associahedron	NOUN
ejpam-3448	71	6	given	give	VERB
ejpam-3448	71	7	in	in	ADP
ejpam-3448	71	8	loday	loday	PROPN
ejpam-3448	71	9	[	[	X
ejpam-3448	71	10	6	6	NUM
ejpam-3448	71	11	]	]	PUNCT
ejpam-3448	71	12	,	,	PUNCT
ejpam-3448	71	13	markl	markl	PROPN
ejpam-3448	72	1	[	[	X
ejpam-3448	72	2	9	9	NUM
ejpam-3448	72	3	]	]	PUNCT
ejpam-3448	72	4	and	and	CCONJ
ejpam-3448	72	5	devadoss	devadoss	ADJ
ejpam-3448	73	1	[	[	X
ejpam-3448	73	2	2	2	NUM
ejpam-3448	73	3	]	]	PUNCT
ejpam-3448	73	4	have	have	VERB
ejpam-3448	73	5	similarities	similarity	NOUN
ejpam-3448	73	6	on	on	ADP
ejpam-3448	73	7	specifying	specify	VERB
ejpam-3448	73	8	the	the	DET
ejpam-3448	73	9	coordinates	coordinate	NOUN
ejpam-3448	73	10	of	of	ADP
ejpam-3448	73	11	the	the	DET
ejpam-3448	73	12	vertices	vertex	NOUN
ejpam-3448	73	13	.	.	PUNCT
ejpam-3448	74	1	basically	basically	ADV
ejpam-3448	74	2	,	,	PUNCT
ejpam-3448	74	3	loday	loday	PROPN
ejpam-3448	74	4	used	use	VERB
ejpam-3448	74	5	the	the	DET
ejpam-3448	74	6	function	function	NOUN
ejpam-3448	74	7	f(n	f(n	PROPN
ejpam-3448	74	8	)	)	PUNCT
ejpam-3448	75	1	=	=	PUNCT
ejpam-3448	75	2	n(n+	n(n+	NOUN
ejpam-3448	75	3	1	1	NUM
ejpam-3448	75	4	)	)	SYM
ejpam-3448	75	5	2	2	NUM
ejpam-3448	75	6	and	and	CCONJ
ejpam-3448	75	7	markl	markl	PROPN
ejpam-3448	75	8	used	use	VERB
ejpam-3448	75	9	an	an	DET
ejpam-3448	75	10	exponential	exponential	ADJ
ejpam-3448	75	11	function	function	NOUN
ejpam-3448	75	12	f(n	f(n	PROPN
ejpam-3448	75	13	)	)	PUNCT
ejpam-3448	76	1	=	=	SYM
ejpam-3448	77	1	3n	3n	NUM
ejpam-3448	77	2	.	.	PUNCT
ejpam-3448	77	3	devadoss	devadoss	ADJ
ejpam-3448	78	1	[	[	X
ejpam-3448	78	2	2	2	NUM
ejpam-3448	78	3	]	]	PUNCT
ejpam-3448	78	4	preferred	prefer	VERB
ejpam-3448	78	5	to	to	PART
ejpam-3448	78	6	use	use	VERB
ejpam-3448	78	7	an	an	DET
ejpam-3448	78	8	exponential	exponential	ADJ
ejpam-3448	78	9	function	function	NOUN
ejpam-3448	78	10	and	and	CCONJ
ejpam-3448	78	11	took	take	VERB
ejpam-3448	78	12	attention	attention	NOUN
ejpam-3448	78	13	to	to	ADP
ejpam-3448	78	14	the	the	DET
ejpam-3448	78	15	chosen	choose	VERB
ejpam-3448	78	16	function	function	NOUN
ejpam-3448	78	17	which	which	PRON
ejpam-3448	78	18	can	can	AUX
ejpam-3448	78	19	cause	cause	VERB
ejpam-3448	78	20	deep	deep	ADJ
ejpam-3448	78	21	cuts	cut	NOUN
ejpam-3448	78	22	during	during	ADP
ejpam-3448	78	23	the	the	DET
ejpam-3448	78	24	truncation	truncation	NOUN
ejpam-3448	78	25	process	process	NOUN
ejpam-3448	78	26	of	of	ADP
ejpam-3448	78	27	the	the	DET
ejpam-3448	78	28	simplex	simplex	NOUN
ejpam-3448	78	29	.	.	PUNCT
ejpam-3448	79	1	in	in	ADP
ejpam-3448	79	2	their	their	PRON
ejpam-3448	79	3	methods	method	NOUN
ejpam-3448	79	4	,	,	PUNCT
ejpam-3448	79	5	it	it	PRON
ejpam-3448	79	6	can	can	AUX
ejpam-3448	79	7	be	be	AUX
ejpam-3448	79	8	easily	easily	ADV
ejpam-3448	79	9	seen	see	VERB
ejpam-3448	79	10	that	that	SCONJ
ejpam-3448	79	11	the	the	DET
ejpam-3448	79	12	boundary	boundary	ADJ
ejpam-3448	79	13	cells	cell	NOUN
ejpam-3448	79	14	of	of	ADP
ejpam-3448	79	15	kn	kn	PROPN
ejpam-3448	79	16	are	be	AUX
ejpam-3448	79	17	of	of	ADP
ejpam-3448	79	18	the	the	DET
ejpam-3448	79	19	form	form	NOUN
ejpam-3448	79	20	kp	kp	PROPN
ejpam-3448	79	21	×kq	×kq	PROPN
ejpam-3448	79	22	,	,	PUNCT
ejpam-3448	79	23	where	where	SCONJ
ejpam-3448	79	24	p+	p+	VERB
ejpam-3448	79	25	q	q	NOUN
ejpam-3448	79	26	=	=	PUNCT
ejpam-3448	79	27	n−	n−	NOUN
ejpam-3448	79	28	1	1	NUM
ejpam-3448	79	29	.	.	PUNCT
ejpam-3448	80	1	there	there	PRON
ejpam-3448	80	2	is	be	VERB
ejpam-3448	80	3	also	also	ADV
ejpam-3448	80	4	another	another	DET
ejpam-3448	80	5	poset	poset	NOUN
ejpam-3448	80	6	structure	structure	NOUN
ejpam-3448	80	7	on	on	ADP
ejpam-3448	80	8	the	the	DET
ejpam-3448	80	9	vertices	vertex	NOUN
ejpam-3448	80	10	of	of	ADP
ejpam-3448	80	11	an	an	DET
ejpam-3448	80	12	associahedron	associahedron	NOUN
ejpam-3448	80	13	.	.	PUNCT
ejpam-3448	81	1	the	the	DET
ejpam-3448	81	2	partial	partial	ADJ
ejpam-3448	81	3	order	order	NOUN
ejpam-3448	81	4	in	in	ADP
ejpam-3448	81	5	this	this	DET
ejpam-3448	81	6	structure	structure	NOUN
ejpam-3448	81	7	is	be	AUX
ejpam-3448	81	8	called	call	VERB
ejpam-3448	81	9	the	the	DET
ejpam-3448	81	10	tamari	tamari	ADJ
ejpam-3448	81	11	order	order	NOUN
ejpam-3448	81	12	on	on	ADP
ejpam-3448	81	13	mp(n	mp(n	NOUN
ejpam-3448	81	14	)	)	PUNCT
ejpam-3448	81	15	and	and	CCONJ
ejpam-3448	81	16	defined	define	VERB
ejpam-3448	81	17	for	for	ADP
ejpam-3448	81	18	two	two	NUM
ejpam-3448	81	19	maximal	maximal	ADJ
ejpam-3448	81	20	tubings	tubing	NOUN
ejpam-3448	81	21	t1	t1	VERB
ejpam-3448	81	22	,	,	PUNCT
ejpam-3448	81	23	t2	t2	NOUN
ejpam-3448	81	24	in	in	ADP
ejpam-3448	81	25	mp(n	mp(n	NOUN
ejpam-3448	81	26	)	)	PUNCT
ejpam-3448	81	27	such	such	ADJ
ejpam-3448	81	28	that	that	SCONJ
ejpam-3448	81	29	t1	t1	NOUN
ejpam-3448	81	30	<	<	X
ejpam-3448	81	31	t2	t2	PROPN
ejpam-3448	81	32	if	if	SCONJ
ejpam-3448	81	33	t2	t2	NOUN
ejpam-3448	81	34	can	can	AUX
ejpam-3448	81	35	be	be	AUX
ejpam-3448	81	36	obtained	obtain	VERB
ejpam-3448	81	37	from	from	ADP
ejpam-3448	81	38	t1	t1	NOUN
ejpam-3448	81	39	by	by	ADP
ejpam-3448	81	40	sliding	slide	VERB
ejpam-3448	81	41	a	a	DET
ejpam-3448	81	42	tube	tube	NOUN
ejpam-3448	81	43	from	from	ADP
ejpam-3448	81	44	left	left	ADJ
ejpam-3448	81	45	to	to	ADP
ejpam-3448	81	46	right	right	NOUN
ejpam-3448	81	47	.	.	PUNCT
ejpam-3448	82	1	by	by	ADP
ejpam-3448	82	2	using	use	VERB
ejpam-3448	82	3	this	this	DET
ejpam-3448	82	4	poset	poset	NOUN
ejpam-3448	82	5	structure	structure	NOUN
ejpam-3448	82	6	,	,	PUNCT
ejpam-3448	82	7	loday	loday	PROPN
ejpam-3448	82	8	[	[	X
ejpam-3448	82	9	7	7	X
ejpam-3448	82	10	]	]	PUNCT
ejpam-3448	82	11	proved	prove	VERB
ejpam-3448	82	12	that	that	SCONJ
ejpam-3448	82	13	an	an	DET
ejpam-3448	82	14	associahedron	associahedron	ADJ
ejpam-3448	82	15	kn	kn	PROPN
ejpam-3448	82	16	admits	admit	VERB
ejpam-3448	82	17	a	a	DET
ejpam-3448	82	18	triangulation	triangulation	NOUN
ejpam-3448	82	19	by	by	ADP
ejpam-3448	82	20	(	(	PUNCT
ejpam-3448	82	21	n+	n+	NUM
ejpam-3448	82	22	1)n−1	1)n−1	NUM
ejpam-3448	82	23	simplices	simplice	NOUN
ejpam-3448	82	24	.	.	PUNCT
ejpam-3448	83	1	this	this	DET
ejpam-3448	83	2	triangulation	triangulation	NOUN
ejpam-3448	83	3	is	be	AUX
ejpam-3448	83	4	compatible	compatible	ADJ
ejpam-3448	83	5	with	with	ADP
ejpam-3448	83	6	the	the	DET
ejpam-3448	83	7	tamari	tamari	ADJ
ejpam-3448	83	8	order	order	NOUN
ejpam-3448	83	9	and	and	CCONJ
ejpam-3448	83	10	one	one	NOUN
ejpam-3448	83	11	can	can	AUX
ejpam-3448	83	12	also	also	ADV
ejpam-3448	83	13	give	give	VERB
ejpam-3448	83	14	an	an	DET
ejpam-3448	83	15	orientation	orientation	NOUN
ejpam-3448	83	16	to	to	ADP
ejpam-3448	83	17	the	the	DET
ejpam-3448	83	18	facets	facet	NOUN
ejpam-3448	83	19	of	of	ADP
ejpam-3448	83	20	an	an	DET
ejpam-3448	83	21	associahedron	associahedron	NOUN
ejpam-3448	83	22	with	with	ADP
ejpam-3448	83	23	respect	respect	NOUN
ejpam-3448	83	24	to	to	ADP
ejpam-3448	83	25	this	this	DET
ejpam-3448	83	26	order	order	NOUN
ejpam-3448	83	27	.	.	PUNCT
ejpam-3448	84	1	the	the	DET
ejpam-3448	84	2	second	second	ADJ
ejpam-3448	84	3	famous	famous	ADJ
ejpam-3448	84	4	graph	graph	NOUN
ejpam-3448	84	5	associahedra	associahedra	NOUN
ejpam-3448	84	6	is	be	AUX
ejpam-3448	84	7	so	so	ADV
ejpam-3448	84	8	called	call	VERB
ejpam-3448	84	9	cyclohedron	cyclohedron	PROPN
ejpam-3448	84	10	wn	wn	PROPN
ejpam-3448	84	11	which	which	PRON
ejpam-3448	84	12	appears	appear	VERB
ejpam-3448	84	13	in	in	ADP
ejpam-3448	84	14	the	the	DET
ejpam-3448	84	15	study	study	NOUN
ejpam-3448	84	16	on	on	ADP
ejpam-3448	84	17	compactifications	compactification	NOUN
ejpam-3448	84	18	of	of	ADP
ejpam-3448	84	19	configuration	configuration	NOUN
ejpam-3448	84	20	spaces	space	NOUN
ejpam-3448	84	21	of	of	ADP
ejpam-3448	84	22	n	n	DET
ejpam-3448	84	23	distinct	distinct	ADJ
ejpam-3448	84	24	points	point	NOUN
ejpam-3448	84	25	on	on	ADP
ejpam-3448	84	26	a	a	DET
ejpam-3448	84	27	circle	circle	NOUN
ejpam-3448	84	28	.	.	PUNCT
ejpam-3448	85	1	with	with	ADP
ejpam-3448	85	2	a	a	DET
ejpam-3448	85	3	view	view	NOUN
ejpam-3448	85	4	of	of	ADP
ejpam-3448	85	5	the	the	DET
ejpam-3448	85	6	graph	graph	NOUN
ejpam-3448	85	7	associahedra	associahedra	PROPN
ejpam-3448	85	8	,	,	PUNCT
ejpam-3448	85	9	an	an	DET
ejpam-3448	85	10	n	n	ADV
ejpam-3448	85	11	-	-	PUNCT
ejpam-3448	85	12	dimensional	dimensional	ADJ
ejpam-3448	85	13	cyclohedron	cyclohedron	NOUN
ejpam-3448	85	14	wn	wn	NOUN
ejpam-3448	85	15	is	be	AUX
ejpam-3448	85	16	a	a	DET
ejpam-3448	85	17	geometric	geometric	ADJ
ejpam-3448	85	18	realization	realization	NOUN
ejpam-3448	85	19	of	of	ADP
ejpam-3448	85	20	the	the	DET
ejpam-3448	85	21	poset	poset	NOUN
ejpam-3448	85	22	pc(n	pc(n	NOUN
ejpam-3448	85	23	+	+	CCONJ
ejpam-3448	85	24	1	1	NUM
ejpam-3448	85	25	)	)	PUNCT
ejpam-3448	85	26	,	,	PUNCT
ejpam-3448	85	27	where	where	SCONJ
ejpam-3448	85	28	c(n	c(n	PROPN
ejpam-3448	85	29	+	+	CCONJ
ejpam-3448	85	30	1	1	X
ejpam-3448	85	31	)	)	PUNCT
ejpam-3448	85	32	denotes	denote	VERB
ejpam-3448	85	33	an	an	DET
ejpam-3448	85	34	oriented	orient	VERB
ejpam-3448	85	35	counterclockwise	counterclockwise	NOUN
ejpam-3448	85	36	cycle	cycle	NOUN
ejpam-3448	85	37	with	with	ADP
ejpam-3448	85	38	n	n	PROPN
ejpam-3448	85	39	+	+	CCONJ
ejpam-3448	85	40	1	1	NUM
ejpam-3448	85	41	-	-	PUNCT
ejpam-3448	85	42	nodes	node	NOUN
ejpam-3448	85	43	labelled	label	VERB
ejpam-3448	85	44	by	by	ADP
ejpam-3448	85	45	the	the	DET
ejpam-3448	85	46	set	set	NOUN
ejpam-3448	85	47	{	{	PUNCT
ejpam-3448	85	48	1	1	NUM
ejpam-3448	85	49	,	,	PUNCT
ejpam-3448	85	50	2	2	NUM
ejpam-3448	85	51	,	,	PUNCT
ejpam-3448	85	52	.	.	PUNCT
ejpam-3448	85	53	.	.	PUNCT
ejpam-3448	86	1	.	.	PUNCT
ejpam-3448	87	1	,	,	PUNCT
ejpam-3448	87	2	n	n	PROPN
ejpam-3448	87	3	+	+	CCONJ
ejpam-3448	87	4	1	1	NUM
ejpam-3448	87	5	}	}	PUNCT
ejpam-3448	87	6	.	.	PUNCT
ejpam-3448	88	1	a	a	DET
ejpam-3448	88	2	tube	tube	NOUN
ejpam-3448	88	3	in	in	ADP
ejpam-3448	88	4	a	a	DET
ejpam-3448	88	5	1	1	NUM
ejpam-3448	88	6	-	-	PUNCT
ejpam-3448	88	7	tubing	tubing	NOUN
ejpam-3448	88	8	on	on	ADP
ejpam-3448	88	9	an	an	PRON
ejpam-3448	88	10	(	(	PUNCT
ejpam-3448	88	11	n	n	NOUN
ejpam-3448	88	12	+	+	X
ejpam-3448	88	13	1)-cycle	1)-cycle	NOUN
ejpam-3448	88	14	can	can	AUX
ejpam-3448	88	15	be	be	AUX
ejpam-3448	88	16	seen	see	VERB
ejpam-3448	88	17	as	as	ADP
ejpam-3448	88	18	k	k	NOUN
ejpam-3448	88	19	-	-	NOUN
ejpam-3448	88	20	paths	path	NOUN
ejpam-3448	88	21	,	,	PUNCT
ejpam-3448	88	22	where	where	SCONJ
ejpam-3448	88	23	k	k	PROPN
ejpam-3448	88	24	=	=	SYM
ejpam-3448	88	25	1	1	NUM
ejpam-3448	88	26	,	,	PUNCT
ejpam-3448	88	27	.	.	PUNCT
ejpam-3448	88	28	.	.	PUNCT
ejpam-3448	89	1	.	.	PUNCT
ejpam-3448	90	1	,	,	PUNCT
ejpam-3448	90	2	n.	n.	NOUN
ejpam-3448	90	3	this	this	PRON
ejpam-3448	90	4	means	mean	VERB
ejpam-3448	90	5	that	that	SCONJ
ejpam-3448	90	6	each	each	DET
ejpam-3448	90	7	1	1	NUM
ejpam-3448	90	8	-	-	PUNCT
ejpam-3448	90	9	tubing	tubing	NOUN
ejpam-3448	90	10	represents	represent	VERB
ejpam-3448	90	11	a	a	DET
ejpam-3448	90	12	face	face	NOUN
ejpam-3448	90	13	of	of	ADP
ejpam-3448	90	14	a	a	DET
ejpam-3448	90	15	cyclohedron	cyclohedron	NOUN
ejpam-3448	90	16	of	of	ADP
ejpam-3448	90	17	the	the	DET
ejpam-3448	90	18	form	form	NOUN
ejpam-3448	90	19	wn−k×kk−1	wn−k×kk−1	PROPN
ejpam-3448	90	20	and	and	CCONJ
ejpam-3448	90	21	there	there	PRON
ejpam-3448	90	22	are	be	VERB
ejpam-3448	90	23	exactly	exactly	ADV
ejpam-3448	90	24	n(n+1	n(n+1	NOUN
ejpam-3448	90	25	)	)	PUNCT
ejpam-3448	90	26	codimension	codimension	NOUN
ejpam-3448	90	27	one	one	NUM
ejpam-3448	90	28	faces	face	NOUN
ejpam-3448	90	29	on	on	ADP
ejpam-3448	90	30	wn	wn	PROPN
ejpam-3448	90	31	.	.	PUNCT
ejpam-3448	91	1	in	in	ADP
ejpam-3448	91	2	addition	addition	NOUN
ejpam-3448	91	3	,	,	PUNCT
ejpam-3448	91	4	there	there	PRON
ejpam-3448	91	5	are	be	VERB
ejpam-3448	91	6	exactly	exactly	ADV
ejpam-3448	91	7	two	two	NUM
ejpam-3448	91	8	types	type	NOUN
ejpam-3448	91	9	of	of	ADP
ejpam-3448	91	10	tubes	tube	NOUN
ejpam-3448	91	11	.	.	PUNCT
ejpam-3448	92	1	the	the	DET
ejpam-3448	92	2	tubes	tube	NOUN
ejpam-3448	92	3	in	in	ADP
ejpam-3448	92	4	the	the	DET
ejpam-3448	92	5	first	first	ADJ
ejpam-3448	92	6	type	type	NOUN
ejpam-3448	92	7	contain	contain	VERB
ejpam-3448	92	8	consecutive	consecutive	ADJ
ejpam-3448	92	9	nodes	node	NOUN
ejpam-3448	92	10	and	and	CCONJ
ejpam-3448	92	11	the	the	DET
ejpam-3448	92	12	tubes	tube	NOUN
ejpam-3448	92	13	in	in	ADP
ejpam-3448	92	14	the	the	DET
ejpam-3448	92	15	second	second	ADJ
ejpam-3448	92	16	type	type	NOUN
ejpam-3448	92	17	contain	contain	VERB
ejpam-3448	92	18	the	the	DET
ejpam-3448	92	19	nodes	node	NOUN
ejpam-3448	92	20	of	of	ADP
ejpam-3448	92	21	the	the	DET
ejpam-3448	92	22	form	form	NOUN
ejpam-3448	92	23	{	{	PUNCT
ejpam-3448	92	24	1	1	NUM
ejpam-3448	92	25	,	,	PUNCT
ejpam-3448	92	26	2	2	NUM
ejpam-3448	92	27	,	,	PUNCT
ejpam-3448	92	28	.	.	PUNCT
ejpam-3448	92	29	.	.	PUNCT
ejpam-3448	93	1	.	.	PUNCT
ejpam-3448	94	1	,	,	PUNCT
ejpam-3448	94	2	i	i	PRON
ejpam-3448	94	3	,	,	PUNCT
ejpam-3448	94	4	j	j	PROPN
ejpam-3448	94	5	,	,	PUNCT
ejpam-3448	94	6	.	.	PUNCT
ejpam-3448	94	7	.	.	PUNCT
ejpam-3448	94	8	.	.	PUNCT
ejpam-3448	94	9	,	,	PUNCT
ejpam-3448	94	10	n	n	CCONJ
ejpam-3448	94	11	}	}	PUNCT
ejpam-3448	94	12	,	,	PUNCT
ejpam-3448	94	13	where	where	SCONJ
ejpam-3448	94	14	1	1	NUM
ejpam-3448	94	15	≤	≤	PUNCT
ejpam-3448	95	1	i	i	PRON
ejpam-3448	95	2	<	<	X
ejpam-3448	95	3	i+	i+	PUNCT
ejpam-3448	95	4	1	1	NUM
ejpam-3448	95	5	<	<	X
ejpam-3448	95	6	j	j	PROPN
ejpam-3448	95	7	≤	≤	PROPN
ejpam-3448	95	8	n.	n.	PROPN
ejpam-3448	95	9	one	one	PRON
ejpam-3448	95	10	can	can	AUX
ejpam-3448	95	11	call	call	VERB
ejpam-3448	95	12	the	the	DET
ejpam-3448	95	13	tubes	tube	NOUN
ejpam-3448	95	14	in	in	ADP
ejpam-3448	95	15	the	the	DET
ejpam-3448	95	16	second	second	ADJ
ejpam-3448	95	17	type	type	NOUN
ejpam-3448	95	18	as	as	ADP
ejpam-3448	95	19	exotic	exotic	ADJ
ejpam-3448	95	20	tubes	tube	NOUN
ejpam-3448	95	21	in	in	ADP
ejpam-3448	95	22	the	the	DET
ejpam-3448	95	23	sense	sense	NOUN
ejpam-3448	95	24	of	of	ADP
ejpam-3448	95	25	the	the	DET
ejpam-3448	95	26	definition	definition	NOUN
ejpam-3448	95	27	of	of	ADP
ejpam-3448	95	28	exotic	exotic	ADJ
ejpam-3448	95	29	subintervals	subinterval	NOUN
ejpam-3448	95	30	in	in	ADP
ejpam-3448	95	31	[	[	X
ejpam-3448	95	32	9	9	NUM
ejpam-3448	95	33	]	]	PUNCT
ejpam-3448	95	34	given	give	VERB
ejpam-3448	95	35	by	by	ADP
ejpam-3448	95	36	markl	markl	PROPN
ejpam-3448	95	37	.	.	PUNCT
ejpam-3448	96	1	it	it	PRON
ejpam-3448	96	2	is	be	AUX
ejpam-3448	96	3	clear	clear	ADJ
ejpam-3448	96	4	that	that	SCONJ
ejpam-3448	96	5	wn	wn	PROPN
ejpam-3448	96	6	can	can	AUX
ejpam-3448	96	7	be	be	AUX
ejpam-3448	96	8	combinatorially	combinatorially	ADV
ejpam-3448	96	9	obtained	obtain	VERB
ejpam-3448	96	10	by	by	ADP
ejpam-3448	96	11	taking	take	VERB
ejpam-3448	96	12	the	the	DET
ejpam-3448	96	13	convex	convex	NOUN
ejpam-3448	96	14	hull	hull	NOUN
ejpam-3448	96	15	of	of	ADP
ejpam-3448	96	16	n+	n+	NOUN
ejpam-3448	96	17	1	1	NUM
ejpam-3448	96	18	disjoint	disjoint	NOUN
ejpam-3448	96	19	copies	copy	NOUN
ejpam-3448	96	20	of	of	ADP
ejpam-3448	96	21	kn−1	kn−1	PROPN
ejpam-3448	96	22	and	and	CCONJ
ejpam-3448	96	23	also	also	ADV
ejpam-3448	96	24	give	give	VERB
ejpam-3448	96	25	an	an	DET
ejpam-3448	96	26	orientation	orientation	NOUN
ejpam-3448	96	27	on	on	ADP
ejpam-3448	96	28	wn	wn	NOUN
ejpam-3448	96	29	using	use	VERB
ejpam-3448	96	30	the	the	DET
ejpam-3448	96	31	tamari	tamari	ADJ
ejpam-3448	96	32	order	order	NOUN
ejpam-3448	96	33	on	on	ADP
ejpam-3448	96	34	these	these	DET
ejpam-3448	96	35	copies	copy	NOUN
ejpam-3448	96	36	of	of	ADP
ejpam-3448	96	37	kn−1	kn−1	PROPN
ejpam-3448	96	38	.	.	PROPN
ejpam-3448	97	1	hence	hence	ADV
ejpam-3448	97	2	we	we	PRON
ejpam-3448	97	3	can	can	AUX
ejpam-3448	97	4	get	get	VERB
ejpam-3448	97	5	a	a	DET
ejpam-3448	97	6	triangulation	triangulation	NOUN
ejpam-3448	97	7	of	of	ADP
ejpam-3448	97	8	cyclohedron	cyclohedron	PRON
ejpam-3448	97	9	similar	similar	ADJ
ejpam-3448	97	10	to	to	ADP
ejpam-3448	97	11	the	the	PRON
ejpam-3448	97	12	once	once	ADV
ejpam-3448	97	13	given	give	VERB
ejpam-3448	97	14	by	by	ADP
ejpam-3448	97	15	loday	loday	PROPN
ejpam-3448	97	16	for	for	ADP
ejpam-3448	97	17	associahedron	associahedron	PROPN
ejpam-3448	97	18	.	.	PUNCT
ejpam-3448	98	1	theorem	theorem	NOUN
ejpam-3448	98	2	2	2	NUM
ejpam-3448	98	3	.	.	PUNCT
ejpam-3448	99	1	the	the	DET
ejpam-3448	99	2	n	n	ADV
ejpam-3448	99	3	-	-	PUNCT
ejpam-3448	99	4	dimensional	dimensional	ADJ
ejpam-3448	99	5	cyclohedron	cyclohedron	NOUN
ejpam-3448	99	6	wn	wn	PROPN
ejpam-3448	99	7	admits	admit	VERB
ejpam-3448	99	8	a	a	DET
ejpam-3448	99	9	triangulation	triangulation	NOUN
ejpam-3448	99	10	by	by	ADP
ejpam-3448	99	11	(	(	PUNCT
ejpam-3448	99	12	n+	n+	X
ejpam-3448	99	13	1)n	1)n	NUM
ejpam-3448	99	14	simplicies	simplicie	NOUN
ejpam-3448	99	15	with	with	ADP
ejpam-3448	99	16	respect	respect	NOUN
ejpam-3448	99	17	to	to	ADP
ejpam-3448	99	18	the	the	DET
ejpam-3448	99	19	orientation	orientation	NOUN
ejpam-3448	99	20	induced	induce	VERB
ejpam-3448	99	21	by	by	ADP
ejpam-3448	99	22	the	the	DET
ejpam-3448	99	23	tamari	tamari	ADJ
ejpam-3448	99	24	order	order	NOUN
ejpam-3448	99	25	on	on	ADP
ejpam-3448	99	26	its	its	PRON
ejpam-3448	99	27	faces	face	NOUN
ejpam-3448	99	28	.	.	PUNCT
ejpam-3448	100	1	proof	proof	NOUN
ejpam-3448	100	2	.	.	PUNCT
ejpam-3448	101	1	by	by	ADP
ejpam-3448	101	2	using	use	VERB
ejpam-3448	101	3	induction	induction	NOUN
ejpam-3448	101	4	on	on	ADP
ejpam-3448	101	5	n	n	CCONJ
ejpam-3448	101	6	,	,	PUNCT
ejpam-3448	101	7	we	we	PRON
ejpam-3448	101	8	assume	assume	VERB
ejpam-3448	101	9	that	that	SCONJ
ejpam-3448	101	10	all	all	DET
ejpam-3448	101	11	the	the	DET
ejpam-3448	101	12	associahedral	associahedral	ADJ
ejpam-3448	101	13	components	component	NOUN
ejpam-3448	101	14	of	of	ADP
ejpam-3448	101	15	the	the	DET
ejpam-3448	101	16	faces	face	NOUN
ejpam-3448	101	17	of	of	ADP
ejpam-3448	101	18	cyclohedron	cyclohedron	NOUN
ejpam-3448	101	19	are	be	AUX
ejpam-3448	101	20	triangulated	triangulate	VERB
ejpam-3448	101	21	with	with	ADP
ejpam-3448	101	22	respect	respect	NOUN
ejpam-3448	101	23	to	to	ADP
ejpam-3448	101	24	the	the	DET
ejpam-3448	101	25	tamari	tamari	ADJ
ejpam-3448	101	26	order	order	NOUN
ejpam-3448	101	27	and	and	CCONJ
ejpam-3448	101	28	take	take	VERB
ejpam-3448	101	29	cones	cone	NOUN
ejpam-3448	101	30	over	over	ADP
ejpam-3448	101	31	all	all	DET
ejpam-3448	101	32	the	the	DET
ejpam-3448	101	33	simplices	simplice	NOUN
ejpam-3448	101	34	on	on	ADP
ejpam-3448	101	35	the	the	DET
ejpam-3448	101	36	faces	face	NOUN
ejpam-3448	101	37	with	with	ADP
ejpam-3448	101	38	a	a	DET
ejpam-3448	101	39	common	common	ADJ
ejpam-3448	101	40	vertex	vertex	NOUN
ejpam-3448	101	41	as	as	ADP
ejpam-3448	101	42	the	the	DET
ejpam-3448	101	43	barycenter	barycenter	NOUN
ejpam-3448	101	44	of	of	ADP
ejpam-3448	101	45	the	the	DET
ejpam-3448	101	46	cyclohedron	cyclohedron	NOUN
ejpam-3448	101	47	.	.	PUNCT
ejpam-3448	102	1	let	let	VERB
ejpam-3448	102	2	dn	dn	PART
ejpam-3448	102	3	denote	denote	VERB
ejpam-3448	102	4	the	the	DET
ejpam-3448	102	5	number	number	NOUN
ejpam-3448	102	6	of	of	ADP
ejpam-3448	102	7	the	the	DET
ejpam-3448	102	8	simplices	simplice	NOUN
ejpam-3448	102	9	in	in	ADP
ejpam-3448	102	10	the	the	DET
ejpam-3448	102	11	triangulation	triangulation	NOUN
ejpam-3448	102	12	of	of	ADP
ejpam-3448	102	13	wn	wn	PROPN
ejpam-3448	102	14	.	.	PUNCT
ejpam-3448	103	1	if	if	SCONJ
ejpam-3448	103	2	n	n	NOUN
ejpam-3448	103	3	=	=	SYM
ejpam-3448	103	4	1	1	NUM
ejpam-3448	103	5	,	,	PUNCT
ejpam-3448	103	6	then	then	ADV
ejpam-3448	103	7	it	it	PRON
ejpam-3448	103	8	is	be	AUX
ejpam-3448	103	9	clear	clear	ADJ
ejpam-3448	103	10	that	that	SCONJ
ejpam-3448	103	11	there	there	PRON
ejpam-3448	103	12	are	be	VERB
ejpam-3448	103	13	exactly	exactly	ADV
ejpam-3448	103	14	2	2	NUM
ejpam-3448	103	15	faces	face	NOUN
ejpam-3448	103	16	of	of	ADP
ejpam-3448	103	17	the	the	DET
ejpam-3448	103	18	form	form	NOUN
ejpam-3448	103	19	w	w	NOUN
ejpam-3448	103	20	0×k0	0×k0	NOUN
ejpam-3448	103	21	and	and	CCONJ
ejpam-3448	103	22	there	there	PRON
ejpam-3448	103	23	are	be	VERB
ejpam-3448	103	24	only	only	ADV
ejpam-3448	103	25	two	two	NUM
ejpam-3448	103	26	simplices	simplice	NOUN
ejpam-3448	103	27	in	in	ADP
ejpam-3448	103	28	the	the	DET
ejpam-3448	103	29	triangulation	triangulation	NOUN
ejpam-3448	103	30	.	.	PUNCT
ejpam-3448	104	1	suppose	suppose	VERB
ejpam-3448	104	2	that	that	SCONJ
ejpam-3448	104	3	for	for	ADP
ejpam-3448	104	4	k	k	PROPN
ejpam-3448	104	5	<	<	X
ejpam-3448	104	6	n	n	CCONJ
ejpam-3448	104	7	,	,	PUNCT
ejpam-3448	104	8	wn−k	wn−k	PROPN
ejpam-3448	104	9	admits	admit	VERB
ejpam-3448	104	10	a	a	DET
ejpam-3448	104	11	triangulation	triangulation	NOUN
ejpam-3448	104	12	by	by	ADP
ejpam-3448	104	13	λn−k	λn−k	PROPN
ejpam-3448	104	14	simplices	simplice	NOUN
ejpam-3448	104	15	.	.	PUNCT
ejpam-3448	105	1	then	then	ADV
ejpam-3448	105	2	we	we	PRON
ejpam-3448	105	3	show	show	VERB
ejpam-3448	105	4	that	that	SCONJ
ejpam-3448	105	5	wn	wn	PROPN
ejpam-3448	105	6	admits	admit	VERB
ejpam-3448	105	7	a	a	DET
ejpam-3448	105	8	triangulation	triangulation	NOUN
ejpam-3448	105	9	by	by	ADP
ejpam-3448	105	10	λn	λn	PROPN
ejpam-3448	105	11	=	=	PUNCT
ejpam-3448	105	12	n∑	n∑	NOUN
ejpam-3448	105	13	k=1	k=1	X
ejpam-3448	106	1	(	(	PUNCT
ejpam-3448	106	2	n+	n+	NOUN
ejpam-3448	106	3	1	1	X
ejpam-3448	106	4	)	)	PUNCT
ejpam-3448	106	5	(	(	PUNCT
ejpam-3448	106	6	n−	n−	NOUN
ejpam-3448	106	7	1	1	NUM
ejpam-3448	106	8	k	k	NOUN
ejpam-3448	106	9	−	−	NOUN
ejpam-3448	106	10	1	1	NUM
ejpam-3448	106	11	)	)	PUNCT
ejpam-3448	106	12	λn−kk	λn−kk	PROPN
ejpam-3448	107	1	k−2	k−2	PROPN
ejpam-3448	107	2	s.	s.	PROPN
ejpam-3448	107	3	k.	k.	PROPN
ejpam-3448	107	4	gürbüzer	gürbüzer	PROPN
ejpam-3448	107	5	,	,	PUNCT
ejpam-3448	107	6	b.	b.	PROPN
ejpam-3448	107	7	akyar	akyar	PROPN
ejpam-3448	107	8	/	/	SYM
ejpam-3448	107	9	eur	eur	PROPN
ejpam-3448	107	10	.	.	PUNCT
ejpam-3448	108	1	j.	j.	PROPN
ejpam-3448	108	2	pure	pure	PROPN
ejpam-3448	108	3	appl	appl	PROPN
ejpam-3448	108	4	.	.	PROPN
ejpam-3448	108	5	math	math	PROPN
ejpam-3448	108	6	,	,	PUNCT
ejpam-3448	108	7	12	12	NUM
ejpam-3448	108	8	(	(	PUNCT
ejpam-3448	108	9	3	3	NUM
ejpam-3448	108	10	)	)	PUNCT
ejpam-3448	108	11	(	(	PUNCT
ejpam-3448	108	12	2019	2019	NUM
ejpam-3448	108	13	)	)	PUNCT
ejpam-3448	108	14	,	,	PUNCT
ejpam-3448	108	15	734	734	NUM
ejpam-3448	108	16	-	-	SYM
ejpam-3448	108	17	748	748	NUM
ejpam-3448	108	18	738	738	NUM
ejpam-3448	108	19	=	=	SYM
ejpam-3448	108	20	n∑	n∑	NOUN
ejpam-3448	108	21	k=1	k=1	X
ejpam-3448	109	1	(	(	PUNCT
ejpam-3448	109	2	n+	n+	NOUN
ejpam-3448	109	3	1	1	X
ejpam-3448	109	4	)	)	PUNCT
ejpam-3448	109	5	(	(	PUNCT
ejpam-3448	109	6	n−	n−	NOUN
ejpam-3448	109	7	1	1	NUM
ejpam-3448	109	8	k	k	NOUN
ejpam-3448	109	9	−	−	NOUN
ejpam-3448	109	10	1	1	NUM
ejpam-3448	109	11	)	)	PUNCT
ejpam-3448	109	12	(	(	PUNCT
ejpam-3448	110	1	n−	n−	NOUN
ejpam-3448	110	2	k	k	NOUN
ejpam-3448	110	3	+	+	PROPN
ejpam-3448	111	1	1)n−kkk−2	1)n−kkk−2	NUM
ejpam-3448	111	2	=	=	SYM
ejpam-3448	111	3	(	(	PUNCT
ejpam-3448	111	4	n+	n+	NOUN
ejpam-3448	111	5	1	1	X
ejpam-3448	111	6	)	)	PUNCT
ejpam-3448	111	7	n−1∑	n−1∑	NOUN
ejpam-3448	111	8	k=0	k=0	PROPN
ejpam-3448	112	1	(	(	PUNCT
ejpam-3448	112	2	n−	n−	NOUN
ejpam-3448	112	3	1	1	NUM
ejpam-3448	112	4	k	k	NOUN
ejpam-3448	112	5	)	)	PUNCT
ejpam-3448	112	6	(	(	PUNCT
ejpam-3448	112	7	n−	n−	NOUN
ejpam-3448	112	8	k)n−k−1(k	k)n−k−1(k	NOUN
ejpam-3448	112	9	+	+	CCONJ
ejpam-3448	112	10	1)k−1	1)k−1	NUM
ejpam-3448	112	11	=	=	SYM
ejpam-3448	112	12	(	(	PUNCT
ejpam-3448	112	13	n+	n+	NUM
ejpam-3448	112	14	1)(n+	1)(n+	NUM
ejpam-3448	112	15	1)n−1	1)n−1	NUM
ejpam-3448	112	16	=	=	SYM
ejpam-3448	112	17	(	(	PUNCT
ejpam-3448	112	18	n+	n+	X
ejpam-3448	112	19	1)n	1)n	X
ejpam-3448	112	20	.	.	PUNCT
ejpam-3448	113	1	simplices	simplices	PROPN
ejpam-3448	113	2	.	.	PUNCT
ejpam-3448	114	1	the	the	DET
ejpam-3448	114	2	last	last	ADJ
ejpam-3448	114	3	row	row	NOUN
ejpam-3448	114	4	follows	follow	VERB
ejpam-3448	114	5	from	from	ADP
ejpam-3448	114	6	the	the	DET
ejpam-3448	114	7	abel	abel	NOUN
ejpam-3448	114	8	’s	’s	PART
ejpam-3448	114	9	equation	equation	NOUN
ejpam-3448	114	10	for	for	ADP
ejpam-3448	114	11	x−1(x	x−1(x	PROPN
ejpam-3448	115	1	+	+	CCONJ
ejpam-3448	115	2	y	y	PROPN
ejpam-3448	115	3	+	+	CCONJ
ejpam-3448	115	4	n	n	CCONJ
ejpam-3448	115	5	−	−	PROPN
ejpam-3448	115	6	1)n−1	1)n−1	NUM
ejpam-3448	115	7	with	with	ADP
ejpam-3448	115	8	x	x	PROPN
ejpam-3448	115	9	=	=	SYM
ejpam-3448	115	10	1	1	NUM
ejpam-3448	115	11	,	,	PUNCT
ejpam-3448	115	12	y	y	PROPN
ejpam-3448	115	13	=	=	SYM
ejpam-3448	115	14	1	1	X
ejpam-3448	115	15	.	.	X
ejpam-3448	116	1	for	for	ADP
ejpam-3448	116	2	further	further	ADJ
ejpam-3448	116	3	details	detail	NOUN
ejpam-3448	116	4	,	,	PUNCT
ejpam-3448	116	5	see	see	VERB
ejpam-3448	116	6	riordan	riordan	PROPN
ejpam-3448	117	1	[	[	X
ejpam-3448	117	2	11	11	NUM
ejpam-3448	117	3	]	]	SYM
ejpam-3448	117	4	.	.	PUNCT
ejpam-3448	118	1	3	3	X
ejpam-3448	118	2	.	.	X
ejpam-3448	118	3	operations	operation	NOUN
ejpam-3448	118	4	on	on	ADP
ejpam-3448	118	5	tubes	tube	NOUN
ejpam-3448	118	6	and	and	CCONJ
ejpam-3448	118	7	loday	loday	PROPN
ejpam-3448	118	8	’s	’s	PART
ejpam-3448	118	9	dendriform	dendriform	NOUN
ejpam-3448	118	10	algebra	algebra	NOUN
ejpam-3448	118	11	in	in	ADP
ejpam-3448	118	12	this	this	DET
ejpam-3448	118	13	section	section	NOUN
ejpam-3448	118	14	,	,	PUNCT
ejpam-3448	118	15	we	we	PRON
ejpam-3448	118	16	define	define	VERB
ejpam-3448	118	17	”	"	PUNCT
ejpam-3448	118	18	name	name	NOUN
ejpam-3448	118	19	”	"	PUNCT
ejpam-3448	118	20	for	for	ADP
ejpam-3448	118	21	a	a	DET
ejpam-3448	118	22	tubing	tubing	NOUN
ejpam-3448	118	23	on	on	ADP
ejpam-3448	118	24	a	a	DET
ejpam-3448	118	25	path	path	NOUN
ejpam-3448	118	26	as	as	ADP
ejpam-3448	118	27	a	a	DET
ejpam-3448	118	28	sequence	sequence	NOUN
ejpam-3448	118	29	of	of	ADP
ejpam-3448	118	30	positive	positive	ADJ
ejpam-3448	118	31	integers	integer	NOUN
ejpam-3448	118	32	for	for	ADP
ejpam-3448	118	33	coding	code	VERB
ejpam-3448	118	34	.	.	PUNCT
ejpam-3448	119	1	we	we	PRON
ejpam-3448	119	2	also	also	ADV
ejpam-3448	119	3	define	define	VERB
ejpam-3448	119	4	some	some	DET
ejpam-3448	119	5	new	new	ADJ
ejpam-3448	119	6	operations	operation	NOUN
ejpam-3448	119	7	on	on	ADP
ejpam-3448	119	8	the	the	DET
ejpam-3448	119	9	collection	collection	NOUN
ejpam-3448	119	10	of	of	ADP
ejpam-3448	119	11	maximal	maximal	ADJ
ejpam-3448	119	12	tubings	tubing	NOUN
ejpam-3448	119	13	on	on	ADP
ejpam-3448	119	14	a	a	DET
ejpam-3448	119	15	path	path	NOUN
ejpam-3448	119	16	motivated	motivate	VERB
ejpam-3448	119	17	by	by	ADP
ejpam-3448	119	18	loday	loday	PROPN
ejpam-3448	119	19	’s	’s	PART
ejpam-3448	119	20	work	work	NOUN
ejpam-3448	119	21	[	[	X
ejpam-3448	119	22	4	4	NUM
ejpam-3448	119	23	]	]	PUNCT
ejpam-3448	119	24	.	.	PUNCT
ejpam-3448	120	1	these	these	DET
ejpam-3448	120	2	operations	operation	NOUN
ejpam-3448	120	3	can	can	AUX
ejpam-3448	120	4	be	be	AUX
ejpam-3448	120	5	visualized	visualize	VERB
ejpam-3448	120	6	as	as	ADP
ejpam-3448	120	7	binding	bind	VERB
ejpam-3448	120	8	or	or	CCONJ
ejpam-3448	120	9	nesting	nest	VERB
ejpam-3448	120	10	two	two	NUM
ejpam-3448	120	11	maximal	maximal	ADJ
ejpam-3448	120	12	tubings	tubing	NOUN
ejpam-3448	120	13	to	to	PART
ejpam-3448	120	14	get	get	VERB
ejpam-3448	120	15	a	a	DET
ejpam-3448	120	16	bigger	big	ADJ
ejpam-3448	120	17	maximal	maximal	ADJ
ejpam-3448	120	18	tubing	tubing	NOUN
ejpam-3448	120	19	.	.	PUNCT
ejpam-3448	121	1	we	we	PRON
ejpam-3448	121	2	give	give	VERB
ejpam-3448	121	3	the	the	DET
ejpam-3448	121	4	sum	sum	NOUN
ejpam-3448	121	5	and	and	CCONJ
ejpam-3448	121	6	the	the	DET
ejpam-3448	121	7	product	product	NOUN
ejpam-3448	121	8	of	of	ADP
ejpam-3448	121	9	maximal	maximal	ADJ
ejpam-3448	121	10	tubings	tubing	NOUN
ejpam-3448	121	11	as	as	ADP
ejpam-3448	121	12	a	a	DET
ejpam-3448	121	13	collection	collection	NOUN
ejpam-3448	121	14	of	of	ADP
ejpam-3448	121	15	maximal	maximal	ADJ
ejpam-3448	121	16	tubings	tubing	NOUN
ejpam-3448	121	17	.	.	PUNCT
ejpam-3448	122	1	furthermore	furthermore	ADV
ejpam-3448	122	2	,	,	PUNCT
ejpam-3448	122	3	we	we	PRON
ejpam-3448	122	4	interpret	interpret	VERB
ejpam-3448	122	5	loday	loday	PROPN
ejpam-3448	122	6	’s	’s	PART
ejpam-3448	122	7	dendriform	dendriform	NOUN
ejpam-3448	122	8	algebra	algebra	NOUN
ejpam-3448	122	9	on	on	ADP
ejpam-3448	122	10	the	the	DET
ejpam-3448	122	11	collection	collection	NOUN
ejpam-3448	122	12	of	of	ADP
ejpam-3448	122	13	maximal	maximal	ADJ
ejpam-3448	122	14	tubings	tubing	NOUN
ejpam-3448	122	15	.	.	PUNCT
ejpam-3448	123	1	definition	definition	NOUN
ejpam-3448	123	2	1	1	NUM
ejpam-3448	123	3	.	.	PUNCT
ejpam-3448	124	1	the	the	DET
ejpam-3448	124	2	name	name	NOUN
ejpam-3448	124	3	of	of	ADP
ejpam-3448	124	4	a	a	DET
ejpam-3448	124	5	tubing	tubing	NOUN
ejpam-3448	124	6	on	on	ADP
ejpam-3448	124	7	an	an	DET
ejpam-3448	124	8	n	n	NUM
ejpam-3448	124	9	-	-	PUNCT
ejpam-3448	124	10	path	path	NOUN
ejpam-3448	124	11	is	be	AUX
ejpam-3448	124	12	a	a	DET
ejpam-3448	124	13	finite	finite	ADJ
ejpam-3448	124	14	sequence	sequence	NOUN
ejpam-3448	124	15	of	of	ADP
ejpam-3448	124	16	positive	positive	ADJ
ejpam-3448	124	17	integers	integer	NOUN
ejpam-3448	124	18	such	such	ADJ
ejpam-3448	124	19	that	that	SCONJ
ejpam-3448	124	20	the	the	DET
ejpam-3448	124	21	j	j	PROPN
ejpam-3448	124	22	-	-	PUNCT
ejpam-3448	124	23	th	th	VERB
ejpam-3448	124	24	term	term	NOUN
ejpam-3448	124	25	of	of	ADP
ejpam-3448	124	26	the	the	DET
ejpam-3448	124	27	sequence	sequence	NOUN
ejpam-3448	124	28	is	be	AUX
ejpam-3448	124	29	the	the	DET
ejpam-3448	124	30	number	number	NOUN
ejpam-3448	124	31	of	of	ADP
ejpam-3448	124	32	tubes	tube	NOUN
ejpam-3448	124	33	including	include	VERB
ejpam-3448	124	34	the	the	DET
ejpam-3448	124	35	universal	universal	ADJ
ejpam-3448	124	36	ones	one	NOUN
ejpam-3448	124	37	containing	contain	VERB
ejpam-3448	124	38	the	the	DET
ejpam-3448	124	39	j	j	PROPN
ejpam-3448	124	40	-	-	PUNCT
ejpam-3448	124	41	th	th	X
ejpam-3448	124	42	node	node	NOUN
ejpam-3448	124	43	of	of	ADP
ejpam-3448	124	44	an	an	DET
ejpam-3448	124	45	n	n	NOUN
ejpam-3448	124	46	-	-	PUNCT
ejpam-3448	124	47	path	path	NOUN
ejpam-3448	124	48	.	.	PUNCT
ejpam-3448	125	1	especially	especially	ADV
ejpam-3448	125	2	,	,	PUNCT
ejpam-3448	125	3	the	the	DET
ejpam-3448	125	4	name	name	NOUN
ejpam-3448	125	5	of	of	ADP
ejpam-3448	125	6	the	the	DET
ejpam-3448	125	7	tubing	tubing	NOUN
ejpam-3448	125	8	0	0	NUM
ejpam-3448	125	9	on	on	ADP
ejpam-3448	125	10	the	the	DET
ejpam-3448	125	11	empty	empty	ADJ
ejpam-3448	125	12	graph	graph	NOUN
ejpam-3448	125	13	is	be	AUX
ejpam-3448	125	14	0	0	NUM
ejpam-3448	125	15	.	.	PUNCT
ejpam-3448	126	1	from	from	ADP
ejpam-3448	126	2	now	now	ADV
ejpam-3448	126	3	on	on	ADV
ejpam-3448	126	4	,	,	PUNCT
ejpam-3448	126	5	t	t	NOUN
ejpam-3448	126	6	=	=	SYM
ejpam-3448	126	7	a1	a1	NOUN
ejpam-3448	126	8	.	.	PUNCT
ejpam-3448	126	9	.	.	PUNCT
ejpam-3448	126	10	.	.	PUNCT
ejpam-3448	127	1	an	an	DET
ejpam-3448	127	2	denotes	denote	NOUN
ejpam-3448	127	3	a	a	DET
ejpam-3448	127	4	tubing	tubing	NOUN
ejpam-3448	127	5	with	with	ADP
ejpam-3448	127	6	the	the	DET
ejpam-3448	127	7	name	name	NOUN
ejpam-3448	127	8	representation	representation	NOUN
ejpam-3448	127	9	.	.	PUNCT
ejpam-3448	128	1	32123	32123	NUM
ejpam-3448	128	2	figure	figure	NOUN
ejpam-3448	128	3	2	2	NUM
ejpam-3448	128	4	:	:	PUNCT
ejpam-3448	128	5	example	example	NOUN
ejpam-3448	128	6	of	of	ADP
ejpam-3448	128	7	the	the	DET
ejpam-3448	128	8	name	name	NOUN
ejpam-3448	128	9	of	of	ADP
ejpam-3448	128	10	a	a	DET
ejpam-3448	128	11	tubing	tubing	NOUN
ejpam-3448	128	12	on	on	ADP
ejpam-3448	128	13	5	5	NUM
ejpam-3448	128	14	-	-	PUNCT
ejpam-3448	128	15	path	path	NOUN
ejpam-3448	128	16	remark	remark	NOUN
ejpam-3448	128	17	1	1	NUM
ejpam-3448	128	18	.	.	PUNCT
ejpam-3448	129	1	a	a	DET
ejpam-3448	129	2	tube	tube	NOUN
ejpam-3448	129	3	t	t	NOUN
ejpam-3448	129	4	can	can	AUX
ejpam-3448	129	5	be	be	AUX
ejpam-3448	129	6	slided	slide	VERB
ejpam-3448	129	7	only	only	ADV
ejpam-3448	129	8	in	in	ADP
ejpam-3448	129	9	the	the	DET
ejpam-3448	129	10	smallest	small	ADJ
ejpam-3448	129	11	tube	tube	NOUN
ejpam-3448	129	12	containing	contain	VERB
ejpam-3448	129	13	it	it	PRON
ejpam-3448	129	14	.	.	PUNCT
ejpam-3448	130	1	let	let	VERB
ejpam-3448	130	2	t1	t1	NOUN
ejpam-3448	130	3	=	=	NOUN
ejpam-3448	130	4	a1	a1	NOUN
ejpam-3448	130	5	.	.	PUNCT
ejpam-3448	130	6	.	.	PUNCT
ejpam-3448	130	7	.	.	PUNCT
ejpam-3448	131	1	an	an	PRON
ejpam-3448	131	2	be	be	AUX
ejpam-3448	131	3	a	a	DET
ejpam-3448	131	4	tubing	tubing	NOUN
ejpam-3448	131	5	and	and	CCONJ
ejpam-3448	131	6	let	let	VERB
ejpam-3448	131	7	t1	t1	PROPN
ejpam-3448	131	8	∈	∈	PROPN
ejpam-3448	131	9	t1	t1	NOUN
ejpam-3448	131	10	be	be	AUX
ejpam-3448	131	11	a	a	DET
ejpam-3448	131	12	tube	tube	NOUN
ejpam-3448	131	13	.	.	PUNCT
ejpam-3448	132	1	if	if	SCONJ
ejpam-3448	132	2	the	the	DET
ejpam-3448	132	3	tube	tube	NOUN
ejpam-3448	132	4	t2	t2	PROPN
ejpam-3448	132	5	∈	∈	PROPN
ejpam-3448	132	6	t2	t2	NOUN
ejpam-3448	132	7	is	be	AUX
ejpam-3448	132	8	obtained	obtain	VERB
ejpam-3448	132	9	by	by	ADP
ejpam-3448	132	10	sliding	slide	VERB
ejpam-3448	132	11	t1	t1	PROPN
ejpam-3448	132	12	∈	∈	PROPN
ejpam-3448	132	13	t1	t1	NOUN
ejpam-3448	132	14	then	then	ADV
ejpam-3448	132	15	the	the	DET
ejpam-3448	132	16	name	name	NOUN
ejpam-3448	132	17	b1	b1	NOUN
ejpam-3448	132	18	.	.	PUNCT
ejpam-3448	133	1	.	.	PUNCT
ejpam-3448	133	2	.	.	PUNCT
ejpam-3448	134	1	bn	bn	INTJ
ejpam-3448	134	2	of	of	ADP
ejpam-3448	134	3	t2	t2	PROPN
ejpam-3448	134	4	is	be	AUX
ejpam-3448	134	5	bi	bi	NOUN
ejpam-3448	134	6	=	=	SYM
ejpam-3448	134	7			PUNCT
ejpam-3448	134	8	ai	ai	VERB
ejpam-3448	134	9	,	,	PUNCT
ejpam-3448	134	10	i	i	PRON
ejpam-3448	134	11	/∈	/∈	PUNCT
ejpam-3448	135	1	t1	t1	NOUN
ejpam-3448	135	2	∪	∪	VERB
ejpam-3448	135	3	t2	t2	PROPN
ejpam-3448	135	4	;	;	PUNCT
ejpam-3448	135	5	ai	ai	VERB
ejpam-3448	135	6	,	,	PUNCT
ejpam-3448	135	7	i	i	PRON
ejpam-3448	135	8	∈	∈	PROPN
ejpam-3448	135	9	t1	t1	NOUN
ejpam-3448	135	10	∩	∩	ADJ
ejpam-3448	135	11	t2	t2	NOUN
ejpam-3448	135	12	;	;	PUNCT
ejpam-3448	135	13	ai	ai	VERB
ejpam-3448	135	14	−	−	PROPN
ejpam-3448	135	15	1	1	NUM
ejpam-3448	135	16	,	,	PUNCT
ejpam-3448	135	17	i	i	PRON
ejpam-3448	135	18	∈	∈	NOUN
ejpam-3448	135	19	t1	t1	NOUN
ejpam-3448	135	20	\	\	PROPN
ejpam-3448	135	21	t2	t2	NOUN
ejpam-3448	135	22	;	;	PUNCT
ejpam-3448	135	23	ai	ai	VERB
ejpam-3448	135	24	+	+	PROPN
ejpam-3448	135	25	1	1	NUM
ejpam-3448	135	26	,	,	PUNCT
ejpam-3448	135	27	i	i	PRON
ejpam-3448	135	28	∈	∈	PROPN
ejpam-3448	135	29	t2	t2	NOUN
ejpam-3448	135	30	\	\	PROPN
ejpam-3448	135	31	t1	t1	NOUN
ejpam-3448	135	32	for	for	ADP
ejpam-3448	135	33	1	1	NUM
ejpam-3448	135	34	≤	≤	NUM
ejpam-3448	135	35	i	i	PRON
ejpam-3448	135	36	≤	≤	ADJ
ejpam-3448	135	37	n.	n.	NOUN
ejpam-3448	135	38	let	let	VERB
ejpam-3448	135	39	t	t	NOUN
ejpam-3448	135	40	=	=	NOUN
ejpam-3448	135	41	a1	a1	PROPN
ejpam-3448	135	42	.	.	PUNCT
ejpam-3448	135	43	.	.	PUNCT
ejpam-3448	135	44	.	.	PUNCT
ejpam-3448	136	1	an	an	DET
ejpam-3448	136	2	be	be	AUX
ejpam-3448	136	3	a	a	DET
ejpam-3448	136	4	maximal	maximal	ADJ
ejpam-3448	136	5	tubing	tubing	NOUN
ejpam-3448	136	6	on	on	ADP
ejpam-3448	136	7	an	an	DET
ejpam-3448	136	8	n−path	n−path	NOUN
ejpam-3448	136	9	,	,	PUNCT
ejpam-3448	136	10	where	where	SCONJ
ejpam-3448	136	11	ai	ai	VERB
ejpam-3448	136	12	=	=	NOUN
ejpam-3448	136	13	1	1	NUM
ejpam-3448	136	14	.	.	PUNCT
ejpam-3448	137	1	the	the	DET
ejpam-3448	137	2	sequences	sequence	NOUN
ejpam-3448	137	3	(	(	PUNCT
ejpam-3448	137	4	a1−1	a1−1	PROPN
ejpam-3448	137	5	)	)	PUNCT
ejpam-3448	137	6	.	.	PUNCT
ejpam-3448	137	7	.	.	PUNCT
ejpam-3448	137	8	.	.	PUNCT
ejpam-3448	138	1	(	(	PUNCT
ejpam-3448	138	2	ai−1−1	ai−1−1	ADJ
ejpam-3448	138	3	)	)	PUNCT
ejpam-3448	138	4	and	and	CCONJ
ejpam-3448	138	5	(	(	PUNCT
ejpam-3448	138	6	ai+1−1	ai+1−1	PROPN
ejpam-3448	138	7	)	)	PUNCT
ejpam-3448	138	8	.	.	PUNCT
ejpam-3448	138	9	.	.	PUNCT
ejpam-3448	138	10	.	.	PUNCT
ejpam-3448	139	1	(	(	PUNCT
ejpam-3448	139	2	an−1	an−1	ADJ
ejpam-3448	139	3	)	)	PUNCT
ejpam-3448	139	4	are	be	AUX
ejpam-3448	139	5	still	still	ADV
ejpam-3448	139	6	possible	possible	ADJ
ejpam-3448	139	7	names	name	NOUN
ejpam-3448	139	8	of	of	ADP
ejpam-3448	139	9	maximal	maximal	ADJ
ejpam-3448	139	10	tubings	tubing	NOUN
ejpam-3448	139	11	on	on	ADP
ejpam-3448	139	12	(	(	PUNCT
ejpam-3448	139	13	i	i	PRON
ejpam-3448	139	14	−	−	PROPN
ejpam-3448	139	15	1)-path	1)-path	NUM
ejpam-3448	139	16	and	and	CCONJ
ejpam-3448	139	17	(	(	PUNCT
ejpam-3448	139	18	n	n	CCONJ
ejpam-3448	139	19	−	−	PROPN
ejpam-3448	139	20	i)-path	i)-path	NOUN
ejpam-3448	139	21	,	,	PUNCT
ejpam-3448	139	22	respectively	respectively	ADV
ejpam-3448	139	23	.	.	PUNCT
ejpam-3448	140	1	such	such	DET
ejpam-3448	140	2	a	a	DET
ejpam-3448	140	3	partition	partition	NOUN
ejpam-3448	140	4	leads	lead	VERB
ejpam-3448	140	5	us	we	PRON
ejpam-3448	140	6	an	an	DET
ejpam-3448	140	7	operation	operation	NOUN
ejpam-3448	140	8	on	on	ADP
ejpam-3448	140	9	maximal	maximal	ADJ
ejpam-3448	140	10	tubings	tubing	NOUN
ejpam-3448	140	11	on	on	ADP
ejpam-3448	140	12	paths	path	NOUN
ejpam-3448	140	13	.	.	PUNCT
ejpam-3448	141	1	s.	s.	PROPN
ejpam-3448	141	2	k.	k.	PROPN
ejpam-3448	141	3	gürbüzer	gürbüzer	PROPN
ejpam-3448	141	4	,	,	PUNCT
ejpam-3448	141	5	b.	b.	PROPN
ejpam-3448	141	6	akyar	akyar	PROPN
ejpam-3448	141	7	/	/	SYM
ejpam-3448	141	8	eur	eur	PROPN
ejpam-3448	141	9	.	.	PUNCT
ejpam-3448	142	1	j.	j.	PROPN
ejpam-3448	142	2	pure	pure	PROPN
ejpam-3448	142	3	appl	appl	PROPN
ejpam-3448	142	4	.	.	PROPN
ejpam-3448	142	5	math	math	PROPN
ejpam-3448	142	6	,	,	PUNCT
ejpam-3448	142	7	12	12	NUM
ejpam-3448	142	8	(	(	PUNCT
ejpam-3448	142	9	3	3	NUM
ejpam-3448	142	10	)	)	PUNCT
ejpam-3448	142	11	(	(	PUNCT
ejpam-3448	142	12	2019	2019	NUM
ejpam-3448	142	13	)	)	PUNCT
ejpam-3448	142	14	,	,	PUNCT
ejpam-3448	142	15	734	734	NUM
ejpam-3448	142	16	-	-	SYM
ejpam-3448	142	17	748	748	NUM
ejpam-3448	142	18	739	739	NUM
ejpam-3448	142	19	definition	definition	NOUN
ejpam-3448	142	20	2	2	NUM
ejpam-3448	142	21	.	.	PUNCT
ejpam-3448	143	1	let	let	VERB
ejpam-3448	143	2	t1	t1	NOUN
ejpam-3448	143	3	=	=	NOUN
ejpam-3448	143	4	a1	a1	NOUN
ejpam-3448	143	5	.	.	PUNCT
ejpam-3448	143	6	.	.	PUNCT
ejpam-3448	143	7	.	.	PUNCT
ejpam-3448	144	1	am	be	AUX
ejpam-3448	144	2	and	and	CCONJ
ejpam-3448	144	3	t2	t2	NOUN
ejpam-3448	144	4	=	=	SYM
ejpam-3448	144	5	b1	b1	NOUN
ejpam-3448	144	6	.	.	PUNCT
ejpam-3448	144	7	.	.	PUNCT
ejpam-3448	144	8	.	.	PUNCT
ejpam-3448	145	1	bn	bn	PROPN
ejpam-3448	145	2	be	be	AUX
ejpam-3448	145	3	two	two	NUM
ejpam-3448	145	4	tubings	tubing	NOUN
ejpam-3448	145	5	on	on	ADP
ejpam-3448	145	6	an	an	DET
ejpam-3448	145	7	m	m	NOUN
ejpam-3448	145	8	-	-	NOUN
ejpam-3448	145	9	path	path	NOUN
ejpam-3448	145	10	and	and	CCONJ
ejpam-3448	145	11	an	an	DET
ejpam-3448	145	12	n	n	NOUN
ejpam-3448	145	13	-	-	PUNCT
ejpam-3448	145	14	path	path	NOUN
ejpam-3448	145	15	,	,	PUNCT
ejpam-3448	145	16	m	m	PROPN
ejpam-3448	145	17	,	,	PUNCT
ejpam-3448	145	18	n	n	PROPN
ejpam-3448	145	19	>	>	X
ejpam-3448	145	20	0	0	NUM
ejpam-3448	145	21	,	,	PUNCT
ejpam-3448	145	22	respectively	respectively	ADV
ejpam-3448	145	23	.	.	PUNCT
ejpam-3448	146	1	the	the	DET
ejpam-3448	146	2	transition	transition	NOUN
ejpam-3448	146	3	operation	operation	NOUN
ejpam-3448	146	4	”	"	PUNCT
ejpam-3448	146	5	∨	∨	PROPN
ejpam-3448	146	6	”	"	PUNCT
ejpam-3448	146	7	between	between	ADP
ejpam-3448	146	8	t1	t1	NOUN
ejpam-3448	146	9	and	and	CCONJ
ejpam-3448	146	10	t2	t2	NOUN
ejpam-3448	146	11	is	be	AUX
ejpam-3448	146	12	defined	define	VERB
ejpam-3448	146	13	by	by	ADP
ejpam-3448	146	14	t1	t1	PROPN
ejpam-3448	146	15	∨	∨	NUM
ejpam-3448	146	16	t2	t2	PROPN
ejpam-3448	146	17	=	=	SYM
ejpam-3448	146	18	(	(	PUNCT
ejpam-3448	146	19	a1	a1	NOUN
ejpam-3448	146	20	+	+	CCONJ
ejpam-3448	146	21	1	1	NUM
ejpam-3448	146	22	)	)	PUNCT
ejpam-3448	146	23	.	.	PUNCT
ejpam-3448	146	24	.	.	PUNCT
ejpam-3448	146	25	.	.	PUNCT
ejpam-3448	147	1	(	(	PUNCT
ejpam-3448	147	2	am	be	AUX
ejpam-3448	147	3	+	+	NOUN
ejpam-3448	147	4	1)1(b1	1)1(b1	NUM
ejpam-3448	147	5	+	+	CCONJ
ejpam-3448	147	6	1	1	NUM
ejpam-3448	147	7	)	)	PUNCT
ejpam-3448	147	8	.	.	PUNCT
ejpam-3448	147	9	.	.	PUNCT
ejpam-3448	147	10	.	.	PUNCT
ejpam-3448	148	1	(	(	PUNCT
ejpam-3448	148	2	bn	bn	X
ejpam-3448	148	3	+	+	NOUN
ejpam-3448	148	4	1	1	NUM
ejpam-3448	148	5	)	)	PUNCT
ejpam-3448	148	6	and	and	CCONJ
ejpam-3448	148	7	0	0	NUM
ejpam-3448	148	8	∨	∨	NUM
ejpam-3448	148	9	t1	t1	NOUN
ejpam-3448	148	10	=	=	SYM
ejpam-3448	148	11	1(a1	1(a1	NUM
ejpam-3448	148	12	+	+	CCONJ
ejpam-3448	148	13	1	1	NUM
ejpam-3448	148	14	)	)	PUNCT
ejpam-3448	148	15	.	.	PUNCT
ejpam-3448	148	16	.	.	PUNCT
ejpam-3448	148	17	.	.	PUNCT
ejpam-3448	149	1	(	(	PUNCT
ejpam-3448	149	2	am	be	AUX
ejpam-3448	149	3	+	+	ADV
ejpam-3448	149	4	1	1	NUM
ejpam-3448	149	5	)	)	PUNCT
ejpam-3448	149	6	and	and	CCONJ
ejpam-3448	149	7	t1	t1	NOUN
ejpam-3448	149	8	∨	∨	NUM
ejpam-3448	149	9	0	0	NUM
ejpam-3448	150	1	=	=	SYM
ejpam-3448	150	2	(	(	PUNCT
ejpam-3448	150	3	a1	a1	NOUN
ejpam-3448	150	4	+	+	CCONJ
ejpam-3448	150	5	1	1	NUM
ejpam-3448	150	6	)	)	PUNCT
ejpam-3448	150	7	.	.	PUNCT
ejpam-3448	150	8	.	.	PUNCT
ejpam-3448	151	1	.	.	PUNCT
ejpam-3448	152	1	(	(	PUNCT
ejpam-3448	152	2	am	be	AUX
ejpam-3448	152	3	+	+	X
ejpam-3448	152	4	1)1	1)1	NUM
ejpam-3448	152	5	.	.	PUNCT
ejpam-3448	153	1	it	it	PRON
ejpam-3448	153	2	is	be	AUX
ejpam-3448	153	3	easily	easily	ADV
ejpam-3448	153	4	seen	see	VERB
ejpam-3448	153	5	that	that	SCONJ
ejpam-3448	153	6	t1	t1	PROPN
ejpam-3448	153	7	∨	∨	NUM
ejpam-3448	153	8	t2	t2	PROPN
ejpam-3448	153	9	is	be	AUX
ejpam-3448	153	10	also	also	ADV
ejpam-3448	153	11	a	a	DET
ejpam-3448	153	12	maximal	maximal	ADJ
ejpam-3448	153	13	tubing	tubing	NOUN
ejpam-3448	153	14	on	on	ADP
ejpam-3448	153	15	an	an	DET
ejpam-3448	153	16	(	(	PUNCT
ejpam-3448	153	17	m	m	PROPN
ejpam-3448	153	18	+	+	NUM
ejpam-3448	153	19	n	n	PROPN
ejpam-3448	153	20	+	+	NUM
ejpam-3448	153	21	1)-path	1)-path	NUM
ejpam-3448	153	22	.	.	PUNCT
ejpam-3448	154	1	this	this	DET
ejpam-3448	154	2	operation	operation	NOUN
ejpam-3448	154	3	is	be	AUX
ejpam-3448	154	4	neither	neither	CCONJ
ejpam-3448	154	5	associative	associative	ADJ
ejpam-3448	154	6	nor	nor	CCONJ
ejpam-3448	154	7	commutative	commutative	ADJ
ejpam-3448	154	8	.	.	PUNCT
ejpam-3448	155	1	a	a	DET
ejpam-3448	155	2	remarkable	remarkable	ADJ
ejpam-3448	155	3	feature	feature	NOUN
ejpam-3448	155	4	of	of	ADP
ejpam-3448	155	5	the	the	DET
ejpam-3448	155	6	transition	transition	NOUN
ejpam-3448	155	7	operation	operation	NOUN
ejpam-3448	155	8	is	be	AUX
ejpam-3448	155	9	that	that	SCONJ
ejpam-3448	155	10	,	,	PUNCT
ejpam-3448	155	11	any	any	DET
ejpam-3448	155	12	maximal	maximal	ADJ
ejpam-3448	155	13	tubing	tubing	NOUN
ejpam-3448	155	14	t	t	NOUN
ejpam-3448	155	15	can	can	AUX
ejpam-3448	155	16	be	be	AUX
ejpam-3448	155	17	divided	divide	VERB
ejpam-3448	155	18	into	into	ADP
ejpam-3448	155	19	two	two	NUM
ejpam-3448	155	20	parts	part	NOUN
ejpam-3448	155	21	,	,	PUNCT
ejpam-3448	155	22	called	call	VERB
ejpam-3448	155	23	left	left	ADJ
ejpam-3448	155	24	t	t	PROPN
ejpam-3448	155	25	l	l	NOUN
ejpam-3448	156	1	and	and	CCONJ
ejpam-3448	156	2	right	right	ADJ
ejpam-3448	156	3	t	t	NOUN
ejpam-3448	156	4	r	r	NOUN
ejpam-3448	156	5	parts	part	NOUN
ejpam-3448	156	6	,	,	PUNCT
ejpam-3448	156	7	from	from	ADP
ejpam-3448	156	8	the	the	DET
ejpam-3448	156	9	combining	combine	VERB
ejpam-3448	156	10	node	node	NOUN
ejpam-3448	156	11	.	.	PUNCT
ejpam-3448	157	1	example	example	NOUN
ejpam-3448	158	1	1	1	NUM
ejpam-3448	158	2	.	.	PUNCT
ejpam-3448	158	3	let	let	VERB
ejpam-3448	158	4	t	t	NOUN
ejpam-3448	158	5	l	l	NOUN
ejpam-3448	158	6	=	=	SYM
ejpam-3448	158	7	123	123	NUM
ejpam-3448	158	8	∈mp(3	∈mp(3	NUM
ejpam-3448	158	9	)	)	PUNCT
ejpam-3448	158	10	and	and	CCONJ
ejpam-3448	158	11	t	t	NOUN
ejpam-3448	158	12	r	r	NOUN
ejpam-3448	158	13	=	=	SYM
ejpam-3448	158	14	2341	2341	NUM
ejpam-3448	158	15	∈mp(4	∈mp(4	NOUN
ejpam-3448	158	16	)	)	PUNCT
ejpam-3448	158	17	be	be	AUX
ejpam-3448	158	18	given	give	VERB
ejpam-3448	158	19	as	as	ADP
ejpam-3448	158	20	on	on	ADP
ejpam-3448	158	21	the	the	DET
ejpam-3448	158	22	left	left	ADJ
ejpam-3448	158	23	hand	hand	NOUN
ejpam-3448	158	24	side	side	NOUN
ejpam-3448	158	25	of	of	ADP
ejpam-3448	158	26	figure	figure	NOUN
ejpam-3448	158	27	3	3	NUM
ejpam-3448	158	28	.	.	PUNCT
ejpam-3448	159	1	the	the	DET
ejpam-3448	159	2	maximal	maximal	ADJ
ejpam-3448	159	3	tubing	tubing	NOUN
ejpam-3448	159	4	t	t	NOUN
ejpam-3448	159	5	=	=	SYM
ejpam-3448	159	6	t	t	PROPN
ejpam-3448	159	7	l	l	NOUN
ejpam-3448	159	8	∨	∨	PROPN
ejpam-3448	159	9	t	t	NOUN
ejpam-3448	159	10	r	r	NOUN
ejpam-3448	159	11	=	=	SYM
ejpam-3448	159	12	23413452	23413452	NUM
ejpam-3448	159	13	∈	∈	PROPN
ejpam-3448	159	14	mp(8	mp(8	NOUN
ejpam-3448	159	15	)	)	PUNCT
ejpam-3448	159	16	can	can	AUX
ejpam-3448	159	17	be	be	AUX
ejpam-3448	159	18	obtained	obtain	VERB
ejpam-3448	159	19	by	by	ADP
ejpam-3448	159	20	connecting	connect	VERB
ejpam-3448	159	21	these	these	DET
ejpam-3448	159	22	tubings	tubing	NOUN
ejpam-3448	159	23	via	via	ADP
ejpam-3448	159	24	a	a	DET
ejpam-3448	159	25	new	new	ADJ
ejpam-3448	159	26	node	node	NOUN
ejpam-3448	159	27	.	.	PUNCT
ejpam-3448	160	1	∨	∨	NOUN
ejpam-3448	160	2	=	=	SYM
ejpam-3448	160	3	figure	figure	NOUN
ejpam-3448	160	4	3	3	NUM
ejpam-3448	160	5	:	:	PUNCT
ejpam-3448	160	6	example	example	NOUN
ejpam-3448	160	7	of	of	ADP
ejpam-3448	160	8	the	the	DET
ejpam-3448	160	9	transition	transition	NOUN
ejpam-3448	160	10	operation	operation	NOUN
ejpam-3448	160	11	between	between	ADP
ejpam-3448	160	12	the	the	DET
ejpam-3448	160	13	tubings	tubing	NOUN
ejpam-3448	160	14	definition	definition	NOUN
ejpam-3448	160	15	3	3	X
ejpam-3448	160	16	.	.	PUNCT
ejpam-3448	161	1	let	let	VERB
ejpam-3448	161	2	t1	t1	NOUN
ejpam-3448	161	3	=	=	NOUN
ejpam-3448	161	4	a1	a1	NOUN
ejpam-3448	161	5	.	.	PUNCT
ejpam-3448	161	6	.	.	PUNCT
ejpam-3448	161	7	.	.	PUNCT
ejpam-3448	162	1	an	an	DET
ejpam-3448	162	2	∈	∈	PROPN
ejpam-3448	162	3	mp(n	mp(n	NUM
ejpam-3448	162	4	)	)	PUNCT
ejpam-3448	162	5	and	and	CCONJ
ejpam-3448	162	6	t2	t2	NOUN
ejpam-3448	162	7	=	=	SYM
ejpam-3448	162	8	b1	b1	PROPN
ejpam-3448	162	9	.	.	PUNCT
ejpam-3448	162	10	.	.	PUNCT
ejpam-3448	162	11	.	.	PUNCT
ejpam-3448	163	1	bm	bm	PROPN
ejpam-3448	163	2	∈	∈	PROPN
ejpam-3448	163	3	mp(m	mp(m	AUX
ejpam-3448	163	4	)	)	PUNCT
ejpam-3448	163	5	be	be	AUX
ejpam-3448	163	6	maximal	maximal	ADJ
ejpam-3448	163	7	tubings	tubing	NOUN
ejpam-3448	163	8	.	.	PUNCT
ejpam-3448	164	1	the	the	DET
ejpam-3448	164	2	operations	operation	NOUN
ejpam-3448	164	3	/	/	PUNCT
ejpam-3448	164	4	,	,	PUNCT
ejpam-3448	164	5	\	\	PUNCT
ejpam-3448	164	6	:	:	PUNCT
ejpam-3448	164	7	mp(n	mp(n	NUM
ejpam-3448	164	8	)	)	PUNCT
ejpam-3448	164	9	×mp(m	×mp(m	NOUN
ejpam-3448	164	10	)	)	PUNCT
ejpam-3448	164	11	→	→	SYM
ejpam-3448	164	12	mp(n	mp(n	X
ejpam-3448	164	13	+	+	SYM
ejpam-3448	164	14	m	m	VERB
ejpam-3448	164	15	)	)	PUNCT
ejpam-3448	164	16	are	be	AUX
ejpam-3448	164	17	called	call	VERB
ejpam-3448	164	18	before	before	ADV
ejpam-3448	164	19	and	and	CCONJ
ejpam-3448	164	20	after	after	ADP
ejpam-3448	164	21	operations	operation	NOUN
ejpam-3448	164	22	and	and	CCONJ
ejpam-3448	164	23	defined	define	VERB
ejpam-3448	164	24	by	by	ADP
ejpam-3448	164	25	a1	a1	NOUN
ejpam-3448	164	26	.	.	PUNCT
ejpam-3448	164	27	.	.	PUNCT
ejpam-3448	164	28	.	.	PUNCT
ejpam-3448	165	1	an	an	DET
ejpam-3448	165	2	/	/	SYM
ejpam-3448	165	3	b1	b1	NOUN
ejpam-3448	165	4	.	.	PUNCT
ejpam-3448	165	5	.	.	PUNCT
ejpam-3448	165	6	.	.	PUNCT
ejpam-3448	166	1	bm	bm	PROPN
ejpam-3448	167	1	=	=	PRON
ejpam-3448	168	1	(	(	PUNCT
ejpam-3448	168	2	a1	a1	NOUN
ejpam-3448	168	3	+	+	CCONJ
ejpam-3448	168	4	b1	b1	NOUN
ejpam-3448	168	5	)	)	PUNCT
ejpam-3448	168	6	.	.	PUNCT
ejpam-3448	168	7	.	.	PUNCT
ejpam-3448	169	1	.	.	PUNCT
ejpam-3448	170	1	(	(	PUNCT
ejpam-3448	170	2	an	an	DET
ejpam-3448	170	3	+	+	NOUN
ejpam-3448	170	4	b1)b1	b1)b1	NOUN
ejpam-3448	170	5	.	.	PUNCT
ejpam-3448	170	6	.	.	PUNCT
ejpam-3448	170	7	.	.	PUNCT
ejpam-3448	171	1	bm	bm	PROPN
ejpam-3448	171	2	a1	a1	PROPN
ejpam-3448	171	3	.	.	PUNCT
ejpam-3448	171	4	.	.	PUNCT
ejpam-3448	171	5	.	.	PUNCT
ejpam-3448	172	1	an	an	DET
ejpam-3448	172	2	\	\	PROPN
ejpam-3448	172	3	b1	b1	NOUN
ejpam-3448	172	4	.	.	PUNCT
ejpam-3448	172	5	.	.	PUNCT
ejpam-3448	172	6	.	.	PUNCT
ejpam-3448	173	1	bm	bm	PROPN
ejpam-3448	173	2	=	=	NOUN
ejpam-3448	173	3	a1	a1	PROPN
ejpam-3448	173	4	.	.	PUNCT
ejpam-3448	173	5	.	.	PUNCT
ejpam-3448	173	6	.	.	PUNCT
ejpam-3448	174	1	an(b1	an(b1	VERB
ejpam-3448	174	2	+	+	ADV
ejpam-3448	174	3	an	an	X
ejpam-3448	174	4	)	)	PUNCT
ejpam-3448	174	5	.	.	PUNCT
ejpam-3448	174	6	.	.	PUNCT
ejpam-3448	174	7	.	.	PUNCT
ejpam-3448	175	1	(	(	PUNCT
ejpam-3448	175	2	bm	bm	PROPN
ejpam-3448	175	3	+	+	CCONJ
ejpam-3448	175	4	an	an	X
ejpam-3448	175	5	)	)	PUNCT
ejpam-3448	175	6	example	example	NOUN
ejpam-3448	175	7	2	2	NUM
ejpam-3448	175	8	.	.	PUNCT
ejpam-3448	176	1	let	let	VERB
ejpam-3448	176	2	t1	t1	NOUN
ejpam-3448	176	3	=	=	NOUN
ejpam-3448	176	4	231	231	NUM
ejpam-3448	176	5	∈mp(3	∈mp(3	NUM
ejpam-3448	176	6	)	)	PUNCT
ejpam-3448	176	7	and	and	CCONJ
ejpam-3448	176	8	t2	t2	PROPN
ejpam-3448	176	9	=	=	SYM
ejpam-3448	176	10	3212	3212	NUM
ejpam-3448	176	11	∈mp(4	∈mp(4	NOUN
ejpam-3448	176	12	)	)	PUNCT
ejpam-3448	176	13	be	be	AUX
ejpam-3448	176	14	given	give	VERB
ejpam-3448	176	15	as	as	ADP
ejpam-3448	176	16	on	on	ADP
ejpam-3448	176	17	the	the	DET
ejpam-3448	176	18	left	left	ADJ
ejpam-3448	176	19	hand	hand	NOUN
ejpam-3448	176	20	side	side	NOUN
ejpam-3448	176	21	in	in	ADP
ejpam-3448	176	22	figure	figure	NOUN
ejpam-3448	176	23	4	4	NUM
ejpam-3448	176	24	.	.	PUNCT
ejpam-3448	177	1	we	we	PRON
ejpam-3448	177	2	illustrate	illustrate	VERB
ejpam-3448	177	3	the	the	DET
ejpam-3448	177	4	before	before	NOUN
ejpam-3448	177	5	and	and	CCONJ
ejpam-3448	177	6	after	after	ADP
ejpam-3448	177	7	operations	operation	NOUN
ejpam-3448	177	8	for	for	ADP
ejpam-3448	177	9	t1	t1	NOUN
ejpam-3448	177	10	and	and	CCONJ
ejpam-3448	177	11	t2	t2	NOUN
ejpam-3448	177	12	in	in	ADP
ejpam-3448	177	13	figure	figure	NOUN
ejpam-3448	177	14	4	4	NUM
ejpam-3448	177	15	.	.	PUNCT
ejpam-3448	177	16	/	/	PUNCT
ejpam-3448	177	17	\	\	NOUN
ejpam-3448	178	1	=	=	PUNCT
ejpam-3448	178	2	=	=	PRON
ejpam-3448	178	3	figure	figure	NOUN
ejpam-3448	178	4	4	4	NUM
ejpam-3448	178	5	:	:	PUNCT
ejpam-3448	178	6	before	before	ADP
ejpam-3448	178	7	and	and	CCONJ
ejpam-3448	178	8	after	after	ADP
ejpam-3448	178	9	operations	operation	NOUN
ejpam-3448	178	10	for	for	ADP
ejpam-3448	178	11	the	the	DET
ejpam-3448	178	12	maximal	maximal	ADJ
ejpam-3448	178	13	tubings	tubing	NOUN
ejpam-3448	178	14	s.	s.	PROPN
ejpam-3448	178	15	k.	k.	PROPN
ejpam-3448	178	16	gürbüzer	gürbüzer	PROPN
ejpam-3448	178	17	,	,	PUNCT
ejpam-3448	178	18	b.	b.	PROPN
ejpam-3448	178	19	akyar	akyar	PROPN
ejpam-3448	178	20	/	/	SYM
ejpam-3448	178	21	eur	eur	PROPN
ejpam-3448	178	22	.	.	PUNCT
ejpam-3448	179	1	j.	j.	PROPN
ejpam-3448	179	2	pure	pure	PROPN
ejpam-3448	179	3	appl	appl	PROPN
ejpam-3448	179	4	.	.	PROPN
ejpam-3448	179	5	math	math	PROPN
ejpam-3448	179	6	,	,	PUNCT
ejpam-3448	179	7	12	12	NUM
ejpam-3448	179	8	(	(	PUNCT
ejpam-3448	179	9	3	3	NUM
ejpam-3448	179	10	)	)	PUNCT
ejpam-3448	179	11	(	(	PUNCT
ejpam-3448	179	12	2019	2019	NUM
ejpam-3448	179	13	)	)	PUNCT
ejpam-3448	179	14	,	,	PUNCT
ejpam-3448	179	15	734	734	NUM
ejpam-3448	179	16	-	-	SYM
ejpam-3448	179	17	748	748	NUM
ejpam-3448	179	18	740	740	NUM
ejpam-3448	179	19	definition	definition	NOUN
ejpam-3448	179	20	4	4	NUM
ejpam-3448	179	21	.	.	PUNCT
ejpam-3448	180	1	the	the	DET
ejpam-3448	180	2	sum	sum	NOUN
ejpam-3448	180	3	of	of	ADP
ejpam-3448	180	4	two	two	NUM
ejpam-3448	180	5	maximal	maximal	ADJ
ejpam-3448	180	6	tubings	tubing	NOUN
ejpam-3448	180	7	t1	t1	VERB
ejpam-3448	180	8	and	and	CCONJ
ejpam-3448	180	9	t2	t2	NOUN
ejpam-3448	180	10	is	be	AUX
ejpam-3448	180	11	defined	define	VERB
ejpam-3448	180	12	by	by	ADP
ejpam-3448	180	13	t1	t1	NOUN
ejpam-3448	180	14	+	+	CCONJ
ejpam-3448	180	15	t2	t2	NOUN
ejpam-3448	180	16	:	:	PUNCT
ejpam-3448	180	17	=	=	SYM
ejpam-3448	180	18	⋃	⋃	NOUN
ejpam-3448	180	19	t1	t1	NOUN
ejpam-3448	180	20	/	/	SYM
ejpam-3448	180	21	t2≤t≤t1\t2	t2≤t≤t1\t2	NUM
ejpam-3448	180	22	t	t	NOUN
ejpam-3448	180	23	as	as	ADP
ejpam-3448	180	24	a	a	DET
ejpam-3448	180	25	set	set	NOUN
ejpam-3448	180	26	of	of	ADP
ejpam-3448	180	27	maximal	maximal	ADJ
ejpam-3448	180	28	tubings	tubing	NOUN
ejpam-3448	180	29	.	.	PUNCT
ejpam-3448	181	1	let	let	VERB
ejpam-3448	181	2	n	n	PRON
ejpam-3448	181	3	denote	denote	VERB
ejpam-3448	181	4	the	the	DET
ejpam-3448	181	5	degree	degree	NOUN
ejpam-3448	181	6	of	of	ADP
ejpam-3448	181	7	t	t	PROPN
ejpam-3448	181	8	∈	∈	PROPN
ejpam-3448	181	9	mp(n	mp(n	PROPN
ejpam-3448	181	10	)	)	PUNCT
ejpam-3448	181	11	which	which	PRON
ejpam-3448	181	12	is	be	AUX
ejpam-3448	181	13	the	the	DET
ejpam-3448	181	14	number	number	NOUN
ejpam-3448	181	15	of	of	ADP
ejpam-3448	181	16	nodes	node	NOUN
ejpam-3448	181	17	in	in	ADP
ejpam-3448	181	18	p(n	p(n	PROPN
ejpam-3448	181	19	)	)	PUNCT
ejpam-3448	181	20	.	.	PUNCT
ejpam-3448	182	1	the	the	DET
ejpam-3448	182	2	degree	degree	NOUN
ejpam-3448	182	3	of	of	ADP
ejpam-3448	182	4	each	each	DET
ejpam-3448	182	5	maximal	maximal	ADJ
ejpam-3448	182	6	tubing	tubing	NOUN
ejpam-3448	182	7	in	in	ADP
ejpam-3448	182	8	a	a	DET
ejpam-3448	182	9	sum	sum	NOUN
ejpam-3448	182	10	of	of	ADP
ejpam-3448	182	11	two	two	NUM
ejpam-3448	182	12	maximal	maximal	ADJ
ejpam-3448	182	13	tubings	tubing	NOUN
ejpam-3448	182	14	is	be	AUX
ejpam-3448	182	15	the	the	DET
ejpam-3448	182	16	sum	sum	NOUN
ejpam-3448	182	17	of	of	ADP
ejpam-3448	182	18	the	the	DET
ejpam-3448	182	19	degrees	degree	NOUN
ejpam-3448	182	20	of	of	ADP
ejpam-3448	182	21	the	the	DET
ejpam-3448	182	22	terms	term	NOUN
ejpam-3448	182	23	.	.	PUNCT
ejpam-3448	183	1	furthermore	furthermore	ADV
ejpam-3448	183	2	,	,	PUNCT
ejpam-3448	183	3	since	since	SCONJ
ejpam-3448	183	4	0	0	NUM
ejpam-3448	183	5	denotes	denote	VERB
ejpam-3448	183	6	the	the	DET
ejpam-3448	183	7	maximal	maximal	ADJ
ejpam-3448	183	8	tubing	tubing	NOUN
ejpam-3448	183	9	without	without	ADP
ejpam-3448	183	10	any	any	DET
ejpam-3448	183	11	node	node	NOUN
ejpam-3448	183	12	,	,	PUNCT
ejpam-3448	183	13	its	its	PRON
ejpam-3448	183	14	degree	degree	NOUN
ejpam-3448	183	15	is	be	AUX
ejpam-3448	183	16	considered	consider	VERB
ejpam-3448	183	17	as	as	ADP
ejpam-3448	183	18	zero	zero	NUM
ejpam-3448	183	19	and	and	CCONJ
ejpam-3448	183	20	hence	hence	ADV
ejpam-3448	183	21	0	0	NUM
ejpam-3448	183	22	is	be	AUX
ejpam-3448	183	23	the	the	DET
ejpam-3448	183	24	unit	unit	NOUN
ejpam-3448	183	25	element	element	NOUN
ejpam-3448	183	26	with	with	ADP
ejpam-3448	183	27	respect	respect	NOUN
ejpam-3448	183	28	to	to	ADP
ejpam-3448	183	29	”	"	PUNCT
ejpam-3448	183	30	+	+	CCONJ
ejpam-3448	183	31	”	"	PUNCT
ejpam-3448	183	32	.	.	PUNCT
ejpam-3448	184	1	example	example	NOUN
ejpam-3448	185	1	3	3	X
ejpam-3448	185	2	.	.	PUNCT
ejpam-3448	185	3	let	let	VERB
ejpam-3448	185	4	t1	t1	NOUN
ejpam-3448	185	5	=	=	PUNCT
ejpam-3448	185	6	123	123	NUM
ejpam-3448	185	7	and	and	CCONJ
ejpam-3448	185	8	t2	t2	NOUN
ejpam-3448	185	9	=	=	SYM
ejpam-3448	185	10	212	212	NUM
ejpam-3448	185	11	be	be	VERB
ejpam-3448	185	12	two	two	NUM
ejpam-3448	185	13	maximal	maximal	ADJ
ejpam-3448	185	14	tubings	tubing	NOUN
ejpam-3448	185	15	of	of	ADP
ejpam-3448	185	16	degree	degree	NOUN
ejpam-3448	185	17	3	3	NUM
ejpam-3448	185	18	.	.	PUNCT
ejpam-3448	186	1	the	the	DET
ejpam-3448	186	2	sum	sum	NOUN
ejpam-3448	186	3	of	of	ADP
ejpam-3448	186	4	t1	t1	NOUN
ejpam-3448	186	5	and	and	CCONJ
ejpam-3448	186	6	t2	t2	NOUN
ejpam-3448	186	7	is	be	AUX
ejpam-3448	186	8	t1	t1	NOUN
ejpam-3448	186	9	+	+	CCONJ
ejpam-3448	186	10	t2	t2	NOUN
ejpam-3448	186	11	=	=	SYM
ejpam-3448	186	12	{	{	PUNCT
ejpam-3448	186	13	345212	345212	NUM
ejpam-3448	186	14	,	,	PUNCT
ejpam-3448	186	15	245312	245312	NUM
ejpam-3448	186	16	,	,	PUNCT
ejpam-3448	186	17	235412	235412	NUM
ejpam-3448	186	18	,	,	PUNCT
ejpam-3448	186	19	234512	234512	NUM
ejpam-3448	186	20	,	,	PUNCT
ejpam-3448	186	21	134523	134523	NUM
ejpam-3448	186	22	,	,	PUNCT
ejpam-3448	186	23	124534	124534	NUM
ejpam-3448	186	24	,	,	PUNCT
ejpam-3448	186	25	123545	123545	NUM
ejpam-3448	186	26	}	}	PUNCT
ejpam-3448	186	27	.	.	PUNCT
ejpam-3448	187	1	definition	definition	NOUN
ejpam-3448	187	2	5	5	NUM
ejpam-3448	187	3	.	.	PUNCT
ejpam-3448	188	1	a	a	DET
ejpam-3448	188	2	plumbing	plumbing	NOUN
ejpam-3448	188	3	of	of	ADP
ejpam-3448	188	4	degree	degree	NOUN
ejpam-3448	188	5	n	n	NOUN
ejpam-3448	188	6	is	be	AUX
ejpam-3448	188	7	a	a	DET
ejpam-3448	188	8	collection	collection	NOUN
ejpam-3448	188	9	of	of	ADP
ejpam-3448	188	10	maximal	maximal	ADJ
ejpam-3448	188	11	tubings	tubing	NOUN
ejpam-3448	188	12	in	in	ADP
ejpam-3448	188	13	mp(n	mp(n	NOUN
ejpam-3448	188	14	)	)	PUNCT
ejpam-3448	188	15	.	.	PUNCT
ejpam-3448	189	1	we	we	PRON
ejpam-3448	189	2	denote	denote	VERB
ejpam-3448	189	3	the	the	DET
ejpam-3448	189	4	set	set	NOUN
ejpam-3448	189	5	of	of	ADP
ejpam-3448	189	6	all	all	DET
ejpam-3448	189	7	plumbings	plumbing	NOUN
ejpam-3448	189	8	of	of	ADP
ejpam-3448	189	9	degree	degree	NOUN
ejpam-3448	189	10	n	n	X
ejpam-3448	189	11	by	by	ADP
ejpam-3448	189	12	mp(n	mp(n	NOUN
ejpam-3448	189	13	)	)	PUNCT
ejpam-3448	189	14	and	and	CCONJ
ejpam-3448	189	15	mp(∞	mp(∞	NOUN
ejpam-3448	189	16	)	)	PUNCT
ejpam-3448	190	1	:	:	PUNCT
ejpam-3448	190	2	=	=	SYM
ejpam-3448	190	3	⋃	⋃	ADP
ejpam-3448	190	4	n≥0	n≥0	ADJ
ejpam-3448	190	5	mp(n	mp(n	NUM
ejpam-3448	190	6	)	)	PUNCT
ejpam-3448	190	7	.	.	PUNCT
ejpam-3448	191	1	the	the	DET
ejpam-3448	191	2	addition	addition	NOUN
ejpam-3448	191	3	operation	operation	NOUN
ejpam-3448	191	4	on	on	ADP
ejpam-3448	191	5	mp(∞	mp(∞	NOUN
ejpam-3448	191	6	)	)	PUNCT
ejpam-3448	191	7	is	be	AUX
ejpam-3448	191	8	obtained	obtain	VERB
ejpam-3448	191	9	from	from	ADP
ejpam-3448	191	10	the	the	DET
ejpam-3448	191	11	one	one	NOUN
ejpam-3448	191	12	+	+	NUM
ejpam-3448	191	13	:	:	PUNCT
ejpam-3448	191	14	mp(n)×mp(m)→mp(n+m	mp(n)×mp(m)→mp(n+m	PROPN
ejpam-3448	191	15	)	)	PUNCT
ejpam-3448	191	16	which	which	PRON
ejpam-3448	191	17	is	be	AUX
ejpam-3448	191	18	defined	define	VERB
ejpam-3448	191	19	by	by	ADP
ejpam-3448	191	20	∪iti	∪iti	NOUN
ejpam-3448	191	21	+	+	CCONJ
ejpam-3448	191	22	∪jtj	∪jtj	NOUN
ejpam-3448	191	23	:	:	PUNCT
ejpam-3448	191	24	=	=	SYM
ejpam-3448	191	25	∪i	∪i	PROPN
ejpam-3448	191	26	,	,	PUNCT
ejpam-3448	191	27	j(ti	j(ti	PROPN
ejpam-3448	191	28	+	+	CCONJ
ejpam-3448	191	29	tj	tj	NOUN
ejpam-3448	191	30	)	)	PUNCT
ejpam-3448	191	31	with	with	ADP
ejpam-3448	191	32	the	the	DET
ejpam-3448	191	33	unit	unit	NOUN
ejpam-3448	191	34	element	element	NOUN
ejpam-3448	191	35	0	0	PROPN
ejpam-3448	191	36	.	.	PUNCT
ejpam-3448	192	1	we	we	PRON
ejpam-3448	192	2	note	note	VERB
ejpam-3448	192	3	that	that	SCONJ
ejpam-3448	192	4	there	there	PRON
ejpam-3448	192	5	is	be	VERB
ejpam-3448	192	6	an	an	DET
ejpam-3448	192	7	involution	involution	NOUN
ejpam-3448	192	8	of	of	ADP
ejpam-3448	192	9	a	a	DET
ejpam-3448	192	10	tubing	tubing	NOUN
ejpam-3448	192	11	t	t	NOUN
ejpam-3448	192	12	in	in	ADP
ejpam-3448	192	13	pp(n	pp(n	PROPN
ejpam-3448	192	14	)	)	PUNCT
ejpam-3448	192	15	denoted	denote	VERB
ejpam-3448	192	16	by	by	ADP
ejpam-3448	192	17	t̄	t̄	PROPN
ejpam-3448	192	18	.	.	PUNCT
ejpam-3448	193	1	let	let	VERB
ejpam-3448	193	2	t	t	NOUN
ejpam-3448	193	3	=	=	NOUN
ejpam-3448	193	4	a1	a1	PROPN
ejpam-3448	193	5	.	.	PUNCT
ejpam-3448	193	6	.	.	PUNCT
ejpam-3448	193	7	.	.	PUNCT
ejpam-3448	194	1	an	an	DET
ejpam-3448	194	2	then	then	ADV
ejpam-3448	194	3	t̄	t̄	PROPN
ejpam-3448	194	4	=	=	PUNCT
ejpam-3448	194	5	an	an	X
ejpam-3448	194	6	.	.	PUNCT
ejpam-3448	194	7	.	.	PUNCT
ejpam-3448	194	8	.	.	PUNCT
ejpam-3448	195	1	a1	a1	PROPN
ejpam-3448	195	2	.	.	PUNCT
ejpam-3448	196	1	the	the	DET
ejpam-3448	196	2	idea	idea	NOUN
ejpam-3448	196	3	of	of	ADP
ejpam-3448	196	4	involution	involution	NOUN
ejpam-3448	196	5	can	can	AUX
ejpam-3448	196	6	be	be	AUX
ejpam-3448	196	7	extended	extend	VERB
ejpam-3448	196	8	to	to	ADP
ejpam-3448	196	9	mp(∞	mp(∞	NOUN
ejpam-3448	196	10	)	)	PUNCT
ejpam-3448	196	11	and	and	CCONJ
ejpam-3448	196	12	it	it	PRON
ejpam-3448	196	13	makes	make	VERB
ejpam-3448	196	14	mp(∞	mp(∞	NOUN
ejpam-3448	196	15	)	)	PUNCT
ejpam-3448	196	16	an	an	DET
ejpam-3448	196	17	involutive	involutive	ADJ
ejpam-3448	196	18	graded	grade	VERB
ejpam-3448	196	19	monoid	monoid	NOUN
ejpam-3448	196	20	.	.	PUNCT
ejpam-3448	197	1	theorem	theorem	NOUN
ejpam-3448	197	2	3	3	X
ejpam-3448	197	3	.	.	PUNCT
ejpam-3448	198	1	let	let	VERB
ejpam-3448	198	2	t1	t1	NOUN
ejpam-3448	198	3	,	,	PUNCT
ejpam-3448	198	4	t2	t2	NOUN
ejpam-3448	198	5	and	and	CCONJ
ejpam-3448	198	6	t3	t3	PROPN
ejpam-3448	198	7	be	be	AUX
ejpam-3448	198	8	three	three	NUM
ejpam-3448	198	9	maximal	maximal	ADJ
ejpam-3448	198	10	tubings	tubing	NOUN
ejpam-3448	198	11	.	.	PUNCT
ejpam-3448	199	1	we	we	PRON
ejpam-3448	199	2	have	have	VERB
ejpam-3448	199	3	the	the	DET
ejpam-3448	199	4	following	follow	VERB
ejpam-3448	199	5	equalities	equality	NOUN
ejpam-3448	199	6	(	(	PUNCT
ejpam-3448	199	7	t1	t1	NOUN
ejpam-3448	199	8	/	/	SYM
ejpam-3448	199	9	t2	t2	PROPN
ejpam-3448	199	10	)	)	PUNCT
ejpam-3448	199	11	\	\	PROPN
ejpam-3448	199	12	t3	t3	NOUN
ejpam-3448	199	13	=	=	PUNCT
ejpam-3448	199	14	t1/(t2	t1/(t2	NOUN
ejpam-3448	199	15	\	\	PROPN
ejpam-3448	199	16	t3	t3	PROPN
ejpam-3448	199	17	)	)	PUNCT
ejpam-3448	199	18	,	,	PUNCT
ejpam-3448	199	19	t1/(t2	t1/(t2	NOUN
ejpam-3448	199	20	∨	∨	NOUN
ejpam-3448	199	21	t3	t3	PROPN
ejpam-3448	199	22	)	)	PUNCT
ejpam-3448	199	23	=	=	PRON
ejpam-3448	199	24	(	(	PUNCT
ejpam-3448	199	25	t1	t1	NOUN
ejpam-3448	199	26	/	/	SYM
ejpam-3448	199	27	t2	t2	PROPN
ejpam-3448	199	28	)	)	PUNCT
ejpam-3448	199	29	∨	∨	NUM
ejpam-3448	199	30	t3	t3	PROPN
ejpam-3448	199	31	,	,	PUNCT
ejpam-3448	199	32	(	(	PUNCT
ejpam-3448	199	33	t1	t1	PROPN
ejpam-3448	199	34	∨	∨	NUM
ejpam-3448	199	35	t2	t2	PROPN
ejpam-3448	199	36	)	)	PUNCT
ejpam-3448	199	37	\	\	PROPN
ejpam-3448	200	1	t3	t3	PROPN
ejpam-3448	200	2	=	=	PROPN
ejpam-3448	200	3	t1	t1	PROPN
ejpam-3448	200	4	∨	∨	NOUN
ejpam-3448	200	5	(	(	PUNCT
ejpam-3448	200	6	t2	t2	PROPN
ejpam-3448	200	7	\	\	PROPN
ejpam-3448	200	8	t3	t3	PROPN
ejpam-3448	200	9	)	)	PUNCT
ejpam-3448	200	10	and	and	CCONJ
ejpam-3448	200	11	t1	t1	NOUN
ejpam-3448	200	12	∨	∨	NUM
ejpam-3448	200	13	t2	t2	PROPN
ejpam-3448	200	14	=	=	SYM
ejpam-3448	200	15	t̄2	t̄2	X
ejpam-3448	200	16	∨	∨	NUM
ejpam-3448	200	17	t̄1	t̄1	NUM
ejpam-3448	200	18	,	,	PUNCT
ejpam-3448	200	19	t1	t1	NOUN
ejpam-3448	200	20	/	/	SYM
ejpam-3448	200	21	t2	t2	NOUN
ejpam-3448	200	22	=	=	SYM
ejpam-3448	200	23	t̄2	t̄2	NOUN
ejpam-3448	200	24	\	\	X
ejpam-3448	200	25	t̄1	t̄1	NOUN
ejpam-3448	200	26	,	,	PUNCT
ejpam-3448	200	27	t1	t1	NOUN
ejpam-3448	200	28	\	\	PROPN
ejpam-3448	200	29	t2	t2	PROPN
ejpam-3448	200	30	=	=	SYM
ejpam-3448	200	31	t̄2	t̄2	NOUN
ejpam-3448	200	32	/	/	SYM
ejpam-3448	200	33	t̄1	t̄1	NOUN
ejpam-3448	200	34	,	,	PUNCT
ejpam-3448	200	35	t1	t1	NOUN
ejpam-3448	200	36	+	+	CCONJ
ejpam-3448	200	37	t2	t2	NOUN
ejpam-3448	200	38	=	=	SYM
ejpam-3448	200	39	t̄2	t̄2	NOUN
ejpam-3448	200	40	+	+	NUM
ejpam-3448	200	41	t̄1	t̄1	NOUN
ejpam-3448	200	42	and	and	CCONJ
ejpam-3448	200	43	also	also	ADV
ejpam-3448	200	44	the	the	DET
ejpam-3448	200	45	inequalities	inequality	NOUN
ejpam-3448	200	46	t	t	PROPN
ejpam-3448	200	47	∨	∨	NUM
ejpam-3448	200	48	t1	t1	PROPN
ejpam-3448	200	49	≤	≤	PROPN
ejpam-3448	200	50	t	t	PROPN
ejpam-3448	200	51	∨	∨	NUM
ejpam-3448	200	52	t2	t2	NOUN
ejpam-3448	200	53	,	,	PUNCT
ejpam-3448	200	54	t1	t1	PROPN
ejpam-3448	200	55	∨	∨	PROPN
ejpam-3448	200	56	t	t	PROPN
ejpam-3448	200	57	≤	≤	NOUN
ejpam-3448	200	58	t2	t2	PROPN
ejpam-3448	200	59	∨	∨	NUM
ejpam-3448	200	60	t	t	PROPN
ejpam-3448	200	61	,	,	PUNCT
ejpam-3448	200	62	t1	t1	PROPN
ejpam-3448	200	63	/	/	SYM
ejpam-3448	200	64	t	t	PROPN
ejpam-3448	200	65	≤	≤	NOUN
ejpam-3448	200	66	t2	t2	PROPN
ejpam-3448	200	67	/	/	SYM
ejpam-3448	200	68	t	t	PROPN
ejpam-3448	200	69	,	,	PUNCT
ejpam-3448	200	70	t	t	PROPN
ejpam-3448	200	71	\	\	PROPN
ejpam-3448	200	72	t1	t1	PROPN
ejpam-3448	200	73	≤	≤	NUM
ejpam-3448	200	74	t	t	PROPN
ejpam-3448	200	75	\	\	PROPN
ejpam-3448	200	76	t2	t2	PROPN
ejpam-3448	200	77	hold	hold	NOUN
ejpam-3448	200	78	.	.	PUNCT
ejpam-3448	201	1	in	in	ADP
ejpam-3448	201	2	addition	addition	NOUN
ejpam-3448	201	3	,	,	PUNCT
ejpam-3448	201	4	for	for	ADP
ejpam-3448	201	5	all	all	DET
ejpam-3448	201	6	t	t	PROPN
ejpam-3448	201	7	,	,	PUNCT
ejpam-3448	201	8	t	t	PROPN
ejpam-3448	201	9	′	′	NUM
ejpam-3448	201	10	∈mp(n	∈mp(n	PROPN
ejpam-3448	201	11	)	)	PUNCT
ejpam-3448	201	12	,	,	PUNCT
ejpam-3448	201	13	if	if	SCONJ
ejpam-3448	201	14	t	t	PROPN
ejpam-3448	201	15	≤	≤	X
ejpam-3448	202	1	t	t	PROPN
ejpam-3448	202	2	′	′	NOUN
ejpam-3448	202	3	then	then	ADV
ejpam-3448	202	4	t̄	t̄	PROPN
ejpam-3448	202	5	′	′	NUM
ejpam-3448	203	1	≤	≤	NUM
ejpam-3448	203	2	t̄	t̄	PROPN
ejpam-3448	203	3	.	.	PUNCT
ejpam-3448	204	1	proof	proof	NOUN
ejpam-3448	204	2	.	.	PUNCT
ejpam-3448	205	1	let	let	VERB
ejpam-3448	205	2	t1	t1	NOUN
ejpam-3448	205	3	=	=	NOUN
ejpam-3448	205	4	a1	a1	NOUN
ejpam-3448	205	5	.	.	PUNCT
ejpam-3448	205	6	.	.	PUNCT
ejpam-3448	205	7	.	.	PUNCT
ejpam-3448	206	1	an	an	PRON
ejpam-3448	206	2	,	,	PUNCT
ejpam-3448	206	3	t2	t2	NOUN
ejpam-3448	206	4	=	=	SYM
ejpam-3448	206	5	b1	b1	NOUN
ejpam-3448	206	6	.	.	PUNCT
ejpam-3448	206	7	.	.	PUNCT
ejpam-3448	206	8	.	.	PUNCT
ejpam-3448	207	1	bm	bm	PROPN
ejpam-3448	207	2	and	and	CCONJ
ejpam-3448	207	3	t3	t3	PROPN
ejpam-3448	207	4	=	=	PROPN
ejpam-3448	207	5	c1	c1	PROPN
ejpam-3448	207	6	.	.	PUNCT
ejpam-3448	207	7	.	.	PUNCT
ejpam-3448	208	1	.	.	PUNCT
ejpam-3448	209	1	cl	cl	NOUN
ejpam-3448	209	2	be	be	AUX
ejpam-3448	209	3	maximal	maximal	ADJ
ejpam-3448	209	4	tubings	tubing	NOUN
ejpam-3448	209	5	.	.	PUNCT
ejpam-3448	210	1	the	the	DET
ejpam-3448	210	2	first	first	ADJ
ejpam-3448	210	3	three	three	NUM
ejpam-3448	210	4	equalities	equality	NOUN
ejpam-3448	210	5	directly	directly	ADV
ejpam-3448	210	6	follow	follow	VERB
ejpam-3448	210	7	from	from	ADP
ejpam-3448	210	8	definition	definition	NOUN
ejpam-3448	210	9	.	.	PUNCT
ejpam-3448	211	1	the	the	DET
ejpam-3448	211	2	next	next	ADJ
ejpam-3448	211	3	three	three	NUM
ejpam-3448	211	4	equalities	equality	NOUN
ejpam-3448	211	5	are	be	AUX
ejpam-3448	211	6	obtained	obtain	VERB
ejpam-3448	211	7	as	as	ADP
ejpam-3448	211	8	follows	follow	VERB
ejpam-3448	211	9	:	:	PUNCT
ejpam-3448	211	10	t1	t1	NOUN
ejpam-3448	211	11	∨	∨	NUM
ejpam-3448	211	12	t2	t2	PROPN
ejpam-3448	211	13	=	=	SYM
ejpam-3448	211	14	a1	a1	NOUN
ejpam-3448	211	15	.	.	PUNCT
ejpam-3448	211	16	.	.	PUNCT
ejpam-3448	211	17	.	.	PUNCT
ejpam-3448	212	1	an	an	DET
ejpam-3448	212	2	∨	∨	NUM
ejpam-3448	212	3	b1	b1	NOUN
ejpam-3448	212	4	.	.	PUNCT
ejpam-3448	212	5	.	.	PUNCT
ejpam-3448	212	6	.	.	PUNCT
ejpam-3448	213	1	bm	bm	PROPN
ejpam-3448	213	2	=	=	NOUN
ejpam-3448	213	3	a1	a1	PROPN
ejpam-3448	213	4	.	.	PUNCT
ejpam-3448	213	5	.	.	PUNCT
ejpam-3448	213	6	.	.	PUNCT
ejpam-3448	214	1	an1b1	an1b1	PROPN
ejpam-3448	214	2	.	.	PUNCT
ejpam-3448	214	3	.	.	PUNCT
ejpam-3448	214	4	.	.	PUNCT
ejpam-3448	215	1	bm	bm	PROPN
ejpam-3448	215	2	=	=	PROPN
ejpam-3448	215	3	bm	bm	PROPN
ejpam-3448	215	4	.	.	PUNCT
ejpam-3448	215	5	.	.	PUNCT
ejpam-3448	215	6	.	.	PUNCT
ejpam-3448	216	1	b11a1	b11a1	PROPN
ejpam-3448	216	2	.	.	PUNCT
ejpam-3448	216	3	.	.	PUNCT
ejpam-3448	216	4	.	.	PUNCT
ejpam-3448	217	1	an	an	DET
ejpam-3448	217	2	=	=	NOUN
ejpam-3448	217	3	t̄2	t̄2	NOUN
ejpam-3448	217	4	∨	∨	NUM
ejpam-3448	217	5	t̄1	t̄1	PROPN
ejpam-3448	217	6	,	,	PUNCT
ejpam-3448	217	7	s.	s.	PROPN
ejpam-3448	217	8	k.	k.	PROPN
ejpam-3448	217	9	gürbüzer	gürbüzer	PROPN
ejpam-3448	217	10	,	,	PUNCT
ejpam-3448	217	11	b.	b.	PROPN
ejpam-3448	217	12	akyar	akyar	PROPN
ejpam-3448	217	13	/	/	SYM
ejpam-3448	217	14	eur	eur	PROPN
ejpam-3448	217	15	.	.	PUNCT
ejpam-3448	218	1	j.	j.	PROPN
ejpam-3448	218	2	pure	pure	PROPN
ejpam-3448	218	3	appl	appl	PROPN
ejpam-3448	218	4	.	.	PROPN
ejpam-3448	218	5	math	math	PROPN
ejpam-3448	218	6	,	,	PUNCT
ejpam-3448	218	7	12	12	NUM
ejpam-3448	218	8	(	(	PUNCT
ejpam-3448	218	9	3	3	NUM
ejpam-3448	218	10	)	)	PUNCT
ejpam-3448	218	11	(	(	PUNCT
ejpam-3448	218	12	2019	2019	NUM
ejpam-3448	218	13	)	)	PUNCT
ejpam-3448	218	14	,	,	PUNCT
ejpam-3448	218	15	734	734	NUM
ejpam-3448	218	16	-	-	SYM
ejpam-3448	218	17	748	748	NUM
ejpam-3448	218	18	741	741	NUM
ejpam-3448	218	19	t1	t1	NOUN
ejpam-3448	218	20	/	/	SYM
ejpam-3448	218	21	t2	t2	NOUN
ejpam-3448	218	22	=	=	SYM
ejpam-3448	218	23	a1	a1	NOUN
ejpam-3448	218	24	.	.	PUNCT
ejpam-3448	218	25	.	.	PUNCT
ejpam-3448	218	26	.	.	PUNCT
ejpam-3448	219	1	an	an	DET
ejpam-3448	219	2	/	/	SYM
ejpam-3448	219	3	b1	b1	NOUN
ejpam-3448	219	4	.	.	PUNCT
ejpam-3448	219	5	.	.	PUNCT
ejpam-3448	219	6	.	.	PUNCT
ejpam-3448	220	1	bm	bm	PROPN
ejpam-3448	221	1	=	=	PRON
ejpam-3448	222	1	(	(	PUNCT
ejpam-3448	222	2	a1	a1	NOUN
ejpam-3448	222	3	+	+	CCONJ
ejpam-3448	222	4	b1	b1	NOUN
ejpam-3448	222	5	)	)	PUNCT
ejpam-3448	222	6	.	.	PUNCT
ejpam-3448	222	7	.	.	PUNCT
ejpam-3448	223	1	.	.	PUNCT
ejpam-3448	224	1	(	(	PUNCT
ejpam-3448	224	2	an	an	DET
ejpam-3448	224	3	+	+	NOUN
ejpam-3448	224	4	b1)b1	b1)b1	NOUN
ejpam-3448	224	5	.	.	PUNCT
ejpam-3448	224	6	.	.	PUNCT
ejpam-3448	224	7	.	.	PUNCT
ejpam-3448	225	1	bm	bm	PROPN
ejpam-3448	225	2	=	=	PROPN
ejpam-3448	225	3	bm	bm	PROPN
ejpam-3448	225	4	.	.	PUNCT
ejpam-3448	225	5	.	.	PUNCT
ejpam-3448	225	6	.	.	PUNCT
ejpam-3448	226	1	b1(an	b1(an	PROPN
ejpam-3448	226	2	+	+	NUM
ejpam-3448	226	3	b1	b1	NOUN
ejpam-3448	226	4	)	)	PUNCT
ejpam-3448	226	5	.	.	PUNCT
ejpam-3448	226	6	.	.	PUNCT
ejpam-3448	227	1	.	.	PUNCT
ejpam-3448	228	1	(	(	PUNCT
ejpam-3448	228	2	a1	a1	NOUN
ejpam-3448	228	3	+	+	CCONJ
ejpam-3448	228	4	b1	b1	NOUN
ejpam-3448	228	5	)	)	PUNCT
ejpam-3448	228	6	=	=	SYM
ejpam-3448	228	7	bm	bm	PROPN
ejpam-3448	228	8	.	.	PUNCT
ejpam-3448	228	9	.	.	PUNCT
ejpam-3448	228	10	.	.	PUNCT
ejpam-3448	229	1	b1	b1	PROPN
ejpam-3448	229	2	\	\	PROPN
ejpam-3448	229	3	an	an	PRON
ejpam-3448	229	4	.	.	PUNCT
ejpam-3448	229	5	.	.	PUNCT
ejpam-3448	229	6	.	.	PUNCT
ejpam-3448	230	1	a1	a1	NOUN
ejpam-3448	230	2	=	=	SYM
ejpam-3448	230	3	t̄2	t̄2	NOUN
ejpam-3448	230	4	\	\	X
ejpam-3448	230	5	t̄1	t̄1	NOUN
ejpam-3448	230	6	,	,	PUNCT
ejpam-3448	230	7	t1	t1	NOUN
ejpam-3448	230	8	\	\	PROPN
ejpam-3448	230	9	t2	t2	PROPN
ejpam-3448	230	10	=	=	SYM
ejpam-3448	230	11	a1	a1	NOUN
ejpam-3448	230	12	.	.	PUNCT
ejpam-3448	230	13	.	.	PUNCT
ejpam-3448	230	14	.	.	PUNCT
ejpam-3448	231	1	an	an	DET
ejpam-3448	231	2	\	\	PROPN
ejpam-3448	231	3	b1	b1	NOUN
ejpam-3448	231	4	.	.	PUNCT
ejpam-3448	231	5	.	.	PUNCT
ejpam-3448	231	6	.	.	PUNCT
ejpam-3448	232	1	bm	bm	PROPN
ejpam-3448	232	2	=	=	NOUN
ejpam-3448	232	3	a1	a1	PROPN
ejpam-3448	232	4	.	.	PUNCT
ejpam-3448	232	5	.	.	PUNCT
ejpam-3448	232	6	.	.	PUNCT
ejpam-3448	233	1	an(b1	an(b1	VERB
ejpam-3448	233	2	+	+	ADV
ejpam-3448	233	3	an	an	X
ejpam-3448	233	4	)	)	PUNCT
ejpam-3448	233	5	.	.	PUNCT
ejpam-3448	233	6	.	.	PUNCT
ejpam-3448	233	7	.	.	PUNCT
ejpam-3448	234	1	(	(	PUNCT
ejpam-3448	234	2	bm	bm	PROPN
ejpam-3448	234	3	+	+	CCONJ
ejpam-3448	234	4	an	an	X
ejpam-3448	234	5	)	)	PUNCT
ejpam-3448	234	6	=	=	SYM
ejpam-3448	234	7	(	(	PUNCT
ejpam-3448	234	8	bm	bm	PROPN
ejpam-3448	234	9	+	+	CCONJ
ejpam-3448	234	10	an	an	X
ejpam-3448	234	11	)	)	PUNCT
ejpam-3448	234	12	.	.	PUNCT
ejpam-3448	234	13	.	.	PUNCT
ejpam-3448	234	14	.	.	PUNCT
ejpam-3448	235	1	(	(	PUNCT
ejpam-3448	235	2	b1	b1	NOUN
ejpam-3448	235	3	+	+	X
ejpam-3448	235	4	an)an	an)an	PUNCT
ejpam-3448	235	5	.	.	PUNCT
ejpam-3448	235	6	.	.	PUNCT
ejpam-3448	235	7	.	.	PUNCT
ejpam-3448	236	1	a1	a1	NOUN
ejpam-3448	236	2	=	=	PROPN
ejpam-3448	236	3	bm	bm	PROPN
ejpam-3448	236	4	.	.	PUNCT
ejpam-3448	236	5	.	.	PUNCT
ejpam-3448	236	6	.	.	PUNCT
ejpam-3448	237	1	b1	b1	PROPN
ejpam-3448	237	2	/	/	SYM
ejpam-3448	237	3	an	an	PRON
ejpam-3448	237	4	.	.	PUNCT
ejpam-3448	237	5	.	.	PUNCT
ejpam-3448	237	6	.	.	PUNCT
ejpam-3448	238	1	an	an	DET
ejpam-3448	238	2	=	=	PUNCT
ejpam-3448	238	3	t̄2	t̄2	NOUN
ejpam-3448	238	4	/	/	SYM
ejpam-3448	238	5	t̄1	t̄1	NOUN
ejpam-3448	238	6	.	.	PUNCT
ejpam-3448	239	1	the	the	DET
ejpam-3448	239	2	inequalities	inequality	NOUN
ejpam-3448	239	3	also	also	ADV
ejpam-3448	239	4	directly	directly	ADV
ejpam-3448	239	5	follow	follow	VERB
ejpam-3448	239	6	from	from	ADP
ejpam-3448	239	7	definitions	definition	NOUN
ejpam-3448	239	8	2	2	NUM
ejpam-3448	239	9	and	and	CCONJ
ejpam-3448	239	10	3	3	NUM
ejpam-3448	239	11	and	and	CCONJ
ejpam-3448	239	12	remark	remark	NOUN
ejpam-3448	239	13	1	1	NUM
ejpam-3448	239	14	.	.	PUNCT
ejpam-3448	240	1	for	for	ADP
ejpam-3448	240	2	the	the	DET
ejpam-3448	240	3	last	last	ADJ
ejpam-3448	240	4	equality	equality	NOUN
ejpam-3448	240	5	,	,	PUNCT
ejpam-3448	240	6	we	we	PRON
ejpam-3448	240	7	combine	combine	VERB
ejpam-3448	240	8	some	some	PRON
ejpam-3448	240	9	of	of	ADP
ejpam-3448	240	10	the	the	DET
ejpam-3448	240	11	equalities	equality	NOUN
ejpam-3448	240	12	and	and	CCONJ
ejpam-3448	240	13	the	the	DET
ejpam-3448	240	14	last	last	ADJ
ejpam-3448	240	15	two	two	NUM
ejpam-3448	240	16	inequalities	inequality	NOUN
ejpam-3448	240	17	.	.	PUNCT
ejpam-3448	241	1	theorem	theorem	ADJ
ejpam-3448	241	2	4	4	NUM
ejpam-3448	241	3	.	.	PUNCT
ejpam-3448	242	1	let	let	VERB
ejpam-3448	242	2	t1	t1	NOUN
ejpam-3448	242	3	and	and	CCONJ
ejpam-3448	242	4	t2	t2	NOUN
ejpam-3448	242	5	be	be	VERB
ejpam-3448	242	6	two	two	NUM
ejpam-3448	242	7	maximal	maximal	ADJ
ejpam-3448	242	8	tubings	tubing	NOUN
ejpam-3448	242	9	different	different	ADJ
ejpam-3448	242	10	from	from	ADP
ejpam-3448	242	11	0	0	NUM
ejpam-3448	242	12	.	.	PUNCT
ejpam-3448	243	1	the	the	DET
ejpam-3448	243	2	sum	sum	NOUN
ejpam-3448	243	3	of	of	ADP
ejpam-3448	243	4	t1	t1	NOUN
ejpam-3448	243	5	and	and	CCONJ
ejpam-3448	243	6	t2	t2	NOUN
ejpam-3448	243	7	is	be	AUX
ejpam-3448	243	8	splitted	splitte	VERB
ejpam-3448	243	9	into	into	ADP
ejpam-3448	243	10	two	two	NUM
ejpam-3448	243	11	parts	part	NOUN
ejpam-3448	243	12	as	as	ADP
ejpam-3448	243	13	t1	t1	NOUN
ejpam-3448	243	14	+	+	CCONJ
ejpam-3448	243	15	t2	t2	NOUN
ejpam-3448	243	16	=	=	SYM
ejpam-3448	243	17	(	(	PUNCT
ejpam-3448	243	18	t1	t1	NOUN
ejpam-3448	243	19	+	+	CCONJ
ejpam-3448	243	20	t	t	PROPN
ejpam-3448	243	21	l	l	NOUN
ejpam-3448	243	22	2	2	NUM
ejpam-3448	243	23	)	)	PUNCT
ejpam-3448	243	24	∨	∨	NOUN
ejpam-3448	243	25	t	t	NOUN
ejpam-3448	243	26	r	r	NOUN
ejpam-3448	243	27	2	2	NUM
ejpam-3448	243	28	∪	∪	ADP
ejpam-3448	243	29	t	t	PROPN
ejpam-3448	243	30	l	l	NOUN
ejpam-3448	243	31	1	1	NUM
ejpam-3448	243	32	∨	∨	NOUN
ejpam-3448	243	33	(	(	PUNCT
ejpam-3448	243	34	t	t	NOUN
ejpam-3448	243	35	r	r	NOUN
ejpam-3448	243	36	1	1	NUM
ejpam-3448	243	37	+	+	NUM
ejpam-3448	243	38	t2	t2	NOUN
ejpam-3448	243	39	)	)	PUNCT
ejpam-3448	243	40	,	,	PUNCT
ejpam-3448	243	41	for	for	ADP
ejpam-3448	243	42	t1	t1	NOUN
ejpam-3448	243	43	=	=	SYM
ejpam-3448	243	44	t	t	PROPN
ejpam-3448	243	45	l	l	NOUN
ejpam-3448	243	46	1	1	NUM
ejpam-3448	243	47	∨	∨	NUM
ejpam-3448	243	48	t	t	NOUN
ejpam-3448	243	49	r	r	NOUN
ejpam-3448	243	50	1	1	NUM
ejpam-3448	243	51	and	and	CCONJ
ejpam-3448	243	52	t2	t2	PROPN
ejpam-3448	243	53	=	=	SYM
ejpam-3448	243	54	t	t	PROPN
ejpam-3448	243	55	l	l	NOUN
ejpam-3448	243	56	2	2	NUM
ejpam-3448	243	57	∨	∨	NUM
ejpam-3448	243	58	t	t	NOUN
ejpam-3448	243	59	r	r	NOUN
ejpam-3448	243	60	2	2	NUM
ejpam-3448	243	61	,	,	PUNCT
ejpam-3448	243	62	where	where	SCONJ
ejpam-3448	243	63	t	t	NOUN
ejpam-3448	243	64	l	l	NOUN
ejpam-3448	244	1	i	i	PRON
ejpam-3448	244	2	and	and	CCONJ
ejpam-3448	244	3	t	t	PROPN
ejpam-3448	244	4	r	r	NOUN
ejpam-3448	245	1	i	i	PRON
ejpam-3448	245	2	are	be	AUX
ejpam-3448	245	3	left	leave	VERB
ejpam-3448	245	4	and	and	CCONJ
ejpam-3448	245	5	right	right	ADJ
ejpam-3448	245	6	parts	part	NOUN
ejpam-3448	245	7	of	of	ADP
ejpam-3448	245	8	the	the	DET
ejpam-3448	245	9	tubing	tubing	NOUN
ejpam-3448	245	10	respectively	respectively	ADV
ejpam-3448	245	11	.	.	PUNCT
ejpam-3448	246	1	proof	proof	NOUN
ejpam-3448	246	2	.	.	PUNCT
ejpam-3448	247	1	let	let	VERB
ejpam-3448	247	2	t1	t1	NOUN
ejpam-3448	247	3	=	=	NOUN
ejpam-3448	247	4	a1	a1	NOUN
ejpam-3448	247	5	.	.	PUNCT
ejpam-3448	247	6	.	.	PUNCT
ejpam-3448	247	7	.	.	PUNCT
ejpam-3448	248	1	an	an	DET
ejpam-3448	248	2	∈	∈	PROPN
ejpam-3448	248	3	mp(n	mp(n	NUM
ejpam-3448	248	4	)	)	PUNCT
ejpam-3448	248	5	and	and	CCONJ
ejpam-3448	248	6	t2	t2	NOUN
ejpam-3448	248	7	=	=	SYM
ejpam-3448	248	8	b1	b1	PROPN
ejpam-3448	248	9	.	.	PUNCT
ejpam-3448	248	10	.	.	PUNCT
ejpam-3448	248	11	.	.	PUNCT
ejpam-3448	249	1	bm	bm	PROPN
ejpam-3448	249	2	∈	∈	PROPN
ejpam-3448	249	3	mp(m	mp(m	AUX
ejpam-3448	249	4	)	)	PUNCT
ejpam-3448	249	5	be	be	AUX
ejpam-3448	249	6	two	two	NUM
ejpam-3448	249	7	maximal	maximal	ADJ
ejpam-3448	249	8	tubings	tubing	NOUN
ejpam-3448	249	9	such	such	ADJ
ejpam-3448	249	10	that	that	PRON
ejpam-3448	249	11	ai	ai	VERB
ejpam-3448	249	12	=	=	NOUN
ejpam-3448	249	13	1	1	NUM
ejpam-3448	249	14	and	and	CCONJ
ejpam-3448	249	15	bj	bj	VERB
ejpam-3448	249	16	=	=	NOUN
ejpam-3448	249	17	1	1	X
ejpam-3448	249	18	.	.	PUNCT
ejpam-3448	250	1	now	now	ADV
ejpam-3448	250	2	we	we	PRON
ejpam-3448	250	3	have	have	VERB
ejpam-3448	250	4	t1	t1	NOUN
ejpam-3448	250	5	+	+	CCONJ
ejpam-3448	250	6	t2	t2	NOUN
ejpam-3448	250	7	=	=	SYM
ejpam-3448	250	8	{	{	PUNCT
ejpam-3448	250	9	t	t	NOUN
ejpam-3448	250	10	∈mp(n+m	∈mp(n+m	PROPN
ejpam-3448	250	11	)	)	PUNCT
ejpam-3448	251	1	|	|	ADV
ejpam-3448	251	2	t1	t1	NOUN
ejpam-3448	251	3	/	/	SYM
ejpam-3448	251	4	t2	t2	NOUN
ejpam-3448	251	5	=	=	SYM
ejpam-3448	251	6	(	(	PUNCT
ejpam-3448	251	7	t1	t1	PROPN
ejpam-3448	251	8	/	/	SYM
ejpam-3448	251	9	t	t	PROPN
ejpam-3448	251	10	l	l	NOUN
ejpam-3448	251	11	2	2	X
ejpam-3448	251	12	)	)	PUNCT
ejpam-3448	251	13	∨	∨	NOUN
ejpam-3448	251	14	t	t	NOUN
ejpam-3448	251	15	r	r	NOUN
ejpam-3448	251	16	2	2	NUM
ejpam-3448	251	17	≤	≤	NOUN
ejpam-3448	251	18	t	t	NOUN
ejpam-3448	251	19	≤	≤	NUM
ejpam-3448	251	20	t	t	PROPN
ejpam-3448	251	21	l	l	NOUN
ejpam-3448	251	22	1	1	NUM
ejpam-3448	251	23	∨	∨	NOUN
ejpam-3448	251	24	(	(	PUNCT
ejpam-3448	251	25	t	t	NOUN
ejpam-3448	251	26	r	r	NOUN
ejpam-3448	251	27	1	1	NUM
ejpam-3448	251	28	\	\	NOUN
ejpam-3448	251	29	t2	t2	NOUN
ejpam-3448	251	30	)	)	PUNCT
ejpam-3448	252	1	=	=	PUNCT
ejpam-3448	252	2	t1	t1	NOUN
ejpam-3448	252	3	\	\	PROPN
ejpam-3448	252	4	t2	t2	PROPN
ejpam-3448	252	5	}	}	PUNCT
ejpam-3448	252	6	=	=	SYM
ejpam-3448	252	7	{	{	PUNCT
ejpam-3448	252	8	t	t	NOUN
ejpam-3448	252	9	=	=	PROPN
ejpam-3448	252	10	c1	c1	PROPN
ejpam-3448	252	11	.	.	PUNCT
ejpam-3448	252	12	.	.	PUNCT
ejpam-3448	252	13	.	.	PUNCT
ejpam-3448	253	1	cm+n	cm+n	PROPN
ejpam-3448	253	2	∈mp(n+m	∈mp(n+m	PROPN
ejpam-3448	253	3	)	)	PUNCT
ejpam-3448	254	1	|	|	ADV
ejpam-3448	254	2	(	(	PUNCT
ejpam-3448	254	3	a1	a1	NOUN
ejpam-3448	254	4	+	+	CCONJ
ejpam-3448	254	5	b1	b1	NOUN
ejpam-3448	254	6	)	)	PUNCT
ejpam-3448	254	7	.	.	PUNCT
ejpam-3448	254	8	.	.	PUNCT
ejpam-3448	254	9	.	.	PUNCT
ejpam-3448	255	1	(	(	PUNCT
ejpam-3448	255	2	an	an	DET
ejpam-3448	255	3	+	+	NOUN
ejpam-3448	255	4	b1)b1	b1)b1	NOUN
ejpam-3448	255	5	.	.	PUNCT
ejpam-3448	255	6	.	.	PUNCT
ejpam-3448	255	7	.	.	PUNCT
ejpam-3448	256	1	bm	bm	PROPN
ejpam-3448	256	2	≤	≤	PROPN
ejpam-3448	256	3	t	t	PROPN
ejpam-3448	256	4	≤	≤	NUM
ejpam-3448	256	5	a1	a1	NOUN
ejpam-3448	256	6	.	.	PUNCT
ejpam-3448	256	7	.	.	PUNCT
ejpam-3448	256	8	.	.	PUNCT
ejpam-3448	257	1	an(b1	an(b1	VERB
ejpam-3448	257	2	+	+	ADV
ejpam-3448	257	3	an	an	X
ejpam-3448	257	4	)	)	PUNCT
ejpam-3448	257	5	.	.	PUNCT
ejpam-3448	257	6	.	.	PUNCT
ejpam-3448	257	7	.	.	PUNCT
ejpam-3448	258	1	(	(	PUNCT
ejpam-3448	258	2	bm	bm	PROPN
ejpam-3448	258	3	+	+	CCONJ
ejpam-3448	258	4	an	an	X
ejpam-3448	258	5	)	)	PUNCT
ejpam-3448	258	6	}	}	PUNCT
ejpam-3448	258	7	.	.	PUNCT
ejpam-3448	259	1	from	from	ADP
ejpam-3448	259	2	definition	definition	NOUN
ejpam-3448	259	3	4	4	NUM
ejpam-3448	259	4	,	,	PUNCT
ejpam-3448	259	5	we	we	PRON
ejpam-3448	259	6	directly	directly	ADV
ejpam-3448	259	7	observe	observe	VERB
ejpam-3448	259	8	that	that	SCONJ
ejpam-3448	259	9	the	the	DET
ejpam-3448	259	10	tubes	tube	NOUN
ejpam-3448	259	11	in	in	ADP
ejpam-3448	259	12	t	t	PROPN
ejpam-3448	259	13	l	l	NOUN
ejpam-3448	259	14	1	1	NUM
ejpam-3448	259	15	and	and	CCONJ
ejpam-3448	259	16	t	t	NOUN
ejpam-3448	259	17	r	r	NOUN
ejpam-3448	259	18	2	2	NUM
ejpam-3448	259	19	can	can	AUX
ejpam-3448	259	20	not	not	PART
ejpam-3448	259	21	be	be	AUX
ejpam-3448	259	22	slided	slide	VERB
ejpam-3448	259	23	from	from	ADP
ejpam-3448	259	24	left	left	ADJ
ejpam-3448	259	25	to	to	ADP
ejpam-3448	259	26	right	right	NOUN
ejpam-3448	259	27	.	.	PUNCT
ejpam-3448	260	1	we	we	PRON
ejpam-3448	260	2	assume	assume	VERB
ejpam-3448	260	3	that	that	SCONJ
ejpam-3448	260	4	there	there	PRON
ejpam-3448	260	5	exist	exist	VERB
ejpam-3448	260	6	two	two	NUM
ejpam-3448	260	7	tubes	tube	NOUN
ejpam-3448	260	8	t1	t1	NOUN
ejpam-3448	260	9	and	and	CCONJ
ejpam-3448	260	10	t2	t2	NOUN
ejpam-3448	260	11	different	different	ADJ
ejpam-3448	260	12	from	from	ADP
ejpam-3448	260	13	the	the	DET
ejpam-3448	260	14	universal	universal	ADJ
ejpam-3448	260	15	tube	tube	NOUN
ejpam-3448	260	16	such	such	ADJ
ejpam-3448	260	17	that	that	SCONJ
ejpam-3448	260	18	t1	t1	PROPN
ejpam-3448	260	19	/∈	/∈	PUNCT
ejpam-3448	261	1	t	t	PROPN
ejpam-3448	261	2	l	l	NOUN
ejpam-3448	261	3	1	1	NUM
ejpam-3448	261	4	and	and	CCONJ
ejpam-3448	261	5	t2	t2	PROPN
ejpam-3448	261	6	/∈	/∈	PUNCT
ejpam-3448	262	1	t	t	NOUN
ejpam-3448	262	2	r	r	NOUN
ejpam-3448	262	3	2	2	NUM
ejpam-3448	262	4	contain	contain	VERB
ejpam-3448	262	5	all	all	DET
ejpam-3448	262	6	nodes	node	NOUN
ejpam-3448	262	7	in	in	ADP
ejpam-3448	262	8	the	the	DET
ejpam-3448	262	9	tubes	tube	NOUN
ejpam-3448	262	10	of	of	ADP
ejpam-3448	262	11	t	t	PROPN
ejpam-3448	262	12	l	l	PROPN
ejpam-3448	262	13	1	1	NUM
ejpam-3448	262	14	and	and	CCONJ
ejpam-3448	262	15	t	t	NOUN
ejpam-3448	262	16	r	r	NOUN
ejpam-3448	262	17	2	2	NUM
ejpam-3448	262	18	,	,	PUNCT
ejpam-3448	262	19	respectively	respectively	ADV
ejpam-3448	262	20	.	.	PUNCT
ejpam-3448	263	1	according	accord	VERB
ejpam-3448	263	2	to	to	ADP
ejpam-3448	263	3	the	the	DET
ejpam-3448	263	4	compatibility	compatibility	NOUN
ejpam-3448	263	5	condition	condition	NOUN
ejpam-3448	263	6	,	,	PUNCT
ejpam-3448	263	7	i	i	PRON
ejpam-3448	263	8	-	-	PUNCT
ejpam-3448	263	9	th	th	X
ejpam-3448	263	10	and	and	CCONJ
ejpam-3448	263	11	(	(	PUNCT
ejpam-3448	263	12	n+j)-th	n+j)-th	ADJ
ejpam-3448	263	13	nodes	node	NOUN
ejpam-3448	263	14	must	must	AUX
ejpam-3448	263	15	be	be	AUX
ejpam-3448	263	16	contained	contain	VERB
ejpam-3448	263	17	in	in	ADP
ejpam-3448	263	18	t1	t1	NOUN
ejpam-3448	263	19	and	and	CCONJ
ejpam-3448	263	20	t2	t2	NOUN
ejpam-3448	263	21	,	,	PUNCT
ejpam-3448	263	22	respectively	respectively	ADV
ejpam-3448	263	23	.	.	PUNCT
ejpam-3448	264	1	since	since	SCONJ
ejpam-3448	264	2	each	each	DET
ejpam-3448	264	3	tubing	tubing	NOUN
ejpam-3448	264	4	t	t	NOUN
ejpam-3448	264	5	in	in	ADP
ejpam-3448	264	6	the	the	DET
ejpam-3448	264	7	sum	sum	NOUN
ejpam-3448	264	8	(	(	PUNCT
ejpam-3448	264	9	t1	t1	NOUN
ejpam-3448	264	10	+	+	NOUN
ejpam-3448	264	11	t2	t2	NOUN
ejpam-3448	264	12	)	)	PUNCT
ejpam-3448	264	13	is	be	AUX
ejpam-3448	264	14	maximal	maximal	ADJ
ejpam-3448	264	15	,	,	PUNCT
ejpam-3448	264	16	there	there	PRON
ejpam-3448	264	17	must	must	AUX
ejpam-3448	264	18	be	be	AUX
ejpam-3448	264	19	a	a	DET
ejpam-3448	264	20	node	node	NOUN
ejpam-3448	264	21	contained	contain	VERB
ejpam-3448	264	22	only	only	ADV
ejpam-3448	264	23	by	by	ADP
ejpam-3448	264	24	the	the	DET
ejpam-3448	264	25	universal	universal	ADJ
ejpam-3448	264	26	tube	tube	NOUN
ejpam-3448	264	27	and	and	CCONJ
ejpam-3448	264	28	this	this	DET
ejpam-3448	264	29	node	node	NOUN
ejpam-3448	264	30	must	must	AUX
ejpam-3448	264	31	be	be	AUX
ejpam-3448	264	32	between	between	ADP
ejpam-3448	264	33	i	i	PROPN
ejpam-3448	264	34	-	-	PUNCT
ejpam-3448	264	35	th	th	PROPN
ejpam-3448	264	36	and	and	CCONJ
ejpam-3448	264	37	(	(	PUNCT
ejpam-3448	264	38	n+j)th	n+j)th	PROPN
ejpam-3448	264	39	nodes	node	NOUN
ejpam-3448	264	40	.	.	PUNCT
ejpam-3448	265	1	this	this	PRON
ejpam-3448	265	2	contradicts	contradict	VERB
ejpam-3448	265	3	with	with	ADP
ejpam-3448	265	4	ak	ak	PROPN
ejpam-3448	265	5	≥	≥	PROPN
ejpam-3448	265	6	2	2	NUM
ejpam-3448	265	7	for	for	ADP
ejpam-3448	265	8	k	k	X
ejpam-3448	265	9	=	=	X
ejpam-3448	265	10	i+	i+	PROPN
ejpam-3448	265	11	1	1	NUM
ejpam-3448	265	12	,	,	PUNCT
ejpam-3448	265	13	.	.	PUNCT
ejpam-3448	265	14	.	.	PUNCT
ejpam-3448	266	1	.	.	PUNCT
ejpam-3448	267	1	,	,	PUNCT
ejpam-3448	267	2	n	n	PROPN
ejpam-3448	267	3	and	and	CCONJ
ejpam-3448	267	4	bk	bk	X
ejpam-3448	267	5	≥	≥	NOUN
ejpam-3448	267	6	2	2	NUM
ejpam-3448	267	7	for	for	ADP
ejpam-3448	267	8	k	k	X
ejpam-3448	267	9	=	=	SYM
ejpam-3448	267	10	1	1	NUM
ejpam-3448	267	11	,	,	PUNCT
ejpam-3448	267	12	.	.	PUNCT
ejpam-3448	268	1	.	.	PUNCT
ejpam-3448	269	1	.	.	PUNCT
ejpam-3448	270	1	,	,	PUNCT
ejpam-3448	270	2	j−	j−	PROPN
ejpam-3448	270	3	1	1	NUM
ejpam-3448	270	4	.	.	PUNCT
ejpam-3448	271	1	so	so	ADV
ejpam-3448	271	2	there	there	PRON
ejpam-3448	271	3	are	be	VERB
ejpam-3448	271	4	exactly	exactly	ADV
ejpam-3448	271	5	two	two	NUM
ejpam-3448	271	6	types	type	NOUN
ejpam-3448	271	7	of	of	ADP
ejpam-3448	271	8	tubings	tubing	NOUN
ejpam-3448	271	9	in	in	ADP
ejpam-3448	271	10	(	(	PUNCT
ejpam-3448	271	11	t1	t1	NOUN
ejpam-3448	271	12	+	+	CCONJ
ejpam-3448	271	13	t2	t2	NOUN
ejpam-3448	271	14	)	)	PUNCT
ejpam-3448	271	15	in	in	ADP
ejpam-3448	271	16	which	which	PRON
ejpam-3448	271	17	the	the	DET
ejpam-3448	271	18	corresponding	corresponding	ADJ
ejpam-3448	271	19	name	name	NOUN
ejpam-3448	271	20	has	have	VERB
ejpam-3448	271	21	either	either	CCONJ
ejpam-3448	271	22	ci	ci	NOUN
ejpam-3448	271	23	=	=	SYM
ejpam-3448	271	24	1	1	NUM
ejpam-3448	271	25	or	or	CCONJ
ejpam-3448	271	26	cn+j	cn+j	PROPN
ejpam-3448	271	27	=	=	SYM
ejpam-3448	271	28	1	1	X
ejpam-3448	271	29	.	.	PUNCT
ejpam-3448	272	1	now	now	ADV
ejpam-3448	272	2	let	let	VERB
ejpam-3448	272	3	us	we	PRON
ejpam-3448	272	4	consider	consider	VERB
ejpam-3448	272	5	the	the	DET
ejpam-3448	272	6	first	first	ADJ
ejpam-3448	272	7	type	type	NOUN
ejpam-3448	272	8	of	of	ADP
ejpam-3448	272	9	the	the	DET
ejpam-3448	272	10	tubings	tubing	NOUN
ejpam-3448	272	11	in	in	ADP
ejpam-3448	272	12	t1+t2	t1+t2	PROPN
ejpam-3448	272	13	,	,	PUNCT
ejpam-3448	272	14	where	where	SCONJ
ejpam-3448	272	15	ci	ci	NOUN
ejpam-3448	272	16	=	=	NOUN
ejpam-3448	272	17	1	1	X
ejpam-3448	272	18	.	.	PUNCT
ejpam-3448	273	1	by	by	ADP
ejpam-3448	273	2	definition	definition	NOUN
ejpam-3448	273	3	,	,	PUNCT
ejpam-3448	273	4	the	the	DET
ejpam-3448	273	5	maximum	maximum	NOUN
ejpam-3448	273	6	of	of	ADP
ejpam-3448	273	7	these	these	DET
ejpam-3448	273	8	tubings	tubing	NOUN
ejpam-3448	273	9	is	be	AUX
ejpam-3448	273	10	t1	t1	NOUN
ejpam-3448	273	11	\t2	\t2	PUNCT
ejpam-3448	274	1	=	=	PUNCT
ejpam-3448	274	2	a1	a1	NOUN
ejpam-3448	274	3	.	.	PUNCT
ejpam-3448	274	4	.	.	PUNCT
ejpam-3448	274	5	.	.	PUNCT
ejpam-3448	275	1	an(b1+an	an(b1+an	ADJ
ejpam-3448	275	2	)	)	PUNCT
ejpam-3448	275	3	.	.	PUNCT
ejpam-3448	275	4	.	.	PUNCT
ejpam-3448	275	5	.	.	PUNCT
ejpam-3448	276	1	(	(	PUNCT
ejpam-3448	276	2	bm+an	bm+an	NOUN
ejpam-3448	276	3	)	)	PUNCT
ejpam-3448	276	4	but	but	CCONJ
ejpam-3448	276	5	the	the	DET
ejpam-3448	276	6	minimum	minimum	ADJ
ejpam-3448	276	7	one	one	NOUN
ejpam-3448	276	8	can	can	AUX
ejpam-3448	276	9	only	only	ADV
ejpam-3448	276	10	be	be	AUX
ejpam-3448	276	11	the	the	DET
ejpam-3448	276	12	tubing	tubing	NOUN
ejpam-3448	276	13	a1	a1	NOUN
ejpam-3448	276	14	.	.	PUNCT
ejpam-3448	276	15	.	.	PUNCT
ejpam-3448	276	16	.	.	PUNCT
ejpam-3448	277	1	ai(ai+1	ai(ai+1	VERB
ejpam-3448	278	1	+	+	CCONJ
ejpam-3448	278	2	b1	b1	NOUN
ejpam-3448	278	3	)	)	PUNCT
ejpam-3448	278	4	.	.	PUNCT
ejpam-3448	278	5	.	.	PUNCT
ejpam-3448	279	1	.	.	PUNCT
ejpam-3448	280	1	(	(	PUNCT
ejpam-3448	280	2	an	an	DET
ejpam-3448	280	3	+	+	NOUN
ejpam-3448	280	4	b1)(b1	b1)(b1	NOUN
ejpam-3448	280	5	+	+	NOUN
ejpam-3448	280	6	1	1	NUM
ejpam-3448	280	7	)	)	PUNCT
ejpam-3448	280	8	.	.	PUNCT
ejpam-3448	280	9	.	.	PUNCT
ejpam-3448	280	10	.	.	PUNCT
ejpam-3448	281	1	(	(	PUNCT
ejpam-3448	281	2	bm	bm	NOUN
ejpam-3448	281	3	+	+	NOUN
ejpam-3448	281	4	1	1	X
ejpam-3448	281	5	)	)	PUNCT
ejpam-3448	281	6	and	and	CCONJ
ejpam-3448	281	7	the	the	DET
ejpam-3448	281	8	rewriting	rewrite	VERB
ejpam-3448	281	9	the	the	DET
ejpam-3448	281	10	name	name	NOUN
ejpam-3448	281	11	of	of	ADP
ejpam-3448	281	12	this	this	DET
ejpam-3448	281	13	tubing	tubing	NOUN
ejpam-3448	281	14	step	step	NOUN
ejpam-3448	281	15	by	by	ADP
ejpam-3448	281	16	step	step	NOUN
ejpam-3448	281	17	as	as	ADP
ejpam-3448	281	18	the	the	DET
ejpam-3448	281	19	following	follow	VERB
ejpam-3448	281	20	form	form	NOUN
ejpam-3448	281	21	(	(	PUNCT
ejpam-3448	281	22	a1	a1	NOUN
ejpam-3448	281	23	−	−	NOUN
ejpam-3448	281	24	1	1	NUM
ejpam-3448	281	25	)	)	PUNCT
ejpam-3448	281	26	.	.	PUNCT
ejpam-3448	281	27	.	.	PUNCT
ejpam-3448	281	28	.	.	PUNCT
ejpam-3448	282	1	(	(	PUNCT
ejpam-3448	282	2	ai−1	ai−1	PROPN
ejpam-3448	282	3	−	−	PROPN
ejpam-3448	282	4	1	1	NUM
ejpam-3448	282	5	)	)	PUNCT
ejpam-3448	282	6	∨	∨	NOUN
ejpam-3448	282	7	(	(	PUNCT
ejpam-3448	282	8	(	(	PUNCT
ejpam-3448	282	9	ai+1	ai+1	X
ejpam-3448	282	10	+	+	X
ejpam-3448	282	11	b1	b1	NOUN
ejpam-3448	282	12	−	−	PROPN
ejpam-3448	282	13	1	1	NUM
ejpam-3448	282	14	)	)	PUNCT
ejpam-3448	282	15	.	.	PUNCT
ejpam-3448	282	16	.	.	PUNCT
ejpam-3448	282	17	.	.	PUNCT
ejpam-3448	283	1	(	(	PUNCT
ejpam-3448	283	2	an	an	DET
ejpam-3448	283	3	+	+	NUM
ejpam-3448	283	4	b1	b1	NOUN
ejpam-3448	283	5	−	−	PROPN
ejpam-3448	283	6	1)b1	1)b1	NUM
ejpam-3448	283	7	.	.	PUNCT
ejpam-3448	283	8	.	.	PUNCT
ejpam-3448	283	9	.	.	PUNCT
ejpam-3448	284	1	bm	bm	PROPN
ejpam-3448	284	2	)	)	PUNCT
ejpam-3448	285	1	=	=	PUNCT
ejpam-3448	285	2	(	(	PUNCT
ejpam-3448	285	3	a1	a1	NOUN
ejpam-3448	285	4	−	−	NOUN
ejpam-3448	285	5	1	1	NUM
ejpam-3448	285	6	)	)	PUNCT
ejpam-3448	285	7	.	.	PUNCT
ejpam-3448	285	8	.	.	PUNCT
ejpam-3448	285	9	.	.	PUNCT
ejpam-3448	286	1	(	(	PUNCT
ejpam-3448	286	2	ai−1	ai−1	PROPN
ejpam-3448	286	3	−	−	PROPN
ejpam-3448	286	4	1	1	NUM
ejpam-3448	286	5	)	)	PUNCT
ejpam-3448	286	6	∨	∨	NOUN
ejpam-3448	286	7	(	(	PUNCT
ejpam-3448	286	8	(	(	PUNCT
ejpam-3448	286	9	ai+1	ai+1	NUM
ejpam-3448	286	10	−	−	PROPN
ejpam-3448	286	11	1	1	NUM
ejpam-3448	286	12	)	)	PUNCT
ejpam-3448	286	13	.	.	PUNCT
ejpam-3448	286	14	.	.	PUNCT
ejpam-3448	286	15	.	.	PUNCT
ejpam-3448	287	1	(	(	PUNCT
ejpam-3448	287	2	an	an	DET
ejpam-3448	287	3	−	−	PROPN
ejpam-3448	287	4	1)/b1	1)/b1	NUM
ejpam-3448	287	5	.	.	PUNCT
ejpam-3448	287	6	.	.	PUNCT
ejpam-3448	287	7	.	.	PUNCT
ejpam-3448	288	1	bm	bm	PROPN
ejpam-3448	288	2	)	)	PUNCT
ejpam-3448	289	1	=	=	PUNCT
ejpam-3448	289	2	t	t	NOUN
ejpam-3448	289	3	l	l	NOUN
ejpam-3448	289	4	1	1	NUM
ejpam-3448	289	5	∨	∨	NUM
ejpam-3448	289	6	t	t	NOUN
ejpam-3448	289	7	r	r	NOUN
ejpam-3448	289	8	1	1	NUM
ejpam-3448	289	9	/t2	/t2	NOUN
ejpam-3448	289	10	gives	give	VERB
ejpam-3448	289	11	that	that	SCONJ
ejpam-3448	289	12	the	the	DET
ejpam-3448	289	13	set	set	NOUN
ejpam-3448	289	14	of	of	ADP
ejpam-3448	289	15	tubings	tubing	NOUN
ejpam-3448	289	16	of	of	ADP
ejpam-3448	289	17	the	the	DET
ejpam-3448	289	18	first	first	ADJ
ejpam-3448	289	19	type	type	NOUN
ejpam-3448	289	20	is	be	AUX
ejpam-3448	289	21	{	{	PUNCT
ejpam-3448	289	22	t	t	NOUN
ejpam-3448	289	23	∈mp(n+m)|t	∈mp(n+m)|t	PROPN
ejpam-3448	289	24	l	l	NOUN
ejpam-3448	289	25	1∨	1∨	NUM
ejpam-3448	289	26	(	(	PUNCT
ejpam-3448	289	27	t	t	NOUN
ejpam-3448	289	28	r	r	NOUN
ejpam-3448	289	29	1	1	NUM
ejpam-3448	289	30	/t2	/t2	NOUN
ejpam-3448	289	31	)	)	PUNCT
ejpam-3448	289	32	≤	≤	PUNCT
ejpam-3448	289	33	t	t	PROPN
ejpam-3448	289	34	≤	≤	NUM
ejpam-3448	289	35	t	t	PROPN
ejpam-3448	289	36	l	l	NOUN
ejpam-3448	289	37	1∨	1∨	NUM
ejpam-3448	289	38	(	(	PUNCT
ejpam-3448	289	39	t	t	NOUN
ejpam-3448	289	40	r	r	NOUN
ejpam-3448	289	41	1	1	NUM
ejpam-3448	289	42	\t2	\t2	NUM
ejpam-3448	289	43	)	)	PUNCT
ejpam-3448	289	44	}	}	PUNCT
ejpam-3448	289	45	.	.	PUNCT
ejpam-3448	290	1	hence	hence	ADV
ejpam-3448	290	2	the	the	DET
ejpam-3448	290	3	set	set	NOUN
ejpam-3448	290	4	of	of	ADP
ejpam-3448	290	5	tubings	tubing	NOUN
ejpam-3448	290	6	of	of	ADP
ejpam-3448	290	7	the	the	DET
ejpam-3448	290	8	first	first	ADJ
ejpam-3448	290	9	type	type	NOUN
ejpam-3448	290	10	is	be	AUX
ejpam-3448	290	11	the	the	DET
ejpam-3448	290	12	plumbing	plumbing	NOUN
ejpam-3448	290	13	t	t	NOUN
ejpam-3448	290	14	l	l	NOUN
ejpam-3448	290	15	1∨(t	1∨(t	NUM
ejpam-3448	290	16	r	r	NOUN
ejpam-3448	290	17	1	1	NUM
ejpam-3448	290	18	+	+	NOUN
ejpam-3448	290	19	t2	t2	NOUN
ejpam-3448	290	20	)	)	PUNCT
ejpam-3448	290	21	.	.	PUNCT
ejpam-3448	291	1	similarly	similarly	ADV
ejpam-3448	291	2	s.	s.	PROPN
ejpam-3448	291	3	k.	k.	PROPN
ejpam-3448	291	4	gürbüzer	gürbüzer	PROPN
ejpam-3448	291	5	,	,	PUNCT
ejpam-3448	291	6	b.	b.	PROPN
ejpam-3448	291	7	akyar	akyar	PROPN
ejpam-3448	291	8	/	/	SYM
ejpam-3448	291	9	eur	eur	PROPN
ejpam-3448	291	10	.	.	PUNCT
ejpam-3448	292	1	j.	j.	PROPN
ejpam-3448	292	2	pure	pure	PROPN
ejpam-3448	292	3	appl	appl	PROPN
ejpam-3448	292	4	.	.	PROPN
ejpam-3448	292	5	math	math	PROPN
ejpam-3448	292	6	,	,	PUNCT
ejpam-3448	292	7	12	12	NUM
ejpam-3448	292	8	(	(	PUNCT
ejpam-3448	292	9	3	3	NUM
ejpam-3448	292	10	)	)	PUNCT
ejpam-3448	292	11	(	(	PUNCT
ejpam-3448	292	12	2019	2019	NUM
ejpam-3448	292	13	)	)	PUNCT
ejpam-3448	292	14	,	,	PUNCT
ejpam-3448	292	15	734	734	NUM
ejpam-3448	292	16	-	-	SYM
ejpam-3448	292	17	748	748	NUM
ejpam-3448	292	18	742	742	NUM
ejpam-3448	292	19	for	for	ADP
ejpam-3448	292	20	the	the	DET
ejpam-3448	292	21	tubings	tubing	NOUN
ejpam-3448	292	22	of	of	ADP
ejpam-3448	292	23	the	the	DET
ejpam-3448	292	24	second	second	ADJ
ejpam-3448	292	25	type	type	NOUN
ejpam-3448	293	1	,	,	PUNCT
ejpam-3448	293	2	the	the	DET
ejpam-3448	293	3	minimum	minimum	NOUN
ejpam-3448	293	4	tubing	tubing	NOUN
ejpam-3448	293	5	is	be	AUX
ejpam-3448	293	6	t1	t1	NOUN
ejpam-3448	293	7	/	/	SYM
ejpam-3448	293	8	t2	t2	PROPN
ejpam-3448	293	9	and	and	CCONJ
ejpam-3448	293	10	the	the	DET
ejpam-3448	293	11	maximum	maximum	ADJ
ejpam-3448	293	12	one	one	NOUN
ejpam-3448	293	13	is	be	AUX
ejpam-3448	293	14	(	(	PUNCT
ejpam-3448	293	15	t1	t1	NOUN
ejpam-3448	293	16	\t	\t	NOUN
ejpam-3448	293	17	l	l	NOUN
ejpam-3448	293	18	2)∨t	2)∨t	NUM
ejpam-3448	293	19	r	r	NOUN
ejpam-3448	293	20	2	2	NUM
ejpam-3448	293	21	.	.	PUNCT
ejpam-3448	294	1	so	so	ADV
ejpam-3448	294	2	the	the	DET
ejpam-3448	294	3	set	set	NOUN
ejpam-3448	294	4	of	of	ADP
ejpam-3448	294	5	tubings	tubing	NOUN
ejpam-3448	294	6	of	of	ADP
ejpam-3448	294	7	the	the	DET
ejpam-3448	294	8	second	second	ADJ
ejpam-3448	294	9	type	type	NOUN
ejpam-3448	294	10	is	be	AUX
ejpam-3448	294	11	{	{	PUNCT
ejpam-3448	294	12	t	t	PROPN
ejpam-3448	294	13	∈mp(n+m)|(t1	∈mp(n+m)|(t1	PROPN
ejpam-3448	294	14	/	/	SYM
ejpam-3448	294	15	t	t	PROPN
ejpam-3448	295	1	l	l	NOUN
ejpam-3448	296	1	2)∨t	2)∨t	NUM
ejpam-3448	296	2	r	r	NOUN
ejpam-3448	296	3	2	2	NUM
ejpam-3448	296	4	≤	≤	NOUN
ejpam-3448	296	5	t	t	NOUN
ejpam-3448	296	6	≤	≤	NUM
ejpam-3448	296	7	(	(	PUNCT
ejpam-3448	296	8	t1	t1	NOUN
ejpam-3448	296	9	\	\	PROPN
ejpam-3448	296	10	t	t	PROPN
ejpam-3448	296	11	l	l	NOUN
ejpam-3448	296	12	2	2	NUM
ejpam-3448	296	13	)	)	PUNCT
ejpam-3448	296	14	∨	∨	NOUN
ejpam-3448	296	15	t	t	NOUN
ejpam-3448	296	16	r	r	NOUN
ejpam-3448	296	17	2	2	NUM
ejpam-3448	296	18	}	}	PUNCT
ejpam-3448	296	19	and	and	CCONJ
ejpam-3448	296	20	clearly	clearly	ADV
ejpam-3448	296	21	this	this	DET
ejpam-3448	296	22	set	set	NOUN
ejpam-3448	296	23	is	be	AUX
ejpam-3448	296	24	the	the	DET
ejpam-3448	296	25	plumbing	plumbing	NOUN
ejpam-3448	296	26	(	(	PUNCT
ejpam-3448	296	27	t1	t1	NOUN
ejpam-3448	296	28	+	+	PROPN
ejpam-3448	296	29	t	t	PROPN
ejpam-3448	296	30	l	l	NOUN
ejpam-3448	296	31	2	2	NUM
ejpam-3448	296	32	)	)	PUNCT
ejpam-3448	296	33	∨	∨	NOUN
ejpam-3448	296	34	t	t	NOUN
ejpam-3448	296	35	r	r	NOUN
ejpam-3448	296	36	2	2	NUM
ejpam-3448	296	37	.	.	PUNCT
ejpam-3448	296	38	definition	definition	NOUN
ejpam-3448	296	39	6	6	NUM
ejpam-3448	296	40	.	.	PUNCT
ejpam-3448	297	1	let	let	VERB
ejpam-3448	297	2	t1	t1	NOUN
ejpam-3448	297	3	and	and	CCONJ
ejpam-3448	297	4	t2	t2	NOUN
ejpam-3448	297	5	be	be	VERB
ejpam-3448	297	6	two	two	NUM
ejpam-3448	297	7	maximal	maximal	ADJ
ejpam-3448	297	8	tubings	tubing	NOUN
ejpam-3448	297	9	.	.	PUNCT
ejpam-3448	298	1	the	the	DET
ejpam-3448	298	2	left	left	ADJ
ejpam-3448	298	3	sum	sum	NOUN
ejpam-3448	298	4	and	and	CCONJ
ejpam-3448	298	5	the	the	DET
ejpam-3448	298	6	right	right	ADJ
ejpam-3448	298	7	sum	sum	NOUN
ejpam-3448	298	8	of	of	ADP
ejpam-3448	298	9	t1	t1	NOUN
ejpam-3448	298	10	and	and	CCONJ
ejpam-3448	298	11	t2	t2	NOUN
ejpam-3448	298	12	are	be	AUX
ejpam-3448	298	13	defined	define	VERB
ejpam-3448	298	14	by	by	ADP
ejpam-3448	298	15	t1	t1	NOUN
ejpam-3448	298	16	a	a	DET
ejpam-3448	298	17	t2	t2	NOUN
ejpam-3448	298	18	:	:	PUNCT
ejpam-3448	299	1	=	=	SYM
ejpam-3448	299	2	t	t	X
ejpam-3448	299	3	l	l	NOUN
ejpam-3448	299	4	1	1	NUM
ejpam-3448	299	5	∨	∨	NOUN
ejpam-3448	299	6	(	(	PUNCT
ejpam-3448	299	7	t	t	NOUN
ejpam-3448	299	8	r	r	NOUN
ejpam-3448	299	9	1	1	NUM
ejpam-3448	299	10	+	+	CCONJ
ejpam-3448	299	11	t2	t2	NOUN
ejpam-3448	299	12	)	)	PUNCT
ejpam-3448	299	13	and	and	CCONJ
ejpam-3448	299	14	t1	t1	NOUN
ejpam-3448	299	15	`	`	PUNCT
ejpam-3448	299	16	t2	t2	NOUN
ejpam-3448	299	17	:	:	PUNCT
ejpam-3448	299	18	=	=	SYM
ejpam-3448	299	19	(	(	PUNCT
ejpam-3448	299	20	t1	t1	NOUN
ejpam-3448	299	21	+	+	CCONJ
ejpam-3448	299	22	t	t	PROPN
ejpam-3448	299	23	l	l	NOUN
ejpam-3448	299	24	2	2	NUM
ejpam-3448	299	25	)	)	PUNCT
ejpam-3448	299	26	∨	∨	NOUN
ejpam-3448	299	27	t	t	NOUN
ejpam-3448	299	28	r	r	NOUN
ejpam-3448	299	29	2	2	NUM
ejpam-3448	299	30	,	,	PUNCT
ejpam-3448	299	31	respectively	respectively	ADV
ejpam-3448	299	32	.	.	PUNCT
ejpam-3448	300	1	this	this	PRON
ejpam-3448	300	2	can	can	AUX
ejpam-3448	300	3	be	be	AUX
ejpam-3448	300	4	extended	extend	VERB
ejpam-3448	300	5	over	over	ADP
ejpam-3448	300	6	plumbings	plumbing	NOUN
ejpam-3448	300	7	.	.	PUNCT
ejpam-3448	301	1	proposition	proposition	NOUN
ejpam-3448	301	2	1	1	NUM
ejpam-3448	301	3	.	.	PUNCT
ejpam-3448	302	1	the	the	DET
ejpam-3448	302	2	left	left	ADJ
ejpam-3448	302	3	and	and	CCONJ
ejpam-3448	302	4	right	right	ADJ
ejpam-3448	302	5	sums	sum	NOUN
ejpam-3448	302	6	of	of	ADP
ejpam-3448	302	7	maximal	maximal	ADJ
ejpam-3448	302	8	tubings	tubing	NOUN
ejpam-3448	302	9	t1	t1	VERB
ejpam-3448	302	10	,	,	PUNCT
ejpam-3448	302	11	t2	t2	NOUN
ejpam-3448	302	12	and	and	CCONJ
ejpam-3448	302	13	t3	t3	PROPN
ejpam-3448	302	14	satisfy	satisfy	VERB
ejpam-3448	302	15	the	the	DET
ejpam-3448	302	16	following	follow	VERB
ejpam-3448	302	17	relations	relation	NOUN
ejpam-3448	302	18	(	(	PUNCT
ejpam-3448	302	19	t1	t1	VERB
ejpam-3448	302	20	a	a	DET
ejpam-3448	302	21	t2	t2	NOUN
ejpam-3448	302	22	)	)	PUNCT
ejpam-3448	303	1	a	a	DET
ejpam-3448	303	2	t3	t3	NOUN
ejpam-3448	303	3	=	=	PROPN
ejpam-3448	303	4	t1	t1	PROPN
ejpam-3448	303	5	a	a	PROPN
ejpam-3448	303	6	(	(	PUNCT
ejpam-3448	303	7	t2	t2	NOUN
ejpam-3448	303	8	+	+	CCONJ
ejpam-3448	303	9	t3	t3	PROPN
ejpam-3448	303	10	)	)	PUNCT
ejpam-3448	303	11	,	,	PUNCT
ejpam-3448	303	12	(	(	PUNCT
ejpam-3448	303	13	1	1	X
ejpam-3448	303	14	)	)	PUNCT
ejpam-3448	303	15	(	(	PUNCT
ejpam-3448	303	16	t1	t1	NOUN
ejpam-3448	303	17	`	`	PUNCT
ejpam-3448	303	18	t2	t2	PROPN
ejpam-3448	303	19	)	)	PUNCT
ejpam-3448	303	20	a	a	DET
ejpam-3448	303	21	t3	t3	PROPN
ejpam-3448	303	22	=	=	SYM
ejpam-3448	303	23	t1	t1	NOUN
ejpam-3448	303	24	`	`	PUNCT
ejpam-3448	303	25	(	(	PUNCT
ejpam-3448	303	26	t2	t2	PROPN
ejpam-3448	303	27	a	a	DET
ejpam-3448	303	28	t3	t3	NOUN
ejpam-3448	303	29	)	)	PUNCT
ejpam-3448	303	30	,	,	PUNCT
ejpam-3448	303	31	(	(	PUNCT
ejpam-3448	303	32	2	2	X
ejpam-3448	303	33	)	)	PUNCT
ejpam-3448	303	34	t1	t1	NOUN
ejpam-3448	303	35	`	`	PUNCT
ejpam-3448	303	36	(	(	PUNCT
ejpam-3448	303	37	t2	t2	PROPN
ejpam-3448	303	38	`	`	PUNCT
ejpam-3448	303	39	t3	t3	PROPN
ejpam-3448	303	40	)	)	PUNCT
ejpam-3448	303	41	=	=	SYM
ejpam-3448	303	42	(	(	PUNCT
ejpam-3448	303	43	t1	t1	NOUN
ejpam-3448	303	44	+	+	NUM
ejpam-3448	303	45	t2	t2	NOUN
ejpam-3448	303	46	)	)	PUNCT
ejpam-3448	303	47	`	`	PUNCT
ejpam-3448	303	48	t3	t3	NOUN
ejpam-3448	303	49	(	(	PUNCT
ejpam-3448	303	50	3	3	NUM
ejpam-3448	303	51	)	)	PUNCT
ejpam-3448	303	52	and	and	CCONJ
ejpam-3448	303	53	0	0	NUM
ejpam-3448	303	54	`	`	PUNCT
ejpam-3448	303	55	t	t	PROPN
ejpam-3448	303	56	=	=	SYM
ejpam-3448	303	57	t	t	PROPN
ejpam-3448	303	58	=	=	SYM
ejpam-3448	303	59	t	t	PROPN
ejpam-3448	303	60	a	a	DET
ejpam-3448	303	61	0	0	NUM
ejpam-3448	303	62	for	for	ADP
ejpam-3448	303	63	all	all	DET
ejpam-3448	303	64	t	t	NOUN
ejpam-3448	303	65	.	.	PUNCT
ejpam-3448	304	1	proof	proof	NOUN
ejpam-3448	304	2	.	.	PUNCT
ejpam-3448	305	1	to	to	PART
ejpam-3448	305	2	prove	prove	VERB
ejpam-3448	305	3	(	(	PUNCT
ejpam-3448	305	4	1	1	NUM
ejpam-3448	305	5	)	)	PUNCT
ejpam-3448	305	6	,	,	PUNCT
ejpam-3448	305	7	we	we	PRON
ejpam-3448	305	8	do	do	VERB
ejpam-3448	305	9	the	the	DET
ejpam-3448	305	10	following	follow	VERB
ejpam-3448	305	11	computation	computation	NOUN
ejpam-3448	305	12	(	(	PUNCT
ejpam-3448	305	13	t1	t1	VERB
ejpam-3448	305	14	a	a	DET
ejpam-3448	305	15	t2	t2	NOUN
ejpam-3448	305	16	)	)	PUNCT
ejpam-3448	305	17	a	a	DET
ejpam-3448	305	18	t3	t3	NOUN
ejpam-3448	305	19	=	=	PUNCT
ejpam-3448	305	20	(	(	PUNCT
ejpam-3448	305	21	t1	t1	NOUN
ejpam-3448	305	22	a	a	DET
ejpam-3448	305	23	t2)l	t2)l	PROPN
ejpam-3448	305	24	∨	∨	NOUN
ejpam-3448	305	25	(	(	PUNCT
ejpam-3448	305	26	(	(	PUNCT
ejpam-3448	305	27	t1	t1	VERB
ejpam-3448	305	28	a	a	DET
ejpam-3448	305	29	t2)r	t2)r	NOUN
ejpam-3448	305	30	+	+	CCONJ
ejpam-3448	305	31	t3	t3	NOUN
ejpam-3448	305	32	)	)	PUNCT
ejpam-3448	305	33	=	=	PUNCT
ejpam-3448	305	34	(	(	PUNCT
ejpam-3448	305	35	t	t	NOUN
ejpam-3448	305	36	l	l	NOUN
ejpam-3448	305	37	1	1	NUM
ejpam-3448	305	38	∨	∨	NOUN
ejpam-3448	305	39	(	(	PUNCT
ejpam-3448	305	40	t	t	NOUN
ejpam-3448	305	41	r	r	NOUN
ejpam-3448	305	42	1	1	NUM
ejpam-3448	305	43	+	+	CCONJ
ejpam-3448	305	44	t2	t2	NOUN
ejpam-3448	305	45	)	)	PUNCT
ejpam-3448	305	46	)	)	PUNCT
ejpam-3448	306	1	l	l	NOUN
ejpam-3448	306	2	∨	∨	X
ejpam-3448	306	3	(	(	PUNCT
ejpam-3448	306	4	(	(	PUNCT
ejpam-3448	306	5	t	t	NOUN
ejpam-3448	306	6	l	l	NOUN
ejpam-3448	306	7	1	1	NUM
ejpam-3448	306	8	∨	∨	NOUN
ejpam-3448	306	9	(	(	PUNCT
ejpam-3448	306	10	t	t	NOUN
ejpam-3448	306	11	r	r	NOUN
ejpam-3448	306	12	1	1	NUM
ejpam-3448	306	13	+	+	CCONJ
ejpam-3448	306	14	t2	t2	NOUN
ejpam-3448	306	15	)	)	PUNCT
ejpam-3448	306	16	)	)	PUNCT
ejpam-3448	307	1	r	r	NOUN
ejpam-3448	307	2	+	+	CCONJ
ejpam-3448	307	3	t3	t3	NOUN
ejpam-3448	307	4	)	)	PUNCT
ejpam-3448	307	5	=	=	SYM
ejpam-3448	308	1	t	t	NOUN
ejpam-3448	308	2	l	l	NOUN
ejpam-3448	308	3	1	1	NUM
ejpam-3448	308	4	∨	∨	NUM
ejpam-3448	308	5	(	(	PUNCT
ejpam-3448	308	6	(	(	PUNCT
ejpam-3448	308	7	t	t	NOUN
ejpam-3448	308	8	r	r	NOUN
ejpam-3448	308	9	1	1	NUM
ejpam-3448	308	10	+	+	CCONJ
ejpam-3448	308	11	t2	t2	NOUN
ejpam-3448	308	12	)	)	PUNCT
ejpam-3448	308	13	+	+	SYM
ejpam-3448	308	14	t3	t3	NOUN
ejpam-3448	308	15	)	)	PUNCT
ejpam-3448	308	16	=	=	SYM
ejpam-3448	308	17	t	t	NOUN
ejpam-3448	308	18	l	l	NOUN
ejpam-3448	308	19	1	1	NUM
ejpam-3448	308	20	∨	∨	NOUN
ejpam-3448	308	21	(	(	PUNCT
ejpam-3448	308	22	t	t	NOUN
ejpam-3448	308	23	r	r	NOUN
ejpam-3448	308	24	1	1	NUM
ejpam-3448	308	25	+	+	CCONJ
ejpam-3448	308	26	(	(	PUNCT
ejpam-3448	308	27	t2	t2	NOUN
ejpam-3448	308	28	+	+	CCONJ
ejpam-3448	308	29	t3	t3	NOUN
ejpam-3448	308	30	)	)	PUNCT
ejpam-3448	308	31	)	)	PUNCT
ejpam-3448	309	1	=	=	PUNCT
ejpam-3448	309	2	t1	t1	NOUN
ejpam-3448	309	3	a	a	PROPN
ejpam-3448	309	4	(	(	PUNCT
ejpam-3448	309	5	t2	t2	NOUN
ejpam-3448	309	6	+	+	CCONJ
ejpam-3448	309	7	t3	t3	PROPN
ejpam-3448	309	8	)	)	PUNCT
ejpam-3448	309	9	.	.	PUNCT
ejpam-3448	310	1	for	for	ADP
ejpam-3448	310	2	(	(	PUNCT
ejpam-3448	310	3	2	2	NUM
ejpam-3448	310	4	)	)	PUNCT
ejpam-3448	310	5	,	,	PUNCT
ejpam-3448	310	6	we	we	PRON
ejpam-3448	310	7	compute	compute	VERB
ejpam-3448	310	8	both	both	DET
ejpam-3448	310	9	sides	side	NOUN
ejpam-3448	310	10	and	and	CCONJ
ejpam-3448	310	11	see	see	VERB
ejpam-3448	310	12	that	that	SCONJ
ejpam-3448	310	13	they	they	PRON
ejpam-3448	310	14	are	be	AUX
ejpam-3448	310	15	equal	equal	ADJ
ejpam-3448	310	16	.	.	PUNCT
ejpam-3448	311	1	(	(	PUNCT
ejpam-3448	311	2	t1	t1	NOUN
ejpam-3448	311	3	`	`	PUNCT
ejpam-3448	311	4	t2	t2	PROPN
ejpam-3448	311	5	)	)	PUNCT
ejpam-3448	311	6	a	a	DET
ejpam-3448	311	7	t3	t3	NOUN
ejpam-3448	311	8	=	=	PUNCT
ejpam-3448	311	9	(	(	PUNCT
ejpam-3448	311	10	t1	t1	NOUN
ejpam-3448	311	11	`	`	PUNCT
ejpam-3448	311	12	t2)l	t2)l	PROPN
ejpam-3448	311	13	∨	∨	PROPN
ejpam-3448	311	14	(	(	PUNCT
ejpam-3448	311	15	(	(	PUNCT
ejpam-3448	311	16	t1	t1	NOUN
ejpam-3448	311	17	`	`	PUNCT
ejpam-3448	311	18	t2)r	t2)r	VERB
ejpam-3448	311	19	+	+	CCONJ
ejpam-3448	311	20	t3	t3	NOUN
ejpam-3448	311	21	)	)	PUNCT
ejpam-3448	311	22	(	(	PUNCT
ejpam-3448	311	23	by	by	ADP
ejpam-3448	311	24	definition	definition	NOUN
ejpam-3448	311	25	of	of	ADP
ejpam-3448	311	26	a	a	PRON
ejpam-3448	311	27	)	)	PUNCT
ejpam-3448	311	28	=	=	SYM
ejpam-3448	311	29	(	(	PUNCT
ejpam-3448	311	30	(	(	PUNCT
ejpam-3448	311	31	t1	t1	NOUN
ejpam-3448	311	32	+	+	PROPN
ejpam-3448	311	33	t	t	PROPN
ejpam-3448	311	34	l	l	NOUN
ejpam-3448	311	35	2	2	NUM
ejpam-3448	311	36	)	)	PUNCT
ejpam-3448	311	37	∨	∨	NOUN
ejpam-3448	311	38	t	t	NOUN
ejpam-3448	311	39	r	r	NOUN
ejpam-3448	311	40	2	2	NUM
ejpam-3448	311	41	)	)	PUNCT
ejpam-3448	311	42	l	l	NOUN
ejpam-3448	311	43	∨	∨	X
ejpam-3448	311	44	(	(	PUNCT
ejpam-3448	311	45	(	(	PUNCT
ejpam-3448	311	46	(	(	PUNCT
ejpam-3448	311	47	t1	t1	NOUN
ejpam-3448	311	48	+	+	PROPN
ejpam-3448	311	49	t	t	PROPN
ejpam-3448	311	50	l	l	NOUN
ejpam-3448	311	51	2	2	NUM
ejpam-3448	311	52	)	)	PUNCT
ejpam-3448	311	53	∨	∨	NOUN
ejpam-3448	311	54	t	t	NOUN
ejpam-3448	311	55	r	r	NOUN
ejpam-3448	311	56	2	2	NUM
ejpam-3448	311	57	)	)	PUNCT
ejpam-3448	311	58	r	r	NOUN
ejpam-3448	311	59	+	+	NOUN
ejpam-3448	311	60	t3	t3	NOUN
ejpam-3448	311	61	)	)	PUNCT
ejpam-3448	311	62	(	(	PUNCT
ejpam-3448	311	63	by	by	ADP
ejpam-3448	311	64	definition	definition	NOUN
ejpam-3448	311	65	of	of	ADP
ejpam-3448	311	66	`	`	PUNCT
ejpam-3448	311	67	)	)	PUNCT
ejpam-3448	311	68	=	=	SYM
ejpam-3448	311	69	(	(	PUNCT
ejpam-3448	311	70	t1	t1	NOUN
ejpam-3448	311	71	+	+	CCONJ
ejpam-3448	311	72	t	t	PROPN
ejpam-3448	311	73	l	l	NOUN
ejpam-3448	311	74	2	2	NUM
ejpam-3448	311	75	)	)	PUNCT
ejpam-3448	311	76	∨	∨	NOUN
ejpam-3448	311	77	(	(	PUNCT
ejpam-3448	311	78	t	t	NOUN
ejpam-3448	311	79	r	r	NOUN
ejpam-3448	311	80	2	2	NUM
ejpam-3448	311	81	+	+	CCONJ
ejpam-3448	311	82	t3	t3	NOUN
ejpam-3448	311	83	)	)	PUNCT
ejpam-3448	311	84	t1	t1	NOUN
ejpam-3448	311	85	`	`	PUNCT
ejpam-3448	311	86	(	(	PUNCT
ejpam-3448	311	87	t2	t2	PROPN
ejpam-3448	311	88	a	a	DET
ejpam-3448	311	89	t3	t3	NOUN
ejpam-3448	311	90	)	)	PUNCT
ejpam-3448	311	91	=	=	SYM
ejpam-3448	312	1	t1	t1	NOUN
ejpam-3448	312	2	`	`	PUNCT
ejpam-3448	312	3	(	(	PUNCT
ejpam-3448	312	4	t	t	NOUN
ejpam-3448	312	5	l	l	NOUN
ejpam-3448	312	6	2	2	NUM
ejpam-3448	312	7	∨	∨	NOUN
ejpam-3448	312	8	(	(	PUNCT
ejpam-3448	312	9	t	t	NOUN
ejpam-3448	312	10	r	r	NOUN
ejpam-3448	312	11	2	2	NUM
ejpam-3448	312	12	+	+	CCONJ
ejpam-3448	312	13	t3	t3	NOUN
ejpam-3448	312	14	)	)	PUNCT
ejpam-3448	312	15	)	)	PUNCT
ejpam-3448	312	16	(	(	PUNCT
ejpam-3448	312	17	by	by	ADP
ejpam-3448	312	18	definition	definition	NOUN
ejpam-3448	312	19	of	of	ADP
ejpam-3448	312	20	a	a	PRON
ejpam-3448	312	21	)	)	PUNCT
ejpam-3448	312	22	=	=	SYM
ejpam-3448	312	23	(	(	PUNCT
ejpam-3448	312	24	t1	t1	NOUN
ejpam-3448	312	25	+	+	X
ejpam-3448	312	26	(	(	PUNCT
ejpam-3448	312	27	t	t	NOUN
ejpam-3448	312	28	l	l	NOUN
ejpam-3448	312	29	2	2	NUM
ejpam-3448	312	30	∨	∨	NOUN
ejpam-3448	312	31	(	(	PUNCT
ejpam-3448	312	32	t	t	NOUN
ejpam-3448	312	33	r	r	NOUN
ejpam-3448	312	34	2	2	NUM
ejpam-3448	312	35	+	+	CCONJ
ejpam-3448	312	36	t3	t3	NOUN
ejpam-3448	312	37	)	)	PUNCT
ejpam-3448	312	38	l	l	NOUN
ejpam-3448	312	39	)	)	PUNCT
ejpam-3448	312	40	∨	∨	PROPN
ejpam-3448	312	41	(	(	PUNCT
ejpam-3448	312	42	t	t	NOUN
ejpam-3448	312	43	l	l	NOUN
ejpam-3448	312	44	2	2	NUM
ejpam-3448	312	45	∨	∨	NOUN
ejpam-3448	312	46	(	(	PUNCT
ejpam-3448	312	47	t	t	NOUN
ejpam-3448	312	48	r	r	NOUN
ejpam-3448	312	49	2	2	NUM
ejpam-3448	312	50	+	+	CCONJ
ejpam-3448	312	51	t3	t3	NOUN
ejpam-3448	312	52	)	)	PUNCT
ejpam-3448	312	53	r	r	NOUN
ejpam-3448	312	54	(	(	PUNCT
ejpam-3448	312	55	by	by	ADP
ejpam-3448	312	56	definition	definition	NOUN
ejpam-3448	312	57	of	of	ADP
ejpam-3448	312	58	`	`	PUNCT
ejpam-3448	312	59	)	)	PUNCT
ejpam-3448	312	60	=	=	SYM
ejpam-3448	312	61	(	(	PUNCT
ejpam-3448	312	62	t1	t1	NOUN
ejpam-3448	312	63	+	+	CCONJ
ejpam-3448	312	64	t	t	PROPN
ejpam-3448	312	65	l	l	NOUN
ejpam-3448	312	66	2	2	NUM
ejpam-3448	312	67	)	)	PUNCT
ejpam-3448	312	68	∨	∨	NOUN
ejpam-3448	312	69	(	(	PUNCT
ejpam-3448	312	70	t	t	NOUN
ejpam-3448	312	71	r	r	NOUN
ejpam-3448	312	72	2	2	NUM
ejpam-3448	312	73	+	+	CCONJ
ejpam-3448	312	74	t3	t3	NOUN
ejpam-3448	312	75	)	)	PUNCT
ejpam-3448	312	76	finally	finally	ADV
ejpam-3448	312	77	,	,	PUNCT
ejpam-3448	312	78	for	for	ADP
ejpam-3448	312	79	(	(	PUNCT
ejpam-3448	312	80	3	3	X
ejpam-3448	312	81	)	)	PUNCT
ejpam-3448	312	82	we	we	PRON
ejpam-3448	312	83	have	have	VERB
ejpam-3448	312	84	the	the	DET
ejpam-3448	312	85	following	follow	VERB
ejpam-3448	312	86	equalities	equality	NOUN
ejpam-3448	312	87	t1	t1	NOUN
ejpam-3448	312	88	`	`	PUNCT
ejpam-3448	312	89	(	(	PUNCT
ejpam-3448	312	90	t2	t2	PROPN
ejpam-3448	312	91	`	`	PUNCT
ejpam-3448	312	92	t3	t3	PROPN
ejpam-3448	312	93	)	)	PUNCT
ejpam-3448	312	94	=	=	SYM
ejpam-3448	313	1	(	(	PUNCT
ejpam-3448	313	2	t1	t1	NOUN
ejpam-3448	313	3	+	+	CCONJ
ejpam-3448	313	4	(	(	PUNCT
ejpam-3448	313	5	t2	t2	PROPN
ejpam-3448	313	6	`	`	PUNCT
ejpam-3448	313	7	t3)l	t3)l	PROPN
ejpam-3448	313	8	)	)	PUNCT
ejpam-3448	313	9	∨	∨	PROPN
ejpam-3448	313	10	(	(	PUNCT
ejpam-3448	313	11	t2	t2	NOUN
ejpam-3448	313	12	`	`	PUNCT
ejpam-3448	313	13	t3)r	t3)r	NOUN
ejpam-3448	313	14	(	(	PUNCT
ejpam-3448	313	15	by	by	ADP
ejpam-3448	313	16	definition	definition	NOUN
ejpam-3448	313	17	of	of	ADP
ejpam-3448	313	18	`	`	PUNCT
ejpam-3448	313	19	)	)	PUNCT
ejpam-3448	313	20	=	=	SYM
ejpam-3448	313	21	(	(	PUNCT
ejpam-3448	313	22	t1	t1	NOUN
ejpam-3448	313	23	+	+	CCONJ
ejpam-3448	313	24	(	(	PUNCT
ejpam-3448	313	25	(	(	PUNCT
ejpam-3448	313	26	t2	t2	PROPN
ejpam-3448	313	27	+	+	CCONJ
ejpam-3448	313	28	t	t	PROPN
ejpam-3448	313	29	l	l	NOUN
ejpam-3448	313	30	3	3	X
ejpam-3448	313	31	)	)	PUNCT
ejpam-3448	313	32	∨	∨	NOUN
ejpam-3448	313	33	t	t	NOUN
ejpam-3448	313	34	r	r	NOUN
ejpam-3448	313	35	3	3	NUM
ejpam-3448	313	36	)	)	PUNCT
ejpam-3448	313	37	l	l	NOUN
ejpam-3448	313	38	)	)	PUNCT
ejpam-3448	313	39	∨	∨	NOUN
ejpam-3448	313	40	(	(	PUNCT
ejpam-3448	313	41	(	(	PUNCT
ejpam-3448	313	42	t2	t2	NOUN
ejpam-3448	313	43	+	+	CCONJ
ejpam-3448	313	44	t	t	PROPN
ejpam-3448	313	45	l	l	NOUN
ejpam-3448	313	46	3	3	X
ejpam-3448	313	47	)	)	PUNCT
ejpam-3448	313	48	∨	∨	NOUN
ejpam-3448	313	49	t	t	NOUN
ejpam-3448	313	50	r	r	NOUN
ejpam-3448	313	51	3	3	NUM
ejpam-3448	313	52	)	)	PUNCT
ejpam-3448	313	53	r	r	NOUN
ejpam-3448	313	54	(	(	PUNCT
ejpam-3448	313	55	by	by	ADP
ejpam-3448	313	56	definition	definition	NOUN
ejpam-3448	313	57	of	of	ADP
ejpam-3448	313	58	`	`	PUNCT
ejpam-3448	313	59	)	)	PUNCT
ejpam-3448	313	60	=	=	SYM
ejpam-3448	313	61	(	(	PUNCT
ejpam-3448	313	62	t1	t1	NOUN
ejpam-3448	313	63	+	+	CCONJ
ejpam-3448	313	64	(	(	PUNCT
ejpam-3448	313	65	(	(	PUNCT
ejpam-3448	313	66	t2	t2	PROPN
ejpam-3448	313	67	+	+	CCONJ
ejpam-3448	313	68	t	t	PROPN
ejpam-3448	313	69	l	l	NOUN
ejpam-3448	313	70	3	3	NUM
ejpam-3448	313	71	)	)	PUNCT
ejpam-3448	313	72	)	)	PUNCT
ejpam-3448	314	1	∨	∨	ADP
ejpam-3448	314	2	t	t	NOUN
ejpam-3448	314	3	r	r	NOUN
ejpam-3448	314	4	3	3	NUM
ejpam-3448	314	5	=	=	SYM
ejpam-3448	314	6	(	(	PUNCT
ejpam-3448	314	7	(	(	PUNCT
ejpam-3448	314	8	t1	t1	NOUN
ejpam-3448	314	9	+	+	NUM
ejpam-3448	314	10	t2	t2	NOUN
ejpam-3448	314	11	)	)	PUNCT
ejpam-3448	315	1	+	+	NUM
ejpam-3448	315	2	t	t	NOUN
ejpam-3448	315	3	l	l	NOUN
ejpam-3448	315	4	3	3	X
ejpam-3448	315	5	)	)	PUNCT
ejpam-3448	315	6	∨	∨	NOUN
ejpam-3448	315	7	t	t	NOUN
ejpam-3448	315	8	r	r	NOUN
ejpam-3448	315	9	3	3	NUM
ejpam-3448	315	10	=	=	SYM
ejpam-3448	315	11	(	(	PUNCT
ejpam-3448	315	12	t1	t1	NOUN
ejpam-3448	315	13	+	+	NUM
ejpam-3448	315	14	t2	t2	PROPN
ejpam-3448	315	15	)	)	PUNCT
ejpam-3448	315	16	`	`	PUNCT
ejpam-3448	316	1	t3	t3	PROPN
ejpam-3448	316	2	.	.	PUNCT
ejpam-3448	316	3	corollary	corollary	ADJ
ejpam-3448	316	4	1	1	NUM
ejpam-3448	316	5	.	.	PUNCT
ejpam-3448	317	1	let	let	VERB
ejpam-3448	317	2	t1	t1	PROPN
ejpam-3448	317	3	∈mp(n	∈mp(n	PROPN
ejpam-3448	317	4	)	)	PUNCT
ejpam-3448	317	5	,	,	PUNCT
ejpam-3448	317	6	t2	t2	NOUN
ejpam-3448	317	7	∈mp(m	∈mp(m	NOUN
ejpam-3448	317	8	)	)	PUNCT
ejpam-3448	317	9	be	be	VERB
ejpam-3448	317	10	two	two	NUM
ejpam-3448	317	11	maximal	maximal	ADJ
ejpam-3448	317	12	tubings	tubing	NOUN
ejpam-3448	317	13	.	.	PUNCT
ejpam-3448	318	1	the	the	DET
ejpam-3448	318	2	left	left	ADJ
ejpam-3448	318	3	and	and	CCONJ
ejpam-3448	318	4	right	right	ADJ
ejpam-3448	318	5	sums	sum	NOUN
ejpam-3448	318	6	satisfy	satisfy	VERB
ejpam-3448	318	7	t1	t1	NOUN
ejpam-3448	318	8	`	`	PUNCT
ejpam-3448	318	9	t2	t2	NOUN
ejpam-3448	318	10	=	=	SYM
ejpam-3448	318	11	t2	t2	PROPN
ejpam-3448	318	12	a	a	DET
ejpam-3448	318	13	t1	t1	NOUN
ejpam-3448	318	14	,	,	PUNCT
ejpam-3448	318	15	t1	t1	VERB
ejpam-3448	318	16	a	a	DET
ejpam-3448	318	17	t2	t2	NOUN
ejpam-3448	318	18	=	=	SYM
ejpam-3448	318	19	t2	t2	PROPN
ejpam-3448	318	20	`	`	PUNCT
ejpam-3448	318	21	t1	t1	PROPN
ejpam-3448	318	22	.	.	PUNCT
ejpam-3448	319	1	definition	definition	NOUN
ejpam-3448	319	2	7	7	NUM
ejpam-3448	319	3	.	.	PUNCT
ejpam-3448	319	4	a	a	DET
ejpam-3448	319	5	unique	unique	ADJ
ejpam-3448	319	6	way	way	NOUN
ejpam-3448	319	7	of	of	ADP
ejpam-3448	319	8	writing	writing	NOUN
ejpam-3448	319	9	t	t	PROPN
ejpam-3448	319	10	as	as	ADP
ejpam-3448	319	11	a	a	DET
ejpam-3448	319	12	composition	composition	NOUN
ejpam-3448	319	13	of	of	ADP
ejpam-3448	319	14	n	n	DET
ejpam-3448	319	15	copies	copy	NOUN
ejpam-3448	319	16	of	of	ADP
ejpam-3448	319	17	the	the	DET
ejpam-3448	319	18	tubing	tubing	NOUN
ejpam-3448	319	19	1	1	NUM
ejpam-3448	319	20	∈	∈	NOUN
ejpam-3448	319	21	mp(1	mp(1	NOUN
ejpam-3448	319	22	)	)	PUNCT
ejpam-3448	319	23	with	with	ADP
ejpam-3448	319	24	the	the	DET
ejpam-3448	319	25	left	left	NOUN
ejpam-3448	319	26	and	and	CCONJ
ejpam-3448	319	27	right	right	ADJ
ejpam-3448	319	28	sums	sum	NOUN
ejpam-3448	319	29	modulo	modulo	VERB
ejpam-3448	319	30	the	the	DET
ejpam-3448	319	31	relations	relation	NOUN
ejpam-3448	319	32	given	give	VERB
ejpam-3448	319	33	in	in	ADP
ejpam-3448	319	34	proposition	proposition	NOUN
ejpam-3448	319	35	1	1	NUM
ejpam-3448	319	36	is	be	AUX
ejpam-3448	319	37	called	call	VERB
ejpam-3448	319	38	the	the	DET
ejpam-3448	319	39	universal	universal	ADJ
ejpam-3448	319	40	expression	expression	NOUN
ejpam-3448	319	41	of	of	ADP
ejpam-3448	319	42	t	t	PROPN
ejpam-3448	319	43	∈mp(n	∈mp(n	PROPN
ejpam-3448	319	44	)	)	PUNCT
ejpam-3448	319	45	and	and	CCONJ
ejpam-3448	319	46	denoted	denote	VERB
ejpam-3448	319	47	by	by	ADP
ejpam-3448	319	48	wt	wt	PROPN
ejpam-3448	319	49	(	(	PUNCT
ejpam-3448	319	50	1	1	NUM
ejpam-3448	319	51	)	)	PUNCT
ejpam-3448	319	52	.	.	PUNCT
ejpam-3448	320	1	s.	s.	PROPN
ejpam-3448	320	2	k.	k.	PROPN
ejpam-3448	320	3	gürbüzer	gürbüzer	PROPN
ejpam-3448	320	4	,	,	PUNCT
ejpam-3448	320	5	b.	b.	PROPN
ejpam-3448	320	6	akyar	akyar	PROPN
ejpam-3448	320	7	/	/	SYM
ejpam-3448	320	8	eur	eur	PROPN
ejpam-3448	320	9	.	.	PUNCT
ejpam-3448	321	1	j.	j.	PROPN
ejpam-3448	321	2	pure	pure	PROPN
ejpam-3448	321	3	appl	appl	PROPN
ejpam-3448	321	4	.	.	PROPN
ejpam-3448	321	5	math	math	PROPN
ejpam-3448	321	6	,	,	PUNCT
ejpam-3448	321	7	12	12	NUM
ejpam-3448	321	8	(	(	PUNCT
ejpam-3448	321	9	3	3	NUM
ejpam-3448	321	10	)	)	PUNCT
ejpam-3448	321	11	(	(	PUNCT
ejpam-3448	321	12	2019	2019	NUM
ejpam-3448	321	13	)	)	PUNCT
ejpam-3448	321	14	,	,	PUNCT
ejpam-3448	321	15	734	734	NUM
ejpam-3448	321	16	-	-	SYM
ejpam-3448	321	17	748	748	NUM
ejpam-3448	321	18	743	743	NUM
ejpam-3448	321	19	example	example	NOUN
ejpam-3448	321	20	4	4	NUM
ejpam-3448	321	21	.	.	PUNCT
ejpam-3448	322	1	the	the	DET
ejpam-3448	322	2	universal	universal	ADJ
ejpam-3448	322	3	expression	expression	NOUN
ejpam-3448	322	4	of	of	ADP
ejpam-3448	322	5	t	t	PROPN
ejpam-3448	322	6	=	=	SYM
ejpam-3448	322	7	2132	2132	NUM
ejpam-3448	322	8	is	be	AUX
ejpam-3448	322	9	wt	wt	X
ejpam-3448	322	10	(	(	PUNCT
ejpam-3448	322	11	1	1	NUM
ejpam-3448	322	12	)	)	PUNCT
ejpam-3448	322	13	=	=	SYM
ejpam-3448	322	14	1	1	NUM
ejpam-3448	322	15	`	`	SYM
ejpam-3448	322	16	1	1	NUM
ejpam-3448	322	17	a	a	PRON
ejpam-3448	322	18	(	(	PUNCT
ejpam-3448	322	19	1	1	NUM
ejpam-3448	322	20	a	a	DET
ejpam-3448	322	21	1	1	NUM
ejpam-3448	322	22	)	)	PUNCT
ejpam-3448	322	23	.	.	PUNCT
ejpam-3448	323	1	definition	definition	NOUN
ejpam-3448	323	2	8	8	NUM
ejpam-3448	323	3	.	.	PUNCT
ejpam-3448	324	1	let	let	VERB
ejpam-3448	324	2	t1	t1	NOUN
ejpam-3448	324	3	and	and	CCONJ
ejpam-3448	324	4	t2	t2	NOUN
ejpam-3448	324	5	be	be	VERB
ejpam-3448	324	6	any	any	DET
ejpam-3448	324	7	two	two	NUM
ejpam-3448	324	8	maximal	maximal	ADJ
ejpam-3448	324	9	tubings	tubing	NOUN
ejpam-3448	324	10	.	.	PUNCT
ejpam-3448	325	1	the	the	DET
ejpam-3448	325	2	product	product	NOUN
ejpam-3448	325	3	t1×	t1×	NOUN
ejpam-3448	325	4	t2	t2	PROPN
ejpam-3448	325	5	of	of	ADP
ejpam-3448	325	6	t1	t1	NOUN
ejpam-3448	325	7	and	and	CCONJ
ejpam-3448	325	8	t2	t2	NOUN
ejpam-3448	325	9	is	be	AUX
ejpam-3448	325	10	the	the	DET
ejpam-3448	325	11	ordered	order	VERB
ejpam-3448	325	12	sum	sum	NOUN
ejpam-3448	325	13	of	of	ADP
ejpam-3448	325	14	the	the	DET
ejpam-3448	325	15	copies	copy	NOUN
ejpam-3448	325	16	of	of	ADP
ejpam-3448	325	17	t2	t2	NOUN
ejpam-3448	325	18	in	in	ADP
ejpam-3448	325	19	the	the	DET
ejpam-3448	325	20	universal	universal	ADJ
ejpam-3448	325	21	expression	expression	NOUN
ejpam-3448	325	22	of	of	ADP
ejpam-3448	325	23	t1	t1	PROPN
ejpam-3448	325	24	.	.	PUNCT
ejpam-3448	326	1	the	the	DET
ejpam-3448	326	2	product	product	NOUN
ejpam-3448	326	3	is	be	AUX
ejpam-3448	326	4	distributive	distributive	ADJ
ejpam-3448	326	5	from	from	ADP
ejpam-3448	326	6	the	the	DET
ejpam-3448	326	7	left	left	NOUN
ejpam-3448	326	8	on	on	ADP
ejpam-3448	326	9	each	each	DET
ejpam-3448	326	10	type	type	NOUN
ejpam-3448	326	11	of	of	ADP
ejpam-3448	326	12	sums	sum	NOUN
ejpam-3448	326	13	and	and	CCONJ
ejpam-3448	326	14	it	it	PRON
ejpam-3448	326	15	is	be	AUX
ejpam-3448	326	16	not	not	PART
ejpam-3448	326	17	commutative	commutative	ADJ
ejpam-3448	326	18	.	.	PUNCT
ejpam-3448	327	1	the	the	DET
ejpam-3448	327	2	product	product	NOUN
ejpam-3448	327	3	of	of	ADP
ejpam-3448	327	4	two	two	NUM
ejpam-3448	327	5	maximal	maximal	ADJ
ejpam-3448	327	6	tubings	tubing	NOUN
ejpam-3448	327	7	can	can	AUX
ejpam-3448	327	8	be	be	AUX
ejpam-3448	327	9	extended	extend	VERB
ejpam-3448	327	10	to	to	ADP
ejpam-3448	327	11	the	the	DET
ejpam-3448	327	12	product	product	NOUN
ejpam-3448	327	13	of	of	ADP
ejpam-3448	327	14	plumbings	plumbing	NOUN
ejpam-3448	327	15	.	.	PUNCT
ejpam-3448	328	1	corollary	corollary	ADJ
ejpam-3448	328	2	2	2	NUM
ejpam-3448	328	3	.	.	PUNCT
ejpam-3448	329	1	let	let	VERB
ejpam-3448	329	2	t1	t1	NOUN
ejpam-3448	329	3	=	=	PUNCT
ejpam-3448	329	4	t	t	PROPN
ejpam-3448	329	5	l	l	NOUN
ejpam-3448	329	6	1	1	NUM
ejpam-3448	329	7	∨	∨	NUM
ejpam-3448	329	8	t	t	NOUN
ejpam-3448	329	9	r	r	NOUN
ejpam-3448	329	10	1	1	NUM
ejpam-3448	329	11	be	be	AUX
ejpam-3448	329	12	a	a	DET
ejpam-3448	329	13	maximal	maximal	ADJ
ejpam-3448	329	14	tubing	tubing	NOUN
ejpam-3448	329	15	.	.	PUNCT
ejpam-3448	330	1	the	the	DET
ejpam-3448	330	2	product	product	NOUN
ejpam-3448	330	3	can	can	AUX
ejpam-3448	330	4	be	be	AUX
ejpam-3448	330	5	given	give	VERB
ejpam-3448	330	6	by	by	ADP
ejpam-3448	330	7	the	the	DET
ejpam-3448	330	8	formula	formula	NOUN
ejpam-3448	330	9	t1	t1	NOUN
ejpam-3448	330	10	×	×	NOUN
ejpam-3448	330	11	t2	t2	NOUN
ejpam-3448	330	12	=	=	SYM
ejpam-3448	330	13	(	(	PUNCT
ejpam-3448	330	14	t	t	NOUN
ejpam-3448	330	15	l	l	NOUN
ejpam-3448	330	16	1	1	NUM
ejpam-3448	330	17	×	×	NOUN
ejpam-3448	330	18	t2	t2	NOUN
ejpam-3448	330	19	)	)	PUNCT
ejpam-3448	330	20	`	`	PUNCT
ejpam-3448	330	21	t2	t2	VERB
ejpam-3448	330	22	a	a	PRON
ejpam-3448	330	23	(	(	PUNCT
ejpam-3448	330	24	t	t	NOUN
ejpam-3448	330	25	r	r	NOUN
ejpam-3448	330	26	1	1	NUM
ejpam-3448	330	27	×	×	NOUN
ejpam-3448	330	28	t2	t2	NOUN
ejpam-3448	330	29	)	)	PUNCT
ejpam-3448	330	30	and	and	CCONJ
ejpam-3448	330	31	0	0	NUM
ejpam-3448	330	32	×	×	NOUN
ejpam-3448	330	33	t2	t2	NOUN
ejpam-3448	330	34	=	=	SYM
ejpam-3448	330	35	0	0	NUM
ejpam-3448	330	36	for	for	ADP
ejpam-3448	330	37	all	all	DET
ejpam-3448	330	38	maximal	maximal	ADJ
ejpam-3448	330	39	tubings	tubing	NOUN
ejpam-3448	330	40	t2	t2	NOUN
ejpam-3448	330	41	.	.	PUNCT
ejpam-3448	331	1	one	one	NOUN
ejpam-3448	331	2	also	also	ADV
ejpam-3448	331	3	has	have	VERB
ejpam-3448	331	4	t1	t1	VERB
ejpam-3448	331	5	×	×	PROPN
ejpam-3448	331	6	t2	t2	NOUN
ejpam-3448	331	7	=	=	SYM
ejpam-3448	331	8	t̄1	t̄1	X
ejpam-3448	331	9	×	×	NOUN
ejpam-3448	331	10	t̄2	t̄2	NOUN
ejpam-3448	331	11	for	for	ADP
ejpam-3448	331	12	any	any	DET
ejpam-3448	331	13	two	two	NUM
ejpam-3448	331	14	maximal	maximal	ADJ
ejpam-3448	331	15	tubings	tubing	NOUN
ejpam-3448	331	16	t1	t1	NOUN
ejpam-3448	331	17	and	and	CCONJ
ejpam-3448	331	18	t2	t2	NOUN
ejpam-3448	331	19	.	.	PUNCT
ejpam-3448	332	1	now	now	ADV
ejpam-3448	332	2	,	,	PUNCT
ejpam-3448	332	3	we	we	PRON
ejpam-3448	332	4	define	define	VERB
ejpam-3448	332	5	the	the	DET
ejpam-3448	332	6	dendriform	dendriform	NOUN
ejpam-3448	332	7	algebra	algebra	NOUN
ejpam-3448	332	8	on	on	ADP
ejpam-3448	332	9	mp(∞	mp(∞	NOUN
ejpam-3448	332	10	)	)	PUNCT
ejpam-3448	332	11	.	.	PUNCT
ejpam-3448	333	1	definition	definition	NOUN
ejpam-3448	333	2	9	9	NUM
ejpam-3448	333	3	.	.	PUNCT
ejpam-3448	334	1	a	a	DET
ejpam-3448	334	2	dendriform	dendriform	NOUN
ejpam-3448	334	3	algebra	algebra	NOUN
ejpam-3448	334	4	is	be	AUX
ejpam-3448	334	5	a	a	DET
ejpam-3448	334	6	vector	vector	NOUN
ejpam-3448	334	7	space	space	NOUN
ejpam-3448	334	8	a	a	DET
ejpam-3448	334	9	equipped	equip	VERB
ejpam-3448	334	10	with	with	ADP
ejpam-3448	334	11	two	two	NUM
ejpam-3448	334	12	binary	binary	ADJ
ejpam-3448	334	13	operations	operation	NOUN
ejpam-3448	334	14	≺	≺	NOUN
ejpam-3448	334	15	,	,	PUNCT
ejpam-3448	334	16	�	�	PROPN
ejpam-3448	334	17	:	:	PUNCT
ejpam-3448	334	18	a⊗a→	a⊗a→	PROPN
ejpam-3448	334	19	a	a	DET
ejpam-3448	334	20	satisfying	satisfy	VERB
ejpam-3448	334	21	the	the	DET
ejpam-3448	334	22	following	follow	VERB
ejpam-3448	334	23	axioms	axiom	NOUN
ejpam-3448	334	24	(	(	PUNCT
ejpam-3448	334	25	a	a	DET
ejpam-3448	334	26	≺	≺	NOUN
ejpam-3448	334	27	b	b	NOUN
ejpam-3448	334	28	)	)	PUNCT
ejpam-3448	334	29	≺	≺	NOUN
ejpam-3448	335	1	c	c	X
ejpam-3448	335	2	=	=	PUNCT
ejpam-3448	335	3	a	a	DET
ejpam-3448	335	4	≺	≺	NOUN
ejpam-3448	335	5	(	(	PUNCT
ejpam-3448	335	6	b	b	NOUN
ejpam-3448	335	7	∗	∗	NOUN
ejpam-3448	335	8	c	c	NOUN
ejpam-3448	335	9	)	)	PUNCT
ejpam-3448	335	10	,	,	PUNCT
ejpam-3448	335	11	(	(	PUNCT
ejpam-3448	335	12	4	4	X
ejpam-3448	335	13	)	)	PUNCT
ejpam-3448	335	14	(	(	PUNCT
ejpam-3448	335	15	a	a	DET
ejpam-3448	335	16	�	�	PROPN
ejpam-3448	335	17	b	b	NOUN
ejpam-3448	335	18	)	)	PUNCT
ejpam-3448	335	19	≺	≺	NOUN
ejpam-3448	335	20	c	c	X
ejpam-3448	335	21	=	=	SYM
ejpam-3448	335	22	a	a	DET
ejpam-3448	335	23	�	�	PROPN
ejpam-3448	335	24	(	(	PUNCT
ejpam-3448	335	25	b	b	NOUN
ejpam-3448	335	26	≺	≺	NOUN
ejpam-3448	335	27	c	c	NOUN
ejpam-3448	335	28	)	)	PUNCT
ejpam-3448	335	29	,	,	PUNCT
ejpam-3448	335	30	(	(	PUNCT
ejpam-3448	335	31	5	5	X
ejpam-3448	335	32	)	)	PUNCT
ejpam-3448	335	33	(	(	PUNCT
ejpam-3448	335	34	a	a	DET
ejpam-3448	335	35	∗	∗	NOUN
ejpam-3448	335	36	b	b	NOUN
ejpam-3448	335	37	)	)	PUNCT
ejpam-3448	335	38	�	�	PROPN
ejpam-3448	335	39	c	c	NOUN
ejpam-3448	335	40	=	=	PUNCT
ejpam-3448	335	41	a	a	DET
ejpam-3448	335	42	�	�	PROPN
ejpam-3448	335	43	(	(	PUNCT
ejpam-3448	335	44	b	b	PROPN
ejpam-3448	335	45	�	�	PROPN
ejpam-3448	335	46	c	c	PROPN
ejpam-3448	335	47	)	)	PUNCT
ejpam-3448	335	48	(	(	PUNCT
ejpam-3448	335	49	6	6	NUM
ejpam-3448	335	50	)	)	PUNCT
ejpam-3448	335	51	for	for	ADP
ejpam-3448	335	52	all	all	DET
ejpam-3448	335	53	a	a	DET
ejpam-3448	335	54	,	,	PUNCT
ejpam-3448	335	55	b	b	NOUN
ejpam-3448	335	56	,	,	PUNCT
ejpam-3448	335	57	c	c	PROPN
ejpam-3448	335	58	∈	∈	PROPN
ejpam-3448	335	59	a	a	PRON
ejpam-3448	335	60	,	,	PUNCT
ejpam-3448	335	61	where	where	SCONJ
ejpam-3448	335	62	the	the	DET
ejpam-3448	335	63	operation	operation	NOUN
ejpam-3448	335	64	∗	∗	NOUN
ejpam-3448	335	65	defined	define	VERB
ejpam-3448	335	66	by	by	ADP
ejpam-3448	335	67	a	a	DET
ejpam-3448	335	68	∗	∗	NOUN
ejpam-3448	335	69	b	b	NOUN
ejpam-3448	335	70	:	:	PUNCT
ejpam-3448	335	71	=	=	PUNCT
ejpam-3448	335	72	a	a	DET
ejpam-3448	335	73	≺	≺	NOUN
ejpam-3448	335	74	b+	b+	VERB
ejpam-3448	335	75	a	a	DET
ejpam-3448	335	76	�	�	PROPN
ejpam-3448	335	77	b	b	PROPN
ejpam-3448	335	78	is	be	AUX
ejpam-3448	335	79	associative	associative	ADJ
ejpam-3448	335	80	.	.	PUNCT
ejpam-3448	336	1	definition	definition	NOUN
ejpam-3448	336	2	10	10	NUM
ejpam-3448	336	3	.	.	PUNCT
ejpam-3448	337	1	let	let	VERB
ejpam-3448	337	2	f	f	PRON
ejpam-3448	337	3	be	be	AUX
ejpam-3448	337	4	a	a	DET
ejpam-3448	337	5	field	field	NOUN
ejpam-3448	337	6	and	and	CCONJ
ejpam-3448	337	7	f	f	X
ejpam-3448	338	1	[	[	X
ejpam-3448	338	2	mp(∞	mp(∞	NOUN
ejpam-3448	338	3	)	)	PUNCT
ejpam-3448	338	4	′	′	PUNCT
ejpam-3448	338	5	]	]	PUNCT
ejpam-3448	338	6	be	be	AUX
ejpam-3448	338	7	the	the	DET
ejpam-3448	338	8	vector	vector	NOUN
ejpam-3448	338	9	space	space	NOUN
ejpam-3448	338	10	generated	generate	VERB
ejpam-3448	338	11	by	by	ADP
ejpam-3448	338	12	the	the	DET
ejpam-3448	338	13	elements	element	NOUN
ejpam-3448	338	14	xt	xt	VERB
ejpam-3448	338	15	,	,	PUNCT
ejpam-3448	338	16	for	for	ADP
ejpam-3448	338	17	t	t	PROPN
ejpam-3448	338	18	∈	∈	PROPN
ejpam-3448	338	19	mp(n	mp(n	NOUN
ejpam-3448	338	20	)	)	PUNCT
ejpam-3448	338	21	and	and	CCONJ
ejpam-3448	338	22	n	n	PRON
ejpam-3448	338	23	≥	≥	NOUN
ejpam-3448	338	24	1	1	NUM
ejpam-3448	338	25	,	,	PUNCT
ejpam-3448	338	26	that	that	ADV
ejpam-3448	338	27	is	is	ADV
ejpam-3448	338	28	,	,	PUNCT
ejpam-3448	338	29	we	we	PRON
ejpam-3448	338	30	do	do	AUX
ejpam-3448	338	31	not	not	PART
ejpam-3448	338	32	consider	consider	VERB
ejpam-3448	338	33	the	the	DET
ejpam-3448	338	34	elements	element	NOUN
ejpam-3448	338	35	of	of	ADP
ejpam-3448	338	36	the	the	DET
ejpam-3448	338	37	form	form	NOUN
ejpam-3448	338	38	x0	x0	PROPN
ejpam-3448	338	39	=	=	SYM
ejpam-3448	338	40	1	1	X
ejpam-3448	338	41	.	.	PUNCT
ejpam-3448	338	42	operations	operation	NOUN
ejpam-3448	338	43	on	on	ADP
ejpam-3448	338	44	f	f	PROPN
ejpam-3448	338	45	[	[	X
ejpam-3448	338	46	mp(∞	mp(∞	NOUN
ejpam-3448	338	47	)	)	PUNCT
ejpam-3448	338	48	′	′	NUM
ejpam-3448	338	49	]	]	PUNCT
ejpam-3448	339	1	are	be	AUX
ejpam-3448	339	2	defined	define	VERB
ejpam-3448	339	3	by	by	ADP
ejpam-3448	339	4	xt	xt	PROPN
ejpam-3448	339	5	≺	≺	NOUN
ejpam-3448	339	6	xt	xt	PROPN
ejpam-3448	340	1	′	′	NUM
ejpam-3448	340	2	:	:	PUNCT
ejpam-3448	341	1	=	=	PUNCT
ejpam-3448	341	2	xt`t	xt`t	PROPN
ejpam-3448	342	1	′	′	NUM
ejpam-3448	342	2	,	,	PUNCT
ejpam-3448	342	3	(	(	PUNCT
ejpam-3448	342	4	7	7	X
ejpam-3448	342	5	)	)	PUNCT
ejpam-3448	342	6	xt	xt	PROPN
ejpam-3448	342	7	�	�	PROPN
ejpam-3448	342	8	xt	xt	PROPN
ejpam-3448	342	9	′	′	NUM
ejpam-3448	342	10	:	:	PUNCT
ejpam-3448	343	1	=	=	SYM
ejpam-3448	343	2	xtat	xtat	X
ejpam-3448	344	1	′	′	NUM
ejpam-3448	344	2	(	(	PUNCT
ejpam-3448	344	3	8)	8)	NUM
ejpam-3448	344	4	for	for	ADP
ejpam-3448	344	5	any	any	DET
ejpam-3448	344	6	two	two	NUM
ejpam-3448	344	7	maximal	maximal	ADJ
ejpam-3448	344	8	tubings	tubing	NOUN
ejpam-3448	344	9	t	t	PROPN
ejpam-3448	344	10	,	,	PUNCT
ejpam-3448	344	11	t	t	PROPN
ejpam-3448	344	12	′	′	NUM
ejpam-3448	345	1	and	and	CCONJ
ejpam-3448	345	2	xt∪t	xt∪t	PROPN
ejpam-3448	346	1	′	′	NUM
ejpam-3448	346	2	:	:	PUNCT
ejpam-3448	347	1	=	=	X
ejpam-3448	347	2	xt	xt	PUNCT
ejpam-3448	348	1	+	+	NOUN
ejpam-3448	348	2	xt	xt	X
ejpam-3448	348	3	′.	′.	NOUN
ejpam-3448	348	4	proposition	proposition	NOUN
ejpam-3448	348	5	2	2	X
ejpam-3448	348	6	.	.	PUNCT
ejpam-3448	349	1	the	the	DET
ejpam-3448	349	2	vector	vector	NOUN
ejpam-3448	349	3	space	space	NOUN
ejpam-3448	349	4	f	f	PROPN
ejpam-3448	350	1	[	[	X
ejpam-3448	350	2	mp(∞	mp(∞	NOUN
ejpam-3448	350	3	)	)	PUNCT
ejpam-3448	350	4	′	′	NUM
ejpam-3448	350	5	]	]	PUNCT
ejpam-3448	351	1	equipped	equip	VERB
ejpam-3448	351	2	with	with	ADP
ejpam-3448	351	3	the	the	DET
ejpam-3448	351	4	two	two	NUM
ejpam-3448	351	5	operations	operation	NOUN
ejpam-3448	351	6	≺	≺	NOUN
ejpam-3448	351	7	and	and	CCONJ
ejpam-3448	351	8	�	�	PROPN
ejpam-3448	351	9	becomes	become	VERB
ejpam-3448	351	10	a	a	DET
ejpam-3448	351	11	dendriform	dendriform	NOUN
ejpam-3448	351	12	algebra	algebra	NOUN
ejpam-3448	351	13	by	by	ADP
ejpam-3448	351	14	defining	define	VERB
ejpam-3448	351	15	xt	xt	PROPN
ejpam-3448	351	16	∗	∗	NOUN
ejpam-3448	351	17	xt	xt	PUNCT
ejpam-3448	352	1	′	′	NUM
ejpam-3448	353	1	=	=	PUNCT
ejpam-3448	354	1	xt+t	xt+t	ADJ
ejpam-3448	354	2	′.	′.	NOUN
ejpam-3448	354	3	the	the	DET
ejpam-3448	354	4	operations	operation	NOUN
ejpam-3448	354	5	≺	≺	NOUN
ejpam-3448	354	6	and	and	CCONJ
ejpam-3448	354	7	�	�	PROPN
ejpam-3448	354	8	can	can	AUX
ejpam-3448	354	9	be	be	AUX
ejpam-3448	354	10	partially	partially	ADV
ejpam-3448	354	11	extended	extend	VERB
ejpam-3448	354	12	to	to	ADP
ejpam-3448	354	13	f	f	PROPN
ejpam-3448	354	14	[	[	X
ejpam-3448	354	15	mp(∞	mp(∞	NOUN
ejpam-3448	354	16	)	)	PUNCT
ejpam-3448	354	17	]	]	PUNCT
ejpam-3448	355	1	as	as	ADP
ejpam-3448	355	2	x0	x0	PROPN
ejpam-3448	355	3	�	�	PROPN
ejpam-3448	355	4	xt	xt	PROPN
ejpam-3448	355	5	=	=	SYM
ejpam-3448	355	6	xt	xt	PROPN
ejpam-3448	355	7	=	=	SYM
ejpam-3448	355	8	xt	xt	PROPN
ejpam-3448	355	9	≺	≺	NOUN
ejpam-3448	355	10	x0	x0	PROPN
ejpam-3448	355	11	for	for	ADP
ejpam-3448	355	12	all	all	DET
ejpam-3448	355	13	t	t	NOUN
ejpam-3448	356	1	and	and	CCONJ
ejpam-3448	356	2	then	then	ADV
ejpam-3448	356	3	f	f	X
ejpam-3448	357	1	[	[	X
ejpam-3448	357	2	mp(∞	mp(∞	NOUN
ejpam-3448	357	3	)	)	PUNCT
ejpam-3448	357	4	]	]	PUNCT
ejpam-3448	358	1	=	=	PUNCT
ejpam-3448	358	2	f	f	X
ejpam-3448	359	1	[	[	X
ejpam-3448	359	2	mp(∞	mp(∞	NOUN
ejpam-3448	359	3	)	)	PUNCT
ejpam-3448	359	4	′	′	NUM
ejpam-3448	360	1	]	]	PUNCT
ejpam-3448	360	2	⊕	⊕	NOUN
ejpam-3448	360	3	f	f	X
ejpam-3448	360	4	·	·	PUNCT
ejpam-3448	360	5	1	1	NUM
ejpam-3448	360	6	becomes	become	VERB
ejpam-3448	360	7	an	an	DET
ejpam-3448	360	8	augmented	augment	VERB
ejpam-3448	360	9	unital	unital	ADJ
ejpam-3448	360	10	associative	associative	ADJ
ejpam-3448	360	11	algebra	algebra	NOUN
ejpam-3448	360	12	.	.	PUNCT
ejpam-3448	361	1	4	4	X
ejpam-3448	361	2	.	.	X
ejpam-3448	361	3	an	an	DET
ejpam-3448	361	4	operad	operad	NOUN
ejpam-3448	361	5	on	on	ADP
ejpam-3448	361	6	paths	path	NOUN
ejpam-3448	361	7	via	via	ADP
ejpam-3448	361	8	tubings	tubing	NOUN
ejpam-3448	361	9	in	in	ADP
ejpam-3448	361	10	[	[	X
ejpam-3448	361	11	9	9	NUM
ejpam-3448	361	12	]	]	PUNCT
ejpam-3448	361	13	,	,	PUNCT
ejpam-3448	361	14	markl	markl	PROPN
ejpam-3448	361	15	gives	give	VERB
ejpam-3448	361	16	a	a	DET
ejpam-3448	361	17	description	description	NOUN
ejpam-3448	361	18	of	of	ADP
ejpam-3448	361	19	the	the	DET
ejpam-3448	361	20	cellular	cellular	ADJ
ejpam-3448	361	21	operad	operad	ADJ
ejpam-3448	361	22	structure	structure	NOUN
ejpam-3448	361	23	of	of	ADP
ejpam-3448	361	24	associahedron	associahedron	PROPN
ejpam-3448	361	25	.	.	PUNCT
ejpam-3448	362	1	here	here	ADV
ejpam-3448	362	2	we	we	PRON
ejpam-3448	362	3	reconstruct	reconstruct	VERB
ejpam-3448	362	4	it	it	PRON
ejpam-3448	362	5	by	by	ADP
ejpam-3448	362	6	using	use	VERB
ejpam-3448	362	7	tubings	tubing	NOUN
ejpam-3448	362	8	on	on	ADP
ejpam-3448	362	9	paths	path	NOUN
ejpam-3448	362	10	.	.	PUNCT
ejpam-3448	363	1	in	in	ADP
ejpam-3448	363	2	order	order	NOUN
ejpam-3448	363	3	to	to	PART
ejpam-3448	363	4	do	do	AUX
ejpam-3448	363	5	that	that	PRON
ejpam-3448	363	6	,	,	PUNCT
ejpam-3448	363	7	first	first	ADV
ejpam-3448	363	8	we	we	PRON
ejpam-3448	363	9	define	define	VERB
ejpam-3448	363	10	the	the	DET
ejpam-3448	363	11	comp	comp	NOUN
ejpam-3448	363	12	or	or	CCONJ
ejpam-3448	363	13	composition	composition	NOUN
ejpam-3448	363	14	maps	map	NOUN
ejpam-3448	363	15	on	on	ADP
ejpam-3448	363	16	the	the	DET
ejpam-3448	363	17	collection	collection	NOUN
ejpam-3448	363	18	{	{	PUNCT
ejpam-3448	363	19	pp(n	pp(n	PROPN
ejpam-3448	363	20	)	)	PUNCT
ejpam-3448	363	21	}	}	PUNCT
ejpam-3448	363	22	.	.	PUNCT
ejpam-3448	364	1	let	let	VERB
ejpam-3448	364	2	t1	t1	NOUN
ejpam-3448	364	3	=	=	NOUN
ejpam-3448	364	4	a1	a1	NOUN
ejpam-3448	364	5	.	.	PUNCT
ejpam-3448	364	6	.	.	PUNCT
ejpam-3448	364	7	.	.	PUNCT
ejpam-3448	365	1	an	an	DET
ejpam-3448	365	2	∈	∈	PROPN
ejpam-3448	365	3	pp(n	pp(n	NUM
ejpam-3448	365	4	)	)	PUNCT
ejpam-3448	365	5	and	and	CCONJ
ejpam-3448	365	6	t2	t2	PROPN
ejpam-3448	365	7	=	=	SYM
ejpam-3448	365	8	b1b2	b1b2	PROPN
ejpam-3448	365	9	.	.	PUNCT
ejpam-3448	365	10	.	.	PUNCT
ejpam-3448	365	11	.	.	PUNCT
ejpam-3448	366	1	bm	bm	PROPN
ejpam-3448	366	2	∈	∈	PROPN
ejpam-3448	366	3	pp(m	pp(m	NOUN
ejpam-3448	366	4	)	)	PUNCT
ejpam-3448	366	5	.	.	PUNCT
ejpam-3448	367	1	for	for	ADP
ejpam-3448	367	2	n	n	CCONJ
ejpam-3448	367	3	,	,	PUNCT
ejpam-3448	367	4	m	m	VERB
ejpam-3448	367	5	≥	≥	NOUN
ejpam-3448	367	6	1	1	NUM
ejpam-3448	367	7	and	and	CCONJ
ejpam-3448	367	8	0	0	NUM
ejpam-3448	367	9	≤	≤	NUM
ejpam-3448	367	10	i	i	PRON
ejpam-3448	367	11	≤	≤	PROPN
ejpam-3448	367	12	n	n	CCONJ
ejpam-3448	367	13	,	,	PUNCT
ejpam-3448	367	14	the	the	DET
ejpam-3448	367	15	comp	comp	NOUN
ejpam-3448	367	16	map	map	NOUN
ejpam-3448	367	17	◦	◦	NOUN
ejpam-3448	367	18	i	i	PRON
ejpam-3448	367	19	:	:	PUNCT
ejpam-3448	367	20	pp(n	pp(n	NUM
ejpam-3448	367	21	)	)	PUNCT
ejpam-3448	367	22	×	×	NOUN
ejpam-3448	367	23	pp(m)→	pp(m)→	ADJ
ejpam-3448	367	24	pp(n+m	pp(n+m	NOUN
ejpam-3448	367	25	)	)	PUNCT
ejpam-3448	367	26	is	be	AUX
ejpam-3448	367	27	given	give	VERB
ejpam-3448	367	28	by	by	ADP
ejpam-3448	367	29	t1	t1	PROPN
ejpam-3448	367	30	◦	◦	NOUN
ejpam-3448	367	31	i	i	NOUN
ejpam-3448	367	32	t2	t2	NOUN
ejpam-3448	367	33	=	=	SYM
ejpam-3448	367	34	a1a2	a1a2	PROPN
ejpam-3448	367	35	.	.	PUNCT
ejpam-3448	367	36	.	.	PUNCT
ejpam-3448	367	37	.	.	PUNCT
ejpam-3448	368	1	ai(b1	ai(b1	VERB
ejpam-3448	369	1	+	+	PUNCT
ejpam-3448	369	2	ãi)(b2	ãi)(b2	NUM
ejpam-3448	369	3	+	+	CCONJ
ejpam-3448	369	4	ãi	ãi	PROPN
ejpam-3448	369	5	)	)	PUNCT
ejpam-3448	369	6	.	.	PUNCT
ejpam-3448	369	7	.	.	PUNCT
ejpam-3448	369	8	.	.	PUNCT
ejpam-3448	370	1	(	(	PUNCT
ejpam-3448	370	2	bm	bm	NOUN
ejpam-3448	370	3	+	+	NOUN
ejpam-3448	371	1	ãi)ai+1	ãi)ai+1	ADV
ejpam-3448	371	2	.	.	PUNCT
ejpam-3448	371	3	.	.	PUNCT
ejpam-3448	371	4	.	.	PUNCT
ejpam-3448	372	1	an	an	DET
ejpam-3448	372	2	(	(	PUNCT
ejpam-3448	372	3	9	9	NUM
ejpam-3448	372	4	)	)	PUNCT
ejpam-3448	372	5	s.	s.	PROPN
ejpam-3448	372	6	k.	k.	PROPN
ejpam-3448	372	7	gürbüzer	gürbüzer	PROPN
ejpam-3448	372	8	,	,	PUNCT
ejpam-3448	372	9	b.	b.	PROPN
ejpam-3448	372	10	akyar	akyar	PROPN
ejpam-3448	372	11	/	/	SYM
ejpam-3448	372	12	eur	eur	PROPN
ejpam-3448	372	13	.	.	PUNCT
ejpam-3448	373	1	j.	j.	PROPN
ejpam-3448	373	2	pure	pure	PROPN
ejpam-3448	373	3	appl	appl	PROPN
ejpam-3448	373	4	.	.	PROPN
ejpam-3448	373	5	math	math	PROPN
ejpam-3448	373	6	,	,	PUNCT
ejpam-3448	373	7	12	12	NUM
ejpam-3448	373	8	(	(	PUNCT
ejpam-3448	373	9	3	3	NUM
ejpam-3448	373	10	)	)	PUNCT
ejpam-3448	373	11	(	(	PUNCT
ejpam-3448	373	12	2019	2019	NUM
ejpam-3448	373	13	)	)	PUNCT
ejpam-3448	373	14	,	,	PUNCT
ejpam-3448	373	15	734	734	NUM
ejpam-3448	373	16	-	-	SYM
ejpam-3448	373	17	748	748	NUM
ejpam-3448	373	18	744	744	NUM
ejpam-3448	373	19	where	where	SCONJ
ejpam-3448	373	20	ãi	ãi	PROPN
ejpam-3448	373	21	is	be	AUX
ejpam-3448	373	22	the	the	DET
ejpam-3448	373	23	maximum	maximum	NOUN
ejpam-3448	373	24	of	of	ADP
ejpam-3448	373	25	the	the	DET
ejpam-3448	373	26	integers	integer	NOUN
ejpam-3448	373	27	ai	ai	VERB
ejpam-3448	373	28	,	,	PUNCT
ejpam-3448	373	29	ai+1	ai+1	PROPN
ejpam-3448	373	30	,	,	PUNCT
ejpam-3448	373	31	that	that	ADV
ejpam-3448	373	32	is	is	ADV
ejpam-3448	373	33	,	,	PUNCT
ejpam-3448	373	34	ãi	ãi	ADJ
ejpam-3448	373	35	=	=	SYM
ejpam-3448	373	36	max(ai	max(ai	NOUN
ejpam-3448	373	37	,	,	PUNCT
ejpam-3448	373	38	ai+1	ai+1	NOUN
ejpam-3448	373	39	)	)	PUNCT
ejpam-3448	373	40	,	,	PUNCT
ejpam-3448	373	41	for	for	ADP
ejpam-3448	373	42	0	0	NUM
ejpam-3448	373	43	<	<	X
ejpam-3448	374	1	i	i	PRON
ejpam-3448	374	2	<	<	X
ejpam-3448	374	3	n	n	PROPN
ejpam-3448	374	4	and	and	CCONJ
ejpam-3448	374	5	ã0	ã0	PROPN
ejpam-3448	374	6	=	=	PUNCT
ejpam-3448	374	7	a1	a1	PROPN
ejpam-3448	374	8	and	and	CCONJ
ejpam-3448	374	9	ãn	ãn	NOUN
ejpam-3448	374	10	=	=	VERB
ejpam-3448	374	11	an	an	X
ejpam-3448	374	12	.	.	PUNCT
ejpam-3448	375	1	it	it	PRON
ejpam-3448	375	2	can	can	AUX
ejpam-3448	375	3	be	be	AUX
ejpam-3448	375	4	easily	easily	ADV
ejpam-3448	375	5	checked	check	VERB
ejpam-3448	375	6	that	that	PRON
ejpam-3448	375	7	for	for	ADP
ejpam-3448	375	8	any	any	DET
ejpam-3448	375	9	three	three	NUM
ejpam-3448	375	10	tubings	tubing	NOUN
ejpam-3448	375	11	t1	t1	VERB
ejpam-3448	375	12	,	,	PUNCT
ejpam-3448	375	13	t2	t2	NOUN
ejpam-3448	375	14	and	and	CCONJ
ejpam-3448	375	15	t3	t3	PROPN
ejpam-3448	375	16	,	,	PUNCT
ejpam-3448	375	17	the	the	DET
ejpam-3448	375	18	comp	comp	NOUN
ejpam-3448	375	19	map	map	NOUN
ejpam-3448	375	20	satisfies	satisfy	VERB
ejpam-3448	375	21	the	the	DET
ejpam-3448	375	22	following	follow	VERB
ejpam-3448	375	23	equations	equation	NOUN
ejpam-3448	375	24	.	.	PUNCT
ejpam-3448	376	1	t1	t1	NOUN
ejpam-3448	376	2	◦	◦	NOUN
ejpam-3448	376	3	i	i	PROPN
ejpam-3448	376	4	(	(	PUNCT
ejpam-3448	376	5	t2	t2	PROPN
ejpam-3448	376	6	◦	◦	PROPN
ejpam-3448	376	7	j	j	PROPN
ejpam-3448	376	8	t3	t3	PROPN
ejpam-3448	376	9	)	)	PUNCT
ejpam-3448	377	1	=	=	PRON
ejpam-3448	377	2	(	(	PUNCT
ejpam-3448	377	3	t1	t1	NOUN
ejpam-3448	377	4	◦	◦	NOUN
ejpam-3448	377	5	i	i	NOUN
ejpam-3448	377	6	t2	t2	NOUN
ejpam-3448	377	7	)	)	PUNCT
ejpam-3448	377	8	◦	◦	NOUN
ejpam-3448	377	9	j+i	j+i	NUM
ejpam-3448	377	10	t3	t3	PROPN
ejpam-3448	377	11	,	,	PUNCT
ejpam-3448	377	12	0	0	NUM
ejpam-3448	377	13	≤	≤	NUM
ejpam-3448	377	14	j	j	PROPN
ejpam-3448	377	15	≤	≤	NUM
ejpam-3448	377	16	m	m	PROPN
ejpam-3448	377	17	,	,	PUNCT
ejpam-3448	377	18	(	(	PUNCT
ejpam-3448	377	19	10	10	NUM
ejpam-3448	377	20	)	)	PUNCT
ejpam-3448	377	21	(	(	PUNCT
ejpam-3448	377	22	t1	t1	NOUN
ejpam-3448	377	23	◦	◦	NOUN
ejpam-3448	377	24	i	i	NOUN
ejpam-3448	377	25	t2	t2	NOUN
ejpam-3448	377	26	)	)	PUNCT
ejpam-3448	377	27	◦	◦	PROPN
ejpam-3448	377	28	j	j	PROPN
ejpam-3448	377	29	t3	t3	PROPN
ejpam-3448	377	30	=	=	PROPN
ejpam-3448	377	31	(	(	PUNCT
ejpam-3448	377	32	t1	t1	NOUN
ejpam-3448	377	33	◦	◦	NOUN
ejpam-3448	377	34	j−m	j−m	ADJ
ejpam-3448	377	35	t3	t3	NOUN
ejpam-3448	377	36	)	)	PUNCT
ejpam-3448	377	37	◦	◦	NOUN
ejpam-3448	377	38	i	i	NOUN
ejpam-3448	377	39	t2	t2	NOUN
ejpam-3448	377	40	,	,	PUNCT
ejpam-3448	377	41	i+m+	i+m+	NOUN
ejpam-3448	377	42	1	1	NUM
ejpam-3448	377	43	<	<	X
ejpam-3448	377	44	j	j	PROPN
ejpam-3448	377	45	≤	≤	PROPN
ejpam-3448	377	46	n+m	n+m	PROPN
ejpam-3448	377	47	.	.	PUNCT
ejpam-3448	378	1	(	(	PUNCT
ejpam-3448	378	2	11	11	NUM
ejpam-3448	378	3	)	)	PUNCT
ejpam-3448	378	4	since	since	SCONJ
ejpam-3448	378	5	we	we	PRON
ejpam-3448	378	6	shift	shift	VERB
ejpam-3448	378	7	the	the	DET
ejpam-3448	378	8	indices	index	NOUN
ejpam-3448	378	9	1	1	NUM
ejpam-3448	378	10	,	,	PUNCT
ejpam-3448	378	11	one	one	PRON
ejpam-3448	378	12	can	can	AUX
ejpam-3448	378	13	think	think	VERB
ejpam-3448	378	14	that	that	SCONJ
ejpam-3448	378	15	they	they	PRON
ejpam-3448	378	16	are	be	AUX
ejpam-3448	378	17	different	different	ADJ
ejpam-3448	378	18	from	from	ADP
ejpam-3448	378	19	the	the	DET
ejpam-3448	378	20	usual	usual	ADJ
ejpam-3448	378	21	definition	definition	NOUN
ejpam-3448	378	22	of	of	ADP
ejpam-3448	378	23	comp	comp	NOUN
ejpam-3448	378	24	maps	map	NOUN
ejpam-3448	378	25	in	in	ADP
ejpam-3448	378	26	a	a	DET
ejpam-3448	378	27	non	non	ADJ
ejpam-3448	378	28	symmetric	symmetric	ADJ
ejpam-3448	378	29	operad	operad	NOUN
ejpam-3448	378	30	.	.	PUNCT
ejpam-3448	379	1	but	but	CCONJ
ejpam-3448	379	2	the	the	DET
ejpam-3448	379	3	operad	operad	ADJ
ejpam-3448	379	4	structure	structure	NOUN
ejpam-3448	379	5	of	of	ADP
ejpam-3448	379	6	pp(∞	pp(∞	NOUN
ejpam-3448	379	7	)	)	PUNCT
ejpam-3448	379	8	:	:	PUNCT
ejpam-3448	380	1	=	=	SYM
ejpam-3448	380	2	{	{	PUNCT
ejpam-3448	380	3	pp(m)}m≥1	pp(m)}m≥1	NOUN
ejpam-3448	380	4	with	with	ADP
ejpam-3448	380	5	these	these	DET
ejpam-3448	380	6	comp	comp	NOUN
ejpam-3448	380	7	maps	map	NOUN
ejpam-3448	380	8	has	have	VERB
ejpam-3448	380	9	a	a	DET
ejpam-3448	380	10	one	one	NUM
ejpam-3448	380	11	to	to	ADP
ejpam-3448	380	12	one	one	NUM
ejpam-3448	380	13	correspondence	correspondence	NOUN
ejpam-3448	380	14	with	with	ADP
ejpam-3448	380	15	the	the	DET
ejpam-3448	380	16	operad	operad	ADJ
ejpam-3448	380	17	structure	structure	NOUN
ejpam-3448	380	18	of	of	ADP
ejpam-3448	380	19	{	{	PUNCT
ejpam-3448	380	20	kn}n≥0	kn}n≥0	PROPN
ejpam-3448	380	21	.	.	PUNCT
ejpam-3448	381	1	if	if	SCONJ
ejpam-3448	381	2	we	we	PRON
ejpam-3448	381	3	let	let	VERB
ejpam-3448	381	4	the	the	DET
ejpam-3448	381	5	comp	comp	NOUN
ejpam-3448	381	6	maps	map	NOUN
ejpam-3448	381	7	to	to	PART
ejpam-3448	381	8	be	be	AUX
ejpam-3448	381	9	distributive	distributive	ADJ
ejpam-3448	381	10	over	over	ADP
ejpam-3448	381	11	the	the	DET
ejpam-3448	381	12	union	union	NOUN
ejpam-3448	381	13	,	,	PUNCT
ejpam-3448	381	14	then	then	ADV
ejpam-3448	381	15	the	the	DET
ejpam-3448	381	16	collection	collection	NOUN
ejpam-3448	381	17	mp(∞	mp(∞	NOUN
ejpam-3448	381	18	)	)	PUNCT
ejpam-3448	381	19	is	be	AUX
ejpam-3448	381	20	closed	close	VERB
ejpam-3448	381	21	under	under	ADP
ejpam-3448	381	22	the	the	DET
ejpam-3448	381	23	comp	comp	PROPN
ejpam-3448	381	24	maps	maps	PROPN
ejpam-3448	381	25	◦	◦	PROPN
ejpam-3448	381	26	i.	i.	NOUN
ejpam-3448	381	27	this	this	DET
ejpam-3448	381	28	property	property	NOUN
ejpam-3448	381	29	leads	lead	VERB
ejpam-3448	381	30	us	we	PRON
ejpam-3448	381	31	to	to	PART
ejpam-3448	381	32	give	give	VERB
ejpam-3448	381	33	the	the	DET
ejpam-3448	381	34	dendriform	dendriform	NOUN
ejpam-3448	381	35	operad	operad	ADJ
ejpam-3448	381	36	{	{	PUNCT
ejpam-3448	381	37	dend(n)}n≥1	dend(n)}n≥1	VERB
ejpam-3448	381	38	in	in	ADP
ejpam-3448	381	39	terms	term	NOUN
ejpam-3448	381	40	of	of	ADP
ejpam-3448	381	41	tubings	tubing	NOUN
ejpam-3448	381	42	on	on	ADP
ejpam-3448	381	43	paths	path	NOUN
ejpam-3448	381	44	.	.	PUNCT
ejpam-3448	382	1	the	the	DET
ejpam-3448	382	2	sequence	sequence	NOUN
ejpam-3448	382	3	{	{	PUNCT
ejpam-3448	382	4	dend(n)}n≥1	dend(n)}n≥1	NOUN
ejpam-3448	382	5	forms	form	VERB
ejpam-3448	382	6	an	an	DET
ejpam-3448	382	7	operad	operad	NOUN
ejpam-3448	382	8	whose	whose	DET
ejpam-3448	382	9	i	i	PRON
ejpam-3448	382	10	-	-	PUNCT
ejpam-3448	382	11	th	th	X
ejpam-3448	382	12	comp	comp	NOUN
ejpam-3448	382	13	map	map	NOUN
ejpam-3448	382	14	◦	◦	NOUN
ejpam-3448	382	15	i	i	PRON
ejpam-3448	382	16	:	:	PUNCT
ejpam-3448	382	17	dend(n	dend(n	NOUN
ejpam-3448	382	18	)	)	PUNCT
ejpam-3448	382	19	×	×	NOUN
ejpam-3448	382	20	dend(m	dend(m	NOUN
ejpam-3448	382	21	)	)	PUNCT
ejpam-3448	382	22	→	→	SYM
ejpam-3448	382	23	dend(n	dend(n	NOUN
ejpam-3448	382	24	+	+	CCONJ
ejpam-3448	382	25	m	m	VERB
ejpam-3448	382	26	−	−	NOUN
ejpam-3448	382	27	1	1	NUM
ejpam-3448	382	28	)	)	PUNCT
ejpam-3448	382	29	is	be	AUX
ejpam-3448	382	30	defined	define	VERB
ejpam-3448	382	31	by	by	ADP
ejpam-3448	382	32	xt	xt	ADP
ejpam-3448	382	33	◦	◦	NOUN
ejpam-3448	382	34	i	i	PRON
ejpam-3448	382	35	xt	xt	VERB
ejpam-3448	383	1	′	′	NUM
ejpam-3448	383	2	=	=	PUNCT
ejpam-3448	384	1	xt	xt	ADP
ejpam-3448	384	2	◦	◦	VERB
ejpam-3448	384	3	it	it	PRON
ejpam-3448	384	4	′	′	NUM
ejpam-3448	384	5	,	,	PUNCT
ejpam-3448	384	6	where	where	SCONJ
ejpam-3448	384	7	dend(n	dend(n	NOUN
ejpam-3448	384	8	)	)	PUNCT
ejpam-3448	384	9	=	=	SYM
ejpam-3448	385	1	f	f	X
ejpam-3448	386	1	[	[	X
ejpam-3448	386	2	mp(n−	mp(n−	PROPN
ejpam-3448	386	3	1	1	NUM
ejpam-3448	386	4	)	)	PUNCT
ejpam-3448	386	5	]	]	PUNCT
ejpam-3448	386	6	for	for	ADP
ejpam-3448	386	7	any	any	DET
ejpam-3448	386	8	field	field	NOUN
ejpam-3448	386	9	f.	f.	PROPN
ejpam-3448	386	10	now	now	ADV
ejpam-3448	386	11	,	,	PUNCT
ejpam-3448	386	12	we	we	PRON
ejpam-3448	386	13	construct	construct	VERB
ejpam-3448	386	14	the	the	DET
ejpam-3448	386	15	cellular	cellular	ADJ
ejpam-3448	386	16	chain	chain	NOUN
ejpam-3448	386	17	complex	complex	NOUN
ejpam-3448	386	18	of	of	ADP
ejpam-3448	386	19	an	an	DET
ejpam-3448	386	20	associahedron	associahedron	NOUN
ejpam-3448	386	21	in	in	ADP
ejpam-3448	386	22	terms	term	NOUN
ejpam-3448	386	23	of	of	ADP
ejpam-3448	386	24	tubings	tubing	NOUN
ejpam-3448	386	25	on	on	ADP
ejpam-3448	386	26	paths	path	NOUN
ejpam-3448	386	27	.	.	PUNCT
ejpam-3448	387	1	let	let	VERB
ejpam-3448	387	2	t	t	PROPN
ejpam-3448	387	3	∈	∈	PROPN
ejpam-3448	387	4	pp(n	pp(n	PROPN
ejpam-3448	387	5	)	)	PUNCT
ejpam-3448	387	6	be	be	AUX
ejpam-3448	387	7	a	a	DET
ejpam-3448	387	8	k	k	NOUN
ejpam-3448	387	9	-	-	NOUN
ejpam-3448	387	10	tubing	tubing	NOUN
ejpam-3448	387	11	whose	whose	DET
ejpam-3448	387	12	tubes	tube	NOUN
ejpam-3448	387	13	are	be	AUX
ejpam-3448	387	14	labelled	label	VERB
ejpam-3448	387	15	by	by	ADP
ejpam-3448	387	16	an	an	DET
ejpam-3448	387	17	order	order	NOUN
ejpam-3448	387	18	e1	e1	NOUN
ejpam-3448	387	19	,	,	PUNCT
ejpam-3448	387	20	.	.	PUNCT
ejpam-3448	387	21	.	.	PUNCT
ejpam-3448	388	1	.	.	PUNCT
ejpam-3448	389	1	,	,	PUNCT
ejpam-3448	389	2	ek	ek	PROPN
ejpam-3448	389	3	except	except	SCONJ
ejpam-3448	389	4	the	the	DET
ejpam-3448	389	5	universal	universal	ADJ
ejpam-3448	389	6	one	one	NUM
ejpam-3448	389	7	.	.	PUNCT
ejpam-3448	390	1	two	two	NUM
ejpam-3448	390	2	orderings	ordering	NOUN
ejpam-3448	390	3	ei1	ei1	ADV
ejpam-3448	390	4	,	,	PUNCT
ejpam-3448	390	5	.	.	PUNCT
ejpam-3448	390	6	.	.	PUNCT
ejpam-3448	391	1	.	.	PUNCT
ejpam-3448	392	1	,	,	PUNCT
ejpam-3448	392	2	eik	eik	PROPN
ejpam-3448	392	3	and	and	CCONJ
ejpam-3448	392	4	ej1	ej1	NOUN
ejpam-3448	392	5	,	,	PUNCT
ejpam-3448	392	6	.	.	PUNCT
ejpam-3448	392	7	.	.	PUNCT
ejpam-3448	393	1	.	.	PUNCT
ejpam-3448	394	1	,	,	PUNCT
ejpam-3448	394	2	ejk	ejk	NOUN
ejpam-3448	394	3	are	be	AUX
ejpam-3448	394	4	equivalent	equivalent	ADJ
ejpam-3448	394	5	if	if	SCONJ
ejpam-3448	394	6	they	they	PRON
ejpam-3448	394	7	are	be	AUX
ejpam-3448	394	8	related	relate	VERB
ejpam-3448	394	9	by	by	ADP
ejpam-3448	394	10	an	an	DET
ejpam-3448	394	11	even	even	ADJ
ejpam-3448	394	12	permutation	permutation	NOUN
ejpam-3448	394	13	.	.	PUNCT
ejpam-3448	395	1	the	the	DET
ejpam-3448	395	2	equivalence	equivalence	NOUN
ejpam-3448	395	3	class	class	NOUN
ejpam-3448	395	4	corresponding	correspond	VERB
ejpam-3448	395	5	to	to	ADP
ejpam-3448	395	6	an	an	DET
ejpam-3448	395	7	ordering	ordering	NOUN
ejpam-3448	395	8	ei1	ei1	NOUN
ejpam-3448	395	9	,	,	PUNCT
ejpam-3448	395	10	.	.	PUNCT
ejpam-3448	395	11	.	.	PUNCT
ejpam-3448	395	12	.	.	PUNCT
ejpam-3448	396	1	,	,	PUNCT
ejpam-3448	396	2	eik	eik	PROPN
ejpam-3448	396	3	is	be	AUX
ejpam-3448	396	4	called	call	VERB
ejpam-3448	396	5	the	the	DET
ejpam-3448	396	6	orientation	orientation	NOUN
ejpam-3448	396	7	and	and	CCONJ
ejpam-3448	396	8	denoted	denote	VERB
ejpam-3448	396	9	by	by	ADP
ejpam-3448	396	10	ei1	ei1	PROPN
ejpam-3448	396	11	∧	∧	PROPN
ejpam-3448	396	12	·	·	PUNCT
ejpam-3448	396	13	·	·	PUNCT
ejpam-3448	396	14	·	·	PUNCT
ejpam-3448	397	1	∧	∧	NOUN
ejpam-3448	397	2	eik	eik	PROPN
ejpam-3448	397	3	=	=	PROPN
ejpam-3448	397	4	ω	ω	PROPN
ejpam-3448	397	5	.	.	PUNCT
ejpam-3448	398	1	an	an	DET
ejpam-3448	398	2	oriented	orient	VERB
ejpam-3448	398	3	ktubing	ktubing	NOUN
ejpam-3448	398	4	t	t	PROPN
ejpam-3448	398	5	∈	∈	PROPN
ejpam-3448	398	6	pp(n	pp(n	PROPN
ejpam-3448	398	7	)	)	PUNCT
ejpam-3448	398	8	with	with	ADP
ejpam-3448	398	9	its	its	PRON
ejpam-3448	398	10	orientation	orientation	NOUN
ejpam-3448	398	11	ω	ω	NOUN
ejpam-3448	398	12	is	be	AUX
ejpam-3448	398	13	a	a	DET
ejpam-3448	398	14	pair	pair	NOUN
ejpam-3448	398	15	(	(	PUNCT
ejpam-3448	398	16	t	t	PROPN
ejpam-3448	398	17	,	,	PUNCT
ejpam-3448	398	18	ω	ω	NOUN
ejpam-3448	398	19	)	)	PUNCT
ejpam-3448	398	20	.	.	PUNCT
ejpam-3448	399	1	let	let	VERB
ejpam-3448	399	2	ccn−k(kn	ccn−k(kn	NOUN
ejpam-3448	399	3	)	)	PUNCT
ejpam-3448	399	4	be	be	AUX
ejpam-3448	399	5	a	a	DET
ejpam-3448	399	6	vector	vector	NOUN
ejpam-3448	399	7	space	space	NOUN
ejpam-3448	399	8	spanned	span	VERB
ejpam-3448	399	9	by	by	ADP
ejpam-3448	399	10	the	the	DET
ejpam-3448	399	11	oriented	orient	VERB
ejpam-3448	399	12	(	(	PUNCT
ejpam-3448	399	13	n	n	CCONJ
ejpam-3448	399	14	−	−	PROPN
ejpam-3448	399	15	k)-cells	k)-cell	NOUN
ejpam-3448	399	16	in	in	ADP
ejpam-3448	399	17	kn	kn	PROPN
ejpam-3448	399	18	which	which	PRON
ejpam-3448	399	19	are	be	AUX
ejpam-3448	399	20	related	relate	VERB
ejpam-3448	399	21	by	by	ADP
ejpam-3448	399	22	the	the	DET
ejpam-3448	399	23	oriented	orient	VERB
ejpam-3448	399	24	ktubings	ktubing	NOUN
ejpam-3448	399	25	in	in	ADP
ejpam-3448	399	26	pp(n+1	pp(n+1	NOUN
ejpam-3448	399	27	)	)	PUNCT
ejpam-3448	400	1	modulo	modulo	VERB
ejpam-3448	400	2	the	the	DET
ejpam-3448	400	3	relation	relation	NOUN
ejpam-3448	400	4	(	(	PUNCT
ejpam-3448	400	5	t	t	PROPN
ejpam-3448	400	6	,	,	PUNCT
ejpam-3448	400	7	ω1	ω1	PROPN
ejpam-3448	400	8	)	)	PUNCT
ejpam-3448	400	9	=	=	SYM
ejpam-3448	400	10	−(t	−(t	PROPN
ejpam-3448	400	11	,	,	PUNCT
ejpam-3448	400	12	ω2	ω2	NUM
ejpam-3448	400	13	)	)	PUNCT
ejpam-3448	400	14	,	,	PUNCT
ejpam-3448	400	15	where	where	SCONJ
ejpam-3448	400	16	ω1	ω1	PROPN
ejpam-3448	400	17	and	and	CCONJ
ejpam-3448	400	18	ω2	ω2	ADJ
ejpam-3448	400	19	are	be	AUX
ejpam-3448	400	20	distinct	distinct	ADJ
ejpam-3448	400	21	orientations	orientation	NOUN
ejpam-3448	400	22	.	.	PUNCT
ejpam-3448	401	1	the	the	DET
ejpam-3448	401	2	boundary	boundary	ADJ
ejpam-3448	401	3	operator	operator	NOUN
ejpam-3448	401	4	on	on	ADP
ejpam-3448	401	5	cc∗(k	cc∗(k	NOUN
ejpam-3448	401	6	n	n	CCONJ
ejpam-3448	401	7	)	)	PUNCT
ejpam-3448	401	8	is	be	AUX
ejpam-3448	401	9	defined	define	VERB
ejpam-3448	401	10	by	by	ADP
ejpam-3448	401	11	∂(t	∂(t	PROPN
ejpam-3448	401	12	,	,	PUNCT
ejpam-3448	401	13	ω	ω	NOUN
ejpam-3448	401	14	)	)	PUNCT
ejpam-3448	401	15	:	:	PUNCT
ejpam-3448	402	1	=	=	PUNCT
ejpam-3448	402	2	∑	∑	PUNCT
ejpam-3448	402	3	t	t	PROPN
ejpam-3448	402	4	′={{1,	′={{1,	NOUN
ejpam-3448	402	5	...	...	PUNCT
ejpam-3448	402	6	n+1},t1,	n+1},t1,	NUM
ejpam-3448	402	7	...	...	PUNCT
ejpam-3448	402	8	,tk+1	,tk+1	PUNCT
ejpam-3448	402	9	}	}	PUNCT
ejpam-3448	402	10	(	(	PUNCT
ejpam-3448	402	11	t	t	PROPN
ejpam-3448	402	12	′	′	NUM
ejpam-3448	402	13	,	,	PUNCT
ejpam-3448	402	14	e′	e′	X
ejpam-3448	402	15	∧	∧	PROPN
ejpam-3448	402	16	ω	ω	PROPN
ejpam-3448	402	17	)	)	PUNCT
ejpam-3448	402	18	(	(	PUNCT
ejpam-3448	402	19	12	12	NUM
ejpam-3448	402	20	)	)	PUNCT
ejpam-3448	402	21	for	for	ADP
ejpam-3448	402	22	oriented	orient	VERB
ejpam-3448	402	23	k	k	NOUN
ejpam-3448	402	24	-	-	NOUN
ejpam-3448	402	25	tubings	tubing	NOUN
ejpam-3448	402	26	on	on	ADP
ejpam-3448	402	27	p(n	p(n	PROPN
ejpam-3448	402	28	+	+	CCONJ
ejpam-3448	402	29	1	1	NUM
ejpam-3448	402	30	)	)	PUNCT
ejpam-3448	402	31	.	.	PUNCT
ejpam-3448	403	1	this	this	DET
ejpam-3448	403	2	sum	sum	NOUN
ejpam-3448	403	3	is	be	AUX
ejpam-3448	403	4	taken	take	VERB
ejpam-3448	403	5	over	over	ADP
ejpam-3448	403	6	all	all	PRON
ejpam-3448	403	7	(	(	PUNCT
ejpam-3448	403	8	k	k	PROPN
ejpam-3448	403	9	+	+	NOUN
ejpam-3448	403	10	1)-tubings	1)-tubings	NUM
ejpam-3448	404	1	such	such	ADJ
ejpam-3448	404	2	that	that	DET
ejpam-3448	404	3	t	t	NOUN
ejpam-3448	404	4	=	=	SYM
ejpam-3448	404	5	t	t	PROPN
ejpam-3448	404	6	′	′	NUM
ejpam-3448	404	7	\	\	NOUN
ejpam-3448	404	8	{	{	PUNCT
ejpam-3448	404	9	ti	ti	NOUN
ejpam-3448	404	10	}	}	PUNCT
ejpam-3448	404	11	for	for	ADP
ejpam-3448	404	12	some	some	DET
ejpam-3448	404	13	i	i	NOUN
ejpam-3448	404	14	=	=	NOUN
ejpam-3448	404	15	1	1	NUM
ejpam-3448	404	16	,	,	PUNCT
ejpam-3448	404	17	.	.	PUNCT
ejpam-3448	404	18	.	.	PUNCT
ejpam-3448	404	19	.	.	PUNCT
ejpam-3448	405	1	,	,	PUNCT
ejpam-3448	406	1	k	k	PROPN
ejpam-3448	406	2	+	+	CCONJ
ejpam-3448	406	3	1	1	NUM
ejpam-3448	406	4	and	and	CCONJ
ejpam-3448	406	5	e′	e′	NOUN
ejpam-3448	406	6	is	be	AUX
ejpam-3448	406	7	the	the	DET
ejpam-3448	406	8	label	label	NOUN
ejpam-3448	406	9	of	of	ADP
ejpam-3448	406	10	ti	ti	PROPN
ejpam-3448	406	11	.	.	PUNCT
ejpam-3448	407	1	the	the	DET
ejpam-3448	407	2	boundary	boundary	ADJ
ejpam-3448	407	3	map	map	NOUN
ejpam-3448	407	4	∂	∂	NUM
ejpam-3448	407	5	satisfies	satisfie	NOUN
ejpam-3448	407	6	∂2	∂2	PROPN
ejpam-3448	407	7	=	=	SYM
ejpam-3448	407	8	0	0	NUM
ejpam-3448	407	9	.	.	PUNCT
ejpam-3448	408	1	moreover	moreover	ADV
ejpam-3448	408	2	,	,	PUNCT
ejpam-3448	408	3	the	the	DET
ejpam-3448	408	4	comp	comp	NOUN
ejpam-3448	408	5	maps	map	NOUN
ejpam-3448	408	6	in	in	ADP
ejpam-3448	408	7	the	the	DET
ejpam-3448	408	8	operad	operad	ADJ
ejpam-3448	408	9	{	{	PUNCT
ejpam-3448	408	10	pp(n)}n≥1	pp(n)}n≥1	NOUN
ejpam-3448	408	11	can	can	AUX
ejpam-3448	408	12	also	also	ADV
ejpam-3448	408	13	be	be	AUX
ejpam-3448	408	14	extended	extend	VERB
ejpam-3448	408	15	on	on	ADP
ejpam-3448	408	16	the	the	DET
ejpam-3448	408	17	oriented	orient	VERB
ejpam-3448	408	18	k	k	NOUN
ejpam-3448	408	19	-	-	NOUN
ejpam-3448	408	20	tubings	tubing	NOUN
ejpam-3448	408	21	with	with	ADP
ejpam-3448	408	22	a	a	DET
ejpam-3448	408	23	sign	sign	NOUN
ejpam-3448	408	24	convention	convention	NOUN
ejpam-3448	408	25	.	.	PUNCT
ejpam-3448	409	1	for	for	ADP
ejpam-3448	409	2	0	0	NUM
ejpam-3448	409	3	≤	≤	NUM
ejpam-3448	409	4	i	i	PRON
ejpam-3448	409	5	≤	≤	PROPN
ejpam-3448	409	6	n	n	CCONJ
ejpam-3448	409	7	,	,	PUNCT
ejpam-3448	409	8	the	the	DET
ejpam-3448	409	9	comp	comp	NOUN
ejpam-3448	409	10	map	map	NOUN
ejpam-3448	409	11	◦	◦	NOUN
ejpam-3448	409	12	i	i	PRON
ejpam-3448	409	13	:	:	PUNCT
ejpam-3448	409	14	pp(n)×	pp(n)×	X
ejpam-3448	409	15	pp(m)→	pp(m)→	X
ejpam-3448	409	16	pp(n+m	pp(n+m	NOUN
ejpam-3448	409	17	)	)	PUNCT
ejpam-3448	409	18	is	be	AUX
ejpam-3448	409	19	given	give	VERB
ejpam-3448	409	20	by	by	ADP
ejpam-3448	409	21	(	(	PUNCT
ejpam-3448	409	22	t1	t1	PROPN
ejpam-3448	409	23	,	,	PUNCT
ejpam-3448	409	24	ω	ω	NOUN
ejpam-3448	409	25	)	)	PUNCT
ejpam-3448	409	26	◦	◦	NOUN
ejpam-3448	409	27	i	i	PROPN
ejpam-3448	409	28	(	(	PUNCT
ejpam-3448	409	29	t2	t2	PROPN
ejpam-3448	409	30	,	,	PUNCT
ejpam-3448	409	31	ω	ω	NUM
ejpam-3448	409	32	′	′	NUM
ejpam-3448	409	33	)	)	PUNCT
ejpam-3448	409	34	:	:	PUNCT
ejpam-3448	410	1	=	=	SYM
ejpam-3448	410	2	(	(	PUNCT
ejpam-3448	410	3	−1)(n+1)l+m(i+1)(t1	−1)(n+1)l+m(i+1)(t1	PROPN
ejpam-3448	410	4	◦	◦	NOUN
ejpam-3448	410	5	i	i	NOUN
ejpam-3448	410	6	t2	t2	NOUN
ejpam-3448	410	7	,	,	PUNCT
ejpam-3448	410	8	ω	ω	NUM
ejpam-3448	410	9	∧	∧	PROPN
ejpam-3448	410	10	ω′	ω′	X
ejpam-3448	410	11	∧	∧	PROPN
ejpam-3448	410	12	e	e	PROPN
ejpam-3448	410	13	)	)	PUNCT
ejpam-3448	410	14	,	,	PUNCT
ejpam-3448	410	15	where	where	SCONJ
ejpam-3448	410	16	t1	t1	NOUN
ejpam-3448	410	17	,	,	PUNCT
ejpam-3448	410	18	t2	t2	NOUN
ejpam-3448	410	19	are	be	AUX
ejpam-3448	410	20	(	(	PUNCT
ejpam-3448	410	21	n−	n−	NOUN
ejpam-3448	410	22	k	k	NOUN
ejpam-3448	410	23	)	)	PUNCT
ejpam-3448	410	24	and	and	CCONJ
ejpam-3448	410	25	(	(	PUNCT
ejpam-3448	410	26	m−	m−	PROPN
ejpam-3448	410	27	l)-tubings	l)-tubing	VERB
ejpam-3448	410	28	and	and	CCONJ
ejpam-3448	410	29	e	e	NOUN
ejpam-3448	410	30	denotes	denote	VERB
ejpam-3448	410	31	the	the	DET
ejpam-3448	410	32	label	label	NOUN
ejpam-3448	410	33	of	of	ADP
ejpam-3448	410	34	the	the	DET
ejpam-3448	410	35	universal	universal	ADJ
ejpam-3448	410	36	tube	tube	NOUN
ejpam-3448	410	37	of	of	ADP
ejpam-3448	410	38	t2	t2	PROPN
ejpam-3448	410	39	and	and	CCONJ
ejpam-3448	410	40	ω	ω	NUM
ejpam-3448	410	41	∧	∧	PROPN
ejpam-3448	410	42	ω′	ω′	X
ejpam-3448	410	43	∧	∧	PROPN
ejpam-3448	410	44	e	e	PROPN
ejpam-3448	410	45	is	be	AUX
ejpam-3448	410	46	the	the	DET
ejpam-3448	410	47	consecutive	consecutive	ADJ
ejpam-3448	410	48	composition	composition	NOUN
ejpam-3448	410	49	of	of	ADP
ejpam-3448	410	50	orientations	orientation	NOUN
ejpam-3448	410	51	.	.	PUNCT
ejpam-3448	411	1	finally	finally	ADV
ejpam-3448	411	2	,	,	PUNCT
ejpam-3448	411	3	we	we	PRON
ejpam-3448	411	4	define	define	VERB
ejpam-3448	411	5	a	a	DET
ejpam-3448	411	6	name	name	NOUN
ejpam-3448	411	7	of	of	ADP
ejpam-3448	411	8	a	a	DET
ejpam-3448	411	9	tubing	tubing	NOUN
ejpam-3448	411	10	on	on	ADP
ejpam-3448	411	11	a	a	DET
ejpam-3448	411	12	cycle	cycle	NOUN
ejpam-3448	411	13	as	as	ADP
ejpam-3448	411	14	a	a	DET
ejpam-3448	411	15	finite	finite	ADJ
ejpam-3448	411	16	sequence	sequence	NOUN
ejpam-3448	411	17	of	of	ADP
ejpam-3448	411	18	positive	positive	ADJ
ejpam-3448	411	19	integers	integer	NOUN
ejpam-3448	411	20	such	such	ADJ
ejpam-3448	411	21	that	that	SCONJ
ejpam-3448	411	22	the	the	DET
ejpam-3448	411	23	j	j	PROPN
ejpam-3448	411	24	-	-	PUNCT
ejpam-3448	411	25	th	th	VERB
ejpam-3448	411	26	term	term	NOUN
ejpam-3448	411	27	of	of	ADP
ejpam-3448	411	28	the	the	DET
ejpam-3448	411	29	sequence	sequence	NOUN
ejpam-3448	411	30	is	be	AUX
ejpam-3448	411	31	the	the	DET
ejpam-3448	411	32	number	number	NOUN
ejpam-3448	411	33	of	of	ADP
ejpam-3448	411	34	tubes	tube	NOUN
ejpam-3448	411	35	containing	contain	VERB
ejpam-3448	411	36	the	the	DET
ejpam-3448	411	37	j	j	PROPN
ejpam-3448	411	38	-	-	PUNCT
ejpam-3448	411	39	th	th	X
ejpam-3448	411	40	node	node	NOUN
ejpam-3448	411	41	of	of	ADP
ejpam-3448	411	42	c(n	c(n	PROPN
ejpam-3448	411	43	)	)	PUNCT
ejpam-3448	411	44	.	.	PUNCT
ejpam-3448	412	1	this	this	PRON
ejpam-3448	412	2	leads	lead	VERB
ejpam-3448	412	3	us	we	PRON
ejpam-3448	412	4	to	to	PART
ejpam-3448	412	5	construct	construct	VERB
ejpam-3448	412	6	the	the	DET
ejpam-3448	412	7	module	module	NOUN
ejpam-3448	412	8	structure	structure	NOUN
ejpam-3448	412	9	of	of	ADP
ejpam-3448	412	10	the	the	DET
ejpam-3448	412	11	collection	collection	NOUN
ejpam-3448	412	12	{	{	PUNCT
ejpam-3448	412	13	wn}n≥0	wn}n≥0	NOUN
ejpam-3448	412	14	via	via	ADP
ejpam-3448	412	15	tubings	tubing	NOUN
ejpam-3448	412	16	.	.	PUNCT
ejpam-3448	413	1	the	the	DET
ejpam-3448	413	2	i	i	PROPN
ejpam-3448	413	3	-	-	PUNCT
ejpam-3448	413	4	th	th	X
ejpam-3448	413	5	(	(	PUNCT
ejpam-3448	413	6	right	right	ADJ
ejpam-3448	413	7	)	)	PUNCT
ejpam-3448	413	8	comp	comp	PROPN
ejpam-3448	413	9	map	map	NOUN
ejpam-3448	413	10	◦	◦	NOUN
ejpam-3448	413	11	ri	ri	NOUN
ejpam-3448	413	12	:	:	PUNCT
ejpam-3448	413	13	pc(n)×	pc(n)×	PROPN
ejpam-3448	413	14	pp(m)→	pp(m)→	PROPN
ejpam-3448	413	15	pc(n+m	pc(n+m	NOUN
ejpam-3448	413	16	)	)	PUNCT
ejpam-3448	413	17	is	be	AUX
ejpam-3448	413	18	defined	define	VERB
ejpam-3448	413	19	by	by	ADP
ejpam-3448	413	20	t2	t2	PROPN
ejpam-3448	413	21	◦	◦	PROPN
ejpam-3448	413	22	ri	ri	PROPN
ejpam-3448	413	23	t1	t1	NOUN
ejpam-3448	413	24	=	=	PUNCT
ejpam-3448	413	25	b1	b1	PROPN
ejpam-3448	413	26	.	.	PUNCT
ejpam-3448	413	27	.	.	PUNCT
ejpam-3448	414	1	.	.	PUNCT
ejpam-3448	415	1	bi(a1	bi(a1	VERB
ejpam-3448	415	2	+	+	CCONJ
ejpam-3448	415	3	b̃i	b̃i	NOUN
ejpam-3448	415	4	)	)	PUNCT
ejpam-3448	415	5	.	.	PUNCT
ejpam-3448	415	6	.	.	PUNCT
ejpam-3448	416	1	.	.	PUNCT
ejpam-3448	417	1	(	(	PUNCT
ejpam-3448	417	2	am	be	AUX
ejpam-3448	417	3	+	+	X
ejpam-3448	417	4	b̃i)bi+1	b̃i)bi+1	NOUN
ejpam-3448	417	5	.	.	PUNCT
ejpam-3448	417	6	.	.	PUNCT
ejpam-3448	417	7	.	.	PUNCT
ejpam-3448	418	1	bn	bn	X
ejpam-3448	418	2	,	,	PUNCT
ejpam-3448	418	3	where	where	SCONJ
ejpam-3448	418	4	t1	t1	NOUN
ejpam-3448	418	5	=	=	NOUN
ejpam-3448	418	6	a1	a1	NOUN
ejpam-3448	418	7	.	.	PUNCT
ejpam-3448	418	8	.	.	PUNCT
ejpam-3448	418	9	.	.	PUNCT
ejpam-3448	419	1	am	be	AUX
ejpam-3448	419	2	∈	∈	PROPN
ejpam-3448	419	3	pp(m	pp(m	NOUN
ejpam-3448	419	4	)	)	PUNCT
ejpam-3448	419	5	,	,	PUNCT
ejpam-3448	419	6	t2	t2	NOUN
ejpam-3448	419	7	=	=	SYM
ejpam-3448	419	8	b1	b1	PROPN
ejpam-3448	419	9	.	.	PUNCT
ejpam-3448	419	10	.	.	PUNCT
ejpam-3448	419	11	.	.	PUNCT
ejpam-3448	420	1	bn	bn	NUM
ejpam-3448	420	2	∈	∈	PROPN
ejpam-3448	420	3	pc(n	pc(n	NOUN
ejpam-3448	420	4	)	)	PUNCT
ejpam-3448	420	5	and	and	CCONJ
ejpam-3448	420	6	b̃i	b̃i	X
ejpam-3448	420	7	=	=	SYM
ejpam-3448	420	8	max(bi	max(bi	PROPN
ejpam-3448	420	9	,	,	PUNCT
ejpam-3448	420	10	bi+1	bi+1	NOUN
ejpam-3448	420	11	)	)	PUNCT
ejpam-3448	420	12	for	for	ADP
ejpam-3448	420	13	1	1	NUM
ejpam-3448	420	14	≤	≤	NUM
ejpam-3448	420	15	i	i	PRON
ejpam-3448	420	16	≤	≤	ADJ
ejpam-3448	420	17	n−	n−	NOUN
ejpam-3448	420	18	1	1	NUM
ejpam-3448	420	19	and	and	CCONJ
ejpam-3448	420	20	b̃i	b̃i	X
ejpam-3448	420	21	=	=	NOUN
ejpam-3448	420	22	max{b1	max{b1	NOUN
ejpam-3448	420	23	,	,	PUNCT
ejpam-3448	420	24	bn	bn	CCONJ
ejpam-3448	420	25	}	}	PUNCT
ejpam-3448	420	26	for	for	ADP
ejpam-3448	420	27	i	i	PROPN
ejpam-3448	420	28	=	=	SYM
ejpam-3448	420	29	0	0	PUNCT
ejpam-3448	421	1	and	and	CCONJ
ejpam-3448	421	2	i	i	PRON
ejpam-3448	421	3	=	=	PROPN
ejpam-3448	421	4	n.	n.	PROPN
ejpam-3448	421	5	s.	s.	PROPN
ejpam-3448	421	6	k.	k.	PROPN
ejpam-3448	421	7	gürbüzer	gürbüzer	PROPN
ejpam-3448	421	8	,	,	PUNCT
ejpam-3448	421	9	b.	b.	PROPN
ejpam-3448	421	10	akyar	akyar	PROPN
ejpam-3448	421	11	/	/	SYM
ejpam-3448	421	12	eur	eur	PROPN
ejpam-3448	421	13	.	.	PUNCT
ejpam-3448	422	1	j.	j.	PROPN
ejpam-3448	422	2	pure	pure	PROPN
ejpam-3448	422	3	appl	appl	PROPN
ejpam-3448	422	4	.	.	PROPN
ejpam-3448	422	5	math	math	PROPN
ejpam-3448	422	6	,	,	PUNCT
ejpam-3448	422	7	12	12	NUM
ejpam-3448	422	8	(	(	PUNCT
ejpam-3448	422	9	3	3	NUM
ejpam-3448	422	10	)	)	PUNCT
ejpam-3448	422	11	(	(	PUNCT
ejpam-3448	422	12	2019	2019	NUM
ejpam-3448	422	13	)	)	PUNCT
ejpam-3448	422	14	,	,	PUNCT
ejpam-3448	422	15	734	734	NUM
ejpam-3448	422	16	-	-	SYM
ejpam-3448	422	17	748	748	NUM
ejpam-3448	422	18	745	745	NUM
ejpam-3448	422	19	proposition	proposition	NOUN
ejpam-3448	422	20	3	3	NUM
ejpam-3448	422	21	.	.	PUNCT
ejpam-3448	423	1	the	the	DET
ejpam-3448	423	2	collection	collection	NOUN
ejpam-3448	423	3	pc(∞	pc(∞	VERB
ejpam-3448	423	4	)	)	PUNCT
ejpam-3448	423	5	:	:	PUNCT
ejpam-3448	423	6	=	=	SYM
ejpam-3448	423	7	{	{	PUNCT
ejpam-3448	423	8	pc(n)}n≥1	pc(n)}n≥1	NOUN
ejpam-3448	423	9	is	be	AUX
ejpam-3448	423	10	a	a	DET
ejpam-3448	423	11	(	(	PUNCT
ejpam-3448	423	12	right	right	ADJ
ejpam-3448	423	13	)	)	PUNCT
ejpam-3448	423	14	module	module	NOUN
ejpam-3448	423	15	over	over	ADP
ejpam-3448	423	16	the	the	DET
ejpam-3448	423	17	operad	operad	NOUN
ejpam-3448	423	18	pp(∞	pp(∞	PROPN
ejpam-3448	423	19	)	)	PUNCT
ejpam-3448	423	20	:	:	PUNCT
ejpam-3448	424	1	=	=	SYM
ejpam-3448	424	2	{	{	PUNCT
ejpam-3448	424	3	pp(m)}m≥1	pp(m)}m≥1	NOUN
ejpam-3448	424	4	.	.	PUNCT
ejpam-3448	425	1	clearly	clearly	ADV
ejpam-3448	425	2	,	,	PUNCT
ejpam-3448	425	3	this	this	DET
ejpam-3448	425	4	module	module	NOUN
ejpam-3448	425	5	structure	structure	NOUN
ejpam-3448	425	6	is	be	AUX
ejpam-3448	425	7	the	the	DET
ejpam-3448	425	8	same	same	ADJ
ejpam-3448	425	9	as	as	ADP
ejpam-3448	425	10	the	the	DET
ejpam-3448	425	11	module	module	NOUN
ejpam-3448	425	12	structure	structure	NOUN
ejpam-3448	425	13	of	of	ADP
ejpam-3448	425	14	{	{	PUNCT
ejpam-3448	425	15	wn}n≥0	wn}n≥0	X
ejpam-3448	425	16	over	over	ADP
ejpam-3448	425	17	{	{	PUNCT
ejpam-3448	425	18	km}m≥0	km}m≥0	NOUN
ejpam-3448	425	19	in	in	ADP
ejpam-3448	425	20	the	the	DET
ejpam-3448	425	21	sense	sense	NOUN
ejpam-3448	425	22	of	of	ADP
ejpam-3448	425	23	given	give	VERB
ejpam-3448	425	24	in	in	ADP
ejpam-3448	425	25	markl	markl	PROPN
ejpam-3448	425	26	[	[	X
ejpam-3448	425	27	9	9	NUM
ejpam-3448	425	28	]	]	SYM
ejpam-3448	425	29	.	.	PUNCT
ejpam-3448	426	1	5	5	X
ejpam-3448	426	2	.	.	X
ejpam-3448	426	3	on	on	ADP
ejpam-3448	426	4	integral	integral	ADJ
ejpam-3448	426	5	sequences	sequence	NOUN
ejpam-3448	426	6	via	via	ADP
ejpam-3448	426	7	tubings	tubing	NOUN
ejpam-3448	426	8	in	in	ADP
ejpam-3448	426	9	this	this	DET
ejpam-3448	426	10	section	section	NOUN
ejpam-3448	426	11	,	,	PUNCT
ejpam-3448	426	12	we	we	PRON
ejpam-3448	426	13	give	give	VERB
ejpam-3448	426	14	the	the	DET
ejpam-3448	426	15	definition	definition	NOUN
ejpam-3448	426	16	of	of	ADP
ejpam-3448	426	17	a	a	DET
ejpam-3448	426	18	labelled	label	VERB
ejpam-3448	426	19	maximal	maximal	ADJ
ejpam-3448	426	20	tubing	tubing	NOUN
ejpam-3448	426	21	on	on	ADP
ejpam-3448	426	22	a	a	DET
ejpam-3448	426	23	path	path	NOUN
ejpam-3448	426	24	.	.	PUNCT
ejpam-3448	427	1	we	we	PRON
ejpam-3448	427	2	work	work	VERB
ejpam-3448	427	3	on	on	ADP
ejpam-3448	427	4	a	a	DET
ejpam-3448	427	5	sequence	sequence	NOUN
ejpam-3448	427	6	in	in	ADP
ejpam-3448	427	7	order	order	NOUN
ejpam-3448	427	8	to	to	PART
ejpam-3448	427	9	construct	construct	VERB
ejpam-3448	427	10	a	a	DET
ejpam-3448	427	11	chain	chain	NOUN
ejpam-3448	427	12	complex	complex	NOUN
ejpam-3448	427	13	and	and	CCONJ
ejpam-3448	427	14	define	define	VERB
ejpam-3448	427	15	the	the	DET
ejpam-3448	427	16	boundary	boundary	ADJ
ejpam-3448	427	17	map	map	NOUN
ejpam-3448	427	18	.	.	PUNCT
ejpam-3448	428	1	finally	finally	ADV
ejpam-3448	428	2	,	,	PUNCT
ejpam-3448	428	3	we	we	PRON
ejpam-3448	428	4	compute	compute	VERB
ejpam-3448	428	5	the	the	DET
ejpam-3448	428	6	corresponding	corresponding	ADJ
ejpam-3448	428	7	homology	homology	NOUN
ejpam-3448	428	8	groups	group	NOUN
ejpam-3448	428	9	.	.	PUNCT
ejpam-3448	429	1	definition	definition	NOUN
ejpam-3448	429	2	11	11	NUM
ejpam-3448	429	3	.	.	PUNCT
ejpam-3448	430	1	a	a	DET
ejpam-3448	430	2	labelled	label	VERB
ejpam-3448	430	3	maximal	maximal	ADJ
ejpam-3448	430	4	tubing	tubing	NOUN
ejpam-3448	430	5	on	on	ADP
ejpam-3448	430	6	a	a	DET
ejpam-3448	430	7	path	path	NOUN
ejpam-3448	430	8	is	be	AUX
ejpam-3448	430	9	a	a	DET
ejpam-3448	430	10	maximal	maximal	ADJ
ejpam-3448	430	11	tubing	tubing	NOUN
ejpam-3448	430	12	such	such	ADJ
ejpam-3448	430	13	that	that	SCONJ
ejpam-3448	430	14	each	each	DET
ejpam-3448	430	15	tube	tube	NOUN
ejpam-3448	430	16	is	be	AUX
ejpam-3448	430	17	labeled	label	VERB
ejpam-3448	430	18	by	by	ADP
ejpam-3448	430	19	an	an	DET
ejpam-3448	430	20	element	element	NOUN
ejpam-3448	430	21	of	of	ADP
ejpam-3448	430	22	a	a	DET
ejpam-3448	430	23	finite	finite	NOUN
ejpam-3448	430	24	set	set	NOUN
ejpam-3448	430	25	i	i	PRON
ejpam-3448	430	26	of	of	ADP
ejpam-3448	430	27	indices	index	NOUN
ejpam-3448	430	28	.	.	PUNCT
ejpam-3448	431	1	note	note	VERB
ejpam-3448	431	2	that	that	SCONJ
ejpam-3448	431	3	these	these	DET
ejpam-3448	431	4	elements	element	NOUN
ejpam-3448	431	5	are	be	AUX
ejpam-3448	431	6	not	not	PART
ejpam-3448	431	7	necessarily	necessarily	ADV
ejpam-3448	431	8	distinct	distinct	ADJ
ejpam-3448	431	9	.	.	PUNCT
ejpam-3448	432	1	a	a	DET
ejpam-3448	432	2	labelled	label	VERB
ejpam-3448	432	3	maximal	maximal	ADJ
ejpam-3448	432	4	tubing	tubing	NOUN
ejpam-3448	432	5	can	can	AUX
ejpam-3448	432	6	be	be	AUX
ejpam-3448	432	7	considered	consider	VERB
ejpam-3448	432	8	as	as	ADP
ejpam-3448	432	9	a	a	DET
ejpam-3448	432	10	pair	pair	NOUN
ejpam-3448	432	11	(	(	PUNCT
ejpam-3448	432	12	t	t	PROPN
ejpam-3448	432	13	,	,	PUNCT
ejpam-3448	432	14	f	f	X
ejpam-3448	432	15	)	)	PUNCT
ejpam-3448	432	16	such	such	ADJ
ejpam-3448	432	17	that	that	SCONJ
ejpam-3448	432	18	f	f	PROPN
ejpam-3448	432	19	:	:	PUNCT
ejpam-3448	432	20	t	t	PROPN
ejpam-3448	432	21	→	→	PUNCT
ejpam-3448	432	22	i	i	PRON
ejpam-3448	432	23	maps	map	VERB
ejpam-3448	432	24	a	a	DET
ejpam-3448	432	25	tube	tube	NOUN
ejpam-3448	432	26	to	to	ADP
ejpam-3448	432	27	its	its	PRON
ejpam-3448	432	28	label	label	NOUN
ejpam-3448	432	29	.	.	PUNCT
ejpam-3448	433	1	clearly	clearly	ADV
ejpam-3448	433	2	,	,	PUNCT
ejpam-3448	433	3	there	there	PRON
ejpam-3448	433	4	is	be	VERB
ejpam-3448	433	5	a	a	DET
ejpam-3448	433	6	bijection	bijection	NOUN
ejpam-3448	433	7	between	between	ADP
ejpam-3448	433	8	the	the	DET
ejpam-3448	433	9	set	set	NOUN
ejpam-3448	433	10	of	of	ADP
ejpam-3448	433	11	labelled	label	VERB
ejpam-3448	433	12	maximal	maximal	ADJ
ejpam-3448	433	13	tubings	tubing	NOUN
ejpam-3448	433	14	on	on	ADP
ejpam-3448	433	15	p(n	p(n	PROPN
ejpam-3448	433	16	)	)	PUNCT
ejpam-3448	433	17	and	and	CCONJ
ejpam-3448	433	18	mp(n)×	mp(n)×	X
ejpam-3448	433	19	in	in	ADP
ejpam-3448	433	20	.	.	PUNCT
ejpam-3448	434	1	in	in	ADP
ejpam-3448	434	2	particular	particular	ADJ
ejpam-3448	434	3	,	,	PUNCT
ejpam-3448	434	4	mp(2	mp(2	X
ejpam-3448	434	5	)	)	PUNCT
ejpam-3448	434	6	has	have	VERB
ejpam-3448	434	7	only	only	ADV
ejpam-3448	434	8	two	two	NUM
ejpam-3448	434	9	elements	element	NOUN
ejpam-3448	434	10	whose	whose	DET
ejpam-3448	434	11	names	name	NOUN
ejpam-3448	434	12	are	be	AUX
ejpam-3448	434	13	21	21	NUM
ejpam-3448	434	14	and	and	CCONJ
ejpam-3448	434	15	12	12	NUM
ejpam-3448	434	16	and	and	CCONJ
ejpam-3448	434	17	there	there	PRON
ejpam-3448	434	18	are	be	VERB
ejpam-3448	434	19	exactly	exactly	ADV
ejpam-3448	434	20	two	two	NUM
ejpam-3448	434	21	types	type	NOUN
ejpam-3448	434	22	of	of	ADP
ejpam-3448	434	23	labelled	label	VERB
ejpam-3448	434	24	maximal	maximal	ADJ
ejpam-3448	434	25	tubings	tubing	NOUN
ejpam-3448	434	26	in	in	ADP
ejpam-3448	434	27	mp(2)×	mp(2)×	PROPN
ejpam-3448	434	28	i2	i2	PROPN
ejpam-3448	434	29	such	such	ADJ
ejpam-3448	434	30	that	that	SCONJ
ejpam-3448	434	31	either	either	PRON
ejpam-3448	434	32	of	of	ADP
ejpam-3448	434	33	the	the	DET
ejpam-3448	434	34	form	form	NOUN
ejpam-3448	434	35	(	(	PUNCT
ejpam-3448	434	36	21	21	NUM
ejpam-3448	434	37	,	,	PUNCT
ejpam-3448	434	38	i1	i1	PROPN
ejpam-3448	434	39	,	,	PUNCT
ejpam-3448	434	40	i2	i2	PROPN
ejpam-3448	434	41	)	)	PUNCT
ejpam-3448	434	42	or	or	CCONJ
ejpam-3448	434	43	(	(	PUNCT
ejpam-3448	434	44	12	12	NUM
ejpam-3448	434	45	,	,	PUNCT
ejpam-3448	434	46	i1	i1	PROPN
ejpam-3448	434	47	,	,	PUNCT
ejpam-3448	434	48	i2	i2	PROPN
ejpam-3448	434	49	)	)	PUNCT
ejpam-3448	434	50	.	.	PUNCT
ejpam-3448	435	1	definition	definition	NOUN
ejpam-3448	435	2	12	12	NUM
ejpam-3448	435	3	.	.	PUNCT
ejpam-3448	436	1	the	the	DET
ejpam-3448	436	2	nested	nest	VERB
ejpam-3448	436	3	tubes	tube	NOUN
ejpam-3448	436	4	t1	t1	NOUN
ejpam-3448	436	5	and	and	CCONJ
ejpam-3448	436	6	t2	t2	NOUN
ejpam-3448	436	7	in	in	ADP
ejpam-3448	436	8	a	a	DET
ejpam-3448	436	9	maximal	maximal	ADJ
ejpam-3448	436	10	tubing	tubing	NOUN
ejpam-3448	436	11	t	t	PROPN
ejpam-3448	436	12	∈	∈	PROPN
ejpam-3448	436	13	mp(n	mp(n	NOUN
ejpam-3448	436	14	)	)	PUNCT
ejpam-3448	436	15	such	such	ADJ
ejpam-3448	436	16	that	that	SCONJ
ejpam-3448	436	17	t1	t1	PROPN
ejpam-3448	436	18	⊂	⊂	PROPN
ejpam-3448	436	19	t2	t2	PROPN
ejpam-3448	436	20	are	be	AUX
ejpam-3448	436	21	called	call	VERB
ejpam-3448	436	22	local	local	ADJ
ejpam-3448	436	23	pattern	pattern	NOUN
ejpam-3448	436	24	in	in	ADP
ejpam-3448	436	25	the	the	DET
ejpam-3448	436	26	sense	sense	NOUN
ejpam-3448	436	27	of	of	ADP
ejpam-3448	436	28	loday	loday	PROPN
ejpam-3448	436	29	[	[	X
ejpam-3448	436	30	5	5	X
ejpam-3448	436	31	]	]	PUNCT
ejpam-3448	436	32	if	if	SCONJ
ejpam-3448	436	33	there	there	PRON
ejpam-3448	436	34	is	be	VERB
ejpam-3448	436	35	no	no	DET
ejpam-3448	436	36	any	any	DET
ejpam-3448	436	37	tube	tube	NOUN
ejpam-3448	436	38	t	t	NOUN
ejpam-3448	436	39	such	such	ADJ
ejpam-3448	436	40	that	that	SCONJ
ejpam-3448	436	41	t1	t1	PROPN
ejpam-3448	436	42	⊂	⊂	PROPN
ejpam-3448	436	43	t	t	PROPN
ejpam-3448	436	44	⊂	⊂	PROPN
ejpam-3448	436	45	t2	t2	PROPN
ejpam-3448	436	46	.	.	PUNCT
ejpam-3448	437	1	in	in	ADP
ejpam-3448	437	2	order	order	NOUN
ejpam-3448	437	3	to	to	PART
ejpam-3448	437	4	construct	construct	VERB
ejpam-3448	437	5	a	a	DET
ejpam-3448	437	6	chain	chain	NOUN
ejpam-3448	437	7	complex	complex	NOUN
ejpam-3448	437	8	,	,	PUNCT
ejpam-3448	437	9	we	we	PRON
ejpam-3448	437	10	define	define	VERB
ejpam-3448	437	11	a	a	DET
ejpam-3448	437	12	sequence	sequence	NOUN
ejpam-3448	437	13	s	s	PART
ejpam-3448	437	14	=	=	PUNCT
ejpam-3448	437	15	{	{	PUNCT
ejpam-3448	437	16	sn	sn	INTJ
ejpam-3448	437	17	×	×	NOUN
ejpam-3448	437	18	in}n≥0	in}n≥0	NOUN
ejpam-3448	437	19	by	by	ADP
ejpam-3448	437	20	an	an	DET
ejpam-3448	437	21	induction	induction	NOUN
ejpam-3448	437	22	on	on	ADP
ejpam-3448	437	23	n	n	PRON
ejpam-3448	437	24	as	as	SCONJ
ejpam-3448	437	25	follows	follow	VERB
ejpam-3448	437	26	:	:	PUNCT
ejpam-3448	437	27	by	by	ADP
ejpam-3448	437	28	convention	convention	NOUN
ejpam-3448	437	29	,	,	PUNCT
ejpam-3448	437	30	we	we	PRON
ejpam-3448	437	31	assume	assume	VERB
ejpam-3448	437	32	that	that	SCONJ
ejpam-3448	437	33	s0×i0	s0×i0	NOUN
ejpam-3448	437	34	=	=	PUNCT
ejpam-3448	437	35	mp(0)×i0	mp(0)×i0	NOUN
ejpam-3448	437	36	,	,	PUNCT
ejpam-3448	437	37	s1×i1	s1×i1	PROPN
ejpam-3448	437	38	=	=	SYM
ejpam-3448	437	39	mp(1)×	mp(1)×	PROPN
ejpam-3448	438	1	i	i	PROPN
ejpam-3448	438	2	,	,	PUNCT
ejpam-3448	438	3	s2×	s2×	PROPN
ejpam-3448	438	4	i2	i2	PROPN
ejpam-3448	438	5	⊂mp(2)×	⊂mp(2)×	PROPN
ejpam-3448	438	6	i2	i2	PROPN
ejpam-3448	438	7	.	.	PUNCT
ejpam-3448	439	1	a	a	DET
ejpam-3448	439	2	labelled	label	VERB
ejpam-3448	439	3	maximal	maximal	ADJ
ejpam-3448	439	4	tubing	tubing	NOUN
ejpam-3448	439	5	t	t	NOUN
ejpam-3448	439	6	is	be	AUX
ejpam-3448	439	7	in	in	ADP
ejpam-3448	439	8	sn×	sn×	NOUN
ejpam-3448	439	9	in	in	ADP
ejpam-3448	439	10	if	if	SCONJ
ejpam-3448	440	1	and	and	CCONJ
ejpam-3448	440	2	only	only	ADV
ejpam-3448	440	3	if	if	SCONJ
ejpam-3448	440	4	all	all	DET
ejpam-3448	440	5	local	local	ADJ
ejpam-3448	440	6	patterns	pattern	NOUN
ejpam-3448	440	7	of	of	ADP
ejpam-3448	440	8	t	t	PROPN
ejpam-3448	440	9	illustrated	illustrate	VERB
ejpam-3448	440	10	either	either	CCONJ
ejpam-3448	440	11	by	by	ADP
ejpam-3448	440	12	the	the	DET
ejpam-3448	440	13	form	form	NOUN
ejpam-3448	440	14	21	21	NUM
ejpam-3448	440	15	or	or	CCONJ
ejpam-3448	440	16	12	12	NUM
ejpam-3448	440	17	are	be	AUX
ejpam-3448	440	18	in	in	ADP
ejpam-3448	440	19	s2	s2	PROPN
ejpam-3448	440	20	.	.	PUNCT
ejpam-3448	441	1	the	the	DET
ejpam-3448	441	2	alternating	alternate	VERB
ejpam-3448	441	3	series	series	NOUN
ejpam-3448	441	4	of	of	ADP
ejpam-3448	441	5	the	the	DET
ejpam-3448	441	6	sequence	sequence	NOUN
ejpam-3448	441	7	s	s	PART
ejpam-3448	441	8	is	be	AUX
ejpam-3448	441	9	determined	determine	VERB
ejpam-3448	441	10	by	by	ADP
ejpam-3448	441	11	the	the	DET
ejpam-3448	441	12	numbers	number	NOUN
ejpam-3448	441	13	of	of	ADP
ejpam-3448	441	14	elements	element	NOUN
ejpam-3448	441	15	in	in	ADP
ejpam-3448	441	16	sn	sn	PROPN
ejpam-3448	441	17	×	×	NOUN
ejpam-3448	441	18	in	in	ADP
ejpam-3448	441	19	as	as	SCONJ
ejpam-3448	441	20	follows	follow	VERB
ejpam-3448	441	21	:	:	PUNCT
ejpam-3448	441	22	f(s	f(s	PROPN
ejpam-3448	441	23	,	,	PUNCT
ejpam-3448	441	24	t	t	PROPN
ejpam-3448	441	25	)	)	PUNCT
ejpam-3448	441	26	=	=	PUNCT
ejpam-3448	442	1	∑	∑	PUNCT
ejpam-3448	442	2	n≥0	n≥0	PROPN
ejpam-3448	442	3	(	(	PUNCT
ejpam-3448	442	4	−1)n+1(#(sn	−1)n+1(#(sn	PROPN
ejpam-3448	442	5	×	×	NOUN
ejpam-3448	442	6	in	in	ADP
ejpam-3448	442	7	)	)	PUNCT
ejpam-3448	442	8	)	)	PUNCT
ejpam-3448	442	9	tn+1	tn+1	PROPN
ejpam-3448	442	10	.	.	PUNCT
ejpam-3448	443	1	let	let	VERB
ejpam-3448	443	2	z	z	NOUN
ejpam-3448	443	3	=	=	PRON
ejpam-3448	443	4	{	{	PUNCT
ejpam-3448	443	5	zn	zn	NOUN
ejpam-3448	443	6	×	×	NOUN
ejpam-3448	443	7	in	in	ADP
ejpam-3448	443	8	}	}	PUNCT
ejpam-3448	443	9	be	be	AUX
ejpam-3448	443	10	another	another	DET
ejpam-3448	443	11	sequence	sequence	NOUN
ejpam-3448	443	12	such	such	ADJ
ejpam-3448	443	13	that	that	SCONJ
ejpam-3448	443	14	z2	z2	PROPN
ejpam-3448	443	15	×	×	PROPN
ejpam-3448	443	16	i2	i2	PROPN
ejpam-3448	443	17	is	be	AUX
ejpam-3448	443	18	the	the	DET
ejpam-3448	443	19	complement	complement	NOUN
ejpam-3448	443	20	of	of	ADP
ejpam-3448	443	21	s2	s2	PROPN
ejpam-3448	443	22	×	×	PROPN
ejpam-3448	443	23	i2	i2	PROPN
ejpam-3448	443	24	in	in	ADP
ejpam-3448	443	25	mp(2	mp(2	ADJ
ejpam-3448	443	26	)	)	PUNCT
ejpam-3448	443	27	×	×	PROPN
ejpam-3448	443	28	i2	i2	NOUN
ejpam-3448	443	29	which	which	PRON
ejpam-3448	443	30	implies	imply	VERB
ejpam-3448	443	31	that	that	SCONJ
ejpam-3448	443	32	a	a	DET
ejpam-3448	443	33	labelled	label	VERB
ejpam-3448	443	34	maximal	maximal	ADJ
ejpam-3448	443	35	tubing	tubing	NOUN
ejpam-3448	443	36	t	t	NOUN
ejpam-3448	443	37	is	be	AUX
ejpam-3448	443	38	in	in	ADP
ejpam-3448	443	39	zn	zn	PROPN
ejpam-3448	443	40	×	×	NOUN
ejpam-3448	443	41	in	in	ADP
ejpam-3448	443	42	if	if	SCONJ
ejpam-3448	443	43	it	it	PRON
ejpam-3448	443	44	has	have	AUX
ejpam-3448	443	45	a	a	DET
ejpam-3448	443	46	local	local	ADJ
ejpam-3448	443	47	pattern	pattern	NOUN
ejpam-3448	443	48	which	which	PRON
ejpam-3448	443	49	is	be	AUX
ejpam-3448	443	50	not	not	PART
ejpam-3448	443	51	contained	contain	VERB
ejpam-3448	443	52	in	in	ADP
ejpam-3448	443	53	s2	s2	PROPN
ejpam-3448	443	54	×	×	PROPN
ejpam-3448	443	55	i2	i2	PROPN
ejpam-3448	443	56	.	.	PUNCT
ejpam-3448	444	1	now	now	ADV
ejpam-3448	444	2	,	,	PUNCT
ejpam-3448	444	3	we	we	PRON
ejpam-3448	444	4	define	define	VERB
ejpam-3448	444	5	a	a	DET
ejpam-3448	444	6	chain	chain	NOUN
ejpam-3448	444	7	complex	complex	ADJ
ejpam-3448	444	8	c∗	c∗	PROPN
ejpam-3448	444	9	=	=	SYM
ejpam-3448	444	10	(	(	PUNCT
ejpam-3448	444	11	cn	cn	PROPN
ejpam-3448	444	12	,	,	PUNCT
ejpam-3448	444	13	∂)n≥0	∂)n≥0	PROPN
ejpam-3448	444	14	over	over	ADP
ejpam-3448	444	15	a	a	DET
ejpam-3448	444	16	field	field	NOUN
ejpam-3448	444	17	f.	f.	NOUN
ejpam-3448	445	1	the	the	DET
ejpam-3448	445	2	space	space	NOUN
ejpam-3448	445	3	of	of	ADP
ejpam-3448	445	4	n	n	PRON
ejpam-3448	445	5	chains	chain	NOUN
ejpam-3448	445	6	is	be	AUX
ejpam-3448	445	7	defined	define	VERB
ejpam-3448	445	8	by	by	ADP
ejpam-3448	445	9	cn	cn	PROPN
ejpam-3448	445	10	=	=	PROPN
ejpam-3448	445	11	⊕	⊕	PROPN
ejpam-3448	445	12	i0,	i0,	PROPN
ejpam-3448	445	13	...	...	PUNCT
ejpam-3448	445	14	,in	,in	X
ejpam-3448	446	1	f	f	PROPN
ejpam-3448	447	1	[	[	X
ejpam-3448	447	2	zn	zn	X
ejpam-3448	447	3	×	×	PROPN
ejpam-3448	447	4	si0	si0	PROPN
ejpam-3448	447	5	×	×	PROPN
ejpam-3448	447	6	·	·	PUNCT
ejpam-3448	447	7	·	·	PUNCT
ejpam-3448	447	8	·	·	PUNCT
ejpam-3448	447	9	×	×	NOUN
ejpam-3448	447	10	sin	sin	NOUN
ejpam-3448	447	11	]	]	PUNCT
ejpam-3448	447	12	where	where	SCONJ
ejpam-3448	447	13	ij	ij	NOUN
ejpam-3448	447	14	≥	≥	NOUN
ejpam-3448	447	15	0	0	NUM
ejpam-3448	447	16	.	.	PUNCT
ejpam-3448	448	1	a	a	DET
ejpam-3448	448	2	vector	vector	NOUN
ejpam-3448	448	3	ω	ω	NOUN
ejpam-3448	448	4	:	:	PUNCT
ejpam-3448	448	5	=	=	SYM
ejpam-3448	448	6	(	(	PUNCT
ejpam-3448	448	7	zn	zn	PROPN
ejpam-3448	448	8	,	,	PUNCT
ejpam-3448	448	9	ti0	ti0	NOUN
ejpam-3448	448	10	,	,	PUNCT
ejpam-3448	448	11	.	.	PUNCT
ejpam-3448	448	12	.	.	PUNCT
ejpam-3448	448	13	.	.	PUNCT
ejpam-3448	449	1	,	,	PUNCT
ejpam-3448	449	2	tin	tin	NOUN
ejpam-3448	449	3	)	)	PUNCT
ejpam-3448	449	4	in	in	ADP
ejpam-3448	449	5	f	f	PROPN
ejpam-3448	450	1	[	[	X
ejpam-3448	450	2	zn	zn	NUM
ejpam-3448	450	3	×	×	PROPN
ejpam-3448	450	4	si0	si0	PROPN
ejpam-3448	450	5	×	×	PROPN
ejpam-3448	450	6	·	·	PUNCT
ejpam-3448	450	7	·	·	PUNCT
ejpam-3448	450	8	·	·	PUNCT
ejpam-3448	450	9	×	×	NOUN
ejpam-3448	450	10	sin	sin	NOUN
ejpam-3448	450	11	]	]	PUNCT
ejpam-3448	450	12	is	be	AUX
ejpam-3448	450	13	of	of	ADP
ejpam-3448	450	14	the	the	DET
ejpam-3448	450	15	form	form	NOUN
ejpam-3448	450	16	ω	ω	NOUN
ejpam-3448	450	17	=	=	SYM
ejpam-3448	450	18	(	(	PUNCT
ejpam-3448	450	19	.	.	PUNCT
ejpam-3448	450	20	.	.	PUNCT
ejpam-3448	450	21	.	.	PUNCT
ejpam-3448	451	1	(	(	PUNCT
ejpam-3448	451	2	(	(	PUNCT
ejpam-3448	451	3	zn	zn	INTJ
ejpam-3448	451	4	◦	◦	NOUN
ejpam-3448	451	5	0	0	NUM
ejpam-3448	451	6	ti0	ti0	NOUN
ejpam-3448	451	7	)	)	PUNCT
ejpam-3448	451	8	◦	◦	NOUN
ejpam-3448	451	9	i0	i0	PROPN
ejpam-3448	451	10	+	+	PROPN
ejpam-3448	451	11	1	1	NUM
ejpam-3448	451	12	ti1	ti1	PROPN
ejpam-3448	451	13	)	)	PUNCT
ejpam-3448	451	14	.	.	PUNCT
ejpam-3448	451	15	.	.	PUNCT
ejpam-3448	451	16	.	.	PUNCT
ejpam-3448	451	17	)	)	PUNCT
ejpam-3448	452	1	◦	◦	NOUN
ejpam-3448	452	2	(	(	PUNCT
ejpam-3448	452	3	n−1∑	n−1∑	PROPN
ejpam-3448	452	4	k=0	k=0	PROPN
ejpam-3448	452	5	ik	ik	X
ejpam-3448	452	6	+	+	PROPN
ejpam-3448	452	7	1	1	X
ejpam-3448	452	8	)	)	PUNCT
ejpam-3448	452	9	tin	tin	NOUN
ejpam-3448	452	10	s.	s.	PROPN
ejpam-3448	452	11	k.	k.	PROPN
ejpam-3448	452	12	gürbüzer	gürbüzer	PROPN
ejpam-3448	452	13	,	,	PUNCT
ejpam-3448	452	14	b.	b.	PROPN
ejpam-3448	452	15	akyar	akyar	PROPN
ejpam-3448	452	16	/	/	SYM
ejpam-3448	452	17	eur	eur	PROPN
ejpam-3448	452	18	.	.	PUNCT
ejpam-3448	453	1	j.	j.	PROPN
ejpam-3448	453	2	pure	pure	PROPN
ejpam-3448	453	3	appl	appl	PROPN
ejpam-3448	453	4	.	.	PROPN
ejpam-3448	453	5	math	math	PROPN
ejpam-3448	453	6	,	,	PUNCT
ejpam-3448	453	7	12	12	NUM
ejpam-3448	453	8	(	(	PUNCT
ejpam-3448	453	9	3	3	NUM
ejpam-3448	453	10	)	)	PUNCT
ejpam-3448	453	11	(	(	PUNCT
ejpam-3448	453	12	2019	2019	NUM
ejpam-3448	453	13	)	)	PUNCT
ejpam-3448	453	14	,	,	PUNCT
ejpam-3448	453	15	734	734	NUM
ejpam-3448	453	16	-	-	SYM
ejpam-3448	453	17	748	748	NUM
ejpam-3448	453	18	746	746	NUM
ejpam-3448	453	19	the	the	DET
ejpam-3448	453	20	boundary	boundary	ADJ
ejpam-3448	453	21	map	map	NOUN
ejpam-3448	453	22	of	of	ADP
ejpam-3448	453	23	the	the	DET
ejpam-3448	453	24	complex	complex	NOUN
ejpam-3448	453	25	is	be	AUX
ejpam-3448	453	26	defined	define	VERB
ejpam-3448	453	27	by	by	ADP
ejpam-3448	453	28	∂	∂	NOUN
ejpam-3448	453	29	=	=	SYM
ejpam-3448	453	30	n∑	n∑	NOUN
ejpam-3448	453	31	k=1	k=1	PROPN
ejpam-3448	454	1	(	(	PUNCT
ejpam-3448	454	2	−1)kdk	−1)kdk	PROPN
ejpam-3448	454	3	,	,	PUNCT
ejpam-3448	454	4	(	(	PUNCT
ejpam-3448	454	5	13	13	NUM
ejpam-3448	454	6	)	)	PUNCT
ejpam-3448	454	7	where	where	SCONJ
ejpam-3448	454	8	dkω	dkω	NOUN
ejpam-3448	454	9	=	=	SYM
ejpam-3448	454	10	dk(zn;t0	dk(zn;t0	PROPN
ejpam-3448	454	11	,	,	PUNCT
ejpam-3448	454	12	.	.	PUNCT
ejpam-3448	454	13	.	.	PUNCT
ejpam-3448	454	14	.	.	PUNCT
ejpam-3448	455	1	,	,	PUNCT
ejpam-3448	455	2	tn	tn	PROPN
ejpam-3448	455	3	)	)	PUNCT
ejpam-3448	456	1	=	=	SYM
ejpam-3448	456	2	0	0	PUNCT
ejpam-3448	457	1	if	if	SCONJ
ejpam-3448	457	2	the	the	DET
ejpam-3448	457	3	minimal	minimal	ADJ
ejpam-3448	457	4	tube	tube	NOUN
ejpam-3448	457	5	containing	contain	VERB
ejpam-3448	457	6	the	the	DET
ejpam-3448	457	7	k	k	NOUN
ejpam-3448	457	8	-	-	PUNCT
ejpam-3448	457	9	th	th	VERB
ejpam-3448	457	10	node	node	NOUN
ejpam-3448	457	11	in	in	ADP
ejpam-3448	457	12	zn	zn	PROPN
ejpam-3448	457	13	is	be	AUX
ejpam-3448	457	14	not	not	PART
ejpam-3448	457	15	a	a	DET
ejpam-3448	457	16	cup	cup	NOUN
ejpam-3448	457	17	,	,	PUNCT
ejpam-3448	457	18	that	that	ADV
ejpam-3448	457	19	is	is	ADV
ejpam-3448	457	20	,	,	PUNCT
ejpam-3448	457	21	it	it	PRON
ejpam-3448	457	22	contains	contain	VERB
ejpam-3448	457	23	only	only	ADV
ejpam-3448	457	24	one	one	NUM
ejpam-3448	457	25	node	node	NOUN
ejpam-3448	457	26	and	and	CCONJ
ejpam-3448	457	27	otherwise	otherwise	ADV
ejpam-3448	457	28	dkω	dkω	NOUN
ejpam-3448	457	29	=	=	SYM
ejpam-3448	457	30	(	(	PUNCT
ejpam-3448	457	31	εk(zn	εk(zn	PROPN
ejpam-3448	457	32	)	)	PUNCT
ejpam-3448	457	33	,	,	PUNCT
ejpam-3448	457	34	t0	t0	PROPN
ejpam-3448	457	35	,	,	PUNCT
ejpam-3448	457	36	.	.	PUNCT
ejpam-3448	457	37	.	.	PUNCT
ejpam-3448	458	1	.	.	PUNCT
ejpam-3448	459	1	,	,	PUNCT
ejpam-3448	459	2	tk−1	tk−1	PROPN
ejpam-3448	459	3	∨	∨	NUM
ejpam-3448	459	4	tk	tk	PROPN
ejpam-3448	459	5	,	,	PUNCT
ejpam-3448	459	6	.	.	PUNCT
ejpam-3448	459	7	.	.	PUNCT
ejpam-3448	460	1	.	.	PUNCT
ejpam-3448	461	1	,	,	PUNCT
ejpam-3448	461	2	tn	tn	PROPN
ejpam-3448	461	3	)	)	PUNCT
ejpam-3448	461	4	where	where	SCONJ
ejpam-3448	461	5	εk	εk	PROPN
ejpam-3448	461	6	deletes	delete	VERB
ejpam-3448	461	7	the	the	DET
ejpam-3448	461	8	k	k	NOUN
ejpam-3448	461	9	-	-	PUNCT
ejpam-3448	461	10	th	th	X
ejpam-3448	461	11	node	node	NOUN
ejpam-3448	461	12	and	and	CCONJ
ejpam-3448	461	13	the	the	DET
ejpam-3448	461	14	cup	cup	NOUN
ejpam-3448	461	15	containing	contain	VERB
ejpam-3448	461	16	it	it	PRON
ejpam-3448	461	17	in	in	ADP
ejpam-3448	461	18	zn	zn	PROPN
ejpam-3448	461	19	.	.	PUNCT
ejpam-3448	462	1	note	note	VERB
ejpam-3448	462	2	that	that	SCONJ
ejpam-3448	462	3	the	the	DET
ejpam-3448	462	4	label	label	NOUN
ejpam-3448	462	5	of	of	ADP
ejpam-3448	462	6	the	the	DET
ejpam-3448	462	7	tube	tube	NOUN
ejpam-3448	462	8	covering	cover	VERB
ejpam-3448	462	9	tk−1	tk−1	PROPN
ejpam-3448	462	10	∨	∨	PROPN
ejpam-3448	462	11	tk	tk	PROPN
ejpam-3448	462	12	is	be	AUX
ejpam-3448	462	13	the	the	DET
ejpam-3448	462	14	label	label	NOUN
ejpam-3448	462	15	of	of	ADP
ejpam-3448	462	16	the	the	DET
ejpam-3448	462	17	deleted	delete	VERB
ejpam-3448	462	18	cup	cup	NOUN
ejpam-3448	462	19	in	in	ADP
ejpam-3448	462	20	zn	zn	PROPN
ejpam-3448	462	21	.	.	PUNCT
ejpam-3448	463	1	if	if	SCONJ
ejpam-3448	463	2	tk−1	tk−1	PROPN
ejpam-3448	463	3	∨	∨	PROPN
ejpam-3448	463	4	tk	tk	PROPN
ejpam-3448	463	5	contains	contain	VERB
ejpam-3448	463	6	a	a	DET
ejpam-3448	463	7	local	local	ADJ
ejpam-3448	463	8	pattern	pattern	NOUN
ejpam-3448	463	9	in	in	ADP
ejpam-3448	463	10	z	z	PROPN
ejpam-3448	463	11	then	then	ADV
ejpam-3448	463	12	dk(zn	dk(zn	PROPN
ejpam-3448	463	13	,	,	PUNCT
ejpam-3448	463	14	t0	t0	PROPN
ejpam-3448	463	15	,	,	PUNCT
ejpam-3448	463	16	.	.	PUNCT
ejpam-3448	463	17	.	.	PUNCT
ejpam-3448	463	18	.	.	PUNCT
ejpam-3448	464	1	tn	tn	X
ejpam-3448	464	2	)	)	PUNCT
ejpam-3448	465	1	=	=	SYM
ejpam-3448	465	2	0	0	X
ejpam-3448	465	3	.	.	PUNCT
ejpam-3448	466	1	the	the	DET
ejpam-3448	466	2	complex	complex	ADJ
ejpam-3448	466	3	c∗	c∗	NOUN
ejpam-3448	466	4	is	be	AUX
ejpam-3448	466	5	called	call	VERB
ejpam-3448	466	6	the	the	DET
ejpam-3448	466	7	koszul	koszul	ADJ
ejpam-3448	466	8	complex	complex	NOUN
ejpam-3448	466	9	of	of	ADP
ejpam-3448	466	10	s.	s.	PROPN
ejpam-3448	466	11	proposition	proposition	PROPN
ejpam-3448	466	12	4	4	NUM
ejpam-3448	466	13	.	.	PUNCT
ejpam-3448	467	1	the	the	DET
ejpam-3448	467	2	boundary	boundary	ADJ
ejpam-3448	467	3	map	map	NOUN
ejpam-3448	467	4	∂	∂	NUM
ejpam-3448	467	5	satisfies	satisfie	NOUN
ejpam-3448	467	6	the	the	DET
ejpam-3448	467	7	boundary	boundary	ADJ
ejpam-3448	467	8	condition	condition	NOUN
ejpam-3448	467	9	∂2	∂2	NOUN
ejpam-3448	467	10	=	=	SYM
ejpam-3448	467	11	0	0	X
ejpam-3448	467	12	.	.	PUNCT
ejpam-3448	468	1	proof	proof	NOUN
ejpam-3448	468	2	.	.	PUNCT
ejpam-3448	469	1	let	let	VERB
ejpam-3448	469	2	ω	ω	PROPN
ejpam-3448	469	3	=	=	SYM
ejpam-3448	469	4	(	(	PUNCT
ejpam-3448	469	5	zn	zn	PROPN
ejpam-3448	469	6	,	,	PUNCT
ejpam-3448	469	7	t0	t0	PROPN
ejpam-3448	469	8	,	,	PUNCT
ejpam-3448	469	9	.	.	PUNCT
ejpam-3448	469	10	.	.	PUNCT
ejpam-3448	470	1	.	.	PUNCT
ejpam-3448	471	1	,	,	PUNCT
ejpam-3448	471	2	tn	tn	PROPN
ejpam-3448	471	3	)	)	PUNCT
ejpam-3448	471	4	.	.	PUNCT
ejpam-3448	472	1	we	we	PRON
ejpam-3448	472	2	need	need	VERB
ejpam-3448	472	3	to	to	PART
ejpam-3448	472	4	prove	prove	VERB
ejpam-3448	472	5	that	that	DET
ejpam-3448	472	6	dkdj	dkdj	NOUN
ejpam-3448	472	7	=	=	PUNCT
ejpam-3448	473	1	dj−1dk	dj−1dk	NUM
ejpam-3448	473	2	for	for	ADP
ejpam-3448	473	3	k	k	PROPN
ejpam-3448	473	4	<	<	X
ejpam-3448	473	5	j.	j.	PROPN
ejpam-3448	474	1	if	if	SCONJ
ejpam-3448	474	2	k	k	PROPN
ejpam-3448	474	3	<	<	X
ejpam-3448	474	4	j	j	PROPN
ejpam-3448	474	5	−	−	NOUN
ejpam-3448	474	6	1	1	NUM
ejpam-3448	474	7	,	,	PUNCT
ejpam-3448	474	8	we	we	PRON
ejpam-3448	474	9	have	have	VERB
ejpam-3448	474	10	the	the	DET
ejpam-3448	474	11	following	follow	VERB
ejpam-3448	474	12	three	three	NUM
ejpam-3448	474	13	cases	case	NOUN
ejpam-3448	474	14	.	.	PUNCT
ejpam-3448	475	1	•	•	INTJ
ejpam-3448	475	2	if	if	SCONJ
ejpam-3448	475	3	zn	zn	PROPN
ejpam-3448	475	4	does	do	AUX
ejpam-3448	475	5	not	not	PART
ejpam-3448	475	6	have	have	VERB
ejpam-3448	475	7	a	a	DET
ejpam-3448	475	8	cup	cup	NOUN
ejpam-3448	475	9	at	at	ADP
ejpam-3448	475	10	the	the	DET
ejpam-3448	475	11	k	k	NOUN
ejpam-3448	475	12	-	-	PUNCT
ejpam-3448	475	13	th	th	VERB
ejpam-3448	475	14	node	node	NOUN
ejpam-3448	475	15	then	then	ADV
ejpam-3448	475	16	dkdj	dkdj	VERB
ejpam-3448	475	17	=	=	PUNCT
ejpam-3448	476	1	dj−1dk	dj−1dk	NUM
ejpam-3448	476	2	=	=	SYM
ejpam-3448	476	3	0	0	NUM
ejpam-3448	476	4	.	.	NOUN
ejpam-3448	477	1	•	•	NOUN
ejpam-3448	477	2	if	if	SCONJ
ejpam-3448	477	3	zn	zn	PROPN
ejpam-3448	477	4	does	do	AUX
ejpam-3448	477	5	not	not	PART
ejpam-3448	477	6	have	have	VERB
ejpam-3448	477	7	a	a	DET
ejpam-3448	477	8	cup	cup	NOUN
ejpam-3448	477	9	at	at	ADP
ejpam-3448	477	10	the	the	DET
ejpam-3448	477	11	j	j	PROPN
ejpam-3448	477	12	-	-	PUNCT
ejpam-3448	477	13	th	th	VERB
ejpam-3448	477	14	node	node	NOUN
ejpam-3448	477	15	then	then	ADV
ejpam-3448	477	16	dkdj	dkdj	VERB
ejpam-3448	477	17	=	=	SYM
ejpam-3448	477	18	0	0	PUNCT
ejpam-3448	477	19	and	and	CCONJ
ejpam-3448	477	20	by	by	ADP
ejpam-3448	477	21	renumbering	renumbere	VERB
ejpam-3448	477	22	the	the	DET
ejpam-3448	477	23	maximal	maximal	ADJ
ejpam-3448	477	24	tubings	tubing	NOUN
ejpam-3448	477	25	we	we	PRON
ejpam-3448	477	26	get	get	VERB
ejpam-3448	477	27	dj−1dk	dj−1dk	NUM
ejpam-3448	477	28	=	=	NOUN
ejpam-3448	477	29	0	0	NUM
ejpam-3448	477	30	.	.	NOUN
ejpam-3448	478	1	•	•	NOUN
ejpam-3448	478	2	if	if	SCONJ
ejpam-3448	478	3	zn	zn	PROPN
ejpam-3448	478	4	does	do	AUX
ejpam-3448	478	5	not	not	PART
ejpam-3448	478	6	have	have	VERB
ejpam-3448	478	7	a	a	DET
ejpam-3448	478	8	cup	cup	NOUN
ejpam-3448	478	9	neither	neither	CCONJ
ejpam-3448	478	10	at	at	ADP
ejpam-3448	478	11	the	the	DET
ejpam-3448	478	12	k	k	NOUN
ejpam-3448	478	13	-	-	PUNCT
ejpam-3448	478	14	th	th	X
ejpam-3448	478	15	nor	nor	CCONJ
ejpam-3448	478	16	j	j	PROPN
ejpam-3448	478	17	-	-	PUNCT
ejpam-3448	478	18	th	th	X
ejpam-3448	478	19	nodes	node	NOUN
ejpam-3448	478	20	then	then	ADV
ejpam-3448	478	21	dkdj(zn	dkdj(zn	PROPN
ejpam-3448	478	22	,	,	PUNCT
ejpam-3448	478	23	t0	t0	PROPN
ejpam-3448	478	24	,	,	PUNCT
ejpam-3448	478	25	.	.	PUNCT
ejpam-3448	478	26	.	.	PUNCT
ejpam-3448	479	1	.	.	PUNCT
ejpam-3448	480	1	,	,	PUNCT
ejpam-3448	480	2	tn	tn	PROPN
ejpam-3448	480	3	)	)	PUNCT
ejpam-3448	480	4	=	=	SYM
ejpam-3448	481	1	dk(εj(zn	dk(εj(zn	NOUN
ejpam-3448	481	2	)	)	PUNCT
ejpam-3448	481	3	,	,	PUNCT
ejpam-3448	481	4	t0	t0	PROPN
ejpam-3448	481	5	,	,	PUNCT
ejpam-3448	481	6	.	.	PUNCT
ejpam-3448	481	7	.	.	PUNCT
ejpam-3448	481	8	.	.	PUNCT
ejpam-3448	482	1	,	,	PUNCT
ejpam-3448	482	2	tj−1	tj−1	PROPN
ejpam-3448	482	3	∨	∨	NUM
ejpam-3448	482	4	tj	tj	NOUN
ejpam-3448	482	5	,	,	PUNCT
ejpam-3448	482	6	.	.	PUNCT
ejpam-3448	482	7	.	.	PUNCT
ejpam-3448	483	1	.	.	PUNCT
ejpam-3448	484	1	,	,	PUNCT
ejpam-3448	484	2	tn	tn	PROPN
ejpam-3448	484	3	)	)	PUNCT
ejpam-3448	484	4	=	=	PUNCT
ejpam-3448	485	1	(	(	PUNCT
ejpam-3448	485	2	εkεj(zn	εkεj(zn	NOUN
ejpam-3448	485	3	)	)	PUNCT
ejpam-3448	485	4	,	,	PUNCT
ejpam-3448	485	5	t0	t0	PROPN
ejpam-3448	485	6	,	,	PUNCT
ejpam-3448	485	7	.	.	PUNCT
ejpam-3448	485	8	.	.	PUNCT
ejpam-3448	486	1	.	.	PUNCT
ejpam-3448	487	1	,	,	PUNCT
ejpam-3448	487	2	tk−1	tk−1	PROPN
ejpam-3448	487	3	∨	∨	NUM
ejpam-3448	487	4	tk	tk	PROPN
ejpam-3448	487	5	,	,	PUNCT
ejpam-3448	487	6	.	.	PUNCT
ejpam-3448	487	7	.	.	PUNCT
ejpam-3448	488	1	.	.	PUNCT
ejpam-3448	489	1	,	,	PUNCT
ejpam-3448	489	2	tj−1	tj−1	PROPN
ejpam-3448	489	3	∨	∨	NUM
ejpam-3448	489	4	tj	tj	NOUN
ejpam-3448	489	5	,	,	PUNCT
ejpam-3448	489	6	.	.	PUNCT
ejpam-3448	489	7	.	.	PUNCT
ejpam-3448	490	1	.	.	PUNCT
ejpam-3448	491	1	,	,	PUNCT
ejpam-3448	491	2	tn	tn	PROPN
ejpam-3448	491	3	)	)	PUNCT
ejpam-3448	491	4	=	=	SYM
ejpam-3448	491	5	(	(	PUNCT
ejpam-3448	491	6	εj−1εk(zn	εj−1εk(zn	NOUN
ejpam-3448	491	7	)	)	PUNCT
ejpam-3448	491	8	,	,	PUNCT
ejpam-3448	491	9	t0	t0	PROPN
ejpam-3448	491	10	,	,	PUNCT
ejpam-3448	491	11	.	.	PUNCT
ejpam-3448	491	12	.	.	PUNCT
ejpam-3448	492	1	.	.	PUNCT
ejpam-3448	493	1	,	,	PUNCT
ejpam-3448	493	2	tk−1	tk−1	PROPN
ejpam-3448	493	3	∨	∨	NUM
ejpam-3448	493	4	tk	tk	PROPN
ejpam-3448	493	5	,	,	PUNCT
ejpam-3448	493	6	.	.	PUNCT
ejpam-3448	493	7	.	.	PUNCT
ejpam-3448	494	1	.	.	PUNCT
ejpam-3448	495	1	,	,	PUNCT
ejpam-3448	495	2	tj−1	tj−1	PROPN
ejpam-3448	495	3	∨	∨	NUM
ejpam-3448	495	4	tj	tj	NOUN
ejpam-3448	495	5	,	,	PUNCT
ejpam-3448	495	6	.	.	PUNCT
ejpam-3448	495	7	.	.	PUNCT
ejpam-3448	496	1	.	.	PUNCT
ejpam-3448	497	1	,	,	PUNCT
ejpam-3448	497	2	tn	tn	PROPN
ejpam-3448	497	3	)	)	PUNCT
ejpam-3448	497	4	=	=	SYM
ejpam-3448	498	1	dj−1(εk(zn	dj−1(εk(zn	NOUN
ejpam-3448	498	2	)	)	PUNCT
ejpam-3448	498	3	,	,	PUNCT
ejpam-3448	498	4	t0	t0	PROPN
ejpam-3448	498	5	,	,	PUNCT
ejpam-3448	498	6	.	.	PUNCT
ejpam-3448	498	7	.	.	PUNCT
ejpam-3448	499	1	.	.	PUNCT
ejpam-3448	500	1	,	,	PUNCT
ejpam-3448	500	2	tk−1	tk−1	PROPN
ejpam-3448	500	3	∨	∨	NUM
ejpam-3448	500	4	tk	tk	PROPN
ejpam-3448	500	5	,	,	PUNCT
ejpam-3448	500	6	.	.	PUNCT
ejpam-3448	500	7	.	.	PUNCT
ejpam-3448	501	1	.	.	PUNCT
ejpam-3448	502	1	,	,	PUNCT
ejpam-3448	502	2	tn	tn	PROPN
ejpam-3448	502	3	)	)	PUNCT
ejpam-3448	502	4	=	=	SYM
ejpam-3448	503	1	dj−1dk(zn	dj−1dk(zn	PROPN
ejpam-3448	503	2	,	,	PUNCT
ejpam-3448	503	3	t0	t0	PROPN
ejpam-3448	503	4	,	,	PUNCT
ejpam-3448	503	5	.	.	PUNCT
ejpam-3448	503	6	.	.	PUNCT
ejpam-3448	504	1	.	.	PUNCT
ejpam-3448	505	1	,	,	PUNCT
ejpam-3448	505	2	tn	tn	PROPN
ejpam-3448	505	3	)	)	PUNCT
ejpam-3448	505	4	for	for	ADP
ejpam-3448	505	5	k	k	PROPN
ejpam-3448	505	6	=	=	PUNCT
ejpam-3448	505	7	j	j	PROPN
ejpam-3448	506	1	−	−	PROPN
ejpam-3448	506	2	1	1	NUM
ejpam-3448	506	3	,	,	PUNCT
ejpam-3448	506	4	we	we	PRON
ejpam-3448	506	5	examine	examine	VERB
ejpam-3448	506	6	dkdk+1	dkdk+1	NOUN
ejpam-3448	506	7	and	and	CCONJ
ejpam-3448	506	8	dkdk	dkdk	NOUN
ejpam-3448	506	9	.	.	PUNCT
ejpam-3448	507	1	it	it	PRON
ejpam-3448	507	2	is	be	AUX
ejpam-3448	507	3	clear	clear	ADJ
ejpam-3448	507	4	that	that	SCONJ
ejpam-3448	507	5	dkdk	dkdk	NOUN
ejpam-3448	507	6	=	=	NOUN
ejpam-3448	507	7	0	0	PUNCT
ejpam-3448	508	1	because	because	SCONJ
ejpam-3448	508	2	εk(zn	εk(zn	PROPN
ejpam-3448	508	3	)	)	PUNCT
ejpam-3448	508	4	can	can	AUX
ejpam-3448	508	5	not	not	PART
ejpam-3448	508	6	have	have	VERB
ejpam-3448	508	7	a	a	DET
ejpam-3448	508	8	cup	cup	NOUN
ejpam-3448	508	9	at	at	ADP
ejpam-3448	508	10	the	the	DET
ejpam-3448	508	11	k	k	NOUN
ejpam-3448	508	12	-	-	PUNCT
ejpam-3448	508	13	th	th	VERB
ejpam-3448	508	14	node	node	NOUN
ejpam-3448	508	15	.	.	PUNCT
ejpam-3448	509	1	on	on	ADP
ejpam-3448	509	2	the	the	DET
ejpam-3448	509	3	other	other	ADJ
ejpam-3448	509	4	hand	hand	NOUN
ejpam-3448	509	5	,	,	PUNCT
ejpam-3448	509	6	if	if	SCONJ
ejpam-3448	509	7	zn	zn	PROPN
ejpam-3448	509	8	does	do	AUX
ejpam-3448	509	9	not	not	PART
ejpam-3448	509	10	have	have	VERB
ejpam-3448	509	11	a	a	DET
ejpam-3448	509	12	cup	cup	NOUN
ejpam-3448	509	13	at	at	ADP
ejpam-3448	509	14	the	the	DET
ejpam-3448	509	15	(	(	PUNCT
ejpam-3448	509	16	k	k	NOUN
ejpam-3448	509	17	+	+	PROPN
ejpam-3448	509	18	1)-st	1)-st	NUM
ejpam-3448	509	19	node	node	NOUN
ejpam-3448	509	20	then	then	ADV
ejpam-3448	509	21	dkdk+1	dkdk+1	NOUN
ejpam-3448	509	22	=	=	SYM
ejpam-3448	509	23	0	0	NUM
ejpam-3448	509	24	,	,	PUNCT
ejpam-3448	509	25	otherwise	otherwise	ADV
ejpam-3448	509	26	dkdk+1(ω	dkdk+1(ω	PROPN
ejpam-3448	509	27	)	)	PUNCT
ejpam-3448	509	28	=	=	SYM
ejpam-3448	509	29	(	(	PUNCT
ejpam-3448	509	30	εkεk+1(zn	εkεk+1(zn	NOUN
ejpam-3448	509	31	)	)	PUNCT
ejpam-3448	509	32	,	,	PUNCT
ejpam-3448	509	33	t0	t0	PROPN
ejpam-3448	509	34	,	,	PUNCT
ejpam-3448	509	35	.	.	PUNCT
ejpam-3448	509	36	.	.	PUNCT
ejpam-3448	510	1	.	.	PUNCT
ejpam-3448	511	1	,	,	PUNCT
ejpam-3448	511	2	tk−1	tk−1	PROPN
ejpam-3448	511	3	∨	∨	PROPN
ejpam-3448	511	4	(	(	PUNCT
ejpam-3448	511	5	tk	tk	PROPN
ejpam-3448	511	6	∨	∨	NUM
ejpam-3448	511	7	tk+1	tk+1	NUM
ejpam-3448	511	8	)	)	PUNCT
ejpam-3448	511	9	,	,	PUNCT
ejpam-3448	511	10	.	.	PUNCT
ejpam-3448	511	11	.	.	PUNCT
ejpam-3448	512	1	.	.	PUNCT
ejpam-3448	513	1	,	,	PUNCT
ejpam-3448	513	2	tn	tn	PROPN
ejpam-3448	513	3	)	)	PUNCT
ejpam-3448	513	4	since	since	SCONJ
ejpam-3448	513	5	εk+1(zn	εk+1(zn	NUM
ejpam-3448	513	6	)	)	PUNCT
ejpam-3448	513	7	have	have	VERB
ejpam-3448	513	8	a	a	DET
ejpam-3448	513	9	cup	cup	NOUN
ejpam-3448	513	10	at	at	ADP
ejpam-3448	513	11	the	the	DET
ejpam-3448	513	12	k	k	NOUN
ejpam-3448	513	13	-	-	PUNCT
ejpam-3448	513	14	th	th	VERB
ejpam-3448	513	15	node	node	NOUN
ejpam-3448	513	16	.	.	PUNCT
ejpam-3448	514	1	the	the	DET
ejpam-3448	514	2	universal	universal	ADJ
ejpam-3448	514	3	tubes	tube	NOUN
ejpam-3448	514	4	of	of	ADP
ejpam-3448	514	5	tk∨tk+1	tk∨tk+1	NOUN
ejpam-3448	514	6	and	and	CCONJ
ejpam-3448	514	7	tk−1∨(tk∨	tk−1∨(tk∨	NOUN
ejpam-3448	514	8	tk+1	tk+1	NOUN
ejpam-3448	514	9	)	)	PUNCT
ejpam-3448	514	10	constitute	constitute	VERB
ejpam-3448	514	11	a	a	DET
ejpam-3448	514	12	local	local	ADJ
ejpam-3448	514	13	pattern	pattern	NOUN
ejpam-3448	514	14	with	with	ADP
ejpam-3448	514	15	the	the	DET
ejpam-3448	514	16	labels	label	NOUN
ejpam-3448	514	17	of	of	ADP
ejpam-3448	514	18	the	the	DET
ejpam-3448	514	19	cups	cup	NOUN
ejpam-3448	514	20	in	in	ADP
ejpam-3448	514	21	zn	zn	PROPN
ejpam-3448	514	22	.	.	PUNCT
ejpam-3448	515	1	hence	hence	ADV
ejpam-3448	515	2	tk−1∨	tk−1∨	X
ejpam-3448	515	3	(	(	PUNCT
ejpam-3448	515	4	tk∨tk+1	tk∨tk+1	NOUN
ejpam-3448	515	5	)	)	PUNCT
ejpam-3448	515	6	is	be	AUX
ejpam-3448	515	7	in	in	ADP
ejpam-3448	515	8	z	z	NOUN
ejpam-3448	515	9	which	which	PRON
ejpam-3448	515	10	gives	give	VERB
ejpam-3448	515	11	that	that	DET
ejpam-3448	515	12	dkdk+1(ω	dkdk+1(ω	NOUN
ejpam-3448	515	13	)	)	PUNCT
ejpam-3448	515	14	=	=	SYM
ejpam-3448	516	1	0	0	X
ejpam-3448	516	2	.	.	PUNCT
ejpam-3448	516	3	definition	definition	NOUN
ejpam-3448	516	4	13	13	NUM
ejpam-3448	516	5	.	.	PUNCT
ejpam-3448	517	1	the	the	DET
ejpam-3448	517	2	basis	basis	NOUN
ejpam-3448	517	3	vector	vector	NOUN
ejpam-3448	517	4	ω	ω	PROPN
ejpam-3448	517	5	=	=	SYM
ejpam-3448	517	6	(	(	PUNCT
ejpam-3448	517	7	zn	zn	PROPN
ejpam-3448	517	8	,	,	PUNCT
ejpam-3448	517	9	t0	t0	PROPN
ejpam-3448	517	10	,	,	PUNCT
ejpam-3448	517	11	.	.	PUNCT
ejpam-3448	517	12	.	.	PUNCT
ejpam-3448	517	13	.	.	PUNCT
ejpam-3448	518	1	,	,	PUNCT
ejpam-3448	518	2	tn	tn	PROPN
ejpam-3448	518	3	)	)	PUNCT
ejpam-3448	518	4	is	be	AUX
ejpam-3448	518	5	called	call	VERB
ejpam-3448	518	6	an	an	DET
ejpam-3448	518	7	extremal	extremal	ADJ
ejpam-3448	518	8	vector	vector	NOUN
ejpam-3448	518	9	with	with	ADP
ejpam-3448	518	10	i	i	PROPN
ejpam-3448	518	11	cups	cup	NOUN
ejpam-3448	518	12	in	in	ADP
ejpam-3448	518	13	zn	zn	PROPN
ejpam-3448	518	14	for	for	ADP
ejpam-3448	518	15	each	each	DET
ejpam-3448	518	16	n	n	PRON
ejpam-3448	518	17	≥	≥	NOUN
ejpam-3448	518	18	0	0	NUM
ejpam-3448	518	19	and	and	CCONJ
ejpam-3448	518	20	0	0	NUM
ejpam-3448	518	21	<	<	X
ejpam-3448	518	22	i	i	PRON
ejpam-3448	518	23	<	<	X
ejpam-3448	518	24	n	n	PROPN
ejpam-3448	518	25	if	if	SCONJ
ejpam-3448	518	26	there	there	PRON
ejpam-3448	518	27	is	be	VERB
ejpam-3448	518	28	no	no	DET
ejpam-3448	518	29	any	any	DET
ejpam-3448	518	30	element	element	NOUN
ejpam-3448	518	31	ω′	ω′	NOUN
ejpam-3448	519	1	such	such	ADJ
ejpam-3448	519	2	that	that	SCONJ
ejpam-3448	519	3	dk(ω′	dk(ω′	X
ejpam-3448	519	4	)	)	PUNCT
ejpam-3448	519	5	=	=	SYM
ejpam-3448	519	6	ω	ω	PROPN
ejpam-3448	519	7	for	for	ADP
ejpam-3448	519	8	some	some	PRON
ejpam-3448	519	9	k	k	PROPN
ejpam-3448	519	10	≥	≥	PROPN
ejpam-3448	519	11	0	0	NUM
ejpam-3448	519	12	.	.	PUNCT
ejpam-3448	520	1	proposition	proposition	NOUN
ejpam-3448	520	2	5	5	NUM
ejpam-3448	520	3	.	.	PUNCT
ejpam-3448	520	4	for	for	ADP
ejpam-3448	520	5	each	each	DET
ejpam-3448	520	6	extremal	extremal	ADJ
ejpam-3448	520	7	vector	vector	NOUN
ejpam-3448	520	8	ω	ω	PROPN
ejpam-3448	520	9	with	with	ADP
ejpam-3448	520	10	k	k	PROPN
ejpam-3448	520	11	cups	cup	NOUN
ejpam-3448	520	12	,	,	PUNCT
ejpam-3448	520	13	the	the	DET
ejpam-3448	520	14	subcomplex	subcomplex	NOUN
ejpam-3448	520	15	cω	cω	NOUN
ejpam-3448	520	16	spanned	span	VERB
ejpam-3448	520	17	by	by	ADP
ejpam-3448	520	18	the	the	DET
ejpam-3448	520	19	basis	basis	NOUN
ejpam-3448	520	20	vectors	vector	NOUN
ejpam-3448	520	21	di1	di1	VERB
ejpam-3448	520	22	.	.	PUNCT
ejpam-3448	520	23	.	.	PUNCT
ejpam-3448	520	24	.	.	PUNCT
ejpam-3448	521	1	dirω	dirω	PROPN
ejpam-3448	521	2	,	,	PUNCT
ejpam-3448	521	3	r	r	NOUN
ejpam-3448	521	4	≤	≤	PUNCT
ejpam-3448	521	5	k	k	NOUN
ejpam-3448	521	6	,	,	PUNCT
ejpam-3448	521	7	is	be	AUX
ejpam-3448	521	8	isomorphic	isomorphic	ADJ
ejpam-3448	521	9	to	to	ADP
ejpam-3448	521	10	the	the	DET
ejpam-3448	521	11	augmented	augment	VERB
ejpam-3448	521	12	chain	chain	NOUN
ejpam-3448	521	13	complex	complex	NOUN
ejpam-3448	521	14	of	of	ADP
ejpam-3448	521	15	the	the	DET
ejpam-3448	521	16	standard	standard	ADJ
ejpam-3448	521	17	simplex	simplex	NOUN
ejpam-3448	521	18	∆k−1	∆k−1	PROPN
ejpam-3448	521	19	.	.	NOUN
ejpam-3448	521	20	references	reference	NOUN
ejpam-3448	521	21	747	747	NUM
ejpam-3448	521	22	proof	proof	NOUN
ejpam-3448	521	23	.	.	PUNCT
ejpam-3448	522	1	the	the	DET
ejpam-3448	522	2	graded	grade	VERB
ejpam-3448	522	3	subvector	subvector	NOUN
ejpam-3448	522	4	space	space	NOUN
ejpam-3448	522	5	of	of	ADP
ejpam-3448	522	6	c∗	c∗	PROPN
ejpam-3448	522	7	spanned	span	VERB
ejpam-3448	522	8	by	by	ADP
ejpam-3448	522	9	the	the	DET
ejpam-3448	522	10	elements	element	NOUN
ejpam-3448	522	11	di1	di1	VERB
ejpam-3448	522	12	.	.	PUNCT
ejpam-3448	522	13	.	.	PUNCT
ejpam-3448	522	14	.	.	PUNCT
ejpam-3448	523	1	dirω	dirω	PROPN
ejpam-3448	523	2	is	be	AUX
ejpam-3448	523	3	stable	stable	ADJ
ejpam-3448	523	4	by	by	ADP
ejpam-3448	523	5	∂	∂	NUM
ejpam-3448	523	6	and	and	CCONJ
ejpam-3448	523	7	forms	form	VERB
ejpam-3448	523	8	a	a	DET
ejpam-3448	523	9	subcomplex	subcomplex	NOUN
ejpam-3448	523	10	.	.	PUNCT
ejpam-3448	524	1	the	the	DET
ejpam-3448	524	2	bijection	bijection	NOUN
ejpam-3448	524	3	between	between	ADP
ejpam-3448	524	4	the	the	DET
ejpam-3448	524	5	cells	cell	NOUN
ejpam-3448	524	6	of	of	ADP
ejpam-3448	524	7	∆k−1	∆k−1	NUM
ejpam-3448	524	8	and	and	CCONJ
ejpam-3448	524	9	the	the	DET
ejpam-3448	524	10	set	set	NOUN
ejpam-3448	524	11	of	of	ADP
ejpam-3448	524	12	non	non	ADJ
ejpam-3448	524	13	-	-	ADJ
ejpam-3448	524	14	zero	zero	NUM
ejpam-3448	524	15	vectors	vector	NOUN
ejpam-3448	524	16	{	{	PUNCT
ejpam-3448	524	17	di1	di1	NOUN
ejpam-3448	524	18	.	.	PUNCT
ejpam-3448	524	19	.	.	PUNCT
ejpam-3448	524	20	.	.	PUNCT
ejpam-3448	525	1	dirω	dirω	PROPN
ejpam-3448	525	2	}	}	PUNCT
ejpam-3448	525	3	is	be	AUX
ejpam-3448	525	4	constructed	construct	VERB
ejpam-3448	525	5	by	by	ADP
ejpam-3448	525	6	sending	send	VERB
ejpam-3448	525	7	the	the	PRON
ejpam-3448	525	8	(	(	PUNCT
ejpam-3448	525	9	j	j	PROPN
ejpam-3448	525	10	−	−	PROPN
ejpam-3448	525	11	1)-st	1)-st	NUM
ejpam-3448	525	12	vertex	vertex	NOUN
ejpam-3448	525	13	of	of	ADP
ejpam-3448	525	14	∆k−1	∆k−1	NUM
ejpam-3448	525	15	to	to	ADP
ejpam-3448	525	16	the	the	DET
ejpam-3448	525	17	vector	vector	NOUN
ejpam-3448	525	18	di1	di1	NOUN
ejpam-3448	525	19	.	.	PUNCT
ejpam-3448	525	20	.	.	PUNCT
ejpam-3448	526	1	.	.	PUNCT
ejpam-3448	527	1	d̂ij	d̂ij	NOUN
ejpam-3448	527	2	.	.	PUNCT
ejpam-3448	527	3	.	.	PUNCT
ejpam-3448	527	4	.	.	PUNCT
ejpam-3448	528	1	dikω	dikω	PROPN
ejpam-3448	528	2	where	where	SCONJ
ejpam-3448	528	3	ij	ij	NOUN
ejpam-3448	528	4	is	be	AUX
ejpam-3448	528	5	the	the	DET
ejpam-3448	528	6	j	j	PROPN
ejpam-3448	528	7	-	-	PUNCT
ejpam-3448	528	8	th	th	PROPN
ejpam-3448	528	9	cup	cup	NOUN
ejpam-3448	528	10	of	of	ADP
ejpam-3448	528	11	zn	zn	PROPN
ejpam-3448	528	12	.	.	PUNCT
ejpam-3448	529	1	here	here	ADV
ejpam-3448	529	2	the	the	DET
ejpam-3448	529	3	vertices	vertex	NOUN
ejpam-3448	529	4	of	of	ADP
ejpam-3448	529	5	∆k−1	∆k−1	NUM
ejpam-3448	529	6	are	be	AUX
ejpam-3448	529	7	enumerated	enumerate	VERB
ejpam-3448	529	8	by	by	ADP
ejpam-3448	529	9	0	0	NUM
ejpam-3448	529	10	to	to	ADP
ejpam-3448	529	11	(	(	PUNCT
ejpam-3448	529	12	k	k	NOUN
ejpam-3448	529	13	−	−	PROPN
ejpam-3448	529	14	1	1	NUM
ejpam-3448	529	15	)	)	PUNCT
ejpam-3448	529	16	.	.	PUNCT
ejpam-3448	530	1	this	this	PRON
ejpam-3448	530	2	leads	lead	VERB
ejpam-3448	530	3	us	we	PRON
ejpam-3448	530	4	that	that	SCONJ
ejpam-3448	530	5	the	the	DET
ejpam-3448	530	6	boundary	boundary	ADJ
ejpam-3448	530	7	map	map	NOUN
ejpam-3448	530	8	on	on	ADP
ejpam-3448	530	9	the	the	DET
ejpam-3448	530	10	chain	chain	NOUN
ejpam-3448	530	11	complex	complex	NOUN
ejpam-3448	530	12	of	of	ADP
ejpam-3448	530	13	the	the	DET
ejpam-3448	530	14	standart	standart	NOUN
ejpam-3448	530	15	simplex	simplex	NOUN
ejpam-3448	530	16	corresponds	correspond	VERB
ejpam-3448	530	17	to	to	ADP
ejpam-3448	530	18	the	the	DET
ejpam-3448	530	19	boundary	boundary	ADJ
ejpam-3448	530	20	map	map	NOUN
ejpam-3448	530	21	∂	∂	NUM
ejpam-3448	530	22	defined	define	VERB
ejpam-3448	530	23	in	in	ADP
ejpam-3448	530	24	(	(	PUNCT
ejpam-3448	530	25	13	13	NUM
ejpam-3448	530	26	)	)	PUNCT
ejpam-3448	530	27	.	.	PUNCT
ejpam-3448	531	1	proposition	proposition	NOUN
ejpam-3448	531	2	6	6	NUM
ejpam-3448	531	3	.	.	PUNCT
ejpam-3448	532	1	the	the	DET
ejpam-3448	532	2	chain	chain	NOUN
ejpam-3448	532	3	complex	complex	ADJ
ejpam-3448	532	4	c∗	c∗	NOUN
ejpam-3448	532	5	is	be	AUX
ejpam-3448	532	6	isomorphic	isomorphic	ADJ
ejpam-3448	532	7	to	to	ADP
ejpam-3448	532	8	⊕	⊕	PROPN
ejpam-3448	532	9	ω	ω	PROPN
ejpam-3448	532	10	cω	cω	PROPN
ejpam-3448	532	11	for	for	ADP
ejpam-3448	532	12	all	all	DET
ejpam-3448	532	13	extremal	extremal	ADJ
ejpam-3448	532	14	vectors	vector	NOUN
ejpam-3448	532	15	ω	ω	NOUN
ejpam-3448	532	16	.	.	PUNCT
ejpam-3448	533	1	proof	proof	NOUN
ejpam-3448	533	2	.	.	PUNCT
ejpam-3448	534	1	if	if	SCONJ
ejpam-3448	534	2	a	a	DET
ejpam-3448	534	3	vector	vector	NOUN
ejpam-3448	534	4	ω	ω	PROPN
ejpam-3448	534	5	∈	∈	PROPN
ejpam-3448	534	6	c∗	c∗	NOUN
ejpam-3448	534	7	is	be	AUX
ejpam-3448	534	8	an	an	DET
ejpam-3448	534	9	extremal	extremal	ADJ
ejpam-3448	534	10	vector	vector	NOUN
ejpam-3448	534	11	,	,	PUNCT
ejpam-3448	534	12	then	then	ADV
ejpam-3448	534	13	it	it	PRON
ejpam-3448	534	14	is	be	AUX
ejpam-3448	534	15	clear	clear	ADJ
ejpam-3448	534	16	that	that	SCONJ
ejpam-3448	534	17	ω	ω	PROPN
ejpam-3448	534	18	∈	∈	PROPN
ejpam-3448	534	19	cω	cω	PROPN
ejpam-3448	534	20	.	.	PUNCT
ejpam-3448	535	1	otherwise	otherwise	ADV
ejpam-3448	535	2	,	,	PUNCT
ejpam-3448	535	3	there	there	PRON
ejpam-3448	535	4	exists	exist	VERB
ejpam-3448	535	5	an	an	DET
ejpam-3448	535	6	extremal	extremal	ADJ
ejpam-3448	535	7	vector	vector	NOUN
ejpam-3448	535	8	ω1	ω1	NOUN
ejpam-3448	535	9	such	such	ADJ
ejpam-3448	535	10	that	that	SCONJ
ejpam-3448	535	11	di1di2	di1di2	ADJ
ejpam-3448	535	12	.	.	PUNCT
ejpam-3448	535	13	.	.	PUNCT
ejpam-3448	535	14	.	.	PUNCT
ejpam-3448	536	1	dir(ω1	dir(ω1	ADP
ejpam-3448	536	2	)	)	PUNCT
ejpam-3448	536	3	=	=	SYM
ejpam-3448	536	4	ω	ω	PROPN
ejpam-3448	536	5	for	for	ADP
ejpam-3448	536	6	some	some	DET
ejpam-3448	536	7	ij	ij	NOUN
ejpam-3448	536	8	,	,	PUNCT
ejpam-3448	536	9	where	where	SCONJ
ejpam-3448	536	10	1	1	NUM
ejpam-3448	536	11	≤	≤	NUM
ejpam-3448	536	12	j	j	NOUN
ejpam-3448	536	13	≤	≤	NOUN
ejpam-3448	536	14	r	r	NOUN
ejpam-3448	536	15	and	and	CCONJ
ejpam-3448	536	16	it	it	PRON
ejpam-3448	536	17	gives	give	VERB
ejpam-3448	536	18	that	that	PRON
ejpam-3448	536	19	ω	ω	PROPN
ejpam-3448	536	20	∈	∈	PROPN
ejpam-3448	536	21	cω1	cω1	NOUN
ejpam-3448	536	22	.	.	PUNCT
ejpam-3448	537	1	now	now	ADV
ejpam-3448	537	2	,	,	PUNCT
ejpam-3448	537	3	we	we	PRON
ejpam-3448	537	4	want	want	VERB
ejpam-3448	537	5	to	to	PART
ejpam-3448	537	6	prove	prove	VERB
ejpam-3448	537	7	that	that	SCONJ
ejpam-3448	537	8	any	any	DET
ejpam-3448	537	9	basis	basis	NOUN
ejpam-3448	537	10	vector	vector	NOUN
ejpam-3448	537	11	belongs	belong	VERB
ejpam-3448	537	12	to	to	ADP
ejpam-3448	537	13	one	one	NUM
ejpam-3448	537	14	and	and	CCONJ
ejpam-3448	537	15	only	only	ADV
ejpam-3448	537	16	one	one	NUM
ejpam-3448	537	17	subcomplex	subcomplex	NOUN
ejpam-3448	537	18	of	of	ADP
ejpam-3448	537	19	the	the	DET
ejpam-3448	537	20	form	form	NOUN
ejpam-3448	537	21	cω	cω	NOUN
ejpam-3448	537	22	,	,	PUNCT
ejpam-3448	537	23	that	that	ADV
ejpam-3448	537	24	is	is	ADV
ejpam-3448	537	25	,	,	PUNCT
ejpam-3448	537	26	if	if	SCONJ
ejpam-3448	537	27	a	a	DET
ejpam-3448	537	28	basis	basis	NOUN
ejpam-3448	537	29	vector	vector	NOUN
ejpam-3448	537	30	belongs	belong	VERB
ejpam-3448	537	31	to	to	ADP
ejpam-3448	537	32	both	both	DET
ejpam-3448	537	33	cω	cω	NOUN
ejpam-3448	537	34	and	and	CCONJ
ejpam-3448	537	35	cω1	cω1	NOUN
ejpam-3448	537	36	then	then	ADV
ejpam-3448	537	37	we	we	PRON
ejpam-3448	537	38	want	want	VERB
ejpam-3448	537	39	to	to	PART
ejpam-3448	537	40	show	show	VERB
ejpam-3448	537	41	that	that	SCONJ
ejpam-3448	537	42	ω	ω	PROPN
ejpam-3448	537	43	=	=	SYM
ejpam-3448	537	44	ω1	ω1	PROPN
ejpam-3448	537	45	.	.	PUNCT
ejpam-3448	538	1	let	let	VERB
ejpam-3448	538	2	ω	ω	PROPN
ejpam-3448	538	3	=	=	SYM
ejpam-3448	538	4	(	(	PUNCT
ejpam-3448	538	5	zn	zn	PROPN
ejpam-3448	538	6	,	,	PUNCT
ejpam-3448	538	7	t0	t0	PROPN
ejpam-3448	538	8	,	,	PUNCT
ejpam-3448	538	9	.	.	PUNCT
ejpam-3448	538	10	.	.	PUNCT
ejpam-3448	539	1	.	.	PUNCT
ejpam-3448	540	1	,	,	PUNCT
ejpam-3448	540	2	tn	tn	PROPN
ejpam-3448	540	3	)	)	PUNCT
ejpam-3448	540	4	and	and	CCONJ
ejpam-3448	540	5	ω1	ω1	PROPN
ejpam-3448	540	6	=	=	SYM
ejpam-3448	540	7	(	(	PUNCT
ejpam-3448	540	8	z′n	z′n	NOUN
ejpam-3448	540	9	,	,	PUNCT
ejpam-3448	540	10	t	t	PROPN
ejpam-3448	540	11	′	′	NUM
ejpam-3448	540	12	0	0	NUM
ejpam-3448	540	13	,	,	PUNCT
ejpam-3448	540	14	.	.	PUNCT
ejpam-3448	540	15	.	.	PUNCT
ejpam-3448	541	1	.	.	PUNCT
ejpam-3448	542	1	,	,	PUNCT
ejpam-3448	542	2	t	t	NOUN
ejpam-3448	542	3	′	′	NUM
ejpam-3448	542	4	n	n	CCONJ
ejpam-3448	542	5	)	)	PUNCT
ejpam-3448	542	6	be	be	AUX
ejpam-3448	542	7	given	give	VERB
ejpam-3448	542	8	.	.	PUNCT
ejpam-3448	543	1	if	if	SCONJ
ejpam-3448	543	2	di(ω	di(ω	NOUN
ejpam-3448	543	3	)	)	PUNCT
ejpam-3448	543	4	=	=	SYM
ejpam-3448	544	1	dj(ω1	dj(ω1	ADJ
ejpam-3448	544	2	)	)	PUNCT
ejpam-3448	544	3	6=	6=	ADP
ejpam-3448	544	4	0	0	NUM
ejpam-3448	544	5	,	,	PUNCT
ejpam-3448	544	6	then	then	ADV
ejpam-3448	544	7	the	the	DET
ejpam-3448	544	8	i	i	PROPN
ejpam-3448	544	9	-	-	PUNCT
ejpam-3448	544	10	th	th	X
ejpam-3448	544	11	node	node	NOUN
ejpam-3448	544	12	is	be	AUX
ejpam-3448	544	13	contained	contain	VERB
ejpam-3448	544	14	by	by	ADP
ejpam-3448	544	15	a	a	DET
ejpam-3448	544	16	cup	cup	NOUN
ejpam-3448	544	17	in	in	ADP
ejpam-3448	544	18	zn	zn	PROPN
ejpam-3448	544	19	and	and	CCONJ
ejpam-3448	544	20	the	the	DET
ejpam-3448	544	21	j	j	PROPN
ejpam-3448	544	22	-	-	PUNCT
ejpam-3448	544	23	th	th	VERB
ejpam-3448	544	24	node	node	NOUN
ejpam-3448	544	25	is	be	AUX
ejpam-3448	544	26	contained	contain	VERB
ejpam-3448	544	27	by	by	ADP
ejpam-3448	544	28	a	a	DET
ejpam-3448	544	29	cup	cup	NOUN
ejpam-3448	544	30	in	in	ADP
ejpam-3448	544	31	z′n	z′n	NOUN
ejpam-3448	544	32	such	such	ADJ
ejpam-3448	544	33	that	that	DET
ejpam-3448	544	34	εi(zn	εi(zn	NOUN
ejpam-3448	544	35	)	)	PUNCT
ejpam-3448	545	1	=	=	PUNCT
ejpam-3448	545	2	εj(z	εj(z	NUM
ejpam-3448	545	3	′	′	NOUN
ejpam-3448	545	4	n	n	CCONJ
ejpam-3448	545	5	)	)	PUNCT
ejpam-3448	545	6	.	.	PUNCT
ejpam-3448	546	1	if	if	SCONJ
ejpam-3448	546	2	i	i	PRON
ejpam-3448	546	3	<	<	X
ejpam-3448	546	4	j	j	PROPN
ejpam-3448	546	5	,	,	PUNCT
ejpam-3448	546	6	then	then	ADV
ejpam-3448	546	7	there	there	PRON
ejpam-3448	546	8	exists	exist	VERB
ejpam-3448	546	9	ω̂	ω̂	PUNCT
ejpam-3448	546	10	such	such	ADJ
ejpam-3448	546	11	that	that	DET
ejpam-3448	546	12	dj(ω̂	dj(ω̂	NOUN
ejpam-3448	546	13	)	)	PUNCT
ejpam-3448	546	14	=	=	SYM
ejpam-3448	546	15	ω	ω	NOUN
ejpam-3448	546	16	and	and	CCONJ
ejpam-3448	546	17	di(ω̂	di(ω̂	NOUN
ejpam-3448	546	18	)	)	PUNCT
ejpam-3448	546	19	=	=	SYM
ejpam-3448	546	20	ω1	ω1	PROPN
ejpam-3448	546	21	.	.	PUNCT
ejpam-3448	547	1	therefore	therefore	ADV
ejpam-3448	547	2	ω	ω	PROPN
ejpam-3448	547	3	and	and	CCONJ
ejpam-3448	547	4	ω1	ω1	PROPN
ejpam-3448	547	5	are	be	AUX
ejpam-3448	547	6	not	not	PART
ejpam-3448	547	7	extremal	extremal	ADJ
ejpam-3448	547	8	which	which	PRON
ejpam-3448	547	9	follows	follow	VERB
ejpam-3448	547	10	that	that	SCONJ
ejpam-3448	547	11	i	i	PRON
ejpam-3448	547	12	=	=	PUNCT
ejpam-3448	547	13	j.	j.	PROPN
ejpam-3448	547	14	in	in	ADP
ejpam-3448	547	15	other	other	ADJ
ejpam-3448	547	16	words	word	NOUN
ejpam-3448	547	17	,	,	PUNCT
ejpam-3448	547	18	di(ω	di(ω	NOUN
ejpam-3448	547	19	)	)	PUNCT
ejpam-3448	547	20	=	=	PUNCT
ejpam-3448	547	21	di(ω1	di(ω1	ADP
ejpam-3448	547	22	)	)	PUNCT
ejpam-3448	547	23	=	=	SYM
ejpam-3448	547	24	(	(	PUNCT
ejpam-3448	547	25	εi(z	εi(z	NOUN
ejpam-3448	547	26	)	)	PUNCT
ejpam-3448	547	27	,	,	PUNCT
ejpam-3448	547	28	t0	t0	PROPN
ejpam-3448	547	29	,	,	PUNCT
ejpam-3448	547	30	.	.	PUNCT
ejpam-3448	547	31	.	.	PUNCT
ejpam-3448	548	1	.	.	PUNCT
ejpam-3448	549	1	,	,	PUNCT
ejpam-3448	549	2	ti−1	ti−1	NOUN
ejpam-3448	549	3	∨	∨	NUM
ejpam-3448	549	4	ti	ti	NOUN
ejpam-3448	549	5	,	,	PUNCT
ejpam-3448	549	6	.	.	PUNCT
ejpam-3448	549	7	.	.	PUNCT
ejpam-3448	550	1	.	.	PUNCT
ejpam-3448	551	1	,	,	PUNCT
ejpam-3448	551	2	tn	tn	PROPN
ejpam-3448	551	3	)	)	PUNCT
ejpam-3448	551	4	.	.	PUNCT
ejpam-3448	552	1	(	(	PUNCT
ejpam-3448	552	2	14	14	NUM
ejpam-3448	552	3	)	)	PUNCT
ejpam-3448	552	4	the	the	DET
ejpam-3448	552	5	only	only	ADJ
ejpam-3448	552	6	vector	vector	NOUN
ejpam-3448	552	7	is	be	AUX
ejpam-3448	552	8	(	(	PUNCT
ejpam-3448	552	9	zn	zn	PROPN
ejpam-3448	552	10	,	,	PUNCT
ejpam-3448	552	11	t0	t0	PROPN
ejpam-3448	552	12	,	,	PUNCT
ejpam-3448	552	13	.	.	PUNCT
ejpam-3448	552	14	.	.	PUNCT
ejpam-3448	553	1	.	.	PUNCT
ejpam-3448	554	1	,	,	PUNCT
ejpam-3448	554	2	tn	tn	NOUN
ejpam-3448	554	3	)	)	PUNCT
ejpam-3448	554	4	satisfying	satisfying	NOUN
ejpam-3448	554	5	(	(	PUNCT
ejpam-3448	554	6	14	14	NUM
ejpam-3448	554	7	)	)	PUNCT
ejpam-3448	554	8	and	and	CCONJ
ejpam-3448	554	9	therefore	therefore	ADV
ejpam-3448	554	10	ω	ω	PROPN
ejpam-3448	554	11	=	=	PROPN
ejpam-3448	554	12	ω1	ω1	PROPN
ejpam-3448	554	13	.	.	PUNCT
ejpam-3448	554	14	proposition	proposition	NOUN
ejpam-3448	554	15	7	7	NUM
ejpam-3448	554	16	.	.	PUNCT
ejpam-3448	555	1	the	the	DET
ejpam-3448	555	2	complex	complex	ADJ
ejpam-3448	555	3	c∗	c∗	NOUN
ejpam-3448	555	4	is	be	AUX
ejpam-3448	555	5	acylic	acylic	ADJ
ejpam-3448	555	6	for	for	ADP
ejpam-3448	555	7	any	any	DET
ejpam-3448	555	8	choice	choice	NOUN
ejpam-3448	555	9	of	of	ADP
ejpam-3448	555	10	a	a	DET
ejpam-3448	555	11	sequence	sequence	NOUN
ejpam-3448	555	12	s	s	NOUN
ejpam-3448	555	13	,	,	PUNCT
ejpam-3448	555	14	that	that	ADV
ejpam-3448	555	15	is	is	ADV
ejpam-3448	555	16	,	,	PUNCT
ejpam-3448	555	17	hn(c∗	hn(c∗	PROPN
ejpam-3448	555	18	)	)	PUNCT
ejpam-3448	556	1	=	=	SYM
ejpam-3448	556	2	0	0	NUM
ejpam-3448	557	1	for	for	ADP
ejpam-3448	557	2	all	all	PRON
ejpam-3448	557	3	n	n	CCONJ
ejpam-3448	557	4	>	>	X
ejpam-3448	557	5	0	0	NUM
ejpam-3448	557	6	and	and	CCONJ
ejpam-3448	557	7	h0(c∗	h0(c∗	NUM
ejpam-3448	557	8	)	)	PUNCT
ejpam-3448	557	9	=	=	SYM
ejpam-3448	557	10	f.	f.	NOUN
ejpam-3448	557	11	proof	proof	NOUN
ejpam-3448	557	12	.	.	PUNCT
ejpam-3448	558	1	by	by	ADP
ejpam-3448	558	2	propositions	proposition	NOUN
ejpam-3448	558	3	5	5	NUM
ejpam-3448	558	4	and	and	CCONJ
ejpam-3448	558	5	6	6	NUM
ejpam-3448	558	6	the	the	DET
ejpam-3448	558	7	homology	homology	NOUN
ejpam-3448	558	8	of	of	ADP
ejpam-3448	558	9	the	the	DET
ejpam-3448	558	10	complex	complex	NOUN
ejpam-3448	558	11	is	be	AUX
ejpam-3448	558	12	trivial	trivial	ADJ
ejpam-3448	558	13	because	because	SCONJ
ejpam-3448	558	14	the	the	DET
ejpam-3448	558	15	standart	standart	NOUN
ejpam-3448	558	16	simplex	simplex	NOUN
ejpam-3448	558	17	is	be	AUX
ejpam-3448	558	18	contractible	contractible	ADJ
ejpam-3448	558	19	.	.	PUNCT
ejpam-3448	559	1	there	there	PRON
ejpam-3448	559	2	is	be	VERB
ejpam-3448	559	3	only	only	ADV
ejpam-3448	559	4	one	one	NUM
ejpam-3448	559	5	exception	exception	NOUN
ejpam-3448	559	6	in	in	ADP
ejpam-3448	559	7	dimension	dimension	NOUN
ejpam-3448	559	8	0	0	PUNCT
ejpam-3448	560	1	because	because	SCONJ
ejpam-3448	560	2	the	the	DET
ejpam-3448	560	3	subcomplex	subcomplex	NOUN
ejpam-3448	560	4	corresponding	correspond	VERB
ejpam-3448	560	5	to	to	ADP
ejpam-3448	560	6	the	the	DET
ejpam-3448	560	7	element	element	NOUN
ejpam-3448	560	8	ω	ω	PROPN
ejpam-3448	560	9	=	=	SYM
ejpam-3448	560	10	(	(	PUNCT
ejpam-3448	560	11	0,0	0,0	NOUN
ejpam-3448	560	12	)	)	PUNCT
ejpam-3448	560	13	is	be	AUX
ejpam-3448	560	14	f	f	PROPN
ejpam-3448	560	15	in	in	ADP
ejpam-3448	560	16	dimension	dimension	NOUN
ejpam-3448	560	17	0	0	NUM
ejpam-3448	560	18	.	.	PUNCT
ejpam-3448	561	1	so	so	ADV
ejpam-3448	561	2	we	we	PRON
ejpam-3448	561	3	have	have	VERB
ejpam-3448	561	4	hn(c∗	hn(c∗	PROPN
ejpam-3448	561	5	)	)	PUNCT
ejpam-3448	562	1	=	=	SYM
ejpam-3448	562	2	0	0	NUM
ejpam-3448	563	1	for	for	ADP
ejpam-3448	563	2	all	all	PRON
ejpam-3448	563	3	n	n	CCONJ
ejpam-3448	563	4	>	>	X
ejpam-3448	563	5	0	0	NUM
ejpam-3448	563	6	and	and	CCONJ
ejpam-3448	563	7	h0(c∗	h0(c∗	NUM
ejpam-3448	563	8	)	)	PUNCT
ejpam-3448	563	9	=	=	SYM
ejpam-3448	563	10	f.	f.	NOUN
ejpam-3448	563	11	proposition	proposition	PROPN
ejpam-3448	563	12	8	8	NUM
ejpam-3448	563	13	.	.	PUNCT
ejpam-3448	564	1	the	the	DET
ejpam-3448	564	2	poincare	poincare	PROPN
ejpam-3448	564	3	series	series	PROPN
ejpam-3448	564	4	of	of	ADP
ejpam-3448	564	5	the	the	DET
ejpam-3448	564	6	complex	complex	ADJ
ejpam-3448	564	7	c∗	c∗	NOUN
ejpam-3448	564	8	is	be	AUX
ejpam-3448	564	9	equal	equal	ADJ
ejpam-3448	564	10	to	to	ADP
ejpam-3448	564	11	f(z	f(z	PROPN
ejpam-3448	564	12	,	,	PUNCT
ejpam-3448	564	13	f(s	f(s	ADV
ejpam-3448	564	14	,	,	PUNCT
ejpam-3448	564	15	t	t	PROPN
ejpam-3448	564	16	)	)	PUNCT
ejpam-3448	564	17	)	)	PUNCT
ejpam-3448	564	18	.	.	PUNCT
ejpam-3448	565	1	this	this	PRON
ejpam-3448	565	2	also	also	ADV
ejpam-3448	565	3	gives	give	VERB
ejpam-3448	565	4	that	that	SCONJ
ejpam-3448	565	5	if	if	SCONJ
ejpam-3448	565	6	z2	z2	PROPN
ejpam-3448	565	7	×	×	PROPN
ejpam-3448	565	8	i2	i2	PROPN
ejpam-3448	565	9	is	be	AUX
ejpam-3448	565	10	the	the	DET
ejpam-3448	565	11	complement	complement	NOUN
ejpam-3448	565	12	of	of	ADP
ejpam-3448	565	13	s2	s2	PROPN
ejpam-3448	565	14	×	×	PROPN
ejpam-3448	565	15	i2	i2	PROPN
ejpam-3448	565	16	in	in	ADP
ejpam-3448	565	17	mp(2)×	mp(2)×	PROPN
ejpam-3448	565	18	i2	i2	PROPN
ejpam-3448	565	19	then	then	ADV
ejpam-3448	565	20	f(z	f(z	PROPN
ejpam-3448	565	21	,	,	PUNCT
ejpam-3448	565	22	f(s	f(s	ADV
ejpam-3448	565	23	,	,	PUNCT
ejpam-3448	565	24	t	t	PROPN
ejpam-3448	565	25	)	)	PUNCT
ejpam-3448	565	26	)	)	PUNCT
ejpam-3448	566	1	=	=	PUNCT
ejpam-3448	566	2	t.	t.	NOUN
ejpam-3448	566	3	proof	proof	NOUN
ejpam-3448	566	4	.	.	PUNCT
ejpam-3448	567	1	by	by	ADP
ejpam-3448	567	2	the	the	DET
ejpam-3448	567	3	construction	construction	NOUN
ejpam-3448	567	4	of	of	ADP
ejpam-3448	567	5	the	the	DET
ejpam-3448	567	6	complex	complex	ADJ
ejpam-3448	567	7	c∗	c∗	NOUN
ejpam-3448	567	8	,	,	PUNCT
ejpam-3448	567	9	it	it	PRON
ejpam-3448	567	10	is	be	AUX
ejpam-3448	567	11	clear	clear	ADJ
ejpam-3448	567	12	that	that	SCONJ
ejpam-3448	567	13	the	the	DET
ejpam-3448	567	14	poincare	poincare	PROPN
ejpam-3448	567	15	series	series	PROPN
ejpam-3448	567	16	of	of	ADP
ejpam-3448	567	17	the	the	DET
ejpam-3448	567	18	complex	complex	ADJ
ejpam-3448	567	19	c∗	c∗	NOUN
ejpam-3448	567	20	is	be	AUX
ejpam-3448	567	21	equal	equal	ADJ
ejpam-3448	567	22	to	to	ADP
ejpam-3448	567	23	f(z	f(z	PROPN
ejpam-3448	567	24	,	,	PUNCT
ejpam-3448	567	25	f(s	f(s	ADV
ejpam-3448	567	26	,	,	PUNCT
ejpam-3448	567	27	t	t	PROPN
ejpam-3448	567	28	)	)	PUNCT
ejpam-3448	567	29	)	)	PUNCT
ejpam-3448	567	30	.	.	PUNCT
ejpam-3448	568	1	since	since	SCONJ
ejpam-3448	568	2	the	the	DET
ejpam-3448	568	3	poincare	poincare	PROPN
ejpam-3448	568	4	series	series	PROPN
ejpam-3448	568	5	of	of	ADP
ejpam-3448	568	6	a	a	DET
ejpam-3448	568	7	complex	complex	NOUN
ejpam-3448	568	8	is	be	AUX
ejpam-3448	568	9	the	the	DET
ejpam-3448	568	10	same	same	ADJ
ejpam-3448	568	11	as	as	ADP
ejpam-3448	568	12	the	the	DET
ejpam-3448	568	13	poincare	poincare	PROPN
ejpam-3448	568	14	series	series	PROPN
ejpam-3448	568	15	of	of	ADP
ejpam-3448	568	16	its	its	PRON
ejpam-3448	568	17	homology	homology	NOUN
ejpam-3448	568	18	and	and	CCONJ
ejpam-3448	568	19	using	use	VERB
ejpam-3448	568	20	proposition	proposition	NOUN
ejpam-3448	568	21	7	7	NUM
ejpam-3448	568	22	,	,	PUNCT
ejpam-3448	568	23	f(z	f(z	PROPN
ejpam-3448	568	24	,	,	PUNCT
ejpam-3448	568	25	f(s	f(s	ADV
ejpam-3448	568	26	,	,	PUNCT
ejpam-3448	568	27	t	t	PROPN
ejpam-3448	568	28	)	)	PUNCT
ejpam-3448	568	29	)	)	PUNCT
ejpam-3448	568	30	becomes	become	VERB
ejpam-3448	568	31	an	an	DET
ejpam-3448	568	32	identity	identity	NOUN
ejpam-3448	568	33	polynomial	polynomial	NOUN
ejpam-3448	568	34	on	on	ADP
ejpam-3448	568	35	the	the	DET
ejpam-3448	568	36	variable	variable	ADJ
ejpam-3448	568	37	t.	t.	NOUN
ejpam-3448	568	38	references	reference	NOUN
ejpam-3448	568	39	[	[	X
ejpam-3448	568	40	1	1	NUM
ejpam-3448	568	41	]	]	PUNCT
ejpam-3448	568	42	m.	m.	NOUN
ejpam-3448	568	43	p.	p.	PROPN
ejpam-3448	568	44	carr	carr	PROPN
ejpam-3448	568	45	and	and	CCONJ
ejpam-3448	568	46	s.	s.	PROPN
ejpam-3448	568	47	l.	l.	PROPN
ejpam-3448	568	48	devadoss	devadoss	PROPN
ejpam-3448	568	49	.	.	PROPN
ejpam-3448	568	50	coxeter	coxeter	NOUN
ejpam-3448	568	51	complexes	complex	NOUN
ejpam-3448	568	52	and	and	CCONJ
ejpam-3448	568	53	graph	graph	NOUN
ejpam-3448	568	54	-	-	PUNCT
ejpam-3448	568	55	associahedra	associahedra	PROPN
ejpam-3448	568	56	.	.	PROPN
ejpam-3448	568	57	topology	topology	PROPN
ejpam-3448	568	58	appl	appl	PROPN
ejpam-3448	568	59	.	.	PROPN
ejpam-3448	568	60	,	,	PUNCT
ejpam-3448	568	61	153(12):2155–2168	153(12):2155–2168	NUM
ejpam-3448	568	62	,	,	PUNCT
ejpam-3448	568	63	2006	2006	NUM
ejpam-3448	568	64	.	.	PUNCT
ejpam-3448	569	1	references	reference	NOUN
ejpam-3448	569	2	748	748	NUM
ejpam-3448	569	3	[	[	X
ejpam-3448	569	4	2	2	NUM
ejpam-3448	569	5	]	]	PUNCT
ejpam-3448	569	6	s.	s.	PROPN
ejpam-3448	569	7	l.	l.	PROPN
ejpam-3448	569	8	devadoss	devadoss	PROPN
ejpam-3448	569	9	.	.	PUNCT
ejpam-3448	570	1	a	a	DET
ejpam-3448	570	2	realization	realization	NOUN
ejpam-3448	570	3	of	of	ADP
ejpam-3448	570	4	graph	graph	NOUN
ejpam-3448	570	5	associahedra	associahedra	PROPN
ejpam-3448	570	6	.	.	PROPN
ejpam-3448	570	7	discrete	discrete	ADJ
ejpam-3448	570	8	mathematics	mathematic	NOUN
ejpam-3448	570	9	,	,	PUNCT
ejpam-3448	570	10	309(1):271	309(1):271	NUM
ejpam-3448	570	11	–	–	PUNCT
ejpam-3448	570	12	276	276	NUM
ejpam-3448	570	13	,	,	PUNCT
ejpam-3448	570	14	2009	2009	NUM
ejpam-3448	570	15	.	.	PUNCT
ejpam-3448	571	1	[	[	X
ejpam-3448	571	2	3	3	X
ejpam-3448	571	3	]	]	X
ejpam-3448	571	4	s.	s.	PROPN
ejpam-3448	571	5	forcey	forcey	PROPN
ejpam-3448	571	6	and	and	CCONJ
ejpam-3448	571	7	d.	d.	PROPN
ejpam-3448	571	8	springfield	springfield	PROPN
ejpam-3448	571	9	.	.	PUNCT
ejpam-3448	572	1	geometric	geometric	ADJ
ejpam-3448	572	2	combinatorial	combinatorial	ADJ
ejpam-3448	572	3	algebras	algebra	NOUN
ejpam-3448	572	4	:	:	PUNCT
ejpam-3448	572	5	cyclohedron	cyclohedron	PROPN
ejpam-3448	572	6	and	and	CCONJ
ejpam-3448	572	7	simplex	simplex	NOUN
ejpam-3448	572	8	.	.	PUNCT
ejpam-3448	573	1	journal	journal	PROPN
ejpam-3448	573	2	of	of	ADP
ejpam-3448	573	3	algebraic	algebraic	PROPN
ejpam-3448	573	4	combinatorics	combinatoric	NOUN
ejpam-3448	573	5	,	,	PUNCT
ejpam-3448	573	6	32(4):597–627	32(4):597–627	PROPN
ejpam-3448	573	7	,	,	PUNCT
ejpam-3448	573	8	2010	2010	NUM
ejpam-3448	573	9	.	.	PUNCT
ejpam-3448	574	1	[	[	X
ejpam-3448	574	2	4	4	X
ejpam-3448	574	3	]	]	PUNCT
ejpam-3448	574	4	j.	j.	PROPN
ejpam-3448	574	5	l.	l.	PROPN
ejpam-3448	574	6	loday	loday	PROPN
ejpam-3448	574	7	.	.	PUNCT
ejpam-3448	575	1	arithmetree	arithmetree	PROPN
ejpam-3448	575	2	.	.	PUNCT
ejpam-3448	576	1	journal	journal	PROPN
ejpam-3448	576	2	of	of	ADP
ejpam-3448	576	3	algebra	algebra	PROPN
ejpam-3448	576	4	,	,	PUNCT
ejpam-3448	576	5	258(1):275	258(1):275	NUM
ejpam-3448	576	6	–	–	PUNCT
ejpam-3448	576	7	309	309	NUM
ejpam-3448	576	8	,	,	PUNCT
ejpam-3448	576	9	2002	2002	NUM
ejpam-3448	576	10	.	.	PUNCT
ejpam-3448	577	1	[	[	X
ejpam-3448	577	2	5	5	X
ejpam-3448	577	3	]	]	PUNCT
ejpam-3448	577	4	j.	j.	PROPN
ejpam-3448	577	5	l.	l.	PROPN
ejpam-3448	577	6	loday	loday	PROPN
ejpam-3448	577	7	.	.	PUNCT
ejpam-3448	578	1	inversion	inversion	NOUN
ejpam-3448	578	2	of	of	ADP
ejpam-3448	578	3	integral	integral	ADJ
ejpam-3448	578	4	series	series	NOUN
ejpam-3448	578	5	enumerating	enumerate	VERB
ejpam-3448	578	6	planar	planar	ADJ
ejpam-3448	578	7	trees	tree	NOUN
ejpam-3448	578	8	.	.	PUNCT
ejpam-3448	579	1	séminaire	séminaire	PROPN
ejpam-3448	579	2	lotharingien	lotharingien	PROPN
ejpam-3448	579	3	de	de	PROPN
ejpam-3448	579	4	combinatoire	combinatoire	NOUN
ejpam-3448	579	5	,	,	PUNCT
ejpam-3448	579	6	53:16	53:16	NUM
ejpam-3448	579	7	,	,	PUNCT
ejpam-3448	579	8	2004	2004	NUM
ejpam-3448	579	9	.	.	PUNCT
ejpam-3448	580	1	[	[	X
ejpam-3448	580	2	6	6	NUM
ejpam-3448	580	3	]	]	PUNCT
ejpam-3448	580	4	j.	j.	PROPN
ejpam-3448	580	5	l.	l.	PROPN
ejpam-3448	580	6	loday	loday	PROPN
ejpam-3448	580	7	.	.	PUNCT
ejpam-3448	581	1	realization	realization	NOUN
ejpam-3448	581	2	of	of	ADP
ejpam-3448	581	3	the	the	DET
ejpam-3448	581	4	stasheff	stasheff	NOUN
ejpam-3448	581	5	polytope	polytope	NOUN
ejpam-3448	581	6	.	.	PUNCT
ejpam-3448	582	1	archive	archive	NOUN
ejpam-3448	582	2	der	der	PROPN
ejpam-3448	582	3	mathematik	mathematik	PROPN
ejpam-3448	582	4	,	,	PUNCT
ejpam-3448	582	5	(	(	PUNCT
ejpam-3448	582	6	83):267	83):267	NUM
ejpam-3448	582	7	–	–	PUNCT
ejpam-3448	582	8	278	278	NUM
ejpam-3448	582	9	,	,	PUNCT
ejpam-3448	582	10	2004	2004	NUM
ejpam-3448	582	11	.	.	PUNCT
ejpam-3448	583	1	[	[	X
ejpam-3448	583	2	7	7	X
ejpam-3448	583	3	]	]	X
ejpam-3448	583	4	j.	j.	PROPN
ejpam-3448	583	5	l.	l.	PROPN
ejpam-3448	583	6	loday	loday	PROPN
ejpam-3448	583	7	.	.	PUNCT
ejpam-3448	584	1	parking	parking	NOUN
ejpam-3448	584	2	functions	function	NOUN
ejpam-3448	584	3	and	and	CCONJ
ejpam-3448	584	4	triangulation	triangulation	NOUN
ejpam-3448	584	5	of	of	ADP
ejpam-3448	584	6	the	the	DET
ejpam-3448	584	7	associahedron	associahedron	NOUN
ejpam-3448	584	8	.	.	PUNCT
ejpam-3448	585	1	in	in	ADP
ejpam-3448	585	2	categories	category	NOUN
ejpam-3448	585	3	in	in	ADP
ejpam-3448	585	4	algebra	algebra	NOUN
ejpam-3448	585	5	,	,	PUNCT
ejpam-3448	585	6	geometry	geometry	NOUN
ejpam-3448	585	7	and	and	CCONJ
ejpam-3448	585	8	mathematical	mathematical	ADJ
ejpam-3448	585	9	physics	physics	NOUN
ejpam-3448	585	10	,	,	PUNCT
ejpam-3448	585	11	volume	volume	NOUN
ejpam-3448	585	12	431	431	NUM
ejpam-3448	585	13	of	of	ADP
ejpam-3448	585	14	contemporary	contemporary	ADJ
ejpam-3448	585	15	mathematics	mathematic	NOUN
ejpam-3448	585	16	,	,	PUNCT
ejpam-3448	585	17	pages	page	NOUN
ejpam-3448	585	18	327–340	327–340	NUM
ejpam-3448	585	19	.	.	PUNCT
ejpam-3448	586	1	american	american	PROPN
ejpam-3448	586	2	mathematical	mathematical	PROPN
ejpam-3448	586	3	society	society	NOUN
ejpam-3448	586	4	,	,	PUNCT
ejpam-3448	586	5	providence	providence	NOUN
ejpam-3448	586	6	,	,	PUNCT
ejpam-3448	586	7	ri	ri	NOUN
ejpam-3448	586	8	,	,	PUNCT
ejpam-3448	586	9	2007	2007	NUM
ejpam-3448	586	10	.	.	PUNCT
ejpam-3448	587	1	[	[	X
ejpam-3448	587	2	8	8	NUM
ejpam-3448	587	3	]	]	PUNCT
ejpam-3448	587	4	m.	m.	NOUN
ejpam-3448	587	5	markl	markl	PROPN
ejpam-3448	587	6	.	.	PUNCT
ejpam-3448	587	7	models	model	NOUN
ejpam-3448	587	8	for	for	ADP
ejpam-3448	587	9	operads	operad	NOUN
ejpam-3448	587	10	.	.	PUNCT
ejpam-3448	588	1	communications	communication	NOUN
ejpam-3448	588	2	in	in	ADP
ejpam-3448	588	3	algebra	algebra	NOUN
ejpam-3448	588	4	,	,	PUNCT
ejpam-3448	588	5	24(4):1471–1500	24(4):1471–1500	NUM
ejpam-3448	588	6	,	,	PUNCT
ejpam-3448	588	7	1996	1996	NUM
ejpam-3448	588	8	.	.	PUNCT
ejpam-3448	589	1	[	[	X
ejpam-3448	589	2	9	9	NUM
ejpam-3448	589	3	]	]	PUNCT
ejpam-3448	589	4	m.	m.	NOUN
ejpam-3448	589	5	markl	markl	PROPN
ejpam-3448	589	6	.	.	PUNCT
ejpam-3448	589	7	simplex	simplex	PROPN
ejpam-3448	589	8	,	,	PUNCT
ejpam-3448	589	9	associahedron	associahedron	NOUN
ejpam-3448	589	10	,	,	PUNCT
ejpam-3448	589	11	and	and	CCONJ
ejpam-3448	589	12	cyclohedron	cyclohedron	NUM
ejpam-3448	589	13	.	.	PUNCT
ejpam-3448	590	1	in	in	ADP
ejpam-3448	590	2	higher	high	ADJ
ejpam-3448	590	3	homotopy	homotopy	NOUN
ejpam-3448	590	4	structures	structure	NOUN
ejpam-3448	590	5	in	in	ADP
ejpam-3448	590	6	topology	topology	NOUN
ejpam-3448	590	7	and	and	CCONJ
ejpam-3448	590	8	mathematical	mathematical	ADJ
ejpam-3448	590	9	physics	physics	NOUN
ejpam-3448	590	10	(	(	PUNCT
ejpam-3448	590	11	poughkeepsie	poughkeepsie	PROPN
ejpam-3448	590	12	,	,	PUNCT
ejpam-3448	590	13	ny	ny	PROPN
ejpam-3448	590	14	,	,	PUNCT
ejpam-3448	590	15	1996	1996	NUM
ejpam-3448	590	16	)	)	PUNCT
ejpam-3448	590	17	,	,	PUNCT
ejpam-3448	590	18	volume	volume	NOUN
ejpam-3448	590	19	227	227	NUM
ejpam-3448	590	20	of	of	ADP
ejpam-3448	590	21	contemporary	contemporary	ADJ
ejpam-3448	590	22	mathematics	mathematic	NOUN
ejpam-3448	590	23	,	,	PUNCT
ejpam-3448	590	24	pages	page	NOUN
ejpam-3448	590	25	235–265	235–265	NUM
ejpam-3448	590	26	.	.	PUNCT
ejpam-3448	591	1	american	american	PROPN
ejpam-3448	591	2	mathematical	mathematical	PROPN
ejpam-3448	591	3	society	society	NOUN
ejpam-3448	591	4	,	,	PUNCT
ejpam-3448	591	5	providence	providence	NOUN
ejpam-3448	591	6	,	,	PUNCT
ejpam-3448	591	7	ri	ri	NOUN
ejpam-3448	591	8	,	,	PUNCT
ejpam-3448	591	9	1999	1999	NUM
ejpam-3448	591	10	.	.	PUNCT
ejpam-3448	592	1	[	[	X
ejpam-3448	592	2	10	10	NUM
ejpam-3448	592	3	]	]	PUNCT
ejpam-3448	592	4	m.	m.	NOUN
ejpam-3448	592	5	markl	markl	PROPN
ejpam-3448	592	6	,	,	PUNCT
ejpam-3448	592	7	s.	s.	PROPN
ejpam-3448	592	8	shnider	shnider	PROPN
ejpam-3448	592	9	,	,	PUNCT
ejpam-3448	592	10	and	and	CCONJ
ejpam-3448	592	11	j.	j.	PROPN
ejpam-3448	592	12	stasheff	stasheff	PROPN
ejpam-3448	592	13	.	.	PUNCT
ejpam-3448	593	1	operads	operad	NOUN
ejpam-3448	593	2	in	in	ADP
ejpam-3448	593	3	algebra	algebra	NOUN
ejpam-3448	593	4	,	,	PUNCT
ejpam-3448	593	5	topology	topology	NOUN
ejpam-3448	593	6	and	and	CCONJ
ejpam-3448	593	7	physics	physics	NOUN
ejpam-3448	593	8	.	.	PUNCT
ejpam-3448	594	1	mathematical	mathematical	ADJ
ejpam-3448	594	2	surveys	survey	NOUN
ejpam-3448	594	3	and	and	CCONJ
ejpam-3448	594	4	monographs	monograph	NOUN
ejpam-3448	594	5	.	.	PUNCT
ejpam-3448	595	1	american	american	PROPN
ejpam-3448	595	2	mathematical	mathematical	PROPN
ejpam-3448	595	3	society	society	NOUN
ejpam-3448	595	4	,	,	PUNCT
ejpam-3448	595	5	2007	2007	NUM
ejpam-3448	595	6	.	.	PUNCT
ejpam-3448	596	1	[	[	X
ejpam-3448	596	2	11	11	NUM
ejpam-3448	596	3	]	]	PUNCT
ejpam-3448	596	4	j.	j.	PROPN
ejpam-3448	596	5	riordan	riordan	PROPN
ejpam-3448	596	6	.	.	PUNCT
ejpam-3448	597	1	combinatorial	combinatorial	ADJ
ejpam-3448	597	2	identities	identity	NOUN
ejpam-3448	597	3	.	.	PUNCT
ejpam-3448	598	1	r.	r.	PROPN
ejpam-3448	598	2	e.	e.	PROPN
ejpam-3448	598	3	krieger	krieger	PROPN
ejpam-3448	598	4	pub	pub	PROPN
ejpam-3448	598	5	.	.	PUNCT
ejpam-3448	599	1	co.	co.	PROPN
ejpam-3448	599	2	,	,	PUNCT
ejpam-3448	599	3	1979	1979	NUM
ejpam-3448	599	4	.	.	PUNCT
ejpam-3448	600	1	[	[	X
ejpam-3448	600	2	12	12	NUM
ejpam-3448	600	3	]	]	PUNCT
ejpam-3448	600	4	s.	s.	PROPN
ejpam-3448	600	5	shnider	shnider	PROPN
ejpam-3448	600	6	and	and	CCONJ
ejpam-3448	600	7	s.	s.	PROPN
ejpam-3448	600	8	sternberg	sternberg	PROPN
ejpam-3448	600	9	.	.	PUNCT
ejpam-3448	601	1	quantum	quantum	ADJ
ejpam-3448	601	2	groups	group	NOUN
ejpam-3448	601	3	.	.	PUNCT
ejpam-3448	602	1	graduate	graduate	NOUN
ejpam-3448	602	2	texts	text	NOUN
ejpam-3448	602	3	in	in	ADP
ejpam-3448	602	4	mathematical	mathematical	ADJ
ejpam-3448	602	5	physics	physics	PROPN
ejpam-3448	602	6	,	,	PUNCT
ejpam-3448	602	7	ii	ii	PROPN
ejpam-3448	602	8	.	.	PUNCT
ejpam-3448	602	9	international	international	PROPN
ejpam-3448	602	10	press	press	PROPN
ejpam-3448	602	11	,	,	PUNCT
ejpam-3448	602	12	cambridge	cambridge	PROPN
ejpam-3448	602	13	,	,	PUNCT
ejpam-3448	602	14	ma	ma	PROPN
ejpam-3448	602	15	,	,	PUNCT
ejpam-3448	602	16	1993	1993	NUM
ejpam-3448	602	17	.	.	PUNCT
ejpam-3448	603	1	from	from	ADP
ejpam-3448	603	2	coalgebras	coalgebra	NOUN
ejpam-3448	603	3	to	to	ADP
ejpam-3448	603	4	drinfel’d	drinfel’d	PROPN
ejpam-3448	603	5	algebras	algebras	PROPN
ejpam-3448	603	6	,	,	PUNCT
ejpam-3448	603	7	a	a	DET
ejpam-3448	603	8	guided	guide	VERB
ejpam-3448	603	9	tour	tour	NOUN
ejpam-3448	603	10	.	.	PUNCT
ejpam-3448	604	1	[	[	X
ejpam-3448	604	2	13	13	NUM
ejpam-3448	604	3	]	]	PUNCT
ejpam-3448	604	4	j.	j.	PROPN
ejpam-3448	604	5	stasheff	stasheff	PROPN
ejpam-3448	604	6	.	.	PUNCT
ejpam-3448	605	1	homotopy	homotopy	PROPN
ejpam-3448	605	2	associative	associative	ADJ
ejpam-3448	605	3	h	h	NOUN
ejpam-3448	605	4	-	-	PUNCT
ejpam-3448	605	5	spaces	space	NOUN
ejpam-3448	605	6	i.	i.	PROPN
ejpam-3448	605	7	ii	ii	PROPN
ejpam-3448	605	8	,	,	PUNCT
ejpam-3448	605	9	transactions	transaction	NOUN
ejpam-3448	605	10	of	of	ADP
ejpam-3448	605	11	the	the	DET
ejpam-3448	605	12	american	american	PROPN
ejpam-3448	605	13	mathematical	mathematical	PROPN
ejpam-3448	605	14	society	society	NOUN
ejpam-3448	605	15	,	,	PUNCT
ejpam-3448	605	16	(	(	PUNCT
ejpam-3448	605	17	108):275–312	108):275–312	NUM
ejpam-3448	605	18	,	,	PUNCT
ejpam-3448	605	19	1963	1963	NUM
ejpam-3448	605	20	.	.	PUNCT