id	sid	tid	token	lemma	pos
ejpam-4783	1	1	european	european	PROPN
ejpam-4783	1	2	journal	journal	PROPN
ejpam-4783	1	3	of	of	ADP
ejpam-4783	1	4	pure	pure	ADJ
ejpam-4783	1	5	and	and	CCONJ
ejpam-4783	1	6	applied	apply	VERB
ejpam-4783	1	7	mathematics	mathematic	NOUN
ejpam-4783	1	8	vol	vol	NOUN
ejpam-4783	1	9	.	.	PUNCT
ejpam-4783	2	1	16	16	NUM
ejpam-4783	2	2	,	,	PUNCT
ejpam-4783	2	3	no	no	INTJ
ejpam-4783	2	4	.	.	NOUN
ejpam-4783	2	5	3	3	NUM
ejpam-4783	2	6	,	,	PUNCT
ejpam-4783	2	7	2023	2023	NUM
ejpam-4783	2	8	,	,	PUNCT
ejpam-4783	2	9	1580	1580	NUM
ejpam-4783	2	10	-	-	SYM
ejpam-4783	2	11	1591	1591	NUM
ejpam-4783	2	12	issn	issn	PROPN
ejpam-4783	2	13	1307	1307	NUM
ejpam-4783	2	14	-	-	SYM
ejpam-4783	2	15	5543	5543	NUM
ejpam-4783	2	16	–	–	PUNCT
ejpam-4783	2	17	ejpam.com	ejpam.com	X
ejpam-4783	2	18	published	publish	VERB
ejpam-4783	2	19	by	by	ADP
ejpam-4783	2	20	new	new	PROPN
ejpam-4783	2	21	york	york	PROPN
ejpam-4783	2	22	business	business	PROPN
ejpam-4783	2	23	global	global	PROPN
ejpam-4783	2	24	schultz	schultz	PROPN
ejpam-4783	2	25	and	and	CCONJ
ejpam-4783	2	26	modified	modify	VERB
ejpam-4783	2	27	schultz	schultz	NOUN
ejpam-4783	2	28	polynomials	polynomial	NOUN
ejpam-4783	2	29	of	of	ADP
ejpam-4783	2	30	edges	edge	NOUN
ejpam-4783	2	31	induce	induce	VERB
ejpam-4783	2	32	chain	chain	NOUN
ejpam-4783	2	33	and	and	CCONJ
ejpam-4783	2	34	ring	ring	NOUN
ejpam-4783	2	35	for	for	ADP
ejpam-4783	2	36	hexagonal	hexagonal	ADJ
ejpam-4783	2	37	graphs	graph	NOUN
ejpam-4783	2	38	asmaa	asmaa	PROPN
ejpam-4783	2	39	s.	s.	PROPN
ejpam-4783	2	40	aziz1,∗	aziz1,∗	PROPN
ejpam-4783	2	41	,	,	PUNCT
ejpam-4783	2	42	haitham	haitham	PROPN
ejpam-4783	2	43	n.	n.	PROPN
ejpam-4783	2	44	mohammed2	mohammed2	PROPN
ejpam-4783	2	45	,	,	PUNCT
ejpam-4783	3	1	ahmed	ahmed	PROPN
ejpam-4783	3	2	m.	m.	PROPN
ejpam-4783	3	3	ali	ali	PROPN
ejpam-4783	3	4	1	1	PROPN
ejpam-4783	3	5	1department	1department	NUM
ejpam-4783	3	6	of	of	ADP
ejpam-4783	3	7	mathematics	mathematic	NOUN
ejpam-4783	3	8	,	,	PUNCT
ejpam-4783	3	9	college	college	NOUN
ejpam-4783	3	10	of	of	ADP
ejpam-4783	3	11	computer	computer	NOUN
ejpam-4783	3	12	sciences	sciences	PROPN
ejpam-4783	3	13	and	and	CCONJ
ejpam-4783	3	14	mathematics	mathematics	PROPN
ejpam-4783	3	15	,	,	PUNCT
ejpam-4783	3	16	mosul	mosul	PROPN
ejpam-4783	3	17	university	university	PROPN
ejpam-4783	3	18	,	,	PUNCT
ejpam-4783	3	19	mosul	mosul	PROPN
ejpam-4783	3	20	,	,	PUNCT
ejpam-4783	3	21	iraq	iraq	PROPN
ejpam-4783	3	22	2nineveh	2nineveh	NUM
ejpam-4783	3	23	education	education	NOUN
ejpam-4783	3	24	directorate	directorate	NOUN
ejpam-4783	3	25	,	,	PUNCT
ejpam-4783	3	26	mosul	mosul	PROPN
ejpam-4783	3	27	,	,	PUNCT
ejpam-4783	3	28	iraq	iraq	PROPN
ejpam-4783	3	29	abstract	abstract	NOUN
ejpam-4783	3	30	.	.	PUNCT
ejpam-4783	4	1	schultz	schultz	PROPN
ejpam-4783	4	2	polynomial	polynomial	PROPN
ejpam-4783	4	3	is	be	AUX
ejpam-4783	4	4	one	one	NUM
ejpam-4783	4	5	of	of	ADP
ejpam-4783	4	6	the	the	DET
ejpam-4783	4	7	must	must	AUX
ejpam-4783	4	8	significant	significant	ADJ
ejpam-4783	4	9	formulas	formula	NOUN
ejpam-4783	4	10	that	that	PRON
ejpam-4783	4	11	represent	represent	VERB
ejpam-4783	4	12	a	a	DET
ejpam-4783	4	13	relationship	relationship	NOUN
ejpam-4783	4	14	between	between	ADP
ejpam-4783	4	15	the	the	DET
ejpam-4783	4	16	degree	degree	NOUN
ejpam-4783	4	17	’s	’s	X
ejpam-4783	4	18	of	of	ADP
ejpam-4783	4	19	vertices	vertex	NOUN
ejpam-4783	4	20	in	in	ADP
ejpam-4783	4	21	a	a	DET
ejpam-4783	4	22	simple	simple	ADJ
ejpam-4783	4	23	connected	connected	ADJ
ejpam-4783	4	24	graph	graph	NOUN
ejpam-4783	4	25	g	g	NOUN
ejpam-4783	4	26	and	and	CCONJ
ejpam-4783	4	27	the	the	DET
ejpam-4783	4	28	distances	distance	NOUN
ejpam-4783	4	29	between	between	ADP
ejpam-4783	4	30	these	these	DET
ejpam-4783	4	31	vertices	vertex	NOUN
ejpam-4783	4	32	.	.	PUNCT
ejpam-4783	5	1	in	in	ADP
ejpam-4783	5	2	this	this	DET
ejpam-4783	5	3	work	work	NOUN
ejpam-4783	5	4	,	,	PUNCT
ejpam-4783	5	5	schultz	schultz	PROPN
ejpam-4783	5	6	and	and	CCONJ
ejpam-4783	5	7	modified	modify	VERB
ejpam-4783	5	8	schultz	schultz	NOUN
ejpam-4783	5	9	polynomials	polynomial	NOUN
ejpam-4783	5	10	,	,	PUNCT
ejpam-4783	5	11	as	as	ADV
ejpam-4783	5	12	well	well	ADV
ejpam-4783	5	13	as	as	ADP
ejpam-4783	5	14	their	their	PRON
ejpam-4783	5	15	topological	topological	ADJ
ejpam-4783	5	16	indices	index	NOUN
ejpam-4783	5	17	of	of	ADP
ejpam-4783	5	18	chain	chain	NOUN
ejpam-4783	5	19	and	and	CCONJ
ejpam-4783	5	20	ring	ring	NOUN
ejpam-4783	5	21	hexagonal	hexagonal	ADJ
ejpam-4783	5	22	graphs	graph	NOUN
ejpam-4783	5	23	,	,	PUNCT
ejpam-4783	5	24	have	have	AUX
ejpam-4783	5	25	been	be	AUX
ejpam-4783	5	26	successfully	successfully	ADV
ejpam-4783	5	27	identified	identify	VERB
ejpam-4783	5	28	.	.	PUNCT
ejpam-4783	6	1	2020	2020	NUM
ejpam-4783	6	2	mathematics	mathematics	PROPN
ejpam-4783	6	3	subject	subject	NOUN
ejpam-4783	6	4	classifications	classification	NOUN
ejpam-4783	6	5	:	:	PUNCT
ejpam-4783	6	6	05c09	05c09	NUM
ejpam-4783	6	7	,	,	PUNCT
ejpam-4783	6	8	05c31	05c31	PRON
ejpam-4783	6	9	key	key	ADJ
ejpam-4783	6	10	words	word	NOUN
ejpam-4783	6	11	and	and	CCONJ
ejpam-4783	6	12	phrases	phrase	NOUN
ejpam-4783	6	13	:	:	PUNCT
ejpam-4783	6	14	graphical	graphical	ADJ
ejpam-4783	6	15	indices	index	NOUN
ejpam-4783	6	16	,	,	PUNCT
ejpam-4783	6	17	graph	graph	NOUN
ejpam-4783	6	18	polynomials	polynomial	NOUN
ejpam-4783	6	19	1	1	NUM
ejpam-4783	6	20	.	.	PUNCT
ejpam-4783	7	1	introduction	introduction	NOUN
ejpam-4783	7	2	mathematical	mathematical	ADJ
ejpam-4783	7	3	chemistry	chemistry	NOUN
ejpam-4783	7	4	is	be	AUX
ejpam-4783	7	5	a	a	DET
ejpam-4783	7	6	field	field	NOUN
ejpam-4783	7	7	of	of	ADP
ejpam-4783	7	8	theoretical	theoretical	ADJ
ejpam-4783	7	9	chemistry	chemistry	NOUN
ejpam-4783	7	10	that	that	PRON
ejpam-4783	7	11	examines	examine	VERB
ejpam-4783	7	12	and	and	CCONJ
ejpam-4783	7	13	predicts	predict	VERB
ejpam-4783	7	14	molecule	molecule	NOUN
ejpam-4783	7	15	structure	structure	NOUN
ejpam-4783	7	16	using	use	VERB
ejpam-4783	7	17	mathematical	mathematical	ADJ
ejpam-4783	7	18	approaches	approach	NOUN
ejpam-4783	7	19	rather	rather	ADV
ejpam-4783	7	20	than	than	ADP
ejpam-4783	7	21	quantum	quantum	ADJ
ejpam-4783	7	22	mechanics	mechanic	NOUN
ejpam-4783	7	23	.	.	PUNCT
ejpam-4783	8	1	chemical	chemical	NOUN
ejpam-4783	8	2	graph	graph	NOUN
ejpam-4783	8	3	theory	theory	NOUN
ejpam-4783	8	4	is	be	AUX
ejpam-4783	8	5	a	a	DET
ejpam-4783	8	6	powerful	powerful	ADJ
ejpam-4783	8	7	method	method	NOUN
ejpam-4783	8	8	for	for	ADP
ejpam-4783	8	9	determining	determine	VERB
ejpam-4783	8	10	molecule	molecule	NOUN
ejpam-4783	8	11	structures	structure	NOUN
ejpam-4783	8	12	that	that	PRON
ejpam-4783	8	13	has	have	AUX
ejpam-4783	8	14	made	make	VERB
ejpam-4783	8	15	significant	significant	ADJ
ejpam-4783	8	16	contributions	contribution	NOUN
ejpam-4783	8	17	to	to	ADP
ejpam-4783	8	18	the	the	DET
ejpam-4783	8	19	advancement	advancement	NOUN
ejpam-4783	8	20	of	of	ADP
ejpam-4783	8	21	chemical	chemical	ADJ
ejpam-4783	8	22	science	science	NOUN
ejpam-4783	8	23	.	.	PUNCT
ejpam-4783	9	1	in	in	ADP
ejpam-4783	9	2	the	the	DET
ejpam-4783	9	3	molecular	molecular	ADJ
ejpam-4783	9	4	graph	graph	NOUN
ejpam-4783	9	5	g	g	NOUN
ejpam-4783	9	6	,	,	PUNCT
ejpam-4783	9	7	atoms	atom	NOUN
ejpam-4783	9	8	and	and	CCONJ
ejpam-4783	9	9	bonds	bond	NOUN
ejpam-4783	9	10	are	be	AUX
ejpam-4783	9	11	represented	represent	VERB
ejpam-4783	9	12	by	by	ADP
ejpam-4783	9	13	vertices	vertex	NOUN
ejpam-4783	9	14	and	and	CCONJ
ejpam-4783	9	15	edges	edge	NOUN
ejpam-4783	9	16	,	,	PUNCT
ejpam-4783	9	17	respectively	respectively	ADV
ejpam-4783	9	18	.	.	PUNCT
ejpam-4783	10	1	the	the	DET
ejpam-4783	10	2	order	order	NOUN
ejpam-4783	10	3	of	of	ADP
ejpam-4783	10	4	the	the	DET
ejpam-4783	10	5	graph	graph	NOUN
ejpam-4783	10	6	g	g	NOUN
ejpam-4783	10	7	in	in	ADP
ejpam-4783	10	8	graph	graph	NOUN
ejpam-4783	10	9	theory	theory	NOUN
ejpam-4783	10	10	is	be	AUX
ejpam-4783	10	11	p	p	NOUN
ejpam-4783	10	12	=	=	SYM
ejpam-4783	10	13	p(g	p(g	NOUN
ejpam-4783	10	14	)	)	PUNCT
ejpam-4783	10	15	=	=	SYM
ejpam-4783	10	16	|v	|v	PROPN
ejpam-4783	10	17	(	(	PUNCT
ejpam-4783	10	18	g)|	g)|	NOUN
ejpam-4783	10	19	,	,	PUNCT
ejpam-4783	10	20	and	and	CCONJ
ejpam-4783	10	21	the	the	DET
ejpam-4783	10	22	size	size	NOUN
ejpam-4783	10	23	of	of	ADP
ejpam-4783	10	24	g	g	PROPN
ejpam-4783	10	25	is	be	AUX
ejpam-4783	10	26	q	q	NOUN
ejpam-4783	10	27	=	=	PUNCT
ejpam-4783	10	28	q(g	q(g	ADJ
ejpam-4783	10	29	)	)	PUNCT
ejpam-4783	10	30	=	=	PUNCT
ejpam-4783	11	1	|e(g)|	|e(g)|	NOUN
ejpam-4783	11	2	,	,	PUNCT
ejpam-4783	11	3	while	while	SCONJ
ejpam-4783	11	4	the	the	DET
ejpam-4783	11	5	degree	degree	NOUN
ejpam-4783	11	6	of	of	ADP
ejpam-4783	11	7	η	η	PROPN
ejpam-4783	11	8	∈	∈	PROPN
ejpam-4783	11	9	v	v	ADP
ejpam-4783	11	10	(	(	PUNCT
ejpam-4783	11	11	g	g	NOUN
ejpam-4783	11	12	)	)	PUNCT
ejpam-4783	11	13	is	be	AUX
ejpam-4783	11	14	the	the	DET
ejpam-4783	11	15	number	number	NOUN
ejpam-4783	11	16	of	of	ADP
ejpam-4783	11	17	vertices	vertex	NOUN
ejpam-4783	11	18	joining	join	VERB
ejpam-4783	11	19	to	to	ADP
ejpam-4783	11	20	η	η	PROPN
ejpam-4783	11	21	and	and	CCONJ
ejpam-4783	11	22	denoted	denote	VERB
ejpam-4783	11	23	by	by	ADP
ejpam-4783	11	24	δη	δη	PROPN
ejpam-4783	11	25	.	.	PUNCT
ejpam-4783	12	1	furthermore	furthermore	ADV
ejpam-4783	12	2	,	,	PUNCT
ejpam-4783	12	3	the	the	DET
ejpam-4783	12	4	distance	distance	NOUN
ejpam-4783	12	5	d(µ	d(µ	PROPN
ejpam-4783	12	6	,	,	PUNCT
ejpam-4783	12	7	η	η	NOUN
ejpam-4783	12	8	)	)	PUNCT
ejpam-4783	12	9	=	=	SYM
ejpam-4783	12	10	d(µ	d(µ	PROPN
ejpam-4783	12	11	,	,	PUNCT
ejpam-4783	12	12	η	η	PROPN
ejpam-4783	12	13	|	|	ADP
ejpam-4783	12	14	g	g	NOUN
ejpam-4783	12	15	)	)	PUNCT
ejpam-4783	12	16	between	between	ADP
ejpam-4783	12	17	any	any	DET
ejpam-4783	12	18	two	two	NUM
ejpam-4783	12	19	vertices	vertex	NOUN
ejpam-4783	12	20	µ	µ	VERB
ejpam-4783	12	21	and	and	CCONJ
ejpam-4783	12	22	η	η	PROPN
ejpam-4783	12	23	is	be	AUX
ejpam-4783	12	24	the	the	DET
ejpam-4783	12	25	length	length	NOUN
ejpam-4783	12	26	of	of	ADP
ejpam-4783	12	27	the	the	DET
ejpam-4783	12	28	shortest	short	ADJ
ejpam-4783	12	29	path	path	NOUN
ejpam-4783	12	30	connecting	connect	VERB
ejpam-4783	12	31	them	they	PRON
ejpam-4783	12	32	in	in	ADP
ejpam-4783	12	33	g.	g.	PROPN
ejpam-4783	12	34	the	the	DET
ejpam-4783	12	35	greatest	great	ADJ
ejpam-4783	12	36	distance	distance	NOUN
ejpam-4783	12	37	in	in	ADP
ejpam-4783	12	38	g	g	PROPN
ejpam-4783	12	39	is	be	AUX
ejpam-4783	12	40	the	the	DET
ejpam-4783	12	41	diameter	diameter	NOUN
ejpam-4783	12	42	denoted	denote	VERB
ejpam-4783	12	43	by	by	ADP
ejpam-4783	12	44	diam(g	diam(g	PROPN
ejpam-4783	12	45	)	)	PUNCT
ejpam-4783	12	46	,	,	PUNCT
ejpam-4783	13	1	[	[	X
ejpam-4783	13	2	7	7	NUM
ejpam-4783	13	3	]	]	PUNCT
ejpam-4783	13	4	.	.	PUNCT
ejpam-4783	14	1	let	let	VERB
ejpam-4783	14	2	d(g	d(g	PROPN
ejpam-4783	14	3	,	,	PUNCT
ejpam-4783	14	4	ξ	ξ	X
ejpam-4783	14	5	)	)	PUNCT
ejpam-4783	14	6	express	express	VERB
ejpam-4783	14	7	the	the	DET
ejpam-4783	14	8	number	number	NOUN
ejpam-4783	14	9	of	of	ADP
ejpam-4783	14	10	random	random	ADJ
ejpam-4783	14	11	pair	pair	NOUN
ejpam-4783	14	12	of	of	ADP
ejpam-4783	14	13	vertices	vertex	NOUN
ejpam-4783	14	14	in	in	ADP
ejpam-4783	14	15	g	g	NOUN
ejpam-4783	14	16	with	with	ADP
ejpam-4783	14	17	ξ	ξ	PROPN
ejpam-4783	14	18	distance	distance	NOUN
ejpam-4783	14	19	.	.	PUNCT
ejpam-4783	15	1	let	let	VERB
ejpam-4783	15	2	aξ(g	aξ(g	PUNCT
ejpam-4783	15	3	)	)	PUNCT
ejpam-4783	15	4	is	be	AUX
ejpam-4783	15	5	the	the	DET
ejpam-4783	15	6	set	set	NOUN
ejpam-4783	15	7	of	of	ADP
ejpam-4783	15	8	all	all	DET
ejpam-4783	15	9	these	these	DET
ejpam-4783	15	10	pairs	pair	NOUN
ejpam-4783	16	1	such	such	ADJ
ejpam-4783	16	2	that	that	DET
ejpam-4783	16	3	|aξ(g)|	|aξ(g)|	NOUN
ejpam-4783	16	4	=	=	PUNCT
ejpam-4783	16	5	|aξ|	|aξ|	NOUN
ejpam-4783	17	1	=	=	SYM
ejpam-4783	17	2	d(g	d(g	PROPN
ejpam-4783	17	3	,	,	PUNCT
ejpam-4783	17	4	ξ	ξ	NOUN
ejpam-4783	17	5	)	)	PUNCT
ejpam-4783	17	6	and	and	CCONJ
ejpam-4783	17	7	∑diam(g	∑diam(g	NUM
ejpam-4783	17	8	)	)	PUNCT
ejpam-4783	18	1	ξ=1	ξ=1	NUM
ejpam-4783	18	2	d(g	d(g	PROPN
ejpam-4783	18	3	,	,	PUNCT
ejpam-4783	18	4	ξ	ξ	X
ejpam-4783	18	5	)	)	PUNCT
ejpam-4783	18	6	=	=	SYM
ejpam-4783	19	1	(	(	PUNCT
ejpam-4783	19	2	p	p	NOUN
ejpam-4783	19	3	2	2	NUM
ejpam-4783	19	4	)	)	PUNCT
ejpam-4783	19	5	,	,	PUNCT
ejpam-4783	19	6	where	where	SCONJ
ejpam-4783	19	7	(	(	PUNCT
ejpam-4783	19	8	p	p	NOUN
ejpam-4783	19	9	2	2	NUM
ejpam-4783	19	10	)	)	PUNCT
ejpam-4783	19	11	represents	represent	VERB
ejpam-4783	19	12	the	the	DET
ejpam-4783	19	13	number	number	NOUN
ejpam-4783	19	14	of	of	ADP
ejpam-4783	19	15	unordered	unordered	ADJ
ejpam-4783	19	16	pairs	pair	NOUN
ejpam-4783	19	17	of	of	ADP
ejpam-4783	19	18	different	different	ADJ
ejpam-4783	19	19	vertices	vertex	NOUN
ejpam-4783	19	20	in	in	ADP
ejpam-4783	19	21	g,[12	g,[12	NOUN
ejpam-4783	19	22	]	]	X
ejpam-4783	19	23	.	.	PUNCT
ejpam-4783	20	1	∗corresponding	∗corresponde	VERB
ejpam-4783	20	2	author	author	NOUN
ejpam-4783	20	3	.	.	PUNCT
ejpam-4783	21	1	doi	doi	NOUN
ejpam-4783	21	2	:	:	PUNCT
ejpam-4783	21	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4783	https://doi.org/10.29020/nybg.ejpam.v16i3.4783	NOUN
ejpam-4783	21	4	email	email	NOUN
ejpam-4783	21	5	addresses	address	NOUN
ejpam-4783	21	6	:	:	PUNCT
ejpam-4783	21	7	asmaas982@uomosul.edu.iq(a	asmaas982@uomosul.edu.iq(a	NOUN
ejpam-4783	21	8	.	.	PUNCT
ejpam-4783	22	1	s.	s.	PROPN
ejpam-4783	22	2	aziz	aziz	PROPN
ejpam-4783	22	3	)	)	PUNCT
ejpam-4783	22	4	,	,	PUNCT
ejpam-4783	22	5	haytham.nashwan@yahoo.com(h	haytham.nashwan@yahoo.com(h	PROPN
ejpam-4783	22	6	.	.	PUNCT
ejpam-4783	23	1	n.	n.	PROPN
ejpam-4783	23	2	mohammed	mohammed	PROPN
ejpam-4783	23	3	)	)	PUNCT
ejpam-4783	23	4	,	,	PUNCT
ejpam-4783	23	5	ahmedgraph@uomosul.edu.iq(a	ahmedgraph@uomosul.edu.iq(a	PROPN
ejpam-4783	23	6	.	.	PUNCT
ejpam-4783	23	7	m.	m.	PROPN
ejpam-4783	23	8	ali	ali	PROPN
ejpam-4783	23	9	)	)	PUNCT
ejpam-4783	23	10	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4783	24	1	1580	1580	NUM
ejpam-4783	24	2	©	©	PROPN
ejpam-4783	24	3	2023	2023	NUM
ejpam-4783	24	4	ejpam	ejpam	NOUN
ejpam-4783	24	5	all	all	DET
ejpam-4783	24	6	rights	right	NOUN
ejpam-4783	24	7	reserved	reserve	VERB
ejpam-4783	24	8	.	.	PUNCT
ejpam-4783	25	1	1581	1581	NUM
ejpam-4783	25	2	topological	topological	ADJ
ejpam-4783	25	3	indices	index	NOUN
ejpam-4783	25	4	were	be	AUX
ejpam-4783	25	5	first	first	ADV
ejpam-4783	25	6	used	use	VERB
ejpam-4783	25	7	in	in	ADP
ejpam-4783	25	8	biology	biology	NOUN
ejpam-4783	25	9	and	and	CCONJ
ejpam-4783	25	10	chemistry	chemistry	NOUN
ejpam-4783	25	11	in	in	ADP
ejpam-4783	25	12	1947	1947	NUM
ejpam-4783	25	13	when	when	SCONJ
ejpam-4783	25	14	scientist	scientist	PROPN
ejpam-4783	25	15	harold	harold	PROPN
ejpam-4783	25	16	wiener	wiener	PROPN
ejpam-4783	25	17	[	[	X
ejpam-4783	25	18	20	20	NUM
ejpam-4783	25	19	]	]	PUNCT
ejpam-4783	25	20	created	create	VERB
ejpam-4783	25	21	the	the	DET
ejpam-4783	25	22	wiener	wiener	NOUN
ejpam-4783	25	23	index	index	NOUN
ejpam-4783	25	24	to	to	PART
ejpam-4783	25	25	show	show	VERB
ejpam-4783	25	26	connections	connection	NOUN
ejpam-4783	25	27	between	between	ADP
ejpam-4783	25	28	the	the	DET
ejpam-4783	25	29	physicochemical	physicochemical	ADJ
ejpam-4783	25	30	features	feature	NOUN
ejpam-4783	25	31	of	of	ADP
ejpam-4783	25	32	organic	organic	ADJ
ejpam-4783	25	33	molecules	molecule	NOUN
ejpam-4783	25	34	in	in	ADP
ejpam-4783	25	35	molecular	molecular	ADJ
ejpam-4783	25	36	graphs	graph	NOUN
ejpam-4783	25	37	.	.	PUNCT
ejpam-4783	26	1	the	the	DET
ejpam-4783	26	2	wiener	wiener	NOUN
ejpam-4783	26	3	index	index	NOUN
ejpam-4783	26	4	,	,	PUNCT
ejpam-4783	26	5	abbreviated	abbreviate	VERB
ejpam-4783	26	6	w(g	w(g	PROPN
ejpam-4783	26	7	)	)	PUNCT
ejpam-4783	26	8	,	,	PUNCT
ejpam-4783	26	9	is	be	AUX
ejpam-4783	26	10	the	the	DET
ejpam-4783	26	11	sum	sum	NOUN
ejpam-4783	26	12	of	of	ADP
ejpam-4783	26	13	all	all	DET
ejpam-4783	26	14	distances	distance	NOUN
ejpam-4783	26	15	between	between	ADP
ejpam-4783	26	16	all	all	DET
ejpam-4783	26	17	unordered	unordered	ADJ
ejpam-4783	26	18	(	(	PUNCT
ejpam-4783	26	19	µ	µ	X
ejpam-4783	26	20	,	,	PUNCT
ejpam-4783	26	21	η	η	NOUN
ejpam-4783	26	22	)	)	PUNCT
ejpam-4783	26	23	pairs	pair	NOUN
ejpam-4783	26	24	in	in	ADP
ejpam-4783	26	25	a	a	DET
ejpam-4783	26	26	connected	connected	ADJ
ejpam-4783	26	27	graph	graph	NOUN
ejpam-4783	26	28	g	g	NOUN
ejpam-4783	26	29	:	:	PUNCT
ejpam-4783	26	30	w	w	X
ejpam-4783	26	31	(	(	PUNCT
ejpam-4783	26	32	g	g	NOUN
ejpam-4783	26	33	)	)	PUNCT
ejpam-4783	26	34	=	=	PUNCT
ejpam-4783	26	35	∑	∑	PUNCT
ejpam-4783	26	36	{	{	PUNCT
ejpam-4783	26	37	µ,η}⊆v	µ,η}⊆v	X
ejpam-4783	26	38	(	(	PUNCT
ejpam-4783	26	39	g	g	NOUN
ejpam-4783	26	40	)	)	PUNCT
ejpam-4783	26	41	d(µ	d(µ	PROPN
ejpam-4783	26	42	,	,	PUNCT
ejpam-4783	26	43	η	η	PROPN
ejpam-4783	26	44	)	)	PUNCT
ejpam-4783	26	45	;	;	PUNCT
ejpam-4783	26	46	where	where	SCONJ
ejpam-4783	26	47	,	,	PUNCT
ejpam-4783	26	48	d(µ	d(µ	PROPN
ejpam-4783	26	49	,	,	PUNCT
ejpam-4783	26	50	η	η	PROPN
ejpam-4783	26	51	)	)	PUNCT
ejpam-4783	26	52	indicates	indicate	VERB
ejpam-4783	26	53	the	the	DET
ejpam-4783	26	54	distance	distance	NOUN
ejpam-4783	26	55	between	between	ADP
ejpam-4783	26	56	µ	µ	NOUN
ejpam-4783	26	57	and	and	CCONJ
ejpam-4783	26	58	η	η	PROPN
ejpam-4783	26	59	.	.	PROPN
ejpam-4783	26	60	based	base	VERB
ejpam-4783	26	61	on	on	ADP
ejpam-4783	26	62	the	the	DET
ejpam-4783	26	63	wiener	wiener	NOUN
ejpam-4783	26	64	index	index	NOUN
ejpam-4783	26	65	,	,	PUNCT
ejpam-4783	26	66	hosoya	hosoya	VERB
ejpam-4783	26	67	in	in	ADP
ejpam-4783	26	68	1988	1988	NUM
ejpam-4783	26	69	[	[	X
ejpam-4783	26	70	14	14	NUM
ejpam-4783	26	71	]	]	PUNCT
ejpam-4783	26	72	invented	invent	VERB
ejpam-4783	26	73	the	the	DET
ejpam-4783	26	74	new	new	ADJ
ejpam-4783	26	75	hosoya	hosoya	NOUN
ejpam-4783	26	76	polynomial	polynomial	ADJ
ejpam-4783	26	77	h(g;x	h(g;x	PROPN
ejpam-4783	26	78	)	)	PUNCT
ejpam-4783	26	79	which	which	PRON
ejpam-4783	26	80	is	be	AUX
ejpam-4783	26	81	defined	define	VERB
ejpam-4783	26	82	as	as	ADP
ejpam-4783	26	83	:	:	PUNCT
ejpam-4783	26	84	h(g;x	h(g;x	NUM
ejpam-4783	26	85	)	)	PUNCT
ejpam-4783	26	86	=	=	PUNCT
ejpam-4783	26	87	∑	∑	PUNCT
ejpam-4783	26	88	{	{	PUNCT
ejpam-4783	26	89	µ,η}⊆v	µ,η}⊆v	X
ejpam-4783	26	90	(	(	PUNCT
ejpam-4783	26	91	g	g	NOUN
ejpam-4783	26	92	)	)	PUNCT
ejpam-4783	26	93	xd(µ,η	xd(µ,η	NUM
ejpam-4783	26	94	)	)	PUNCT
ejpam-4783	26	95	;	;	PUNCT
ejpam-4783	26	96	recently	recently	ADV
ejpam-4783	26	97	,	,	PUNCT
ejpam-4783	26	98	many	many	ADJ
ejpam-4783	26	99	other	other	ADJ
ejpam-4783	26	100	polynomials	polynomial	NOUN
ejpam-4783	26	101	have	have	AUX
ejpam-4783	26	102	been	be	AUX
ejpam-4783	26	103	obtainted	obtainte	VERB
ejpam-4783	26	104	such	such	ADJ
ejpam-4783	26	105	as	as	ADP
ejpam-4783	26	106	detour	detour	NOUN
ejpam-4783	26	107	polynomial	polynomial	ADJ
ejpam-4783	26	108	[	[	X
ejpam-4783	26	109	3	3	NUM
ejpam-4783	26	110	]	]	PUNCT
ejpam-4783	26	111	,	,	PUNCT
ejpam-4783	26	112	m	m	NOUN
ejpam-4783	26	113	-	-	ADJ
ejpam-4783	26	114	polynomial	polynomial	ADJ
ejpam-4783	26	115	[	[	X
ejpam-4783	26	116	16],[17	16],[17	PROPN
ejpam-4783	26	117	]	]	X
ejpam-4783	26	118	.	.	PUNCT
ejpam-4783	27	1	the	the	DET
ejpam-4783	27	2	schultz	schultz	PROPN
ejpam-4783	27	3	index	index	PROPN
ejpam-4783	27	4	(	(	PUNCT
ejpam-4783	27	5	sc	sc	PROPN
ejpam-4783	27	6	)	)	PUNCT
ejpam-4783	27	7	is	be	AUX
ejpam-4783	27	8	another	another	DET
ejpam-4783	27	9	based	base	VERB
ejpam-4783	27	10	structure	structure	NOUN
ejpam-4783	27	11	which	which	PRON
ejpam-4783	27	12	was	be	AUX
ejpam-4783	27	13	first	first	ADV
ejpam-4783	27	14	introduced	introduce	VERB
ejpam-4783	27	15	by	by	ADP
ejpam-4783	27	16	harry	harry	PROPN
ejpam-4783	27	17	schultz	schultz	PROPN
ejpam-4783	28	1	[	[	X
ejpam-4783	28	2	18	18	NUM
ejpam-4783	28	3	]	]	PUNCT
ejpam-4783	28	4	the	the	DET
ejpam-4783	28	5	molecular	molecular	ADJ
ejpam-4783	28	6	topological	topological	ADJ
ejpam-4783	28	7	index	index	NOUN
ejpam-4783	28	8	and	and	CCONJ
ejpam-4783	28	9	is	be	AUX
ejpam-4783	28	10	characterized	characterize	VERB
ejpam-4783	28	11	by	by	ADP
ejpam-4783	28	12	:	:	PUNCT
ejpam-4783	28	13	sc(g	sc(g	X
ejpam-4783	28	14	)	)	PUNCT
ejpam-4783	29	1	=	=	PUNCT
ejpam-4783	29	2	∑	∑	PUNCT
ejpam-4783	29	3	{	{	PUNCT
ejpam-4783	29	4	µ,η}⊆v	µ,η}⊆v	X
ejpam-4783	29	5	(	(	PUNCT
ejpam-4783	29	6	g	g	NOUN
ejpam-4783	29	7	)	)	PUNCT
ejpam-4783	29	8	(	(	PUNCT
ejpam-4783	29	9	δµ	δµ	X
ejpam-4783	29	10	+	+	PROPN
ejpam-4783	29	11	δη)d(µ	δη)d(µ	PROPN
ejpam-4783	29	12	,	,	PUNCT
ejpam-4783	29	13	η	η	NOUN
ejpam-4783	29	14	)	)	PUNCT
ejpam-4783	29	15	,	,	PUNCT
ejpam-4783	29	16	where	where	SCONJ
ejpam-4783	29	17	δµ	δµ	NOUN
ejpam-4783	29	18	is	be	AUX
ejpam-4783	29	19	the	the	DET
ejpam-4783	29	20	degree	degree	NOUN
ejpam-4783	29	21	of	of	ADP
ejpam-4783	29	22	the	the	DET
ejpam-4783	29	23	vertex	vertex	NOUN
ejpam-4783	29	24	µ	µ	X
ejpam-4783	29	25	and	and	CCONJ
ejpam-4783	29	26	δη	δη	PROPN
ejpam-4783	29	27	is	be	AUX
ejpam-4783	29	28	the	the	DET
ejpam-4783	29	29	degree	degree	NOUN
ejpam-4783	29	30	of	of	ADP
ejpam-4783	29	31	η	η	PROPN
ejpam-4783	29	32	.	.	PUNCT
ejpam-4783	30	1	the	the	DET
ejpam-4783	30	2	schultz	schultz	PROPN
ejpam-4783	30	3	index	index	NOUN
ejpam-4783	30	4	is	be	AUX
ejpam-4783	30	5	based	base	VERB
ejpam-4783	30	6	on	on	ADP
ejpam-4783	30	7	this	this	PRON
ejpam-4783	30	8	.	.	PUNCT
ejpam-4783	31	1	in	in	ADP
ejpam-4783	31	2	1997	1997	NUM
ejpam-4783	31	3	,	,	PUNCT
ejpam-4783	31	4	klavžar	klavžar	PROPN
ejpam-4783	31	5	and	and	CCONJ
ejpam-4783	31	6	gutman	gutman	NOUN
ejpam-4783	31	7	[	[	X
ejpam-4783	31	8	15	15	NUM
ejpam-4783	31	9	]	]	PUNCT
ejpam-4783	31	10	proposed	propose	VERB
ejpam-4783	31	11	the	the	DET
ejpam-4783	31	12	mod	mod	PROPN
ejpam-4783	31	13	.	.	PUNCT
ejpam-4783	32	1	sch	sch	PROPN
ejpam-4783	32	2	.	.	PROPN
ejpam-4783	32	3	index	index	PROPN
ejpam-4783	32	4	,	,	PUNCT
ejpam-4783	32	5	which	which	PRON
ejpam-4783	32	6	is	be	AUX
ejpam-4783	32	7	defined	define	VERB
ejpam-4783	32	8	as	as	ADP
ejpam-4783	32	9	:	:	PUNCT
ejpam-4783	32	10	sc∗(g	sc∗(g	PROPN
ejpam-4783	32	11	)	)	PUNCT
ejpam-4783	33	1	=	=	PUNCT
ejpam-4783	33	2	∑	∑	PUNCT
ejpam-4783	33	3	{	{	PUNCT
ejpam-4783	33	4	µ,η}⊆v	µ,η}⊆v	X
ejpam-4783	33	5	(	(	PUNCT
ejpam-4783	33	6	g	g	NOUN
ejpam-4783	33	7	)	)	PUNCT
ejpam-4783	33	8	(	(	PUNCT
ejpam-4783	33	9	δµδη)d(µ	δµδη)d(µ	PROPN
ejpam-4783	33	10	,	,	PUNCT
ejpam-4783	33	11	η	η	PROPN
ejpam-4783	33	12	)	)	PUNCT
ejpam-4783	33	13	,	,	PUNCT
ejpam-4783	33	14	there	there	PRON
ejpam-4783	33	15	are	be	VERB
ejpam-4783	33	16	two	two	NUM
ejpam-4783	33	17	significant	significant	ADJ
ejpam-4783	33	18	polynomials	polynomial	NOUN
ejpam-4783	33	19	for	for	ADP
ejpam-4783	33	20	these	these	DET
ejpam-4783	33	21	structural	structural	ADJ
ejpam-4783	33	22	descriptors	descriptor	NOUN
ejpam-4783	33	23	in	in	ADP
ejpam-4783	33	24	chemical	chemical	NOUN
ejpam-4783	33	25	graph	graph	NOUN
ejpam-4783	33	26	theory	theory	NOUN
ejpam-4783	33	27	,	,	PUNCT
ejpam-4783	33	28	“	"	PUNCT
ejpam-4783	33	29	schultz	schultz	PROPN
ejpam-4783	33	30	polynomial(scp	polynomial(scp	PROPN
ejpam-4783	33	31	)	)	PUNCT
ejpam-4783	33	32	”	"	PUNCT
ejpam-4783	33	33	and	and	CCONJ
ejpam-4783	33	34	”	"	PUNCT
ejpam-4783	33	35	modified	modify	VERB
ejpam-4783	33	36	schultz	schultz	PROPN
ejpam-4783	33	37	polynomial(mscp	polynomial(mscp	PROPN
ejpam-4783	33	38	)	)	PUNCT
ejpam-4783	33	39	”	"	PUNCT
ejpam-4783	33	40	of	of	ADP
ejpam-4783	33	41	g	g	PROPN
ejpam-4783	33	42	are	be	AUX
ejpam-4783	33	43	respectively	respectively	ADV
ejpam-4783	33	44	defined	define	VERB
ejpam-4783	33	45	as	as	ADP
ejpam-4783	33	46	:	:	PUNCT
ejpam-4783	33	47	sc(g;x	sc(g;x	PROPN
ejpam-4783	33	48	)	)	PUNCT
ejpam-4783	33	49	=	=	SYM
ejpam-4783	34	1	∑	∑	PUNCT
ejpam-4783	34	2	µ,η⊆v	µ,η⊆v	NOUN
ejpam-4783	34	3	(	(	PUNCT
ejpam-4783	34	4	g	g	NOUN
ejpam-4783	34	5	)	)	PUNCT
ejpam-4783	34	6	(	(	PUNCT
ejpam-4783	34	7	δµ	δµ	X
ejpam-4783	34	8	+	+	X
ejpam-4783	34	9	δη)x	δη)x	PRON
ejpam-4783	34	10	d(µ,η	d(µ,η	NUM
ejpam-4783	34	11	)	)	PUNCT
ejpam-4783	34	12	;	;	PUNCT
ejpam-4783	34	13	sc∗(g;x	sc∗(g;x	NUM
ejpam-4783	34	14	)	)	PUNCT
ejpam-4783	34	15	=	=	PUNCT
ejpam-4783	34	16	∑	∑	PUNCT
ejpam-4783	34	17	µ,η⊆v	µ,η⊆v	NOUN
ejpam-4783	34	18	(	(	PUNCT
ejpam-4783	34	19	g	g	NOUN
ejpam-4783	34	20	)	)	PUNCT
ejpam-4783	34	21	(	(	PUNCT
ejpam-4783	34	22	δµδη)x	δµδη)x	X
ejpam-4783	34	23	d(µ,η	d(µ,η	ADJ
ejpam-4783	34	24	)	)	PUNCT
ejpam-4783	34	25	,	,	PUNCT
ejpam-4783	34	26	in	in	ADP
ejpam-4783	34	27	2009	2009	NUM
ejpam-4783	34	28	,	,	PUNCT
ejpam-4783	34	29	hassani	hassani	PROPN
ejpam-4783	34	30	et	et	PROPN
ejpam-4783	34	31	al	al	PROPN
ejpam-4783	34	32	.	.	PUNCT
ejpam-4783	35	1	[	[	X
ejpam-4783	35	2	13	13	NUM
ejpam-4783	35	3	]	]	PUNCT
ejpam-4783	35	4	computed	compute	VERB
ejpam-4783	35	5	the	the	DET
ejpam-4783	35	6	(	(	PUNCT
ejpam-4783	35	7	scp	scp	PROPN
ejpam-4783	35	8	)	)	PUNCT
ejpam-4783	35	9	and	and	CCONJ
ejpam-4783	35	10	(	(	PUNCT
ejpam-4783	35	11	mscp	mscp	ADJ
ejpam-4783	35	12	)	)	PUNCT
ejpam-4783	35	13	of	of	ADP
ejpam-4783	35	14	c100	c100	PROPN
ejpam-4783	35	15	fullerene	fullerene	NOUN
ejpam-4783	35	16	isomers	isomer	NOUN
ejpam-4783	35	17	using	use	VERB
ejpam-4783	35	18	the	the	DET
ejpam-4783	35	19	gap	gap	NOUN
ejpam-4783	35	20	program	program	NOUN
ejpam-4783	35	21	,	,	PUNCT
ejpam-4783	35	22	while	while	SCONJ
ejpam-4783	35	23	behmaram	behmaram	VERB
ejpam-4783	35	24	et	et	PROPN
ejpam-4783	35	25	al	al	PROPN
ejpam-4783	35	26	.	.	PUNCT
ejpam-4783	36	1	[	[	X
ejpam-4783	36	2	6	6	NUM
ejpam-4783	36	3	]	]	PUNCT
ejpam-4783	36	4	obtained	obtain	VERB
ejpam-4783	36	5	(	(	PUNCT
ejpam-4783	36	6	scp	scp	PROPN
ejpam-4783	36	7	)	)	PUNCT
ejpam-4783	36	8	of	of	ADP
ejpam-4783	36	9	some	some	DET
ejpam-4783	36	10	graph	graph	NOUN
ejpam-4783	36	11	operations	operation	NOUN
ejpam-4783	36	12	.	.	PUNCT
ejpam-4783	37	1	farahani	farahani	X
ejpam-4783	38	1	[	[	X
ejpam-4783	38	2	8	8	NUM
ejpam-4783	38	3	]	]	PUNCT
ejpam-4783	38	4	discovered	discover	VERB
ejpam-4783	38	5	hosoya	hosoya	NOUN
ejpam-4783	38	6	,	,	PUNCT
ejpam-4783	38	7	(	(	PUNCT
ejpam-4783	38	8	scp	scp	PROPN
ejpam-4783	38	9	)	)	PUNCT
ejpam-4783	38	10	and	and	CCONJ
ejpam-4783	38	11	(	(	PUNCT
ejpam-4783	38	12	mscp	mscp	ADJ
ejpam-4783	38	13	)	)	PUNCT
ejpam-4783	38	14	and	and	CCONJ
ejpam-4783	38	15	their	their	PRON
ejpam-4783	38	16	topological	topological	ADJ
ejpam-4783	38	17	indices	index	NOUN
ejpam-4783	38	18	for	for	ADP
ejpam-4783	38	19	benzene	benzene	NOUN
ejpam-4783	38	20	,	,	PUNCT
ejpam-4783	38	21	followed	follow	VERB
ejpam-4783	38	22	by	by	ADP
ejpam-4783	38	23	(	(	PUNCT
ejpam-4783	38	24	scp	scp	PROPN
ejpam-4783	38	25	)	)	PUNCT
ejpam-4783	38	26	and	and	CCONJ
ejpam-4783	38	27	(	(	PUNCT
ejpam-4783	38	28	mscp)of	mscp)of	ADJ
ejpam-4783	38	29	coronene	coronene	NOUN
ejpam-4783	38	30	polycyclic	polycyclic	NOUN
ejpam-4783	38	31	aromatic	aromatic	ADJ
ejpam-4783	38	32	hydrocarbons	hydrocarbon	NOUN
ejpam-4783	38	33	in	in	ADP
ejpam-4783	38	34	a	a	DET
ejpam-4783	38	35	subsequent	subsequent	ADJ
ejpam-4783	38	36	study	study	NOUN
ejpam-4783	38	37	[	[	X
ejpam-4783	38	38	9	9	NUM
ejpam-4783	38	39	]	]	PUNCT
ejpam-4783	38	40	.	.	PUNCT
ejpam-4783	39	1	many	many	ADJ
ejpam-4783	39	2	researchers	researcher	NOUN
ejpam-4783	39	3	have	have	AUX
ejpam-4783	39	4	worked	work	VERB
ejpam-4783	39	5	over	over	ADP
ejpam-4783	39	6	the	the	DET
ejpam-4783	39	7	last	last	ADJ
ejpam-4783	39	8	decade	decade	NOUN
ejpam-4783	39	9	to	to	PART
ejpam-4783	39	10	determine	determine	VERB
ejpam-4783	39	11	(	(	PUNCT
ejpam-4783	39	12	scp	scp	PROPN
ejpam-4783	39	13	)	)	PUNCT
ejpam-4783	39	14	and	and	CCONJ
ejpam-4783	39	15	(	(	PUNCT
ejpam-4783	39	16	mscp	mscp	ADJ
ejpam-4783	39	17	)	)	PUNCT
ejpam-4783	39	18	and	and	CCONJ
ejpam-4783	39	19	their	their	PRON
ejpam-4783	39	20	indices	index	NOUN
ejpam-4783	39	21	for	for	ADP
ejpam-4783	39	22	graphs	graph	NOUN
ejpam-4783	39	23	consisting	consist	VERB
ejpam-4783	39	24	of	of	ADP
ejpam-4783	39	25	chains	chain	NOUN
ejpam-4783	39	26	and	and	CCONJ
ejpam-4783	39	27	rings	ring	NOUN
ejpam-4783	39	28	of	of	ADP
ejpam-4783	39	29	special	special	ADJ
ejpam-4783	39	30	graphs	graph	NOUN
ejpam-4783	39	31	with	with	ADP
ejpam-4783	39	32	chemical	chemical	ADJ
ejpam-4783	39	33	applications	application	NOUN
ejpam-4783	39	34	[	[	X
ejpam-4783	39	35	10],[19],[5],[11	10],[19],[5],[11	X
ejpam-4783	39	36	]	]	X
ejpam-4783	39	37	,	,	PUNCT
ejpam-4783	39	38	[	[	X
ejpam-4783	39	39	4	4	NUM
ejpam-4783	39	40	]	]	PUNCT
ejpam-4783	39	41	,	,	PUNCT
ejpam-4783	39	42	[	[	X
ejpam-4783	39	43	1	1	NUM
ejpam-4783	39	44	]	]	PUNCT
ejpam-4783	39	45	,	,	PUNCT
ejpam-4783	39	46	[	[	X
ejpam-4783	39	47	2	2	NUM
ejpam-4783	39	48	]	]	PUNCT
ejpam-4783	39	49	.	.	PUNCT
ejpam-4783	40	1	1582	1582	NUM
ejpam-4783	40	2	2	2	NUM
ejpam-4783	40	3	.	.	PUNCT
ejpam-4783	40	4	results	result	VERB
ejpam-4783	40	5	2.1	2.1	NUM
ejpam-4783	40	6	.	.	PUNCT
ejpam-4783	41	1	the	the	DET
ejpam-4783	41	2	edges	edge	NOUN
ejpam-4783	41	3	induce	induce	VERB
ejpam-4783	41	4	chain	chain	NOUN
ejpam-4783	41	5	for	for	ADP
ejpam-4783	41	6	hexagonal	hexagonal	ADJ
ejpam-4783	41	7	graphs	graph	NOUN
ejpam-4783	41	8	ce(c6)γ	ce(c6)γ	ADP
ejpam-4783	41	9	the	the	DET
ejpam-4783	41	10	edges	edge	NOUN
ejpam-4783	41	11	induce	induce	VERB
ejpam-4783	41	12	chain	chain	NOUN
ejpam-4783	41	13	for	for	ADP
ejpam-4783	41	14	hexagonal	hexagonal	ADJ
ejpam-4783	41	15	graphs	graph	NOUN
ejpam-4783	41	16	which	which	PRON
ejpam-4783	41	17	is	be	AUX
ejpam-4783	41	18	denoted	denote	VERB
ejpam-4783	41	19	by	by	ADP
ejpam-4783	41	20	ce(c6)γ	ce(c6)γ	PROPN
ejpam-4783	41	21	is	be	AUX
ejpam-4783	41	22	a	a	DET
ejpam-4783	41	23	graph	graph	NOUN
ejpam-4783	41	24	consisting	consist	VERB
ejpam-4783	41	25	of	of	ADP
ejpam-4783	41	26	m	m	PROPN
ejpam-4783	41	27	hexagonal	hexagonal	ADJ
ejpam-4783	41	28	rings	ring	NOUN
ejpam-4783	41	29	,	,	PUNCT
ejpam-4783	41	30	m	m	VERB
ejpam-4783	41	31	≥	≥	NOUN
ejpam-4783	41	32	3	3	NUM
ejpam-4783	41	33	,	,	PUNCT
ejpam-4783	41	34	γ	γ	X
ejpam-4783	41	35	=	=	SYM
ejpam-4783	41	36	4	4	NUM
ejpam-4783	41	37	m	m	NOUN
ejpam-4783	41	38	−	−	NUM
ejpam-4783	41	39	1	1	NUM
ejpam-4783	41	40	every	every	DET
ejpam-4783	41	41	two	two	NUM
ejpam-4783	41	42	successive	successive	ADJ
ejpam-4783	41	43	rings	ring	NOUN
ejpam-4783	41	44	have	have	VERB
ejpam-4783	41	45	a	a	DET
ejpam-4783	41	46	common	common	ADJ
ejpam-4783	41	47	edge	edge	NOUN
ejpam-4783	41	48	induce	induce	NOUN
ejpam-4783	41	49	,	,	PUNCT
ejpam-4783	41	50	forming	form	VERB
ejpam-4783	41	51	a	a	DET
ejpam-4783	41	52	chain	chain	NOUN
ejpam-4783	41	53	as	as	SCONJ
ejpam-4783	41	54	shown	show	VERB
ejpam-4783	41	55	in	in	ADP
ejpam-4783	41	56	fig	fig	NOUN
ejpam-4783	41	57	.	.	PUNCT
ejpam-4783	42	1	1	1	X
ejpam-4783	42	2	.	.	X
ejpam-4783	42	3	figure	figure	NOUN
ejpam-4783	42	4	1	1	NUM
ejpam-4783	42	5	:	:	PUNCT
ejpam-4783	42	6	edges	edge	NOUN
ejpam-4783	42	7	induce	induce	VERB
ejpam-4783	42	8	chain	chain	NOUN
ejpam-4783	42	9	for	for	ADP
ejpam-4783	42	10	hexagonal	hexagonal	ADJ
ejpam-4783	42	11	graphs	graph	NOUN
ejpam-4783	42	12	ce(c6)γ	ce(c6)γ	NOUN
ejpam-4783	42	13	.	.	PUNCT
ejpam-4783	43	1	from	from	ADP
ejpam-4783	43	2	fig.1	fig.1	PROPN
ejpam-4783	43	3	we	we	PRON
ejpam-4783	43	4	note	note	VERB
ejpam-4783	43	5	,	,	PUNCT
ejpam-4783	43	6	p(ce(c6)γ	p(ce(c6)γ	NOUN
ejpam-4783	43	7	)	)	PUNCT
ejpam-4783	44	1	=	=	PUNCT
ejpam-4783	44	2	6	6	NUM
ejpam-4783	44	3	m	m	NOUN
ejpam-4783	44	4	,	,	PUNCT
ejpam-4783	44	5	q(ce(c6)γ	q(ce(c6)γ	NOUN
ejpam-4783	44	6	)	)	PUNCT
ejpam-4783	44	7	=	=	PUNCT
ejpam-4783	45	1	7	7	NUM
ejpam-4783	45	2	m	m	NOUN
ejpam-4783	45	3	−	−	NUM
ejpam-4783	45	4	1	1	NUM
ejpam-4783	45	5	and	and	CCONJ
ejpam-4783	45	6	diam(ce(c6)γ	diam(ce(c6)γ	PROPN
ejpam-4783	45	7	)	)	PUNCT
ejpam-4783	46	1	=	=	PUNCT
ejpam-4783	47	1	4m−	4m−	PROPN
ejpam-4783	47	2	1	1	NUM
ejpam-4783	47	3	.	.	PUNCT
ejpam-4783	47	4	table	table	NOUN
ejpam-4783	47	5	1	1	NUM
ejpam-4783	47	6	:	:	PUNCT
ejpam-4783	47	7	degree	degree	NOUN
ejpam-4783	47	8	matrix	matrix	NOUN
ejpam-4783	47	9	of	of	ADP
ejpam-4783	47	10	ce(c6)γ	ce(c6)γ	NOUN
ejpam-4783	47	11	for	for	ADP
ejpam-4783	47	12	1	1	NUM
ejpam-4783	47	13	≤	≤	NUM
ejpam-4783	47	14	i	i	PRON
ejpam-4783	47	15	,	,	PUNCT
ejpam-4783	48	1	j	j	PROPN
ejpam-4783	48	2	≤	≤	PROPN
ejpam-4783	48	3	γ	γ	PROPN
ejpam-4783	48	4	−	−	PROPN
ejpam-4783	48	5	2,and	2,and	NUM
ejpam-4783	48	6	1	1	NUM
ejpam-4783	48	7	≤	≤	NOUN
ejpam-4783	48	8	r	r	NOUN
ejpam-4783	48	9	,	,	PUNCT
ejpam-4783	48	10	s	s	PART
ejpam-4783	48	11	≤	≤	NUM
ejpam-4783	48	12	m−	m−	PROPN
ejpam-4783	48	13	1	1	NUM
ejpam-4783	48	14	,	,	PUNCT
ejpam-4783	48	15	r	r	PROPN
ejpam-4783	48	16	̸=	̸=	PROPN
ejpam-4783	48	17	s	s	PART
ejpam-4783	48	18	and	and	CCONJ
ejpam-4783	48	19	i	i	PRON
ejpam-4783	48	20	,	,	PUNCT
ejpam-4783	48	21	j	j	PROPN
ejpam-4783	48	22	̸=	̸=	PROPN
ejpam-4783	48	23	r	r	PROPN
ejpam-4783	48	24	,	,	PUNCT
ejpam-4783	48	25	s.	s.	PROPN
ejpam-4783	48	26	theorem	theorem	VERB
ejpam-4783	48	27	1	1	NUM
ejpam-4783	48	28	.	.	PUNCT
ejpam-4783	49	1	for	for	ADP
ejpam-4783	49	2	m	m	PROPN
ejpam-4783	49	3	≥	≥	NOUN
ejpam-4783	49	4	3	3	NUM
ejpam-4783	49	5	,	,	PUNCT
ejpam-4783	49	6	γ	γ	X
ejpam-4783	49	7	=	=	SYM
ejpam-4783	49	8	4m−	4m−	PROPN
ejpam-4783	49	9	1	1	NUM
ejpam-4783	49	10	,	,	PUNCT
ejpam-4783	49	11	then	then	ADV
ejpam-4783	49	12	:	:	PUNCT
ejpam-4783	49	13	(	(	PUNCT
ejpam-4783	49	14	i	i	NOUN
ejpam-4783	49	15	)	)	PUNCT
ejpam-4783	49	16	sc(ce(c6)γ	sc(ce(c6)γ	NOUN
ejpam-4783	49	17	;	;	PUNCT
ejpam-4783	49	18	x	x	X
ejpam-4783	49	19	)	)	PUNCT
ejpam-4783	49	20	=	=	SYM
ejpam-4783	49	21	1	1	NUM
ejpam-4783	49	22	2(17γ−3)x+12(γ−1)x2	2(17γ−3)x+12(γ−1)x2	NUM
ejpam-4783	49	23	+	+	CCONJ
ejpam-4783	49	24	1	1	NUM
ejpam-4783	49	25	2(25γ−51)x3	2(25γ−51)x3	NUM
ejpam-4783	49	26	+	+	CCONJ
ejpam-4783	49	27	∑	∑	PROPN
ejpam-4783	49	28	ξ=4,8,	ξ=4,8,	PART
ejpam-4783	49	29	...	...	PUNCT
ejpam-4783	49	30	,γ−3(11γ−11ξ	,γ−3(11γ−11ξ	PUNCT
ejpam-4783	49	31	+9)xξ	+9)xξ	PROPN
ejpam-4783	49	32	+	+	NOUN
ejpam-4783	49	33	1	1	NUM
ejpam-4783	49	34	2	2	NUM
ejpam-4783	49	35	∑	∑	ADV
ejpam-4783	49	36	ξ=5,9,	ξ=5,9,	VERB
ejpam-4783	49	37	...	...	PUNCT
ejpam-4783	49	38	,γ−2	,γ−2	PUNCT
ejpam-4783	49	39	(	(	PUNCT
ejpam-4783	49	40	21γ	21γ	NUM
ejpam-4783	49	41	−	−	NOUN
ejpam-4783	49	42	21ξ	21ξ	NOUN
ejpam-4783	49	43	+	+	CCONJ
ejpam-4783	49	44	22)xξ	22)xξ	NUM
ejpam-4783	49	45	+	+	CCONJ
ejpam-4783	49	46	2	2	NUM
ejpam-4783	49	47	∑	∑	NOUN
ejpam-4783	49	48	ξ=6,10,	ξ=6,10,	NOUN
ejpam-4783	49	49	...	...	PUNCT
ejpam-4783	49	50	,γ−1	,γ−1	PUNCT
ejpam-4783	49	51	(	(	PUNCT
ejpam-4783	49	52	5γ	5γ	NOUN
ejpam-4783	49	53	−	−	NOUN
ejpam-4783	49	54	5ξ	5ξ	NOUN
ejpam-4783	50	1	+	+	CCONJ
ejpam-4783	50	2	3)xξ	3)xξ	NUM
ejpam-4783	50	3	+1	+1	ADJ
ejpam-4783	50	4	2	2	NUM
ejpam-4783	50	5	∑	∑	PUNCT
ejpam-4783	50	6	ξ=7,11,	ξ=7,11,	NUM
ejpam-4783	50	7	...	...	PUNCT
ejpam-4783	50	8	,γ	,γ	PUNCT
ejpam-4783	50	9	(	(	PUNCT
ejpam-4783	50	10	21γ	21γ	NUM
ejpam-4783	50	11	−	−	NOUN
ejpam-4783	50	12	21ξ	21ξ	NOUN
ejpam-4783	50	13	+	+	X
ejpam-4783	50	14	8)xξ	8)xξ	ADJ
ejpam-4783	50	15	.	.	PUNCT
ejpam-4783	50	16	(	(	PUNCT
ejpam-4783	50	17	ii	ii	NOUN
ejpam-4783	50	18	)	)	PUNCT
ejpam-4783	50	19	sc∗(ce(c6)γ	sc∗(ce(c6)γ	PROPN
ejpam-4783	50	20	;	;	PUNCT
ejpam-4783	50	21	x	x	X
ejpam-4783	50	22	)	)	PUNCT
ejpam-4783	50	23	=	=	SYM
ejpam-4783	51	1	1	1	NUM
ejpam-4783	51	2	4(41γ−27)x+2(7γ−9)x2	4(41γ−27)x+2(7γ−9)x2	NUM
ejpam-4783	51	3	+	+	NOUN
ejpam-4783	51	4	1	1	NUM
ejpam-4783	51	5	4(57γ−127)x3	4(57γ−127)x3	NUM
ejpam-4783	51	6	+	+	CCONJ
ejpam-4783	51	7	1	1	NUM
ejpam-4783	51	8	2	2	NUM
ejpam-4783	51	9	∑	∑	PUNCT
ejpam-4783	51	10	ξ=4,8,	ξ=4,8,	ADV
ejpam-4783	51	11	...	...	PUNCT
ejpam-4783	51	12	,γ−3(25γ	,γ−3(25γ	PUNCT
ejpam-4783	51	13	−25ξ+13)xξ+	−25ξ+13)xξ+	PROPN
ejpam-4783	51	14	1	1	NUM
ejpam-4783	51	15	4	4	NUM
ejpam-4783	51	16	∑	∑	ADV
ejpam-4783	51	17	ξ=5,9,	ξ=5,9,	VERB
ejpam-4783	51	18	...	...	PUNCT
ejpam-4783	51	19	,γ−2	,γ−2	PUNCT
ejpam-4783	51	20	(	(	PUNCT
ejpam-4783	51	21	49γ	49γ	NOUN
ejpam-4783	51	22	−	−	NOUN
ejpam-4783	51	23	49ξ	49ξ	NOUN
ejpam-4783	51	24	+	+	CCONJ
ejpam-4783	51	25	30)xξ+4	30)xξ+4	NOUN
ejpam-4783	51	26	∑	∑	PUNCT
ejpam-4783	51	27	ξ=6,10,	ξ=6,10,	NOUN
ejpam-4783	51	28	...	...	PUNCT
ejpam-4783	51	29	,γ−1	,γ−1	PUNCT
ejpam-4783	51	30	(	(	PUNCT
ejpam-4783	51	31	3γ	3γ	NUM
ejpam-4783	51	32	−	−	NOUN
ejpam-4783	52	1	3ξ	3ξ	PROPN
ejpam-4783	53	1	+	+	CCONJ
ejpam-4783	53	2	1)xξ+	1)xξ+	NUM
ejpam-4783	53	3	1	1	NUM
ejpam-4783	53	4	4	4	NUM
ejpam-4783	53	5	∑	∑	ADV
ejpam-4783	53	6	ξ=7,11,	ξ=7,11,	NUM
ejpam-4783	53	7	...	...	PUNCT
ejpam-4783	53	8	,γ−4	,γ−4	PUNCT
ejpam-4783	53	9	(	(	PUNCT
ejpam-4783	53	10	49γ	49γ	NOUN
ejpam-4783	53	11	−	−	NOUN
ejpam-4783	53	12	49ξ	49ξ	NOUN
ejpam-4783	53	13	+	+	CCONJ
ejpam-4783	53	14	12)xξ	12)xξ	NUM
ejpam-4783	53	15	+	+	CCONJ
ejpam-4783	53	16	4xγ	4xγ	NOUN
ejpam-4783	53	17	.	.	PUNCT
ejpam-4783	54	1	proof	proof	NOUN
ejpam-4783	54	2	.	.	PUNCT
ejpam-4783	55	1	for	for	ADP
ejpam-4783	55	2	vertex	vertex	NOUN
ejpam-4783	55	3	y	y	PROPN
ejpam-4783	55	4	,	,	PUNCT
ejpam-4783	55	5	z	z	PROPN
ejpam-4783	55	6	∈	∈	PROPN
ejpam-4783	55	7	v	v	NOUN
ejpam-4783	55	8	(	(	PUNCT
ejpam-4783	55	9	ce(c6)γ	ce(c6)γ	NOUN
ejpam-4783	55	10	)	)	PUNCT
ejpam-4783	55	11	there	there	PRON
ejpam-4783	55	12	is	be	VERB
ejpam-4783	55	13	d(y	d(y	NOUN
ejpam-4783	55	14	,	,	PUNCT
ejpam-4783	55	15	z	z	NOUN
ejpam-4783	55	16	)	)	PUNCT
ejpam-4783	55	17	=	=	SYM
ejpam-4783	55	18	ξ	ξ	PROPN
ejpam-4783	55	19	,	,	PUNCT
ejpam-4783	55	20	1	1	NUM
ejpam-4783	55	21	≤	≤	NUM
ejpam-4783	55	22	ξ	ξ	PRON
ejpam-4783	55	23	≤	≤	NUM
ejpam-4783	55	24	γ	γ	X
ejpam-4783	55	25	.	.	PROPN
ejpam-4783	55	26	and	and	CCONJ
ejpam-4783	55	27	obviously:∑γ	obviously:∑γ	PROPN
ejpam-4783	55	28	i=1	i=1	X
ejpam-4783	56	1	|ai|	|ai|	PROPN
ejpam-4783	56	2	=	=	SYM
ejpam-4783	56	3	(	(	PUNCT
ejpam-4783	56	4	18γ2	18γ2	NUM
ejpam-4783	56	5	+	+	NUM
ejpam-4783	56	6	7γ	7γ	NOUN
ejpam-4783	56	7	+	+	CCONJ
ejpam-4783	56	8	193)/16	193)/16	NUM
ejpam-4783	56	9	.	.	PUNCT
ejpam-4783	57	1	the	the	DET
ejpam-4783	57	2	proof	proof	NOUN
ejpam-4783	57	3	is	be	AUX
ejpam-4783	57	4	consist	consist	VERB
ejpam-4783	57	5	of	of	ADP
ejpam-4783	57	6	the	the	DET
ejpam-4783	57	7	following	follow	VERB
ejpam-4783	57	8	twelve	twelve	NUM
ejpam-4783	57	9	cases	case	NOUN
ejpam-4783	57	10	:	:	PUNCT
ejpam-4783	57	11	(	(	PUNCT
ejpam-4783	57	12	i	i	NOUN
ejpam-4783	57	13	)	)	PUNCT
ejpam-4783	57	14	if	if	SCONJ
ejpam-4783	57	15	d(y	d(y	PROPN
ejpam-4783	57	16	,	,	PUNCT
ejpam-4783	57	17	z	z	NOUN
ejpam-4783	57	18	)	)	PUNCT
ejpam-4783	57	19	=	=	SYM
ejpam-4783	58	1	ξ	ξ	X
ejpam-4783	58	2	=	=	SYM
ejpam-4783	58	3	1	1	NUM
ejpam-4783	58	4	,	,	PUNCT
ejpam-4783	58	5	then	then	ADV
ejpam-4783	58	6	|a1|	|a1|	PROPN
ejpam-4783	58	7	=	=	SYM
ejpam-4783	58	8	(	(	PUNCT
ejpam-4783	58	9	7γ	7γ	NOUN
ejpam-4783	58	10	+	+	CCONJ
ejpam-4783	58	11	3)/4	3)/4	NUM
ejpam-4783	58	12	,	,	PUNCT
ejpam-4783	58	13	also	also	ADV
ejpam-4783	58	14	is	be	AUX
ejpam-4783	58	15	equal	equal	ADJ
ejpam-4783	58	16	to	to	ADP
ejpam-4783	58	17	q(ce(c6)γ	q(ce(c6)γ	NOUN
ejpam-4783	58	18	)	)	PUNCT
ejpam-4783	58	19	,	,	PUNCT
ejpam-4783	58	20	we	we	PRON
ejpam-4783	58	21	have	have	VERB
ejpam-4783	58	22	four	four	NUM
ejpam-4783	58	23	subsets	subset	NOUN
ejpam-4783	58	24	of	of	ADP
ejpam-4783	58	25	it	it	PRON
ejpam-4783	58	26	:	:	PUNCT
ejpam-4783	58	27	(	(	PUNCT
ejpam-4783	58	28	a	a	X
ejpam-4783	58	29	)	)	PUNCT
ejpam-4783	58	30	∣∣{(µ1(γ−1	∣∣{(µ1(γ−1	NOUN
ejpam-4783	58	31	)	)	PUNCT
ejpam-4783	58	32	,	,	PUNCT
ejpam-4783	58	33	ω0(γ	ω0(γ	NOUN
ejpam-4783	58	34	)	)	PUNCT
ejpam-4783	58	35	)	)	PUNCT
ejpam-4783	58	36	,	,	PUNCT
ejpam-4783	58	37	(	(	PUNCT
ejpam-4783	58	38	η1(γ−1	η1(γ−1	NOUN
ejpam-4783	58	39	)	)	PUNCT
ejpam-4783	58	40	,	,	PUNCT
ejpam-4783	58	41	ω0(γ	ω0(γ	NOUN
ejpam-4783	58	42	)	)	PUNCT
ejpam-4783	58	43	)	)	PUNCT
ejpam-4783	58	44	}	}	PUNCT
ejpam-4783	58	45	∣∣	∣∣	X
ejpam-4783	58	46	=	=	SYM
ejpam-4783	58	47	4	4	X
ejpam-4783	58	48	.	.	PUNCT
ejpam-4783	58	49	(	(	PUNCT
ejpam-4783	58	50	b	b	X
ejpam-4783	58	51	)	)	PUNCT
ejpam-4783	58	52	|{(µ4i+1	|{(µ4i+1	PROPN
ejpam-4783	58	53	,	,	PUNCT
ejpam-4783	58	54	µ4i+2	µ4i+2	PROPN
ejpam-4783	58	55	)	)	PUNCT
ejpam-4783	58	56	,	,	PUNCT
ejpam-4783	58	57	(	(	PUNCT
ejpam-4783	58	58	η4i+1	η4i+1	NOUN
ejpam-4783	58	59	,	,	PUNCT
ejpam-4783	58	60	η4i+2	η4i+2	PROPN
ejpam-4783	58	61	)	)	PUNCT
ejpam-4783	58	62	:	:	PUNCT
ejpam-4783	58	63	0	0	NUM
ejpam-4783	58	64	≤	≤	NUM
ejpam-4783	58	65	i	i	PRON
ejpam-4783	58	66	≤	≤	NOUN
ejpam-4783	58	67	(	(	PUNCT
ejpam-4783	58	68	γ	γ	X
ejpam-4783	58	69	−	−	PROPN
ejpam-4783	58	70	3)/4}|	3)/4}|	NUM
ejpam-4783	58	71	=	=	SYM
ejpam-4783	58	72	(	(	PUNCT
ejpam-4783	58	73	γ	γ	X
ejpam-4783	58	74	+	+	X
ejpam-4783	58	75	1)/2	1)/2	NOUN
ejpam-4783	58	76	.	.	NOUN
ejpam-4783	58	77	2.1	2.1	NUM
ejpam-4783	58	78	the	the	DET
ejpam-4783	58	79	edges	edge	NOUN
ejpam-4783	58	80	induce	induce	VERB
ejpam-4783	58	81	chain	chain	NOUN
ejpam-4783	58	82	for	for	ADP
ejpam-4783	58	83	hexagonal	hexagonal	ADJ
ejpam-4783	58	84	graphs	graph	NOUN
ejpam-4783	58	85	ce(c6)γ	ce(c6)γ	PROPN
ejpam-4783	58	86	1583	1583	NUM
ejpam-4783	58	87	(	(	PUNCT
ejpam-4783	58	88	c	c	NOUN
ejpam-4783	58	89	)	)	PUNCT
ejpam-4783	58	90	|{(µ4i+2	|{(µ4i+2	PROPN
ejpam-4783	58	91	,	,	PUNCT
ejpam-4783	58	92	ω4i+3	ω4i+3	NOUN
ejpam-4783	58	93	)	)	PUNCT
ejpam-4783	58	94	,	,	PUNCT
ejpam-4783	58	95	(	(	PUNCT
ejpam-4783	58	96	η4i+2	η4i+2	PROPN
ejpam-4783	58	97	,	,	PUNCT
ejpam-4783	58	98	ω4i+3	ω4i+3	NOUN
ejpam-4783	58	99	)	)	PUNCT
ejpam-4783	58	100	:	:	PUNCT
ejpam-4783	58	101	0	0	NUM
ejpam-4783	58	102	≤	≤	NUM
ejpam-4783	58	103	i	i	PRON
ejpam-4783	58	104	≤	≤	NOUN
ejpam-4783	58	105	(	(	PUNCT
ejpam-4783	58	106	γ	γ	PROPN
ejpam-4783	58	107	−	−	PROPN
ejpam-4783	58	108	7)/4}|	7)/4}|	NOUN
ejpam-4783	58	109	=	=	SYM
ejpam-4783	58	110	(	(	PUNCT
ejpam-4783	58	111	γ	γ	PROPN
ejpam-4783	58	112	−	−	PROPN
ejpam-4783	58	113	3)/2	3)/2	NUM
ejpam-4783	58	114	.	.	PUNCT
ejpam-4783	59	1	(	(	PUNCT
ejpam-4783	59	2	d	d	X
ejpam-4783	59	3	)	)	PUNCT
ejpam-4783	59	4	|{(µ4i+1	|{(µ4i+1	PROPN
ejpam-4783	59	5	,	,	PUNCT
ejpam-4783	59	6	ω4i	ω4i	PUNCT
ejpam-4783	59	7	)	)	PUNCT
ejpam-4783	59	8	,	,	PUNCT
ejpam-4783	59	9	(	(	PUNCT
ejpam-4783	59	10	η4i+1	η4i+1	NOUN
ejpam-4783	59	11	,	,	PUNCT
ejpam-4783	59	12	ω4i	ω4i	PUNCT
ejpam-4783	59	13	)	)	PUNCT
ejpam-4783	59	14	,	,	PUNCT
ejpam-4783	59	15	(	(	PUNCT
ejpam-4783	59	16	ω4i−1	ω4i−1	PROPN
ejpam-4783	59	17	,	,	PUNCT
ejpam-4783	59	18	ω4i	ω4i	NUM
ejpam-4783	59	19	)	)	PUNCT
ejpam-4783	59	20	:	:	PUNCT
ejpam-4783	59	21	1	1	NUM
ejpam-4783	59	22	≤	≤	NUM
ejpam-4783	59	23	i	i	PRON
ejpam-4783	59	24	≤	≤	NOUN
ejpam-4783	59	25	(	(	PUNCT
ejpam-4783	59	26	γ	γ	X
ejpam-4783	59	27	−	−	PROPN
ejpam-4783	59	28	3)/4}|	3)/4}|	NUM
ejpam-4783	59	29	=	=	SYM
ejpam-4783	60	1	3(γ	3(γ	NUM
ejpam-4783	60	2	−	−	NOUN
ejpam-4783	61	1	3)/4	3)/4	NUM
ejpam-4783	61	2	.	.	PUNCT
ejpam-4783	61	3	(	(	PUNCT
ejpam-4783	61	4	ii	ii	NOUN
ejpam-4783	61	5	)	)	PUNCT
ejpam-4783	61	6	if	if	SCONJ
ejpam-4783	61	7	d(y	d(y	PROPN
ejpam-4783	61	8	,	,	PUNCT
ejpam-4783	61	9	z	z	NOUN
ejpam-4783	61	10	)	)	PUNCT
ejpam-4783	61	11	=	=	SYM
ejpam-4783	62	1	ξ	ξ	X
ejpam-4783	62	2	=	=	SYM
ejpam-4783	62	3	2	2	NUM
ejpam-4783	62	4	,	,	PUNCT
ejpam-4783	62	5	then	then	ADV
ejpam-4783	62	6	|a2|	|a2|	NOUN
ejpam-4783	62	7	=	=	SYM
ejpam-4783	62	8	(	(	PUNCT
ejpam-4783	62	9	5γ	5γ	NOUN
ejpam-4783	62	10	−	−	PROPN
ejpam-4783	62	11	3)/2	3)/2	NUM
ejpam-4783	62	12	,	,	PUNCT
ejpam-4783	62	13	we	we	PRON
ejpam-4783	62	14	have	have	VERB
ejpam-4783	62	15	six	six	NUM
ejpam-4783	62	16	subsets	subset	NOUN
ejpam-4783	62	17	of	of	ADP
ejpam-4783	62	18	it	it	PRON
ejpam-4783	62	19	:	:	PUNCT
ejpam-4783	62	20	(	(	PUNCT
ejpam-4783	62	21	a	a	X
ejpam-4783	62	22	)	)	PUNCT
ejpam-4783	62	23	|{(µξ(ηξ	|{(µξ(ηξ	NOUN
ejpam-4783	62	24	)	)	PUNCT
ejpam-4783	62	25	,	,	PUNCT
ejpam-4783	62	26	ω0)}|	ω0)}|	NUM
ejpam-4783	62	27	=	=	SYM
ejpam-4783	62	28	2	2	X
ejpam-4783	62	29	.	.	PUNCT
ejpam-4783	62	30	(	(	PUNCT
ejpam-4783	62	31	b	b	NOUN
ejpam-4783	62	32	)	)	PUNCT
ejpam-4783	62	33	|{(µγ−ξ(ηγ−ξ	|{(µγ−ξ(ηγ−ξ	NOUN
ejpam-4783	62	34	)	)	PUNCT
ejpam-4783	62	35	,	,	PUNCT
ejpam-4783	62	36	ωγ)}|	ωγ)}|	NOUN
ejpam-4783	62	37	=	=	SYM
ejpam-4783	62	38	2	2	X
ejpam-4783	62	39	.	.	PUNCT
ejpam-4783	62	40	(	(	PUNCT
ejpam-4783	62	41	c	c	X
ejpam-4783	62	42	)	)	PUNCT
ejpam-4783	62	43	|{(µ4i+1(η4i+1	|{(µ4i+1(η4i+1	NOUN
ejpam-4783	62	44	)	)	PUNCT
ejpam-4783	62	45	,	,	PUNCT
ejpam-4783	62	46	ω4i+ξ+1	ω4i+ξ+1	NUM
ejpam-4783	62	47	)	)	PUNCT
ejpam-4783	62	48	:	:	PUNCT
ejpam-4783	62	49	0	0	NUM
ejpam-4783	62	50	≤	≤	NUM
ejpam-4783	62	51	i	i	PRON
ejpam-4783	62	52	≤	≤	NOUN
ejpam-4783	62	53	(	(	PUNCT
ejpam-4783	62	54	γ	γ	X
ejpam-4783	62	55	−	−	PROPN
ejpam-4783	62	56	ξ	ξ	PROPN
ejpam-4783	62	57	−	−	PROPN
ejpam-4783	62	58	5)/4}|	5)/4}|	NUM
ejpam-4783	62	59	=	=	SYM
ejpam-4783	62	60	(	(	PUNCT
ejpam-4783	62	61	γ	γ	X
ejpam-4783	62	62	−	−	PROPN
ejpam-4783	62	63	ξ	ξ	X
ejpam-4783	62	64	−	−	PROPN
ejpam-4783	62	65	1)/2	1)/2	NUM
ejpam-4783	62	66	.	.	PUNCT
ejpam-4783	63	1	(	(	PUNCT
ejpam-4783	63	2	d	d	X
ejpam-4783	63	3	)	)	PUNCT
ejpam-4783	63	4	|{(ω4i−1	|{(ω4i−1	PROPN
ejpam-4783	63	5	,	,	PUNCT
ejpam-4783	63	6	µ4i+ξ−1(η4i+ξ−1	µ4i+ξ−1(η4i+ξ−1	PUNCT
ejpam-4783	63	7	)	)	PUNCT
ejpam-4783	63	8	)	)	PUNCT
ejpam-4783	63	9	:	:	PUNCT
ejpam-4783	64	1	1	1	NUM
ejpam-4783	64	2	≤	≤	NUM
ejpam-4783	64	3	i	i	PRON
ejpam-4783	64	4	≤	≤	NOUN
ejpam-4783	64	5	(	(	PUNCT
ejpam-4783	64	6	γ	γ	X
ejpam-4783	64	7	−	−	PROPN
ejpam-4783	64	8	ξ	ξ	PROPN
ejpam-4783	64	9	−	−	PROPN
ejpam-4783	64	10	1)/4}|	1)/4}|	NUM
ejpam-4783	64	11	=	=	SYM
ejpam-4783	64	12	(	(	PUNCT
ejpam-4783	64	13	γ	γ	X
ejpam-4783	64	14	−	−	PROPN
ejpam-4783	64	15	ξ	ξ	X
ejpam-4783	64	16	−	−	PROPN
ejpam-4783	64	17	1)/2	1)/2	NUM
ejpam-4783	64	18	.	.	PUNCT
ejpam-4783	65	1	(	(	PUNCT
ejpam-4783	65	2	e	e	NOUN
ejpam-4783	65	3	)	)	PUNCT
ejpam-4783	65	4	|{(µ4i+2(η4i+2	|{(µ4i+2(η4i+2	PROPN
ejpam-4783	65	5	)	)	PUNCT
ejpam-4783	65	6	,	,	PUNCT
ejpam-4783	65	7	ω4i+ξ+2	ω4i+ξ+2	NUM
ejpam-4783	65	8	)	)	PUNCT
ejpam-4783	65	9	:	:	PUNCT
ejpam-4783	66	1	0	0	NUM
ejpam-4783	66	2	≤	≤	NUM
ejpam-4783	66	3	i	i	PRON
ejpam-4783	66	4	≤	≤	NOUN
ejpam-4783	66	5	(	(	PUNCT
ejpam-4783	66	6	γ	γ	X
ejpam-4783	66	7	−	−	PROPN
ejpam-4783	66	8	ξ	ξ	PROPN
ejpam-4783	66	9	−	−	PROPN
ejpam-4783	66	10	5)/4}|	5)/4}|	NUM
ejpam-4783	66	11	=	=	SYM
ejpam-4783	66	12	(	(	PUNCT
ejpam-4783	66	13	γ	γ	X
ejpam-4783	66	14	−	−	PROPN
ejpam-4783	66	15	ξ	ξ	X
ejpam-4783	66	16	−	−	PROPN
ejpam-4783	66	17	1)/2	1)/2	NUM
ejpam-4783	66	18	.	.	PUNCT
ejpam-4783	67	1	(	(	PUNCT
ejpam-4783	67	2	f	f	X
ejpam-4783	67	3	)	)	PUNCT
ejpam-4783	67	4	|{(ω4i	|{(ω4i	PROPN
ejpam-4783	67	5	,	,	PUNCT
ejpam-4783	67	6	µ4i+ξ(η4i+ξ	µ4i+ξ(η4i+ξ	NOUN
ejpam-4783	67	7	)	)	PUNCT
ejpam-4783	67	8	)	)	PUNCT
ejpam-4783	67	9	:	:	PUNCT
ejpam-4783	68	1	1	1	NUM
ejpam-4783	68	2	≤	≤	NUM
ejpam-4783	68	3	i	i	PRON
ejpam-4783	68	4	≤	≤	NOUN
ejpam-4783	68	5	(	(	PUNCT
ejpam-4783	68	6	γ	γ	X
ejpam-4783	68	7	−	−	PROPN
ejpam-4783	68	8	ξ	ξ	PROPN
ejpam-4783	68	9	−	−	PROPN
ejpam-4783	68	10	1)/4}|	1)/4}|	NUM
ejpam-4783	68	11	=	=	SYM
ejpam-4783	68	12	(	(	PUNCT
ejpam-4783	68	13	γ	γ	X
ejpam-4783	68	14	−	−	PROPN
ejpam-4783	68	15	ξ	ξ	X
ejpam-4783	68	16	−	−	PROPN
ejpam-4783	68	17	1)/2	1)/2	NUM
ejpam-4783	68	18	.	.	PUNCT
ejpam-4783	68	19	(	(	PUNCT
ejpam-4783	68	20	iii	iii	X
ejpam-4783	68	21	)	)	PUNCT
ejpam-4783	68	22	if	if	SCONJ
ejpam-4783	68	23	d(y	d(y	PROPN
ejpam-4783	68	24	,	,	PUNCT
ejpam-4783	68	25	z	z	NOUN
ejpam-4783	68	26	)	)	PUNCT
ejpam-4783	68	27	=	=	SYM
ejpam-4783	68	28	3	3	NUM
ejpam-4783	68	29	,	,	PUNCT
ejpam-4783	68	30	then	then	ADV
ejpam-4783	68	31	|a3|	|a3|	VERB
ejpam-4783	68	32	=	=	PRON
ejpam-4783	68	33	(	(	PUNCT
ejpam-4783	68	34	11γ	11γ	NOUN
ejpam-4783	68	35	−	−	NOUN
ejpam-4783	68	36	21)/4	21)/4	NUM
ejpam-4783	68	37	,	,	PUNCT
ejpam-4783	68	38	we	we	PRON
ejpam-4783	68	39	have	have	VERB
ejpam-4783	68	40	eight	eight	NUM
ejpam-4783	68	41	subsets	subset	NOUN
ejpam-4783	68	42	of	of	ADP
ejpam-4783	68	43	it	it	PRON
ejpam-4783	68	44	:	:	PUNCT
ejpam-4783	68	45	(	(	PUNCT
ejpam-4783	68	46	a	a	X
ejpam-4783	68	47	)	)	PUNCT
ejpam-4783	68	48	∣∣{(ω0(γ−ξ	∣∣{(ω0(γ−ξ	NOUN
ejpam-4783	68	49	)	)	PUNCT
ejpam-4783	68	50	,	,	PUNCT
ejpam-4783	68	51	ωξ(γ	ωξ(γ	NUM
ejpam-4783	68	52	)	)	PUNCT
ejpam-4783	68	53	)	)	PUNCT
ejpam-4783	68	54	}	}	PUNCT
ejpam-4783	68	55	∣∣	∣∣	X
ejpam-4783	68	56	=	=	SYM
ejpam-4783	68	57	2	2	X
ejpam-4783	68	58	.	.	PUNCT
ejpam-4783	68	59	(	(	PUNCT
ejpam-4783	68	60	b	b	X
ejpam-4783	68	61	)	)	PUNCT
ejpam-4783	68	62	|{(ω4i	|{(ω4i	PROPN
ejpam-4783	68	63	,	,	PUNCT
ejpam-4783	68	64	ω4i+ξ	ω4i+ξ	NOUN
ejpam-4783	68	65	)	)	PUNCT
ejpam-4783	68	66	:	:	PUNCT
ejpam-4783	68	67	1	1	NUM
ejpam-4783	68	68	≤	≤	NUM
ejpam-4783	68	69	i	i	PRON
ejpam-4783	68	70	≤	≤	NOUN
ejpam-4783	68	71	(	(	PUNCT
ejpam-4783	68	72	γ	γ	X
ejpam-4783	68	73	−	−	PROPN
ejpam-4783	68	74	ξ	ξ	PROPN
ejpam-4783	68	75	−	−	PROPN
ejpam-4783	68	76	4)/4}|	4)/4}|	NUM
ejpam-4783	68	77	=	=	SYM
ejpam-4783	68	78	(	(	PUNCT
ejpam-4783	68	79	γ	γ	X
ejpam-4783	68	80	−	−	PROPN
ejpam-4783	68	81	ξ	ξ	X
ejpam-4783	68	82	−	−	PROPN
ejpam-4783	68	83	4)/4	4)/4	NUM
ejpam-4783	68	84	.	.	PUNCT
ejpam-4783	69	1	(	(	PUNCT
ejpam-4783	69	2	c	c	X
ejpam-4783	69	3	)	)	PUNCT
ejpam-4783	69	4	|{(µ4i−2	|{(µ4i−2	NOUN
ejpam-4783	69	5	,	,	PUNCT
ejpam-4783	69	6	µ4i−2+ξ(η4i−2+ξ	µ4i−2+ξ(η4i−2+ξ	NOUN
ejpam-4783	69	7	)	)	PUNCT
ejpam-4783	69	8	)	)	PUNCT
ejpam-4783	69	9	:	:	PUNCT
ejpam-4783	70	1	1	1	NUM
ejpam-4783	70	2	≤	≤	NUM
ejpam-4783	70	3	i	i	PRON
ejpam-4783	70	4	≤	≤	NOUN
ejpam-4783	70	5	(	(	PUNCT
ejpam-4783	70	6	γ	γ	X
ejpam-4783	70	7	−	−	PROPN
ejpam-4783	70	8	ξ)/4}|	ξ)/4}|	NOUN
ejpam-4783	70	9	=	=	SYM
ejpam-4783	70	10	(	(	PUNCT
ejpam-4783	70	11	γ	γ	X
ejpam-4783	70	12	−	−	PROPN
ejpam-4783	70	13	ξ)/2	ξ)/2	PROPN
ejpam-4783	70	14	.	.	PUNCT
ejpam-4783	71	1	(	(	PUNCT
ejpam-4783	71	2	d	d	X
ejpam-4783	71	3	)	)	PUNCT
ejpam-4783	71	4	|{(η4i−2	|{(η4i−2	PROPN
ejpam-4783	71	5	,	,	PUNCT
ejpam-4783	71	6	µ4i−2+ξ(η4i−2+ξ	µ4i−2+ξ(η4i−2+ξ	NOUN
ejpam-4783	71	7	)	)	PUNCT
ejpam-4783	71	8	)	)	PUNCT
ejpam-4783	71	9	:	:	PUNCT
ejpam-4783	72	1	1	1	NUM
ejpam-4783	72	2	≤	≤	NUM
ejpam-4783	72	3	i	i	PRON
ejpam-4783	72	4	≤	≤	NOUN
ejpam-4783	72	5	(	(	PUNCT
ejpam-4783	72	6	γ	γ	X
ejpam-4783	72	7	−	−	PROPN
ejpam-4783	72	8	ξ)/4}|	ξ)/4}|	NOUN
ejpam-4783	72	9	=	=	SYM
ejpam-4783	72	10	(	(	PUNCT
ejpam-4783	72	11	γ	γ	X
ejpam-4783	72	12	−	−	PROPN
ejpam-4783	72	13	ξ)/2	ξ)/2	PROPN
ejpam-4783	72	14	.	.	PUNCT
ejpam-4783	73	1	(	(	PUNCT
ejpam-4783	73	2	e	e	NOUN
ejpam-4783	73	3	)	)	PUNCT
ejpam-4783	73	4	|{(µ4i+1	|{(µ4i+1	PROPN
ejpam-4783	73	5	,	,	PUNCT
ejpam-4783	73	6	η4i+2	η4i+2	PROPN
ejpam-4783	73	7	)	)	PUNCT
ejpam-4783	73	8	:	:	PUNCT
ejpam-4783	74	1	0	0	NUM
ejpam-4783	74	2	≤	≤	NUM
ejpam-4783	74	3	i	i	PRON
ejpam-4783	74	4	≤	≤	NOUN
ejpam-4783	74	5	(	(	PUNCT
ejpam-4783	74	6	γ	γ	X
ejpam-4783	74	7	−	−	PROPN
ejpam-4783	74	8	ξ)/4}|	ξ)/4}|	NOUN
ejpam-4783	74	9	=	=	SYM
ejpam-4783	74	10	(	(	PUNCT
ejpam-4783	74	11	γ	γ	X
ejpam-4783	74	12	+	+	NOUN
ejpam-4783	74	13	1)/4	1)/4	NUM
ejpam-4783	74	14	.	.	PUNCT
ejpam-4783	75	1	(	(	PUNCT
ejpam-4783	75	2	f	f	X
ejpam-4783	75	3	)	)	PUNCT
ejpam-4783	75	4	|{(µ4i+2	|{(µ4i+2	PROPN
ejpam-4783	75	5	,	,	PUNCT
ejpam-4783	75	6	η4i+1	η4i+1	PROPN
ejpam-4783	75	7	)	)	PUNCT
ejpam-4783	75	8	:	:	PUNCT
ejpam-4783	75	9	0	0	NUM
ejpam-4783	75	10	≤	≤	NUM
ejpam-4783	76	1	i	i	PRON
ejpam-4783	76	2	≤	≤	NOUN
ejpam-4783	76	3	(	(	PUNCT
ejpam-4783	76	4	γ	γ	X
ejpam-4783	76	5	−	−	PROPN
ejpam-4783	76	6	ξ)/4}|	ξ)/4}|	NOUN
ejpam-4783	76	7	=	=	SYM
ejpam-4783	76	8	(	(	PUNCT
ejpam-4783	76	9	γ	γ	X
ejpam-4783	76	10	+	+	NOUN
ejpam-4783	76	11	1)/4	1)/4	NUM
ejpam-4783	76	12	.	.	PUNCT
ejpam-4783	77	1	(	(	PUNCT
ejpam-4783	77	2	g	g	NOUN
ejpam-4783	77	3	)	)	PUNCT
ejpam-4783	77	4	|{(µ4i−3(η4i−3	|{(µ4i−3(η4i−3	NOUN
ejpam-4783	77	5	)	)	PUNCT
ejpam-4783	77	6	,	,	PUNCT
ejpam-4783	77	7	ω4i−3+ξ	ω4i−3+ξ	NUM
ejpam-4783	77	8	)	)	PUNCT
ejpam-4783	77	9	:	:	PUNCT
ejpam-4783	77	10	1	1	NUM
ejpam-4783	77	11	≤	≤	NUM
ejpam-4783	77	12	i	i	PRON
ejpam-4783	77	13	≤	≤	NOUN
ejpam-4783	77	14	(	(	PUNCT
ejpam-4783	77	15	γ	γ	X
ejpam-4783	77	16	−	−	PROPN
ejpam-4783	77	17	ξ)/4}|	ξ)/4}|	NOUN
ejpam-4783	77	18	=	=	SYM
ejpam-4783	77	19	(	(	PUNCT
ejpam-4783	77	20	γ	γ	X
ejpam-4783	77	21	−	−	PROPN
ejpam-4783	77	22	ξ)/2	ξ)/2	PROPN
ejpam-4783	77	23	.	.	PUNCT
ejpam-4783	78	1	(	(	PUNCT
ejpam-4783	78	2	h	h	NOUN
ejpam-4783	78	3	)	)	PUNCT
ejpam-4783	78	4	∣∣{(ω4i−1	∣∣{(ω4i−1	PROPN
ejpam-4783	78	5	,	,	PUNCT
ejpam-4783	78	6	µ4i+ξ−1(η4i+ξ−1	µ4i+ξ−1(η4i+ξ−1	PUNCT
ejpam-4783	78	7	)	)	PUNCT
ejpam-4783	78	8	)	)	PUNCT
ejpam-4783	78	9	:	:	PUNCT
ejpam-4783	79	1	1	1	NUM
ejpam-4783	79	2	≤	≤	NUM
ejpam-4783	79	3	i	i	PRON
ejpam-4783	79	4	≤	≤	NOUN
ejpam-4783	79	5	(	(	PUNCT
ejpam-4783	79	6	γ	γ	PROPN
ejpam-4783	79	7	−	−	PROPN
ejpam-4783	79	8	ξ)/4	ξ)/4	PROPN
ejpam-4783	79	9	}	}	PUNCT
ejpam-4783	79	10	∣∣	∣∣	X
ejpam-4783	79	11	=	=	SYM
ejpam-4783	79	12	(	(	PUNCT
ejpam-4783	79	13	γ	γ	X
ejpam-4783	79	14	−	−	PROPN
ejpam-4783	79	15	ξ)/2	ξ)/2	PROPN
ejpam-4783	79	16	.	.	PUNCT
ejpam-4783	80	1	(	(	PUNCT
ejpam-4783	80	2	iv	iv	X
ejpam-4783	80	3	)	)	PUNCT
ejpam-4783	80	4	if	if	SCONJ
ejpam-4783	80	5	d(y	d(y	PROPN
ejpam-4783	80	6	,	,	PUNCT
ejpam-4783	80	7	z	z	NOUN
ejpam-4783	80	8	)	)	PUNCT
ejpam-4783	80	9	=	=	SYM
ejpam-4783	80	10	ξ	ξ	PROPN
ejpam-4783	80	11	,	,	PUNCT
ejpam-4783	80	12	ξ	ξ	X
ejpam-4783	80	13	=	=	SYM
ejpam-4783	80	14	4	4	NUM
ejpam-4783	80	15	,	,	PUNCT
ejpam-4783	80	16	8	8	NUM
ejpam-4783	80	17	,	,	PUNCT
ejpam-4783	80	18	.	.	PUNCT
ejpam-4783	80	19	.	.	PUNCT
ejpam-4783	80	20	.	.	PUNCT
ejpam-4783	81	1	,	,	PUNCT
ejpam-4783	81	2	γ	γ	X
ejpam-4783	81	3	−	−	PROPN
ejpam-4783	81	4	7	7	NUM
ejpam-4783	81	5	,	,	PUNCT
ejpam-4783	81	6	then	then	ADV
ejpam-4783	81	7	∑	∑	PUNCT
ejpam-4783	81	8	ξ=4,8,	ξ=4,8,	X
ejpam-4783	81	9	...	...	PUNCT
ejpam-4783	81	10	,γ−7	,γ−7	PUNCT
ejpam-4783	81	11	|aξ|	|aξ|	NOUN
ejpam-4783	81	12	=	=	NOUN
ejpam-4783	82	1	5(γ	5(γ	NUM
ejpam-4783	82	2	−	−	NUM
ejpam-4783	82	3	7)(γ	7)(γ	NUM
ejpam-4783	82	4	+	+	NUM
ejpam-4783	82	5	5)/16	5)/16	NUM
ejpam-4783	82	6	,	,	PUNCT
ejpam-4783	82	7	we	we	PRON
ejpam-4783	82	8	have	have	VERB
ejpam-4783	82	9	seven	seven	NUM
ejpam-4783	82	10	subsets	subset	NOUN
ejpam-4783	82	11	of	of	ADP
ejpam-4783	82	12	it	it	PRON
ejpam-4783	82	13	:	:	PUNCT
ejpam-4783	82	14	(	(	PUNCT
ejpam-4783	82	15	a	a	X
ejpam-4783	82	16	)	)	PUNCT
ejpam-4783	82	17	|{(µ4i+1	|{(µ4i+1	NOUN
ejpam-4783	82	18	,	,	PUNCT
ejpam-4783	82	19	µ4i+1+ξ(η4i+1+ξ	µ4i+1+ξ(η4i+1+ξ	NOUN
ejpam-4783	82	20	)	)	PUNCT
ejpam-4783	82	21	)	)	PUNCT
ejpam-4783	82	22	:	:	PUNCT
ejpam-4783	83	1	0	0	NUM
ejpam-4783	83	2	≤	≤	NUM
ejpam-4783	83	3	i	i	PRON
ejpam-4783	83	4	≤	≤	NOUN
ejpam-4783	83	5	(	(	PUNCT
ejpam-4783	83	6	γ	γ	X
ejpam-4783	83	7	−	−	PROPN
ejpam-4783	83	8	ξ	ξ	PROPN
ejpam-4783	83	9	−	−	PROPN
ejpam-4783	83	10	3)/4}|	3)/4}|	NUM
ejpam-4783	83	11	=	=	SYM
ejpam-4783	83	12	(	(	PUNCT
ejpam-4783	83	13	γ	γ	X
ejpam-4783	83	14	+	+	X
ejpam-4783	83	15	1−	1−	NUM
ejpam-4783	83	16	ξ)/2	ξ)/2	NOUN
ejpam-4783	83	17	.	.	PUNCT
ejpam-4783	84	1	(	(	PUNCT
ejpam-4783	84	2	b	b	X
ejpam-4783	84	3	)	)	PUNCT
ejpam-4783	84	4	|{(µ4i+2	|{(µ4i+2	PROPN
ejpam-4783	84	5	,	,	PUNCT
ejpam-4783	84	6	µ4i+2+ξ(η4i+2+ξ	µ4i+2+ξ(η4i+2+ξ	PROPN
ejpam-4783	84	7	)	)	PUNCT
ejpam-4783	84	8	)	)	PUNCT
ejpam-4783	84	9	:	:	PUNCT
ejpam-4783	85	1	0	0	NUM
ejpam-4783	85	2	≤	≤	NUM
ejpam-4783	85	3	i	i	PRON
ejpam-4783	85	4	≤	≤	NOUN
ejpam-4783	85	5	(	(	PUNCT
ejpam-4783	85	6	γ	γ	X
ejpam-4783	85	7	−	−	PROPN
ejpam-4783	85	8	ξ	ξ	PROPN
ejpam-4783	85	9	−	−	PROPN
ejpam-4783	85	10	3)/4}|	3)/4}|	NUM
ejpam-4783	85	11	=	=	SYM
ejpam-4783	85	12	(	(	PUNCT
ejpam-4783	85	13	γ	γ	X
ejpam-4783	85	14	+	+	X
ejpam-4783	85	15	1−	1−	NUM
ejpam-4783	85	16	ξ)/2	ξ)/2	NOUN
ejpam-4783	85	17	.	.	PUNCT
ejpam-4783	86	1	(	(	PUNCT
ejpam-4783	86	2	c	c	X
ejpam-4783	86	3	)	)	PUNCT
ejpam-4783	86	4	|{(η4i+1	|{(η4i+1	PROPN
ejpam-4783	86	5	,	,	PUNCT
ejpam-4783	86	6	η4i+1+ξ(µ4i+1+ξ	η4i+1+ξ(µ4i+1+ξ	NOUN
ejpam-4783	86	7	)	)	PUNCT
ejpam-4783	86	8	)	)	PUNCT
ejpam-4783	86	9	:	:	PUNCT
ejpam-4783	87	1	0	0	NUM
ejpam-4783	87	2	≤	≤	NUM
ejpam-4783	87	3	i	i	PRON
ejpam-4783	87	4	≤	≤	NOUN
ejpam-4783	87	5	(	(	PUNCT
ejpam-4783	87	6	γ	γ	X
ejpam-4783	87	7	−	−	PROPN
ejpam-4783	87	8	ξ	ξ	PROPN
ejpam-4783	87	9	−	−	PROPN
ejpam-4783	87	10	3)/4}|	3)/4}|	NUM
ejpam-4783	87	11	=	=	SYM
ejpam-4783	87	12	(	(	PUNCT
ejpam-4783	87	13	γ	γ	X
ejpam-4783	87	14	+	+	X
ejpam-4783	87	15	1−	1−	NUM
ejpam-4783	87	16	ξ)/2	ξ)/2	NOUN
ejpam-4783	87	17	.	.	PUNCT
ejpam-4783	88	1	(	(	PUNCT
ejpam-4783	88	2	d	d	X
ejpam-4783	88	3	)	)	PUNCT
ejpam-4783	88	4	|{(η4i+2	|{(η4i+2	PROPN
ejpam-4783	88	5	,	,	PUNCT
ejpam-4783	88	6	η4i+2+ξ(µ4i+2+ξ	η4i+2+ξ(µ4i+2+ξ	NOUN
ejpam-4783	88	7	)	)	PUNCT
ejpam-4783	88	8	)	)	PUNCT
ejpam-4783	88	9	:	:	PUNCT
ejpam-4783	89	1	0	0	NUM
ejpam-4783	89	2	≤	≤	NUM
ejpam-4783	89	3	i	i	PRON
ejpam-4783	89	4	≤	≤	NOUN
ejpam-4783	89	5	(	(	PUNCT
ejpam-4783	89	6	γ	γ	X
ejpam-4783	89	7	−	−	PROPN
ejpam-4783	89	8	ξ	ξ	PROPN
ejpam-4783	89	9	−	−	PROPN
ejpam-4783	89	10	3)/4}|	3)/4}|	NUM
ejpam-4783	89	11	=	=	SYM
ejpam-4783	89	12	(	(	PUNCT
ejpam-4783	89	13	γ	γ	X
ejpam-4783	89	14	+	+	X
ejpam-4783	89	15	1−	1−	NUM
ejpam-4783	89	16	ξ)/2	ξ)/2	NOUN
ejpam-4783	89	17	.	.	PUNCT
ejpam-4783	90	1	(	(	PUNCT
ejpam-4783	90	2	e	e	NOUN
ejpam-4783	90	3	)	)	PUNCT
ejpam-4783	90	4	∣∣{(ω0(γ	∣∣{(ω0(γ	NUM
ejpam-4783	90	5	)	)	PUNCT
ejpam-4783	90	6	,	,	PUNCT
ejpam-4783	90	7	ωξ(γ−ξ	ωξ(γ−ξ	NOUN
ejpam-4783	90	8	)	)	PUNCT
ejpam-4783	90	9	)	)	PUNCT
ejpam-4783	91	1	}	}	PUNCT
ejpam-4783	91	2	∣∣	∣∣	X
ejpam-4783	91	3	=	=	SYM
ejpam-4783	91	4	2	2	X
ejpam-4783	91	5	.	.	PUNCT
ejpam-4783	91	6	(	(	PUNCT
ejpam-4783	91	7	f	f	X
ejpam-4783	91	8	)	)	PUNCT
ejpam-4783	91	9	|{(ω4i−1	|{(ω4i−1	PROPN
ejpam-4783	91	10	,	,	PUNCT
ejpam-4783	91	11	ω4i−1+ξ	ω4i−1+ξ	NUM
ejpam-4783	91	12	)	)	PUNCT
ejpam-4783	91	13	:	:	PUNCT
ejpam-4783	91	14	1	1	NUM
ejpam-4783	91	15	≤	≤	NUM
ejpam-4783	91	16	i	i	PRON
ejpam-4783	91	17	≤	≤	NOUN
ejpam-4783	91	18	(	(	PUNCT
ejpam-4783	91	19	γ	γ	X
ejpam-4783	91	20	−	−	PROPN
ejpam-4783	91	21	ξ	ξ	PROPN
ejpam-4783	91	22	−	−	PROPN
ejpam-4783	91	23	3)/4}|	3)/4}|	NUM
ejpam-4783	91	24	=	=	SYM
ejpam-4783	91	25	(	(	PUNCT
ejpam-4783	91	26	γ	γ	X
ejpam-4783	91	27	−	−	PROPN
ejpam-4783	91	28	3−	3−	PROPN
ejpam-4783	91	29	ξ)/4	ξ)/4	PROPN
ejpam-4783	91	30	.	.	PUNCT
ejpam-4783	92	1	(	(	PUNCT
ejpam-4783	92	2	g	g	NOUN
ejpam-4783	92	3	)	)	PUNCT
ejpam-4783	92	4	|{(ω4i	|{(ω4i	PROPN
ejpam-4783	92	5	,	,	PUNCT
ejpam-4783	92	6	ω4i+ξ	ω4i+ξ	NOUN
ejpam-4783	92	7	)	)	PUNCT
ejpam-4783	92	8	:	:	PUNCT
ejpam-4783	93	1	1	1	NUM
ejpam-4783	93	2	≤	≤	NUM
ejpam-4783	93	3	i	i	PRON
ejpam-4783	93	4	≤	≤	NOUN
ejpam-4783	93	5	(	(	PUNCT
ejpam-4783	93	6	γ	γ	X
ejpam-4783	93	7	−	−	PROPN
ejpam-4783	93	8	ξ	ξ	PROPN
ejpam-4783	93	9	−	−	PROPN
ejpam-4783	93	10	3)/4}|	3)/4}|	NUM
ejpam-4783	93	11	=	=	SYM
ejpam-4783	93	12	(	(	PUNCT
ejpam-4783	93	13	γ	γ	X
ejpam-4783	93	14	−	−	PROPN
ejpam-4783	93	15	3−	3−	PROPN
ejpam-4783	93	16	ξ)/4	ξ)/4	PROPN
ejpam-4783	93	17	.	.	PUNCT
ejpam-4783	94	1	(	(	PUNCT
ejpam-4783	94	2	v	v	NOUN
ejpam-4783	94	3	)	)	PUNCT
ejpam-4783	94	4	if	if	SCONJ
ejpam-4783	94	5	d(y	d(y	PROPN
ejpam-4783	94	6	,	,	PUNCT
ejpam-4783	94	7	z	z	NOUN
ejpam-4783	94	8	)	)	PUNCT
ejpam-4783	94	9	=	=	SYM
ejpam-4783	94	10	ξ	ξ	PROPN
ejpam-4783	94	11	,	,	PUNCT
ejpam-4783	94	12	ξ	ξ	X
ejpam-4783	94	13	=	=	SYM
ejpam-4783	94	14	5	5	NUM
ejpam-4783	94	15	,	,	PUNCT
ejpam-4783	94	16	9	9	NUM
ejpam-4783	94	17	,	,	PUNCT
ejpam-4783	94	18	.	.	PUNCT
ejpam-4783	94	19	.	.	PUNCT
ejpam-4783	95	1	.	.	PUNCT
ejpam-4783	96	1	,	,	PUNCT
ejpam-4783	96	2	γ	γ	X
ejpam-4783	96	3	−	−	PROPN
ejpam-4783	96	4	6	6	NUM
ejpam-4783	96	5	,	,	PUNCT
ejpam-4783	96	6	then	then	ADV
ejpam-4783	96	7	∑	∑	PUNCT
ejpam-4783	96	8	ξ=5,9,	ξ=5,9,	VERB
ejpam-4783	96	9	...	...	PUNCT
ejpam-4783	96	10	,γ−6	,γ−6	PUNCT
ejpam-4783	96	11	|aξ|	|aξ|	NOUN
ejpam-4783	96	12	=	=	SYM
ejpam-4783	96	13	(	(	PUNCT
ejpam-4783	96	14	γ	γ	X
ejpam-4783	96	15	−	−	PROPN
ejpam-4783	96	16	7)(9γ	7)(9γ	NUM
ejpam-4783	96	17	+	+	SYM
ejpam-4783	97	1	37)/32	37)/32	NUM
ejpam-4783	97	2	,	,	PUNCT
ejpam-4783	97	3	we	we	PRON
ejpam-4783	97	4	have	have	VERB
ejpam-4783	97	5	seven	seven	NUM
ejpam-4783	97	6	subsets	subset	NOUN
ejpam-4783	97	7	of	of	ADP
ejpam-4783	97	8	it	it	PRON
ejpam-4783	97	9	:	:	PUNCT
ejpam-4783	97	10	(	(	PUNCT
ejpam-4783	97	11	a	a	X
ejpam-4783	97	12	)	)	PUNCT
ejpam-4783	97	13	|{(µ4i+1	|{(µ4i+1	NOUN
ejpam-4783	97	14	,	,	PUNCT
ejpam-4783	97	15	µ4i+1+ξ(η4i+1+ξ	µ4i+1+ξ(η4i+1+ξ	NOUN
ejpam-4783	97	16	)	)	PUNCT
ejpam-4783	97	17	)	)	PUNCT
ejpam-4783	97	18	:	:	PUNCT
ejpam-4783	97	19	0	0	NUM
ejpam-4783	97	20	≤	≤	NUM
ejpam-4783	97	21	i	i	PRON
ejpam-4783	97	22	≤	≤	NOUN
ejpam-4783	97	23	(	(	PUNCT
ejpam-4783	97	24	γ	γ	X
ejpam-4783	97	25	−	−	PROPN
ejpam-4783	97	26	ξ	ξ	PROPN
ejpam-4783	97	27	−	−	PROPN
ejpam-4783	97	28	2)/4}|	2)/4}|	NUM
ejpam-4783	97	29	=	=	SYM
ejpam-4783	97	30	(	(	PUNCT
ejpam-4783	97	31	γ	γ	X
ejpam-4783	97	32	+	+	NOUN
ejpam-4783	97	33	2−	2−	NUM
ejpam-4783	97	34	ξ)/2	ξ)/2	NOUN
ejpam-4783	97	35	.	.	PUNCT
ejpam-4783	98	1	(	(	PUNCT
ejpam-4783	98	2	b	b	X
ejpam-4783	98	3	)	)	PUNCT
ejpam-4783	98	4	|{(η4i+1	|{(η4i+1	PROPN
ejpam-4783	98	5	,	,	PUNCT
ejpam-4783	98	6	η4i+1+ξ(µ4i+1+ξ	η4i+1+ξ(µ4i+1+ξ	NOUN
ejpam-4783	98	7	)	)	PUNCT
ejpam-4783	98	8	)	)	PUNCT
ejpam-4783	98	9	:	:	PUNCT
ejpam-4783	99	1	0	0	NUM
ejpam-4783	99	2	≤	≤	NUM
ejpam-4783	99	3	i	i	PRON
ejpam-4783	99	4	≤	≤	NOUN
ejpam-4783	99	5	(	(	PUNCT
ejpam-4783	99	6	γ	γ	X
ejpam-4783	99	7	−	−	PROPN
ejpam-4783	99	8	ξ	ξ	PROPN
ejpam-4783	99	9	−	−	PROPN
ejpam-4783	99	10	2)/4}|	2)/4}|	NUM
ejpam-4783	99	11	=	=	SYM
ejpam-4783	99	12	(	(	PUNCT
ejpam-4783	99	13	γ	γ	X
ejpam-4783	99	14	+	+	NOUN
ejpam-4783	99	15	2−	2−	NUM
ejpam-4783	99	16	ξ)/2	ξ)/2	NOUN
ejpam-4783	99	17	.	.	PUNCT
ejpam-4783	100	1	(	(	PUNCT
ejpam-4783	100	2	c	c	NOUN
ejpam-4783	100	3	)	)	PUNCT
ejpam-4783	100	4	|{(µξ(ηξ	|{(µξ(ηξ	NOUN
ejpam-4783	100	5	)	)	PUNCT
ejpam-4783	100	6	,	,	PUNCT
ejpam-4783	100	7	ω0)}|	ω0)}|	NUM
ejpam-4783	100	8	=	=	SYM
ejpam-4783	100	9	2	2	NUM
ejpam-4783	100	10	.	.	NUM
ejpam-4783	100	11	2.2	2.2	NUM
ejpam-4783	100	12	the	the	DET
ejpam-4783	100	13	edges	edge	NOUN
ejpam-4783	100	14	induce	induce	VERB
ejpam-4783	100	15	ring	ring	NOUN
ejpam-4783	100	16	for	for	ADP
ejpam-4783	100	17	hexagonal	hexagonal	ADJ
ejpam-4783	100	18	graphs	graph	NOUN
ejpam-4783	100	19	re(c6)γ	re(c6)γ	NOUN
ejpam-4783	100	20	1584	1584	NUM
ejpam-4783	100	21	(	(	PUNCT
ejpam-4783	100	22	d	d	NOUN
ejpam-4783	100	23	)	)	PUNCT
ejpam-4783	100	24	|{(µγ−ξ(ηγ−ξ	|{(µγ−ξ(ηγ−ξ	NOUN
ejpam-4783	100	25	)	)	PUNCT
ejpam-4783	100	26	,	,	PUNCT
ejpam-4783	100	27	ωγ)}|	ωγ)}|	NOUN
ejpam-4783	100	28	=	=	SYM
ejpam-4783	100	29	2	2	X
ejpam-4783	100	30	.	.	PUNCT
ejpam-4783	100	31	(	(	PUNCT
ejpam-4783	100	32	e	e	NOUN
ejpam-4783	100	33	)	)	PUNCT
ejpam-4783	100	34	|{(µ4i+2(η4i+2	|{(µ4i+2(η4i+2	PROPN
ejpam-4783	100	35	)	)	PUNCT
ejpam-4783	100	36	,	,	PUNCT
ejpam-4783	100	37	ω4i+2+ξ	ω4i+2+ξ	NOUN
ejpam-4783	100	38	)	)	PUNCT
ejpam-4783	100	39	:	:	PUNCT
ejpam-4783	100	40	0	0	NUM
ejpam-4783	100	41	≤	≤	NUM
ejpam-4783	101	1	i	i	PRON
ejpam-4783	101	2	≤	≤	NOUN
ejpam-4783	101	3	(	(	PUNCT
ejpam-4783	101	4	γ	γ	X
ejpam-4783	101	5	−	−	PROPN
ejpam-4783	101	6	ξ	ξ	PROPN
ejpam-4783	101	7	−	−	PROPN
ejpam-4783	101	8	6)/4}|	6)/4}|	NUM
ejpam-4783	101	9	=	=	SYM
ejpam-4783	101	10	(	(	PUNCT
ejpam-4783	101	11	γ	γ	PROPN
ejpam-4783	101	12	−	−	PROPN
ejpam-4783	101	13	2−	2−	NUM
ejpam-4783	101	14	ξ)/2	ξ)/2	NOUN
ejpam-4783	101	15	.	.	PUNCT
ejpam-4783	102	1	(	(	PUNCT
ejpam-4783	102	2	f	f	X
ejpam-4783	102	3	)	)	PUNCT
ejpam-4783	102	4	|{(ω4i	|{(ω4i	PROPN
ejpam-4783	102	5	,	,	PUNCT
ejpam-4783	102	6	µ4i+ξ(η4i+ξ	µ4i+ξ(η4i+ξ	NOUN
ejpam-4783	102	7	)	)	PUNCT
ejpam-4783	102	8	)	)	PUNCT
ejpam-4783	102	9	:	:	PUNCT
ejpam-4783	103	1	0	0	NUM
ejpam-4783	103	2	≤	≤	NUM
ejpam-4783	103	3	i	i	PRON
ejpam-4783	103	4	≤	≤	NOUN
ejpam-4783	103	5	(	(	PUNCT
ejpam-4783	103	6	γ	γ	X
ejpam-4783	103	7	−	−	PROPN
ejpam-4783	103	8	ξ	ξ	PROPN
ejpam-4783	103	9	−	−	PROPN
ejpam-4783	103	10	2)/4}|	2)/4}|	NUM
ejpam-4783	103	11	=	=	SYM
ejpam-4783	103	12	(	(	PUNCT
ejpam-4783	103	13	γ	γ	PROPN
ejpam-4783	103	14	−	−	PROPN
ejpam-4783	103	15	2−	2−	NUM
ejpam-4783	103	16	ξ)/2	ξ)/2	NOUN
ejpam-4783	103	17	.	.	PUNCT
ejpam-4783	104	1	(	(	PUNCT
ejpam-4783	104	2	g	g	NOUN
ejpam-4783	104	3	)	)	PUNCT
ejpam-4783	104	4	|{(ω4i−1	|{(ω4i−1	PROPN
ejpam-4783	104	5	,	,	PUNCT
ejpam-4783	104	6	ω4i−1+ξ	ω4i−1+ξ	NUM
ejpam-4783	104	7	)	)	PUNCT
ejpam-4783	104	8	:	:	PUNCT
ejpam-4783	104	9	1	1	NUM
ejpam-4783	104	10	≤	≤	NUM
ejpam-4783	104	11	i	i	PRON
ejpam-4783	104	12	≤	≤	NOUN
ejpam-4783	104	13	(	(	PUNCT
ejpam-4783	104	14	γ	γ	X
ejpam-4783	104	15	−	−	PROPN
ejpam-4783	104	16	ξ	ξ	PROPN
ejpam-4783	104	17	−	−	PROPN
ejpam-4783	104	18	2)/4}|	2)/4}|	NUM
ejpam-4783	105	1	=	=	SYM
ejpam-4783	105	2	(	(	PUNCT
ejpam-4783	105	3	γ	γ	PROPN
ejpam-4783	105	4	−	−	PROPN
ejpam-4783	105	5	2−	2−	NUM
ejpam-4783	105	6	ξ)/4	ξ)/4	PROPN
ejpam-4783	105	7	.	.	PUNCT
ejpam-4783	106	1	(	(	PUNCT
ejpam-4783	106	2	vi	vi	X
ejpam-4783	106	3	)	)	PUNCT
ejpam-4783	106	4	if	if	SCONJ
ejpam-4783	106	5	d(y	d(y	PROPN
ejpam-4783	106	6	,	,	PUNCT
ejpam-4783	106	7	z	z	NOUN
ejpam-4783	106	8	)	)	PUNCT
ejpam-4783	106	9	=	=	SYM
ejpam-4783	106	10	ξ	ξ	PROPN
ejpam-4783	106	11	,	,	PUNCT
ejpam-4783	106	12	ξ	ξ	X
ejpam-4783	106	13	=	=	SYM
ejpam-4783	106	14	6	6	NUM
ejpam-4783	106	15	,	,	PUNCT
ejpam-4783	106	16	10	10	NUM
ejpam-4783	106	17	,	,	PUNCT
ejpam-4783	106	18	...	...	PUNCT
ejpam-4783	106	19	,	,	PUNCT
ejpam-4783	106	20	γ−5	γ−5	PROPN
ejpam-4783	106	21	,	,	PUNCT
ejpam-4783	106	22	then	then	ADV
ejpam-4783	106	23	∑	∑	PUNCT
ejpam-4783	106	24	ξ=7,11,	ξ=7,11,	NUM
ejpam-4783	106	25	...	...	PUNCT
ejpam-4783	106	26	,γ−5	,γ−5	PUNCT
ejpam-4783	106	27	|aξ|	|aξ|	NOUN
ejpam-4783	107	1	=	=	SYM
ejpam-4783	107	2	(	(	PUNCT
ejpam-4783	107	3	γ	γ	X
ejpam-4783	107	4	−	−	PROPN
ejpam-4783	107	5	7)(γ	7)(γ	PROPN
ejpam-4783	107	6	+	+	CCONJ
ejpam-4783	107	7	1)/4	1)/4	NUM
ejpam-4783	107	8	,	,	PUNCT
ejpam-4783	107	9	we	we	PRON
ejpam-4783	107	10	have	have	VERB
ejpam-4783	107	11	six	six	NUM
ejpam-4783	107	12	subsets	subset	NOUN
ejpam-4783	107	13	of	of	ADP
ejpam-4783	107	14	it	it	PRON
ejpam-4783	107	15	:	:	PUNCT
ejpam-4783	107	16	similar	similar	ADJ
ejpam-4783	107	17	to	to	ADP
ejpam-4783	107	18	(	(	PUNCT
ejpam-4783	107	19	ii(a−	ii(a−	PROPN
ejpam-4783	107	20	f	f	NOUN
ejpam-4783	107	21	)	)	PUNCT
ejpam-4783	107	22	)	)	PUNCT
ejpam-4783	107	23	,	,	PUNCT
ejpam-4783	107	24	put	put	VERB
ejpam-4783	107	25	ξ	ξ	PROPN
ejpam-4783	107	26	=	=	SYM
ejpam-4783	107	27	6	6	NUM
ejpam-4783	107	28	,	,	PUNCT
ejpam-4783	107	29	10	10	NUM
ejpam-4783	107	30	,	,	PUNCT
ejpam-4783	107	31	...	...	PUNCT
ejpam-4783	107	32	,	,	PUNCT
ejpam-4783	107	33	γ	γ	X
ejpam-4783	107	34	−	−	PROPN
ejpam-4783	107	35	5	5	NUM
ejpam-4783	107	36	.	.	PUNCT
ejpam-4783	107	37	(	(	PUNCT
ejpam-4783	107	38	vii	vii	PROPN
ejpam-4783	107	39	)	)	PUNCT
ejpam-4783	108	1	if	if	SCONJ
ejpam-4783	108	2	d(y	d(y	PROPN
ejpam-4783	108	3	,	,	PUNCT
ejpam-4783	108	4	z	z	NOUN
ejpam-4783	108	5	)	)	PUNCT
ejpam-4783	108	6	=	=	SYM
ejpam-4783	108	7	ξ	ξ	PROPN
ejpam-4783	108	8	,	,	PUNCT
ejpam-4783	108	9	ξ	ξ	X
ejpam-4783	108	10	=	=	SYM
ejpam-4783	108	11	7	7	NUM
ejpam-4783	108	12	,	,	PUNCT
ejpam-4783	108	13	11	11	NUM
ejpam-4783	108	14	,	,	PUNCT
ejpam-4783	108	15	...	...	PUNCT
ejpam-4783	108	16	,	,	PUNCT
ejpam-4783	108	17	γ	γ	X
ejpam-4783	108	18	−	−	PROPN
ejpam-4783	108	19	8	8	NUM
ejpam-4783	108	20	,	,	PUNCT
ejpam-4783	108	21	then	then	ADV
ejpam-4783	108	22	∑	∑	PUNCT
ejpam-4783	108	23	ξ=7,11,	ξ=7,11,	NUM
ejpam-4783	108	24	...	...	PUNCT
ejpam-4783	108	25	,γ−8	,γ−8	PUNCT
ejpam-4783	108	26	|aξ|	|aξ|	NOUN
ejpam-4783	109	1	=	=	SYM
ejpam-4783	109	2	(	(	PUNCT
ejpam-4783	109	3	γ	γ	X
ejpam-4783	109	4	−	−	PROPN
ejpam-4783	109	5	11)(9γ	11)(9γ	NUM
ejpam-4783	109	6	+	+	CCONJ
ejpam-4783	109	7	17)/32	17)/32	NUM
ejpam-4783	109	8	,	,	PUNCT
ejpam-4783	109	9	we	we	PRON
ejpam-4783	109	10	have	have	VERB
ejpam-4783	109	11	six	six	NUM
ejpam-4783	109	12	subsets	subset	NOUN
ejpam-4783	109	13	of	of	ADP
ejpam-4783	109	14	it	it	PRON
ejpam-4783	109	15	:	:	PUNCT
ejpam-4783	109	16	similar	similar	ADJ
ejpam-4783	109	17	to	to	ADP
ejpam-4783	109	18	(	(	PUNCT
ejpam-4783	109	19	iii(a−	iii(a−	PROPN
ejpam-4783	109	20	d	d	PROPN
ejpam-4783	109	21	)	)	PUNCT
ejpam-4783	109	22	,	,	PUNCT
ejpam-4783	109	23	(	(	PUNCT
ejpam-4783	109	24	g	g	NOUN
ejpam-4783	109	25	)	)	PUNCT
ejpam-4783	109	26	and	and	CCONJ
ejpam-4783	109	27	(	(	PUNCT
ejpam-4783	109	28	h	h	NOUN
ejpam-4783	109	29	)	)	PUNCT
ejpam-4783	109	30	)	)	PUNCT
ejpam-4783	109	31	,	,	PUNCT
ejpam-4783	109	32	put	put	VERB
ejpam-4783	109	33	ξ	ξ	NOUN
ejpam-4783	109	34	=	=	SYM
ejpam-4783	109	35	7	7	NUM
ejpam-4783	109	36	,	,	PUNCT
ejpam-4783	109	37	11	11	NUM
ejpam-4783	109	38	,	,	PUNCT
ejpam-4783	109	39	...	...	PUNCT
ejpam-4783	109	40	,	,	PUNCT
ejpam-4783	109	41	γ	γ	X
ejpam-4783	109	42	−	−	PROPN
ejpam-4783	109	43	9	9	NUM
ejpam-4783	109	44	.	.	PUNCT
ejpam-4783	110	1	(	(	PUNCT
ejpam-4783	110	2	viii	viii	NOUN
ejpam-4783	110	3	)	)	PUNCT
ejpam-4783	110	4	if	if	SCONJ
ejpam-4783	110	5	d(y	d(y	PROPN
ejpam-4783	110	6	,	,	PUNCT
ejpam-4783	110	7	z	z	NOUN
ejpam-4783	110	8	)	)	PUNCT
ejpam-4783	110	9	=	=	SYM
ejpam-4783	110	10	γ−4	γ−4	PROPN
ejpam-4783	110	11	,	,	PUNCT
ejpam-4783	110	12	|aγ−4|	|aγ−4|	PROPN
ejpam-4783	110	13	=	=	NOUN
ejpam-4783	110	14	10	10	NUM
ejpam-4783	111	1	then	then	ADV
ejpam-4783	111	2	we	we	PRON
ejpam-4783	111	3	have	have	VERB
ejpam-4783	111	4	six	six	NUM
ejpam-4783	111	5	subsets	subset	NOUN
ejpam-4783	111	6	of	of	ADP
ejpam-4783	111	7	it	it	PRON
ejpam-4783	111	8	:	:	PUNCT
ejpam-4783	111	9	similar	similar	ADJ
ejpam-4783	111	10	to	to	ADP
ejpam-4783	111	11	(	(	PUNCT
ejpam-4783	111	12	iii(a−d	iii(a−d	X
ejpam-4783	111	13	)	)	PUNCT
ejpam-4783	111	14	,	,	PUNCT
ejpam-4783	111	15	(	(	PUNCT
ejpam-4783	111	16	f	f	X
ejpam-4783	111	17	)	)	PUNCT
ejpam-4783	111	18	and	and	CCONJ
ejpam-4783	111	19	(	(	PUNCT
ejpam-4783	111	20	h	h	NOUN
ejpam-4783	111	21	)	)	PUNCT
ejpam-4783	111	22	)	)	PUNCT
ejpam-4783	111	23	,	,	PUNCT
ejpam-4783	111	24	put	put	VERB
ejpam-4783	111	25	ξ	ξ	X
ejpam-4783	111	26	=	=	SYM
ejpam-4783	111	27	γ	γ	X
ejpam-4783	111	28	−	−	PROPN
ejpam-4783	111	29	4	4	NUM
ejpam-4783	111	30	.	.	PUNCT
ejpam-4783	112	1	(	(	PUNCT
ejpam-4783	112	2	ix	ix	ADP
ejpam-4783	112	3	)	)	PUNCT
ejpam-4783	112	4	if	if	SCONJ
ejpam-4783	112	5	d(y	d(y	PROPN
ejpam-4783	112	6	,	,	PUNCT
ejpam-4783	112	7	z	z	NOUN
ejpam-4783	112	8	)	)	PUNCT
ejpam-4783	112	9	=	=	PUNCT
ejpam-4783	112	10	γ−	γ−	PROPN
ejpam-4783	112	11	3	3	NUM
ejpam-4783	112	12	,	,	PUNCT
ejpam-4783	112	13	|aγ−3|	|aγ−3|	ADJ
ejpam-4783	112	14	=	=	SYM
ejpam-4783	112	15	10	10	NUM
ejpam-4783	112	16	,	,	PUNCT
ejpam-4783	112	17	there	there	PRON
ejpam-4783	112	18	are	be	VERB
ejpam-4783	112	19	five	five	NUM
ejpam-4783	112	20	subsets	subset	NOUN
ejpam-4783	112	21	of	of	ADP
ejpam-4783	112	22	it	it	PRON
ejpam-4783	112	23	:	:	PUNCT
ejpam-4783	112	24	similar	similar	ADJ
ejpam-4783	112	25	to	to	ADP
ejpam-4783	112	26	(	(	PUNCT
ejpam-4783	112	27	iv(a−	iv(a−	DET
ejpam-4783	112	28	e	e	NOUN
ejpam-4783	112	29	)	)	PUNCT
ejpam-4783	112	30	)	)	PUNCT
ejpam-4783	112	31	,	,	PUNCT
ejpam-4783	112	32	put	put	VERB
ejpam-4783	112	33	ξ	ξ	X
ejpam-4783	112	34	=	=	SYM
ejpam-4783	112	35	γ	γ	X
ejpam-4783	112	36	−	−	PROPN
ejpam-4783	112	37	3	3	NUM
ejpam-4783	112	38	.	.	PUNCT
ejpam-4783	113	1	(	(	PUNCT
ejpam-4783	113	2	x	x	X
ejpam-4783	113	3	)	)	PUNCT
ejpam-4783	113	4	if	if	SCONJ
ejpam-4783	113	5	d(y	d(y	PROPN
ejpam-4783	113	6	,	,	PUNCT
ejpam-4783	113	7	z	z	NOUN
ejpam-4783	113	8	)	)	PUNCT
ejpam-4783	114	1	=	=	SYM
ejpam-4783	114	2	γ	γ	X
ejpam-4783	114	3	−	−	PROPN
ejpam-4783	114	4	2	2	NUM
ejpam-4783	114	5	,	,	PUNCT
ejpam-4783	114	6	|aγ−2|	|aγ−2|	PROPN
ejpam-4783	114	7	=	=	SYM
ejpam-4783	114	8	8	8	NUM
ejpam-4783	114	9	,	,	PUNCT
ejpam-4783	114	10	the	the	DET
ejpam-4783	114	11	four	four	NUM
ejpam-4783	114	12	subsets	subset	NOUN
ejpam-4783	114	13	of	of	ADP
ejpam-4783	114	14	it	it	PRON
ejpam-4783	114	15	:	:	PUNCT
ejpam-4783	114	16	similar	similar	ADJ
ejpam-4783	114	17	to	to	ADP
ejpam-4783	114	18	(	(	PUNCT
ejpam-4783	114	19	iv(a	iv(a	NUM
ejpam-4783	114	20	−	−	PROPN
ejpam-4783	114	21	d	d	NOUN
ejpam-4783	114	22	)	)	PUNCT
ejpam-4783	114	23	)	)	PUNCT
ejpam-4783	114	24	,	,	PUNCT
ejpam-4783	114	25	put	put	VERB
ejpam-4783	114	26	ξ	ξ	X
ejpam-4783	114	27	=	=	SYM
ejpam-4783	114	28	γ	γ	X
ejpam-4783	114	29	−	−	PROPN
ejpam-4783	114	30	2	2	NUM
ejpam-4783	114	31	.	.	PUNCT
ejpam-4783	115	1	(	(	PUNCT
ejpam-4783	115	2	xi	xi	ADP
ejpam-4783	115	3	)	)	PUNCT
ejpam-4783	115	4	if	if	SCONJ
ejpam-4783	115	5	d(y	d(y	PROPN
ejpam-4783	115	6	,	,	PUNCT
ejpam-4783	115	7	z	z	NOUN
ejpam-4783	115	8	)	)	PUNCT
ejpam-4783	115	9	=	=	SYM
ejpam-4783	116	1	γ	γ	X
ejpam-4783	116	2	−	−	PROPN
ejpam-4783	116	3	1	1	NUM
ejpam-4783	116	4	,	,	PUNCT
ejpam-4783	116	5	|aγ−1|	|aγ−1|	VERB
ejpam-4783	116	6	=	=	SYM
ejpam-4783	116	7	4	4	NUM
ejpam-4783	116	8	then	then	ADV
ejpam-4783	116	9	two	two	NUM
ejpam-4783	116	10	subsets	subset	NOUN
ejpam-4783	116	11	of	of	ADP
ejpam-4783	116	12	it	it	PRON
ejpam-4783	116	13	:	:	PUNCT
ejpam-4783	116	14	similar	similar	ADJ
ejpam-4783	116	15	to	to	ADP
ejpam-4783	116	16	(	(	PUNCT
ejpam-4783	116	17	ii(a	ii(a	NUM
ejpam-4783	116	18	−	−	PROPN
ejpam-4783	116	19	b	b	NOUN
ejpam-4783	116	20	)	)	PUNCT
ejpam-4783	116	21	)	)	PUNCT
ejpam-4783	116	22	,	,	PUNCT
ejpam-4783	116	23	put	put	VERB
ejpam-4783	116	24	ξ	ξ	X
ejpam-4783	116	25	=	=	SYM
ejpam-4783	116	26	γ	γ	X
ejpam-4783	116	27	−	−	PROPN
ejpam-4783	116	28	1	1	NUM
ejpam-4783	116	29	.	.	PUNCT
ejpam-4783	117	1	(	(	PUNCT
ejpam-4783	117	2	xii	xii	NOUN
ejpam-4783	117	3	)	)	PUNCT
ejpam-4783	118	1	if	if	SCONJ
ejpam-4783	118	2	d(µ	d(µ	PROPN
ejpam-4783	118	3	,	,	PUNCT
ejpam-4783	118	4	η	η	PROPN
ejpam-4783	118	5	)	)	PUNCT
ejpam-4783	118	6	=	=	SYM
ejpam-4783	118	7	γ	γ	X
ejpam-4783	118	8	then	then	ADV
ejpam-4783	118	9	|aγ	|aγ	PRON
ejpam-4783	119	1	|	|	NOUN
ejpam-4783	119	2	=	=	NOUN
ejpam-4783	119	3	1	1	NUM
ejpam-4783	119	4	,	,	PUNCT
ejpam-4783	119	5	we	we	PRON
ejpam-4783	119	6	have	have	AUX
ejpam-4783	119	7	:	:	PUNCT
ejpam-4783	119	8	|{(ω0	|{(ω0	NUM
ejpam-4783	119	9	,	,	PUNCT
ejpam-4783	119	10	ωγ)}|	ωγ)}|	NOUN
ejpam-4783	119	11	=	=	SYM
ejpam-4783	119	12	1	1	X
ejpam-4783	119	13	.	.	PUNCT
ejpam-4783	119	14	corollary	corollary	ADJ
ejpam-4783	119	15	1	1	NUM
ejpam-4783	119	16	.	.	PUNCT
ejpam-4783	120	1	for	for	ADP
ejpam-4783	120	2	m	m	PROPN
ejpam-4783	120	3	≥	≥	NOUN
ejpam-4783	120	4	3	3	NUM
ejpam-4783	120	5	,	,	PUNCT
ejpam-4783	120	6	γ	γ	X
ejpam-4783	120	7	=	=	SYM
ejpam-4783	120	8	4m−	4m−	PROPN
ejpam-4783	120	9	1	1	NUM
ejpam-4783	120	10	,	,	PUNCT
ejpam-4783	120	11	then	then	ADV
ejpam-4783	120	12	:	:	PUNCT
ejpam-4783	120	13	(	(	PUNCT
ejpam-4783	120	14	i	i	NOUN
ejpam-4783	120	15	)	)	PUNCT
ejpam-4783	120	16	sc(ce(c6)γ	sc(ce(c6)γ	NOUN
ejpam-4783	120	17	)	)	PUNCT
ejpam-4783	120	18	=	=	PUNCT
ejpam-4783	121	1	(	(	PUNCT
ejpam-4783	121	2	7γ3	7γ3	NUM
ejpam-4783	121	3	+	+	CCONJ
ejpam-4783	121	4	15γ2	15γ2	NUM
ejpam-4783	121	5	+	+	NUM
ejpam-4783	121	6	29γ	29γ	NOUN
ejpam-4783	121	7	+	+	CCONJ
ejpam-4783	121	8	21)/4	21)/4	NUM
ejpam-4783	121	9	.	.	PUNCT
ejpam-4783	122	1	(	(	PUNCT
ejpam-4783	122	2	ii	ii	NOUN
ejpam-4783	122	3	)	)	PUNCT
ejpam-4783	122	4	sc∗(ce(c6)γ	sc∗(ce(c6)γ	PROPN
ejpam-4783	122	5	)	)	PUNCT
ejpam-4783	122	6	=	=	PUNCT
ejpam-4783	123	1	(	(	PUNCT
ejpam-4783	123	2	49γ3	49γ3	NUM
ejpam-4783	123	3	+	+	CCONJ
ejpam-4783	123	4	63γ2	63γ2	NUM
ejpam-4783	123	5	+	+	NUM
ejpam-4783	123	6	185γ	185γ	NUM
ejpam-4783	123	7	+	+	CCONJ
ejpam-4783	123	8	147)/24	147)/24	NUM
ejpam-4783	123	9	.	.	PUNCT
ejpam-4783	123	10	2.2	2.2	NUM
ejpam-4783	123	11	.	.	PUNCT
ejpam-4783	124	1	the	the	DET
ejpam-4783	124	2	edges	edge	NOUN
ejpam-4783	124	3	induce	induce	VERB
ejpam-4783	124	4	ring	ring	NOUN
ejpam-4783	124	5	for	for	ADP
ejpam-4783	124	6	hexagonal	hexagonal	ADJ
ejpam-4783	124	7	graphs	graph	NOUN
ejpam-4783	124	8	re(c6)γ	re(c6)γ	NOUN
ejpam-4783	124	9	this	this	DET
ejpam-4783	124	10	graph	graph	NOUN
ejpam-4783	124	11	is	be	AUX
ejpam-4783	124	12	said	say	VERB
ejpam-4783	124	13	to	to	PART
ejpam-4783	124	14	be	be	AUX
ejpam-4783	124	15	a	a	DET
ejpam-4783	124	16	hexagonal	hexagonal	ADJ
ejpam-4783	124	17	bracelet	bracelet	NOUN
ejpam-4783	124	18	graphs	graph	NOUN
ejpam-4783	124	19	re(c6)γ	re(c6)γ	NOUN
ejpam-4783	124	20	which	which	PRON
ejpam-4783	124	21	is	be	AUX
ejpam-4783	124	22	a	a	DET
ejpam-4783	124	23	connected	connected	ADJ
ejpam-4783	124	24	graph	graph	NOUN
ejpam-4783	124	25	consisting	consist	VERB
ejpam-4783	124	26	of	of	ADP
ejpam-4783	124	27	m	m	PROPN
ejpam-4783	124	28	≥	≥	NOUN
ejpam-4783	124	29	3	3	NUM
ejpam-4783	124	30	,	,	PUNCT
ejpam-4783	124	31	hexagonal	hexagonal	ADJ
ejpam-4783	124	32	rings	ring	NOUN
ejpam-4783	124	33	such	such	ADJ
ejpam-4783	124	34	that	that	SCONJ
ejpam-4783	124	35	two	two	NUM
ejpam-4783	124	36	hexagons	hexagon	NOUN
ejpam-4783	124	37	are	be	AUX
ejpam-4783	124	38	joined	join	VERB
ejpam-4783	124	39	by	by	ADP
ejpam-4783	124	40	exactly	exactly	ADV
ejpam-4783	124	41	one	one	NUM
ejpam-4783	124	42	added	add	VERB
ejpam-4783	124	43	edge	edge	NOUN
ejpam-4783	124	44	as	as	SCONJ
ejpam-4783	124	45	shown	show	VERB
ejpam-4783	124	46	in	in	ADP
ejpam-4783	124	47	fig	fig	NOUN
ejpam-4783	124	48	.	.	PUNCT
ejpam-4783	125	1	2	2	X
ejpam-4783	125	2	.	.	X
ejpam-4783	125	3	figure	figure	NOUN
ejpam-4783	125	4	2	2	NUM
ejpam-4783	125	5	:	:	PUNCT
ejpam-4783	125	6	edges	edge	NOUN
ejpam-4783	125	7	induce	induce	VERB
ejpam-4783	125	8	ring	ring	NOUN
ejpam-4783	125	9	for	for	ADP
ejpam-4783	125	10	hexagonal	hexagonal	ADJ
ejpam-4783	125	11	graphs	graph	NOUN
ejpam-4783	125	12	re(c6)γ	re(c6)γ	NOUN
ejpam-4783	125	13	.	.	PUNCT
ejpam-4783	126	1	2.2	2.2	NUM
ejpam-4783	126	2	the	the	DET
ejpam-4783	126	3	edges	edge	NOUN
ejpam-4783	126	4	induce	induce	VERB
ejpam-4783	126	5	ring	ring	NOUN
ejpam-4783	126	6	for	for	ADP
ejpam-4783	126	7	hexagonal	hexagonal	ADJ
ejpam-4783	126	8	graphs	graph	NOUN
ejpam-4783	126	9	re(c6)γ	re(c6)γ	NOUN
ejpam-4783	126	10	1585	1585	NUM
ejpam-4783	126	11	table	table	NOUN
ejpam-4783	126	12	2	2	NUM
ejpam-4783	126	13	:	:	PUNCT
ejpam-4783	126	14	degree	degree	NOUN
ejpam-4783	126	15	matrix	matrix	NOUN
ejpam-4783	126	16	of	of	ADP
ejpam-4783	126	17	re(c6)γ	re(c6)γ	NOUN
ejpam-4783	126	18	for	for	ADP
ejpam-4783	126	19	1	1	NUM
ejpam-4783	126	20	≤	≤	NUM
ejpam-4783	126	21	i	i	PRON
ejpam-4783	126	22	,	,	PUNCT
ejpam-4783	126	23	j	j	PROPN
ejpam-4783	126	24	≤	≤	NOUN
ejpam-4783	126	25	2γ	2γ	NUM
ejpam-4783	126	26	−	−	PROPN
ejpam-4783	126	27	1	1	NUM
ejpam-4783	126	28	,	,	PUNCT
ejpam-4783	126	29	and	and	CCONJ
ejpam-4783	126	30	1	1	NUM
ejpam-4783	126	31	≤	≤	NOUN
ejpam-4783	126	32	r	r	NOUN
ejpam-4783	126	33	,	,	PUNCT
ejpam-4783	126	34	s	s	PART
ejpam-4783	126	35	≤	≤	NUM
ejpam-4783	126	36	m−	m−	PROPN
ejpam-4783	126	37	1	1	NUM
ejpam-4783	126	38	,	,	PUNCT
ejpam-4783	126	39	r	r	NOUN
ejpam-4783	126	40	̸=	̸=	PROPN
ejpam-4783	126	41	s	s	PART
ejpam-4783	126	42	,	,	PUNCT
ejpam-4783	126	43	and	and	CCONJ
ejpam-4783	126	44	i	i	PRON
ejpam-4783	126	45	,	,	PUNCT
ejpam-4783	126	46	j	j	PROPN
ejpam-4783	126	47	̸=	̸=	PROPN
ejpam-4783	126	48	r	r	PROPN
ejpam-4783	126	49	,	,	PUNCT
ejpam-4783	126	50	s.	s.	PROPN
ejpam-4783	126	51	theorem	theorem	VERB
ejpam-4783	126	52	2	2	NUM
ejpam-4783	126	53	.	.	X
ejpam-4783	127	1	for	for	ADP
ejpam-4783	127	2	m	m	PROPN
ejpam-4783	127	3	≥	≥	NOUN
ejpam-4783	127	4	3	3	NUM
ejpam-4783	127	5	,	,	PUNCT
ejpam-4783	127	6	γ	γ	X
ejpam-4783	127	7	=	=	SYM
ejpam-4783	127	8	m	m	PROPN
ejpam-4783	127	9	,	,	PUNCT
ejpam-4783	127	10	then	then	ADV
ejpam-4783	127	11	:	:	PUNCT
ejpam-4783	127	12	(	(	PUNCT
ejpam-4783	127	13	i	i	NOUN
ejpam-4783	127	14	)	)	PUNCT
ejpam-4783	127	15	sc(re(c6);x	sc(re(c6);x	PROPN
ejpam-4783	127	16	)	)	PUNCT
ejpam-4783	127	17	=	=	PUNCT
ejpam-4783	127	18	34γx+	34γx+	NUM
ejpam-4783	127	19	48γx2	48γx2	NOUN
ejpam-4783	127	20	+	+	CCONJ
ejpam-4783	127	21	50γx3	50γx3	NUM
ejpam-4783	127	22	+	+	CCONJ
ejpam-4783	127	23	[	[	PUNCT
ejpam-4783	127	24	∑2γ−4	∑2γ−4	PROPN
ejpam-4783	127	25	ξ=4,8	ξ=4,8	PROPN
ejpam-4783	127	26	44γx	44γx	PROPN
ejpam-4783	127	27	ξ	ξ	PROPN
ejpam-4783	127	28	,	,	PUNCT
ejpam-4783	127	29	γ	γ	PROPN
ejpam-4783	127	30	is	be	AUX
ejpam-4783	127	31	an	an	DET
ejpam-4783	127	32	even∑2γ−2	even∑2γ−2	ADJ
ejpam-4783	127	33	ξ=4,8	ξ=4,8	NOUN
ejpam-4783	127	34	44γx	44γx	NOUN
ejpam-4783	127	35	ξ	ξ	PROPN
ejpam-4783	127	36	,	,	PUNCT
ejpam-4783	127	37	γ	γ	X
ejpam-4783	127	38	is	be	AUX
ejpam-4783	127	39	an	an	DET
ejpam-4783	127	40	odd	odd	ADJ
ejpam-4783	127	41	+	+	CCONJ
ejpam-4783	127	42	∑2γ−1	∑2γ−1	PROPN
ejpam-4783	127	43	ξ=5,7	ξ=5,7	NUM
ejpam-4783	127	44	42γx	42γx	NOUN
ejpam-4783	127	45	ξ	ξ	PROPN
ejpam-4783	127	46	[	[	PUNCT
ejpam-4783	127	47	∑2γ−2	∑2γ−2	PROPN
ejpam-4783	127	48	ξ=4,8	ξ=4,8	PROPN
ejpam-4783	127	49	40γx	40γx	NOUN
ejpam-4783	127	50	ξ	ξ	PROPN
ejpam-4783	127	51	,	,	PUNCT
ejpam-4783	127	52	γ	γ	X
ejpam-4783	127	53	is	be	AUX
ejpam-4783	127	54	an	an	DET
ejpam-4783	127	55	even∑2γ−2	even∑2γ−2	ADJ
ejpam-4783	127	56	ξ=4,8	ξ=4,8	NOUN
ejpam-4783	127	57	40γx	40γx	NOUN
ejpam-4783	127	58	ξ	ξ	PROPN
ejpam-4783	127	59	,	,	PUNCT
ejpam-4783	127	60	γ	γ	X
ejpam-4783	127	61	is	be	AUX
ejpam-4783	127	62	an	an	DET
ejpam-4783	127	63	odd	odd	ADJ
ejpam-4783	127	64	+	+	NOUN
ejpam-4783	127	65	[	[	PUNCT
ejpam-4783	127	66	22γx2γ	22γx2γ	NUM
ejpam-4783	127	67	,	,	PUNCT
ejpam-4783	127	68	γ	γ	X
ejpam-4783	127	69	is	be	AUX
ejpam-4783	127	70	an	an	DET
ejpam-4783	127	71	even	even	ADJ
ejpam-4783	127	72	,	,	PUNCT
ejpam-4783	127	73	20γx2γ	20γx2γ	NUM
ejpam-4783	127	74	,	,	PUNCT
ejpam-4783	127	75	γ	γ	X
ejpam-4783	127	76	is	be	AUX
ejpam-4783	127	77	an	an	DET
ejpam-4783	127	78	odd	odd	ADJ
ejpam-4783	127	79	.	.	PUNCT
ejpam-4783	128	1	(	(	PUNCT
ejpam-4783	128	2	ii	ii	X
ejpam-4783	128	3	)	)	PUNCT
ejpam-4783	128	4	sc∗(re(c6);x	sc∗(re(c6);x	PROPN
ejpam-4783	128	5	)	)	PUNCT
ejpam-4783	129	1	=	=	SYM
ejpam-4783	129	2	41γx+	41γx+	NUM
ejpam-4783	129	3	56γx2	56γx2	NUM
ejpam-4783	129	4	+	+	CCONJ
ejpam-4783	129	5	57γx3	57γx3	NUM
ejpam-4783	129	6	+	+	CCONJ
ejpam-4783	129	7	[	[	PUNCT
ejpam-4783	129	8	∑2γ−4	∑2γ−4	PROPN
ejpam-4783	129	9	ξ=4,8	ξ=4,8	NOUN
ejpam-4783	129	10	50γx	50γx	ADJ
ejpam-4783	129	11	ξ	ξ	PROPN
ejpam-4783	129	12	,	,	PUNCT
ejpam-4783	129	13	γ	γ	PROPN
ejpam-4783	129	14	is	be	AUX
ejpam-4783	129	15	an	an	DET
ejpam-4783	129	16	even∑2γ−2	even∑2γ−2	ADJ
ejpam-4783	129	17	ξ=4,8	ξ=4,8	NOUN
ejpam-4783	129	18	50γx	50γx	NOUN
ejpam-4783	129	19	ξ	ξ	PROPN
ejpam-4783	129	20	,	,	PUNCT
ejpam-4783	129	21	γ	γ	X
ejpam-4783	129	22	is	be	AUX
ejpam-4783	129	23	an	an	DET
ejpam-4783	129	24	odd	odd	ADJ
ejpam-4783	129	25	+	+	CCONJ
ejpam-4783	129	26	∑2γ−1	∑2γ−1	PROPN
ejpam-4783	129	27	ξ=5,7	ξ=5,7	NUM
ejpam-4783	129	28	49γx	49γx	NOUN
ejpam-4783	129	29	ξ	ξ	X
ejpam-4783	129	30	+	+	PUNCT
ejpam-4783	129	31	[	[	PUNCT
ejpam-4783	129	32	∑2γ−2	∑2γ−2	PROPN
ejpam-4783	129	33	ξ=4,8	ξ=4,8	PROPN
ejpam-4783	129	34	48γx	48γx	NOUN
ejpam-4783	129	35	ξ	ξ	PROPN
ejpam-4783	129	36	,	,	PUNCT
ejpam-4783	129	37	γ	γ	X
ejpam-4783	129	38	is	be	AUX
ejpam-4783	129	39	an	an	DET
ejpam-4783	129	40	even∑2γ−2	even∑2γ−2	ADJ
ejpam-4783	129	41	ξ=4,8	ξ=4,8	PROPN
ejpam-4783	129	42	48γx	48γx	NOUN
ejpam-4783	129	43	ξ	ξ	PROPN
ejpam-4783	129	44	,	,	PUNCT
ejpam-4783	129	45	γ	γ	X
ejpam-4783	129	46	is	be	AUX
ejpam-4783	129	47	an	an	DET
ejpam-4783	129	48	odd	odd	ADJ
ejpam-4783	129	49	+	+	NOUN
ejpam-4783	129	50	[	[	PUNCT
ejpam-4783	129	51	25γx2γ	25γx2γ	NUM
ejpam-4783	129	52	,	,	PUNCT
ejpam-4783	129	53	γ	γ	PROPN
ejpam-4783	129	54	is	be	AUX
ejpam-4783	129	55	an	an	DET
ejpam-4783	129	56	even	even	ADJ
ejpam-4783	129	57	,	,	PUNCT
ejpam-4783	129	58	24γx2γ	24γx2γ	NUM
ejpam-4783	129	59	,	,	PUNCT
ejpam-4783	129	60	γ	γ	X
ejpam-4783	129	61	is	be	AUX
ejpam-4783	129	62	an	an	DET
ejpam-4783	129	63	odd	odd	ADJ
ejpam-4783	129	64	.	.	PUNCT
ejpam-4783	130	1	proof	proof	NOUN
ejpam-4783	130	2	.	.	PUNCT
ejpam-4783	131	1	for	for	ADP
ejpam-4783	131	2	any	any	DET
ejpam-4783	131	3	two	two	NUM
ejpam-4783	131	4	vertices	vertex	NOUN
ejpam-4783	131	5	y	y	PROPN
ejpam-4783	131	6	,	,	PUNCT
ejpam-4783	131	7	z	z	PROPN
ejpam-4783	131	8	∈	∈	PROPN
ejpam-4783	131	9	v	v	ADP
ejpam-4783	131	10	(	(	PUNCT
ejpam-4783	131	11	re(c6	re(c6	NOUN
ejpam-4783	131	12	)	)	PUNCT
ejpam-4783	131	13	)	)	PUNCT
ejpam-4783	132	1	there	there	PRON
ejpam-4783	132	2	is	be	VERB
ejpam-4783	132	3	d(y	d(y	NOUN
ejpam-4783	132	4	,	,	PUNCT
ejpam-4783	132	5	z	z	NOUN
ejpam-4783	132	6	)	)	PUNCT
ejpam-4783	132	7	=	=	SYM
ejpam-4783	132	8	ξ	ξ	PROPN
ejpam-4783	132	9	,	,	PUNCT
ejpam-4783	132	10	1	1	NUM
ejpam-4783	132	11	≤	≤	NUM
ejpam-4783	132	12	ξ	ξ	PRON
ejpam-4783	132	13	≤	≤	NOUN
ejpam-4783	132	14	2γ	2γ	NOUN
ejpam-4783	132	15	.	.	PUNCT
ejpam-4783	133	1	and	and	CCONJ
ejpam-4783	133	2	clearly	clearly	ADV
ejpam-4783	133	3	∑γ	∑γ	PROPN
ejpam-4783	133	4	ξ=1	ξ=1	PROPN
ejpam-4783	133	5	d(re(c6)γ	d(re(c6)γ	PROPN
ejpam-4783	133	6	,	,	PUNCT
ejpam-4783	133	7	ξ	ξ	PROPN
ejpam-4783	133	8	)	)	PUNCT
ejpam-4783	134	1	=	=	NOUN
ejpam-4783	135	1	[	[	PUNCT
ejpam-4783	135	2	3γ(6γ	3γ(6γ	NUM
ejpam-4783	135	3	−	−	PROPN
ejpam-4783	135	4	1	1	NUM
ejpam-4783	135	5	)	)	PUNCT
ejpam-4783	135	6	,	,	PUNCT
ejpam-4783	135	7	γ	γ	X
ejpam-4783	135	8	is	be	AUX
ejpam-4783	135	9	an	an	DET
ejpam-4783	135	10	even	even	ADJ
ejpam-4783	135	11	,	,	PUNCT
ejpam-4783	135	12	(	(	PUNCT
ejpam-4783	135	13	1/2)γ(36γ	1/2)γ(36γ	NUM
ejpam-4783	135	14	+	+	NOUN
ejpam-4783	135	15	11	11	NUM
ejpam-4783	135	16	)	)	PUNCT
ejpam-4783	135	17	,	,	PUNCT
ejpam-4783	135	18	γ	γ	X
ejpam-4783	135	19	is	be	AUX
ejpam-4783	135	20	an	an	DET
ejpam-4783	135	21	odd	odd	ADJ
ejpam-4783	135	22	.	.	PUNCT
ejpam-4783	136	1	proof	proof	NOUN
ejpam-4783	136	2	will	will	AUX
ejpam-4783	136	3	be	be	AUX
ejpam-4783	136	4	divided	divide	VERB
ejpam-4783	136	5	into	into	ADP
ejpam-4783	136	6	eight	eight	NUM
ejpam-4783	136	7	cases	case	NOUN
ejpam-4783	136	8	:	:	PUNCT
ejpam-4783	136	9	(	(	PUNCT
ejpam-4783	136	10	i	i	NOUN
ejpam-4783	136	11	)	)	PUNCT
ejpam-4783	136	12	if	if	SCONJ
ejpam-4783	136	13	d(y	d(y	PROPN
ejpam-4783	136	14	,	,	PUNCT
ejpam-4783	136	15	z	z	NOUN
ejpam-4783	136	16	)	)	PUNCT
ejpam-4783	136	17	=	=	SYM
ejpam-4783	136	18	1	1	NUM
ejpam-4783	136	19	,	,	PUNCT
ejpam-4783	136	20	then	then	ADV
ejpam-4783	136	21	|a1|	|a1|	PROPN
ejpam-4783	136	22	=	=	SYM
ejpam-4783	136	23	7γ	7γ	NUM
ejpam-4783	136	24	,	,	PUNCT
ejpam-4783	136	25	there	there	PRON
ejpam-4783	136	26	are	be	VERB
ejpam-4783	136	27	three	three	NUM
ejpam-4783	136	28	subsets	subset	NOUN
ejpam-4783	136	29	of	of	ADP
ejpam-4783	136	30	it	it	PRON
ejpam-4783	136	31	:	:	PUNCT
ejpam-4783	136	32	(	(	PUNCT
ejpam-4783	136	33	a	a	X
ejpam-4783	136	34	)	)	PUNCT
ejpam-4783	136	35	|{(ωi	|{(ωi	PROPN
ejpam-4783	136	36	,	,	PUNCT
ejpam-4783	136	37	µi	µi	PROPN
ejpam-4783	136	38	)	)	PUNCT
ejpam-4783	136	39	,	,	PUNCT
ejpam-4783	136	40	(	(	PUNCT
ejpam-4783	136	41	ωi	ωi	NOUN
ejpam-4783	136	42	,	,	PUNCT
ejpam-4783	136	43	ηi	ηi	PROPN
ejpam-4783	136	44	)	)	PUNCT
ejpam-4783	136	45	:	:	PUNCT
ejpam-4783	136	46	1	1	NUM
ejpam-4783	136	47	≤	≤	NUM
ejpam-4783	136	48	i	i	PRON
ejpam-4783	136	49	≤	≤	NOUN
ejpam-4783	136	50	2γ}|	2γ}|	NUM
ejpam-4783	136	51	=	=	NOUN
ejpam-4783	136	52	4γ	4γ	NOUN
ejpam-4783	136	53	.	.	PUNCT
ejpam-4783	137	1	(	(	PUNCT
ejpam-4783	137	2	b	b	X
ejpam-4783	137	3	)	)	PUNCT
ejpam-4783	137	4	|{(µi	|{(µi	NUM
ejpam-4783	137	5	,	,	PUNCT
ejpam-4783	137	6	µi+1	µi+1	NUM
ejpam-4783	137	7	)	)	PUNCT
ejpam-4783	137	8	,	,	PUNCT
ejpam-4783	137	9	(	(	PUNCT
ejpam-4783	137	10	ηi	ηi	PROPN
ejpam-4783	137	11	,	,	PUNCT
ejpam-4783	137	12	ηi+1	ηi+1	PROPN
ejpam-4783	137	13	)	)	PUNCT
ejpam-4783	137	14	:	:	PUNCT
ejpam-4783	138	1	i	i	NOUN
ejpam-4783	138	2	=	=	NOUN
ejpam-4783	138	3	1	1	NUM
ejpam-4783	138	4	,	,	PUNCT
ejpam-4783	138	5	3	3	NUM
ejpam-4783	138	6	,	,	PUNCT
ejpam-4783	138	7	5	5	NUM
ejpam-4783	138	8	,	,	PUNCT
ejpam-4783	138	9	.	.	PUNCT
ejpam-4783	138	10	.	.	PUNCT
ejpam-4783	138	11	.	.	PUNCT
ejpam-4783	139	1	,	,	PUNCT
ejpam-4783	139	2	2γ	2γ	VERB
ejpam-4783	139	3	−	−	PROPN
ejpam-4783	139	4	1}|	1}|	NUM
ejpam-4783	139	5	=	=	SYM
ejpam-4783	139	6	2γ	2γ	X
ejpam-4783	139	7	.	.	PUNCT
ejpam-4783	140	1	(	(	PUNCT
ejpam-4783	140	2	c	c	X
ejpam-4783	140	3	)	)	PUNCT
ejpam-4783	140	4	|{(ωi	|{(ωi	PROPN
ejpam-4783	140	5	,	,	PUNCT
ejpam-4783	140	6	ωi+1	ωi+1	NUM
ejpam-4783	140	7	)	)	PUNCT
ejpam-4783	140	8	:	:	PUNCT
ejpam-4783	141	1	i	i	NOUN
ejpam-4783	141	2	=	=	NOUN
ejpam-4783	141	3	2	2	NUM
ejpam-4783	141	4	,	,	PUNCT
ejpam-4783	141	5	4	4	NUM
ejpam-4783	141	6	,	,	PUNCT
ejpam-4783	141	7	6	6	NUM
ejpam-4783	141	8	,	,	PUNCT
ejpam-4783	141	9	.	.	PUNCT
ejpam-4783	141	10	.	.	PUNCT
ejpam-4783	141	11	.	.	PUNCT
ejpam-4783	142	1	,	,	PUNCT
ejpam-4783	142	2	2γ	2γ	NOUN
ejpam-4783	142	3	,	,	PUNCT
ejpam-4783	142	4	(	(	PUNCT
ejpam-4783	142	5	ω2γ+1	ω2γ+1	NOUN
ejpam-4783	142	6	≡	≡	PROPN
ejpam-4783	142	7	ω1)}|	ω1)}|	NUM
ejpam-4783	142	8	=	=	SYM
ejpam-4783	142	9	γ	γ	X
ejpam-4783	142	10	.	.	PROPN
ejpam-4783	142	11	(	(	PUNCT
ejpam-4783	142	12	ii	ii	NOUN
ejpam-4783	142	13	)	)	PUNCT
ejpam-4783	142	14	if	if	SCONJ
ejpam-4783	142	15	d(y	d(y	PROPN
ejpam-4783	142	16	,	,	PUNCT
ejpam-4783	142	17	z	z	NOUN
ejpam-4783	142	18	)	)	PUNCT
ejpam-4783	142	19	=	=	SYM
ejpam-4783	142	20	2	2	NUM
ejpam-4783	142	21	,	,	PUNCT
ejpam-4783	142	22	then	then	ADV
ejpam-4783	142	23	|a2|=	|a2|=	PROPN
ejpam-4783	142	24	10γ	10γ	NUM
ejpam-4783	142	25	,	,	PUNCT
ejpam-4783	142	26	there	there	PRON
ejpam-4783	142	27	are	be	VERB
ejpam-4783	142	28	three	three	NUM
ejpam-4783	142	29	subsets	subset	NOUN
ejpam-4783	142	30	of	of	ADP
ejpam-4783	142	31	it	it	PRON
ejpam-4783	142	32	:	:	PUNCT
ejpam-4783	142	33	(	(	PUNCT
ejpam-4783	142	34	a	a	X
ejpam-4783	142	35	)	)	PUNCT
ejpam-4783	142	36	|{(µi	|{(µi	NUM
ejpam-4783	142	37	,	,	PUNCT
ejpam-4783	142	38	ηi	ηi	PROPN
ejpam-4783	142	39	)	)	PUNCT
ejpam-4783	142	40	:	:	PUNCT
ejpam-4783	142	41	1	1	NUM
ejpam-4783	142	42	≤	≤	NUM
ejpam-4783	142	43	i	i	PRON
ejpam-4783	142	44	≤	≤	NOUN
ejpam-4783	142	45	2γ}|	2γ}|	NUM
ejpam-4783	142	46	=	=	NOUN
ejpam-4783	142	47	2γ	2γ	NOUN
ejpam-4783	142	48	.	.	PUNCT
ejpam-4783	143	1	(	(	PUNCT
ejpam-4783	143	2	b	b	X
ejpam-4783	143	3	)	)	PUNCT
ejpam-4783	143	4	|{(ωi	|{(ωi	PROPN
ejpam-4783	143	5	,	,	PUNCT
ejpam-4783	143	6	µi+1	µi+1	NUM
ejpam-4783	143	7	)	)	PUNCT
ejpam-4783	143	8	,	,	PUNCT
ejpam-4783	143	9	(	(	PUNCT
ejpam-4783	143	10	ωi	ωi	NOUN
ejpam-4783	143	11	,	,	PUNCT
ejpam-4783	143	12	ηi+1	ηi+1	PROPN
ejpam-4783	143	13	)	)	PUNCT
ejpam-4783	143	14	:	:	PUNCT
ejpam-4783	144	1	i	i	NOUN
ejpam-4783	144	2	=	=	NOUN
ejpam-4783	144	3	1	1	NUM
ejpam-4783	144	4	,	,	PUNCT
ejpam-4783	144	5	3	3	NUM
ejpam-4783	144	6	,	,	PUNCT
ejpam-4783	144	7	5	5	NUM
ejpam-4783	144	8	,	,	PUNCT
ejpam-4783	144	9	.	.	PUNCT
ejpam-4783	144	10	.	.	PUNCT
ejpam-4783	144	11	.	.	PUNCT
ejpam-4783	145	1	,	,	PUNCT
ejpam-4783	145	2	2γ	2γ	VERB
ejpam-4783	145	3	−	−	PROPN
ejpam-4783	145	4	1}|	1}|	NUM
ejpam-4783	145	5	=	=	SYM
ejpam-4783	145	6	2γ	2γ	X
ejpam-4783	145	7	.	.	PUNCT
ejpam-4783	146	1	(	(	PUNCT
ejpam-4783	146	2	c	c	X
ejpam-4783	146	3	)	)	PUNCT
ejpam-4783	146	4	|{(ωi	|{(ωi	PROPN
ejpam-4783	146	5	,	,	PUNCT
ejpam-4783	146	6	µi−1	µi−1	PROPN
ejpam-4783	146	7	)	)	PUNCT
ejpam-4783	146	8	,	,	PUNCT
ejpam-4783	146	9	(	(	PUNCT
ejpam-4783	146	10	ωi	ωi	PROPN
ejpam-4783	146	11	,	,	PUNCT
ejpam-4783	146	12	ηi−1	ηi−1	PROPN
ejpam-4783	146	13	)	)	PUNCT
ejpam-4783	146	14	,	,	PUNCT
ejpam-4783	146	15	(	(	PUNCT
ejpam-4783	146	16	µi	µi	INTJ
ejpam-4783	146	17	,	,	PUNCT
ejpam-4783	146	18	ωi+1	ωi+1	NUM
ejpam-4783	146	19	)	)	PUNCT
ejpam-4783	146	20	,	,	PUNCT
ejpam-4783	146	21	(	(	PUNCT
ejpam-4783	146	22	ηi	ηi	PROPN
ejpam-4783	146	23	,	,	PUNCT
ejpam-4783	146	24	ωi+1	ωi+1	NUM
ejpam-4783	146	25	)	)	PUNCT
ejpam-4783	146	26	,	,	PUNCT
ejpam-4783	146	27	(	(	PUNCT
ejpam-4783	146	28	ωi	ωi	NOUN
ejpam-4783	146	29	,	,	PUNCT
ejpam-4783	146	30	µi+1	µi+1	NUM
ejpam-4783	146	31	)	)	PUNCT
ejpam-4783	146	32	,	,	PUNCT
ejpam-4783	146	33	(	(	PUNCT
ejpam-4783	146	34	ωi	ωi	NOUN
ejpam-4783	146	35	,	,	PUNCT
ejpam-4783	146	36	ηi+1	ηi+1	PROPN
ejpam-4783	146	37	)	)	PUNCT
ejpam-4783	146	38	:	:	PUNCT
ejpam-4783	147	1	i	i	NOUN
ejpam-4783	147	2	=	=	NOUN
ejpam-4783	147	3	2	2	NUM
ejpam-4783	147	4	,	,	PUNCT
ejpam-4783	147	5	4	4	NUM
ejpam-4783	147	6	,	,	PUNCT
ejpam-4783	147	7	6	6	NUM
ejpam-4783	147	8	,	,	PUNCT
ejpam-4783	147	9	.	.	PUNCT
ejpam-4783	147	10	.	.	PUNCT
ejpam-4783	147	11	.	.	PUNCT
ejpam-4783	148	1	,	,	PUNCT
ejpam-4783	148	2	2γ	2γ	NOUN
ejpam-4783	148	3	,	,	PUNCT
ejpam-4783	148	4	(	(	PUNCT
ejpam-4783	148	5	ω2γ+1	ω2γ+1	PROPN
ejpam-4783	148	6	≡	≡	PROPN
ejpam-4783	148	7	ω1	ω1	PROPN
ejpam-4783	148	8	)	)	PUNCT
ejpam-4783	148	9	,	,	PUNCT
ejpam-4783	148	10	(	(	PUNCT
ejpam-4783	148	11	µ2γ+1	µ2γ+1	NUM
ejpam-4783	148	12	≡	≡	PROPN
ejpam-4783	148	13	u1	u1	NOUN
ejpam-4783	148	14	)	)	PUNCT
ejpam-4783	148	15	,	,	PUNCT
ejpam-4783	148	16	(	(	PUNCT
ejpam-4783	148	17	η2γ+1	η2γ+1	PROPN
ejpam-4783	148	18	≡	≡	PROPN
ejpam-4783	148	19	η1)}|	η1)}|	PROPN
ejpam-4783	148	20	=	=	SYM
ejpam-4783	148	21	6γ	6γ	NOUN
ejpam-4783	148	22	.	.	PUNCT
ejpam-4783	149	1	(	(	PUNCT
ejpam-4783	149	2	iii	iii	X
ejpam-4783	149	3	)	)	PUNCT
ejpam-4783	149	4	if	if	SCONJ
ejpam-4783	149	5	d(y	d(y	PROPN
ejpam-4783	149	6	,	,	PUNCT
ejpam-4783	149	7	z	z	NOUN
ejpam-4783	149	8	)	)	PUNCT
ejpam-4783	149	9	=	=	SYM
ejpam-4783	149	10	3	3	NUM
ejpam-4783	149	11	,	,	PUNCT
ejpam-4783	149	12	then	then	ADV
ejpam-4783	149	13	|a3|	|a3|	VERB
ejpam-4783	149	14	=	=	PRON
ejpam-4783	149	15	11γ	11γ	NUM
ejpam-4783	149	16	,	,	PUNCT
ejpam-4783	149	17	there	there	PRON
ejpam-4783	149	18	are	be	VERB
ejpam-4783	149	19	three	three	NUM
ejpam-4783	149	20	subsets	subset	NOUN
ejpam-4783	149	21	:	:	PUNCT
ejpam-4783	149	22	(	(	PUNCT
ejpam-4783	149	23	a	a	X
ejpam-4783	149	24	)	)	PUNCT
ejpam-4783	149	25	|	|	NOUN
ejpam-4783	149	26	{	{	PUNCT
ejpam-4783	149	27	(	(	PUNCT
ejpam-4783	149	28	ωi	ωi	NOUN
ejpam-4783	149	29	,	,	PUNCT
ejpam-4783	149	30	ωi+1	ωi+1	NUM
ejpam-4783	149	31	)	)	PUNCT
ejpam-4783	149	32	:	:	PUNCT
ejpam-4783	150	1	i	i	NOUN
ejpam-4783	150	2	=	=	NOUN
ejpam-4783	150	3	1	1	NUM
ejpam-4783	150	4	,	,	PUNCT
ejpam-4783	150	5	3	3	NUM
ejpam-4783	150	6	,	,	PUNCT
ejpam-4783	150	7	5	5	NUM
ejpam-4783	150	8	,	,	PUNCT
ejpam-4783	150	9	.	.	PUNCT
ejpam-4783	150	10	.	.	PUNCT
ejpam-4783	150	11	.	.	PUNCT
ejpam-4783	151	1	,	,	PUNCT
ejpam-4783	151	2	2γ	2γ	NOUN
ejpam-4783	151	3	−	−	PROPN
ejpam-4783	151	4	1	1	X
ejpam-4783	151	5	}	}	PUNCT
ejpam-4783	151	6	|	|	NOUN
ejpam-4783	151	7	=	=	SYM
ejpam-4783	151	8	γ	γ	X
ejpam-4783	151	9	.	.	PROPN
ejpam-4783	151	10	2.2	2.2	NUM
ejpam-4783	151	11	the	the	DET
ejpam-4783	151	12	edges	edge	NOUN
ejpam-4783	151	13	induce	induce	VERB
ejpam-4783	151	14	ring	ring	NOUN
ejpam-4783	151	15	for	for	ADP
ejpam-4783	151	16	hexagonal	hexagonal	ADJ
ejpam-4783	151	17	graphs	graph	NOUN
ejpam-4783	151	18	re(c6)γ	re(c6)γ	PROPN
ejpam-4783	151	19	1586	1586	NUM
ejpam-4783	151	20	(	(	PUNCT
ejpam-4783	151	21	b	b	NOUN
ejpam-4783	151	22	)	)	PUNCT
ejpam-4783	151	23	|{(µi	|{(µi	PROPN
ejpam-4783	151	24	,	,	PUNCT
ejpam-4783	151	25	ωi+2	ωi+2	NUM
ejpam-4783	151	26	)	)	PUNCT
ejpam-4783	151	27	,	,	PUNCT
ejpam-4783	151	28	(	(	PUNCT
ejpam-4783	151	29	ηi	ηi	PROPN
ejpam-4783	151	30	,	,	PUNCT
ejpam-4783	151	31	ωi+2	ωi+2	NUM
ejpam-4783	151	32	)	)	PUNCT
ejpam-4783	151	33	,	,	PUNCT
ejpam-4783	151	34	(	(	PUNCT
ejpam-4783	151	35	µi	µi	PROPN
ejpam-4783	151	36	,	,	PUNCT
ejpam-4783	151	37	ηi+1	ηi+1	PROPN
ejpam-4783	151	38	)	)	PUNCT
ejpam-4783	151	39	,	,	PUNCT
ejpam-4783	151	40	(	(	PUNCT
ejpam-4783	151	41	ηi	ηi	INTJ
ejpam-4783	151	42	,	,	PUNCT
ejpam-4783	151	43	µi+1	µi+1	NUM
ejpam-4783	151	44	)	)	PUNCT
ejpam-4783	151	45	:	:	PUNCT
ejpam-4783	152	1	i	i	NOUN
ejpam-4783	152	2	=	=	NOUN
ejpam-4783	152	3	1	1	NUM
ejpam-4783	152	4	,	,	PUNCT
ejpam-4783	152	5	3	3	NUM
ejpam-4783	152	6	,	,	PUNCT
ejpam-4783	152	7	5	5	NUM
ejpam-4783	152	8	,	,	PUNCT
ejpam-4783	152	9	.	.	PUNCT
ejpam-4783	152	10	.	.	PUNCT
ejpam-4783	152	11	.	.	PUNCT
ejpam-4783	153	1	,	,	PUNCT
ejpam-4783	153	2	2γ	2γ	NOUN
ejpam-4783	153	3	−	−	PROPN
ejpam-4783	153	4	1	1	NUM
ejpam-4783	153	5	,	,	PUNCT
ejpam-4783	153	6	(	(	PUNCT
ejpam-4783	153	7	ω2γ+1	ω2γ+1	NOUN
ejpam-4783	153	8	≡	≡	PROPN
ejpam-4783	153	9	ω1)}|	ω1)}|	NUM
ejpam-4783	153	10	=	=	NOUN
ejpam-4783	153	11	4γ	4γ	NOUN
ejpam-4783	153	12	.	.	PUNCT
ejpam-4783	154	1	(	(	PUNCT
ejpam-4783	154	2	c	c	X
ejpam-4783	154	3	)	)	PUNCT
ejpam-4783	154	4	|	|	ADV
ejpam-4783	154	5	{	{	PUNCT
ejpam-4783	154	6	(	(	PUNCT
ejpam-4783	154	7	µi	µi	INTJ
ejpam-4783	154	8	,	,	PUNCT
ejpam-4783	154	9	µi+1	µi+1	NOUN
ejpam-4783	154	10	)	)	PUNCT
ejpam-4783	154	11	,	,	PUNCT
ejpam-4783	154	12	(	(	PUNCT
ejpam-4783	154	13	µi	µi	PROPN
ejpam-4783	154	14	,	,	PUNCT
ejpam-4783	154	15	ηi+1	ηi+1	PROPN
ejpam-4783	154	16	)	)	PUNCT
ejpam-4783	154	17	,	,	PUNCT
ejpam-4783	154	18	(	(	PUNCT
ejpam-4783	154	19	ηi	ηi	INTJ
ejpam-4783	154	20	,	,	PUNCT
ejpam-4783	154	21	µi+1	µi+1	NUM
ejpam-4783	154	22	)	)	PUNCT
ejpam-4783	154	23	,	,	PUNCT
ejpam-4783	154	24	(	(	PUNCT
ejpam-4783	154	25	ηi	ηi	PROPN
ejpam-4783	154	26	,	,	PUNCT
ejpam-4783	154	27	ηi+1	ηi+1	PROPN
ejpam-4783	154	28	)	)	PUNCT
ejpam-4783	154	29	,	,	PUNCT
ejpam-4783	154	30	(	(	PUNCT
ejpam-4783	154	31	ωi	ωi	NOUN
ejpam-4783	154	32	,	,	PUNCT
ejpam-4783	154	33	µi+2	µi+2	NUM
ejpam-4783	154	34	)	)	PUNCT
ejpam-4783	154	35	,	,	PUNCT
ejpam-4783	154	36	(	(	PUNCT
ejpam-4783	154	37	ωi	ωi	NOUN
ejpam-4783	154	38	,	,	PUNCT
ejpam-4783	154	39	ηi+2	ηi+2	PROPN
ejpam-4783	154	40	)	)	PUNCT
ejpam-4783	154	41	:	:	PUNCT
ejpam-4783	155	1	i	i	NOUN
ejpam-4783	155	2	=	=	NOUN
ejpam-4783	155	3	2	2	NUM
ejpam-4783	155	4	,	,	PUNCT
ejpam-4783	155	5	4	4	NUM
ejpam-4783	155	6	,	,	PUNCT
ejpam-4783	155	7	6	6	NUM
ejpam-4783	155	8	,	,	PUNCT
ejpam-4783	155	9	.	.	PUNCT
ejpam-4783	155	10	.	.	PUNCT
ejpam-4783	155	11	.	.	PUNCT
ejpam-4783	156	1	,	,	PUNCT
ejpam-4783	156	2	2γ	2γ	NOUN
ejpam-4783	156	3	,	,	PUNCT
ejpam-4783	156	4	(	(	PUNCT
ejpam-4783	156	5	µ2γ+1	µ2γ+1	PROPN
ejpam-4783	156	6	≡	≡	PROPN
ejpam-4783	156	7	µ1	µ1	PROPN
ejpam-4783	156	8	)	)	PUNCT
ejpam-4783	156	9	,	,	PUNCT
ejpam-4783	156	10	(	(	PUNCT
ejpam-4783	156	11	η2γ+1	η2γ+1	PROPN
ejpam-4783	156	12	≡	≡	PROPN
ejpam-4783	156	13	η1	η1	PROPN
ejpam-4783	156	14	)	)	PUNCT
ejpam-4783	156	15	,	,	PUNCT
ejpam-4783	156	16	(	(	PUNCT
ejpam-4783	156	17	µ2γ+2	µ2γ+2	PROPN
ejpam-4783	156	18	≡	≡	PROPN
ejpam-4783	156	19	µ2	µ2	PROPN
ejpam-4783	156	20	)	)	PUNCT
ejpam-4783	156	21	,	,	PUNCT
ejpam-4783	156	22	(	(	PUNCT
ejpam-4783	156	23	η2γ+2	η2γ+2	PROPN
ejpam-4783	156	24	≡	≡	PROPN
ejpam-4783	156	25	η2)}|	η2)}|	PROPN
ejpam-4783	156	26	=	=	SYM
ejpam-4783	156	27	6γ	6γ	NOUN
ejpam-4783	156	28	.	.	PUNCT
ejpam-4783	157	1	(	(	PUNCT
ejpam-4783	157	2	iv	iv	X
ejpam-4783	157	3	)	)	PUNCT
ejpam-4783	157	4	if	if	SCONJ
ejpam-4783	157	5	d(y	d(y	PROPN
ejpam-4783	157	6	,	,	PUNCT
ejpam-4783	157	7	z	z	NOUN
ejpam-4783	157	8	)	)	PUNCT
ejpam-4783	157	9	=	=	SYM
ejpam-4783	157	10	ξ	ξ	PROPN
ejpam-4783	157	11	,	,	PUNCT
ejpam-4783	157	12	ξ	ξ	X
ejpam-4783	157	13	=	=	SYM
ejpam-4783	157	14	4	4	NUM
ejpam-4783	157	15	,	,	PUNCT
ejpam-4783	157	16	8	8	NUM
ejpam-4783	157	17	,	,	PUNCT
ejpam-4783	157	18	.	.	PUNCT
ejpam-4783	157	19	.	.	PUNCT
ejpam-4783	158	1	.	.	PUNCT
ejpam-4783	159	1	,	,	PUNCT
ejpam-4783	159	2	2γ	2γ	NOUN
ejpam-4783	159	3	−	−	PROPN
ejpam-4783	159	4	4	4	NUM
ejpam-4783	159	5	,	,	PUNCT
ejpam-4783	159	6	then	then	ADV
ejpam-4783	159	7	we	we	PRON
ejpam-4783	159	8	have	have	VERB
ejpam-4783	159	9	:	:	PUNCT
ejpam-4783	159	10	a	a	X
ejpam-4783	159	11	:	:	PUNCT
ejpam-4783	159	12	if	if	SCONJ
ejpam-4783	159	13	γ	γ	X
ejpam-4783	159	14	is	be	AUX
ejpam-4783	159	15	an	an	DET
ejpam-4783	159	16	even	even	ADJ
ejpam-4783	159	17	number	number	NOUN
ejpam-4783	159	18	,	,	PUNCT
ejpam-4783	159	19	then	then	ADV
ejpam-4783	159	20	we	we	PRON
ejpam-4783	159	21	have	have	VERB
ejpam-4783	159	22	two	two	NUM
ejpam-4783	159	23	subsets	subset	NOUN
ejpam-4783	159	24	of	of	ADP
ejpam-4783	159	25	it	it	PRON
ejpam-4783	159	26	(	(	PUNCT
ejpam-4783	159	27	a	a	X
ejpam-4783	159	28	)	)	PUNCT
ejpam-4783	159	29	|	|	NOUN
ejpam-4783	159	30	{	{	PUNCT
ejpam-4783	159	31	(	(	PUNCT
ejpam-4783	159	32	ωi	ωi	NOUN
ejpam-4783	159	33	,	,	PUNCT
ejpam-4783	159	34	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	159	35	)	)	PUNCT
ejpam-4783	159	36	)	)	PUNCT
ejpam-4783	159	37	,	,	PUNCT
ejpam-4783	159	38	(	(	PUNCT
ejpam-4783	159	39	µi	µi	INTJ
ejpam-4783	159	40	,	,	PUNCT
ejpam-4783	159	41	µi+(ξ/2	µi+(ξ/2	PROPN
ejpam-4783	159	42	)	)	PUNCT
ejpam-4783	159	43	)	)	PUNCT
ejpam-4783	159	44	,	,	PUNCT
ejpam-4783	159	45	(	(	PUNCT
ejpam-4783	159	46	µi	µi	INTJ
ejpam-4783	159	47	,	,	PUNCT
ejpam-4783	159	48	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	159	49	)	)	PUNCT
ejpam-4783	159	50	)	)	PUNCT
ejpam-4783	159	51	,	,	PUNCT
ejpam-4783	159	52	(	(	PUNCT
ejpam-4783	159	53	ηi	ηi	X
ejpam-4783	159	54	,	,	PUNCT
ejpam-4783	159	55	µi+(ξ/2	µi+(ξ/2	NOUN
ejpam-4783	159	56	)	)	PUNCT
ejpam-4783	159	57	)	)	PUNCT
ejpam-4783	159	58	,	,	PUNCT
ejpam-4783	159	59	(	(	PUNCT
ejpam-4783	159	60	ηi	ηi	NOUN
ejpam-4783	159	61	,	,	PUNCT
ejpam-4783	159	62	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	159	63	)	)	PUNCT
ejpam-4783	159	64	)	)	PUNCT
ejpam-4783	159	65	:	:	PUNCT
ejpam-4783	160	1	i	i	NOUN
ejpam-4783	160	2	=	=	NOUN
ejpam-4783	160	3	1	1	NUM
ejpam-4783	160	4	,	,	PUNCT
ejpam-4783	160	5	3	3	NUM
ejpam-4783	160	6	,	,	PUNCT
ejpam-4783	160	7	5	5	NUM
ejpam-4783	160	8	,	,	PUNCT
ejpam-4783	160	9	.	.	PUNCT
ejpam-4783	160	10	.	.	PUNCT
ejpam-4783	160	11	.	.	PUNCT
ejpam-4783	161	1	,	,	PUNCT
ejpam-4783	161	2	2γ	2γ	NOUN
ejpam-4783	161	3	−	−	PROPN
ejpam-4783	161	4	1	1	X
ejpam-4783	161	5	}	}	PUNCT
ejpam-4783	161	6	|	|	NOUN
ejpam-4783	161	7	=	=	SYM
ejpam-4783	161	8	5γ	5γ	NOUN
ejpam-4783	161	9	.	.	PUNCT
ejpam-4783	162	1	if	if	SCONJ
ejpam-4783	162	2	i+	i+	NUM
ejpam-4783	162	3	ξ	ξ	SYM
ejpam-4783	162	4	2	2	NUM
ejpam-4783	162	5	>	>	X
ejpam-4783	162	6	2γ	2γ	NOUN
ejpam-4783	162	7	,	,	PUNCT
ejpam-4783	162	8	then	then	ADV
ejpam-4783	162	9	(	(	PUNCT
ejpam-4783	162	10	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	162	11	)	)	PUNCT
ejpam-4783	162	12	≡	≡	PROPN
ejpam-4783	162	13	ωi+(ξ/2)−2γ	ωi+(ξ/2)−2γ	PRON
ejpam-4783	162	14	)	)	PUNCT
ejpam-4783	162	15	,	,	PUNCT
ejpam-4783	162	16	(	(	PUNCT
ejpam-4783	162	17	µi+(ξ/2	µi+(ξ/2	PROPN
ejpam-4783	162	18	)	)	PUNCT
ejpam-4783	162	19	≡	≡	PROPN
ejpam-4783	162	20	µi+(ξ/2)−2γ	µi+(ξ/2)−2γ	ADP
ejpam-4783	162	21	)	)	PUNCT
ejpam-4783	162	22	,	,	PUNCT
ejpam-4783	162	23	(	(	PUNCT
ejpam-4783	162	24	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	162	25	)	)	PUNCT
ejpam-4783	162	26	≡	≡	PROPN
ejpam-4783	162	27	ηi+(ξ/2)−2γ	ηi+(ξ/2)−2γ	PROPN
ejpam-4783	162	28	)	)	PUNCT
ejpam-4783	162	29	.	.	PUNCT
ejpam-4783	163	1	(	(	PUNCT
ejpam-4783	163	2	b	b	X
ejpam-4783	163	3	)	)	PUNCT
ejpam-4783	163	4	|	|	ADV
ejpam-4783	163	5	{	{	PUNCT
ejpam-4783	163	6	(	(	PUNCT
ejpam-4783	163	7	ωi	ωi	NOUN
ejpam-4783	163	8	,	,	PUNCT
ejpam-4783	163	9	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	163	10	)	)	PUNCT
ejpam-4783	163	11	)	)	PUNCT
ejpam-4783	163	12	,	,	PUNCT
ejpam-4783	163	13	(	(	PUNCT
ejpam-4783	163	14	µi	µi	INTJ
ejpam-4783	163	15	,	,	PUNCT
ejpam-4783	163	16	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	163	17	)	)	PUNCT
ejpam-4783	163	18	)	)	PUNCT
ejpam-4783	163	19	,	,	PUNCT
ejpam-4783	163	20	(	(	PUNCT
ejpam-4783	163	21	µi	µi	INTJ
ejpam-4783	163	22	,	,	PUNCT
ejpam-4783	163	23	µi+(ξ/2	µi+(ξ/2	PROPN
ejpam-4783	163	24	)	)	PUNCT
ejpam-4783	163	25	)	)	PUNCT
ejpam-4783	163	26	,	,	PUNCT
ejpam-4783	163	27	(	(	PUNCT
ejpam-4783	163	28	ηi	ηi	X
ejpam-4783	163	29	,	,	PUNCT
ejpam-4783	163	30	µi+(ξ/2	µi+(ξ/2	NOUN
ejpam-4783	163	31	)	)	PUNCT
ejpam-4783	163	32	)	)	PUNCT
ejpam-4783	163	33	,	,	PUNCT
ejpam-4783	163	34	(	(	PUNCT
ejpam-4783	163	35	ηi	ηi	NOUN
ejpam-4783	163	36	,	,	PUNCT
ejpam-4783	163	37	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	163	38	)	)	PUNCT
ejpam-4783	163	39	)	)	PUNCT
ejpam-4783	163	40	:	:	PUNCT
ejpam-4783	164	1	i	i	NOUN
ejpam-4783	164	2	=	=	NOUN
ejpam-4783	164	3	2	2	NUM
ejpam-4783	164	4	,	,	PUNCT
ejpam-4783	164	5	4	4	NUM
ejpam-4783	164	6	,	,	PUNCT
ejpam-4783	164	7	6	6	NUM
ejpam-4783	164	8	,	,	PUNCT
ejpam-4783	164	9	.	.	PUNCT
ejpam-4783	164	10	.	.	PUNCT
ejpam-4783	164	11	.	.	PUNCT
ejpam-4783	165	1	,	,	PUNCT
ejpam-4783	165	2	2γ	2γ	NOUN
ejpam-4783	165	3	}	}	PUNCT
ejpam-4783	165	4	|	|	ADV
ejpam-4783	165	5	=	=	SYM
ejpam-4783	165	6	5γ	5γ	NOUN
ejpam-4783	165	7	.	.	PUNCT
ejpam-4783	166	1	if	if	SCONJ
ejpam-4783	166	2	i+(ξ/2	i+(ξ/2	NOUN
ejpam-4783	166	3	)	)	PUNCT
ejpam-4783	166	4	>	>	X
ejpam-4783	166	5	2γ	2γ	NOUN
ejpam-4783	166	6	,	,	PUNCT
ejpam-4783	166	7	then	then	ADV
ejpam-4783	166	8	(	(	PUNCT
ejpam-4783	166	9	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	166	10	)	)	PUNCT
ejpam-4783	166	11	≡	≡	PROPN
ejpam-4783	166	12	ωi+(ξ/2)−2γ	ωi+(ξ/2)−2γ	PRON
ejpam-4783	166	13	)	)	PUNCT
ejpam-4783	166	14	,	,	PUNCT
ejpam-4783	166	15	(	(	PUNCT
ejpam-4783	166	16	µi+(ξ/2	µi+(ξ/2	PROPN
ejpam-4783	166	17	)	)	PUNCT
ejpam-4783	166	18	≡	≡	PROPN
ejpam-4783	166	19	µi+(ξ/2)−2γ	µi+(ξ/2)−2γ	ADP
ejpam-4783	166	20	)	)	PUNCT
ejpam-4783	166	21	,	,	PUNCT
ejpam-4783	166	22	(	(	PUNCT
ejpam-4783	166	23	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	166	24	)	)	PUNCT
ejpam-4783	166	25	≡	≡	PROPN
ejpam-4783	166	26	ηi+(ξ/2)−2γ	ηi+(ξ/2)−2γ	PROPN
ejpam-4783	166	27	)	)	PUNCT
ejpam-4783	166	28	.	.	PUNCT
ejpam-4783	167	1	hence	hence	ADV
ejpam-4783	167	2	∑2γ−4	∑2γ−4	PROPN
ejpam-4783	167	3	ξ=4,8	ξ=4,8	NOUN
ejpam-4783	167	4	|aξ|	|aξ|	NOUN
ejpam-4783	168	1	=	=	NOUN
ejpam-4783	168	2	10γ	10γ	NUM
ejpam-4783	168	3	b	b	X
ejpam-4783	168	4	:	:	PUNCT
ejpam-4783	168	5	if	if	SCONJ
ejpam-4783	168	6	γ	γ	X
ejpam-4783	168	7	is	be	AUX
ejpam-4783	168	8	an	an	DET
ejpam-4783	168	9	odd	odd	ADJ
ejpam-4783	168	10	number	number	NOUN
ejpam-4783	168	11	,	,	PUNCT
ejpam-4783	168	12	we	we	PRON
ejpam-4783	168	13	get	get	VERB
ejpam-4783	168	14	∑2γ−2	∑2γ−2	PROPN
ejpam-4783	168	15	ξ=4,8	ξ=4,8	NOUN
ejpam-4783	168	16	|aξ|	|aξ|	NOUN
ejpam-4783	169	1	=	=	PRON
ejpam-4783	169	2	10γ	10γ	NOUN
ejpam-4783	169	3	,	,	PUNCT
ejpam-4783	169	4	note	note	VERB
ejpam-4783	169	5	we	we	PRON
ejpam-4783	169	6	add	add	VERB
ejpam-4783	169	7	the	the	DET
ejpam-4783	169	8	distance	distance	NOUN
ejpam-4783	169	9	of	of	ADP
ejpam-4783	169	10	ξ	ξ	NOUN
ejpam-4783	169	11	=	=	NOUN
ejpam-4783	169	12	2γ	2γ	NOUN
ejpam-4783	169	13	−	−	PROPN
ejpam-4783	169	14	2	2	X
ejpam-4783	169	15	.	.	PUNCT
ejpam-4783	169	16	(	(	PUNCT
ejpam-4783	169	17	v	v	NOUN
ejpam-4783	169	18	)	)	PUNCT
ejpam-4783	169	19	if	if	SCONJ
ejpam-4783	169	20	d(y	d(y	PROPN
ejpam-4783	169	21	,	,	PUNCT
ejpam-4783	169	22	z	z	NOUN
ejpam-4783	169	23	)	)	PUNCT
ejpam-4783	169	24	=	=	SYM
ejpam-4783	169	25	ξ	ξ	PROPN
ejpam-4783	169	26	,	,	PUNCT
ejpam-4783	169	27	ξ	ξ	X
ejpam-4783	169	28	=	=	SYM
ejpam-4783	169	29	5	5	NUM
ejpam-4783	169	30	,	,	PUNCT
ejpam-4783	169	31	9	9	NUM
ejpam-4783	169	32	,	,	PUNCT
ejpam-4783	169	33	13	13	NUM
ejpam-4783	169	34	,	,	PUNCT
ejpam-4783	169	35	.	.	PUNCT
ejpam-4783	169	36	.	.	PUNCT
ejpam-4783	170	1	.	.	PUNCT
ejpam-4783	171	1	,	,	PUNCT
ejpam-4783	171	2	2γ	2γ	NOUN
ejpam-4783	171	3	−	−	PROPN
ejpam-4783	171	4	3	3	NUM
ejpam-4783	171	5	,	,	PUNCT
ejpam-4783	171	6	then	then	ADV
ejpam-4783	171	7	we	we	PRON
ejpam-4783	171	8	have	have	VERB
ejpam-4783	171	9	:	:	PUNCT
ejpam-4783	171	10	a	a	X
ejpam-4783	171	11	:	:	PUNCT
ejpam-4783	171	12	if	if	SCONJ
ejpam-4783	171	13	γ	γ	X
ejpam-4783	171	14	is	be	AUX
ejpam-4783	171	15	an	an	DET
ejpam-4783	171	16	even	even	ADJ
ejpam-4783	171	17	number	number	NOUN
ejpam-4783	171	18	,	,	PUNCT
ejpam-4783	171	19	then	then	ADV
ejpam-4783	171	20	we	we	PRON
ejpam-4783	171	21	have	have	VERB
ejpam-4783	171	22	four	four	NUM
ejpam-4783	171	23	subsets	subset	NOUN
ejpam-4783	171	24	of	of	ADP
ejpam-4783	171	25	it	it	PRON
ejpam-4783	171	26	(	(	PUNCT
ejpam-4783	171	27	a	a	X
ejpam-4783	171	28	)	)	PUNCT
ejpam-4783	171	29	|	|	NOUN
ejpam-4783	171	30	{	{	PUNCT
ejpam-4783	171	31	(	(	PUNCT
ejpam-4783	171	32	ωi	ωi	NOUN
ejpam-4783	171	33	,	,	PUNCT
ejpam-4783	171	34	µi+(ξ−1)/2	µi+(ξ−1)/2	NOUN
ejpam-4783	171	35	)	)	PUNCT
ejpam-4783	171	36	,	,	PUNCT
ejpam-4783	171	37	(	(	PUNCT
ejpam-4783	171	38	ωi	ωi	NOUN
ejpam-4783	171	39	,	,	PUNCT
ejpam-4783	171	40	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	171	41	)	)	PUNCT
ejpam-4783	171	42	:	:	PUNCT
ejpam-4783	172	1	i	i	NOUN
ejpam-4783	172	2	=	=	NOUN
ejpam-4783	172	3	1	1	NUM
ejpam-4783	172	4	,	,	PUNCT
ejpam-4783	172	5	3	3	NUM
ejpam-4783	172	6	,	,	PUNCT
ejpam-4783	172	7	5	5	NUM
ejpam-4783	172	8	,	,	PUNCT
ejpam-4783	172	9	.	.	PUNCT
ejpam-4783	172	10	.	.	PUNCT
ejpam-4783	172	11	.	.	PUNCT
ejpam-4783	173	1	,	,	PUNCT
ejpam-4783	173	2	2γ	2γ	NOUN
ejpam-4783	173	3	−	−	PROPN
ejpam-4783	173	4	1	1	X
ejpam-4783	173	5	}	}	PUNCT
ejpam-4783	173	6	|	|	ADV
ejpam-4783	173	7	=	=	SYM
ejpam-4783	173	8	2γ	2γ	NOUN
ejpam-4783	173	9	.	.	PUNCT
ejpam-4783	174	1	if	if	SCONJ
ejpam-4783	174	2	i+(ξ−1/2	i+(ξ−1/2	NOUN
ejpam-4783	174	3	)	)	PUNCT
ejpam-4783	174	4	>	>	X
ejpam-4783	174	5	2γ	2γ	NOUN
ejpam-4783	174	6	,	,	PUNCT
ejpam-4783	174	7	then	then	ADV
ejpam-4783	174	8	(	(	PUNCT
ejpam-4783	174	9	µi+(ξ−1/2	µi+(ξ−1/2	PROPN
ejpam-4783	174	10	)	)	PUNCT
ejpam-4783	174	11	≡	≡	PROPN
ejpam-4783	174	12	µi+(ξ−1)/2−2γ	µi+(ξ−1)/2−2γ	PROPN
ejpam-4783	174	13	)	)	PUNCT
ejpam-4783	174	14	,	,	PUNCT
ejpam-4783	174	15	(	(	PUNCT
ejpam-4783	174	16	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	174	17	≡	≡	PROPN
ejpam-4783	174	18	ηi+(ξ−1)/2−2γ	ηi+(ξ−1)/2−2γ	PROPN
ejpam-4783	174	19	)	)	PUNCT
ejpam-4783	174	20	.	.	PUNCT
ejpam-4783	175	1	(	(	PUNCT
ejpam-4783	175	2	b	b	X
ejpam-4783	175	3	)	)	PUNCT
ejpam-4783	175	4	|	|	ADV
ejpam-4783	175	5	{	{	PUNCT
ejpam-4783	175	6	(	(	PUNCT
ejpam-4783	175	7	µi	µi	INTJ
ejpam-4783	175	8	,	,	PUNCT
ejpam-4783	175	9	µi+(ξ−1)/2	µi+(ξ−1)/2	NOUN
ejpam-4783	175	10	+	+	NOUN
ejpam-4783	175	11	1	1	NUM
ejpam-4783	175	12	)	)	PUNCT
ejpam-4783	175	13	,	,	PUNCT
ejpam-4783	175	14	(	(	PUNCT
ejpam-4783	175	15	µi	µi	INTJ
ejpam-4783	175	16	,	,	PUNCT
ejpam-4783	175	17	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	175	18	+	+	PROPN
ejpam-4783	175	19	1	1	NUM
ejpam-4783	175	20	)	)	PUNCT
ejpam-4783	175	21	,	,	PUNCT
ejpam-4783	175	22	(	(	PUNCT
ejpam-4783	175	23	ηi	ηi	INTJ
ejpam-4783	175	24	,	,	PUNCT
ejpam-4783	175	25	µi+(ξ−1)/2	µi+(ξ−1)/2	NOUN
ejpam-4783	175	26	+	+	NOUN
ejpam-4783	175	27	1	1	NUM
ejpam-4783	175	28	)	)	PUNCT
ejpam-4783	175	29	,	,	PUNCT
ejpam-4783	175	30	(	(	PUNCT
ejpam-4783	175	31	ηi	ηi	INTJ
ejpam-4783	175	32	,	,	PUNCT
ejpam-4783	175	33	ηi+(ξ−1)/2	ηi+(ξ−1)/2	ADJ
ejpam-4783	175	34	+	+	PROPN
ejpam-4783	175	35	1	1	NUM
ejpam-4783	175	36	)	)	PUNCT
ejpam-4783	175	37	:	:	PUNCT
ejpam-4783	176	1	i	i	NOUN
ejpam-4783	176	2	=	=	NOUN
ejpam-4783	176	3	1	1	NUM
ejpam-4783	176	4	,	,	PUNCT
ejpam-4783	176	5	3	3	NUM
ejpam-4783	176	6	,	,	PUNCT
ejpam-4783	176	7	5	5	NUM
ejpam-4783	176	8	,	,	PUNCT
ejpam-4783	176	9	.	.	PUNCT
ejpam-4783	176	10	.	.	PUNCT
ejpam-4783	176	11	.	.	PUNCT
ejpam-4783	177	1	,	,	PUNCT
ejpam-4783	177	2	2γ	2γ	NOUN
ejpam-4783	177	3	−	−	PROPN
ejpam-4783	177	4	1	1	X
ejpam-4783	177	5	}	}	PUNCT
ejpam-4783	177	6	|	|	NOUN
ejpam-4783	177	7	=	=	SYM
ejpam-4783	177	8	4γ	4γ	NOUN
ejpam-4783	177	9	.	.	PUNCT
ejpam-4783	178	1	if	if	SCONJ
ejpam-4783	178	2	i+(ξ−	i+(ξ−	NOUN
ejpam-4783	178	3	1)/2	1)/2	NUM
ejpam-4783	178	4	+	+	ADP
ejpam-4783	178	5	1	1	NUM
ejpam-4783	178	6	>	>	X
ejpam-4783	178	7	2γ	2γ	NOUN
ejpam-4783	178	8	,	,	PUNCT
ejpam-4783	178	9	then	then	ADV
ejpam-4783	178	10	(	(	PUNCT
ejpam-4783	178	11	µi+(ξ−1)/2	µi+(ξ−1)/2	X
ejpam-4783	178	12	+	+	ADJ
ejpam-4783	178	13	1	1	NUM
ejpam-4783	178	14	≡	≡	NOUN
ejpam-4783	178	15	µi+(ξ−1)/2	µi+(ξ−1)/2	X
ejpam-4783	178	16	+	+	NOUN
ejpam-4783	178	17	1−2γ	1−2γ	NUM
ejpam-4783	178	18	)	)	PUNCT
ejpam-4783	178	19	,	,	PUNCT
ejpam-4783	178	20	(	(	PUNCT
ejpam-4783	178	21	ηi+(ξ−1)/2	ηi+(ξ−1)/2	ADJ
ejpam-4783	178	22	+	+	ADJ
ejpam-4783	178	23	1	1	NUM
ejpam-4783	178	24	≡	≡	ADJ
ejpam-4783	178	25	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	178	26	+	+	PROPN
ejpam-4783	178	27	1−2γ	1−2γ	NUM
ejpam-4783	178	28	)	)	PUNCT
ejpam-4783	178	29	.	.	PUNCT
ejpam-4783	179	1	(	(	PUNCT
ejpam-4783	179	2	c	c	X
ejpam-4783	179	3	)	)	PUNCT
ejpam-4783	179	4	|	|	ADV
ejpam-4783	179	5	{	{	PUNCT
ejpam-4783	179	6	(	(	PUNCT
ejpam-4783	179	7	µi	µi	INTJ
ejpam-4783	179	8	,	,	PUNCT
ejpam-4783	179	9	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	179	10	)	)	PUNCT
ejpam-4783	179	11	,	,	PUNCT
ejpam-4783	179	12	(	(	PUNCT
ejpam-4783	179	13	ηi	ηi	PROPN
ejpam-4783	179	14	,	,	PUNCT
ejpam-4783	179	15	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	179	16	)	)	PUNCT
ejpam-4783	179	17	:	:	PUNCT
ejpam-4783	180	1	i	i	NOUN
ejpam-4783	180	2	=	=	NOUN
ejpam-4783	180	3	2	2	NUM
ejpam-4783	180	4	,	,	PUNCT
ejpam-4783	180	5	4	4	NUM
ejpam-4783	180	6	,	,	PUNCT
ejpam-4783	180	7	6	6	NUM
ejpam-4783	180	8	,	,	PUNCT
ejpam-4783	180	9	.	.	PUNCT
ejpam-4783	180	10	.	.	PUNCT
ejpam-4783	180	11	.	.	PUNCT
ejpam-4783	181	1	,	,	PUNCT
ejpam-4783	181	2	2γ	2γ	NOUN
ejpam-4783	181	3	}	}	PUNCT
ejpam-4783	181	4	|	|	ADV
ejpam-4783	181	5	=	=	SYM
ejpam-4783	181	6	2γ	2γ	NOUN
ejpam-4783	181	7	.	.	PUNCT
ejpam-4783	182	1	if	if	SCONJ
ejpam-4783	182	2	i+	i+	NUM
ejpam-4783	182	3	(	(	PUNCT
ejpam-4783	182	4	ξ	ξ	X
ejpam-4783	182	5	−	−	PROPN
ejpam-4783	182	6	1)/2	1)/2	NUM
ejpam-4783	182	7	>	>	X
ejpam-4783	182	8	2γ	2γ	NOUN
ejpam-4783	182	9	,	,	PUNCT
ejpam-4783	182	10	then	then	ADV
ejpam-4783	182	11	(	(	PUNCT
ejpam-4783	182	12	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	182	13	≡	≡	PROPN
ejpam-4783	182	14	ωi+(ξ−1)/2−2γ	ωi+(ξ−1)/2−2γ	PROPN
ejpam-4783	182	15	)	)	PUNCT
ejpam-4783	182	16	.	.	PUNCT
ejpam-4783	183	1	(	(	PUNCT
ejpam-4783	183	2	d	d	X
ejpam-4783	183	3	)	)	PUNCT
ejpam-4783	183	4	|	|	ADV
ejpam-4783	183	5	{	{	PUNCT
ejpam-4783	183	6	(	(	PUNCT
ejpam-4783	183	7	ωi	ωi	NOUN
ejpam-4783	183	8	,	,	PUNCT
ejpam-4783	183	9	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	183	10	+	+	PROPN
ejpam-4783	183	11	1	1	NUM
ejpam-4783	183	12	)	)	PUNCT
ejpam-4783	183	13	:	:	PUNCT
ejpam-4783	184	1	i	i	NOUN
ejpam-4783	184	2	=	=	NOUN
ejpam-4783	184	3	2	2	NUM
ejpam-4783	184	4	,	,	PUNCT
ejpam-4783	184	5	4	4	NUM
ejpam-4783	184	6	,	,	PUNCT
ejpam-4783	184	7	6	6	NUM
ejpam-4783	184	8	,	,	PUNCT
ejpam-4783	184	9	.	.	PUNCT
ejpam-4783	184	10	.	.	PUNCT
ejpam-4783	184	11	.	.	PUNCT
ejpam-4783	185	1	,	,	PUNCT
ejpam-4783	185	2	2γ	2γ	NOUN
ejpam-4783	185	3	}	}	PUNCT
ejpam-4783	185	4	|	|	NOUN
ejpam-4783	185	5	=	=	SYM
ejpam-4783	185	6	γ	γ	X
ejpam-4783	185	7	.	.	PUNCT
ejpam-4783	186	1	if	if	SCONJ
ejpam-4783	186	2	i	i	PRON
ejpam-4783	186	3	+	+	X
ejpam-4783	186	4	(	(	PUNCT
ejpam-4783	186	5	ξ	ξ	X
ejpam-4783	186	6	−	−	PROPN
ejpam-4783	186	7	1)/2	1)/2	NUM
ejpam-4783	186	8	+	+	CCONJ
ejpam-4783	186	9	1	1	NUM
ejpam-4783	186	10	>	>	ADP
ejpam-4783	186	11	2γ	2γ	NOUN
ejpam-4783	186	12	,	,	PUNCT
ejpam-4783	186	13	then	then	ADV
ejpam-4783	186	14	(	(	PUNCT
ejpam-4783	186	15	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	186	16	+	+	PROPN
ejpam-4783	186	17	1	1	NUM
ejpam-4783	186	18	≡	≡	PROPN
ejpam-4783	186	19	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	186	20	+	+	PROPN
ejpam-4783	186	21	1−2γ	1−2γ	NUM
ejpam-4783	186	22	)	)	PUNCT
ejpam-4783	186	23	.	.	PUNCT
ejpam-4783	187	1	hence	hence	ADV
ejpam-4783	187	2	∑2γ−3	∑2γ−3	PROPN
ejpam-4783	187	3	ξ=5,9	ξ=5,9	NOUN
ejpam-4783	187	4	|aξ|	|aξ|	NOUN
ejpam-4783	188	1	=	=	NOUN
ejpam-4783	188	2	9γ	9γ	NUM
ejpam-4783	188	3	,	,	PUNCT
ejpam-4783	188	4	b	b	NOUN
ejpam-4783	188	5	:	:	PUNCT
ejpam-4783	188	6	if	if	SCONJ
ejpam-4783	188	7	γ	γ	X
ejpam-4783	188	8	is	be	AUX
ejpam-4783	188	9	an	an	DET
ejpam-4783	188	10	odd	odd	ADJ
ejpam-4783	188	11	number	number	NOUN
ejpam-4783	188	12	,	,	PUNCT
ejpam-4783	188	13	we	we	PRON
ejpam-4783	188	14	get	get	VERB
ejpam-4783	188	15	∑2γ−1	∑2γ−1	PROPN
ejpam-4783	188	16	ξ=5,9	ξ=5,9	NOUN
ejpam-4783	188	17	|aξ|	|aξ|	NOUN
ejpam-4783	189	1	=	=	NOUN
ejpam-4783	189	2	9γ	9γ	NUM
ejpam-4783	189	3	,	,	PUNCT
ejpam-4783	189	4	note	note	VERB
ejpam-4783	189	5	we	we	PRON
ejpam-4783	189	6	add	add	VERB
ejpam-4783	189	7	the	the	DET
ejpam-4783	189	8	distance	distance	NOUN
ejpam-4783	189	9	of	of	ADP
ejpam-4783	189	10	ξ	ξ	NOUN
ejpam-4783	189	11	=	=	NOUN
ejpam-4783	189	12	2γ	2γ	NOUN
ejpam-4783	189	13	−	−	PROPN
ejpam-4783	189	14	1	1	X
ejpam-4783	189	15	.	.	PUNCT
ejpam-4783	190	1	if	if	SCONJ
ejpam-4783	190	2	d(y	d(y	PROPN
ejpam-4783	190	3	,	,	PUNCT
ejpam-4783	190	4	z	z	NOUN
ejpam-4783	190	5	)	)	PUNCT
ejpam-4783	190	6	=	=	SYM
ejpam-4783	190	7	ξ	ξ	PROPN
ejpam-4783	190	8	,	,	PUNCT
ejpam-4783	190	9	ξ	ξ	X
ejpam-4783	190	10	=	=	SYM
ejpam-4783	190	11	6	6	NUM
ejpam-4783	190	12	,	,	PUNCT
ejpam-4783	190	13	10	10	NUM
ejpam-4783	190	14	,	,	PUNCT
ejpam-4783	190	15	14	14	NUM
ejpam-4783	190	16	,	,	PUNCT
ejpam-4783	190	17	.	.	PUNCT
ejpam-4783	190	18	.	.	PUNCT
ejpam-4783	191	1	.	.	PUNCT
ejpam-4783	192	1	,	,	PUNCT
ejpam-4783	192	2	2γ	2γ	NOUN
ejpam-4783	192	3	−	−	PROPN
ejpam-4783	192	4	2	2	NUM
ejpam-4783	192	5	,	,	PUNCT
ejpam-4783	192	6	then∑2γ−2	then∑2γ−2	PROPN
ejpam-4783	192	7	ξ=6,10	ξ=6,10	NOUN
ejpam-4783	192	8	|aξ|	|aξ|	NOUN
ejpam-4783	193	1	=	=	SYM
ejpam-4783	193	2	8γ	8γ	NOUN
ejpam-4783	193	3	,	,	PUNCT
ejpam-4783	193	4	we	we	PRON
ejpam-4783	193	5	have	have	VERB
ejpam-4783	193	6	two	two	NUM
ejpam-4783	193	7	subsets	subset	NOUN
ejpam-4783	193	8	of	of	ADP
ejpam-4783	193	9	it	it	PRON
ejpam-4783	193	10	:	:	PUNCT
ejpam-4783	193	11	(	(	PUNCT
ejpam-4783	193	12	a	a	X
ejpam-4783	193	13	)	)	PUNCT
ejpam-4783	193	14	|	|	NOUN
ejpam-4783	193	15	{	{	PUNCT
ejpam-4783	193	16	(	(	PUNCT
ejpam-4783	193	17	ωi	ωi	NOUN
ejpam-4783	193	18	,	,	PUNCT
ejpam-4783	193	19	µi+(ξ/2	µi+(ξ/2	NOUN
ejpam-4783	193	20	)	)	PUNCT
ejpam-4783	193	21	)	)	PUNCT
ejpam-4783	193	22	,	,	PUNCT
ejpam-4783	193	23	(	(	PUNCT
ejpam-4783	193	24	ωi	ωi	NOUN
ejpam-4783	193	25	,	,	PUNCT
ejpam-4783	193	26	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	193	27	)	)	PUNCT
ejpam-4783	193	28	)	)	PUNCT
ejpam-4783	193	29	,	,	PUNCT
ejpam-4783	193	30	(	(	PUNCT
ejpam-4783	193	31	µi	µi	INTJ
ejpam-4783	193	32	,	,	PUNCT
ejpam-4783	193	33	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	193	34	)	)	PUNCT
ejpam-4783	193	35	)	)	PUNCT
ejpam-4783	193	36	,	,	PUNCT
ejpam-4783	193	37	(	(	PUNCT
ejpam-4783	193	38	ηi	ηi	INTJ
ejpam-4783	193	39	,	,	PUNCT
ejpam-4783	193	40	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	193	41	)	)	PUNCT
ejpam-4783	193	42	)	)	PUNCT
ejpam-4783	193	43	:	:	PUNCT
ejpam-4783	194	1	i	i	NOUN
ejpam-4783	194	2	=	=	NOUN
ejpam-4783	194	3	1	1	NUM
ejpam-4783	194	4	,	,	PUNCT
ejpam-4783	194	5	3	3	NUM
ejpam-4783	194	6	,	,	PUNCT
ejpam-4783	194	7	5	5	NUM
ejpam-4783	194	8	,	,	PUNCT
ejpam-4783	194	9	.	.	PUNCT
ejpam-4783	194	10	.	.	PUNCT
ejpam-4783	194	11	.	.	PUNCT
ejpam-4783	195	1	,	,	PUNCT
ejpam-4783	195	2	2γ	2γ	NOUN
ejpam-4783	195	3	−	−	PROPN
ejpam-4783	195	4	1	1	X
ejpam-4783	195	5	}	}	PUNCT
ejpam-4783	195	6	|	|	NOUN
ejpam-4783	195	7	=	=	SYM
ejpam-4783	195	8	4γ	4γ	NOUN
ejpam-4783	195	9	.	.	PUNCT
ejpam-4783	196	1	2.2	2.2	NUM
ejpam-4783	196	2	the	the	DET
ejpam-4783	196	3	edges	edge	NOUN
ejpam-4783	196	4	induce	induce	VERB
ejpam-4783	196	5	ring	ring	NOUN
ejpam-4783	196	6	for	for	ADP
ejpam-4783	196	7	hexagonal	hexagonal	ADJ
ejpam-4783	196	8	graphs	graph	NOUN
ejpam-4783	196	9	re(c6)γ	re(c6)γ	PROPN
ejpam-4783	196	10	1587	1587	NUM
ejpam-4783	196	11	if	if	SCONJ
ejpam-4783	196	12	i+(ξ/2	i+(ξ/2	NOUN
ejpam-4783	196	13	)	)	PUNCT
ejpam-4783	196	14	>	>	X
ejpam-4783	196	15	2γ	2γ	NOUN
ejpam-4783	196	16	,	,	PUNCT
ejpam-4783	196	17	then	then	ADV
ejpam-4783	196	18	(	(	PUNCT
ejpam-4783	196	19	µi+(ξ/2	µi+(ξ/2	PROPN
ejpam-4783	196	20	)	)	PUNCT
ejpam-4783	196	21	≡	≡	PROPN
ejpam-4783	196	22	µi+(ξ/2)−2γ	µi+(ξ/2)−2γ	ADP
ejpam-4783	196	23	)	)	PUNCT
ejpam-4783	196	24	,	,	PUNCT
ejpam-4783	196	25	(	(	PUNCT
ejpam-4783	196	26	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	196	27	)	)	PUNCT
ejpam-4783	196	28	≡	≡	PROPN
ejpam-4783	196	29	ηi+(ξ/2)−2γ	ηi+(ξ/2)−2γ	PROPN
ejpam-4783	196	30	)	)	PUNCT
ejpam-4783	196	31	,	,	PUNCT
ejpam-4783	196	32	(	(	PUNCT
ejpam-4783	196	33	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	196	34	)	)	PUNCT
ejpam-4783	196	35	≡	≡	PROPN
ejpam-4783	196	36	ωi+(ξ/2)−2γ	ωi+(ξ/2)−2γ	PROPN
ejpam-4783	196	37	)	)	PUNCT
ejpam-4783	196	38	.	.	PUNCT
ejpam-4783	197	1	(	(	PUNCT
ejpam-4783	197	2	b	b	X
ejpam-4783	197	3	)	)	PUNCT
ejpam-4783	197	4	|	|	ADV
ejpam-4783	197	5	{	{	PUNCT
ejpam-4783	197	6	(	(	PUNCT
ejpam-4783	197	7	µi	µi	INTJ
ejpam-4783	197	8	,	,	PUNCT
ejpam-4783	197	9	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	197	10	)	)	PUNCT
ejpam-4783	197	11	)	)	PUNCT
ejpam-4783	197	12	,	,	PUNCT
ejpam-4783	197	13	(	(	PUNCT
ejpam-4783	197	14	ηi	ηi	INTJ
ejpam-4783	197	15	,	,	PUNCT
ejpam-4783	197	16	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	197	17	)	)	PUNCT
ejpam-4783	197	18	)	)	PUNCT
ejpam-4783	197	19	,	,	PUNCT
ejpam-4783	197	20	(	(	PUNCT
ejpam-4783	197	21	ωi	ωi	NOUN
ejpam-4783	197	22	,	,	PUNCT
ejpam-4783	197	23	µi+(ξ/2	µi+(ξ/2	NOUN
ejpam-4783	197	24	)	)	PUNCT
ejpam-4783	197	25	)	)	PUNCT
ejpam-4783	197	26	,	,	PUNCT
ejpam-4783	197	27	(	(	PUNCT
ejpam-4783	197	28	ωi	ωi	NOUN
ejpam-4783	197	29	,	,	PUNCT
ejpam-4783	197	30	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	197	31	)	)	PUNCT
ejpam-4783	197	32	)	)	PUNCT
ejpam-4783	197	33	:	:	PUNCT
ejpam-4783	198	1	i	i	NOUN
ejpam-4783	198	2	=	=	NOUN
ejpam-4783	198	3	2	2	NUM
ejpam-4783	198	4	,	,	PUNCT
ejpam-4783	198	5	4	4	NUM
ejpam-4783	198	6	,	,	PUNCT
ejpam-4783	198	7	6	6	NUM
ejpam-4783	198	8	,	,	PUNCT
ejpam-4783	198	9	.	.	PUNCT
ejpam-4783	198	10	.	.	PUNCT
ejpam-4783	198	11	.	.	PUNCT
ejpam-4783	199	1	,	,	PUNCT
ejpam-4783	199	2	2γ	2γ	NOUN
ejpam-4783	199	3	}	}	PUNCT
ejpam-4783	199	4	|	|	ADV
ejpam-4783	199	5	=	=	SYM
ejpam-4783	199	6	4γ	4γ	NOUN
ejpam-4783	199	7	.	.	PUNCT
ejpam-4783	200	1	if	if	SCONJ
ejpam-4783	200	2	i+(ξ/2	i+(ξ/2	NOUN
ejpam-4783	200	3	)	)	PUNCT
ejpam-4783	200	4	>	>	X
ejpam-4783	200	5	2γ	2γ	NOUN
ejpam-4783	200	6	,	,	PUNCT
ejpam-4783	200	7	then	then	ADV
ejpam-4783	200	8	(	(	PUNCT
ejpam-4783	200	9	ωi+(ξ/2	ωi+(ξ/2	NUM
ejpam-4783	200	10	)	)	PUNCT
ejpam-4783	200	11	≡	≡	PROPN
ejpam-4783	200	12	ωi+(ξ/2)−2γ	ωi+(ξ/2)−2γ	PRON
ejpam-4783	200	13	)	)	PUNCT
ejpam-4783	200	14	,	,	PUNCT
ejpam-4783	200	15	(	(	PUNCT
ejpam-4783	200	16	µi+(ξ/2	µi+(ξ/2	PROPN
ejpam-4783	200	17	)	)	PUNCT
ejpam-4783	200	18	≡	≡	PROPN
ejpam-4783	200	19	µi+(ξ/2)−2γ	µi+(ξ/2)−2γ	ADP
ejpam-4783	200	20	)	)	PUNCT
ejpam-4783	200	21	,	,	PUNCT
ejpam-4783	200	22	(	(	PUNCT
ejpam-4783	200	23	ηi+(ξ/2	ηi+(ξ/2	NOUN
ejpam-4783	200	24	)	)	PUNCT
ejpam-4783	200	25	≡	≡	PROPN
ejpam-4783	200	26	ηi+(ξ/2)−2γ	ηi+(ξ/2)−2γ	PROPN
ejpam-4783	200	27	)	)	PUNCT
ejpam-4783	200	28	.	.	PUNCT
ejpam-4783	201	1	(	(	PUNCT
ejpam-4783	201	2	vi	vi	X
ejpam-4783	201	3	)	)	PUNCT
ejpam-4783	201	4	if	if	SCONJ
ejpam-4783	201	5	d(y	d(y	PROPN
ejpam-4783	201	6	,	,	PUNCT
ejpam-4783	201	7	z	z	NOUN
ejpam-4783	201	8	)	)	PUNCT
ejpam-4783	201	9	=	=	SYM
ejpam-4783	201	10	ξ	ξ	PROPN
ejpam-4783	201	11	,	,	PUNCT
ejpam-4783	201	12	ξ	ξ	X
ejpam-4783	201	13	=	=	SYM
ejpam-4783	201	14	7	7	NUM
ejpam-4783	201	15	,	,	PUNCT
ejpam-4783	201	16	11	11	NUM
ejpam-4783	201	17	,	,	PUNCT
ejpam-4783	201	18	15	15	NUM
ejpam-4783	201	19	,	,	PUNCT
ejpam-4783	201	20	.	.	PUNCT
ejpam-4783	201	21	.	.	PUNCT
ejpam-4783	202	1	.	.	PUNCT
ejpam-4783	203	1	,	,	PUNCT
ejpam-4783	203	2	2γ	2γ	NOUN
ejpam-4783	203	3	−	−	PROPN
ejpam-4783	203	4	1	1	NUM
ejpam-4783	203	5	,	,	PUNCT
ejpam-4783	203	6	then	then	ADV
ejpam-4783	203	7	∑2γ−1	∑2γ−1	PROPN
ejpam-4783	203	8	ξ=7,11	ξ=7,11	PROPN
ejpam-4783	203	9	|aξ|	|aξ|	NOUN
ejpam-4783	204	1	=	=	SYM
ejpam-4783	204	2	9γ	9γ	NUM
ejpam-4783	204	3	,	,	PUNCT
ejpam-4783	204	4	we	we	PRON
ejpam-4783	204	5	have	have	VERB
ejpam-4783	204	6	three	three	NUM
ejpam-4783	204	7	subsets	subset	NOUN
ejpam-4783	204	8	of	of	ADP
ejpam-4783	204	9	it	it	PRON
ejpam-4783	204	10	:	:	PUNCT
ejpam-4783	204	11	(	(	PUNCT
ejpam-4783	204	12	a	a	X
ejpam-4783	204	13	)	)	PUNCT
ejpam-4783	204	14	|	|	NOUN
ejpam-4783	204	15	{	{	PUNCT
ejpam-4783	204	16	(	(	PUNCT
ejpam-4783	204	17	ωi	ωi	NOUN
ejpam-4783	204	18	,	,	PUNCT
ejpam-4783	204	19	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	204	20	)	)	PUNCT
ejpam-4783	204	21	,	,	PUNCT
ejpam-4783	204	22	(	(	PUNCT
ejpam-4783	204	23	µi	µi	PROPN
ejpam-4783	204	24	,	,	PUNCT
ejpam-4783	204	25	ωi+(ξ+1)/2	ωi+(ξ+1)/2	ADJ
ejpam-4783	204	26	)	)	PUNCT
ejpam-4783	204	27	,	,	PUNCT
ejpam-4783	204	28	(	(	PUNCT
ejpam-4783	204	29	ηi	ηi	INTJ
ejpam-4783	204	30	,	,	PUNCT
ejpam-4783	204	31	ωi+(ξ+1)/2	ωi+(ξ+1)/2	PROPN
ejpam-4783	204	32	)	)	PUNCT
ejpam-4783	204	33	:	:	PUNCT
ejpam-4783	205	1	i	i	NOUN
ejpam-4783	205	2	=	=	NOUN
ejpam-4783	205	3	1	1	NUM
ejpam-4783	205	4	,	,	PUNCT
ejpam-4783	205	5	3	3	NUM
ejpam-4783	205	6	,	,	PUNCT
ejpam-4783	205	7	5	5	NUM
ejpam-4783	205	8	,	,	PUNCT
ejpam-4783	205	9	.	.	PUNCT
ejpam-4783	205	10	.	.	PUNCT
ejpam-4783	205	11	.	.	PUNCT
ejpam-4783	206	1	,	,	PUNCT
ejpam-4783	206	2	2γ	2γ	NOUN
ejpam-4783	206	3	−	−	PROPN
ejpam-4783	206	4	1	1	X
ejpam-4783	206	5	}	}	PUNCT
ejpam-4783	206	6	|	|	NOUN
ejpam-4783	206	7	=	=	SYM
ejpam-4783	206	8	3γ	3γ	NUM
ejpam-4783	206	9	.	.	PUNCT
ejpam-4783	207	1	if	if	SCONJ
ejpam-4783	207	2	i+(ξ−1)/2	i+(ξ−1)/2	NOUN
ejpam-4783	207	3	,	,	PUNCT
ejpam-4783	207	4	i+(ξ+1)/2	i+(ξ+1)/2	ADJ
ejpam-4783	207	5	>	>	SYM
ejpam-4783	207	6	2γ	2γ	NOUN
ejpam-4783	207	7	,	,	PUNCT
ejpam-4783	207	8	then	then	ADV
ejpam-4783	207	9	(	(	PUNCT
ejpam-4783	207	10	ωi+(ξ−1)/2	ωi+(ξ−1)/2	PROPN
ejpam-4783	207	11	≡	≡	PROPN
ejpam-4783	207	12	ωi+(ξ−1)/2−2γ	ωi+(ξ−1)/2−2γ	PROPN
ejpam-4783	207	13	)	)	PUNCT
ejpam-4783	207	14	,	,	PUNCT
ejpam-4783	207	15	(	(	PUNCT
ejpam-4783	207	16	ωi+(ξ+1)/2	ωi+(ξ+1)/2	PROPN
ejpam-4783	207	17	≡	≡	PROPN
ejpam-4783	207	18	ωi+(ξ+1)/2−2γ	ωi+(ξ+1)/2−2γ	PROPN
ejpam-4783	207	19	)	)	PUNCT
ejpam-4783	207	20	.	.	PUNCT
ejpam-4783	208	1	(	(	PUNCT
ejpam-4783	208	2	b	b	X
ejpam-4783	208	3	)	)	PUNCT
ejpam-4783	208	4	|	|	ADV
ejpam-4783	208	5	{	{	PUNCT
ejpam-4783	208	6	(	(	PUNCT
ejpam-4783	208	7	µi	µi	INTJ
ejpam-4783	208	8	,	,	PUNCT
ejpam-4783	208	9	µi+(ξ−1)/2	µi+(ξ−1)/2	NOUN
ejpam-4783	208	10	)	)	PUNCT
ejpam-4783	208	11	,	,	PUNCT
ejpam-4783	208	12	(	(	PUNCT
ejpam-4783	208	13	µi	µi	INTJ
ejpam-4783	208	14	,	,	PUNCT
ejpam-4783	208	15	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	208	16	)	)	PUNCT
ejpam-4783	208	17	,	,	PUNCT
ejpam-4783	208	18	(	(	PUNCT
ejpam-4783	208	19	ηi	ηi	INTJ
ejpam-4783	208	20	,	,	PUNCT
ejpam-4783	208	21	µi+(ξ−1)/2	µi+(ξ−1)/2	NOUN
ejpam-4783	208	22	)	)	PUNCT
ejpam-4783	208	23	,	,	PUNCT
ejpam-4783	208	24	(	(	PUNCT
ejpam-4783	208	25	ηi	ηi	X
ejpam-4783	208	26	,	,	PUNCT
ejpam-4783	208	27	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	208	28	)	)	PUNCT
ejpam-4783	208	29	:	:	PUNCT
ejpam-4783	209	1	i	i	NOUN
ejpam-4783	209	2	=	=	NOUN
ejpam-4783	209	3	2	2	NUM
ejpam-4783	209	4	,	,	PUNCT
ejpam-4783	209	5	4	4	NUM
ejpam-4783	209	6	,	,	PUNCT
ejpam-4783	209	7	6	6	NUM
ejpam-4783	209	8	,	,	PUNCT
ejpam-4783	209	9	.	.	PUNCT
ejpam-4783	209	10	.	.	PUNCT
ejpam-4783	209	11	.	.	PUNCT
ejpam-4783	210	1	,	,	PUNCT
ejpam-4783	210	2	2γ	2γ	NOUN
ejpam-4783	210	3	}	}	PUNCT
ejpam-4783	210	4	|	|	ADV
ejpam-4783	210	5	=	=	SYM
ejpam-4783	210	6	4γ	4γ	NOUN
ejpam-4783	210	7	.	.	PUNCT
ejpam-4783	211	1	if	if	SCONJ
ejpam-4783	211	2	i+(ξ−1)/2	i+(ξ−1)/2	PROPN
ejpam-4783	211	3	>	>	X
ejpam-4783	211	4	2γ	2γ	NOUN
ejpam-4783	211	5	,	,	PUNCT
ejpam-4783	211	6	then	then	ADV
ejpam-4783	211	7	(	(	PUNCT
ejpam-4783	211	8	µi+(ξ−1)/2	µi+(ξ−1)/2	PROPN
ejpam-4783	211	9	≡	≡	PROPN
ejpam-4783	211	10	µi+(ξ−1)/2−2γ	µi+(ξ−1)/2−2γ	NOUN
ejpam-4783	211	11	)	)	PUNCT
ejpam-4783	211	12	,	,	PUNCT
ejpam-4783	211	13	(	(	PUNCT
ejpam-4783	211	14	ηi+(ξ−1)/2	ηi+(ξ−1)/2	PROPN
ejpam-4783	211	15	≡	≡	PROPN
ejpam-4783	211	16	ηi+(ξ−1)/2−2γ	ηi+(ξ−1)/2−2γ	PROPN
ejpam-4783	211	17	)	)	PUNCT
ejpam-4783	211	18	.	.	PUNCT
ejpam-4783	212	1	(	(	PUNCT
ejpam-4783	212	2	c	c	X
ejpam-4783	212	3	)	)	PUNCT
ejpam-4783	212	4	|	|	ADV
ejpam-4783	212	5	{	{	PUNCT
ejpam-4783	212	6	(	(	PUNCT
ejpam-4783	212	7	ωi	ωi	NOUN
ejpam-4783	212	8	,	,	PUNCT
ejpam-4783	212	9	µi+(ξ+1)/2	µi+(ξ+1)/2	NOUN
ejpam-4783	212	10	)	)	PUNCT
ejpam-4783	212	11	,	,	PUNCT
ejpam-4783	212	12	(	(	PUNCT
ejpam-4783	212	13	ωi	ωi	NOUN
ejpam-4783	212	14	,	,	PUNCT
ejpam-4783	212	15	ηi+(ξ+1)/2	ηi+(ξ+1)/2	NOUN
ejpam-4783	212	16	)	)	PUNCT
ejpam-4783	212	17	:	:	PUNCT
ejpam-4783	213	1	i	i	NOUN
ejpam-4783	213	2	=	=	NOUN
ejpam-4783	213	3	2	2	NUM
ejpam-4783	213	4	,	,	PUNCT
ejpam-4783	213	5	4	4	NUM
ejpam-4783	213	6	,	,	PUNCT
ejpam-4783	213	7	6	6	NUM
ejpam-4783	213	8	,	,	PUNCT
ejpam-4783	213	9	.	.	PUNCT
ejpam-4783	213	10	.	.	PUNCT
ejpam-4783	213	11	.	.	PUNCT
ejpam-4783	214	1	,	,	PUNCT
ejpam-4783	214	2	2γ	2γ	NOUN
ejpam-4783	214	3	}	}	PUNCT
ejpam-4783	214	4	|	|	ADV
ejpam-4783	214	5	=	=	SYM
ejpam-4783	214	6	2γ	2γ	NOUN
ejpam-4783	214	7	.	.	PUNCT
ejpam-4783	215	1	if	if	SCONJ
ejpam-4783	215	2	i+(ξ+1)/2	i+(ξ+1)/2	PROPN
ejpam-4783	215	3	>	>	SYM
ejpam-4783	215	4	2γ	2γ	NOUN
ejpam-4783	215	5	,	,	PUNCT
ejpam-4783	215	6	then	then	ADV
ejpam-4783	215	7	(	(	PUNCT
ejpam-4783	215	8	µi+(ξ+1)/2	µi+(ξ+1)/2	NOUN
ejpam-4783	215	9	≡	≡	PROPN
ejpam-4783	215	10	µi+(ξ+1)/2−2γ	µi+(ξ+1)/2−2γ	NUM
ejpam-4783	215	11	)	)	PUNCT
ejpam-4783	215	12	,	,	PUNCT
ejpam-4783	215	13	(	(	PUNCT
ejpam-4783	215	14	ηi+(ξ+1)/2	ηi+(ξ+1)/2	NOUN
ejpam-4783	215	15	≡	≡	PROPN
ejpam-4783	215	16	ηi+(ξ+1)/2−2γ	ηi+(ξ+1)/2−2γ	NOUN
ejpam-4783	215	17	)	)	PUNCT
ejpam-4783	215	18	.	.	PUNCT
ejpam-4783	216	1	(	(	PUNCT
ejpam-4783	216	2	vii	vii	PROPN
ejpam-4783	216	3	)	)	PUNCT
ejpam-4783	216	4	if	if	SCONJ
ejpam-4783	216	5	d(y	d(y	PROPN
ejpam-4783	216	6	,	,	PUNCT
ejpam-4783	216	7	z	z	NOUN
ejpam-4783	216	8	)	)	PUNCT
ejpam-4783	216	9	=	=	NOUN
ejpam-4783	216	10	2γ	2γ	NOUN
ejpam-4783	216	11	,	,	PUNCT
ejpam-4783	216	12	then	then	ADV
ejpam-4783	216	13	we	we	PRON
ejpam-4783	216	14	have	have	VERB
ejpam-4783	216	15	:	:	PUNCT
ejpam-4783	216	16	a	a	X
ejpam-4783	216	17	:	:	PUNCT
ejpam-4783	216	18	if	if	SCONJ
ejpam-4783	216	19	γ	γ	X
ejpam-4783	216	20	is	be	AUX
ejpam-4783	216	21	an	an	DET
ejpam-4783	216	22	even	even	ADJ
ejpam-4783	216	23	number	number	NOUN
ejpam-4783	216	24	,	,	PUNCT
ejpam-4783	216	25	then	then	ADV
ejpam-4783	216	26	we	we	PRON
ejpam-4783	216	27	have	have	VERB
ejpam-4783	216	28	two	two	NUM
ejpam-4783	216	29	subsets	subset	NOUN
ejpam-4783	216	30	of	of	ADP
ejpam-4783	216	31	it	it	PRON
ejpam-4783	216	32	(	(	PUNCT
ejpam-4783	216	33	a	a	X
ejpam-4783	216	34	)	)	PUNCT
ejpam-4783	216	35	|	|	NOUN
ejpam-4783	216	36	{	{	PUNCT
ejpam-4783	216	37	(	(	PUNCT
ejpam-4783	216	38	ωi	ωi	NOUN
ejpam-4783	216	39	,	,	PUNCT
ejpam-4783	216	40	ωi+γ	ωi+γ	NUM
ejpam-4783	216	41	)	)	PUNCT
ejpam-4783	216	42	,	,	PUNCT
ejpam-4783	216	43	(	(	PUNCT
ejpam-4783	216	44	µi	µi	INTJ
ejpam-4783	216	45	,	,	PUNCT
ejpam-4783	216	46	µi+γ	µi+γ	NUM
ejpam-4783	216	47	)	)	PUNCT
ejpam-4783	216	48	,	,	PUNCT
ejpam-4783	216	49	(	(	PUNCT
ejpam-4783	216	50	µi	µi	INTJ
ejpam-4783	216	51	,	,	PUNCT
ejpam-4783	216	52	ηi+γ	ηi+γ	PROPN
ejpam-4783	216	53	)	)	PUNCT
ejpam-4783	216	54	,	,	PUNCT
ejpam-4783	216	55	(	(	PUNCT
ejpam-4783	216	56	µi	µi	INTJ
ejpam-4783	216	57	,	,	PUNCT
ejpam-4783	216	58	ηi+γ	ηi+γ	PROPN
ejpam-4783	216	59	)	)	PUNCT
ejpam-4783	216	60	,	,	PUNCT
ejpam-4783	216	61	(	(	PUNCT
ejpam-4783	216	62	ηi	ηi	PROPN
ejpam-4783	216	63	,	,	PUNCT
ejpam-4783	216	64	ηi+γ	ηi+γ	PROPN
ejpam-4783	216	65	)	)	PUNCT
ejpam-4783	216	66	:	:	PUNCT
ejpam-4783	217	1	i	i	NOUN
ejpam-4783	217	2	=	=	NOUN
ejpam-4783	217	3	1	1	NUM
ejpam-4783	217	4	,	,	PUNCT
ejpam-4783	217	5	3	3	NUM
ejpam-4783	217	6	,	,	PUNCT
ejpam-4783	217	7	5	5	NUM
ejpam-4783	217	8	,	,	PUNCT
ejpam-4783	217	9	.	.	PUNCT
ejpam-4783	217	10	.	.	PUNCT
ejpam-4783	217	11	.	.	PUNCT
ejpam-4783	218	1	,	,	PUNCT
ejpam-4783	218	2	γ	γ	X
ejpam-4783	218	3	−	−	PROPN
ejpam-4783	218	4	1	1	NUM
ejpam-4783	218	5	}	}	PUNCT
ejpam-4783	218	6	|	|	NOUN
ejpam-4783	218	7	=	=	SYM
ejpam-4783	218	8	5γ/2	5γ/2	NUM
ejpam-4783	218	9	.	.	PUNCT
ejpam-4783	219	1	(	(	PUNCT
ejpam-4783	219	2	b	b	X
ejpam-4783	219	3	)	)	PUNCT
ejpam-4783	219	4	|	|	ADV
ejpam-4783	219	5	{	{	PUNCT
ejpam-4783	219	6	(	(	PUNCT
ejpam-4783	219	7	µi	µi	INTJ
ejpam-4783	219	8	,	,	PUNCT
ejpam-4783	219	9	µi+γ	µi+γ	NUM
ejpam-4783	219	10	)	)	PUNCT
ejpam-4783	219	11	,	,	PUNCT
ejpam-4783	219	12	(	(	PUNCT
ejpam-4783	219	13	µi	µi	INTJ
ejpam-4783	219	14	,	,	PUNCT
ejpam-4783	219	15	ηi+γ	ηi+γ	PROPN
ejpam-4783	219	16	)	)	PUNCT
ejpam-4783	219	17	,	,	PUNCT
ejpam-4783	219	18	(	(	PUNCT
ejpam-4783	219	19	ηi	ηi	PROPN
ejpam-4783	219	20	,	,	PUNCT
ejpam-4783	219	21	µi+γ	µi+γ	NUM
ejpam-4783	219	22	)	)	PUNCT
ejpam-4783	219	23	,	,	PUNCT
ejpam-4783	219	24	(	(	PUNCT
ejpam-4783	219	25	ηi	ηi	PROPN
ejpam-4783	219	26	,	,	PUNCT
ejpam-4783	219	27	ηi+γ	ηi+γ	NOUN
ejpam-4783	219	28	)	)	PUNCT
ejpam-4783	219	29	,	,	PUNCT
ejpam-4783	219	30	(	(	PUNCT
ejpam-4783	219	31	ωi	ωi	NOUN
ejpam-4783	219	32	,	,	PUNCT
ejpam-4783	219	33	ωi+γ	ωi+γ	NUM
ejpam-4783	219	34	)	)	PUNCT
ejpam-4783	219	35	:	:	PUNCT
ejpam-4783	220	1	i	i	NOUN
ejpam-4783	220	2	=	=	NOUN
ejpam-4783	220	3	2	2	NUM
ejpam-4783	220	4	,	,	PUNCT
ejpam-4783	220	5	4	4	NUM
ejpam-4783	220	6	,	,	PUNCT
ejpam-4783	220	7	6	6	NUM
ejpam-4783	220	8	,	,	PUNCT
ejpam-4783	220	9	.	.	PUNCT
ejpam-4783	220	10	.	.	PUNCT
ejpam-4783	220	11	.	.	PUNCT
ejpam-4783	221	1	,	,	PUNCT
ejpam-4783	221	2	γ	γ	NOUN
ejpam-4783	221	3	}	}	PUNCT
ejpam-4783	221	4	|	|	NOUN
ejpam-4783	221	5	=	=	SYM
ejpam-4783	221	6	5γ/2	5γ/2	NUM
ejpam-4783	221	7	.	.	PUNCT
ejpam-4783	222	1	hence	hence	ADV
ejpam-4783	222	2	|a2γ	|a2γ	PROPN
ejpam-4783	223	1	|	|	ADV
ejpam-4783	223	2	=	=	NOUN
ejpam-4783	223	3	5γ	5γ	NOUN
ejpam-4783	223	4	.	.	PUNCT
ejpam-4783	224	1	b	b	X
ejpam-4783	224	2	:	:	PUNCT
ejpam-4783	224	3	if	if	SCONJ
ejpam-4783	224	4	n	n	PRON
ejpam-4783	224	5	is	be	AUX
ejpam-4783	224	6	an	an	DET
ejpam-4783	224	7	odd	odd	ADJ
ejpam-4783	224	8	number	number	NOUN
ejpam-4783	224	9	,	,	PUNCT
ejpam-4783	224	10	then	then	ADV
ejpam-4783	224	11	we	we	PRON
ejpam-4783	224	12	have	have	VERB
ejpam-4783	224	13	:	:	PUNCT
ejpam-4783	224	14	|	|	ADV
ejpam-4783	224	15	{	{	PUNCT
ejpam-4783	224	16	(	(	PUNCT
ejpam-4783	224	17	ωi	ωi	NOUN
ejpam-4783	224	18	,	,	PUNCT
ejpam-4783	224	19	µi+γ	µi+γ	NUM
ejpam-4783	224	20	)	)	PUNCT
ejpam-4783	224	21	,	,	PUNCT
ejpam-4783	224	22	(	(	PUNCT
ejpam-4783	224	23	ωi	ωi	NOUN
ejpam-4783	224	24	,	,	PUNCT
ejpam-4783	224	25	ηi+γ	ηi+γ	NOUN
ejpam-4783	224	26	)	)	PUNCT
ejpam-4783	224	27	,	,	PUNCT
ejpam-4783	224	28	(	(	PUNCT
ejpam-4783	224	29	µi	µi	INTJ
ejpam-4783	224	30	,	,	PUNCT
ejpam-4783	224	31	ωi+γ	ωi+γ	NUM
ejpam-4783	224	32	)	)	PUNCT
ejpam-4783	224	33	,	,	PUNCT
ejpam-4783	224	34	(	(	PUNCT
ejpam-4783	224	35	ηi	ηi	PROPN
ejpam-4783	224	36	,	,	PUNCT
ejpam-4783	224	37	ωi+γ	ωi+γ	NUM
ejpam-4783	224	38	)	)	PUNCT
ejpam-4783	224	39	:	:	PUNCT
ejpam-4783	225	1	i	i	NOUN
ejpam-4783	225	2	=	=	NOUN
ejpam-4783	225	3	1	1	NUM
ejpam-4783	225	4	,	,	PUNCT
ejpam-4783	225	5	3	3	NUM
ejpam-4783	225	6	,	,	PUNCT
ejpam-4783	225	7	5	5	NUM
ejpam-4783	225	8	,	,	PUNCT
ejpam-4783	225	9	.	.	PUNCT
ejpam-4783	225	10	.	.	PUNCT
ejpam-4783	225	11	.	.	PUNCT
ejpam-4783	226	1	,	,	PUNCT
ejpam-4783	226	2	2γ	2γ	NOUN
ejpam-4783	226	3	−	−	PROPN
ejpam-4783	226	4	1	1	X
ejpam-4783	226	5	}	}	PUNCT
ejpam-4783	226	6	|	|	NOUN
ejpam-4783	226	7	=	=	SYM
ejpam-4783	226	8	4γ	4γ	NOUN
ejpam-4783	226	9	.	.	PUNCT
ejpam-4783	227	1	if	if	SCONJ
ejpam-4783	227	2	i+	i+	NOUN
ejpam-4783	227	3	γ	γ	X
ejpam-4783	227	4	>	>	X
ejpam-4783	227	5	2γ	2γ	NOUN
ejpam-4783	227	6	,	,	PUNCT
ejpam-4783	227	7	then	then	ADV
ejpam-4783	227	8	(	(	PUNCT
ejpam-4783	227	9	µi+γ	µi+γ	PROPN
ejpam-4783	227	10	≡	≡	PROPN
ejpam-4783	227	11	µi−γ	µi−γ	NOUN
ejpam-4783	227	12	)	)	PUNCT
ejpam-4783	227	13	,	,	PUNCT
ejpam-4783	227	14	(	(	PUNCT
ejpam-4783	227	15	ηi+γ	ηi+γ	PROPN
ejpam-4783	227	16	≡	≡	PROPN
ejpam-4783	227	17	ηi−γ	ηi−γ	PROPN
ejpam-4783	227	18	)	)	PUNCT
ejpam-4783	227	19	,	,	PUNCT
ejpam-4783	227	20	(	(	PUNCT
ejpam-4783	227	21	ωi+γ	ωi+γ	PROPN
ejpam-4783	227	22	≡	≡	PROPN
ejpam-4783	227	23	ωi−γ	ωi−γ	NOUN
ejpam-4783	227	24	)	)	PUNCT
ejpam-4783	227	25	.	.	PUNCT
ejpam-4783	228	1	hence	hence	ADV
ejpam-4783	228	2	|a2γ	|a2γ	PROPN
ejpam-4783	228	3	|	|	CCONJ
ejpam-4783	228	4	=	=	SYM
ejpam-4783	228	5	4γ	4γ	NOUN
ejpam-4783	228	6	.	.	PUNCT
ejpam-4783	229	1	corollary	corollary	ADJ
ejpam-4783	229	2	2	2	NUM
ejpam-4783	229	3	.	.	PUNCT
ejpam-4783	230	1	for	for	ADP
ejpam-4783	230	2	m	m	PROPN
ejpam-4783	230	3	≥	≥	NOUN
ejpam-4783	230	4	3	3	NUM
ejpam-4783	230	5	,	,	PUNCT
ejpam-4783	230	6	γ	γ	X
ejpam-4783	230	7	=	=	SYM
ejpam-4783	230	8	m	m	PROPN
ejpam-4783	230	9	,	,	PUNCT
ejpam-4783	230	10	we	we	PRON
ejpam-4783	230	11	have	have	VERB
ejpam-4783	230	12	:	:	PUNCT
ejpam-4783	230	13	sc(re(c6)γ	sc(re(c6)γ	X
ejpam-4783	230	14	)	)	PUNCT
ejpam-4783	231	1	=	=	PUNCT
ejpam-4783	231	2	[	[	PUNCT
ejpam-4783	231	3	4γ(21γ2	4γ(21γ2	NUM
ejpam-4783	231	4	+	+	SYM
ejpam-4783	231	5	8)	8)	NUM
ejpam-4783	231	6	,	,	PUNCT
ejpam-4783	231	7	γ	γ	X
ejpam-4783	231	8	is	be	AUX
ejpam-4783	231	9	an	an	DET
ejpam-4783	231	10	even	even	ADJ
ejpam-4783	231	11	,	,	PUNCT
ejpam-4783	231	12	6γ(14γ2	6γ(14γ2	NUM
ejpam-4783	231	13	+	+	NOUN
ejpam-4783	231	14	5	5	NUM
ejpam-4783	231	15	)	)	PUNCT
ejpam-4783	231	16	,	,	PUNCT
ejpam-4783	231	17	γ	γ	X
ejpam-4783	231	18	is	be	AUX
ejpam-4783	231	19	an	an	DET
ejpam-4783	231	20	odd	odd	ADJ
ejpam-4783	231	21	.	.	PUNCT
ejpam-4783	231	22	]	]	PUNCT
ejpam-4783	231	23	.	.	PUNCT
ejpam-4783	232	1	sc∗(re(c6)γ	sc∗(re(c6)γ	NOUN
ejpam-4783	232	2	)	)	PUNCT
ejpam-4783	232	3	=	=	PUNCT
ejpam-4783	233	1	[	[	PUNCT
ejpam-4783	233	2	2γ(49γ2	2γ(49γ2	NUM
ejpam-4783	233	3	+	+	CCONJ
ejpam-4783	233	4	16	16	NUM
ejpam-4783	233	5	)	)	PUNCT
ejpam-4783	233	6	,	,	PUNCT
ejpam-4783	233	7	γ	γ	PROPN
ejpam-4783	233	8	is	be	AUX
ejpam-4783	233	9	an	an	DET
ejpam-4783	233	10	even	even	ADJ
ejpam-4783	233	11	,	,	PUNCT
ejpam-4783	233	12	γ(98γ2	γ(98γ2	ADJ
ejpam-4783	233	13	+	+	NOUN
ejpam-4783	233	14	31	31	NUM
ejpam-4783	233	15	)	)	PUNCT
ejpam-4783	233	16	,	,	PUNCT
ejpam-4783	233	17	γ	γ	X
ejpam-4783	233	18	is	be	AUX
ejpam-4783	233	19	an	an	DET
ejpam-4783	233	20	odd	odd	ADJ
ejpam-4783	233	21	.	.	PUNCT
ejpam-4783	233	22	]	]	PUNCT
ejpam-4783	233	23	.	.	PUNCT
ejpam-4783	234	1	1588	1588	NUM
ejpam-4783	234	2	3	3	NUM
ejpam-4783	234	3	.	.	PUNCT
ejpam-4783	235	1	examples	example	NOUN
ejpam-4783	235	2	:	:	PUNCT
ejpam-4783	235	3	to	to	PART
ejpam-4783	235	4	clarify	clarify	VERB
ejpam-4783	235	5	the	the	DET
ejpam-4783	235	6	previous	previous	ADJ
ejpam-4783	235	7	results	result	NOUN
ejpam-4783	235	8	,	,	PUNCT
ejpam-4783	235	9	some	some	DET
ejpam-4783	235	10	examples	example	NOUN
ejpam-4783	235	11	were	be	AUX
ejpam-4783	235	12	taken	take	VERB
ejpam-4783	235	13	,	,	PUNCT
ejpam-4783	235	14	which	which	PRON
ejpam-4783	235	15	were	be	AUX
ejpam-4783	235	16	verified	verify	VERB
ejpam-4783	235	17	programmatically	programmatically	ADV
ejpam-4783	235	18	using	use	VERB
ejpam-4783	235	19	the	the	DET
ejpam-4783	235	20	mathematica	mathematica	PROPN
ejpam-4783	235	21	program	program	PROPN
ejpam-4783	235	22	.	.	PUNCT
ejpam-4783	236	1	table	table	NOUN
ejpam-4783	236	2	3	3	NUM
ejpam-4783	236	3	:	:	PUNCT
ejpam-4783	236	4	the	the	DET
ejpam-4783	236	5	edges	edge	NOUN
ejpam-4783	236	6	induce	induce	VERB
ejpam-4783	236	7	chain	chain	NOUN
ejpam-4783	236	8	for	for	ADP
ejpam-4783	236	9	hexagonal	hexagonal	ADJ
ejpam-4783	236	10	graphs	graph	NOUN
ejpam-4783	236	11	ce(c6)γ	ce(c6)γ	NOUN
ejpam-4783	236	12	,	,	PUNCT
ejpam-4783	236	13	γ	γ	X
ejpam-4783	236	14	=	=	SYM
ejpam-4783	236	15	15	15	NUM
ejpam-4783	236	16	,	,	PUNCT
ejpam-4783	236	17	19	19	NUM
ejpam-4783	236	18	.	.	NOUN
ejpam-4783	236	19	1589	1589	NUM
ejpam-4783	236	20	table	table	NOUN
ejpam-4783	236	21	4	4	NUM
ejpam-4783	236	22	:	:	PUNCT
ejpam-4783	236	23	the	the	DET
ejpam-4783	236	24	edges	edge	NOUN
ejpam-4783	236	25	induce	induce	VERB
ejpam-4783	236	26	chain	chain	NOUN
ejpam-4783	236	27	for	for	ADP
ejpam-4783	236	28	hexagonal	hexagonal	ADJ
ejpam-4783	236	29	graphs	graph	NOUN
ejpam-4783	236	30	ce(c6)γ	ce(c6)γ	NOUN
ejpam-4783	236	31	,	,	PUNCT
ejpam-4783	236	32	γ	γ	X
ejpam-4783	236	33	=	=	SYM
ejpam-4783	236	34	15	15	NUM
ejpam-4783	236	35	,	,	PUNCT
ejpam-4783	236	36	19	19	NUM
ejpam-4783	236	37	.	.	NOUN
ejpam-4783	236	38	1590	1590	NUM
ejpam-4783	236	39	4	4	NUM
ejpam-4783	236	40	.	.	PUNCT
ejpam-4783	236	41	conclusion	conclusion	NOUN
ejpam-4783	236	42	in	in	ADP
ejpam-4783	236	43	this	this	DET
ejpam-4783	236	44	paper	paper	NOUN
ejpam-4783	236	45	,	,	PUNCT
ejpam-4783	236	46	we	we	PRON
ejpam-4783	236	47	were	be	AUX
ejpam-4783	236	48	able	able	ADJ
ejpam-4783	236	49	to	to	PART
ejpam-4783	236	50	obtain	obtain	VERB
ejpam-4783	236	51	general	general	ADJ
ejpam-4783	236	52	formulas	formula	NOUN
ejpam-4783	236	53	for	for	ADP
ejpam-4783	236	54	the	the	DET
ejpam-4783	236	55	schultz	schultz	PROPN
ejpam-4783	236	56	and	and	CCONJ
ejpam-4783	236	57	modified	modify	VERB
ejpam-4783	236	58	schultz	schultz	NOUN
ejpam-4783	236	59	polynomials	polynomial	NOUN
ejpam-4783	236	60	with	with	ADP
ejpam-4783	236	61	their	their	PRON
ejpam-4783	236	62	indices	index	NOUN
ejpam-4783	236	63	for	for	ADP
ejpam-4783	236	64	both	both	DET
ejpam-4783	236	65	types	type	NOUN
ejpam-4783	236	66	of	of	ADP
ejpam-4783	236	67	hexagonal	hexagonal	ADJ
ejpam-4783	236	68	rings	ring	NOUN
ejpam-4783	236	69	joining	join	VERB
ejpam-4783	236	70	to	to	ADP
ejpam-4783	236	71	each	each	DET
ejpam-4783	236	72	other	other	ADJ
ejpam-4783	236	73	by	by	ADP
ejpam-4783	236	74	an	an	DET
ejpam-4783	236	75	edge	edge	NOUN
ejpam-4783	236	76	or	or	CCONJ
ejpam-4783	236	77	bridge	bridge	NOUN
ejpam-4783	236	78	,	,	PUNCT
ejpam-4783	236	79	and	and	CCONJ
ejpam-4783	236	80	we	we	PRON
ejpam-4783	236	81	compared	compare	VERB
ejpam-4783	236	82	the	the	DET
ejpam-4783	236	83	results	result	NOUN
ejpam-4783	236	84	using	use	VERB
ejpam-4783	236	85	mathematica	mathematica	PROPN
ejpam-4783	236	86	program	program	NOUN
ejpam-4783	236	87	for	for	ADP
ejpam-4783	236	88	many	many	ADJ
ejpam-4783	236	89	examples	example	NOUN
ejpam-4783	236	90	,	,	PUNCT
ejpam-4783	236	91	and	and	CCONJ
ejpam-4783	236	92	the	the	DET
ejpam-4783	236	93	results	result	NOUN
ejpam-4783	236	94	were	be	AUX
ejpam-4783	236	95	identical	identical	ADJ
ejpam-4783	236	96	acknowledgements	acknowledgement	NOUN
ejpam-4783	236	97	this	this	DET
ejpam-4783	236	98	paper	paper	NOUN
ejpam-4783	236	99	was	be	AUX
ejpam-4783	236	100	supported	support	VERB
ejpam-4783	236	101	by	by	ADP
ejpam-4783	236	102	mosul	mosul	PROPN
ejpam-4783	236	103	university	university	PROPN
ejpam-4783	236	104	-	-	PUNCT
ejpam-4783	236	105	college	college	NOUN
ejpam-4783	236	106	of	of	ADP
ejpam-4783	236	107	computer	computer	NOUN
ejpam-4783	236	108	sciences	sciences	PROPN
ejpam-4783	236	109	and	and	CCONJ
ejpam-4783	236	110	mathematics	mathematic	NOUN
ejpam-4783	236	111	and	and	CCONJ
ejpam-4783	236	112	the	the	DET
ejpam-4783	236	113	general	general	ADJ
ejpam-4783	236	114	directorate	directorate	NOUN
ejpam-4783	236	115	of	of	ADP
ejpam-4783	236	116	education	education	NOUN
ejpam-4783	236	117	in	in	ADP
ejpam-4783	236	118	nineveh	nineveh	PROPN
ejpam-4783	236	119	governorate/	governorate/	NUM
ejpam-4783	236	120	iraq	iraq	PROPN
ejpam-4783	236	121	.	.	PUNCT
ejpam-4783	237	1	references	reference	NOUN
ejpam-4783	237	2	[	[	X
ejpam-4783	237	3	1	1	X
ejpam-4783	237	4	]	]	X
ejpam-4783	237	5	mahmood	mahmood	PROPN
ejpam-4783	237	6	m	m	PROPN
ejpam-4783	237	7	abdullah	abdullah	PROPN
ejpam-4783	237	8	and	and	CCONJ
ejpam-4783	237	9	ahmed	ahmed	PROPN
ejpam-4783	237	10	m	m	PROPN
ejpam-4783	237	11	ali	ali	PROPN
ejpam-4783	237	12	.	.	PUNCT
ejpam-4783	238	1	schultz	schultz	PROPN
ejpam-4783	238	2	and	and	CCONJ
ejpam-4783	238	3	modified	modify	VERB
ejpam-4783	238	4	schultz	schultz	NOUN
ejpam-4783	238	5	polynomials	polynomial	NOUN
ejpam-4783	238	6	of	of	ADP
ejpam-4783	238	7	vertex	vertex	NOUN
ejpam-4783	238	8	identification	identification	NOUN
ejpam-4783	238	9	chain	chain	NOUN
ejpam-4783	238	10	for	for	ADP
ejpam-4783	238	11	square	square	ADJ
ejpam-4783	238	12	and	and	CCONJ
ejpam-4783	238	13	complete	complete	ADJ
ejpam-4783	238	14	square	square	ADJ
ejpam-4783	238	15	graphs	graph	NOUN
ejpam-4783	238	16	.	.	PUNCT
ejpam-4783	239	1	open	open	ADJ
ejpam-4783	239	2	access	access	NOUN
ejpam-4783	239	3	library	library	PROPN
ejpam-4783	239	4	journal	journal	NOUN
ejpam-4783	239	5	,	,	PUNCT
ejpam-4783	239	6	7(5):1–10	7(5):1–10	NUM
ejpam-4783	239	7	,	,	PUNCT
ejpam-4783	239	8	2020	2020	NUM
ejpam-4783	239	9	.	.	PUNCT
ejpam-4783	240	1	[	[	X
ejpam-4783	240	2	2	2	X
ejpam-4783	240	3	]	]	X
ejpam-4783	240	4	mahmood	mahmood	PROPN
ejpam-4783	240	5	m	m	PROPN
ejpam-4783	240	6	abdullah	abdullah	PROPN
ejpam-4783	240	7	and	and	CCONJ
ejpam-4783	240	8	ahmed	ahmed	PROPN
ejpam-4783	240	9	m	m	PROPN
ejpam-4783	240	10	ali	ali	PROPN
ejpam-4783	240	11	.	.	PUNCT
ejpam-4783	241	1	schultz	schultz	PROPN
ejpam-4783	241	2	and	and	CCONJ
ejpam-4783	241	3	modified	modify	VERB
ejpam-4783	241	4	schultz	schultz	NOUN
ejpam-4783	241	5	polynomials	polynomial	NOUN
ejpam-4783	241	6	for	for	ADP
ejpam-4783	241	7	edge	edge	NOUN
ejpam-4783	241	8	–	–	PUNCT
ejpam-4783	241	9	identification	identification	NOUN
ejpam-4783	241	10	chain	chain	NOUN
ejpam-4783	241	11	and	and	CCONJ
ejpam-4783	241	12	ring	ring	NOUN
ejpam-4783	241	13	–	–	PUNCT
ejpam-4783	241	14	for	for	ADP
ejpam-4783	241	15	pentagon	pentagon	PROPN
ejpam-4783	241	16	and	and	CCONJ
ejpam-4783	241	17	hexagon	hexagon	NOUN
ejpam-4783	241	18	graphs	graph	NOUN
ejpam-4783	241	19	.	.	PUNCT
ejpam-4783	242	1	in	in	ADP
ejpam-4783	242	2	journal	journal	PROPN
ejpam-4783	242	3	of	of	ADP
ejpam-4783	242	4	physics	physics	PROPN
ejpam-4783	242	5	:	:	PUNCT
ejpam-4783	242	6	conference	conference	NOUN
ejpam-4783	242	7	series	series	NOUN
ejpam-4783	242	8	,	,	PUNCT
ejpam-4783	242	9	volume	volume	NOUN
ejpam-4783	242	10	1818	1818	NUM
ejpam-4783	242	11	,	,	PUNCT
ejpam-4783	242	12	page	page	NOUN
ejpam-4783	242	13	012063	012063	NUM
ejpam-4783	242	14	.	.	PUNCT
ejpam-4783	243	1	iop	iop	PROPN
ejpam-4783	243	2	publishing	publishing	NOUN
ejpam-4783	243	3	,	,	PUNCT
ejpam-4783	243	4	2021	2021	NUM
ejpam-4783	243	5	.	.	PUNCT
ejpam-4783	244	1	[	[	X
ejpam-4783	244	2	3	3	NUM
ejpam-4783	244	3	]	]	SYM
ejpam-4783	244	4	haveen	haveen	NOUN
ejpam-4783	244	5	j	j	PROPN
ejpam-4783	244	6	ahmed	ahmed	PROPN
ejpam-4783	244	7	,	,	PUNCT
ejpam-4783	244	8	ahmed	ahmed	PROPN
ejpam-4783	244	9	m	m	PROPN
ejpam-4783	244	10	ali	ali	PROPN
ejpam-4783	244	11	,	,	PUNCT
ejpam-4783	244	12	and	and	CCONJ
ejpam-4783	244	13	gashaw	gashaw	NOUN
ejpam-4783	244	14	a	a	DET
ejpam-4783	244	15	mohammed	mohammed	PROPN
ejpam-4783	244	16	saleh	saleh	NOUN
ejpam-4783	244	17	.	.	PUNCT
ejpam-4783	245	1	detour	detour	NOUN
ejpam-4783	245	2	polynomials	polynomial	NOUN
ejpam-4783	245	3	of	of	ADP
ejpam-4783	245	4	vertex	vertex	NOUN
ejpam-4783	245	5	coalenscence	coalenscence	NOUN
ejpam-4783	245	6	and	and	CCONJ
ejpam-4783	245	7	bridges	bridge	NOUN
ejpam-4783	245	8	coalenscence	coalenscence	NOUN
ejpam-4783	245	9	graphs	graph	NOUN
ejpam-4783	245	10	.	.	PUNCT
ejpam-4783	246	1	asian	asian	ADJ
ejpam-4783	246	2	-	-	PUNCT
ejpam-4783	246	3	european	european	ADJ
ejpam-4783	246	4	journal	journal	NOUN
ejpam-4783	246	5	of	of	ADP
ejpam-4783	246	6	mathematics	mathematic	NOUN
ejpam-4783	246	7	,	,	PUNCT
ejpam-4783	246	8	15(02):2250025	15(02):2250025	NUM
ejpam-4783	246	9	,	,	PUNCT
ejpam-4783	246	10	2022	2022	NUM
ejpam-4783	246	11	.	.	PUNCT
ejpam-4783	247	1	[	[	X
ejpam-4783	247	2	4	4	X
ejpam-4783	247	3	]	]	X
ejpam-4783	247	4	ahmed	ahmed	PROPN
ejpam-4783	247	5	m	m	PROPN
ejpam-4783	247	6	ali	ali	PROPN
ejpam-4783	247	7	et	et	PROPN
ejpam-4783	247	8	al	al	PROPN
ejpam-4783	247	9	.	.	PUNCT
ejpam-4783	247	10	schultz	schultz	PROPN
ejpam-4783	247	11	and	and	CCONJ
ejpam-4783	247	12	modified	modify	VERB
ejpam-4783	247	13	schultz	schultz	NOUN
ejpam-4783	247	14	polynomials	polynomial	NOUN
ejpam-4783	247	15	of	of	ADP
ejpam-4783	247	16	some	some	DET
ejpam-4783	247	17	cog	cog	NOUN
ejpam-4783	247	18	-	-	PUNCT
ejpam-4783	247	19	special	special	ADJ
ejpam-4783	247	20	graphs	graph	NOUN
ejpam-4783	247	21	.	.	PUNCT
ejpam-4783	248	1	open	open	ADJ
ejpam-4783	248	2	access	access	NOUN
ejpam-4783	248	3	library	library	PROPN
ejpam-4783	248	4	journal	journal	NOUN
ejpam-4783	248	5	,	,	PUNCT
ejpam-4783	248	6	6(08):1	6(08):1	PROPN
ejpam-4783	248	7	,	,	PUNCT
ejpam-4783	248	8	2019	2019	NUM
ejpam-4783	248	9	.	.	PUNCT
ejpam-4783	249	1	[	[	X
ejpam-4783	249	2	5	5	X
ejpam-4783	249	3	]	]	PUNCT
ejpam-4783	249	4	ahmed	ahmed	PROPN
ejpam-4783	249	5	m	m	PROPN
ejpam-4783	249	6	ali	ali	PROPN
ejpam-4783	249	7	and	and	CCONJ
ejpam-4783	249	8	haitham	haitham	PROPN
ejpam-4783	249	9	n	n	PROPN
ejpam-4783	249	10	mohammed	mohammed	PROPN
ejpam-4783	249	11	.	.	PUNCT
ejpam-4783	250	1	schultz	schultz	PROPN
ejpam-4783	250	2	and	and	CCONJ
ejpam-4783	250	3	modified	modify	VERB
ejpam-4783	250	4	schultz	schultz	NOUN
ejpam-4783	250	5	polynomials	polynomial	NOUN
ejpam-4783	250	6	of	of	ADP
ejpam-4783	250	7	two	two	NUM
ejpam-4783	250	8	operations	operation	NOUN
ejpam-4783	250	9	gutman	gutman	NOUN
ejpam-4783	250	10	’s	’s	NOUN
ejpam-4783	250	11	.	.	PUNCT
ejpam-4783	251	1	[	[	X
ejpam-4783	251	2	6	6	NUM
ejpam-4783	251	3	]	]	PUNCT
ejpam-4783	251	4	a	a	DET
ejpam-4783	251	5	behmaram	behmaram	NOUN
ejpam-4783	251	6	,	,	PUNCT
ejpam-4783	251	7	h	h	NOUN
ejpam-4783	251	8	yousefi	yousefi	NOUN
ejpam-4783	251	9	-	-	PUNCT
ejpam-4783	251	10	azari	azari	ADJ
ejpam-4783	251	11	,	,	PUNCT
ejpam-4783	251	12	and	and	CCONJ
ejpam-4783	251	13	ar	ar	NOUN
ejpam-4783	251	14	ashrafi	ashrafi	PROPN
ejpam-4783	251	15	.	.	PUNCT
ejpam-4783	252	1	some	some	DET
ejpam-4783	252	2	new	new	ADJ
ejpam-4783	252	3	results	result	NOUN
ejpam-4783	252	4	on	on	ADP
ejpam-4783	252	5	distance	distance	NOUN
ejpam-4783	252	6	-	-	PUNCT
ejpam-4783	252	7	based	base	VERB
ejpam-4783	252	8	polynomials	polynomial	NOUN
ejpam-4783	252	9	.	.	PUNCT
ejpam-4783	253	1	match	match	PROPN
ejpam-4783	253	2	commun	commun	PROPN
ejpam-4783	253	3	.	.	PUNCT
ejpam-4783	253	4	math	math	PROPN
ejpam-4783	253	5	.	.	PUNCT
ejpam-4783	254	1	comput	comput	NOUN
ejpam-4783	254	2	.	.	PUNCT
ejpam-4783	255	1	chem	chem	NOUN
ejpam-4783	255	2	,	,	PUNCT
ejpam-4783	255	3	65(1):39–50	65(1):39–50	NUM
ejpam-4783	255	4	,	,	PUNCT
ejpam-4783	255	5	2011	2011	NUM
ejpam-4783	255	6	.	.	PUNCT
ejpam-4783	256	1	[	[	X
ejpam-4783	256	2	7	7	X
ejpam-4783	256	3	]	]	X
ejpam-4783	256	4	g	g	PROPN
ejpam-4783	256	5	chartrand	chartrand	NOUN
ejpam-4783	256	6	,	,	PUNCT
ejpam-4783	256	7	l	l	PROPN
ejpam-4783	256	8	lesniak	lesniak	PROPN
ejpam-4783	256	9	,	,	PUNCT
ejpam-4783	256	10	and	and	CCONJ
ejpam-4783	256	11	p	p	PROPN
ejpam-4783	256	12	zhang	zhang	PROPN
ejpam-4783	256	13	.	.	PUNCT
ejpam-4783	257	1	textbooks	textbooks	PROPN
ejpam-4783	257	2	in	in	ADP
ejpam-4783	257	3	mathematics	mathematic	NOUN
ejpam-4783	257	4	(	(	PUNCT
ejpam-4783	257	5	graphs	graph	NOUN
ejpam-4783	257	6	and	and	CCONJ
ejpam-4783	257	7	digraphs	digraph	NOUN
ejpam-4783	257	8	)	)	PUNCT
ejpam-4783	257	9	,	,	PUNCT
ejpam-4783	257	10	2016	2016	NUM
ejpam-4783	257	11	.	.	PUNCT
ejpam-4783	258	1	[	[	X
ejpam-4783	258	2	8	8	NUM
ejpam-4783	258	3	]	]	X
ejpam-4783	258	4	mohammad	mohammad	PROPN
ejpam-4783	258	5	reza	reza	PROPN
ejpam-4783	258	6	farahani	farahani	PROPN
ejpam-4783	258	7	.	.	PUNCT
ejpam-4783	259	1	hosoya	hosoya	PROPN
ejpam-4783	259	2	,	,	PUNCT
ejpam-4783	259	3	schultz	schultz	PROPN
ejpam-4783	259	4	,	,	PUNCT
ejpam-4783	259	5	modified	modify	VERB
ejpam-4783	259	6	schultz	schultz	NOUN
ejpam-4783	259	7	polynomials	polynomial	NOUN
ejpam-4783	259	8	and	and	CCONJ
ejpam-4783	259	9	their	their	PRON
ejpam-4783	259	10	topological	topological	ADJ
ejpam-4783	259	11	indices	index	NOUN
ejpam-4783	259	12	of	of	ADP
ejpam-4783	259	13	benzene	benzene	NOUN
ejpam-4783	259	14	molecules	molecule	NOUN
ejpam-4783	259	15	:	:	PUNCT
ejpam-4783	259	16	first	first	ADJ
ejpam-4783	259	17	members	member	NOUN
ejpam-4783	259	18	of	of	ADP
ejpam-4783	259	19	polycyclic	polycyclic	ADJ
ejpam-4783	259	20	aromatic	aromatic	ADJ
ejpam-4783	259	21	hydrocarbons	hydrocarbon	NOUN
ejpam-4783	259	22	(	(	PUNCT
ejpam-4783	259	23	pahs	pahs	PROPN
ejpam-4783	259	24	)	)	PUNCT
ejpam-4783	259	25	.	.	PUNCT
ejpam-4783	260	1	international	international	ADJ
ejpam-4783	260	2	journal	journal	PROPN
ejpam-4783	260	3	of	of	ADP
ejpam-4783	260	4	theoretical	theoretical	ADJ
ejpam-4783	260	5	chemistry	chemistry	NOUN
ejpam-4783	260	6	,	,	PUNCT
ejpam-4783	260	7	1(2):09–16	1(2):09–16	NUM
ejpam-4783	260	8	,	,	PUNCT
ejpam-4783	260	9	2013	2013	NUM
ejpam-4783	260	10	.	.	PUNCT
ejpam-4783	261	1	[	[	X
ejpam-4783	261	2	9	9	NUM
ejpam-4783	261	3	]	]	X
ejpam-4783	261	4	mohammad	mohammad	PROPN
ejpam-4783	261	5	reza	reza	PROPN
ejpam-4783	261	6	farahani	farahani	PROPN
ejpam-4783	261	7	.	.	PUNCT
ejpam-4783	262	1	schultz	schultz	PROPN
ejpam-4783	262	2	and	and	CCONJ
ejpam-4783	262	3	modified	modify	VERB
ejpam-4783	262	4	schultz	schultz	NOUN
ejpam-4783	262	5	polynomials	polynomial	NOUN
ejpam-4783	262	6	of	of	ADP
ejpam-4783	262	7	coronene	coronene	NOUN
ejpam-4783	262	8	polycyclic	polycyclic	NOUN
ejpam-4783	262	9	aromatic	aromatic	ADJ
ejpam-4783	262	10	hydrocarbons	hydrocarbon	NOUN
ejpam-4783	262	11	.	.	PUNCT
ejpam-4783	263	1	international	international	ADJ
ejpam-4783	263	2	letters	letter	NOUN
ejpam-4783	263	3	of	of	ADP
ejpam-4783	263	4	chemistry	chemistry	NOUN
ejpam-4783	263	5	,	,	PUNCT
ejpam-4783	263	6	physics	physics	NOUN
ejpam-4783	263	7	and	and	CCONJ
ejpam-4783	263	8	astronomy	astronomy	NOUN
ejpam-4783	263	9	,	,	PUNCT
ejpam-4783	263	10	13:1–10	13:1–10	NUM
ejpam-4783	263	11	,	,	PUNCT
ejpam-4783	263	12	2014	2014	NUM
ejpam-4783	263	13	.	.	PUNCT
ejpam-4783	264	1	references	reference	NOUN
ejpam-4783	264	2	1591	1591	NUM
ejpam-4783	265	1	[	[	X
ejpam-4783	265	2	10	10	NUM
ejpam-4783	265	3	]	]	X
ejpam-4783	265	4	mohammad	mohammad	PROPN
ejpam-4783	265	5	reza	reza	PROPN
ejpam-4783	265	6	farahani	farahani	PROPN
ejpam-4783	265	7	,	,	PUNCT
ejpam-4783	265	8	wei	wei	PROPN
ejpam-4783	265	9	gao	gao	PROPN
ejpam-4783	265	10	,	,	PUNCT
ejpam-4783	265	11	et	et	PROPN
ejpam-4783	265	12	al	al	PROPN
ejpam-4783	265	13	.	.	PUNCT
ejpam-4783	266	1	the	the	DET
ejpam-4783	266	2	schultz	schultz	PROPN
ejpam-4783	266	3	index	index	PROPN
ejpam-4783	266	4	and	and	CCONJ
ejpam-4783	266	5	schultz	schultz	PROPN
ejpam-4783	266	6	polynomial	polynomial	PROPN
ejpam-4783	266	7	of	of	ADP
ejpam-4783	266	8	the	the	DET
ejpam-4783	266	9	jahangir	jahangir	PROPN
ejpam-4783	266	10	graphs	graphs	PROPN
ejpam-4783	266	11	j5	j5	PROPN
ejpam-4783	266	12	,	,	PUNCT
ejpam-4783	266	13	m.	m.	NOUN
ejpam-4783	266	14	applied	apply	VERB
ejpam-4783	266	15	mathematics	mathematic	NOUN
ejpam-4783	266	16	,	,	PUNCT
ejpam-4783	266	17	6(14):2319–2325	6(14):2319–2325	NUM
ejpam-4783	266	18	,	,	PUNCT
ejpam-4783	266	19	2015	2015	NUM
ejpam-4783	266	20	.	.	PUNCT
ejpam-4783	267	1	[	[	X
ejpam-4783	267	2	11	11	NUM
ejpam-4783	267	3	]	]	X
ejpam-4783	267	4	mohammad	mohammad	PROPN
ejpam-4783	267	5	reza	reza	PROPN
ejpam-4783	267	6	farahani	farahani	PROPN
ejpam-4783	267	7	,	,	PUNCT
ejpam-4783	267	8	mk	mk	PROPN
ejpam-4783	267	9	jamil	jamil	PROPN
ejpam-4783	267	10	,	,	PUNCT
ejpam-4783	267	11	s	s	PROPN
ejpam-4783	267	12	wang	wang	PROPN
ejpam-4783	267	13	,	,	PUNCT
ejpam-4783	267	14	w	w	PROPN
ejpam-4783	267	15	gao	gao	PROPN
ejpam-4783	267	16	,	,	PUNCT
ejpam-4783	267	17	and	and	CCONJ
ejpam-4783	267	18	b	b	PROPN
ejpam-4783	267	19	wei	wei	PROPN
ejpam-4783	267	20	.	.	PUNCT
ejpam-4783	268	1	the	the	DET
ejpam-4783	268	2	hosoya	hosoya	PROPN
ejpam-4783	268	3	,	,	PUNCT
ejpam-4783	268	4	schultz	schultz	PROPN
ejpam-4783	268	5	and	and	CCONJ
ejpam-4783	268	6	modified	modify	VERB
ejpam-4783	268	7	schultz	schultz	NOUN
ejpam-4783	268	8	polynomials	polynomial	NOUN
ejpam-4783	268	9	of	of	ADP
ejpam-4783	268	10	a	a	DET
ejpam-4783	268	11	class	class	NOUN
ejpam-4783	268	12	of	of	ADP
ejpam-4783	268	13	dutch	dutch	ADJ
ejpam-4783	268	14	windmill	windmill	NOUN
ejpam-4783	268	15	graph	graph	NOUN
ejpam-4783	268	16	d(m	d(m	PROPN
ejpam-4783	268	17	)	)	PUNCT
ejpam-4783	268	18	.	.	PUNCT
ejpam-4783	269	1	commun	commun	PROPN
ejpam-4783	269	2	.	.	PUNCT
ejpam-4783	270	1	appl	appl	PROPN
ejpam-4783	270	2	.	.	PUNCT
ejpam-4783	271	1	anal	anal	PROPN
ejpam-4783	271	2	,	,	PUNCT
ejpam-4783	271	3	22(1):43–62	22(1):43–62	NUM
ejpam-4783	271	4	,	,	PUNCT
ejpam-4783	271	5	2017	2017	NUM
ejpam-4783	271	6	.	.	PUNCT
ejpam-4783	272	1	[	[	X
ejpam-4783	272	2	12	12	NUM
ejpam-4783	272	3	]	]	X
ejpam-4783	272	4	ivan	ivan	PROPN
ejpam-4783	272	5	gutman	gutman	PROPN
ejpam-4783	272	6	.	.	PUNCT
ejpam-4783	273	1	some	some	DET
ejpam-4783	273	2	properties	property	NOUN
ejpam-4783	273	3	of	of	ADP
ejpam-4783	273	4	the	the	DET
ejpam-4783	273	5	wiener	wiener	NOUN
ejpam-4783	273	6	polynomial	polynomial	NOUN
ejpam-4783	273	7	.	.	PUNCT
ejpam-4783	274	1	graph	graph	NOUN
ejpam-4783	274	2	theory	theory	NOUN
ejpam-4783	274	3	notes	note	VERB
ejpam-4783	274	4	new	new	PROPN
ejpam-4783	274	5	york	york	PROPN
ejpam-4783	274	6	,	,	PUNCT
ejpam-4783	274	7	125:13–18	125:13–18	NUM
ejpam-4783	274	8	,	,	PUNCT
ejpam-4783	274	9	1993	1993	NUM
ejpam-4783	274	10	.	.	PUNCT
ejpam-4783	275	1	[	[	X
ejpam-4783	275	2	13	13	NUM
ejpam-4783	275	3	]	]	X
ejpam-4783	275	4	f	f	PROPN
ejpam-4783	275	5	hassani	hassani	PROPN
ejpam-4783	275	6	,	,	PUNCT
ejpam-4783	275	7	ali	ali	PROPN
ejpam-4783	275	8	iranmanesh	iranmanesh	PROPN
ejpam-4783	275	9	,	,	PUNCT
ejpam-4783	275	10	and	and	CCONJ
ejpam-4783	275	11	samaneh	samaneh	PROPN
ejpam-4783	275	12	mirzaie	mirzaie	PROPN
ejpam-4783	275	13	.	.	PUNCT
ejpam-4783	276	1	schultz	schultz	PROPN
ejpam-4783	276	2	and	and	CCONJ
ejpam-4783	276	3	modified	modify	VERB
ejpam-4783	276	4	schultz	schultz	NOUN
ejpam-4783	276	5	polynomials	polynomial	NOUN
ejpam-4783	276	6	of	of	ADP
ejpam-4783	276	7	c100	c100	PROPN
ejpam-4783	276	8	fullerene	fullerene	NOUN
ejpam-4783	276	9	.	.	PUNCT
ejpam-4783	277	1	match	match	PROPN
ejpam-4783	277	2	commun	commun	PROPN
ejpam-4783	277	3	.	.	PUNCT
ejpam-4783	277	4	math	math	PROPN
ejpam-4783	277	5	.	.	PUNCT
ejpam-4783	278	1	comput	comput	NOUN
ejpam-4783	278	2	.	.	PUNCT
ejpam-4783	279	1	chem	chem	PROPN
ejpam-4783	279	2	,	,	PUNCT
ejpam-4783	279	3	69:87–92	69:87–92	PROPN
ejpam-4783	279	4	,	,	PUNCT
ejpam-4783	279	5	2013	2013	NUM
ejpam-4783	279	6	.	.	PUNCT
ejpam-4783	280	1	[	[	X
ejpam-4783	280	2	14	14	NUM
ejpam-4783	280	3	]	]	X
ejpam-4783	280	4	haruo	haruo	NOUN
ejpam-4783	280	5	hosoya	hosoya	PROPN
ejpam-4783	280	6	.	.	PUNCT
ejpam-4783	281	1	on	on	ADP
ejpam-4783	281	2	some	some	DET
ejpam-4783	281	3	counting	counting	NOUN
ejpam-4783	281	4	polynomials	polynomial	NOUN
ejpam-4783	281	5	in	in	ADP
ejpam-4783	281	6	chemistry	chemistry	NOUN
ejpam-4783	281	7	.	.	PUNCT
ejpam-4783	282	1	discrete	discrete	ADJ
ejpam-4783	282	2	applied	applied	ADJ
ejpam-4783	282	3	mathematics	mathematic	NOUN
ejpam-4783	282	4	,	,	PUNCT
ejpam-4783	282	5	19(1	19(1	NUM
ejpam-4783	282	6	-	-	SYM
ejpam-4783	282	7	3):239–257	3):239–257	NUM
ejpam-4783	282	8	,	,	PUNCT
ejpam-4783	282	9	1988	1988	NUM
ejpam-4783	282	10	.	.	PUNCT
ejpam-4783	283	1	[	[	X
ejpam-4783	283	2	15	15	NUM
ejpam-4783	283	3	]	]	X
ejpam-4783	283	4	sandi	sandi	NOUN
ejpam-4783	283	5	klavvzar	klavvzar	PROPN
ejpam-4783	283	6	and	and	CCONJ
ejpam-4783	283	7	ivan	ivan	PROPN
ejpam-4783	283	8	gutman	gutman	PROPN
ejpam-4783	283	9	.	.	PUNCT
ejpam-4783	284	1	wiener	wiener	NOUN
ejpam-4783	284	2	number	number	NOUN
ejpam-4783	284	3	of	of	ADP
ejpam-4783	284	4	vertex	vertex	NOUN
ejpam-4783	284	5	-	-	PUNCT
ejpam-4783	284	6	weighted	weight	VERB
ejpam-4783	284	7	graphs	graph	NOUN
ejpam-4783	284	8	and	and	CCONJ
ejpam-4783	284	9	a	a	DET
ejpam-4783	284	10	chemical	chemical	NOUN
ejpam-4783	284	11	application	application	NOUN
ejpam-4783	284	12	.	.	PUNCT
ejpam-4783	285	1	discrete	discrete	ADJ
ejpam-4783	285	2	applied	apply	VERB
ejpam-4783	285	3	mathematics	mathematic	NOUN
ejpam-4783	285	4	,	,	PUNCT
ejpam-4783	285	5	80(1):73–81	80(1):73–81	NUM
ejpam-4783	285	6	,	,	PUNCT
ejpam-4783	285	7	1997	1997	NUM
ejpam-4783	285	8	.	.	PUNCT
ejpam-4783	286	1	[	[	X
ejpam-4783	286	2	16	16	NUM
ejpam-4783	286	3	]	]	PUNCT
ejpam-4783	286	4	raghad	raghad	VERB
ejpam-4783	286	5	a	a	DET
ejpam-4783	286	6	mustafa	mustafa	PROPN
ejpam-4783	286	7	,	,	PUNCT
ejpam-4783	286	8	ahmed	ahmed	PROPN
ejpam-4783	286	9	m	m	PROPN
ejpam-4783	286	10	ali	ali	PROPN
ejpam-4783	286	11	,	,	PUNCT
ejpam-4783	286	12	and	and	CCONJ
ejpam-4783	286	13	abdulsattar	abdulsattar	PROPN
ejpam-4783	286	14	m	m	PROPN
ejpam-4783	286	15	khidhir	khidhir	NOUN
ejpam-4783	286	16	.	.	PUNCT
ejpam-4783	287	1	mn	mn	PROPN
ejpam-4783	287	2	–	–	PUNCT
ejpam-4783	287	3	polynomials	polynomial	NOUN
ejpam-4783	287	4	of	of	ADP
ejpam-4783	287	5	some	some	DET
ejpam-4783	287	6	special	special	NOUN
ejpam-4783	287	7	for	for	ADP
ejpam-4783	287	8	cog	cog	NOUN
ejpam-4783	287	9	-	-	PUNCT
ejpam-4783	287	10	graphs	graph	NOUN
ejpam-4783	287	11	.	.	PUNCT
ejpam-4783	288	1	journal	journal	NOUN
ejpam-4783	288	2	of	of	ADP
ejpam-4783	288	3	discrete	discrete	ADJ
ejpam-4783	288	4	mathematical	mathematical	ADJ
ejpam-4783	288	5	sciences	science	NOUN
ejpam-4783	288	6	and	and	CCONJ
ejpam-4783	288	7	cryptography	cryptography	NOUN
ejpam-4783	288	8	,	,	PUNCT
ejpam-4783	288	9	pages	page	NOUN
ejpam-4783	288	10	1–16	1–16	PROPN
ejpam-4783	288	11	,	,	PUNCT
ejpam-4783	288	12	2022	2022	NUM
ejpam-4783	288	13	.	.	PUNCT
ejpam-4783	289	1	[	[	X
ejpam-4783	289	2	17	17	NUM
ejpam-4783	289	3	]	]	PUNCT
ejpam-4783	289	4	raghad	raghad	VERB
ejpam-4783	289	5	a	a	DET
ejpam-4783	289	6	mustafa	mustafa	PROPN
ejpam-4783	289	7	,	,	PUNCT
ejpam-4783	289	8	ahmed	ahmed	PROPN
ejpam-4783	289	9	m	m	PROPN
ejpam-4783	289	10	ali	ali	PROPN
ejpam-4783	289	11	,	,	PUNCT
ejpam-4783	289	12	and	and	CCONJ
ejpam-4783	289	13	abdulsattar	abdulsattar	PROPN
ejpam-4783	289	14	m	m	PROPN
ejpam-4783	289	15	khidhir	khidhir	NOUN
ejpam-4783	289	16	.	.	PUNCT
ejpam-4783	290	1	mn	mn	PROPN
ejpam-4783	290	2	–	–	PUNCT
ejpam-4783	290	3	polynomials	polynomial	NOUN
ejpam-4783	290	4	of	of	ADP
ejpam-4783	290	5	theta	theta	NOUN
ejpam-4783	290	6	and	and	CCONJ
ejpam-4783	290	7	wagner	wagner	NOUN
ejpam-4783	290	8	graphs	graph	NOUN
ejpam-4783	290	9	.	.	PUNCT
ejpam-4783	291	1	palestine	palestine	PROPN
ejpam-4783	291	2	journal	journal	PROPN
ejpam-4783	291	3	of	of	ADP
ejpam-4783	291	4	mathematics	mathematic	NOUN
ejpam-4783	291	5	,	,	PUNCT
ejpam-4783	291	6	11(1	11(1	NUM
ejpam-4783	291	7	)	)	PUNCT
ejpam-4783	291	8	,	,	PUNCT
ejpam-4783	291	9	2022	2022	NUM
ejpam-4783	291	10	.	.	PUNCT
ejpam-4783	292	1	[	[	X
ejpam-4783	292	2	18	18	NUM
ejpam-4783	292	3	]	]	X
ejpam-4783	292	4	harry	harry	PROPN
ejpam-4783	292	5	p	p	PROPN
ejpam-4783	292	6	schultz	schultz	PROPN
ejpam-4783	292	7	.	.	PUNCT
ejpam-4783	293	1	topological	topological	ADJ
ejpam-4783	293	2	organic	organic	ADJ
ejpam-4783	293	3	chemistry	chemistry	NOUN
ejpam-4783	293	4	.	.	PUNCT
ejpam-4783	294	1	1	1	X
ejpam-4783	294	2	.	.	X
ejpam-4783	294	3	graph	graph	NOUN
ejpam-4783	294	4	theory	theory	NOUN
ejpam-4783	294	5	and	and	CCONJ
ejpam-4783	294	6	topological	topological	ADJ
ejpam-4783	294	7	indices	index	NOUN
ejpam-4783	294	8	of	of	ADP
ejpam-4783	294	9	alkanes	alkane	NOUN
ejpam-4783	294	10	.	.	PUNCT
ejpam-4783	295	1	journal	journal	PROPN
ejpam-4783	295	2	of	of	ADP
ejpam-4783	295	3	chemical	chemical	ADJ
ejpam-4783	295	4	information	information	NOUN
ejpam-4783	295	5	and	and	CCONJ
ejpam-4783	295	6	computer	computer	NOUN
ejpam-4783	295	7	sciences	science	NOUN
ejpam-4783	295	8	,	,	PUNCT
ejpam-4783	295	9	29(3):227	29(3):227	NUM
ejpam-4783	295	10	–	–	PUNCT
ejpam-4783	295	11	228	228	NUM
ejpam-4783	295	12	,	,	PUNCT
ejpam-4783	295	13	1989	1989	NUM
ejpam-4783	295	14	.	.	PUNCT
ejpam-4783	296	1	[	[	X
ejpam-4783	296	2	19	19	NUM
ejpam-4783	296	3	]	]	PUNCT
ejpam-4783	296	4	shaohui	shaohui	PROPN
ejpam-4783	296	5	wang	wang	PROPN
ejpam-4783	296	6	,	,	PUNCT
ejpam-4783	296	7	mohammad	mohammad	PROPN
ejpam-4783	296	8	reza	reza	PROPN
ejpam-4783	296	9	farahani	farahani	PROPN
ejpam-4783	296	10	,	,	PUNCT
ejpam-4783	296	11	mr	mr	PROPN
ejpam-4783	296	12	rajesh	rajesh	PROPN
ejpam-4783	296	13	kanna	kanna	PROPN
ejpam-4783	296	14	,	,	PUNCT
ejpam-4783	296	15	r	r	PROPN
ejpam-4783	296	16	pradeep	pradeep	PROPN
ejpam-4783	296	17	kumar	kumar	PROPN
ejpam-4783	296	18	,	,	PUNCT
ejpam-4783	296	19	et	et	PROPN
ejpam-4783	296	20	al	al	PROPN
ejpam-4783	296	21	.	.	PUNCT
ejpam-4783	296	22	schultz	schultz	PROPN
ejpam-4783	296	23	polynomials	polynomial	NOUN
ejpam-4783	296	24	and	and	CCONJ
ejpam-4783	296	25	their	their	PRON
ejpam-4783	296	26	topological	topological	ADJ
ejpam-4783	296	27	indices	index	NOUN
ejpam-4783	296	28	of	of	ADP
ejpam-4783	296	29	jahangir	jahangir	PROPN
ejpam-4783	296	30	graphs	graphs	PROPN
ejpam-4783	296	31	j2	j2	PROPN
ejpam-4783	296	32	,	,	PUNCT
ejpam-4783	296	33	m.	m.	NOUN
ejpam-4783	296	34	applied	apply	VERB
ejpam-4783	296	35	mathematics	mathematic	NOUN
ejpam-4783	296	36	,	,	PUNCT
ejpam-4783	296	37	7(14):1632–1637	7(14):1632–1637	NUM
ejpam-4783	296	38	,	,	PUNCT
ejpam-4783	296	39	2016	2016	NUM
ejpam-4783	296	40	.	.	PUNCT
ejpam-4783	297	1	[	[	X
ejpam-4783	297	2	20	20	NUM
ejpam-4783	297	3	]	]	X
ejpam-4783	297	4	harry	harry	PROPN
ejpam-4783	297	5	wiener	wiener	PROPN
ejpam-4783	297	6	.	.	PUNCT
ejpam-4783	298	1	structural	structural	ADJ
ejpam-4783	298	2	determination	determination	NOUN
ejpam-4783	298	3	of	of	ADP
ejpam-4783	298	4	paraffin	paraffin	NOUN
ejpam-4783	298	5	boiling	boiling	NOUN
ejpam-4783	298	6	points	point	NOUN
ejpam-4783	298	7	.	.	PUNCT
ejpam-4783	299	1	journal	journal	NOUN
ejpam-4783	299	2	of	of	ADP
ejpam-4783	299	3	the	the	DET
ejpam-4783	299	4	american	american	PROPN
ejpam-4783	299	5	chemical	chemical	PROPN
ejpam-4783	299	6	society	society	PROPN
ejpam-4783	299	7	,	,	PUNCT
ejpam-4783	299	8	69(1):17–20	69(1):17–20	NUM
ejpam-4783	299	9	,	,	PUNCT
ejpam-4783	299	10	1947	1947	NUM
ejpam-4783	299	11	.	.	PUNCT