id	sid	tid	token	lemma	pos
ejpam-1951	1	1	compile	compile	NOUN
ejpam-1951	1	2	/	/	SYM
ejpam-1951	1	3	output.dvi	output.dvi	NOUN
ejpam-1951	1	4	european	european	ADJ
ejpam-1951	1	5	journal	journal	NOUN
ejpam-1951	1	6	of	of	ADP
ejpam-1951	1	7	pure	pure	ADJ
ejpam-1951	1	8	and	and	CCONJ
ejpam-1951	1	9	applied	apply	VERB
ejpam-1951	1	10	mathematics	mathematic	NOUN
ejpam-1951	1	11	vol	vol	NOUN
ejpam-1951	1	12	.	.	PROPN
ejpam-1951	2	1	9	9	NUM
ejpam-1951	2	2	,	,	PUNCT
ejpam-1951	2	3	no	no	INTJ
ejpam-1951	2	4	.	.	NOUN
ejpam-1951	2	5	1	1	NUM
ejpam-1951	2	6	,	,	PUNCT
ejpam-1951	2	7	2016	2016	NUM
ejpam-1951	2	8	,	,	PUNCT
ejpam-1951	2	9	84	84	NUM
ejpam-1951	2	10	-	-	SYM
ejpam-1951	2	11	113	113	NUM
ejpam-1951	2	12	issn	issn	PROPN
ejpam-1951	2	13	1307	1307	NUM
ejpam-1951	2	14	-	-	SYM
ejpam-1951	2	15	5543	5543	NUM
ejpam-1951	2	16	–	–	PUNCT
ejpam-1951	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1951	2	18	counting	count	VERB
ejpam-1951	2	19	symmetries	symmetry	NOUN
ejpam-1951	2	20	with	with	ADP
ejpam-1951	2	21	burnside	burnside	PROPN
ejpam-1951	2	22	’s	’s	PART
ejpam-1951	2	23	lemma	lemma	PROPN
ejpam-1951	2	24	and	and	CCONJ
ejpam-1951	2	25	pólya	pólya	PROPN
ejpam-1951	2	26	’s	’s	PART
ejpam-1951	2	27	theorem	theorem	PROPN
ejpam-1951	2	28	md	md	PROPN
ejpam-1951	2	29	.	.	PROPN
ejpam-1951	2	30	taufiq	taufiq	PROPN
ejpam-1951	2	31	nasseef	nasseef	PROPN
ejpam-1951	2	32	department	department	PROPN
ejpam-1951	2	33	of	of	ADP
ejpam-1951	2	34	mathematics	mathematic	NOUN
ejpam-1951	2	35	,	,	PUNCT
ejpam-1951	2	36	school	school	NOUN
ejpam-1951	2	37	of	of	ADP
ejpam-1951	2	38	mathematics	mathematic	NOUN
ejpam-1951	2	39	,	,	PUNCT
ejpam-1951	2	40	statistics	statistic	NOUN
ejpam-1951	2	41	and	and	CCONJ
ejpam-1951	2	42	actuarial	actuarial	ADJ
ejpam-1951	2	43	science	science	NOUN
ejpam-1951	2	44	,	,	PUNCT
ejpam-1951	2	45	university	university	PROPN
ejpam-1951	2	46	of	of	ADP
ejpam-1951	2	47	kent	kent	PROPN
ejpam-1951	2	48	,	,	PUNCT
ejpam-1951	2	49	kent	kent	PROPN
ejpam-1951	2	50	,	,	PUNCT
ejpam-1951	2	51	united	united	ADJ
ejpam-1951	2	52	kingdom	kingdom	PROPN
ejpam-1951	2	53	abstract	abstract	NOUN
ejpam-1951	2	54	.	.	PUNCT
ejpam-1951	3	1	counting	count	VERB
ejpam-1951	3	2	concerns	concern	NOUN
ejpam-1951	3	3	a	a	DET
ejpam-1951	3	4	large	large	ADJ
ejpam-1951	3	5	part	part	NOUN
ejpam-1951	3	6	of	of	ADP
ejpam-1951	3	7	combinational	combinational	ADJ
ejpam-1951	3	8	analysis	analysis	NOUN
ejpam-1951	3	9	.	.	PUNCT
ejpam-1951	4	1	burnside	burnside	PROPN
ejpam-1951	4	2	’s	’s	PART
ejpam-1951	4	3	lemma	lemma	PROPN
ejpam-1951	4	4	,	,	PUNCT
ejpam-1951	4	5	sometimes	sometimes	ADV
ejpam-1951	4	6	also	also	ADV
ejpam-1951	4	7	called	call	VERB
ejpam-1951	4	8	burnside	burnside	PROPN
ejpam-1951	4	9	’s	’s	PART
ejpam-1951	4	10	counting	counting	NOUN
ejpam-1951	4	11	theorem	theorem	VERB
ejpam-1951	4	12	,	,	PUNCT
ejpam-1951	4	13	the	the	DET
ejpam-1951	4	14	cauchy	cauchy	NOUN
ejpam-1951	4	15	-	-	PUNCT
ejpam-1951	4	16	frobenius	frobenius	NOUN
ejpam-1951	4	17	lemma	lemma	PROPN
ejpam-1951	4	18	or	or	CCONJ
ejpam-1951	4	19	the	the	DET
ejpam-1951	4	20	orbit	orbit	NOUN
ejpam-1951	4	21	-	-	PUNCT
ejpam-1951	4	22	counting	counting	NOUN
ejpam-1951	4	23	theorem	theorem	NOUN
ejpam-1951	4	24	[	[	X
ejpam-1951	4	25	5	5	NUM
ejpam-1951	4	26	]	]	PUNCT
ejpam-1951	4	27	,	,	PUNCT
ejpam-1951	4	28	is	be	AUX
ejpam-1951	4	29	often	often	ADV
ejpam-1951	4	30	useful	useful	ADJ
ejpam-1951	4	31	in	in	ADP
ejpam-1951	4	32	taking	take	VERB
ejpam-1951	4	33	account	account	NOUN
ejpam-1951	4	34	of	of	ADP
ejpam-1951	4	35	symmetry	symmetry	NOUN
ejpam-1951	4	36	when	when	SCONJ
ejpam-1951	4	37	counting	count	VERB
ejpam-1951	4	38	mathematical	mathematical	ADJ
ejpam-1951	4	39	objects	object	NOUN
ejpam-1951	4	40	.	.	PUNCT
ejpam-1951	5	1	the	the	DET
ejpam-1951	5	2	pólya	pólya	NOUN
ejpam-1951	5	3	’s	’s	PART
ejpam-1951	5	4	theorem	theorem	NOUN
ejpam-1951	5	5	is	be	AUX
ejpam-1951	5	6	also	also	ADV
ejpam-1951	5	7	known	know	VERB
ejpam-1951	5	8	as	as	ADP
ejpam-1951	5	9	the	the	DET
ejpam-1951	5	10	redfield	redfield	PROPN
ejpam-1951	5	11	-	-	PUNCT
ejpam-1951	5	12	pólya	pólya	NOUN
ejpam-1951	5	13	theorem	theorem	NOUN
ejpam-1951	5	14	which	which	PRON
ejpam-1951	5	15	both	both	PRON
ejpam-1951	5	16	follows	follow	VERB
ejpam-1951	5	17	and	and	CCONJ
ejpam-1951	5	18	ultimately	ultimately	ADV
ejpam-1951	5	19	generalizes	generalize	VERB
ejpam-1951	5	20	burnside	burnside	PROPN
ejpam-1951	5	21	’s	’s	PART
ejpam-1951	5	22	lemma	lemma	PROPN
ejpam-1951	5	23	on	on	ADP
ejpam-1951	5	24	the	the	DET
ejpam-1951	5	25	number	number	NOUN
ejpam-1951	5	26	of	of	ADP
ejpam-1951	5	27	orbits	orbit	NOUN
ejpam-1951	5	28	of	of	ADP
ejpam-1951	5	29	a	a	DET
ejpam-1951	5	30	group	group	NOUN
ejpam-1951	5	31	action	action	NOUN
ejpam-1951	5	32	on	on	ADP
ejpam-1951	5	33	a	a	DET
ejpam-1951	5	34	set	set	NOUN
ejpam-1951	5	35	.	.	PUNCT
ejpam-1951	6	1	pólya	pólya	PROPN
ejpam-1951	6	2	’s	’s	PART
ejpam-1951	6	3	theory	theory	NOUN
ejpam-1951	6	4	is	be	AUX
ejpam-1951	6	5	a	a	DET
ejpam-1951	6	6	spectacular	spectacular	ADJ
ejpam-1951	6	7	tool	tool	NOUN
ejpam-1951	6	8	that	that	PRON
ejpam-1951	6	9	allows	allow	VERB
ejpam-1951	6	10	us	we	PRON
ejpam-1951	6	11	to	to	PART
ejpam-1951	6	12	count	count	VERB
ejpam-1951	6	13	the	the	DET
ejpam-1951	6	14	number	number	NOUN
ejpam-1951	6	15	of	of	ADP
ejpam-1951	6	16	distinct	distinct	ADJ
ejpam-1951	6	17	items	item	NOUN
ejpam-1951	6	18	given	give	VERB
ejpam-1951	6	19	a	a	DET
ejpam-1951	6	20	certain	certain	ADJ
ejpam-1951	6	21	number	number	NOUN
ejpam-1951	6	22	of	of	ADP
ejpam-1951	6	23	colors	color	NOUN
ejpam-1951	6	24	or	or	CCONJ
ejpam-1951	6	25	other	other	ADJ
ejpam-1951	6	26	characteristics	characteristic	NOUN
ejpam-1951	6	27	.	.	PUNCT
ejpam-1951	7	1	sometimes	sometimes	ADV
ejpam-1951	7	2	it	it	PRON
ejpam-1951	7	3	is	be	AUX
ejpam-1951	7	4	interesting	interesting	ADJ
ejpam-1951	7	5	to	to	PART
ejpam-1951	7	6	know	know	VERB
ejpam-1951	7	7	more	more	ADJ
ejpam-1951	7	8	information	information	NOUN
ejpam-1951	7	9	about	about	ADP
ejpam-1951	7	10	the	the	DET
ejpam-1951	7	11	characteristics	characteristic	NOUN
ejpam-1951	7	12	of	of	ADP
ejpam-1951	7	13	these	these	DET
ejpam-1951	7	14	distinct	distinct	ADJ
ejpam-1951	7	15	objects	object	NOUN
ejpam-1951	7	16	.	.	PUNCT
ejpam-1951	8	1	pólya	pólya	PROPN
ejpam-1951	8	2	’s	’s	PART
ejpam-1951	8	3	theory	theory	NOUN
ejpam-1951	8	4	is	be	AUX
ejpam-1951	8	5	a	a	DET
ejpam-1951	8	6	unique	unique	ADJ
ejpam-1951	8	7	and	and	CCONJ
ejpam-1951	8	8	useful	useful	ADJ
ejpam-1951	8	9	theory	theory	NOUN
ejpam-1951	8	10	which	which	PRON
ejpam-1951	8	11	acts	act	VERB
ejpam-1951	8	12	as	as	ADP
ejpam-1951	8	13	a	a	DET
ejpam-1951	8	14	picture	picture	NOUN
ejpam-1951	8	15	function	function	NOUN
ejpam-1951	8	16	by	by	ADP
ejpam-1951	8	17	producing	produce	VERB
ejpam-1951	8	18	a	a	DET
ejpam-1951	8	19	polynomial	polynomial	NOUN
ejpam-1951	8	20	that	that	PRON
ejpam-1951	8	21	demonstrates	demonstrate	VERB
ejpam-1951	8	22	what	what	PRON
ejpam-1951	8	23	the	the	DET
ejpam-1951	8	24	different	different	ADJ
ejpam-1951	8	25	configurations	configuration	NOUN
ejpam-1951	8	26	are	be	AUX
ejpam-1951	8	27	,	,	PUNCT
ejpam-1951	8	28	and	and	CCONJ
ejpam-1951	8	29	how	how	SCONJ
ejpam-1951	8	30	many	many	ADJ
ejpam-1951	8	31	of	of	ADP
ejpam-1951	8	32	each	each	DET
ejpam-1951	8	33	exist.the	exist.the	NOUN
ejpam-1951	8	34	dynamics	dynamic	NOUN
ejpam-1951	8	35	of	of	ADP
ejpam-1951	8	36	counting	count	VERB
ejpam-1951	8	37	symmetries	symmetry	NOUN
ejpam-1951	8	38	are	be	AUX
ejpam-1951	8	39	the	the	DET
ejpam-1951	8	40	most	most	ADV
ejpam-1951	8	41	interesting	interesting	ADJ
ejpam-1951	8	42	part	part	NOUN
ejpam-1951	8	43	.	.	PUNCT
ejpam-1951	9	1	this	this	DET
ejpam-1951	9	2	subject	subject	NOUN
ejpam-1951	9	3	has	have	AUX
ejpam-1951	9	4	been	be	AUX
ejpam-1951	9	5	a	a	DET
ejpam-1951	9	6	fascination	fascination	NOUN
ejpam-1951	9	7	for	for	ADP
ejpam-1951	9	8	mathematicians	mathematician	NOUN
ejpam-1951	9	9	and	and	CCONJ
ejpam-1951	9	10	scientist	scientist	NOUN
ejpam-1951	9	11	for	for	ADP
ejpam-1951	9	12	ages	age	NOUN
ejpam-1951	9	13	.	.	PUNCT
ejpam-1951	10	1	here	here	ADV
ejpam-1951	10	2	16	16	NUM
ejpam-1951	10	3	bead	bead	NOUN
ejpam-1951	10	4	necklace	necklace	NOUN
ejpam-1951	10	5	,	,	PUNCT
ejpam-1951	10	6	patterns	pattern	NOUN
ejpam-1951	10	7	of	of	ADP
ejpam-1951	10	8	n	n	DET
ejpam-1951	10	9	tetrahedron	tetrahedron	NOUN
ejpam-1951	10	10	with	with	ADP
ejpam-1951	10	11	2	2	NUM
ejpam-1951	10	12	colors	color	NOUN
ejpam-1951	10	13	,	,	PUNCT
ejpam-1951	10	14	patterns	pattern	NOUN
ejpam-1951	10	15	of	of	ADP
ejpam-1951	10	16	n	n	PRON
ejpam-1951	10	17	cubes	cube	NOUN
ejpam-1951	10	18	with	with	ADP
ejpam-1951	10	19	3	3	NUM
ejpam-1951	10	20	and	and	CCONJ
ejpam-1951	10	21	4	4	NUM
ejpam-1951	10	22	colorings	coloring	NOUN
ejpam-1951	10	23	and	and	CCONJ
ejpam-1951	10	24	so	so	ADV
ejpam-1951	10	25	on	on	ADV
ejpam-1951	10	26	have	have	AUX
ejpam-1951	10	27	been	be	AUX
ejpam-1951	10	28	solved	solve	VERB
ejpam-1951	10	29	.	.	PUNCT
ejpam-1951	11	1	2010	2010	NUM
ejpam-1951	11	2	mathematics	mathematic	NOUN
ejpam-1951	11	3	subject	subject	NOUN
ejpam-1951	11	4	classifications	classification	NOUN
ejpam-1951	11	5	:	:	PUNCT
ejpam-1951	11	6	14l,14p,14q	14l,14p,14q	NUM
ejpam-1951	11	7	key	key	ADJ
ejpam-1951	11	8	words	word	NOUN
ejpam-1951	11	9	and	and	CCONJ
ejpam-1951	11	10	phrases	phrase	NOUN
ejpam-1951	11	11	:	:	PUNCT
ejpam-1951	11	12	burnside	burnside	PROPN
ejpam-1951	11	13	’s	’s	PART
ejpam-1951	11	14	lemma	lemma	PROPN
ejpam-1951	11	15	,	,	PUNCT
ejpam-1951	11	16	pólya	pólya	NOUN
ejpam-1951	11	17	’s	’s	PART
ejpam-1951	11	18	theorem	theorem	PROPN
ejpam-1951	11	19	,	,	PUNCT
ejpam-1951	11	20	counting	count	VERB
ejpam-1951	11	21	symmetries	symmetry	NOUN
ejpam-1951	11	22	,	,	PUNCT
ejpam-1951	11	23	group	group	NOUN
ejpam-1951	11	24	1	1	NUM
ejpam-1951	11	25	.	.	PUNCT
ejpam-1951	11	26	introduction	introduction	NOUN
ejpam-1951	11	27	and	and	CCONJ
ejpam-1951	11	28	preliminaries	preliminary	NOUN
ejpam-1951	11	29	1.1	1.1	NUM
ejpam-1951	11	30	.	.	PUNCT
ejpam-1951	12	1	group	group	NOUN
ejpam-1951	12	2	action	action	NOUN
ejpam-1951	12	3	let	let	VERB
ejpam-1951	12	4	g	g	PRON
ejpam-1951	12	5	be	be	AUX
ejpam-1951	12	6	a	a	DET
ejpam-1951	12	7	group	group	NOUN
ejpam-1951	12	8	and	and	CCONJ
ejpam-1951	12	9	a	a	PRON
ejpam-1951	12	10	is	be	AUX
ejpam-1951	12	11	a	a	DET
ejpam-1951	12	12	set	set	NOUN
ejpam-1951	12	13	which	which	PRON
ejpam-1951	12	14	is	be	AUX
ejpam-1951	12	15	nonempty	nonempty	ADJ
ejpam-1951	12	16	.	.	PUNCT
ejpam-1951	13	1	suppose	suppose	VERB
ejpam-1951	13	2	that	that	SCONJ
ejpam-1951	13	3	g	g	PROPN
ejpam-1951	13	4	is	be	AUX
ejpam-1951	13	5	a	a	DET
ejpam-1951	13	6	permutation	permutation	NOUN
ejpam-1951	13	7	group	group	NOUN
ejpam-1951	13	8	acting	act	VERB
ejpam-1951	13	9	on	on	ADP
ejpam-1951	13	10	a	a	DET
ejpam-1951	13	11	set	set	NOUN
ejpam-1951	13	12	a	a	PRON
ejpam-1951	13	13	,	,	PUNCT
ejpam-1951	13	14	and	and	CCONJ
ejpam-1951	13	15	consider	consider	VERB
ejpam-1951	13	16	the	the	DET
ejpam-1951	13	17	set	set	NOUN
ejpam-1951	13	18	ba	ba	PROPN
ejpam-1951	13	19	of	of	ADP
ejpam-1951	13	20	all	all	DET
ejpam-1951	13	21	functions	function	NOUN
ejpam-1951	13	22	f	f	X
ejpam-1951	13	23	:	:	PUNCT
ejpam-1951	13	24	a→	a→	PROPN
ejpam-1951	13	25	b.	b.	NOUN
ejpam-1951	13	26	then	then	ADV
ejpam-1951	13	27	g	g	PROPN
ejpam-1951	13	28	acts	act	VERB
ejpam-1951	13	29	naturally	naturally	ADV
ejpam-1951	13	30	on	on	ADP
ejpam-1951	13	31	ba	ba	PROPN
ejpam-1951	13	32	as	as	SCONJ
ejpam-1951	13	33	follows	follow	VERB
ejpam-1951	13	34	:	:	PUNCT
ejpam-1951	13	35	if	if	SCONJ
ejpam-1951	13	36	g	g	PROPN
ejpam-1951	13	37	∈	∈	PROPN
ejpam-1951	13	38	g	g	PROPN
ejpam-1951	13	39	and	and	CCONJ
ejpam-1951	13	40	f	f	PROPN
ejpam-1951	13	41	∈	∈	PROPN
ejpam-1951	13	42	ba	ba	PROPN
ejpam-1951	13	43	then	then	ADV
ejpam-1951	13	44	define	define	VERB
ejpam-1951	13	45	the	the	DET
ejpam-1951	13	46	function	function	NOUN
ejpam-1951	13	47	f	f	PROPN
ejpam-1951	13	48	g	g	NOUN
ejpam-1951	13	49	by	by	ADP
ejpam-1951	13	50	[	[	X
ejpam-1951	13	51	8	8	NUM
ejpam-1951	13	52	]	]	X
ejpam-1951	13	53	f	f	PROPN
ejpam-1951	13	54	g(a	g(a	PROPN
ejpam-1951	13	55	)	)	PUNCT
ejpam-1951	14	1	=	=	SYM
ejpam-1951	14	2	f	f	PROPN
ejpam-1951	14	3	(	(	PUNCT
ejpam-1951	14	4	ag−1	ag−1	PROPN
ejpam-1951	14	5	)	)	PUNCT
ejpam-1951	14	6	.	.	PUNCT
ejpam-1951	15	1	email	email	NOUN
ejpam-1951	15	2	address	address	NOUN
ejpam-1951	15	3	:	:	PUNCT
ejpam-1951	15	4	taufiq278@gmail.com	taufiq278@gmail.com	X
ejpam-1951	15	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1951	15	6	84	84	NUM
ejpam-1951	16	1	c	c	X
ejpam-1951	16	2	©	©	NOUN
ejpam-1951	16	3	2016	2016	NUM
ejpam-1951	16	4	ejpam	ejpam	VERB
ejpam-1951	16	5	all	all	DET
ejpam-1951	16	6	rights	right	NOUN
ejpam-1951	16	7	reserved	reserve	VERB
ejpam-1951	16	8	.	.	PUNCT
ejpam-1951	17	1	t.	t.	PROPN
ejpam-1951	17	2	nasseef	nasseef	PROPN
ejpam-1951	17	3	/	/	SYM
ejpam-1951	17	4	eur	eur	PROPN
ejpam-1951	17	5	.	.	PUNCT
ejpam-1951	18	1	j.	j.	PROPN
ejpam-1951	18	2	pure	pure	PROPN
ejpam-1951	18	3	appl	appl	PROPN
ejpam-1951	18	4	.	.	PROPN
ejpam-1951	18	5	math	math	PROPN
ejpam-1951	18	6	,	,	PUNCT
ejpam-1951	18	7	9	9	NUM
ejpam-1951	18	8	(	(	PUNCT
ejpam-1951	18	9	2016	2016	NUM
ejpam-1951	18	10	)	)	PUNCT
ejpam-1951	18	11	,	,	PUNCT
ejpam-1951	18	12	84	84	NUM
ejpam-1951	18	13	-	-	SYM
ejpam-1951	18	14	113	113	NUM
ejpam-1951	18	15	85	85	NUM
ejpam-1951	18	16	1.2	1.2	NUM
ejpam-1951	18	17	.	.	PUNCT
ejpam-1951	19	1	the	the	DET
ejpam-1951	19	2	cycle	cycle	NOUN
ejpam-1951	19	3	index	index	NOUN
ejpam-1951	19	4	of	of	ADP
ejpam-1951	19	5	a	a	DET
ejpam-1951	19	6	permutation	permutation	NOUN
ejpam-1951	19	7	group	group	NOUN
ejpam-1951	19	8	let	let	VERB
ejpam-1951	19	9	us	we	PRON
ejpam-1951	19	10	consider	consider	VERB
ejpam-1951	19	11	g	g	PROPN
ejpam-1951	19	12	is	be	AUX
ejpam-1951	19	13	a	a	DET
ejpam-1951	19	14	permutation	permutation	NOUN
ejpam-1951	19	15	group	group	NOUN
ejpam-1951	19	16	acting	act	VERB
ejpam-1951	19	17	on	on	ADP
ejpam-1951	19	18	a	a	DET
ejpam-1951	19	19	set	set	NOUN
ejpam-1951	19	20	a	a	PRON
ejpam-1951	19	21	which	which	PRON
ejpam-1951	19	22	contains	contain	VERB
ejpam-1951	19	23	p	p	ADJ
ejpam-1951	19	24	number	number	NOUN
ejpam-1951	19	25	of	of	ADP
ejpam-1951	19	26	elements	element	NOUN
ejpam-1951	19	27	.	.	PUNCT
ejpam-1951	20	1	suppose	suppose	VERB
ejpam-1951	20	2	x	x	SYM
ejpam-1951	20	3	∈	∈	PROPN
ejpam-1951	20	4	g	g	PROPN
ejpam-1951	20	5	which	which	PRON
ejpam-1951	20	6	can	can	AUX
ejpam-1951	20	7	be	be	AUX
ejpam-1951	20	8	written	write	VERB
ejpam-1951	20	9	as	as	ADP
ejpam-1951	20	10	the	the	DET
ejpam-1951	20	11	product	product	NOUN
ejpam-1951	20	12	of	of	ADP
ejpam-1951	20	13	t1	t1	PROPN
ejpam-1951	20	14	disjoint	disjoint	NOUN
ejpam-1951	20	15	cycles	cycle	NOUN
ejpam-1951	20	16	of	of	ADP
ejpam-1951	20	17	length	length	NOUN
ejpam-1951	20	18	1	1	NUM
ejpam-1951	20	19	,	,	PUNCT
ejpam-1951	20	20	t2	t2	NOUN
ejpam-1951	20	21	disjoint	disjoint	NOUN
ejpam-1951	20	22	cycles	cycle	NOUN
ejpam-1951	20	23	of	of	ADP
ejpam-1951	20	24	length	length	NOUN
ejpam-1951	20	25	2	2	NUM
ejpam-1951	20	26	,	,	PUNCT
ejpam-1951	20	27	.	.	PUNCT
ejpam-1951	20	28	.	.	PUNCT
ejpam-1951	21	1	.	.	PUNCT
ejpam-1951	22	1	,	,	PUNCT
ejpam-1951	22	2	tp	tp	X
ejpam-1951	22	3	disjoint	disjoint	NOUN
ejpam-1951	22	4	cycles	cycle	NOUN
ejpam-1951	22	5	of	of	ADP
ejpam-1951	22	6	length	length	NOUN
ejpam-1951	23	1	p	p	PROPN
ejpam-1951	24	1	then	then	ADV
ejpam-1951	24	2	x	x	INTJ
ejpam-1951	24	3	is	be	AUX
ejpam-1951	24	4	called	call	VERB
ejpam-1951	24	5	of	of	ADP
ejpam-1951	24	6	cycle	cycle	NOUN
ejpam-1951	24	7	type	type	NOUN
ejpam-1951	24	8	(	(	PUNCT
ejpam-1951	24	9	t1	t1	NOUN
ejpam-1951	24	10	,	,	PUNCT
ejpam-1951	24	11	t2	t2	NOUN
ejpam-1951	24	12	,	,	PUNCT
ejpam-1951	24	13	.	.	PUNCT
ejpam-1951	24	14	.	.	PUNCT
ejpam-1951	25	1	.	.	PUNCT
ejpam-1951	26	1	,	,	PUNCT
ejpam-1951	26	2	tp	tp	NOUN
ejpam-1951	26	3	)	)	PUNCT
ejpam-1951	26	4	.	.	PUNCT
ejpam-1951	27	1	example	example	NOUN
ejpam-1951	28	1	1	1	NUM
ejpam-1951	28	2	.	.	PUNCT
ejpam-1951	28	3	let	let	VERB
ejpam-1951	28	4	g	g	NOUN
ejpam-1951	28	5	=	=	PUNCT
ejpam-1951	28	6	{	{	PUNCT
ejpam-1951	28	7	x1	x1	PROPN
ejpam-1951	28	8	,	,	PUNCT
ejpam-1951	28	9	x2	x2	PROPN
ejpam-1951	28	10	,	,	PUNCT
ejpam-1951	28	11	x3	x3	ADJ
ejpam-1951	28	12	}	}	PUNCT
ejpam-1951	28	13	be	be	AUX
ejpam-1951	28	14	a	a	DET
ejpam-1951	28	15	cyclic	cyclic	ADJ
ejpam-1951	28	16	group	group	NOUN
ejpam-1951	28	17	of	of	ADP
ejpam-1951	28	18	order	order	NOUN
ejpam-1951	28	19	3	3	NUM
ejpam-1951	28	20	and	and	CCONJ
ejpam-1951	28	21	the	the	DET
ejpam-1951	28	22	set	set	VERB
ejpam-1951	28	23	a=	a=	NOUN
ejpam-1951	28	24	{	{	PUNCT
ejpam-1951	28	25	1,2,3	1,2,3	NUM
ejpam-1951	28	26	}	}	PUNCT
ejpam-1951	28	27	.	.	PUNCT
ejpam-1951	29	1	then	then	ADV
ejpam-1951	29	2	we	we	PRON
ejpam-1951	29	3	have	have	VERB
ejpam-1951	29	4	x1	x1	PROPN
ejpam-1951	29	5	=	=	SYM
ejpam-1951	29	6	�	�	PROPN
ejpam-1951	29	7	1	1	NUM
ejpam-1951	29	8	2	2	NUM
ejpam-1951	29	9	3	3	NUM
ejpam-1951	29	10	1	1	NUM
ejpam-1951	29	11	2	2	NUM
ejpam-1951	29	12	3	3	NUM
ejpam-1951	29	13	�	�	NOUN
ejpam-1951	29	14	=	=	SYM
ejpam-1951	29	15	(	(	PUNCT
ejpam-1951	29	16	1)(2)(3	1)(2)(3	PROPN
ejpam-1951	29	17	)	)	PUNCT
ejpam-1951	29	18	x2	x2	NOUN
ejpam-1951	30	1	=	=	PUNCT
ejpam-1951	30	2	�	�	PROPN
ejpam-1951	30	3	1	1	NUM
ejpam-1951	30	4	2	2	NUM
ejpam-1951	30	5	3	3	NUM
ejpam-1951	30	6	2	2	NUM
ejpam-1951	30	7	3	3	NUM
ejpam-1951	30	8	1	1	NUM
ejpam-1951	30	9	�	�	NOUN
ejpam-1951	30	10	=	=	SYM
ejpam-1951	30	11	(	(	PUNCT
ejpam-1951	30	12	123	123	NUM
ejpam-1951	30	13	)	)	PUNCT
ejpam-1951	30	14	x3	x3	NOUN
ejpam-1951	30	15	=	=	SYM
ejpam-1951	30	16	�	�	PROPN
ejpam-1951	30	17	1	1	NUM
ejpam-1951	30	18	2	2	NUM
ejpam-1951	30	19	3	3	NUM
ejpam-1951	30	20	3	3	NUM
ejpam-1951	30	21	1	1	NUM
ejpam-1951	30	22	2	2	NUM
ejpam-1951	30	23	�	�	NOUN
ejpam-1951	30	24	=	=	SYM
ejpam-1951	30	25	(	(	PUNCT
ejpam-1951	30	26	132	132	NUM
ejpam-1951	30	27	)	)	PUNCT
ejpam-1951	30	28	here	here	ADV
ejpam-1951	30	29	x1	x1	PROPN
ejpam-1951	30	30	has	have	VERB
ejpam-1951	30	31	3	3	NUM
ejpam-1951	30	32	cycle	cycle	NOUN
ejpam-1951	30	33	type	type	NOUN
ejpam-1951	30	34	of	of	ADP
ejpam-1951	30	35	length	length	NOUN
ejpam-1951	30	36	1	1	NUM
ejpam-1951	30	37	.	.	PUNCT
ejpam-1951	31	1	it	it	PRON
ejpam-1951	31	2	is	be	AUX
ejpam-1951	31	3	of	of	ADP
ejpam-1951	31	4	type	type	NOUN
ejpam-1951	31	5	(	(	PUNCT
ejpam-1951	31	6	3,0,0	3,0,0	NUM
ejpam-1951	31	7	)	)	PUNCT
ejpam-1951	31	8	,	,	PUNCT
ejpam-1951	31	9	known	know	VERB
ejpam-1951	31	10	as	as	ADP
ejpam-1951	31	11	identity	identity	NOUN
ejpam-1951	31	12	mapping	mapping	NOUN
ejpam-1951	31	13	.	.	PUNCT
ejpam-1951	32	1	x2	x2	PROPN
ejpam-1951	32	2	and	and	CCONJ
ejpam-1951	32	3	x3	x3	ADJ
ejpam-1951	32	4	each	each	PRON
ejpam-1951	32	5	has	have	VERB
ejpam-1951	32	6	1	1	NUM
ejpam-1951	32	7	cycle	cycle	NOUN
ejpam-1951	32	8	type	type	NOUN
ejpam-1951	32	9	of	of	ADP
ejpam-1951	32	10	length	length	NOUN
ejpam-1951	32	11	3	3	NUM
ejpam-1951	32	12	and	and	CCONJ
ejpam-1951	32	13	are	be	AUX
ejpam-1951	32	14	of	of	ADP
ejpam-1951	32	15	type	type	NOUN
ejpam-1951	32	16	(	(	PUNCT
ejpam-1951	32	17	0,0,1	0,0,1	NOUN
ejpam-1951	32	18	)	)	PUNCT
ejpam-1951	33	1	[	[	X
ejpam-1951	33	2	6	6	NUM
ejpam-1951	33	3	]	]	PUNCT
ejpam-1951	33	4	.	.	PUNCT
ejpam-1951	34	1	note	note	VERB
ejpam-1951	34	2	that	that	SCONJ
ejpam-1951	34	3	if	if	SCONJ
ejpam-1951	34	4	we	we	PRON
ejpam-1951	34	5	split	split	VERB
ejpam-1951	34	6	a	a	PRON
ejpam-1951	34	7	into	into	ADP
ejpam-1951	34	8	k1	k1	NOUN
ejpam-1951	34	9	cycles	cycle	NOUN
ejpam-1951	34	10	of	of	ADP
ejpam-1951	34	11	length	length	NOUN
ejpam-1951	34	12	1	1	NUM
ejpam-1951	34	13	,	,	PUNCT
ejpam-1951	34	14	k2	k2	ADJ
ejpam-1951	34	15	cycles	cycle	NOUN
ejpam-1951	34	16	of	of	ADP
ejpam-1951	34	17	length	length	NOUN
ejpam-1951	34	18	2	2	NUM
ejpam-1951	34	19	,	,	PUNCT
ejpam-1951	34	20	.	.	PUNCT
ejpam-1951	34	21	.	.	PUNCT
ejpam-1951	35	1	.	.	PUNCT
ejpam-1951	36	1	,	,	PUNCT
ejpam-1951	36	2	kp	kp	PROPN
ejpam-1951	36	3	cycles	cycle	NOUN
ejpam-1951	36	4	of	of	ADP
ejpam-1951	36	5	length	length	NOUN
ejpam-1951	36	6	p	p	NOUN
ejpam-1951	37	1	then	then	ADV
ejpam-1951	37	2	we	we	PRON
ejpam-1951	37	3	have	have	VERB
ejpam-1951	37	4	k1	k1	NOUN
ejpam-1951	37	5	+	+	CCONJ
ejpam-1951	37	6	2k2	2k2	NUM
ejpam-1951	37	7	+	+	CCONJ
ejpam-1951	37	8	3k3	3k3	NUM
ejpam-1951	37	9	+	+	X
ejpam-1951	37	10	.	.	PUNCT
ejpam-1951	37	11	.	.	PUNCT
ejpam-1951	38	1	.+	.+	NOUN
ejpam-1951	38	2	pkp	pkp	PROPN
ejpam-1951	38	3	=	=	SYM
ejpam-1951	38	4	p	p	PROPN
ejpam-1951	38	5	,	,	PUNCT
ejpam-1951	38	6	the	the	DET
ejpam-1951	38	7	sum	sum	NOUN
ejpam-1951	38	8	of	of	ADP
ejpam-1951	38	9	lengths	length	NOUN
ejpam-1951	38	10	of	of	ADP
ejpam-1951	38	11	the	the	DET
ejpam-1951	38	12	cycles	cycle	NOUN
ejpam-1951	38	13	are	be	AUX
ejpam-1951	38	14	the	the	DET
ejpam-1951	38	15	total	total	ADJ
ejpam-1951	38	16	number	number	NOUN
ejpam-1951	38	17	of	of	ADP
ejpam-1951	38	18	elements	element	NOUN
ejpam-1951	38	19	in	in	ADP
ejpam-1951	38	20	a	a	DET
ejpam-1951	38	21	[	[	X
ejpam-1951	38	22	2	2	NUM
ejpam-1951	38	23	]	]	PUNCT
ejpam-1951	38	24	.	.	PUNCT
ejpam-1951	39	1	definition	definition	NOUN
ejpam-1951	39	2	1	1	NUM
ejpam-1951	39	3	.	.	PUNCT
ejpam-1951	40	1	let	let	VERB
ejpam-1951	40	2	g	g	PRON
ejpam-1951	40	3	be	be	AUX
ejpam-1951	40	4	a	a	DET
ejpam-1951	40	5	group	group	NOUN
ejpam-1951	40	6	and	and	CCONJ
ejpam-1951	40	7	its	its	PRON
ejpam-1951	40	8	elements	element	NOUN
ejpam-1951	40	9	are	be	AUX
ejpam-1951	40	10	the	the	DET
ejpam-1951	40	11	permutations	permutation	NOUN
ejpam-1951	40	12	of	of	ADP
ejpam-1951	40	13	the	the	DET
ejpam-1951	40	14	set	set	NOUN
ejpam-1951	40	15	a.	a.	NOUN
ejpam-1951	40	16	consider	consider	VERB
ejpam-1951	40	17	the	the	DET
ejpam-1951	40	18	group	group	NOUN
ejpam-1951	40	19	operation	operation	NOUN
ejpam-1951	40	20	be	be	AUX
ejpam-1951	40	21	multiplication	multiplication	NOUN
ejpam-1951	40	22	and	and	CCONJ
ejpam-1951	40	23	let	let	VERB
ejpam-1951	40	24	us	we	PRON
ejpam-1951	40	25	define	define	VERB
ejpam-1951	40	26	a	a	DET
ejpam-1951	40	27	polynomial	polynomial	NOUN
ejpam-1951	40	28	in	in	ADP
ejpam-1951	40	29	p	p	PROPN
ejpam-1951	40	30	variables	variable	NOUN
ejpam-1951	40	31	t1	t1	PROPN
ejpam-1951	40	32	,	,	PUNCT
ejpam-1951	40	33	t2	t2	NOUN
ejpam-1951	40	34	,	,	PUNCT
ejpam-1951	40	35	t3	t3	PROPN
ejpam-1951	40	36	,	,	PUNCT
ejpam-1951	40	37	.	.	PUNCT
ejpam-1951	40	38	.	.	PUNCT
ejpam-1951	41	1	.	.	PUNCT
ejpam-1951	42	1	,	,	PUNCT
ejpam-1951	42	2	tp	tp	ADP
ejpam-1951	42	3	where	where	SCONJ
ejpam-1951	42	4	the	the	DET
ejpam-1951	42	5	coefficients	coefficient	NOUN
ejpam-1951	42	6	are	be	AUX
ejpam-1951	42	7	non	non	X
ejpam-1951	42	8	negative	negative	ADJ
ejpam-1951	42	9	.	.	PUNCT
ejpam-1951	43	1	then	then	ADV
ejpam-1951	43	2	for	for	ADP
ejpam-1951	43	3	every	every	DET
ejpam-1951	43	4	g	g	PROPN
ejpam-1951	43	5	∈	∈	PROPN
ejpam-1951	43	6	g	g	NOUN
ejpam-1951	43	7	we	we	PRON
ejpam-1951	43	8	can	can	AUX
ejpam-1951	43	9	form	form	VERB
ejpam-1951	43	10	the	the	DET
ejpam-1951	43	11	product	product	NOUN
ejpam-1951	43	12	t	t	NOUN
ejpam-1951	43	13	k1	k1	PROPN
ejpam-1951	43	14	1	1	NUM
ejpam-1951	43	15	,	,	PUNCT
ejpam-1951	43	16	t	t	PROPN
ejpam-1951	43	17	k2	k2	PROPN
ejpam-1951	43	18	2	2	NUM
ejpam-1951	43	19	,	,	PUNCT
ejpam-1951	43	20	t	t	PROPN
ejpam-1951	43	21	k3	k3	VERB
ejpam-1951	43	22	3	3	NUM
ejpam-1951	43	23	,	,	PUNCT
ejpam-1951	43	24	.	.	PUNCT
ejpam-1951	43	25	.	.	PUNCT
ejpam-1951	44	1	.	.	PUNCT
ejpam-1951	45	1	,	,	PUNCT
ejpam-1951	45	2	t	t	PROPN
ejpam-1951	45	3	kp	kp	PROPN
ejpam-1951	45	4	p	p	PROPN
ejpam-1951	45	5	.	.	PUNCT
ejpam-1951	46	1	so	so	ADV
ejpam-1951	46	2	the	the	DET
ejpam-1951	46	3	cycle	cycle	NOUN
ejpam-1951	46	4	index	index	NOUN
ejpam-1951	46	5	g	g	PROPN
ejpam-1951	46	6	is	be	AUX
ejpam-1951	46	7	the	the	DET
ejpam-1951	46	8	polynomial	polynomial	ADJ
ejpam-1951	46	9	defined	define	VERB
ejpam-1951	46	10	by	by	ADP
ejpam-1951	46	11	z(g	z(g	NOUN
ejpam-1951	46	12	,	,	PUNCT
ejpam-1951	46	13	t1	t1	NOUN
ejpam-1951	46	14	,	,	PUNCT
ejpam-1951	46	15	t2	t2	NOUN
ejpam-1951	46	16	,	,	PUNCT
ejpam-1951	46	17	t3	t3	PROPN
ejpam-1951	46	18	,	,	PUNCT
ejpam-1951	46	19	.	.	PUNCT
ejpam-1951	46	20	.	.	PUNCT
ejpam-1951	47	1	.	.	PUNCT
ejpam-1951	48	1	,	,	PUNCT
ejpam-1951	48	2	tp	tp	AUX
ejpam-1951	48	3	)	)	PUNCT
ejpam-1951	48	4	=	=	SYM
ejpam-1951	48	5	1	1	NUM
ejpam-1951	48	6	|g|	|g|	PROPN
ejpam-1951	48	7	{	{	PUNCT
ejpam-1951	48	8	∑	∑	PROPN
ejpam-1951	48	9	g∈g	g∈g	PROPN
ejpam-1951	48	10	t	t	PROPN
ejpam-1951	48	11	k1	k1	PROPN
ejpam-1951	48	12	1	1	NUM
ejpam-1951	48	13	t	t	NOUN
ejpam-1951	48	14	k2	k2	PROPN
ejpam-1951	48	15	2	2	NUM
ejpam-1951	48	16	t	t	NOUN
ejpam-1951	48	17	k3	k3	VERB
ejpam-1951	48	18	3	3	NUM
ejpam-1951	48	19	.	.	PUNCT
ejpam-1951	48	20	.	.	PUNCT
ejpam-1951	49	1	.	.	PUNCT
ejpam-1951	50	1	t	t	PROPN
ejpam-1951	50	2	kp	kp	PROPN
ejpam-1951	50	3	p	p	PROPN
ejpam-1951	50	4	}	}	PUNCT
ejpam-1951	50	5	example	example	NOUN
ejpam-1951	50	6	2	2	NUM
ejpam-1951	50	7	.	.	X
ejpam-1951	50	8	consider	consider	VERB
ejpam-1951	50	9	g	g	NOUN
ejpam-1951	50	10	=	=	PROPN
ejpam-1951	50	11	s3	s3	PROPN
ejpam-1951	50	12	=	=	SYM
ejpam-1951	50	13	{	{	PUNCT
ejpam-1951	50	14	x1	x1	PROPN
ejpam-1951	50	15	,	,	PUNCT
ejpam-1951	50	16	x2	x2	PROPN
ejpam-1951	50	17	,	,	PUNCT
ejpam-1951	50	18	x3	x3	PROPN
ejpam-1951	50	19	,	,	PUNCT
ejpam-1951	50	20	x4	x4	PROPN
ejpam-1951	50	21	,	,	PUNCT
ejpam-1951	50	22	x5	x5	PROPN
ejpam-1951	50	23	,	,	PUNCT
ejpam-1951	50	24	x6	x6	PROPN
ejpam-1951	50	25	}	}	PUNCT
ejpam-1951	50	26	where	where	SCONJ
ejpam-1951	50	27	x1	x1	PROPN
ejpam-1951	50	28	=	=	SYM
ejpam-1951	50	29	�	�	PROPN
ejpam-1951	50	30	1	1	NUM
ejpam-1951	50	31	2	2	NUM
ejpam-1951	50	32	3	3	NUM
ejpam-1951	50	33	1	1	NUM
ejpam-1951	50	34	2	2	NUM
ejpam-1951	50	35	3	3	NUM
ejpam-1951	50	36	�	�	NOUN
ejpam-1951	50	37	=	=	SYM
ejpam-1951	50	38	(	(	PUNCT
ejpam-1951	50	39	1)(2)(3	1)(2)(3	PROPN
ejpam-1951	50	40	)	)	PUNCT
ejpam-1951	50	41	x2	x2	NOUN
ejpam-1951	50	42	=	=	PUNCT
ejpam-1951	50	43	�	�	PROPN
ejpam-1951	50	44	1	1	NUM
ejpam-1951	50	45	2	2	NUM
ejpam-1951	50	46	3	3	NUM
ejpam-1951	50	47	2	2	NUM
ejpam-1951	50	48	3	3	NUM
ejpam-1951	50	49	1	1	NUM
ejpam-1951	50	50	�	�	NOUN
ejpam-1951	50	51	=	=	SYM
ejpam-1951	50	52	(	(	PUNCT
ejpam-1951	50	53	123	123	NUM
ejpam-1951	50	54	)	)	PUNCT
ejpam-1951	50	55	x3	x3	NOUN
ejpam-1951	50	56	=	=	SYM
ejpam-1951	50	57	�	�	PROPN
ejpam-1951	50	58	1	1	NUM
ejpam-1951	50	59	2	2	NUM
ejpam-1951	50	60	3	3	NUM
ejpam-1951	50	61	3	3	NUM
ejpam-1951	50	62	1	1	NUM
ejpam-1951	50	63	2	2	NUM
ejpam-1951	50	64	�	�	NOUN
ejpam-1951	50	65	=	=	SYM
ejpam-1951	50	66	(	(	PUNCT
ejpam-1951	50	67	132	132	NUM
ejpam-1951	50	68	)	)	PUNCT
ejpam-1951	50	69	x4	x4	PROPN
ejpam-1951	50	70	=	=	SYM
ejpam-1951	50	71	�	�	PROPN
ejpam-1951	50	72	1	1	NUM
ejpam-1951	50	73	2	2	NUM
ejpam-1951	50	74	3	3	NUM
ejpam-1951	50	75	3	3	NUM
ejpam-1951	50	76	2	2	NUM
ejpam-1951	50	77	1	1	NUM
ejpam-1951	50	78	�	�	NOUN
ejpam-1951	50	79	=	=	SYM
ejpam-1951	50	80	(	(	PUNCT
ejpam-1951	50	81	2)(13	2)(13	NUM
ejpam-1951	50	82	)	)	PUNCT
ejpam-1951	50	83	x5	x5	NOUN
ejpam-1951	50	84	=	=	SYM
ejpam-1951	50	85	�	�	PROPN
ejpam-1951	50	86	1	1	NUM
ejpam-1951	50	87	2	2	NUM
ejpam-1951	50	88	3	3	NUM
ejpam-1951	50	89	1	1	NUM
ejpam-1951	50	90	3	3	NUM
ejpam-1951	50	91	2	2	NUM
ejpam-1951	50	92	�	�	NOUN
ejpam-1951	50	93	=	=	SYM
ejpam-1951	50	94	(	(	PUNCT
ejpam-1951	50	95	1)(23	1)(23	NOUN
ejpam-1951	50	96	)	)	PUNCT
ejpam-1951	50	97	t.	t.	NOUN
ejpam-1951	50	98	nasseef	nasseef	PROPN
ejpam-1951	50	99	/	/	SYM
ejpam-1951	50	100	eur	eur	PROPN
ejpam-1951	50	101	.	.	PUNCT
ejpam-1951	51	1	j.	j.	PROPN
ejpam-1951	51	2	pure	pure	PROPN
ejpam-1951	51	3	appl	appl	PROPN
ejpam-1951	51	4	.	.	PROPN
ejpam-1951	51	5	math	math	PROPN
ejpam-1951	51	6	,	,	PUNCT
ejpam-1951	51	7	9	9	NUM
ejpam-1951	51	8	(	(	PUNCT
ejpam-1951	51	9	2016	2016	NUM
ejpam-1951	51	10	)	)	PUNCT
ejpam-1951	51	11	,	,	PUNCT
ejpam-1951	51	12	84	84	NUM
ejpam-1951	51	13	-	-	SYM
ejpam-1951	51	14	113	113	NUM
ejpam-1951	51	15	86	86	NUM
ejpam-1951	51	16	x6	x6	PROPN
ejpam-1951	51	17	=	=	SYM
ejpam-1951	51	18	�	�	PROPN
ejpam-1951	51	19	1	1	NUM
ejpam-1951	51	20	2	2	NUM
ejpam-1951	51	21	3	3	NUM
ejpam-1951	51	22	2	2	NUM
ejpam-1951	51	23	1	1	NUM
ejpam-1951	51	24	3	3	NUM
ejpam-1951	51	25	�	�	NOUN
ejpam-1951	51	26	=	=	SYM
ejpam-1951	51	27	(	(	PUNCT
ejpam-1951	51	28	12)(3	12)(3	X
ejpam-1951	51	29	)	)	PUNCT
ejpam-1951	51	30	we	we	PRON
ejpam-1951	51	31	observe	observe	VERB
ejpam-1951	51	32	that	that	SCONJ
ejpam-1951	51	33	the	the	DET
ejpam-1951	51	34	permutations	permutation	NOUN
ejpam-1951	51	35	of	of	ADP
ejpam-1951	51	36	each	each	DET
ejpam-1951	51	37	x4	x4	PROPN
ejpam-1951	51	38	,	,	PUNCT
ejpam-1951	51	39	x5	x5	PROPN
ejpam-1951	51	40	and	and	CCONJ
ejpam-1951	51	41	x6	x6	PROPN
ejpam-1951	51	42	has	have	VERB
ejpam-1951	51	43	one	one	NUM
ejpam-1951	51	44	cycle	cycle	NOUN
ejpam-1951	51	45	of	of	ADP
ejpam-1951	51	46	length	length	NOUN
ejpam-1951	51	47	2	2	NUM
ejpam-1951	51	48	and	and	CCONJ
ejpam-1951	51	49	one	one	NUM
ejpam-1951	51	50	cycle	cycle	NOUN
ejpam-1951	51	51	of	of	ADP
ejpam-1951	51	52	length	length	NOUN
ejpam-1951	51	53	1	1	NUM
ejpam-1951	51	54	and	and	CCONJ
ejpam-1951	51	55	are	be	AUX
ejpam-1951	51	56	of	of	ADP
ejpam-1951	51	57	type	type	NOUN
ejpam-1951	51	58	(	(	PUNCT
ejpam-1951	51	59	1,1,0	1,1,0	NUM
ejpam-1951	51	60	)	)	PUNCT
ejpam-1951	51	61	.	.	PUNCT
ejpam-1951	52	1	x1	x1	NUM
ejpam-1951	52	2	,	,	PUNCT
ejpam-1951	52	3	x2	x2	PROPN
ejpam-1951	52	4	and	and	CCONJ
ejpam-1951	52	5	x3	x3	PROPN
ejpam-1951	52	6	are	be	AUX
ejpam-1951	52	7	known	know	VERB
ejpam-1951	52	8	to	to	ADP
ejpam-1951	52	9	us	we	PRON
ejpam-1951	52	10	by	by	ADP
ejpam-1951	52	11	the	the	DET
ejpam-1951	52	12	example	example	NOUN
ejpam-1951	52	13	1	1	NUM
ejpam-1951	52	14	.	.	PUNCT
ejpam-1951	53	1	the	the	DET
ejpam-1951	53	2	order	order	NOUN
ejpam-1951	53	3	of	of	ADP
ejpam-1951	53	4	this	this	DET
ejpam-1951	53	5	group	group	NOUN
ejpam-1951	53	6	is	be	AUX
ejpam-1951	53	7	3!=	3!=	NUM
ejpam-1951	53	8	6	6	NUM
ejpam-1951	53	9	.	.	PUNCT
ejpam-1951	54	1	hence	hence	ADV
ejpam-1951	54	2	by	by	ADP
ejpam-1951	54	3	the	the	DET
ejpam-1951	54	4	definition	definition	NOUN
ejpam-1951	54	5	the	the	DET
ejpam-1951	54	6	cycle	cycle	NOUN
ejpam-1951	54	7	index	index	NOUN
ejpam-1951	54	8	of	of	ADP
ejpam-1951	54	9	s3	s3	PROPN
ejpam-1951	54	10	is	be	AUX
ejpam-1951	54	11	[	[	X
ejpam-1951	54	12	6	6	NUM
ejpam-1951	54	13	]	]	PUNCT
ejpam-1951	54	14	z(s3	z(s3	NUM
ejpam-1951	54	15	,	,	PUNCT
ejpam-1951	54	16	t1	t1	NOUN
ejpam-1951	54	17	,	,	PUNCT
ejpam-1951	54	18	t2	t2	NOUN
ejpam-1951	54	19	,	,	PUNCT
ejpam-1951	54	20	t3	t3	PROPN
ejpam-1951	54	21	)	)	PUNCT
ejpam-1951	54	22	=	=	SYM
ejpam-1951	54	23	1	1	NUM
ejpam-1951	54	24	6	6	NUM
ejpam-1951	54	25	{	{	PUNCT
ejpam-1951	54	26	t3	t3	PROPN
ejpam-1951	54	27	1	1	NUM
ejpam-1951	54	28	+	+	NUM
ejpam-1951	54	29	3t1	3t1	NUM
ejpam-1951	54	30	t2	t2	NOUN
ejpam-1951	54	31	+	+	CCONJ
ejpam-1951	54	32	2t3	2t3	NUM
ejpam-1951	54	33	}	}	PUNCT
ejpam-1951	54	34	.	.	PUNCT
ejpam-1951	55	1	theorem	theorem	NOUN
ejpam-1951	55	2	1	1	NUM
ejpam-1951	55	3	.	.	PUNCT
ejpam-1951	56	1	the	the	DET
ejpam-1951	56	2	cycle	cycle	NOUN
ejpam-1951	56	3	index	index	NOUN
ejpam-1951	56	4	of	of	ADP
ejpam-1951	56	5	the	the	DET
ejpam-1951	56	6	symmetric	symmetric	ADJ
ejpam-1951	56	7	group	group	NOUN
ejpam-1951	56	8	z(sp	z(sp	NOUN
ejpam-1951	56	9	)	)	PUNCT
ejpam-1951	56	10	can	can	AUX
ejpam-1951	56	11	be	be	AUX
ejpam-1951	56	12	defined	define	VERB
ejpam-1951	56	13	by	by	ADP
ejpam-1951	56	14	z(sp	z(sp	NUM
ejpam-1951	56	15	)	)	PUNCT
ejpam-1951	56	16	=	=	SYM
ejpam-1951	57	1	1	1	NUM
ejpam-1951	57	2	p	p	NOUN
ejpam-1951	57	3	!	!	PUNCT
ejpam-1951	57	4	{	{	PUNCT
ejpam-1951	58	1	∑	∑	PUNCT
ejpam-1951	58	2	t(t	t(t	NOUN
ejpam-1951	58	3	k1	k1	NOUN
ejpam-1951	58	4	1	1	NUM
ejpam-1951	58	5	t	t	NOUN
ejpam-1951	58	6	k2	k2	PROPN
ejpam-1951	58	7	2	2	NUM
ejpam-1951	58	8	t	t	NOUN
ejpam-1951	58	9	k3	k3	VERB
ejpam-1951	58	10	3	3	NUM
ejpam-1951	58	11	.	.	PUNCT
ejpam-1951	58	12	.	.	PUNCT
ejpam-1951	58	13	.	.	PUNCT
ejpam-1951	59	1	t	t	PROPN
ejpam-1951	59	2	kp	kp	PROPN
ejpam-1951	59	3	p	p	PROPN
ejpam-1951	59	4	)	)	PUNCT
ejpam-1951	59	5	}	}	PUNCT
ejpam-1951	59	6	where	where	SCONJ
ejpam-1951	59	7	t	t	NOUN
ejpam-1951	59	8	=	=	SYM
ejpam-1951	60	1	p	p	X
ejpam-1951	60	2	!	!	PUNCT
ejpam-1951	60	3	(	(	PUNCT
ejpam-1951	60	4	1k1!)(2k2!)(3k3	1k1!)(2k2!)(3k3	NUM
ejpam-1951	60	5	!	!	PUNCT
ejpam-1951	60	6	)	)	PUNCT
ejpam-1951	60	7	.	.	PUNCT
ejpam-1951	60	8	.	.	PUNCT
ejpam-1951	60	9	.	.	PUNCT
ejpam-1951	61	1	(	(	PUNCT
ejpam-1951	61	2	pkp	pkp	PROPN
ejpam-1951	61	3	!	!	PUNCT
ejpam-1951	61	4	)	)	PUNCT
ejpam-1951	62	1	and	and	CCONJ
ejpam-1951	62	2	the	the	DET
ejpam-1951	62	3	summation	summation	NOUN
ejpam-1951	62	4	is	be	AUX
ejpam-1951	62	5	over	over	ADP
ejpam-1951	62	6	p	p	NOUN
ejpam-1951	62	7	-	-	PUNCT
ejpam-1951	62	8	tuple	tuple	NOUN
ejpam-1951	62	9	(	(	PUNCT
ejpam-1951	62	10	k1	k1	PROPN
ejpam-1951	62	11	,	,	PUNCT
ejpam-1951	62	12	k2	k2	NOUN
ejpam-1951	62	13	,	,	PUNCT
ejpam-1951	62	14	k3	k3	VERB
ejpam-1951	62	15	,	,	PUNCT
ejpam-1951	62	16	.	.	PUNCT
ejpam-1951	62	17	.	.	PUNCT
ejpam-1951	63	1	.	.	PUNCT
ejpam-1951	64	1	,	,	PUNCT
ejpam-1951	64	2	kp	kp	PROPN
ejpam-1951	64	3	)	)	PUNCT
ejpam-1951	64	4	which	which	PRON
ejpam-1951	64	5	are	be	AUX
ejpam-1951	64	6	nonnegative	nonnegative	ADJ
ejpam-1951	64	7	integers	integer	NOUN
ejpam-1951	64	8	ki	ki	X
ejpam-1951	64	9	satisfying	satisfy	VERB
ejpam-1951	64	10	1k1	1k1	NUM
ejpam-1951	64	11	+	+	CCONJ
ejpam-1951	64	12	2k2	2k2	NUM
ejpam-1951	65	1	+	+	CCONJ
ejpam-1951	65	2	3k3	3k3	NUM
ejpam-1951	65	3	+	+	X
ejpam-1951	65	4	.	.	PUNCT
ejpam-1951	65	5	.	.	PUNCT
ejpam-1951	66	1	.+	.+	NOUN
ejpam-1951	67	1	pkp	pkp	X
ejpam-1951	68	1	=	=	PUNCT
ejpam-1951	68	2	p	p	X
ejpam-1951	69	1	[	[	X
ejpam-1951	69	2	6	6	NUM
ejpam-1951	69	3	]	]	PUNCT
ejpam-1951	69	4	.	.	PUNCT
ejpam-1951	70	1	there	there	PRON
ejpam-1951	70	2	are	be	VERB
ejpam-1951	70	3	some	some	DET
ejpam-1951	70	4	formulas	formula	NOUN
ejpam-1951	70	5	for	for	ADP
ejpam-1951	70	6	cycle	cycle	NOUN
ejpam-1951	70	7	indices	index	NOUN
ejpam-1951	70	8	.	.	PUNCT
ejpam-1951	71	1	in	in	ADP
ejpam-1951	71	2	this	this	DET
ejpam-1951	71	3	study	study	NOUN
ejpam-1951	71	4	we	we	PRON
ejpam-1951	71	5	will	will	AUX
ejpam-1951	71	6	use	use	VERB
ejpam-1951	71	7	indices	index	NOUN
ejpam-1951	71	8	for	for	ADP
ejpam-1951	71	9	symmetric	symmetric	ADJ
ejpam-1951	71	10	groups	group	NOUN
ejpam-1951	71	11	,	,	PUNCT
ejpam-1951	71	12	cyclic	cyclic	ADJ
ejpam-1951	71	13	groups	group	NOUN
ejpam-1951	71	14	,	,	PUNCT
ejpam-1951	71	15	and	and	CCONJ
ejpam-1951	71	16	dihedral	dihedral	ADJ
ejpam-1951	71	17	groups	group	NOUN
ejpam-1951	71	18	.	.	PUNCT
ejpam-1951	72	1	definition	definition	NOUN
ejpam-1951	72	2	2	2	NUM
ejpam-1951	72	3	.	.	PUNCT
ejpam-1951	73	1	the	the	DET
ejpam-1951	73	2	totient	totient	NOUN
ejpam-1951	73	3	function	function	NOUN
ejpam-1951	73	4	φ(n	φ(n	NOUN
ejpam-1951	73	5	)	)	PUNCT
ejpam-1951	73	6	,	,	PUNCT
ejpam-1951	73	7	also	also	ADV
ejpam-1951	73	8	called	call	VERB
ejpam-1951	73	9	euler	euler	NOUN
ejpam-1951	73	10	’s	’s	PART
ejpam-1951	73	11	totient	totient	PROPN
ejpam-1951	73	12	function	function	NOUN
ejpam-1951	73	13	or	or	CCONJ
ejpam-1951	73	14	the	the	DET
ejpam-1951	73	15	euler	euler	NOUN
ejpam-1951	73	16	-	-	PUNCT
ejpam-1951	73	17	phi	phi	NOUN
ejpam-1951	73	18	function	function	NOUN
ejpam-1951	73	19	,	,	PUNCT
ejpam-1951	73	20	is	be	AUX
ejpam-1951	73	21	defined	define	VERB
ejpam-1951	73	22	as	as	ADP
ejpam-1951	73	23	the	the	DET
ejpam-1951	73	24	number	number	NOUN
ejpam-1951	73	25	of	of	ADP
ejpam-1951	73	26	positive	positive	ADJ
ejpam-1951	73	27	integers	integer	NOUN
ejpam-1951	73	28	≤	≤	NUM
ejpam-1951	74	1	n	n	CCONJ
ejpam-1951	74	2	that	that	PRON
ejpam-1951	74	3	are	be	AUX
ejpam-1951	74	4	relatively	relatively	ADV
ejpam-1951	74	5	prime	prime	ADJ
ejpam-1951	74	6	to	to	ADP
ejpam-1951	74	7	n	n	CCONJ
ejpam-1951	74	8	,	,	PUNCT
ejpam-1951	74	9	where	where	SCONJ
ejpam-1951	74	10	1	1	NUM
ejpam-1951	74	11	is	be	AUX
ejpam-1951	74	12	counted	count	VERB
ejpam-1951	74	13	as	as	ADP
ejpam-1951	74	14	being	be	AUX
ejpam-1951	74	15	relatively	relatively	ADV
ejpam-1951	74	16	prime	prime	ADJ
ejpam-1951	74	17	to	to	ADP
ejpam-1951	74	18	all	all	DET
ejpam-1951	74	19	numbers∗.	numbers∗.	PROPN
ejpam-1951	74	20	for	for	ADP
ejpam-1951	74	21	example	example	NOUN
ejpam-1951	74	22	,	,	PUNCT
ejpam-1951	74	23	there	there	PRON
ejpam-1951	74	24	are	be	VERB
ejpam-1951	74	25	four	four	NUM
ejpam-1951	74	26	numbers	number	NOUN
ejpam-1951	74	27	relatively	relatively	ADV
ejpam-1951	74	28	prime	prime	ADJ
ejpam-1951	74	29	to	to	ADP
ejpam-1951	74	30	12	12	NUM
ejpam-1951	74	31	that	that	PRON
ejpam-1951	74	32	are	be	AUX
ejpam-1951	74	33	less	less	ADJ
ejpam-1951	74	34	than	than	ADP
ejpam-1951	74	35	12	12	NUM
ejpam-1951	74	36	(	(	PUNCT
ejpam-1951	74	37	1,5,7	1,5,7	NUM
ejpam-1951	74	38	,	,	PUNCT
ejpam-1951	74	39	and	and	CCONJ
ejpam-1951	74	40	11	11	NUM
ejpam-1951	74	41	)	)	PUNCT
ejpam-1951	74	42	,	,	PUNCT
ejpam-1951	74	43	so	so	ADV
ejpam-1951	74	44	φ(12	φ(12	ADJ
ejpam-1951	74	45	)	)	PUNCT
ejpam-1951	74	46	=	=	SYM
ejpam-1951	74	47	4	4	X
ejpam-1951	74	48	.	.	X
ejpam-1951	74	49	for	for	ADP
ejpam-1951	74	50	cyclic	cyclic	ADJ
ejpam-1951	74	51	groups	group	NOUN
ejpam-1951	74	52	and	and	CCONJ
ejpam-1951	74	53	dihedral	dihedral	ADJ
ejpam-1951	74	54	groups	group	NOUN
ejpam-1951	74	55	we	we	PRON
ejpam-1951	74	56	have	have	VERB
ejpam-1951	74	57	the	the	DET
ejpam-1951	74	58	following	follow	VERB
ejpam-1951	74	59	formulas	formula	NOUN
ejpam-1951	74	60	:	:	PUNCT
ejpam-1951	74	61	z(cn	z(cn	NUM
ejpam-1951	74	62	)	)	PUNCT
ejpam-1951	74	63	=	=	SYM
ejpam-1951	74	64	1	1	NUM
ejpam-1951	74	65	n	n	NUM
ejpam-1951	74	66	∑	∑	ADV
ejpam-1951	74	67	k	k	X
ejpam-1951	74	68	/	/	SYM
ejpam-1951	74	69	n	n	CCONJ
ejpam-1951	74	70	φ(k)t	φ(k)t	PROPN
ejpam-1951	74	71	n	n	CCONJ
ejpam-1951	74	72	/	/	SYM
ejpam-1951	74	73	k	k	PROPN
ejpam-1951	74	74	k	k	PROPN
ejpam-1951	74	75	,	,	PUNCT
ejpam-1951	74	76	(	(	PUNCT
ejpam-1951	74	77	1	1	NUM
ejpam-1951	74	78	)	)	PUNCT
ejpam-1951	74	79	and	and	CCONJ
ejpam-1951	74	80	z(dn	z(dn	NUM
ejpam-1951	74	81	)	)	PUNCT
ejpam-1951	74	82	=	=	SYM
ejpam-1951	74	83	1	1	NUM
ejpam-1951	74	84	2	2	NUM
ejpam-1951	74	85	z(cn	z(cn	NUM
ejpam-1951	74	86	)	)	PUNCT
ejpam-1951	75	1	+	+	NOUN
ejpam-1951	75	2	¨	¨	NOUN
ejpam-1951	75	3	1	1	NUM
ejpam-1951	75	4	2	2	NUM
ejpam-1951	75	5	t1	t1	NOUN
ejpam-1951	75	6	t	t	PROPN
ejpam-1951	75	7	(	(	PUNCT
ejpam-1951	75	8	n−1)/2	n−1)/2	NOUN
ejpam-1951	75	9	2	2	NUM
ejpam-1951	75	10	if	if	SCONJ
ejpam-1951	75	11	n	n	PRON
ejpam-1951	75	12	odd	odd	ADJ
ejpam-1951	75	13	,	,	PUNCT
ejpam-1951	75	14	1	1	NUM
ejpam-1951	75	15	4(t	4(t	NUM
ejpam-1951	75	16	n/2	n/2	NOUN
ejpam-1951	75	17	2	2	NUM
ejpam-1951	75	18	+	+	NUM
ejpam-1951	75	19	t2	t2	NOUN
ejpam-1951	75	20	1	1	NUM
ejpam-1951	75	21	t	t	NOUN
ejpam-1951	75	22	(	(	PUNCT
ejpam-1951	75	23	n−2)/2	n−2)/2	NOUN
ejpam-1951	75	24	2	2	NUM
ejpam-1951	75	25	)	)	PUNCT
ejpam-1951	75	26	if	if	SCONJ
ejpam-1951	75	27	n	n	X
ejpam-1951	75	28	even	even	ADV
ejpam-1951	75	29	.	.	PUNCT
ejpam-1951	76	1	z(dn	z(dn	NOUN
ejpam-1951	76	2	)	)	PUNCT
ejpam-1951	76	3	is	be	AUX
ejpam-1951	76	4	divided	divide	VERB
ejpam-1951	76	5	into	into	ADP
ejpam-1951	76	6	two	two	NUM
ejpam-1951	76	7	cases	case	NOUN
ejpam-1951	76	8	by	by	ADP
ejpam-1951	76	9	imagining	imagine	VERB
ejpam-1951	76	10	a	a	DET
ejpam-1951	76	11	necklace	necklace	NOUN
ejpam-1951	76	12	of	of	ADP
ejpam-1951	76	13	four	four	NUM
ejpam-1951	76	14	beads	bead	NOUN
ejpam-1951	76	15	versus	versus	ADP
ejpam-1951	76	16	a	a	DET
ejpam-1951	76	17	necklace	necklace	NOUN
ejpam-1951	76	18	of	of	ADP
ejpam-1951	76	19	five	five	NUM
ejpam-1951	76	20	beads	bead	NOUN
ejpam-1951	76	21	.	.	PUNCT
ejpam-1951	77	1	with	with	ADP
ejpam-1951	77	2	four	four	NUM
ejpam-1951	77	3	beads	bead	NOUN
ejpam-1951	77	4	,	,	PUNCT
ejpam-1951	77	5	there	there	PRON
ejpam-1951	77	6	are	be	VERB
ejpam-1951	77	7	two	two	NUM
ejpam-1951	77	8	types	type	NOUN
ejpam-1951	77	9	of	of	ADP
ejpam-1951	77	10	flips	flip	NOUN
ejpam-1951	77	11	:	:	PUNCT
ejpam-1951	77	12	those	those	PRON
ejpam-1951	77	13	over	over	ADP
ejpam-1951	77	14	the	the	DET
ejpam-1951	77	15	line	line	NOUN
ejpam-1951	77	16	through	through	ADP
ejpam-1951	77	17	the	the	DET
ejpam-1951	77	18	centers	center	NOUN
ejpam-1951	77	19	of	of	ADP
ejpam-1951	77	20	opposite	opposite	ADJ
ejpam-1951	77	21	edges	edge	NOUN
ejpam-1951	77	22	,	,	PUNCT
ejpam-1951	77	23	and	and	CCONJ
ejpam-1951	77	24	those	those	PRON
ejpam-1951	77	25	over	over	ADP
ejpam-1951	77	26	the	the	DET
ejpam-1951	77	27	line	line	NOUN
ejpam-1951	77	28	connecting	connect	VERB
ejpam-1951	77	29	opposite	opposite	ADJ
ejpam-1951	77	30	vertices	vertex	NOUN
ejpam-1951	77	31	.	.	PUNCT
ejpam-1951	78	1	however	however	ADV
ejpam-1951	78	2	,	,	PUNCT
ejpam-1951	78	3	with	with	ADP
ejpam-1951	78	4	five	five	NUM
ejpam-1951	78	5	beads	bead	NOUN
ejpam-1951	78	6	,	,	PUNCT
ejpam-1951	78	7	there	there	PRON
ejpam-1951	78	8	is	be	VERB
ejpam-1951	78	9	only	only	ADV
ejpam-1951	78	10	one	one	NUM
ejpam-1951	78	11	type	type	NOUN
ejpam-1951	78	12	of	of	ADP
ejpam-1951	78	13	flip	flip	NOUN
ejpam-1951	78	14	:	:	PUNCT
ejpam-1951	78	15	those	those	PRON
ejpam-1951	78	16	over	over	ADP
ejpam-1951	78	17	lines	line	NOUN
ejpam-1951	78	18	connecting	connect	VERB
ejpam-1951	78	19	a	a	DET
ejpam-1951	78	20	vertex	vertex	NOUN
ejpam-1951	78	21	with	with	ADP
ejpam-1951	78	22	the	the	DET
ejpam-1951	78	23	center	center	NOUN
ejpam-1951	78	24	of	of	ADP
ejpam-1951	78	25	an	an	DET
ejpam-1951	78	26	opposite	opposite	ADJ
ejpam-1951	78	27	edge	edge	NOUN
ejpam-1951	78	28	.	.	PUNCT
ejpam-1951	79	1	this	this	PRON
ejpam-1951	79	2	can	can	AUX
ejpam-1951	79	3	be	be	AUX
ejpam-1951	79	4	extended	extend	VERB
ejpam-1951	79	5	to	to	ADP
ejpam-1951	79	6	any	any	DET
ejpam-1951	79	7	even	even	ADJ
ejpam-1951	79	8	or	or	CCONJ
ejpam-1951	79	9	odd	odd	ADJ
ejpam-1951	79	10	number	number	NOUN
ejpam-1951	79	11	of	of	ADP
ejpam-1951	79	12	beads	bead	NOUN
ejpam-1951	79	13	,	,	PUNCT
ejpam-1951	79	14	respectively	respectively	ADV
ejpam-1951	79	15	[	[	X
ejpam-1951	79	16	4	4	NUM
ejpam-1951	79	17	]	]	PUNCT
ejpam-1951	79	18	.	.	PUNCT
ejpam-1951	80	1	∗k	∗k	NOUN
ejpam-1951	80	2	.	.	PUNCT
ejpam-1951	81	1	r.	r.	PROPN
ejpam-1951	81	2	rumery	rumery	PROPN
ejpam-1951	81	3	,	,	PUNCT
ejpam-1951	81	4	twelve	twelve	NUM
ejpam-1951	81	5	-	-	PUNCT
ejpam-1951	81	6	tone	tone	NOUN
ejpam-1951	81	7	composition	composition	NOUN
ejpam-1951	81	8	,	,	PUNCT
ejpam-1951	81	9	part	part	NOUN
ejpam-1951	81	10	one	one	NUM
ejpam-1951	81	11	,	,	PUNCT
ejpam-1951	81	12	http://jan.ucc.nau.edu/~krr2/12tone/12tone1	http://jan.ucc.nau.edu/~krr2/12tone/12tone1	PROPN
ejpam-1951	81	13	.	.	PROPN
ejpam-1951	81	14	html	html	PROPN
ejpam-1951	81	15	t.	t.	PROPN
ejpam-1951	81	16	nasseef	nasseef	PROPN
ejpam-1951	81	17	/	/	SYM
ejpam-1951	81	18	eur	eur	PROPN
ejpam-1951	81	19	.	.	PUNCT
ejpam-1951	82	1	j.	j.	PROPN
ejpam-1951	82	2	pure	pure	PROPN
ejpam-1951	82	3	appl	appl	PROPN
ejpam-1951	82	4	.	.	PROPN
ejpam-1951	82	5	math	math	PROPN
ejpam-1951	82	6	,	,	PUNCT
ejpam-1951	82	7	9	9	NUM
ejpam-1951	82	8	(	(	PUNCT
ejpam-1951	82	9	2016	2016	NUM
ejpam-1951	82	10	)	)	PUNCT
ejpam-1951	82	11	,	,	PUNCT
ejpam-1951	82	12	84	84	NUM
ejpam-1951	82	13	-	-	SYM
ejpam-1951	82	14	113	113	NUM
ejpam-1951	82	15	87	87	NUM
ejpam-1951	82	16	example	example	NOUN
ejpam-1951	82	17	3	3	X
ejpam-1951	82	18	.	.	PUNCT
ejpam-1951	83	1	let	let	VERB
ejpam-1951	83	2	us	we	PRON
ejpam-1951	83	3	use	use	VERB
ejpam-1951	83	4	this	this	DET
ejpam-1951	83	5	formula	formula	NOUN
ejpam-1951	83	6	to	to	PART
ejpam-1951	83	7	compute	compute	VERB
ejpam-1951	83	8	the	the	DET
ejpam-1951	83	9	cycle	cycle	NOUN
ejpam-1951	83	10	index	index	NOUN
ejpam-1951	83	11	of	of	ADP
ejpam-1951	83	12	c4	c4	NOUN
ejpam-1951	83	13	,	,	PUNCT
ejpam-1951	83	14	zc4	zc4	NOUN
ejpam-1951	83	15	=	=	SYM
ejpam-1951	83	16	1	1	NUM
ejpam-1951	83	17	4	4	NUM
ejpam-1951	83	18	∑	∑	SYM
ejpam-1951	83	19	l/4	l/4	PUNCT
ejpam-1951	83	20	φ(l)t	φ(l)t	PROPN
ejpam-1951	83	21	4	4	NUM
ejpam-1951	83	22	/	/	SYM
ejpam-1951	83	23	l	l	NOUN
ejpam-1951	83	24	l	l	NOUN
ejpam-1951	84	1	=	=	SYM
ejpam-1951	84	2	1	1	NUM
ejpam-1951	84	3	4	4	NUM
ejpam-1951	84	4	(	(	PUNCT
ejpam-1951	84	5	φ(1)t	φ(1)t	PROPN
ejpam-1951	84	6	4/1	4/1	NUM
ejpam-1951	84	7	1	1	NUM
ejpam-1951	85	1	+	+	ADJ
ejpam-1951	85	2	φ(2)t	φ(2)t	PRON
ejpam-1951	85	3	4/2	4/2	NUM
ejpam-1951	85	4	2	2	NUM
ejpam-1951	86	1	+	+	ADP
ejpam-1951	86	2	φ(4)t	φ(4)t	X
ejpam-1951	86	3	4/4	4/4	NUM
ejpam-1951	86	4	4	4	NUM
ejpam-1951	86	5	)	)	PUNCT
ejpam-1951	86	6	=	=	SYM
ejpam-1951	86	7	1	1	NUM
ejpam-1951	86	8	4	4	NUM
ejpam-1951	86	9	(	(	PUNCT
ejpam-1951	86	10	t4	t4	PROPN
ejpam-1951	86	11	1	1	NUM
ejpam-1951	86	12	+	+	CCONJ
ejpam-1951	86	13	t2	t2	NOUN
ejpam-1951	86	14	2	2	NUM
ejpam-1951	86	15	+	+	NUM
ejpam-1951	86	16	2t4	2t4	NUM
ejpam-1951	86	17	)	)	PUNCT
ejpam-1951	86	18	example	example	NOUN
ejpam-1951	87	1	4	4	NUM
ejpam-1951	87	2	.	.	PUNCT
ejpam-1951	88	1	here	here	ADV
ejpam-1951	88	2	we	we	PRON
ejpam-1951	88	3	will	will	AUX
ejpam-1951	88	4	illustrate	illustrate	VERB
ejpam-1951	88	5	the	the	DET
ejpam-1951	88	6	formula	formula	NOUN
ejpam-1951	88	7	by	by	ADP
ejpam-1951	88	8	computing	compute	VERB
ejpam-1951	88	9	the	the	DET
ejpam-1951	88	10	cycle	cycle	NOUN
ejpam-1951	88	11	index	index	NOUN
ejpam-1951	88	12	of	of	ADP
ejpam-1951	88	13	d4	d4	PROPN
ejpam-1951	88	14	,	,	PUNCT
ejpam-1951	88	15	zd4	zd4	NOUN
ejpam-1951	88	16	=	=	NOUN
ejpam-1951	88	17	1	1	NUM
ejpam-1951	88	18	2	2	NUM
ejpam-1951	88	19	zc4	zc4	NOUN
ejpam-1951	88	20	+	+	CCONJ
ejpam-1951	88	21	1	1	NUM
ejpam-1951	88	22	4	4	NUM
ejpam-1951	88	23	(	(	PUNCT
ejpam-1951	88	24	t	t	PROPN
ejpam-1951	88	25	4	4	NUM
ejpam-1951	88	26	2	2	NUM
ejpam-1951	88	27	2	2	NUM
ejpam-1951	88	28	+	+	NOUN
ejpam-1951	88	29	t2	t2	NOUN
ejpam-1951	88	30	1	1	NUM
ejpam-1951	88	31	t	t	NOUN
ejpam-1951	88	32	4−2	4−2	NUM
ejpam-1951	88	33	2	2	NUM
ejpam-1951	88	34	2	2	NUM
ejpam-1951	88	35	)	)	PUNCT
ejpam-1951	88	36	=	=	SYM
ejpam-1951	88	37	1	1	NUM
ejpam-1951	88	38	2	2	NUM
ejpam-1951	88	39	(	(	PUNCT
ejpam-1951	88	40	1	1	NUM
ejpam-1951	88	41	4	4	NUM
ejpam-1951	88	42	(	(	PUNCT
ejpam-1951	88	43	t4	t4	PROPN
ejpam-1951	88	44	1	1	NUM
ejpam-1951	88	45	+	+	CCONJ
ejpam-1951	88	46	t2	t2	NOUN
ejpam-1951	88	47	2	2	NUM
ejpam-1951	88	48	+	+	NUM
ejpam-1951	88	49	2t4	2t4	NUM
ejpam-1951	88	50	)	)	PUNCT
ejpam-1951	88	51	)	)	PUNCT
ejpam-1951	89	1	+	+	CCONJ
ejpam-1951	89	2	1	1	NUM
ejpam-1951	89	3	4	4	NUM
ejpam-1951	89	4	(	(	PUNCT
ejpam-1951	89	5	t	t	PROPN
ejpam-1951	89	6	4	4	NUM
ejpam-1951	89	7	2	2	NUM
ejpam-1951	89	8	2	2	NUM
ejpam-1951	89	9	+	+	NOUN
ejpam-1951	89	10	t2	t2	NOUN
ejpam-1951	89	11	1	1	NUM
ejpam-1951	89	12	t	t	NOUN
ejpam-1951	89	13	4−2	4−2	NUM
ejpam-1951	89	14	2	2	NUM
ejpam-1951	89	15	2	2	NUM
ejpam-1951	89	16	)	)	PUNCT
ejpam-1951	89	17	=	=	SYM
ejpam-1951	89	18	1	1	NUM
ejpam-1951	89	19	8	8	NUM
ejpam-1951	89	20	(	(	PUNCT
ejpam-1951	89	21	t4	t4	PROPN
ejpam-1951	89	22	1	1	NUM
ejpam-1951	89	23	+	+	CCONJ
ejpam-1951	89	24	t2	t2	NOUN
ejpam-1951	89	25	2	2	NUM
ejpam-1951	89	26	+	+	NUM
ejpam-1951	89	27	2t4	2t4	NUM
ejpam-1951	89	28	)	)	PUNCT
ejpam-1951	90	1	+	+	CCONJ
ejpam-1951	90	2	1	1	NUM
ejpam-1951	90	3	4	4	NUM
ejpam-1951	90	4	(	(	PUNCT
ejpam-1951	90	5	t2	t2	NOUN
ejpam-1951	90	6	2	2	NUM
ejpam-1951	90	7	+	+	CCONJ
ejpam-1951	90	8	t2	t2	NOUN
ejpam-1951	90	9	1	1	NUM
ejpam-1951	90	10	t2	t2	NOUN
ejpam-1951	90	11	)	)	PUNCT
ejpam-1951	90	12	=	=	SYM
ejpam-1951	90	13	1	1	NUM
ejpam-1951	90	14	8	8	NUM
ejpam-1951	90	15	(	(	PUNCT
ejpam-1951	90	16	t4	t4	PROPN
ejpam-1951	90	17	1	1	NUM
ejpam-1951	90	18	+	+	CCONJ
ejpam-1951	90	19	2t2	2t2	NUM
ejpam-1951	90	20	1	1	NUM
ejpam-1951	90	21	t2	t2	NOUN
ejpam-1951	90	22	+	+	CCONJ
ejpam-1951	90	23	3t2	3t2	NUM
ejpam-1951	90	24	2	2	NUM
ejpam-1951	90	25	+	+	NUM
ejpam-1951	90	26	2t4	2t4	NUM
ejpam-1951	90	27	)	)	PUNCT
ejpam-1951	90	28	now	now	ADV
ejpam-1951	90	29	we	we	PRON
ejpam-1951	90	30	have	have	AUX
ejpam-1951	90	31	already	already	ADV
ejpam-1951	90	32	got	get	VERB
ejpam-1951	90	33	the	the	DET
ejpam-1951	90	34	cycle	cycle	NOUN
ejpam-1951	90	35	index	index	NOUN
ejpam-1951	90	36	of	of	ADP
ejpam-1951	90	37	the	the	DET
ejpam-1951	90	38	symmetric	symmetric	ADJ
ejpam-1951	90	39	groups	group	NOUN
ejpam-1951	90	40	from	from	ADP
ejpam-1951	90	41	theorem	theorem	ADJ
ejpam-1951	90	42	1	1	NUM
ejpam-1951	90	43	.	.	PUNCT
ejpam-1951	91	1	the	the	DET
ejpam-1951	91	2	following	follow	VERB
ejpam-1951	91	3	example	example	NOUN
ejpam-1951	91	4	will	will	AUX
ejpam-1951	91	5	find	find	VERB
ejpam-1951	91	6	the	the	DET
ejpam-1951	91	7	coefficient	coefficient	NOUN
ejpam-1951	91	8	on	on	ADP
ejpam-1951	91	9	n	n	CCONJ
ejpam-1951	91	10	-	-	PUNCT
ejpam-1951	91	11	th	th	VERB
ejpam-1951	91	12	term	term	NOUN
ejpam-1951	91	13	.	.	PUNCT
ejpam-1951	92	1	example	example	NOUN
ejpam-1951	93	1	5	5	NUM
ejpam-1951	93	2	.	.	PUNCT
ejpam-1951	93	3	let	let	VERB
ejpam-1951	93	4	a	a	DET
ejpam-1951	93	5	be	be	AUX
ejpam-1951	93	6	a	a	DET
ejpam-1951	93	7	set	set	NOUN
ejpam-1951	93	8	of	of	ADP
ejpam-1951	93	9	n	n	NOUN
ejpam-1951	93	10	elements	element	NOUN
ejpam-1951	93	11	and	and	CCONJ
ejpam-1951	93	12	let	let	VERB
ejpam-1951	93	13	g	g	PROPN
ejpam-1951	93	14	be	be	AUX
ejpam-1951	93	15	the	the	DET
ejpam-1951	93	16	group	group	NOUN
ejpam-1951	93	17	of	of	ADP
ejpam-1951	93	18	all	all	DET
ejpam-1951	93	19	permutations	permutation	NOUN
ejpam-1951	93	20	of	of	ADP
ejpam-1951	93	21	a.	a.	NOUN
ejpam-1951	93	22	that	that	PRON
ejpam-1951	93	23	is	be	AUX
ejpam-1951	93	24	g	g	NOUN
ejpam-1951	93	25	is	be	AUX
ejpam-1951	93	26	a	a	DET
ejpam-1951	93	27	symmetric	symmetric	ADJ
ejpam-1951	93	28	group	group	NOUN
ejpam-1951	93	29	of	of	ADP
ejpam-1951	93	30	degree	degree	NOUN
ejpam-1951	93	31	n.	n.	NOUN
ejpam-1951	93	32	its	its	PRON
ejpam-1951	93	33	cycle	cycle	NOUN
ejpam-1951	93	34	index	index	NOUN
ejpam-1951	93	35	turns	turn	VERB
ejpam-1951	93	36	out	out	ADP
ejpam-1951	93	37	to	to	PART
ejpam-1951	93	38	be	be	AUX
ejpam-1951	93	39	equal	equal	ADJ
ejpam-1951	93	40	to	to	ADP
ejpam-1951	93	41	the	the	DET
ejpam-1951	93	42	coefficient	coefficient	NOUN
ejpam-1951	93	43	of	of	ADP
ejpam-1951	93	44	xn	xn	PROPN
ejpam-1951	93	45	in	in	ADP
ejpam-1951	93	46	the	the	DET
ejpam-1951	93	47	development	development	NOUN
ejpam-1951	93	48	of	of	ADP
ejpam-1951	93	49	ex	ex	ADJ
ejpam-1951	93	50	p(x	p(x	PROPN
ejpam-1951	93	51	t1	t1	PROPN
ejpam-1951	93	52	+	+	CCONJ
ejpam-1951	93	53	x2	x2	PROPN
ejpam-1951	93	54	t2	t2	NOUN
ejpam-1951	93	55	2	2	NUM
ejpam-1951	94	1	+	+	CCONJ
ejpam-1951	94	2	x3	x3	ADJ
ejpam-1951	94	3	t3	t3	NOUN
ejpam-1951	94	4	3	3	NUM
ejpam-1951	95	1	+	+	CCONJ
ejpam-1951	95	2	.	.	PUNCT
ejpam-1951	95	3	.	.	PUNCT
ejpam-1951	95	4	.	.	PUNCT
ejpam-1951	95	5	)	)	PUNCT
ejpam-1951	96	1	as	as	ADP
ejpam-1951	96	2	a	a	DET
ejpam-1951	96	3	power	power	NOUN
ejpam-1951	96	4	series	series	NOUN
ejpam-1951	96	5	of	of	ADP
ejpam-1951	96	6	in	in	ADP
ejpam-1951	96	7	x.	x.	NOUN
ejpam-1951	96	8	this	this	DET
ejpam-1951	96	9	expression	expression	NOUN
ejpam-1951	96	10	can	can	AUX
ejpam-1951	96	11	be	be	AUX
ejpam-1951	96	12	written	write	VERB
ejpam-1951	96	13	as	as	ADP
ejpam-1951	96	14	∞	∞	PROPN
ejpam-1951	96	15	∑	∑	PROPN
ejpam-1951	96	16	g1=0	g1=0	PROPN
ejpam-1951	96	17	x	x	SYM
ejpam-1951	96	18	g1	g1	PROPN
ejpam-1951	96	19	t	t	PROPN
ejpam-1951	96	20	g1	g1	PROPN
ejpam-1951	96	21	1	1	NUM
ejpam-1951	96	22	g1	g1	NOUN
ejpam-1951	96	23	!	!	PUNCT
ejpam-1951	97	1	∞	∞	NUM
ejpam-1951	97	2	∑	∑	PUNCT
ejpam-1951	98	1	g1=0	g1=0	PROPN
ejpam-1951	98	2	x2g2	x2g2	PROPN
ejpam-1951	99	1	t	t	PROPN
ejpam-1951	99	2	g2	g2	PROPN
ejpam-1951	99	3	2	2	NUM
ejpam-1951	99	4	g2!2g2	g2!2g2	NOUN
ejpam-1951	99	5	.	.	PUNCT
ejpam-1951	99	6	.	.	PUNCT
ejpam-1951	99	7	.	.	PUNCT
ejpam-1951	100	1	the	the	DET
ejpam-1951	100	2	coefficient	coefficient	NOUN
ejpam-1951	100	3	of	of	ADP
ejpam-1951	100	4	xn	xn	PROPN
ejpam-1951	100	5	is	be	AUX
ejpam-1951	100	6	obtained	obtain	VERB
ejpam-1951	100	7	by	by	ADP
ejpam-1951	100	8	summing	sum	VERB
ejpam-1951	100	9	the	the	DET
ejpam-1951	100	10	expression	expression	NOUN
ejpam-1951	100	11	t	t	PROPN
ejpam-1951	100	12	g1	g1	PROPN
ejpam-1951	100	13	1	1	NUM
ejpam-1951	100	14	t	t	NOUN
ejpam-1951	100	15	g2	g2	PROPN
ejpam-1951	100	16	2	2	NUM
ejpam-1951	100	17	.	.	PUNCT
ejpam-1951	100	18	.	.	PUNCT
ejpam-1951	100	19	.	.	PUNCT
ejpam-1951	101	1	(	(	PUNCT
ejpam-1951	101	2	g1!g2!2g2	g1!g2!2g2	PROPN
ejpam-1951	101	3	.	.	PUNCT
ejpam-1951	101	4	.	.	PUNCT
ejpam-1951	102	1	.)−1	.)−1	VERB
ejpam-1951	102	2	over	over	ADP
ejpam-1951	102	3	all	all	DET
ejpam-1951	102	4	possible	possible	ADJ
ejpam-1951	102	5	g1	g1	NOUN
ejpam-1951	102	6	,	,	PUNCT
ejpam-1951	102	7	g2	g2	PROPN
ejpam-1951	102	8	,	,	PUNCT
ejpam-1951	102	9	.	.	PUNCT
ejpam-1951	102	10	.	.	PUNCT
ejpam-1951	102	11	.	.	PUNCT
ejpam-1951	103	1	satisfying	satisfy	VERB
ejpam-1951	103	2	g1	g1	PROPN
ejpam-1951	103	3	+	+	CCONJ
ejpam-1951	103	4	2g2	2g2	NUM
ejpam-1951	103	5	+	+	CCONJ
ejpam-1951	103	6	.	.	PUNCT
ejpam-1951	103	7	.	.	PUNCT
ejpam-1951	104	1	.=	.=	VERB
ejpam-1951	104	2	n	n	PRON
ejpam-1951	105	1	[	[	X
ejpam-1951	105	2	2	2	NUM
ejpam-1951	105	3	]	]	PUNCT
ejpam-1951	105	4	.	.	PUNCT
ejpam-1951	106	1	definition	definition	NOUN
ejpam-1951	106	2	3	3	NUM
ejpam-1951	106	3	.	.	PUNCT
ejpam-1951	107	1	the	the	DET
ejpam-1951	107	2	set	set	NOUN
ejpam-1951	107	3	of	of	ADP
ejpam-1951	107	4	elements	element	NOUN
ejpam-1951	107	5	g	g	NOUN
ejpam-1951	107	6	of	of	ADP
ejpam-1951	107	7	a	a	DET
ejpam-1951	107	8	group	group	NOUN
ejpam-1951	107	9	g	g	PROPN
ejpam-1951	107	10	such	such	DET
ejpam-1951	107	11	that	that	DET
ejpam-1951	107	12	g−1h	g−1h	NOUN
ejpam-1951	107	13	g	g	NOUN
ejpam-1951	107	14	=	=	SYM
ejpam-1951	107	15	h	h	NOUN
ejpam-1951	107	16	,	,	PUNCT
ejpam-1951	107	17	is	be	AUX
ejpam-1951	107	18	said	say	VERB
ejpam-1951	107	19	to	to	PART
ejpam-1951	107	20	be	be	AUX
ejpam-1951	107	21	the	the	DET
ejpam-1951	107	22	normalizer	normalizer	PROPN
ejpam-1951	107	23	ng	ng	PROPN
ejpam-1951	107	24	with	with	ADP
ejpam-1951	107	25	respect	respect	NOUN
ejpam-1951	107	26	to	to	ADP
ejpam-1951	107	27	a	a	DET
ejpam-1951	107	28	subset	subset	NOUN
ejpam-1951	107	29	of	of	ADP
ejpam-1951	107	30	group	group	NOUN
ejpam-1951	107	31	elements	element	NOUN
ejpam-1951	107	32	of	of	ADP
ejpam-1951	107	33	h.	h.	PROPN
ejpam-1951	107	34	if	if	SCONJ
ejpam-1951	107	35	h	h	NOUN
ejpam-1951	107	36	is	be	AUX
ejpam-1951	107	37	a	a	DET
ejpam-1951	107	38	subgroup	subgroup	NOUN
ejpam-1951	107	39	of	of	ADP
ejpam-1951	107	40	g	g	PROPN
ejpam-1951	107	41	,	,	PUNCT
ejpam-1951	107	42	ng(h	ng(h	ADV
ejpam-1951	107	43	)	)	PUNCT
ejpam-1951	107	44	is	be	AUX
ejpam-1951	107	45	also	also	ADV
ejpam-1951	107	46	a	a	DET
ejpam-1951	107	47	subgroup	subgroup	NOUN
ejpam-1951	107	48	containing	contain	VERB
ejpam-1951	107	49	h.	h.	PROPN
ejpam-1951	107	50	t.	t.	PROPN
ejpam-1951	107	51	nasseef	nasseef	PROPN
ejpam-1951	107	52	/	/	SYM
ejpam-1951	107	53	eur	eur	PROPN
ejpam-1951	107	54	.	.	PUNCT
ejpam-1951	108	1	j.	j.	PROPN
ejpam-1951	108	2	pure	pure	PROPN
ejpam-1951	108	3	appl	appl	PROPN
ejpam-1951	108	4	.	.	PROPN
ejpam-1951	108	5	math	math	PROPN
ejpam-1951	108	6	,	,	PUNCT
ejpam-1951	108	7	9	9	NUM
ejpam-1951	108	8	(	(	PUNCT
ejpam-1951	108	9	2016	2016	NUM
ejpam-1951	108	10	)	)	PUNCT
ejpam-1951	108	11	,	,	PUNCT
ejpam-1951	108	12	84	84	NUM
ejpam-1951	108	13	-	-	SYM
ejpam-1951	108	14	113	113	NUM
ejpam-1951	108	15	88	88	NUM
ejpam-1951	108	16	1.3	1.3	NUM
ejpam-1951	108	17	.	.	PUNCT
ejpam-1951	109	1	equivalence	equivalence	NOUN
ejpam-1951	109	2	relations	relation	NOUN
ejpam-1951	109	3	let	let	VERB
ejpam-1951	109	4	a	a	PRON
ejpam-1951	109	5	be	be	AUX
ejpam-1951	109	6	a	a	DET
ejpam-1951	109	7	set	set	NOUN
ejpam-1951	109	8	and	and	CCONJ
ejpam-1951	109	9	∼	∼	NOUN
ejpam-1951	109	10	be	be	AUX
ejpam-1951	109	11	a	a	DET
ejpam-1951	109	12	binary	binary	ADJ
ejpam-1951	109	13	relation	relation	NOUN
ejpam-1951	109	14	of	of	ADP
ejpam-1951	109	15	a.	a.	NOUN
ejpam-1951	109	16	then	then	ADV
ejpam-1951	109	17	∼	∼	NOUN
ejpam-1951	109	18	is	be	AUX
ejpam-1951	109	19	an	an	DET
ejpam-1951	109	20	equivalence	equivalence	NOUN
ejpam-1951	109	21	relation	relation	NOUN
ejpam-1951	109	22	if	if	SCONJ
ejpam-1951	109	23	and	and	CCONJ
ejpam-1951	109	24	only	only	ADV
ejpam-1951	109	25	if	if	SCONJ
ejpam-1951	109	26	for	for	ADP
ejpam-1951	109	27	all	all	DET
ejpam-1951	109	28	p	p	NOUN
ejpam-1951	109	29	,	,	PUNCT
ejpam-1951	109	30	q	q	NOUN
ejpam-1951	109	31	,	,	PUNCT
ejpam-1951	109	32	r	r	NOUN
ejpam-1951	109	33	∈	∈	PROPN
ejpam-1951	109	34	a	a	DET
ejpam-1951	109	35	the	the	DET
ejpam-1951	109	36	following	following	ADJ
ejpam-1951	109	37	conditions	condition	NOUN
ejpam-1951	109	38	are	be	AUX
ejpam-1951	109	39	satisfied	satisfied	ADJ
ejpam-1951	109	40	:	:	PUNCT
ejpam-1951	109	41	reflexivity	reflexivity	NOUN
ejpam-1951	109	42	p	p	NOUN
ejpam-1951	109	43	∼	∼	NOUN
ejpam-1951	109	44	p	p	NOUN
ejpam-1951	109	45	symmetry	symmetry	NOUN
ejpam-1951	109	46	if	if	SCONJ
ejpam-1951	109	47	p	p	NOUN
ejpam-1951	109	48	∼	∼	NOUN
ejpam-1951	109	49	q	q	NOUN
ejpam-1951	109	50	then	then	ADV
ejpam-1951	109	51	q	q	ADJ
ejpam-1951	109	52	∼	∼	NOUN
ejpam-1951	109	53	p	p	NOUN
ejpam-1951	109	54	transitivity	transitivity	NOUN
ejpam-1951	109	55	if	if	SCONJ
ejpam-1951	109	56	p	p	NOUN
ejpam-1951	109	57	∼	∼	NOUN
ejpam-1951	109	58	q	q	NOUN
ejpam-1951	109	59	and	and	CCONJ
ejpam-1951	109	60	q	q	ADJ
ejpam-1951	109	61	∼	∼	NOUN
ejpam-1951	109	62	r	r	NOUN
ejpam-1951	109	63	then	then	ADV
ejpam-1951	109	64	p	p	NOUN
ejpam-1951	109	65	∼	∼	NOUN
ejpam-1951	109	66	r	r	NOUN
ejpam-1951	109	67	the	the	DET
ejpam-1951	109	68	equivalence	equivalence	NOUN
ejpam-1951	109	69	class	class	NOUN
ejpam-1951	109	70	of	of	ADP
ejpam-1951	109	71	p	p	NOUN
ejpam-1951	109	72	under	under	ADP
ejpam-1951	109	73	∼	∼	NOUN
ejpam-1951	109	74	is	be	AUX
ejpam-1951	109	75	the	the	DET
ejpam-1951	109	76	set	set	NOUN
ejpam-1951	109	77	{	{	PUNCT
ejpam-1951	109	78	p	p	NOUN
ejpam-1951	109	79	∈	∈	PROPN
ejpam-1951	109	80	a|p	a|p	NOUN
ejpam-1951	109	81	∼	∼	NOUN
ejpam-1951	109	82	q	q	NOUN
ejpam-1951	109	83	}	}	PUNCT
ejpam-1951	109	84	[	[	X
ejpam-1951	109	85	1	1	NUM
ejpam-1951	109	86	]	]	PUNCT
ejpam-1951	109	87	.	.	PUNCT
ejpam-1951	110	1	these	these	DET
ejpam-1951	110	2	equivalence	equivalence	NOUN
ejpam-1951	110	3	classes	class	NOUN
ejpam-1951	110	4	are	be	AUX
ejpam-1951	110	5	called	call	VERB
ejpam-1951	110	6	patterns	pattern	NOUN
ejpam-1951	110	7	.	.	PUNCT
ejpam-1951	111	1	1.4	1.4	NUM
ejpam-1951	111	2	.	.	PUNCT
ejpam-1951	111	3	weights	weight	NOUN
ejpam-1951	111	4	and	and	CCONJ
ejpam-1951	111	5	inventory	inventory	NOUN
ejpam-1951	111	6	definition	definition	NOUN
ejpam-1951	111	7	4	4	NUM
ejpam-1951	111	8	.	.	PUNCT
ejpam-1951	112	1	given	give	VERB
ejpam-1951	112	2	a	a	DET
ejpam-1951	112	3	set	set	NOUN
ejpam-1951	112	4	of	of	ADP
ejpam-1951	112	5	colors	color	NOUN
ejpam-1951	112	6	c	c	VERB
ejpam-1951	112	7	we	we	PRON
ejpam-1951	112	8	want	want	VERB
ejpam-1951	112	9	to	to	PART
ejpam-1951	112	10	associate	associate	VERB
ejpam-1951	112	11	a	a	DET
ejpam-1951	112	12	weight	weight	NOUN
ejpam-1951	112	13	wc	wc	NOUN
ejpam-1951	112	14	for	for	ADP
ejpam-1951	112	15	all	all	DET
ejpam-1951	112	16	c	c	PROPN
ejpam-1951	112	17	∈	∈	PROPN
ejpam-1951	112	18	c.	c.	NOUN
ejpam-1951	112	19	then	then	ADV
ejpam-1951	112	20	we	we	PRON
ejpam-1951	112	21	will	will	AUX
ejpam-1951	112	22	define	define	VERB
ejpam-1951	112	23	the	the	DET
ejpam-1951	112	24	weight	weight	NOUN
ejpam-1951	112	25	of	of	ADP
ejpam-1951	112	26	a	a	DET
ejpam-1951	112	27	coloring	coloring	NOUN
ejpam-1951	112	28	a	a	DET
ejpam-1951	112	29	∈	∈	PROPN
ejpam-1951	112	30	a	a	PRON
ejpam-1951	112	31	to	to	PART
ejpam-1951	112	32	be	be	AUX
ejpam-1951	112	33	the	the	DET
ejpam-1951	112	34	product	product	NOUN
ejpam-1951	112	35	of	of	ADP
ejpam-1951	112	36	the	the	DET
ejpam-1951	112	37	weights	weight	NOUN
ejpam-1951	112	38	of	of	ADP
ejpam-1951	112	39	the	the	DET
ejpam-1951	112	40	colored	colored	ADJ
ejpam-1951	112	41	elements	element	NOUN
ejpam-1951	112	42	[	[	X
ejpam-1951	112	43	1	1	NUM
ejpam-1951	112	44	]	]	PUNCT
ejpam-1951	112	45	.	.	PUNCT
ejpam-1951	113	1	w(a	w(a	VERB
ejpam-1951	113	2	)	)	PUNCT
ejpam-1951	114	1	=	=	SYM
ejpam-1951	114	2	∏	∏	NUM
ejpam-1951	114	3	i∈n	i∈n	NOUN
ejpam-1951	114	4	wa(i	wa(i	NOUN
ejpam-1951	114	5	)	)	PUNCT
ejpam-1951	114	6	this	this	PRON
ejpam-1951	114	7	is	be	AUX
ejpam-1951	114	8	also	also	ADV
ejpam-1951	114	9	called	call	VERB
ejpam-1951	114	10	the	the	DET
ejpam-1951	114	11	inventory	inventory	NOUN
ejpam-1951	114	12	of	of	ADP
ejpam-1951	114	13	a.	a.	NOUN
ejpam-1951	114	14	example	example	NOUN
ejpam-1951	114	15	6	6	NUM
ejpam-1951	114	16	.	.	X
ejpam-1951	115	1	consider	consider	VERB
ejpam-1951	115	2	4	4	NUM
ejpam-1951	115	3	bead	bead	VERB
ejpam-1951	115	4	necklace	necklace	NOUN
ejpam-1951	115	5	to	to	PART
ejpam-1951	115	6	illustrate	illustrate	VERB
ejpam-1951	115	7	with	with	ADP
ejpam-1951	115	8	c={red(r	c={red(r	NOUN
ejpam-1951	115	9	)	)	PUNCT
ejpam-1951	115	10	,	,	PUNCT
ejpam-1951	115	11	yellow(y	yellow(y	NOUN
ejpam-1951	115	12	)	)	PUNCT
ejpam-1951	115	13	}	}	PUNCT
ejpam-1951	115	14	.	.	PUNCT
ejpam-1951	116	1	let	let	VERB
ejpam-1951	116	2	a	a	DET
ejpam-1951	116	3	=	=	SYM
ejpam-1951	116	4	r	r	NOUN
ejpam-1951	116	5	r	r	NOUN
ejpam-1951	116	6	y	y	NOUN
ejpam-1951	116	7	y	y	PROPN
ejpam-1951	116	8	where	where	SCONJ
ejpam-1951	116	9	a(1	a(1	NOUN
ejpam-1951	116	10	)	)	PUNCT
ejpam-1951	116	11	=	=	SYM
ejpam-1951	116	12	red	red	ADJ
ejpam-1951	116	13	,	,	PUNCT
ejpam-1951	116	14	a(2	a(2	PROPN
ejpam-1951	116	15	)	)	PUNCT
ejpam-1951	116	16	=	=	SYM
ejpam-1951	116	17	red	red	ADJ
ejpam-1951	116	18	,	,	PUNCT
ejpam-1951	116	19	a(3	a(3	PROPN
ejpam-1951	116	20	)	)	PUNCT
ejpam-1951	116	21	=	=	SYM
ejpam-1951	116	22	yel	yel	PROPN
ejpam-1951	116	23	low	low	ADJ
ejpam-1951	116	24	and	and	CCONJ
ejpam-1951	116	25	a(4	a(4	PROPN
ejpam-1951	116	26	)	)	PUNCT
ejpam-1951	117	1	=	=	NOUN
ejpam-1951	117	2	yel	yel	PROPN
ejpam-1951	117	3	low	low	ADV
ejpam-1951	117	4	let	let	VERB
ejpam-1951	117	5	the	the	DET
ejpam-1951	117	6	colors	color	NOUN
ejpam-1951	117	7	red	red	ADJ
ejpam-1951	117	8	and	and	CCONJ
ejpam-1951	117	9	yellow	yellow	NOUN
ejpam-1951	117	10	have	have	VERB
ejpam-1951	117	11	weights	weight	NOUN
ejpam-1951	117	12	r	r	NOUN
ejpam-1951	117	13	and	and	CCONJ
ejpam-1951	117	14	y	y	PROPN
ejpam-1951	117	15	respectively	respectively	ADV
ejpam-1951	117	16	.	.	PUNCT
ejpam-1951	118	1	then	then	ADV
ejpam-1951	118	2	the	the	DET
ejpam-1951	118	3	coloring	coloring	NOUN
ejpam-1951	118	4	of	of	ADP
ejpam-1951	118	5	a	a	PRON
ejpam-1951	118	6	as	as	ADP
ejpam-1951	118	7	follows	follow	VERB
ejpam-1951	118	8	w(a	w(a	NOUN
ejpam-1951	118	9	)	)	PUNCT
ejpam-1951	118	10	=	=	SYM
ejpam-1951	118	11	∏	∏	NUM
ejpam-1951	118	12	i∈n	i∈n	NOUN
ejpam-1951	118	13	wa(i	wa(i	NOUN
ejpam-1951	118	14	)	)	PUNCT
ejpam-1951	119	1	=	=	SYM
ejpam-1951	119	2	wa(1)wa(2)wa(3)wa(4	wa(1)wa(2)wa(3)wa(4	NOUN
ejpam-1951	119	3	)	)	PUNCT
ejpam-1951	120	1	=	=	NOUN
ejpam-1951	120	2	rry	rry	PROPN
ejpam-1951	120	3	y	y	PROPN
ejpam-1951	120	4	=	=	PROPN
ejpam-1951	120	5	r2y	r2y	PART
ejpam-1951	120	6	2	2	NUM
ejpam-1951	120	7	definition	definition	NOUN
ejpam-1951	120	8	5	5	NUM
ejpam-1951	120	9	.	.	PUNCT
ejpam-1951	121	1	let	let	VERB
ejpam-1951	121	2	g	g	PRON
ejpam-1951	121	3	be	be	AUX
ejpam-1951	121	4	a	a	DET
ejpam-1951	121	5	permutation	permutation	NOUN
ejpam-1951	121	6	group	group	NOUN
ejpam-1951	121	7	on	on	ADP
ejpam-1951	121	8	a	a	DET
ejpam-1951	121	9	set	set	NOUN
ejpam-1951	121	10	a.	a.	NOUN
ejpam-1951	121	11	suppose	suppose	VERB
ejpam-1951	121	12	that	that	SCONJ
ejpam-1951	121	13	∼	∼	NOUN
ejpam-1951	121	14	defines	define	VERB
ejpam-1951	121	15	an	an	DET
ejpam-1951	121	16	equivalence	equivalence	NOUN
ejpam-1951	121	17	relation	relation	NOUN
ejpam-1951	121	18	on	on	ADP
ejpam-1951	121	19	a.	a.	NOUN
ejpam-1951	121	20	then	then	ADV
ejpam-1951	121	21	the	the	DET
ejpam-1951	121	22	equivalence	equivalence	NOUN
ejpam-1951	121	23	class	class	NOUN
ejpam-1951	121	24	containing	contain	VERB
ejpam-1951	121	25	the	the	DET
ejpam-1951	121	26	element	element	NOUN
ejpam-1951	121	27	a	a	PRON
ejpam-1951	121	28	,	,	PUNCT
ejpam-1951	121	29	denoted	denote	VERB
ejpam-1951	121	30	by	by	ADP
ejpam-1951	121	31	or	or	CCONJ
ejpam-1951	121	32	b(a	b(a	NOUN
ejpam-1951	121	33	)	)	PUNCT
ejpam-1951	121	34	is	be	AUX
ejpam-1951	121	35	called	call	VERB
ejpam-1951	121	36	the	the	DET
ejpam-1951	121	37	g	g	NOUN
ejpam-1951	121	38	-	-	PUNCT
ejpam-1951	121	39	orbit	orbit	NOUN
ejpam-1951	121	40	of	of	ADP
ejpam-1951	121	41	a.	a.	NOUN
ejpam-1951	122	1	it	it	PRON
ejpam-1951	122	2	is	be	AUX
ejpam-1951	122	3	defined	define	VERB
ejpam-1951	122	4	as	as	ADP
ejpam-1951	122	5	[	[	X
ejpam-1951	122	6	6	6	NUM
ejpam-1951	122	7	]	]	PUNCT
ejpam-1951	122	8	or	or	CCONJ
ejpam-1951	122	9	b(a	b(a	NOUN
ejpam-1951	122	10	)	)	PUNCT
ejpam-1951	123	1	=	=	SYM
ejpam-1951	123	2	{	{	PUNCT
ejpam-1951	123	3	π(a	π(a	PROPN
ejpam-1951	123	4	)	)	PUNCT
ejpam-1951	123	5	:	:	PUNCT
ejpam-1951	124	1	π	π	X
ejpam-1951	124	2	∈	∈	PROPN
ejpam-1951	124	3	g	g	NOUN
ejpam-1951	124	4	}	}	PUNCT
ejpam-1951	124	5	example	example	NOUN
ejpam-1951	124	6	7	7	NUM
ejpam-1951	124	7	.	.	X
ejpam-1951	124	8	consider	consider	VERB
ejpam-1951	124	9	4	4	NUM
ejpam-1951	124	10	bead	bead	VERB
ejpam-1951	124	11	necklace	necklace	NOUN
ejpam-1951	124	12	where	where	SCONJ
ejpam-1951	124	13	a	a	PRON
ejpam-1951	124	14	=	=	X
ejpam-1951	124	15	{	{	PUNCT
ejpam-1951	124	16	1,2,3,4	1,2,3,4	NUM
ejpam-1951	124	17	}	}	PUNCT
ejpam-1951	124	18	,	,	PUNCT
ejpam-1951	124	19	b	b	X
ejpam-1951	124	20	=	=	PRON
ejpam-1951	124	21	{	{	PUNCT
ejpam-1951	124	22	red(r	red(r	PROPN
ejpam-1951	124	23	)	)	PUNCT
ejpam-1951	124	24	,	,	PUNCT
ejpam-1951	124	25	yel	yel	X
ejpam-1951	124	26	low(y	low(y	PROPN
ejpam-1951	124	27	)	)	PUNCT
ejpam-1951	124	28	}	}	PUNCT
ejpam-1951	124	29	,	,	PUNCT
ejpam-1951	124	30	c	c	X
ejpam-1951	124	31	be	be	AUX
ejpam-1951	124	32	the	the	DET
ejpam-1951	124	33	group	group	NOUN
ejpam-1951	124	34	of	of	ADP
ejpam-1951	124	35	coloring	color	VERB
ejpam-1951	124	36	with	with	ADP
ejpam-1951	124	37	f	f	PROPN
ejpam-1951	124	38	:	:	PUNCT
ejpam-1951	124	39	a→	a→	PROPN
ejpam-1951	124	40	b	b	NOUN
ejpam-1951	124	41	and	and	CCONJ
ejpam-1951	124	42	g	g	NOUN
ejpam-1951	124	43	=	=	SYM
ejpam-1951	124	44	{	{	PUNCT
ejpam-1951	124	45	e	e	NOUN
ejpam-1951	124	46	,	,	PUNCT
ejpam-1951	124	47	(	(	PUNCT
ejpam-1951	124	48	12	12	NUM
ejpam-1951	124	49	)	)	PUNCT
ejpam-1951	124	50	,	,	PUNCT
ejpam-1951	124	51	(	(	PUNCT
ejpam-1951	124	52	34	34	NUM
ejpam-1951	124	53	)	)	PUNCT
ejpam-1951	124	54	,	,	PUNCT
ejpam-1951	124	55	(	(	PUNCT
ejpam-1951	124	56	12)(34	12)(34	NUM
ejpam-1951	124	57	)	)	PUNCT
ejpam-1951	124	58	}	}	PUNCT
ejpam-1951	124	59	be	be	AUX
ejpam-1951	124	60	the	the	DET
ejpam-1951	124	61	permutation	permutation	NOUN
ejpam-1951	124	62	group	group	NOUN
ejpam-1951	125	1	[	[	X
ejpam-1951	125	2	1	1	NUM
ejpam-1951	125	3	]	]	PUNCT
ejpam-1951	125	4	.	.	PUNCT
ejpam-1951	126	1	then	then	ADV
ejpam-1951	126	2	or	or	CCONJ
ejpam-1951	126	3	b(rrrr	b(rrrr	NOUN
ejpam-1951	126	4	)	)	PUNCT
ejpam-1951	127	1	=	=	NOUN
ejpam-1951	127	2	{	{	PUNCT
ejpam-1951	127	3	rrrr}or	rrrr}or	NOUN
ejpam-1951	127	4	b(rrry	b(rrry	NOUN
ejpam-1951	127	5	)	)	PUNCT
ejpam-1951	127	6	=	=	SYM
ejpam-1951	127	7	or	or	CCONJ
ejpam-1951	127	8	b(rry	b(rry	ADJ
ejpam-1951	127	9	r	r	NOUN
ejpam-1951	127	10	)	)	PUNCT
ejpam-1951	127	11	=	=	NOUN
ejpam-1951	127	12	{	{	PUNCT
ejpam-1951	127	13	rrry	rrry	NOUN
ejpam-1951	127	14	,	,	PUNCT
ejpam-1951	127	15	rry	rry	PROPN
ejpam-1951	127	16	r	r	NOUN
ejpam-1951	127	17	}	}	PUNCT
ejpam-1951	127	18	t.	t.	NOUN
ejpam-1951	127	19	nasseef	nasseef	PROPN
ejpam-1951	127	20	/	/	SYM
ejpam-1951	127	21	eur	eur	PROPN
ejpam-1951	127	22	.	.	PUNCT
ejpam-1951	128	1	j.	j.	PROPN
ejpam-1951	128	2	pure	pure	PROPN
ejpam-1951	128	3	appl	appl	PROPN
ejpam-1951	128	4	.	.	PROPN
ejpam-1951	128	5	math	math	PROPN
ejpam-1951	128	6	,	,	PUNCT
ejpam-1951	128	7	9	9	NUM
ejpam-1951	128	8	(	(	PUNCT
ejpam-1951	128	9	2016	2016	NUM
ejpam-1951	128	10	)	)	PUNCT
ejpam-1951	128	11	,	,	PUNCT
ejpam-1951	128	12	84	84	NUM
ejpam-1951	128	13	-	-	SYM
ejpam-1951	128	14	113	113	NUM
ejpam-1951	128	15	89	89	NUM
ejpam-1951	128	16	or	or	CCONJ
ejpam-1951	128	17	b(rry	b(rry	ADJ
ejpam-1951	128	18	y	y	PROPN
ejpam-1951	128	19	)	)	PUNCT
ejpam-1951	129	1	=	=	PRON
ejpam-1951	129	2	{	{	PUNCT
ejpam-1951	129	3	rry	rry	NOUN
ejpam-1951	129	4	y	y	PROPN
ejpam-1951	129	5	}	}	PUNCT
ejpam-1951	129	6	or	or	CCONJ
ejpam-1951	129	7	b(ry	b(ry	PROPN
ejpam-1951	129	8	rr	rr	NOUN
ejpam-1951	129	9	)	)	PUNCT
ejpam-1951	129	10	=	=	SYM
ejpam-1951	129	11	or	or	CCONJ
ejpam-1951	129	12	b(y	b(y	PROPN
ejpam-1951	129	13	rrr	rrr	NOUN
ejpam-1951	129	14	)	)	PUNCT
ejpam-1951	129	15	=	=	PRON
ejpam-1951	129	16	{	{	PUNCT
ejpam-1951	129	17	ry	ry	PROPN
ejpam-1951	129	18	rr	rr	PROPN
ejpam-1951	129	19	,	,	PUNCT
ejpam-1951	129	20	y	y	PROPN
ejpam-1951	129	21	rrr	rrr	PROPN
ejpam-1951	129	22	}	}	PUNCT
ejpam-1951	129	23	or	or	CCONJ
ejpam-1951	129	24	b(y	b(y	X
ejpam-1951	129	25	y	y	PROPN
ejpam-1951	129	26	y	y	PROPN
ejpam-1951	129	27	y	y	PROPN
ejpam-1951	129	28	)	)	PUNCT
ejpam-1951	130	1	=	=	PRON
ejpam-1951	130	2	{	{	PUNCT
ejpam-1951	130	3	y	y	NOUN
ejpam-1951	130	4	y	y	PROPN
ejpam-1951	130	5	y	y	PROPN
ejpam-1951	130	6	y	y	PROPN
ejpam-1951	130	7	}	}	PUNCT
ejpam-1951	130	8	or	or	CCONJ
ejpam-1951	130	9	b(y	b(y	X
ejpam-1951	130	10	y	y	PROPN
ejpam-1951	130	11	y	y	PROPN
ejpam-1951	130	12	r	r	PROPN
ejpam-1951	130	13	)	)	PUNCT
ejpam-1951	130	14	=	=	SYM
ejpam-1951	130	15	or	or	CCONJ
ejpam-1951	130	16	b(y	b(y	PROPN
ejpam-1951	130	17	y	y	PROPN
ejpam-1951	130	18	ry	ry	PROPN
ejpam-1951	130	19	)	)	PUNCT
ejpam-1951	131	1	=	=	PRON
ejpam-1951	131	2	{	{	PUNCT
ejpam-1951	131	3	y	y	NOUN
ejpam-1951	131	4	y	y	PROPN
ejpam-1951	131	5	y	y	PROPN
ejpam-1951	131	6	r	r	PROPN
ejpam-1951	131	7	,	,	PUNCT
ejpam-1951	131	8	y	y	PROPN
ejpam-1951	131	9	y	y	PROPN
ejpam-1951	132	1	ry	ry	PROPN
ejpam-1951	132	2	}	}	PUNCT
ejpam-1951	132	3	or	or	CCONJ
ejpam-1951	132	4	b(y	b(y	PROPN
ejpam-1951	132	5	y	y	PROPN
ejpam-1951	132	6	rr	rr	PROPN
ejpam-1951	132	7	)	)	PUNCT
ejpam-1951	133	1	=	=	PRON
ejpam-1951	133	2	{	{	PUNCT
ejpam-1951	133	3	y	y	PROPN
ejpam-1951	133	4	y	y	PROPN
ejpam-1951	133	5	rr}or	rr}or	PROPN
ejpam-1951	133	6	b(y	b(y	PROPN
ejpam-1951	133	7	ry	ry	NOUN
ejpam-1951	133	8	y	y	PROPN
ejpam-1951	133	9	)	)	PUNCT
ejpam-1951	133	10	=	=	SYM
ejpam-1951	133	11	or	or	CCONJ
ejpam-1951	133	12	b(ry	b(ry	PROPN
ejpam-1951	133	13	y	y	PROPN
ejpam-1951	133	14	y	y	PROPN
ejpam-1951	133	15	)	)	PUNCT
ejpam-1951	134	1	=	=	PRON
ejpam-1951	134	2	{	{	PUNCT
ejpam-1951	134	3	y	y	PROPN
ejpam-1951	134	4	ry	ry	PROPN
ejpam-1951	134	5	y	y	PROPN
ejpam-1951	134	6	,	,	PUNCT
ejpam-1951	134	7	ry	ry	VERB
ejpam-1951	134	8	y	y	PROPN
ejpam-1951	134	9	y	y	PROPN
ejpam-1951	134	10	}	}	PUNCT
ejpam-1951	134	11	or	or	CCONJ
ejpam-1951	134	12	b(ry	b(ry	PROPN
ejpam-1951	134	13	ry	ry	NOUN
ejpam-1951	134	14	)	)	PUNCT
ejpam-1951	135	1	=	=	SYM
ejpam-1951	135	2	or	or	CCONJ
ejpam-1951	135	3	b(y	b(y	PROPN
ejpam-1951	135	4	ry	ry	NOUN
ejpam-1951	135	5	r	r	NOUN
ejpam-1951	135	6	)	)	PUNCT
ejpam-1951	135	7	=	=	SYM
ejpam-1951	135	8	or	or	CCONJ
ejpam-1951	135	9	b(ry	b(ry	PROPN
ejpam-1951	135	10	y	y	PROPN
ejpam-1951	135	11	r	r	NOUN
ejpam-1951	135	12	)	)	PUNCT
ejpam-1951	135	13	=	=	SYM
ejpam-1951	135	14	or	or	CCONJ
ejpam-1951	135	15	b(y	b(y	PROPN
ejpam-1951	135	16	rry	rry	PROPN
ejpam-1951	135	17	)	)	PUNCT
ejpam-1951	136	1	=	=	PRON
ejpam-1951	136	2	{	{	PUNCT
ejpam-1951	136	3	ry	ry	VERB
ejpam-1951	136	4	ry	ry	PROPN
ejpam-1951	136	5	,	,	PUNCT
ejpam-1951	136	6	y	y	PROPN
ejpam-1951	136	7	ry	ry	PROPN
ejpam-1951	136	8	r	r	PROPN
ejpam-1951	136	9	,	,	PUNCT
ejpam-1951	136	10	ry	ry	NOUN
ejpam-1951	136	11	y	y	PROPN
ejpam-1951	136	12	r	r	PROPN
ejpam-1951	136	13	,	,	PUNCT
ejpam-1951	136	14	y	y	PROPN
ejpam-1951	136	15	rry	rry	PROPN
ejpam-1951	136	16	}	}	PUNCT
ejpam-1951	136	17	the	the	DET
ejpam-1951	136	18	problem	problem	NOUN
ejpam-1951	136	19	of	of	ADP
ejpam-1951	136	20	determining	determine	VERB
ejpam-1951	136	21	the	the	DET
ejpam-1951	136	22	equivalent	equivalent	ADJ
ejpam-1951	136	23	objects	object	NOUN
ejpam-1951	136	24	in	in	ADP
ejpam-1951	136	25	a	a	PRON
ejpam-1951	136	26	is	be	AUX
ejpam-1951	136	27	to	to	PART
ejpam-1951	136	28	count	count	VERB
ejpam-1951	136	29	all	all	DET
ejpam-1951	136	30	g	g	NOUN
ejpam-1951	136	31	-	-	PUNCT
ejpam-1951	136	32	orbits	orbit	NOUN
ejpam-1951	136	33	.	.	PUNCT
ejpam-1951	137	1	however	however	ADV
ejpam-1951	137	2	this	this	DET
ejpam-1951	137	3	method	method	NOUN
ejpam-1951	137	4	looks	look	VERB
ejpam-1951	137	5	impractical	impractical	ADJ
ejpam-1951	137	6	and	and	CCONJ
ejpam-1951	137	7	even	even	ADV
ejpam-1951	137	8	more	more	ADV
ejpam-1951	137	9	boring	boring	ADJ
ejpam-1951	137	10	in	in	ADP
ejpam-1951	137	11	complex	complex	ADJ
ejpam-1951	137	12	situations	situation	NOUN
ejpam-1951	137	13	.	.	PUNCT
ejpam-1951	138	1	fortunately	fortunately	ADV
ejpam-1951	138	2	,	,	PUNCT
ejpam-1951	138	3	burnside	burnside	PROPN
ejpam-1951	138	4	’s	’s	PART
ejpam-1951	138	5	lemma	lemma	PROPN
ejpam-1951	138	6	gives	give	VERB
ejpam-1951	138	7	an	an	DET
ejpam-1951	138	8	analytical	analytical	ADJ
ejpam-1951	138	9	formula	formula	NOUN
ejpam-1951	138	10	for	for	ADP
ejpam-1951	138	11	such	such	ADJ
ejpam-1951	138	12	counting	counting	NOUN
ejpam-1951	138	13	of	of	ADP
ejpam-1951	138	14	g	g	NOUN
ejpam-1951	138	15	-	-	PUNCT
ejpam-1951	138	16	orbits	orbit	NOUN
ejpam-1951	138	17	.	.	PUNCT
ejpam-1951	139	1	it	it	PRON
ejpam-1951	139	2	is	be	AUX
ejpam-1951	139	3	a	a	DET
ejpam-1951	139	4	powerful	powerful	ADJ
ejpam-1951	139	5	technique	technique	NOUN
ejpam-1951	139	6	and	and	CCONJ
ejpam-1951	139	7	particularly	particularly	ADV
ejpam-1951	139	8	efficient	efficient	ADJ
ejpam-1951	139	9	when	when	SCONJ
ejpam-1951	139	10	the	the	DET
ejpam-1951	139	11	order	order	NOUN
ejpam-1951	139	12	of	of	ADP
ejpam-1951	139	13	the	the	DET
ejpam-1951	139	14	group	group	NOUN
ejpam-1951	139	15	is	be	AUX
ejpam-1951	139	16	small	small	ADJ
ejpam-1951	139	17	.	.	PUNCT
ejpam-1951	140	1	it	it	PRON
ejpam-1951	140	2	is	be	AUX
ejpam-1951	140	3	also	also	ADV
ejpam-1951	140	4	considered	consider	VERB
ejpam-1951	140	5	one	one	NUM
ejpam-1951	140	6	of	of	ADP
ejpam-1951	140	7	the	the	DET
ejpam-1951	140	8	essential	essential	ADJ
ejpam-1951	140	9	parts	part	NOUN
ejpam-1951	140	10	in	in	ADP
ejpam-1951	140	11	development	development	NOUN
ejpam-1951	140	12	of	of	ADP
ejpam-1951	140	13	the	the	DET
ejpam-1951	140	14	pólya	pólya	NOUN
ejpam-1951	140	15	theory	theory	NOUN
ejpam-1951	140	16	.	.	PUNCT
ejpam-1951	141	1	definition	definition	NOUN
ejpam-1951	141	2	6	6	NUM
ejpam-1951	141	3	.	.	PUNCT
ejpam-1951	142	1	let	let	VERB
ejpam-1951	142	2	g	g	PRON
ejpam-1951	142	3	be	be	AUX
ejpam-1951	142	4	a	a	DET
ejpam-1951	142	5	permutation	permutation	NOUN
ejpam-1951	142	6	group	group	NOUN
ejpam-1951	142	7	on	on	ADP
ejpam-1951	142	8	a	a	DET
ejpam-1951	142	9	set	set	NOUN
ejpam-1951	142	10	a.	a.	NOUN
ejpam-1951	142	11	an	an	DET
ejpam-1951	142	12	element	element	NOUN
ejpam-1951	142	13	a	a	PRON
ejpam-1951	142	14	in	in	ADP
ejpam-1951	142	15	a	a	PRON
ejpam-1951	142	16	is	be	AUX
ejpam-1951	142	17	said	say	VERB
ejpam-1951	142	18	to	to	PART
ejpam-1951	142	19	be	be	AUX
ejpam-1951	142	20	invariant	invariant	ADJ
ejpam-1951	142	21	under	under	ADP
ejpam-1951	142	22	a	a	DET
ejpam-1951	142	23	permutation	permutation	NOUN
ejpam-1951	142	24	π	π	X
ejpam-1951	142	25	∈	∈	PROPN
ejpam-1951	142	26	g	g	PROPN
ejpam-1951	143	1	if	if	SCONJ
ejpam-1951	143	2	and	and	CCONJ
ejpam-1951	143	3	only	only	ADV
ejpam-1951	143	4	if	if	SCONJ
ejpam-1951	143	5	π(a	π(a	PROPN
ejpam-1951	143	6	)	)	PUNCT
ejpam-1951	143	7	=	=	PUNCT
ejpam-1951	143	8	a.	a.	NOUN
ejpam-1951	143	9	to	to	ADP
ejpam-1951	143	10	each	each	DET
ejpam-1951	143	11	a	a	DET
ejpam-1951	143	12	∈	∈	PROPN
ejpam-1951	143	13	a	a	PRON
ejpam-1951	143	14	,	,	PUNCT
ejpam-1951	143	15	the	the	DET
ejpam-1951	143	16	stabilizer	stabilizer	NOUN
ejpam-1951	143	17	of	of	ADP
ejpam-1951	143	18	a	a	PRON
ejpam-1951	143	19	,	,	PUNCT
ejpam-1951	143	20	denoted	denote	VERB
ejpam-1951	143	21	by	by	ADP
ejpam-1951	143	22	stab(a	stab(a	NOUN
ejpam-1951	143	23	)	)	PUNCT
ejpam-1951	143	24	is	be	AUX
ejpam-1951	143	25	defined	define	VERB
ejpam-1951	143	26	to	to	PART
ejpam-1951	143	27	be	be	AUX
ejpam-1951	143	28	the	the	DET
ejpam-1951	143	29	set	set	NOUN
ejpam-1951	143	30	stab(a	stab(a	PROPN
ejpam-1951	143	31	)	)	PUNCT
ejpam-1951	143	32	=	=	SYM
ejpam-1951	144	1	{	{	PUNCT
ejpam-1951	144	2	π	π	PROPN
ejpam-1951	144	3	∈	∈	PROPN
ejpam-1951	144	4	g	g	NOUN
ejpam-1951	144	5	:	:	PUNCT
ejpam-1951	144	6	π(a	π(a	PROPN
ejpam-1951	144	7	)	)	PUNCT
ejpam-1951	144	8	=	=	SYM
ejpam-1951	144	9	a	a	X
ejpam-1951	144	10	}	}	PUNCT
ejpam-1951	144	11	and	and	CCONJ
ejpam-1951	144	12	∀a	∀a	NOUN
ejpam-1951	144	13	∈	∈	NOUN
ejpam-1951	144	14	g.	g.	NOUN
ejpam-1951	144	15	let	let	VERB
ejpam-1951	144	16	η(π	η(π	NOUN
ejpam-1951	144	17	)	)	PUNCT
ejpam-1951	144	18	denotes	denote	VERB
ejpam-1951	144	19	the	the	DET
ejpam-1951	144	20	number	number	NOUN
ejpam-1951	144	21	of	of	ADP
ejpam-1951	144	22	elements	element	NOUN
ejpam-1951	144	23	of	of	ADP
ejpam-1951	144	24	a	a	PRON
ejpam-1951	144	25	that	that	PRON
ejpam-1951	144	26	are	be	AUX
ejpam-1951	144	27	invariant	invariant	ADJ
ejpam-1951	144	28	under	under	ADP
ejpam-1951	144	29	π	π	PROPN
ejpam-1951	144	30	that	that	PRON
ejpam-1951	144	31	is	be	AUX
ejpam-1951	144	32	[	[	X
ejpam-1951	144	33	6	6	NUM
ejpam-1951	144	34	]	]	SYM
ejpam-1951	144	35	η(π	η(π	PROPN
ejpam-1951	144	36	)	)	PUNCT
ejpam-1951	144	37	=	=	PRON
ejpam-1951	144	38	{	{	PUNCT
ejpam-1951	144	39	a	a	PRON
ejpam-1951	144	40	∈	∈	PROPN
ejpam-1951	144	41	a	a	DET
ejpam-1951	144	42	:	:	PUNCT
ejpam-1951	144	43	π(a	π(a	PROPN
ejpam-1951	144	44	)	)	PUNCT
ejpam-1951	144	45	=	=	SYM
ejpam-1951	145	1	a	a	DET
ejpam-1951	145	2	}	}	PUNCT
ejpam-1951	145	3	example	example	NOUN
ejpam-1951	145	4	8	8	NUM
ejpam-1951	145	5	.	.	PUNCT
ejpam-1951	146	1	following	follow	VERB
ejpam-1951	146	2	the	the	DET
ejpam-1951	146	3	example	example	NOUN
ejpam-1951	146	4	7	7	NUM
ejpam-1951	146	5	the	the	DET
ejpam-1951	146	6	stabilizer	stabilizer	NOUN
ejpam-1951	146	7	sets	set	NOUN
ejpam-1951	146	8	for	for	ADP
ejpam-1951	146	9	each	each	DET
ejpam-1951	146	10	coloring	coloring	NOUN
ejpam-1951	146	11	in	in	ADP
ejpam-1951	146	12	c	c	PROPN
ejpam-1951	146	13	are	be	AUX
ejpam-1951	146	14	given	give	VERB
ejpam-1951	146	15	below	below	ADP
ejpam-1951	146	16	stab(rrrr	stab(rrrr	PROPN
ejpam-1951	146	17	)	)	PUNCT
ejpam-1951	147	1	=	=	PRON
ejpam-1951	147	2	stab(y	stab(y	VERB
ejpam-1951	147	3	y	y	PROPN
ejpam-1951	147	4	y	y	PROPN
ejpam-1951	147	5	y	y	PROPN
ejpam-1951	147	6	)	)	PUNCT
ejpam-1951	148	1	=	=	PUNCT
ejpam-1951	148	2	stab(rry	stab(rry	NOUN
ejpam-1951	148	3	y	y	PROPN
ejpam-1951	148	4	)	)	PUNCT
ejpam-1951	149	1	=	=	VERB
ejpam-1951	150	1	stab(y	stab(y	PROPN
ejpam-1951	150	2	y	y	PROPN
ejpam-1951	150	3	rr	rr	PROPN
ejpam-1951	150	4	)	)	PUNCT
ejpam-1951	151	1	=	=	PRON
ejpam-1951	151	2	{	{	PUNCT
ejpam-1951	151	3	e	e	NOUN
ejpam-1951	151	4	,	,	PUNCT
ejpam-1951	151	5	(	(	PUNCT
ejpam-1951	151	6	12	12	NUM
ejpam-1951	151	7	)	)	PUNCT
ejpam-1951	151	8	,	,	PUNCT
ejpam-1951	151	9	(	(	PUNCT
ejpam-1951	151	10	34	34	NUM
ejpam-1951	151	11	)	)	PUNCT
ejpam-1951	151	12	,	,	PUNCT
ejpam-1951	151	13	(	(	PUNCT
ejpam-1951	151	14	12)(34	12)(34	NUM
ejpam-1951	151	15	)	)	PUNCT
ejpam-1951	151	16	}	}	PUNCT
ejpam-1951	151	17	stab(rrry	stab(rrry	PROPN
ejpam-1951	151	18	)	)	PUNCT
ejpam-1951	152	1	=	=	PRON
ejpam-1951	152	2	stab(y	stab(y	VERB
ejpam-1951	152	3	y	y	PROPN
ejpam-1951	152	4	y	y	PROPN
ejpam-1951	152	5	r	r	PROPN
ejpam-1951	152	6	)	)	PUNCT
ejpam-1951	152	7	=	=	PUNCT
ejpam-1951	152	8	stab(rrry	stab(rrry	ADJ
ejpam-1951	152	9	)	)	PUNCT
ejpam-1951	153	1	=	=	PUNCT
ejpam-1951	153	2	stab(y	stab(y	VERB
ejpam-1951	153	3	y	y	PROPN
ejpam-1951	153	4	y	y	PROPN
ejpam-1951	153	5	r	r	PROPN
ejpam-1951	153	6	)	)	PUNCT
ejpam-1951	153	7	=	=	SYM
ejpam-1951	153	8	{	{	PUNCT
ejpam-1951	153	9	e	e	NOUN
ejpam-1951	153	10	,	,	PUNCT
ejpam-1951	153	11	(	(	PUNCT
ejpam-1951	153	12	12	12	NUM
ejpam-1951	153	13	)	)	PUNCT
ejpam-1951	153	14	}	}	PUNCT
ejpam-1951	153	15	stab(ry	stab(ry	PROPN
ejpam-1951	153	16	rr	rr	NOUN
ejpam-1951	153	17	)	)	PUNCT
ejpam-1951	154	1	=	=	PRON
ejpam-1951	154	2	stab(y	stab(y	PROPN
ejpam-1951	154	3	ry	ry	NOUN
ejpam-1951	154	4	y	y	PROPN
ejpam-1951	154	5	)	)	PUNCT
ejpam-1951	155	1	=	=	PUNCT
ejpam-1951	155	2	stab(ry	stab(ry	PROPN
ejpam-1951	155	3	y	y	PROPN
ejpam-1951	155	4	y	y	PROPN
ejpam-1951	155	5	)	)	PUNCT
ejpam-1951	156	1	=	=	PUNCT
ejpam-1951	156	2	stab(y	stab(y	ADJ
ejpam-1951	156	3	rrr	rrr	NOUN
ejpam-1951	156	4	)	)	PUNCT
ejpam-1951	156	5	=	=	PRON
ejpam-1951	156	6	{	{	PUNCT
ejpam-1951	156	7	e	e	NOUN
ejpam-1951	156	8	,	,	PUNCT
ejpam-1951	156	9	(	(	PUNCT
ejpam-1951	156	10	34	34	NUM
ejpam-1951	156	11	)	)	PUNCT
ejpam-1951	156	12	}	}	PUNCT
ejpam-1951	156	13	stab(y	stab(y	PROPN
ejpam-1951	156	14	rry	rry	PROPN
ejpam-1951	156	15	)	)	PUNCT
ejpam-1951	157	1	=	=	VERB
ejpam-1951	157	2	stab(ry	stab(ry	ADJ
ejpam-1951	157	3	y	y	NOUN
ejpam-1951	157	4	r	r	NOUN
ejpam-1951	157	5	)	)	PUNCT
ejpam-1951	157	6	=	=	NOUN
ejpam-1951	157	7	stab(ry	stab(ry	PROPN
ejpam-1951	157	8	ry	ry	NOUN
ejpam-1951	157	9	)	)	PUNCT
ejpam-1951	158	1	=	=	VERB
ejpam-1951	158	2	stab(y	stab(y	INTJ
ejpam-1951	158	3	ry	ry	NOUN
ejpam-1951	158	4	r	r	NOUN
ejpam-1951	158	5	)	)	PUNCT
ejpam-1951	158	6	=	=	SYM
ejpam-1951	158	7	{	{	PUNCT
ejpam-1951	158	8	e	e	NOUN
ejpam-1951	158	9	}	}	PUNCT
ejpam-1951	158	10	2	2	NUM
ejpam-1951	158	11	.	.	X
ejpam-1951	158	12	burnside	burnside	PROPN
ejpam-1951	158	13	’s	’s	PART
ejpam-1951	158	14	lemma	lemma	PROPN
ejpam-1951	158	15	and	and	CCONJ
ejpam-1951	158	16	pólya	pólya	NOUN
ejpam-1951	158	17	’s	’s	PART
ejpam-1951	158	18	theorem	theorem	ADJ
ejpam-1951	158	19	2.1	2.1	NUM
ejpam-1951	158	20	.	.	PUNCT
ejpam-1951	159	1	orbit	orbit	NOUN
ejpam-1951	159	2	-	-	PUNCT
ejpam-1951	159	3	stabilizer	stabilizer	NOUN
ejpam-1951	159	4	formula	formula	NOUN
ejpam-1951	159	5	let	let	VERB
ejpam-1951	159	6	g	g	PRON
ejpam-1951	159	7	be	be	AUX
ejpam-1951	159	8	a	a	DET
ejpam-1951	159	9	group	group	NOUN
ejpam-1951	159	10	,	,	PUNCT
ejpam-1951	159	11	acting	act	VERB
ejpam-1951	159	12	on	on	ADP
ejpam-1951	159	13	a	a	DET
ejpam-1951	159	14	set	set	NOUN
ejpam-1951	159	15	a	a	PRON
ejpam-1951	159	16	,	,	PUNCT
ejpam-1951	159	17	then	then	ADV
ejpam-1951	159	18	for	for	ADP
ejpam-1951	159	19	all	all	DET
ejpam-1951	159	20	a	a	DET
ejpam-1951	159	21	∈	∈	PROPN
ejpam-1951	159	22	a	a	PRON
ejpam-1951	159	23	,	,	PUNCT
ejpam-1951	159	24	|g|=	|g|=	NOUN
ejpam-1951	159	25	|stab(a)||or	|stab(a)||or	ADJ
ejpam-1951	159	26	b(a)|	b(a)|	NOUN
ejpam-1951	159	27	[	[	X
ejpam-1951	159	28	6	6	NUM
ejpam-1951	159	29	]	]	PUNCT
ejpam-1951	159	30	.	.	PUNCT
ejpam-1951	160	1	example	example	NOUN
ejpam-1951	160	2	9	9	NUM
ejpam-1951	160	3	.	.	PUNCT
ejpam-1951	161	1	by	by	ADP
ejpam-1951	161	2	following	follow	VERB
ejpam-1951	161	3	the	the	DET
ejpam-1951	161	4	example	example	NOUN
ejpam-1951	161	5	7	7	NUM
ejpam-1951	161	6	and	and	CCONJ
ejpam-1951	161	7	8	8	NUM
ejpam-1951	161	8	we	we	PRON
ejpam-1951	161	9	have	have	AUX
ejpam-1951	161	10	stab(y	stab(y	PROPN
ejpam-1951	161	11	y	y	PROPN
ejpam-1951	161	12	rr	rr	VERB
ejpam-1951	161	13	)	)	PUNCT
ejpam-1951	161	14	=	=	NOUN
ejpam-1951	161	15	{	{	PUNCT
ejpam-1951	161	16	e	e	NOUN
ejpam-1951	161	17	,	,	PUNCT
ejpam-1951	161	18	(	(	PUNCT
ejpam-1951	161	19	12	12	NUM
ejpam-1951	161	20	)	)	PUNCT
ejpam-1951	161	21	,	,	PUNCT
ejpam-1951	161	22	(	(	PUNCT
ejpam-1951	161	23	34	34	NUM
ejpam-1951	161	24	)	)	PUNCT
ejpam-1951	161	25	,	,	PUNCT
ejpam-1951	161	26	(	(	PUNCT
ejpam-1951	161	27	12)(34)}stab(y	12)(34)}stab(y	NUM
ejpam-1951	161	28	rrr	rrr	NOUN
ejpam-1951	161	29	)	)	PUNCT
ejpam-1951	161	30	=	=	PRON
ejpam-1951	161	31	{	{	PUNCT
ejpam-1951	161	32	e	e	NOUN
ejpam-1951	161	33	,	,	PUNCT
ejpam-1951	161	34	(	(	PUNCT
ejpam-1951	161	35	34	34	NUM
ejpam-1951	161	36	)	)	PUNCT
ejpam-1951	161	37	}	}	PUNCT
ejpam-1951	161	38	or	or	CCONJ
ejpam-1951	161	39	b(y	b(y	PROPN
ejpam-1951	161	40	y	y	PROPN
ejpam-1951	161	41	rr	rr	PROPN
ejpam-1951	161	42	)	)	PUNCT
ejpam-1951	162	1	=	=	PRON
ejpam-1951	162	2	{	{	PUNCT
ejpam-1951	162	3	y	y	PROPN
ejpam-1951	162	4	y	y	PROPN
ejpam-1951	162	5	rr}or	rr}or	NOUN
ejpam-1951	162	6	b(y	b(y	PROPN
ejpam-1951	162	7	rrr	rrr	NOUN
ejpam-1951	162	8	)	)	PUNCT
ejpam-1951	162	9	=	=	PRON
ejpam-1951	162	10	{	{	PUNCT
ejpam-1951	162	11	ry	ry	PROPN
ejpam-1951	162	12	rr	rr	PROPN
ejpam-1951	162	13	,	,	PUNCT
ejpam-1951	162	14	y	y	PROPN
ejpam-1951	162	15	rrr	rrr	PROPN
ejpam-1951	162	16	}	}	PUNCT
ejpam-1951	162	17	therefore	therefore	ADV
ejpam-1951	162	18	|stab(y	|stab(y	PROPN
ejpam-1951	162	19	y	y	NOUN
ejpam-1951	162	20	rr)|=	rr)|=	VERB
ejpam-1951	162	21	4	4	NUM
ejpam-1951	162	22	|stab(y	|stab(y	PROPN
ejpam-1951	162	23	rrr)|=	rrr)|=	NOUN
ejpam-1951	162	24	2	2	NUM
ejpam-1951	162	25	|or	|or	ADP
ejpam-1951	162	26	b(y	b(y	PROPN
ejpam-1951	162	27	y	y	PROPN
ejpam-1951	162	28	rr)|=	rr)|=	VERB
ejpam-1951	162	29	1	1	NUM
ejpam-1951	162	30	|or	|or	ADP
ejpam-1951	162	31	b(y	b(y	PROPN
ejpam-1951	162	32	rrr)|=	rrr)|=	NOUN
ejpam-1951	162	33	2	2	NUM
ejpam-1951	162	34	⇒	⇒	NOUN
ejpam-1951	162	35	|stab(y	|stab(y	PROPN
ejpam-1951	162	36	y	y	PROPN
ejpam-1951	162	37	rr)||or	rr)||or	VERB
ejpam-1951	162	38	b(y	b(y	PROPN
ejpam-1951	162	39	y	y	PROPN
ejpam-1951	162	40	rr)|=	rr)|=	VERB
ejpam-1951	162	41	4.1=	4.1=	PROPN
ejpam-1951	162	42	4	4	NUM
ejpam-1951	162	43	⇒	⇒	NOUN
ejpam-1951	162	44	|stab(y	|stab(y	PROPN
ejpam-1951	162	45	rrr)||or	rrr)||or	PROPN
ejpam-1951	163	1	b(y	b(y	PROPN
ejpam-1951	163	2	rrr)|=	rrr)|=	PROPN
ejpam-1951	163	3	2.2=	2.2=	PROPN
ejpam-1951	163	4	4	4	NUM
ejpam-1951	163	5	t.	t.	NOUN
ejpam-1951	163	6	nasseef	nasseef	PROPN
ejpam-1951	163	7	/	/	SYM
ejpam-1951	163	8	eur	eur	PROPN
ejpam-1951	163	9	.	.	PUNCT
ejpam-1951	164	1	j.	j.	PROPN
ejpam-1951	164	2	pure	pure	PROPN
ejpam-1951	164	3	appl	appl	PROPN
ejpam-1951	164	4	.	.	PROPN
ejpam-1951	164	5	math	math	PROPN
ejpam-1951	164	6	,	,	PUNCT
ejpam-1951	164	7	9	9	NUM
ejpam-1951	164	8	(	(	PUNCT
ejpam-1951	164	9	2016	2016	NUM
ejpam-1951	164	10	)	)	PUNCT
ejpam-1951	164	11	,	,	PUNCT
ejpam-1951	164	12	84	84	NUM
ejpam-1951	164	13	-	-	SYM
ejpam-1951	164	14	113	113	NUM
ejpam-1951	164	15	90	90	NUM
ejpam-1951	164	16	2.2	2.2	NUM
ejpam-1951	164	17	.	.	PUNCT
ejpam-1951	165	1	burnside	burnside	PROPN
ejpam-1951	165	2	’s	’s	PART
ejpam-1951	165	3	lemma	lemma	PROPN
ejpam-1951	165	4	lemma	lemma	PROPN
ejpam-1951	165	5	1	1	X
ejpam-1951	165	6	.	.	PUNCT
ejpam-1951	166	1	let	let	VERB
ejpam-1951	166	2	g	g	PRON
ejpam-1951	166	3	be	be	AUX
ejpam-1951	166	4	a	a	DET
ejpam-1951	166	5	finite	finite	ADJ
ejpam-1951	166	6	group	group	NOUN
ejpam-1951	166	7	that	that	PRON
ejpam-1951	166	8	acts	act	VERB
ejpam-1951	166	9	on	on	ADP
ejpam-1951	166	10	a	a	DET
ejpam-1951	166	11	set	set	NOUN
ejpam-1951	166	12	a.	a.	NOUN
ejpam-1951	166	13	for	for	ADP
ejpam-1951	166	14	each	each	DET
ejpam-1951	166	15	g	g	PROPN
ejpam-1951	166	16	∈	∈	PROPN
ejpam-1951	166	17	g	g	NOUN
ejpam-1951	166	18	,	,	PUNCT
ejpam-1951	166	19	let	let	VERB
ejpam-1951	166	20	ag	ag	PROPN
ejpam-1951	166	21	denote	denote	VERB
ejpam-1951	166	22	the	the	DET
ejpam-1951	166	23	set	set	NOUN
ejpam-1951	166	24	of	of	ADP
ejpam-1951	166	25	elements	element	NOUN
ejpam-1951	166	26	in	in	ADP
ejpam-1951	166	27	a	a	PRON
ejpam-1951	166	28	that	that	PRON
ejpam-1951	166	29	are	be	AUX
ejpam-1951	166	30	fixed	fix	VERB
ejpam-1951	166	31	by	by	ADP
ejpam-1951	166	32	g.	g.	PROPN
ejpam-1951	166	33	burnside	burnside	PROPN
ejpam-1951	166	34	’s	’s	PART
ejpam-1951	166	35	lemma	lemma	PROPN
ejpam-1951	166	36	asserts	assert	VERB
ejpam-1951	166	37	the	the	DET
ejpam-1951	166	38	following	follow	VERB
ejpam-1951	166	39	formula	formula	NOUN
ejpam-1951	166	40	for	for	ADP
ejpam-1951	166	41	the	the	DET
ejpam-1951	166	42	number	number	NOUN
ejpam-1951	166	43	of	of	ADP
ejpam-1951	166	44	orbits	orbit	NOUN
ejpam-1951	166	45	,	,	PUNCT
ejpam-1951	166	46	denoted	denote	VERB
ejpam-1951	166	47	|a	|a	PROPN
ejpam-1951	166	48	/	/	SYM
ejpam-1951	166	49	g|	g|	PROPN
ejpam-1951	166	50	:	:	PUNCT
ejpam-1951	166	51	|a	|a	NOUN
ejpam-1951	166	52	/	/	SYM
ejpam-1951	166	53	g|=	g|=	PROPN
ejpam-1951	166	54	1	1	NUM
ejpam-1951	166	55	|g|	|g|	PROPN
ejpam-1951	166	56	∑	∑	PROPN
ejpam-1951	166	57	g∈g	g∈g	PROPN
ejpam-1951	167	1	|ag	|ag	NOUN
ejpam-1951	167	2	|	|	ADV
ejpam-1951	167	3	thus	thus	ADV
ejpam-1951	167	4	the	the	DET
ejpam-1951	167	5	number	number	NOUN
ejpam-1951	167	6	of	of	ADP
ejpam-1951	167	7	orbits	orbit	NOUN
ejpam-1951	167	8	(	(	PUNCT
ejpam-1951	167	9	a	a	DET
ejpam-1951	167	10	natural	natural	ADJ
ejpam-1951	167	11	number	number	NOUN
ejpam-1951	167	12	or	or	CCONJ
ejpam-1951	167	13	+	+	NOUN
ejpam-1951	167	14	∞	∞	NOUN
ejpam-1951	167	15	)	)	PUNCT
ejpam-1951	167	16	is	be	AUX
ejpam-1951	167	17	equal	equal	ADJ
ejpam-1951	167	18	to	to	ADP
ejpam-1951	167	19	the	the	DET
ejpam-1951	167	20	average	average	ADJ
ejpam-1951	167	21	number	number	NOUN
ejpam-1951	167	22	of	of	ADP
ejpam-1951	167	23	points	point	NOUN
ejpam-1951	167	24	fixed	fix	VERB
ejpam-1951	167	25	by	by	ADP
ejpam-1951	167	26	an	an	DET
ejpam-1951	167	27	element	element	NOUN
ejpam-1951	167	28	of	of	ADP
ejpam-1951	167	29	g	g	PROPN
ejpam-1951	168	1	[	[	X
ejpam-1951	168	2	3	3	NUM
ejpam-1951	168	3	]	]	PUNCT
ejpam-1951	168	4	.	.	PUNCT
ejpam-1951	169	1	proof	proof	NOUN
ejpam-1951	169	2	.	.	PUNCT
ejpam-1951	170	1	the	the	DET
ejpam-1951	170	2	proof	proof	NOUN
ejpam-1951	170	3	uses	use	VERB
ejpam-1951	170	4	orbit	orbit	NOUN
ejpam-1951	170	5	-	-	PUNCT
ejpam-1951	170	6	stabilizer	stabilizer	NOUN
ejpam-1951	170	7	theorem	theorem	NOUN
ejpam-1951	170	8	and	and	CCONJ
ejpam-1951	170	9	the	the	DET
ejpam-1951	170	10	fact	fact	NOUN
ejpam-1951	170	11	that	that	SCONJ
ejpam-1951	170	12	a	a	PRON
ejpam-1951	170	13	is	be	AUX
ejpam-1951	170	14	the	the	DET
ejpam-1951	170	15	disjoint	disjoint	PROPN
ejpam-1951	170	16	union	union	NOUN
ejpam-1951	170	17	of	of	ADP
ejpam-1951	170	18	the	the	DET
ejpam-1951	170	19	orbits	orbit	NOUN
ejpam-1951	170	20	:	:	PUNCT
ejpam-1951	170	21	∑	∑	PUNCT
ejpam-1951	170	22	g∈g	g∈g	NOUN
ejpam-1951	170	23	|ag	|ag	PROPN
ejpam-1951	170	24	|=|{(g	|=|{(g	PROPN
ejpam-1951	170	25	,	,	PUNCT
ejpam-1951	170	26	a	a	PRON
ejpam-1951	170	27	)	)	PUNCT
ejpam-1951	170	28	∈	∈	PROPN
ejpam-1951	170	29	g	g	NOUN
ejpam-1951	170	30	×	×	NOUN
ejpam-1951	170	31	a|g	a|g	NOUN
ejpam-1951	170	32	·	·	PUNCT
ejpam-1951	170	33	a	a	DET
ejpam-1951	170	34	=	=	NOUN
ejpam-1951	170	35	a}|=	a}|=	NOUN
ejpam-1951	170	36	∑	∑	PROPN
ejpam-1951	170	37	a∈a	a∈a	ADJ
ejpam-1951	170	38	|stab(a)|=	|stab(a)|=	PUNCT
ejpam-1951	170	39	∑	∑	PUNCT
ejpam-1951	170	40	a∈a	a∈a	ADJ
ejpam-1951	170	41	|g|	|g|	PROPN
ejpam-1951	170	42	|or	|or	ADP
ejpam-1951	170	43	b(a)|	b(a)|	NOUN
ejpam-1951	170	44	=	=	SYM
ejpam-1951	170	45	|g|	|g|	PROPN
ejpam-1951	170	46	∑	∑	PUNCT
ejpam-1951	170	47	a∈a	a∈a	ADJ
ejpam-1951	170	48	1	1	NUM
ejpam-1951	170	49	|or	|or	ADP
ejpam-1951	170	50	b(a)|	b(a)|	NOUN
ejpam-1951	170	51	=	=	PUNCT
ejpam-1951	170	52	|g|	|g|	ADJ
ejpam-1951	170	53	∑	∑	SYM
ejpam-1951	170	54	p∈a	p∈a	PROPN
ejpam-1951	170	55	/	/	SYM
ejpam-1951	170	56	g	g	PROPN
ejpam-1951	170	57	∑	∑	PUNCT
ejpam-1951	170	58	a∈p	a∈p	VERB
ejpam-1951	170	59	1	1	NUM
ejpam-1951	170	60	|p|	|p|	NOUN
ejpam-1951	170	61	=	=	PUNCT
ejpam-1951	170	62	|g|	|g|	PROPN
ejpam-1951	170	63	∑	∑	SYM
ejpam-1951	170	64	p∈a	p∈a	PROPN
ejpam-1951	170	65	/	/	SYM
ejpam-1951	170	66	g	g	NOUN
ejpam-1951	170	67	1=	1=	X
ejpam-1951	170	68	|g|	|g|	PROPN
ejpam-1951	170	69	·	·	PUNCT
ejpam-1951	170	70	|a	|a	X
ejpam-1951	170	71	/	/	SYM
ejpam-1951	170	72	g|	g|	PROPN
ejpam-1951	170	73	therefore	therefore	ADV
ejpam-1951	171	1	[	[	X
ejpam-1951	171	2	6	6	NUM
ejpam-1951	171	3	]	]	SYM
ejpam-1951	171	4	1	1	NUM
ejpam-1951	171	5	|g|	|g|	PROPN
ejpam-1951	171	6	∑	∑	ADP
ejpam-1951	171	7	g∈g	g∈g	PROPN
ejpam-1951	171	8	|ag	|ag	NOUN
ejpam-1951	171	9	|=	|=	NOUN
ejpam-1951	171	10	|a	|a	NOUN
ejpam-1951	171	11	/	/	SYM
ejpam-1951	171	12	g|	g|	PROPN
ejpam-1951	171	13	this	this	PRON
ejpam-1951	171	14	proves	prove	VERB
ejpam-1951	171	15	the	the	DET
ejpam-1951	171	16	lemma	lemma	PROPN
ejpam-1951	171	17	.	.	PUNCT
ejpam-1951	171	18	example	example	NOUN
ejpam-1951	171	19	10	10	NUM
ejpam-1951	171	20	.	.	PUNCT
ejpam-1951	172	1	continuing	continue	VERB
ejpam-1951	172	2	with	with	ADP
ejpam-1951	172	3	the	the	DET
ejpam-1951	172	4	example	example	NOUN
ejpam-1951	172	5	7	7	NUM
ejpam-1951	172	6	and	and	CCONJ
ejpam-1951	172	7	8	8	NUM
ejpam-1951	172	8	,	,	PUNCT
ejpam-1951	172	9	we	we	PRON
ejpam-1951	172	10	have	have	VERB
ejpam-1951	172	11	a(e	a(e	PROPN
ejpam-1951	172	12	)	)	PUNCT
ejpam-1951	173	1	=	=	SYM
ejpam-1951	173	2	c	c	NOUN
ejpam-1951	173	3	a(12	a(12	ADV
ejpam-1951	173	4	)	)	PUNCT
ejpam-1951	174	1	=	=	PRON
ejpam-1951	174	2	{	{	PUNCT
ejpam-1951	174	3	rrrr	rrrr	PROPN
ejpam-1951	174	4	,	,	PUNCT
ejpam-1951	174	5	rry	rry	PROPN
ejpam-1951	174	6	r	r	NOUN
ejpam-1951	174	7	,	,	PUNCT
ejpam-1951	174	8	rrry	rrry	NOUN
ejpam-1951	174	9	,	,	PUNCT
ejpam-1951	174	10	rry	rry	PROPN
ejpam-1951	174	11	y	y	PROPN
ejpam-1951	174	12	,	,	PUNCT
ejpam-1951	174	13	y	y	PROPN
ejpam-1951	174	14	y	y	PROPN
ejpam-1951	174	15	rr	rr	PROPN
ejpam-1951	174	16	,	,	PUNCT
ejpam-1951	174	17	y	y	PROPN
ejpam-1951	174	18	y	y	PROPN
ejpam-1951	174	19	y	y	PROPN
ejpam-1951	174	20	r	r	PROPN
ejpam-1951	174	21	,	,	PUNCT
ejpam-1951	174	22	y	y	PROPN
ejpam-1951	174	23	y	y	PROPN
ejpam-1951	174	24	ry	ry	PROPN
ejpam-1951	174	25	,	,	PUNCT
ejpam-1951	174	26	y	y	PROPN
ejpam-1951	174	27	y	y	PROPN
ejpam-1951	174	28	y	y	PROPN
ejpam-1951	174	29	y	y	PROPN
ejpam-1951	174	30	}	}	PUNCT
ejpam-1951	174	31	a(34	a(34	ADV
ejpam-1951	174	32	)	)	PUNCT
ejpam-1951	174	33	=	=	X
ejpam-1951	174	34	{	{	PUNCT
ejpam-1951	174	35	rrrr	rrrr	PROPN
ejpam-1951	174	36	,	,	PUNCT
ejpam-1951	174	37	y	y	PROPN
ejpam-1951	174	38	rrr	rrr	PROPN
ejpam-1951	174	39	,	,	PUNCT
ejpam-1951	174	40	ry	ry	PROPN
ejpam-1951	174	41	rr	rr	PROPN
ejpam-1951	174	42	,	,	PUNCT
ejpam-1951	174	43	rry	rry	PROPN
ejpam-1951	174	44	y	y	PROPN
ejpam-1951	174	45	,	,	PUNCT
ejpam-1951	174	46	y	y	PROPN
ejpam-1951	174	47	y	y	PROPN
ejpam-1951	174	48	rr	rr	PROPN
ejpam-1951	174	49	,	,	PUNCT
ejpam-1951	174	50	ry	ry	PROPN
ejpam-1951	174	51	y	y	PROPN
ejpam-1951	174	52	y	y	PROPN
ejpam-1951	174	53	,	,	PUNCT
ejpam-1951	174	54	y	y	PROPN
ejpam-1951	174	55	ry	ry	PROPN
ejpam-1951	174	56	y	y	PROPN
ejpam-1951	174	57	,	,	PUNCT
ejpam-1951	174	58	y	y	PROPN
ejpam-1951	174	59	y	y	PROPN
ejpam-1951	174	60	y	y	PROPN
ejpam-1951	174	61	y	y	PROPN
ejpam-1951	174	62	}	}	PUNCT
ejpam-1951	174	63	a((12)(34	a((12)(34	NOUN
ejpam-1951	174	64	)	)	PUNCT
ejpam-1951	174	65	)	)	PUNCT
ejpam-1951	175	1	=	=	PRON
ejpam-1951	175	2	{	{	PUNCT
ejpam-1951	175	3	rrrr	rrrr	PROPN
ejpam-1951	175	4	,	,	PUNCT
ejpam-1951	175	5	rry	rry	PROPN
ejpam-1951	175	6	y	y	PROPN
ejpam-1951	175	7	,	,	PUNCT
ejpam-1951	175	8	y	y	PROPN
ejpam-1951	175	9	y	y	PROPN
ejpam-1951	175	10	rr	rr	PROPN
ejpam-1951	175	11	,	,	PUNCT
ejpam-1951	175	12	y	y	PROPN
ejpam-1951	175	13	y	y	PROPN
ejpam-1951	175	14	y	y	PROPN
ejpam-1951	175	15	y	y	PROPN
ejpam-1951	175	16	}	}	PUNCT
ejpam-1951	175	17	by	by	ADP
ejpam-1951	175	18	applying	apply	VERB
ejpam-1951	175	19	burnside	burnside	NOUN
ejpam-1951	175	20	’s	’s	PART
ejpam-1951	175	21	lemma	lemma	PROPN
ejpam-1951	175	22	,	,	PUNCT
ejpam-1951	175	23	we	we	PRON
ejpam-1951	175	24	have	have	VERB
ejpam-1951	175	25	1	1	NUM
ejpam-1951	175	26	|g|	|g|	PROPN
ejpam-1951	175	27	∑	∑	ADP
ejpam-1951	175	28	g∈g	g∈g	PROPN
ejpam-1951	175	29	|ag	|ag	NOUN
ejpam-1951	175	30	|=	|=	NOUN
ejpam-1951	175	31	1	1	NUM
ejpam-1951	175	32	4	4	NUM
ejpam-1951	175	33	(	(	PUNCT
ejpam-1951	175	34	16	16	NUM
ejpam-1951	175	35	+	+	NUM
ejpam-1951	175	36	8	8	NUM
ejpam-1951	175	37	+	+	NUM
ejpam-1951	175	38	8	8	NUM
ejpam-1951	175	39	+	+	NUM
ejpam-1951	175	40	4	4	NUM
ejpam-1951	175	41	)	)	PUNCT
ejpam-1951	175	42	=	=	SYM
ejpam-1951	175	43	9	9	NUM
ejpam-1951	175	44	example	example	NOUN
ejpam-1951	175	45	11	11	NUM
ejpam-1951	175	46	.	.	PUNCT
ejpam-1951	176	1	let	let	VERB
ejpam-1951	176	2	g	g	NOUN
ejpam-1951	176	3	be	be	AUX
ejpam-1951	176	4	the	the	DET
ejpam-1951	176	5	group	group	NOUN
ejpam-1951	176	6	of	of	ADP
ejpam-1951	176	7	rotations	rotation	NOUN
ejpam-1951	176	8	of	of	ADP
ejpam-1951	176	9	a	a	DET
ejpam-1951	176	10	cube	cube	NOUN
ejpam-1951	176	11	induced	induce	VERB
ejpam-1951	176	12	on	on	ADP
ejpam-1951	176	13	the	the	DET
ejpam-1951	176	14	set	set	NOUN
ejpam-1951	176	15	of	of	ADP
ejpam-1951	176	16	6	6	NUM
ejpam-1951	176	17	faces	face	NOUN
ejpam-1951	176	18	(	(	PUNCT
ejpam-1951	176	19	fig	fig	NOUN
ejpam-1951	176	20	.	.	NOUN
ejpam-1951	177	1	1	1	NUM
ejpam-1951	177	2	)	)	PUNCT
ejpam-1951	177	3	.	.	PUNCT
ejpam-1951	178	1	the	the	DET
ejpam-1951	178	2	rotations	rotation	NOUN
ejpam-1951	178	3	of	of	ADP
ejpam-1951	178	4	the	the	DET
ejpam-1951	178	5	cube	cube	NOUN
ejpam-1951	178	6	which	which	PRON
ejpam-1951	178	7	leaves	leave	VERB
ejpam-1951	178	8	it	it	PRON
ejpam-1951	178	9	invariant	invariant	ADJ
ejpam-1951	178	10	are	be	AUX
ejpam-1951	178	11	(	(	PUNCT
ejpam-1951	178	12	i	i	NOUN
ejpam-1951	178	13	)	)	PUNCT
ejpam-1951	178	14	6	6	NUM
ejpam-1951	178	15	rotations	rotation	NOUN
ejpam-1951	178	16	of	of	ADP
ejpam-1951	178	17	90	90	NUM
ejpam-1951	178	18	degree(clockwise	degree(clockwise	ADJ
ejpam-1951	178	19	or	or	CCONJ
ejpam-1951	178	20	anti	anti	ADJ
ejpam-1951	178	21	-	-	NOUN
ejpam-1951	178	22	clockwise	clockwise	NOUN
ejpam-1951	178	23	)	)	PUNCT
ejpam-1951	178	24	about	about	ADP
ejpam-1951	178	25	the	the	DET
ejpam-1951	178	26	axes	axis	NOUN
ejpam-1951	178	27	joining	join	VERB
ejpam-1951	178	28	the	the	DET
ejpam-1951	178	29	centers	center	NOUN
ejpam-1951	178	30	of	of	ADP
ejpam-1951	178	31	the	the	DET
ejpam-1951	178	32	opposite	opposite	ADJ
ejpam-1951	178	33	faces	face	NOUN
ejpam-1951	178	34	;	;	PUNCT
ejpam-1951	178	35	(	(	PUNCT
ejpam-1951	178	36	ii	ii	NOUN
ejpam-1951	178	37	)	)	PUNCT
ejpam-1951	178	38	3	3	NUM
ejpam-1951	178	39	rotations	rotation	NOUN
ejpam-1951	178	40	of	of	ADP
ejpam-1951	178	41	180	180	NUM
ejpam-1951	178	42	degree	degree	NOUN
ejpam-1951	178	43	each	each	PRON
ejpam-1951	178	44	of	of	ADP
ejpam-1951	178	45	the	the	DET
ejpam-1951	178	46	above	above	ADJ
ejpam-1951	178	47	axes	axis	NOUN
ejpam-1951	178	48	;	;	PUNCT
ejpam-1951	178	49	(	(	PUNCT
ejpam-1951	178	50	iii	iii	NOUN
ejpam-1951	178	51	)	)	PUNCT
ejpam-1951	178	52	8	8	NUM
ejpam-1951	178	53	rotations	rotation	NOUN
ejpam-1951	178	54	of	of	ADP
ejpam-1951	178	55	120	120	NUM
ejpam-1951	178	56	degree(clockwise	degree(clockwise	ADJ
ejpam-1951	178	57	or	or	CCONJ
ejpam-1951	178	58	anti	anti	ADJ
ejpam-1951	178	59	-	-	NOUN
ejpam-1951	178	60	clockwise	clockwise	NOUN
ejpam-1951	178	61	)	)	PUNCT
ejpam-1951	178	62	about	about	ADP
ejpam-1951	178	63	the	the	DET
ejpam-1951	178	64	axes	axis	NOUN
ejpam-1951	178	65	joining	join	VERB
ejpam-1951	178	66	the	the	DET
ejpam-1951	178	67	opposite	opposite	ADJ
ejpam-1951	178	68	vertices	vertex	NOUN
ejpam-1951	178	69	;	;	PUNCT
ejpam-1951	178	70	t.	t.	PROPN
ejpam-1951	178	71	nasseef	nasseef	PROPN
ejpam-1951	178	72	/	/	SYM
ejpam-1951	178	73	eur	eur	PROPN
ejpam-1951	178	74	.	.	PUNCT
ejpam-1951	179	1	j.	j.	PROPN
ejpam-1951	179	2	pure	pure	PROPN
ejpam-1951	179	3	appl	appl	PROPN
ejpam-1951	179	4	.	.	PROPN
ejpam-1951	179	5	math	math	PROPN
ejpam-1951	179	6	,	,	PUNCT
ejpam-1951	179	7	9	9	NUM
ejpam-1951	179	8	(	(	PUNCT
ejpam-1951	179	9	2016	2016	NUM
ejpam-1951	179	10	)	)	PUNCT
ejpam-1951	179	11	,	,	PUNCT
ejpam-1951	179	12	84	84	NUM
ejpam-1951	179	13	-	-	SYM
ejpam-1951	179	14	113	113	NUM
ejpam-1951	179	15	91	91	NUM
ejpam-1951	179	16	(	(	PUNCT
ejpam-1951	179	17	iv	iv	X
ejpam-1951	179	18	)	)	PUNCT
ejpam-1951	179	19	6	6	NUM
ejpam-1951	179	20	rotations	rotation	NOUN
ejpam-1951	179	21	of	of	ADP
ejpam-1951	179	22	180	180	NUM
ejpam-1951	179	23	degree	degree	NOUN
ejpam-1951	179	24	about	about	ADP
ejpam-1951	179	25	the	the	DET
ejpam-1951	179	26	axes	axis	NOUN
ejpam-1951	179	27	joining	join	VERB
ejpam-1951	179	28	the	the	DET
ejpam-1951	179	29	midpoints	midpoint	NOUN
ejpam-1951	179	30	of	of	ADP
ejpam-1951	179	31	the	the	DET
ejpam-1951	179	32	opposite	opposite	ADJ
ejpam-1951	179	33	edges	edge	NOUN
ejpam-1951	179	34	and	and	CCONJ
ejpam-1951	179	35	(	(	PUNCT
ejpam-1951	179	36	v	v	NOUN
ejpam-1951	179	37	)	)	PUNCT
ejpam-1951	179	38	the	the	DET
ejpam-1951	179	39	identity	identity	NOUN
ejpam-1951	179	40	.	.	PUNCT
ejpam-1951	180	1	to	to	PART
ejpam-1951	180	2	determine	determine	VERB
ejpam-1951	180	3	the	the	DET
ejpam-1951	180	4	cyclic	cyclic	ADJ
ejpam-1951	180	5	index	index	NOUN
ejpam-1951	180	6	of	of	ADP
ejpam-1951	180	7	its	its	PRON
ejpam-1951	180	8	action	action	NOUN
ejpam-1951	180	9	on	on	ADP
ejpam-1951	180	10	the	the	DET
ejpam-1951	180	11	set	set	NOUN
ejpam-1951	180	12	of	of	ADP
ejpam-1951	180	13	faces	face	NOUN
ejpam-1951	180	14	it	it	PRON
ejpam-1951	180	15	is	be	AUX
ejpam-1951	180	16	observed	observe	VERB
ejpam-1951	180	17	that	that	SCONJ
ejpam-1951	180	18	(	(	PUNCT
ejpam-1951	180	19	i	i	NOUN
ejpam-1951	180	20	)	)	PUNCT
ejpam-1951	180	21	has	have	VERB
ejpam-1951	180	22	rotations	rotation	NOUN
ejpam-1951	180	23	of	of	ADP
ejpam-1951	180	24	order	order	NOUN
ejpam-1951	180	25	4	4	NUM
ejpam-1951	180	26	and	and	CCONJ
ejpam-1951	180	27	cycle	cycle	NOUN
ejpam-1951	180	28	type	type	NOUN
ejpam-1951	180	29	t2	t2	PROPN
ejpam-1951	180	30	1	1	NUM
ejpam-1951	180	31	t4	t4	PROPN
ejpam-1951	180	32	;	;	PUNCT
ejpam-1951	180	33	(	(	PUNCT
ejpam-1951	180	34	ii	ii	NOUN
ejpam-1951	180	35	)	)	PUNCT
ejpam-1951	180	36	has	have	AUX
ejpam-1951	180	37	rotations	rotation	NOUN
ejpam-1951	180	38	of	of	ADP
ejpam-1951	180	39	order	order	NOUN
ejpam-1951	180	40	2	2	NUM
ejpam-1951	180	41	and	and	CCONJ
ejpam-1951	180	42	cycle	cycle	NOUN
ejpam-1951	180	43	type	type	NOUN
ejpam-1951	180	44	t2	t2	NOUN
ejpam-1951	180	45	1	1	NUM
ejpam-1951	180	46	t2	t2	NOUN
ejpam-1951	180	47	2	2	NUM
ejpam-1951	180	48	;	;	PUNCT
ejpam-1951	180	49	(	(	PUNCT
ejpam-1951	180	50	iii	iii	X
ejpam-1951	180	51	)	)	PUNCT
ejpam-1951	180	52	has	have	VERB
ejpam-1951	180	53	rotations	rotation	NOUN
ejpam-1951	180	54	of	of	ADP
ejpam-1951	180	55	order	order	NOUN
ejpam-1951	180	56	3	3	NUM
ejpam-1951	180	57	and	and	CCONJ
ejpam-1951	180	58	cycle	cycle	NOUN
ejpam-1951	180	59	type	type	NOUN
ejpam-1951	180	60	t2	t2	PROPN
ejpam-1951	180	61	3	3	NUM
ejpam-1951	180	62	(	(	PUNCT
ejpam-1951	180	63	iv	iv	X
ejpam-1951	180	64	)	)	PUNCT
ejpam-1951	180	65	has	have	AUX
ejpam-1951	180	66	rotations	rotation	NOUN
ejpam-1951	180	67	of	of	ADP
ejpam-1951	180	68	order	order	NOUN
ejpam-1951	180	69	2	2	NUM
ejpam-1951	180	70	and	and	CCONJ
ejpam-1951	180	71	cycle	cycle	NOUN
ejpam-1951	180	72	type	type	NOUN
ejpam-1951	180	73	t3	t3	PROPN
ejpam-1951	180	74	2	2	NUM
ejpam-1951	180	75	(	(	PUNCT
ejpam-1951	180	76	v	v	NOUN
ejpam-1951	180	77	)	)	PUNCT
ejpam-1951	180	78	has	have	AUX
ejpam-1951	180	79	rotations	rotation	NOUN
ejpam-1951	180	80	of	of	ADP
ejpam-1951	180	81	order	order	NOUN
ejpam-1951	180	82	1	1	NUM
ejpam-1951	180	83	and	and	CCONJ
ejpam-1951	180	84	cycle	cycle	NOUN
ejpam-1951	180	85	type	type	NOUN
ejpam-1951	180	86	t6	t6	PROPN
ejpam-1951	180	87	1	1	NUM
ejpam-1951	180	88	therefore	therefore	ADV
ejpam-1951	180	89	the	the	DET
ejpam-1951	180	90	cycle	cycle	NOUN
ejpam-1951	180	91	index	index	NOUN
ejpam-1951	180	92	of	of	ADP
ejpam-1951	180	93	g	g	PROPN
ejpam-1951	180	94	is	be	AUX
ejpam-1951	180	95	z(g	z(g	NOUN
ejpam-1951	180	96	,	,	PUNCT
ejpam-1951	180	97	t1	t1	NOUN
ejpam-1951	180	98	,	,	PUNCT
ejpam-1951	180	99	t2	t2	NOUN
ejpam-1951	180	100	,	,	PUNCT
ejpam-1951	180	101	.	.	PUNCT
ejpam-1951	180	102	.	.	PUNCT
ejpam-1951	181	1	.	.	PUNCT
ejpam-1951	182	1	,	,	PUNCT
ejpam-1951	182	2	t6	t6	PROPN
ejpam-1951	182	3	)	)	PUNCT
ejpam-1951	183	1	=	=	SYM
ejpam-1951	183	2	1	1	NUM
ejpam-1951	183	3	24	24	NUM
ejpam-1951	183	4	(	(	PUNCT
ejpam-1951	183	5	6t2	6t2	NUM
ejpam-1951	183	6	1	1	NUM
ejpam-1951	183	7	t4	t4	PROPN
ejpam-1951	183	8	+	+	NUM
ejpam-1951	183	9	3t2	3t2	NUM
ejpam-1951	183	10	1	1	NUM
ejpam-1951	183	11	t2	t2	NOUN
ejpam-1951	183	12	2	2	NUM
ejpam-1951	183	13	+	+	CCONJ
ejpam-1951	183	14	8t2	8t2	NUM
ejpam-1951	183	15	3	3	NUM
ejpam-1951	183	16	+	+	SYM
ejpam-1951	183	17	6t3	6t3	NUM
ejpam-1951	183	18	2	2	NUM
ejpam-1951	183	19	+	+	CCONJ
ejpam-1951	183	20	t6	t6	PROPN
ejpam-1951	183	21	1	1	NUM
ejpam-1951	183	22	)	)	PUNCT
ejpam-1951	183	23	.	.	PUNCT
ejpam-1951	184	1	figure	figure	VERB
ejpam-1951	184	2	1	1	NUM
ejpam-1951	184	3	:	:	PUNCT
ejpam-1951	184	4	faces	face	NOUN
ejpam-1951	184	5	of	of	ADP
ejpam-1951	184	6	the	the	DET
ejpam-1951	184	7	cube	cube	NOUN
ejpam-1951	184	8	(	(	PUNCT
ejpam-1951	184	9	a	a	DET
ejpam-1951	184	10	)	)	PUNCT
ejpam-1951	184	11	axis	axis	NOUN
ejpam-1951	184	12	(	(	PUNCT
ejpam-1951	184	13	b	b	NOUN
ejpam-1951	184	14	)	)	PUNCT
ejpam-1951	184	15	corner	corner	NOUN
ejpam-1951	184	16	(	(	PUNCT
ejpam-1951	184	17	c	c	NOUN
ejpam-1951	184	18	)	)	PUNCT
ejpam-1951	184	19	midpoint	midpoint	NOUN
ejpam-1951	184	20	figure	figure	NOUN
ejpam-1951	184	21	2	2	NUM
ejpam-1951	184	22	:	:	PUNCT
ejpam-1951	184	23	types	type	NOUN
ejpam-1951	184	24	of	of	ADP
ejpam-1951	184	25	rotations	rotation	NOUN
ejpam-1951	184	26	of	of	ADP
ejpam-1951	184	27	the	the	DET
ejpam-1951	184	28	cube	cube	NOUN
ejpam-1951	184	29	consider	consider	VERB
ejpam-1951	184	30	g	g	NOUN
ejpam-1951	184	31	=	=	SYM
ejpam-1951	184	32	cn	cn	PROPN
ejpam-1951	184	33	be	be	AUX
ejpam-1951	184	34	cyclic	cyclic	ADJ
ejpam-1951	184	35	group	group	NOUN
ejpam-1951	184	36	of	of	ADP
ejpam-1951	184	37	order	order	NOUN
ejpam-1951	184	38	n	n	PRON
ejpam-1951	184	39	with	with	ADP
ejpam-1951	184	40	regarded	regard	VERB
ejpam-1951	184	41	as	as	ADP
ejpam-1951	184	42	the	the	DET
ejpam-1951	184	43	group	group	NOUN
ejpam-1951	184	44	of	of	ADP
ejpam-1951	184	45	permutations	permutation	NOUN
ejpam-1951	184	46	of	of	ADP
ejpam-1951	184	47	the	the	DET
ejpam-1951	184	48	vertices	vertex	NOUN
ejpam-1951	184	49	of	of	ADP
ejpam-1951	184	50	a	a	DET
ejpam-1951	184	51	regular	regular	ADJ
ejpam-1951	184	52	n	n	CCONJ
ejpam-1951	184	53	-	-	PUNCT
ejpam-1951	184	54	gon	gon	NOUN
ejpam-1951	184	55	.	.	PUNCT
ejpam-1951	185	1	however	however	ADV
ejpam-1951	185	2	it	it	PRON
ejpam-1951	185	3	is	be	AUX
ejpam-1951	185	4	the	the	DET
ejpam-1951	185	5	subgroup	subgroup	NOUN
ejpam-1951	185	6	of	of	ADP
ejpam-1951	185	7	sn	sn	PROPN
ejpam-1951	185	8	generated	generate	VERB
ejpam-1951	185	9	by	by	ADP
ejpam-1951	185	10	an	an	DET
ejpam-1951	185	11	n	n	CCONJ
ejpam-1951	185	12	-	-	PUNCT
ejpam-1951	185	13	cycle(1,2	cycle(1,2	NOUN
ejpam-1951	185	14	,	,	PUNCT
ejpam-1951	185	15	.	.	PUNCT
ejpam-1951	185	16	.	.	PUNCT
ejpam-1951	186	1	.	.	PUNCT
ejpam-1951	187	1	,	,	PUNCT
ejpam-1951	188	1	n	n	CCONJ
ejpam-1951	188	2	)	)	PUNCT
ejpam-1951	188	3	.	.	PUNCT
ejpam-1951	189	1	for	for	ADP
ejpam-1951	189	2	a	a	DET
ejpam-1951	189	3	generator	generator	NOUN
ejpam-1951	189	4	g	g	NOUN
ejpam-1951	189	5	of	of	ADP
ejpam-1951	189	6	sn	sn	PROPN
ejpam-1951	189	7	,	,	PUNCT
ejpam-1951	189	8	the	the	DET
ejpam-1951	189	9	element	element	NOUN
ejpam-1951	189	10	g	g	PROPN
ejpam-1951	189	11	i	i	PRON
ejpam-1951	189	12	has	have	VERB
ejpam-1951	189	13	the	the	DET
ejpam-1951	189	14	same	same	ADJ
ejpam-1951	189	15	cyclic	cyclic	ADJ
ejpam-1951	189	16	structure	structure	NOUN
ejpam-1951	189	17	as	as	ADP
ejpam-1951	189	18	that	that	PRON
ejpam-1951	189	19	of	of	ADP
ejpam-1951	189	20	gcd{i	gcd{i	PROPN
ejpam-1951	189	21	,	,	PUNCT
ejpam-1951	189	22	n	n	CCONJ
ejpam-1951	189	23	}	}	PUNCT
ejpam-1951	189	24	and	and	CCONJ
ejpam-1951	189	25	cycle	cycle	NOUN
ejpam-1951	189	26	of	of	ADP
ejpam-1951	189	27	length	length	NOUN
ejpam-1951	190	1	d	d	PROPN
ejpam-1951	190	2	=	=	SYM
ejpam-1951	190	3	n	n	PROPN
ejpam-1951	190	4	gcd(i	gcd(i	PROPN
ejpam-1951	190	5	,	,	PUNCT
ejpam-1951	190	6	n	n	CCONJ
ejpam-1951	190	7	)	)	PUNCT
ejpam-1951	190	8	and	and	CCONJ
ejpam-1951	190	9	therefore	therefore	ADV
ejpam-1951	190	10	has	have	AUX
ejpam-1951	190	11	of	of	ADP
ejpam-1951	190	12	order	order	NOUN
ejpam-1951	190	13	d.	d.	NOUN
ejpam-1951	190	14	the	the	DET
ejpam-1951	190	15	number	number	NOUN
ejpam-1951	190	16	of	of	ADP
ejpam-1951	190	17	elements	element	NOUN
ejpam-1951	190	18	of	of	ADP
ejpam-1951	190	19	order	order	NOUN
ejpam-1951	190	20	d	d	NOUN
ejpam-1951	190	21	is	be	AUX
ejpam-1951	190	22	equal	equal	ADJ
ejpam-1951	190	23	to	to	ADP
ejpam-1951	190	24	t.	t.	PROPN
ejpam-1951	190	25	nasseef	nasseef	PROPN
ejpam-1951	190	26	/	/	SYM
ejpam-1951	190	27	eur	eur	PROPN
ejpam-1951	190	28	.	.	PUNCT
ejpam-1951	191	1	j.	j.	PROPN
ejpam-1951	191	2	pure	pure	PROPN
ejpam-1951	191	3	appl	appl	PROPN
ejpam-1951	191	4	.	.	PROPN
ejpam-1951	191	5	math	math	PROPN
ejpam-1951	191	6	,	,	PUNCT
ejpam-1951	191	7	9	9	NUM
ejpam-1951	191	8	(	(	PUNCT
ejpam-1951	191	9	2016	2016	NUM
ejpam-1951	191	10	)	)	PUNCT
ejpam-1951	191	11	,	,	PUNCT
ejpam-1951	191	12	84	84	NUM
ejpam-1951	191	13	-	-	SYM
ejpam-1951	191	14	113	113	NUM
ejpam-1951	191	15	92	92	NUM
ejpam-1951	191	16	the	the	DET
ejpam-1951	191	17	number	number	NOUN
ejpam-1951	191	18	of	of	ADP
ejpam-1951	191	19	integers	integer	NOUN
ejpam-1951	191	20	1	1	NUM
ejpam-1951	191	21	≤	≤	NOUN
ejpam-1951	191	22	p	p	NOUN
ejpam-1951	191	23	≤	≤	PROPN
ejpam-1951	191	24	d	d	NOUN
ejpam-1951	191	25	with	with	ADP
ejpam-1951	191	26	gcd(p	gcd(p	PROPN
ejpam-1951	191	27	,	,	PUNCT
ejpam-1951	191	28	d	d	NOUN
ejpam-1951	191	29	)	)	PUNCT
ejpam-1951	191	30	=	=	SYM
ejpam-1951	191	31	1	1	NUM
ejpam-1951	191	32	,	,	PUNCT
ejpam-1951	191	33	which	which	PRON
ejpam-1951	191	34	is	be	AUX
ejpam-1951	191	35	already	already	ADV
ejpam-1951	191	36	given	give	VERB
ejpam-1951	191	37	by	by	ADP
ejpam-1951	191	38	euler	euler	NOUN
ejpam-1951	191	39	’s	’s	PART
ejpam-1951	191	40	function	function	PROPN
ejpam-1951	191	41	φ	φ	PROPN
ejpam-1951	191	42	from	from	ADP
ejpam-1951	191	43	the	the	DET
ejpam-1951	191	44	elementary	elementary	ADJ
ejpam-1951	191	45	theory	theory	NOUN
ejpam-1951	191	46	(	(	PUNCT
ejpam-1951	191	47	definition	definition	NOUN
ejpam-1951	191	48	4	4	NUM
ejpam-1951	191	49	)	)	PUNCT
ejpam-1951	191	50	.	.	PUNCT
ejpam-1951	192	1	thus	thus	ADV
ejpam-1951	192	2	from	from	ADP
ejpam-1951	192	3	(	(	PUNCT
ejpam-1951	192	4	eq1	eq1	PROPN
ejpam-1951	192	5	)	)	PUNCT
ejpam-1951	192	6	we	we	PRON
ejpam-1951	192	7	obtain	obtain	VERB
ejpam-1951	192	8	z(g	z(g	NOUN
ejpam-1951	192	9	,	,	PUNCT
ejpam-1951	192	10	t1	t1	NOUN
ejpam-1951	192	11	,	,	PUNCT
ejpam-1951	192	12	t2	t2	NOUN
ejpam-1951	192	13	,	,	PUNCT
ejpam-1951	192	14	.	.	PUNCT
ejpam-1951	192	15	.	.	PUNCT
ejpam-1951	193	1	.	.	PUNCT
ejpam-1951	194	1	,	,	PUNCT
ejpam-1951	194	2	tn	tn	PROPN
ejpam-1951	194	3	)	)	PUNCT
ejpam-1951	194	4	=	=	SYM
ejpam-1951	195	1	1	1	NUM
ejpam-1951	195	2	n	n	NUM
ejpam-1951	195	3	∑	∑	ADV
ejpam-1951	195	4	d	d	PROPN
ejpam-1951	195	5	/	/	SYM
ejpam-1951	195	6	n	n	CCONJ
ejpam-1951	195	7	φ(d)t	φ(d)t	PROPN
ejpam-1951	195	8	n	n	CCONJ
ejpam-1951	195	9	/	/	SYM
ejpam-1951	195	10	d	d	PROPN
ejpam-1951	195	11	d	d	NOUN
ejpam-1951	195	12	where	where	SCONJ
ejpam-1951	195	13	φ(pn	φ(pn	NOUN
ejpam-1951	195	14	)	)	PUNCT
ejpam-1951	195	15	=	=	SYM
ejpam-1951	196	1	(	(	PUNCT
ejpam-1951	196	2	p−	p−	NOUN
ejpam-1951	196	3	1)pn−1	1)pn−1	NUM
ejpam-1951	196	4	for	for	ADP
ejpam-1951	196	5	prime	prime	ADJ
ejpam-1951	196	6	powers	power	NOUN
ejpam-1951	196	7	and	and	CCONJ
ejpam-1951	196	8	φ(m	φ(m	NOUN
ejpam-1951	196	9	)	)	PUNCT
ejpam-1951	197	1	=	=	SYM
ejpam-1951	197	2	πk	πk	ADP
ejpam-1951	197	3	i=1	i=1	PROPN
ejpam-1951	198	1	φ(p	φ(p	PROPN
ejpam-1951	198	2	ni	ni	PROPN
ejpam-1951	198	3	i	i	PROPN
ejpam-1951	198	4	)	)	PUNCT
ejpam-1951	198	5	for	for	ADP
ejpam-1951	198	6	m=	m=	X
ejpam-1951	198	7	πk	πk	VERB
ejpam-1951	198	8	i=1	i=1	PROPN
ejpam-1951	199	1	p	p	X
ejpam-1951	199	2	ni	ni	PROPN
ejpam-1951	200	1	i	i	PROPN
ejpam-1951	200	2	[	[	X
ejpam-1951	200	3	3	3	NUM
ejpam-1951	200	4	]	]	PUNCT
ejpam-1951	200	5	.	.	PUNCT
ejpam-1951	201	1	example	example	NOUN
ejpam-1951	201	2	12	12	NUM
ejpam-1951	201	3	.	.	PUNCT
ejpam-1951	202	1	again	again	ADV
ejpam-1951	202	2	let	let	VERB
ejpam-1951	202	3	g	g	NOUN
ejpam-1951	202	4	be	be	AUX
ejpam-1951	202	5	the	the	DET
ejpam-1951	202	6	group	group	NOUN
ejpam-1951	202	7	of	of	ADP
ejpam-1951	202	8	rotations	rotation	NOUN
ejpam-1951	202	9	of	of	ADP
ejpam-1951	202	10	a	a	DET
ejpam-1951	202	11	cube	cube	NOUN
ejpam-1951	202	12	induced	induce	VERB
ejpam-1951	202	13	on	on	ADP
ejpam-1951	202	14	the	the	DET
ejpam-1951	202	15	set	set	NOUN
ejpam-1951	202	16	of	of	ADP
ejpam-1951	202	17	8	8	NUM
ejpam-1951	202	18	vertices	vertex	NOUN
ejpam-1951	202	19	.	.	PUNCT
ejpam-1951	203	1	the	the	DET
ejpam-1951	203	2	rotations	rotation	NOUN
ejpam-1951	203	3	of	of	ADP
ejpam-1951	203	4	the	the	DET
ejpam-1951	203	5	cube	cube	NOUN
ejpam-1951	203	6	which	which	PRON
ejpam-1951	203	7	leaves	leave	VERB
ejpam-1951	203	8	it	it	PRON
ejpam-1951	203	9	invariant	invariant	ADJ
ejpam-1951	203	10	are	be	AUX
ejpam-1951	203	11	the	the	DET
ejpam-1951	203	12	same	same	ADJ
ejpam-1951	203	13	as	as	ADP
ejpam-1951	203	14	example	example	NOUN
ejpam-1951	203	15	11	11	NUM
ejpam-1951	203	16	.	.	PUNCT
ejpam-1951	204	1	it	it	PRON
ejpam-1951	204	2	is	be	AUX
ejpam-1951	204	3	now	now	ADV
ejpam-1951	204	4	necessary	necessary	ADJ
ejpam-1951	204	5	to	to	PART
ejpam-1951	204	6	see	see	VERB
ejpam-1951	204	7	what	what	PRON
ejpam-1951	204	8	the	the	DET
ejpam-1951	204	9	rotations	rotation	NOUN
ejpam-1951	204	10	do	do	VERB
ejpam-1951	204	11	with	with	ADP
ejpam-1951	204	12	the	the	DET
ejpam-1951	204	13	vertices	vertex	NOUN
ejpam-1951	204	14	.	.	PUNCT
ejpam-1951	205	1	to	to	PART
ejpam-1951	205	2	determine	determine	VERB
ejpam-1951	205	3	the	the	DET
ejpam-1951	205	4	cycle	cycle	NOUN
ejpam-1951	205	5	index	index	NOUN
ejpam-1951	205	6	of	of	ADP
ejpam-1951	205	7	its	its	PRON
ejpam-1951	205	8	action	action	NOUN
ejpam-1951	205	9	on	on	ADP
ejpam-1951	205	10	the	the	DET
ejpam-1951	205	11	set	set	NOUN
ejpam-1951	205	12	of	of	ADP
ejpam-1951	205	13	faces	face	NOUN
ejpam-1951	205	14	it	it	PRON
ejpam-1951	205	15	is	be	AUX
ejpam-1951	205	16	observed	observe	VERB
ejpam-1951	205	17	that	that	SCONJ
ejpam-1951	205	18	(	(	PUNCT
ejpam-1951	205	19	i	i	NOUN
ejpam-1951	205	20	)	)	PUNCT
ejpam-1951	205	21	has	have	VERB
ejpam-1951	205	22	rotations	rotation	NOUN
ejpam-1951	205	23	of	of	ADP
ejpam-1951	205	24	order	order	NOUN
ejpam-1951	205	25	4	4	NUM
ejpam-1951	205	26	and	and	CCONJ
ejpam-1951	205	27	cycle	cycle	NOUN
ejpam-1951	205	28	type	type	NOUN
ejpam-1951	205	29	t2	t2	PROPN
ejpam-1951	205	30	4	4	NUM
ejpam-1951	205	31	;	;	PUNCT
ejpam-1951	205	32	(	(	PUNCT
ejpam-1951	205	33	ii	ii	NOUN
ejpam-1951	205	34	)	)	PUNCT
ejpam-1951	205	35	has	have	VERB
ejpam-1951	205	36	rotations	rotation	NOUN
ejpam-1951	205	37	of	of	ADP
ejpam-1951	205	38	order	order	NOUN
ejpam-1951	205	39	2	2	NUM
ejpam-1951	205	40	and	and	CCONJ
ejpam-1951	205	41	cycle	cycle	NOUN
ejpam-1951	205	42	type	type	NOUN
ejpam-1951	205	43	t4	t4	PROPN
ejpam-1951	205	44	2	2	NUM
ejpam-1951	205	45	;	;	PUNCT
ejpam-1951	205	46	(	(	PUNCT
ejpam-1951	205	47	iii	iii	X
ejpam-1951	205	48	)	)	PUNCT
ejpam-1951	205	49	has	have	VERB
ejpam-1951	205	50	rotations	rotation	NOUN
ejpam-1951	205	51	of	of	ADP
ejpam-1951	205	52	order	order	NOUN
ejpam-1951	205	53	4	4	NUM
ejpam-1951	205	54	and	and	CCONJ
ejpam-1951	205	55	cycle	cycle	NOUN
ejpam-1951	205	56	type	type	NOUN
ejpam-1951	205	57	t2	t2	NOUN
ejpam-1951	205	58	1	1	NUM
ejpam-1951	205	59	t2	t2	NOUN
ejpam-1951	205	60	3	3	NUM
ejpam-1951	205	61	(	(	PUNCT
ejpam-1951	205	62	iv	iv	X
ejpam-1951	205	63	)	)	PUNCT
ejpam-1951	205	64	has	have	AUX
ejpam-1951	205	65	rotations	rotation	NOUN
ejpam-1951	205	66	of	of	ADP
ejpam-1951	205	67	order	order	NOUN
ejpam-1951	205	68	2	2	NUM
ejpam-1951	205	69	and	and	CCONJ
ejpam-1951	205	70	cycle	cycle	NOUN
ejpam-1951	205	71	type	type	NOUN
ejpam-1951	205	72	t4	t4	PROPN
ejpam-1951	205	73	2	2	NUM
ejpam-1951	205	74	(	(	PUNCT
ejpam-1951	205	75	v	v	NOUN
ejpam-1951	205	76	)	)	PUNCT
ejpam-1951	205	77	has	have	AUX
ejpam-1951	205	78	rotations	rotation	NOUN
ejpam-1951	205	79	of	of	ADP
ejpam-1951	205	80	order	order	NOUN
ejpam-1951	205	81	1	1	NUM
ejpam-1951	205	82	and	and	CCONJ
ejpam-1951	205	83	cycle	cycle	NOUN
ejpam-1951	205	84	type	type	NOUN
ejpam-1951	205	85	t8	t8	VERB
ejpam-1951	205	86	1	1	NUM
ejpam-1951	205	87	therefore	therefore	ADV
ejpam-1951	205	88	the	the	DET
ejpam-1951	205	89	cycle	cycle	NOUN
ejpam-1951	205	90	index	index	NOUN
ejpam-1951	205	91	of	of	ADP
ejpam-1951	205	92	g	g	PROPN
ejpam-1951	205	93	is	be	AUX
ejpam-1951	205	94	[	[	X
ejpam-1951	205	95	2	2	NUM
ejpam-1951	205	96	]	]	PUNCT
ejpam-1951	205	97	z(g	z(g	NOUN
ejpam-1951	205	98	,	,	PUNCT
ejpam-1951	205	99	t1	t1	NOUN
ejpam-1951	205	100	,	,	PUNCT
ejpam-1951	205	101	t2	t2	NOUN
ejpam-1951	205	102	,	,	PUNCT
ejpam-1951	205	103	.	.	PUNCT
ejpam-1951	205	104	.	.	PUNCT
ejpam-1951	206	1	.	.	PUNCT
ejpam-1951	207	1	,	,	PUNCT
ejpam-1951	207	2	t8	t8	NOUN
ejpam-1951	207	3	)	)	PUNCT
ejpam-1951	207	4	=	=	SYM
ejpam-1951	207	5	1	1	NUM
ejpam-1951	207	6	24	24	NUM
ejpam-1951	207	7	(	(	PUNCT
ejpam-1951	207	8	6t2	6t2	NUM
ejpam-1951	207	9	4	4	NUM
ejpam-1951	207	10	+	+	NOUN
ejpam-1951	207	11	9t4	9t4	NUM
ejpam-1951	207	12	2	2	NUM
ejpam-1951	207	13	+	+	CCONJ
ejpam-1951	207	14	8t2	8t2	NUM
ejpam-1951	207	15	1	1	NUM
ejpam-1951	207	16	t2	t2	NOUN
ejpam-1951	207	17	3	3	NUM
ejpam-1951	207	18	+	+	SYM
ejpam-1951	207	19	6t3	6t3	NUM
ejpam-1951	207	20	2	2	NUM
ejpam-1951	207	21	+	+	CCONJ
ejpam-1951	207	22	t8	t8	NOUN
ejpam-1951	207	23	1	1	NUM
ejpam-1951	207	24	)	)	PUNCT
ejpam-1951	207	25	.	.	PUNCT
ejpam-1951	208	1	2.3	2.3	NUM
ejpam-1951	208	2	.	.	PUNCT
ejpam-1951	209	1	pólya	pólya	NOUN
ejpam-1951	209	2	’s	’s	PART
ejpam-1951	209	3	substitution	substitution	NOUN
ejpam-1951	209	4	let	let	VERB
ejpam-1951	209	5	σ(c1	σ(c1	PROPN
ejpam-1951	209	6	,	,	PUNCT
ejpam-1951	209	7	c2	c2	PROPN
ejpam-1951	209	8	,	,	PUNCT
ejpam-1951	209	9	.	.	PUNCT
ejpam-1951	209	10	.	.	PUNCT
ejpam-1951	210	1	.	.	PUNCT
ejpam-1951	211	1	,	,	PUNCT
ejpam-1951	211	2	ck	ck	X
ejpam-1951	211	3	)	)	PUNCT
ejpam-1951	211	4	be	be	VERB
ejpam-1951	211	5	the	the	DET
ejpam-1951	211	6	polynomial	polynomial	NOUN
ejpam-1951	211	7	obtained	obtain	VERB
ejpam-1951	211	8	from	from	ADP
ejpam-1951	211	9	the	the	DET
ejpam-1951	211	10	cycle	cycle	NOUN
ejpam-1951	211	11	index	index	NOUN
ejpam-1951	211	12	z(g	z(g	NOUN
ejpam-1951	211	13	,	,	PUNCT
ejpam-1951	211	14	t1	t1	NOUN
ejpam-1951	211	15	,	,	PUNCT
ejpam-1951	211	16	t2	t2	NOUN
ejpam-1951	211	17	,	,	PUNCT
ejpam-1951	211	18	.	.	PUNCT
ejpam-1951	211	19	.	.	PUNCT
ejpam-1951	212	1	.	.	PUNCT
ejpam-1951	213	1	,	,	PUNCT
ejpam-1951	213	2	tn	tn	PROPN
ejpam-1951	213	3	)	)	PUNCT
ejpam-1951	213	4	by	by	ADP
ejpam-1951	213	5	substituting	substitute	VERB
ejpam-1951	213	6	t1	t1	NOUN
ejpam-1951	213	7	7−→c1	7−→c1	NUM
ejpam-1951	214	1	+	+	CCONJ
ejpam-1951	214	2	c2	c2	PROPN
ejpam-1951	214	3	+	+	X
ejpam-1951	214	4	.	.	PUNCT
ejpam-1951	214	5	.	.	PUNCT
ejpam-1951	215	1	.+	.+	NOUN
ejpam-1951	215	2	ck	ck	PROPN
ejpam-1951	215	3	,	,	PUNCT
ejpam-1951	215	4	t2	t2	NOUN
ejpam-1951	215	5	7−→c2	7−→c2	NUM
ejpam-1951	215	6	1	1	NUM
ejpam-1951	215	7	+	+	NUM
ejpam-1951	215	8	c2	c2	PROPN
ejpam-1951	215	9	2	2	NUM
ejpam-1951	215	10	+	+	CCONJ
ejpam-1951	215	11	.	.	PUNCT
ejpam-1951	215	12	.	.	PUNCT
ejpam-1951	216	1	.+	.+	PROPN
ejpam-1951	216	2	c2	c2	PROPN
ejpam-1951	216	3	k	k	PROPN
ejpam-1951	216	4	,	,	PUNCT
ejpam-1951	216	5	.	.	PUNCT
ejpam-1951	216	6	.	.	PUNCT
ejpam-1951	216	7	.	.	PUNCT
ejpam-1951	217	1	tn	tn	NOUN
ejpam-1951	218	1	7−→cn	7−→cn	NUM
ejpam-1951	218	2	1	1	NUM
ejpam-1951	218	3	+	+	CCONJ
ejpam-1951	218	4	cn	cn	X
ejpam-1951	218	5	2	2	NUM
ejpam-1951	218	6	+	+	CCONJ
ejpam-1951	218	7	.	.	PUNCT
ejpam-1951	218	8	.	.	PUNCT
ejpam-1951	219	1	.+	.+	NOUN
ejpam-1951	220	1	cn	cn	PROPN
ejpam-1951	221	1	k	k	PROPN
ejpam-1951	221	2	,	,	PUNCT
ejpam-1951	221	3	then	then	ADV
ejpam-1951	221	4	the	the	DET
ejpam-1951	221	5	number	number	NOUN
ejpam-1951	221	6	of	of	ADP
ejpam-1951	221	7	non	non	ADJ
ejpam-1951	221	8	-	-	ADJ
ejpam-1951	221	9	equivalent	equivalent	ADJ
ejpam-1951	221	10	k	k	PROPN
ejpam-1951	221	11	colorings	coloring	NOUN
ejpam-1951	221	12	of	of	ADP
ejpam-1951	221	13	a	a	DET
ejpam-1951	221	14	pattern	pattern	NOUN
ejpam-1951	221	15	[	[	X
ejpam-1951	221	16	p1	p1	NOUN
ejpam-1951	221	17	,	,	PUNCT
ejpam-1951	221	18	p2	p2	NOUN
ejpam-1951	221	19	,	,	PUNCT
ejpam-1951	221	20	.	.	PUNCT
ejpam-1951	221	21	.	.	PUNCT
ejpam-1951	221	22	.	.	PUNCT
ejpam-1951	222	1	,	,	PUNCT
ejpam-1951	222	2	pk	pk	NOUN
ejpam-1951	222	3	]	]	X
ejpam-1951	222	4	is	be	AUX
ejpam-1951	222	5	equal	equal	ADJ
ejpam-1951	222	6	to	to	ADP
ejpam-1951	222	7	the	the	DET
ejpam-1951	222	8	coefficient	coefficient	NOUN
ejpam-1951	222	9	of	of	ADP
ejpam-1951	222	10	the	the	DET
ejpam-1951	222	11	term	term	NOUN
ejpam-1951	222	12	c	c	PROPN
ejpam-1951	222	13	p1	p1	PROPN
ejpam-1951	222	14	1	1	NUM
ejpam-1951	222	15	c	c	NOUN
ejpam-1951	222	16	p2	p2	PROPN
ejpam-1951	222	17	2	2	NUM
ejpam-1951	222	18	.	.	PUNCT
ejpam-1951	222	19	.	.	PUNCT
ejpam-1951	222	20	.	.	PUNCT
ejpam-1951	223	1	c	c	PROPN
ejpam-1951	223	2	pk	pk	PROPN
ejpam-1951	223	3	k	k	PROPN
ejpam-1951	223	4	in	in	ADP
ejpam-1951	223	5	σ(c1	σ(c1	PROPN
ejpam-1951	223	6	,	,	PUNCT
ejpam-1951	223	7	c2	c2	PROPN
ejpam-1951	223	8	,	,	PUNCT
ejpam-1951	223	9	.	.	PUNCT
ejpam-1951	223	10	.	.	PUNCT
ejpam-1951	224	1	.	.	PUNCT
ejpam-1951	225	1	,	,	PUNCT
ejpam-1951	225	2	ck	ck	X
ejpam-1951	225	3	)	)	PUNCT
ejpam-1951	226	1	[	[	X
ejpam-1951	226	2	3	3	NUM
ejpam-1951	226	3	]	]	PUNCT
ejpam-1951	226	4	.	.	PUNCT
ejpam-1951	227	1	then	then	ADV
ejpam-1951	227	2	we	we	PRON
ejpam-1951	227	3	find	find	VERB
ejpam-1951	227	4	the	the	DET
ejpam-1951	227	5	generating	generate	VERB
ejpam-1951	227	6	function	function	NOUN
ejpam-1951	227	7	zg	zg	PROPN
ejpam-1951	227	8	k	k	NOUN
ejpam-1951	227	9	∑	∑	PROPN
ejpam-1951	227	10	i=1	i=1	PROPN
ejpam-1951	227	11	ci	ci	PROPN
ejpam-1951	227	12	,	,	PUNCT
ejpam-1951	228	1	k	k	PROPN
ejpam-1951	228	2	∑	∑	PUNCT
ejpam-1951	228	3	i=1	i=1	PROPN
ejpam-1951	228	4	c2	c2	PROPN
ejpam-1951	228	5	i	i	PRON
ejpam-1951	228	6	,	,	PUNCT
ejpam-1951	228	7	.	.	PUNCT
ejpam-1951	228	8	.	.	PUNCT
ejpam-1951	228	9	.	.	PUNCT
ejpam-1951	229	1	,	,	PUNCT
ejpam-1951	230	1	k	k	PROPN
ejpam-1951	230	2	∑	∑	PUNCT
ejpam-1951	230	3	i=1	i=1	PROPN
ejpam-1951	231	1	cn	cn	INTJ
ejpam-1951	232	1	i	i	PRON
ejpam-1951	232	2	!	!	PUNCT
ejpam-1951	233	1	,	,	PUNCT
ejpam-1951	233	2	where	where	SCONJ
ejpam-1951	233	3	n	n	PRON
ejpam-1951	233	4	stands	stand	VERB
ejpam-1951	233	5	for	for	ADP
ejpam-1951	233	6	the	the	DET
ejpam-1951	233	7	largest	large	ADJ
ejpam-1951	233	8	cycle	cycle	NOUN
ejpam-1951	233	9	length	length	NOUN
ejpam-1951	233	10	.	.	PUNCT
ejpam-1951	234	1	this	this	PRON
ejpam-1951	234	2	is	be	AUX
ejpam-1951	234	3	known	know	VERB
ejpam-1951	234	4	as	as	ADP
ejpam-1951	234	5	pólya	pólya	NOUN
ejpam-1951	234	6	’s	’s	PART
ejpam-1951	234	7	enumeration	enumeration	NOUN
ejpam-1951	234	8	formula	formula	NOUN
ejpam-1951	234	9	.	.	PUNCT
ejpam-1951	235	1	t.	t.	PROPN
ejpam-1951	235	2	nasseef	nasseef	PROPN
ejpam-1951	235	3	/	/	SYM
ejpam-1951	235	4	eur	eur	PROPN
ejpam-1951	235	5	.	.	PUNCT
ejpam-1951	236	1	j.	j.	PROPN
ejpam-1951	236	2	pure	pure	PROPN
ejpam-1951	236	3	appl	appl	PROPN
ejpam-1951	236	4	.	.	PROPN
ejpam-1951	236	5	math	math	PROPN
ejpam-1951	236	6	,	,	PUNCT
ejpam-1951	236	7	9	9	NUM
ejpam-1951	236	8	(	(	PUNCT
ejpam-1951	236	9	2016	2016	NUM
ejpam-1951	236	10	)	)	PUNCT
ejpam-1951	236	11	,	,	PUNCT
ejpam-1951	236	12	84	84	NUM
ejpam-1951	236	13	-	-	SYM
ejpam-1951	236	14	113	113	NUM
ejpam-1951	236	15	93	93	NUM
ejpam-1951	236	16	problem	problem	NOUN
ejpam-1951	236	17	1	1	NUM
ejpam-1951	236	18	(	(	PUNCT
ejpam-1951	236	19	edge	edge	NOUN
ejpam-1951	236	20	coloring	coloring	NOUN
ejpam-1951	236	21	of	of	ADP
ejpam-1951	236	22	a	a	DET
ejpam-1951	236	23	tetrahedron	tetrahedron	NOUN
ejpam-1951	236	24	)	)	PUNCT
ejpam-1951	236	25	.	.	PUNCT
ejpam-1951	237	1	a	a	DET
ejpam-1951	237	2	tetrahedron	tetrahedron	NOUN
ejpam-1951	237	3	has	have	VERB
ejpam-1951	237	4	6	6	NUM
ejpam-1951	237	5	edges	edge	NOUN
ejpam-1951	237	6	.	.	PUNCT
ejpam-1951	238	1	how	how	SCONJ
ejpam-1951	238	2	many	many	ADJ
ejpam-1951	238	3	inequivalent	inequivalent	NOUN
ejpam-1951	238	4	ways	way	NOUN
ejpam-1951	238	5	are	be	AUX
ejpam-1951	238	6	there	there	ADV
ejpam-1951	238	7	to	to	PART
ejpam-1951	238	8	color	color	VERB
ejpam-1951	238	9	it	it	PRON
ejpam-1951	238	10	with	with	ADP
ejpam-1951	238	11	(	(	PUNCT
ejpam-1951	238	12	a	a	X
ejpam-1951	238	13	)	)	PUNCT
ejpam-1951	238	14	2	2	NUM
ejpam-1951	238	15	colors	color	NOUN
ejpam-1951	238	16	?	?	PUNCT
ejpam-1951	239	1	(	(	PUNCT
ejpam-1951	239	2	b	b	X
ejpam-1951	239	3	)	)	PUNCT
ejpam-1951	239	4	3	3	NUM
ejpam-1951	239	5	black	black	ADJ
ejpam-1951	239	6	and	and	CCONJ
ejpam-1951	239	7	3	3	NUM
ejpam-1951	239	8	yellow	yellow	ADJ
ejpam-1951	239	9	edges	edge	NOUN
ejpam-1951	239	10	?	?	PUNCT
ejpam-1951	240	1	solution	solution	NOUN
ejpam-1951	240	2	:	:	PUNCT
ejpam-1951	240	3	first	first	ADV
ejpam-1951	240	4	we	we	PRON
ejpam-1951	240	5	need	need	VERB
ejpam-1951	240	6	to	to	PART
ejpam-1951	240	7	find	find	VERB
ejpam-1951	240	8	out	out	ADP
ejpam-1951	240	9	the	the	DET
ejpam-1951	240	10	symmetries	symmetry	NOUN
ejpam-1951	240	11	of	of	ADP
ejpam-1951	240	12	the	the	DET
ejpam-1951	240	13	tetrahedron	tetrahedron	NOUN
ejpam-1951	240	14	with	with	ADP
ejpam-1951	240	15	permutations	permutation	NOUN
ejpam-1951	240	16	of	of	ADP
ejpam-1951	240	17	the	the	DET
ejpam-1951	240	18	edges	edge	NOUN
ejpam-1951	240	19	.	.	PUNCT
ejpam-1951	241	1	let	let	VERB
ejpam-1951	241	2	us	we	PRON
ejpam-1951	241	3	consider	consider	VERB
ejpam-1951	241	4	the	the	DET
ejpam-1951	241	5	set	set	NOUN
ejpam-1951	241	6	a	a	PRON
ejpam-1951	241	7	of	of	ADP
ejpam-1951	241	8	the	the	DET
ejpam-1951	241	9	edges	edge	NOUN
ejpam-1951	241	10	of	of	ADP
ejpam-1951	241	11	a	a	DET
ejpam-1951	241	12	tetrahedron	tetrahedron	NOUN
ejpam-1951	241	13	and	and	CCONJ
ejpam-1951	241	14	g	g	NOUN
ejpam-1951	241	15	be	be	AUX
ejpam-1951	241	16	the	the	DET
ejpam-1951	241	17	set	set	NOUN
ejpam-1951	241	18	of	of	ADP
ejpam-1951	241	19	permutations	permutation	NOUN
ejpam-1951	241	20	of	of	ADP
ejpam-1951	241	21	a	a	PRON
ejpam-1951	241	22	which	which	PRON
ejpam-1951	241	23	will	will	AUX
ejpam-1951	241	24	be	be	AUX
ejpam-1951	241	25	produced	produce	VERB
ejpam-1951	241	26	by	by	ADP
ejpam-1951	241	27	rotating	rotate	VERB
ejpam-1951	241	28	the	the	DET
ejpam-1951	241	29	tetrahedron	tetrahedron	NOUN
ejpam-1951	241	30	.	.	PUNCT
ejpam-1951	242	1	their	their	PRON
ejpam-1951	242	2	cyclic	cyclic	ADJ
ejpam-1951	242	3	structures	structure	NOUN
ejpam-1951	242	4	are	be	AUX
ejpam-1951	242	5	given	give	VERB
ejpam-1951	242	6	as	as	SCONJ
ejpam-1951	242	7	follows	follow	VERB
ejpam-1951	242	8	(	(	PUNCT
ejpam-1951	242	9	i	i	NOUN
ejpam-1951	242	10	)	)	PUNCT
ejpam-1951	242	11	the	the	DET
ejpam-1951	242	12	identity	identity	NOUN
ejpam-1951	242	13	leaves	leave	VERB
ejpam-1951	242	14	all	all	DET
ejpam-1951	242	15	6	6	NUM
ejpam-1951	242	16	edges	edge	NOUN
ejpam-1951	242	17	fixed	fix	VERB
ejpam-1951	242	18	with	with	ADP
ejpam-1951	242	19	structure	structure	NOUN
ejpam-1951	242	20	t6	t6	PROPN
ejpam-1951	242	21	1	1	NUM
ejpam-1951	242	22	.	.	PUNCT
ejpam-1951	243	1	(	(	PUNCT
ejpam-1951	243	2	ii	ii	NOUN
ejpam-1951	243	3	)	)	PUNCT
ejpam-1951	243	4	there	there	PRON
ejpam-1951	243	5	are	be	VERB
ejpam-1951	243	6	four	four	NUM
ejpam-1951	243	7	120	120	NUM
ejpam-1951	243	8	◦	◦	NOUN
ejpam-1951	243	9	rotations	rotation	NOUN
ejpam-1951	243	10	about	about	ADP
ejpam-1951	243	11	a	a	DET
ejpam-1951	243	12	corner	corner	NOUN
ejpam-1951	243	13	and	and	CCONJ
ejpam-1951	243	14	the	the	DET
ejpam-1951	243	15	middle	middle	NOUN
ejpam-1951	243	16	of	of	ADP
ejpam-1951	243	17	the	the	DET
ejpam-1951	243	18	opposite	opposite	ADJ
ejpam-1951	243	19	face	face	NOUN
ejpam-1951	243	20	(	(	PUNCT
ejpam-1951	243	21	fig	fig	NOUN
ejpam-1951	243	22	.	.	PUNCT
ejpam-1951	244	1	3	3	NUM
ejpam-1951	244	2	)	)	PUNCT
ejpam-1951	244	3	.	.	PUNCT
ejpam-1951	245	1	they	they	PRON
ejpam-1951	245	2	are	be	AUX
ejpam-1951	245	3	two	two	NUM
ejpam-1951	245	4	cycles	cycle	NOUN
ejpam-1951	245	5	of	of	ADP
ejpam-1951	245	6	length	length	NOUN
ejpam-1951	245	7	three	three	NUM
ejpam-1951	245	8	.	.	PUNCT
ejpam-1951	246	1	they	they	PRON
ejpam-1951	246	2	cyclically	cyclically	ADV
ejpam-1951	246	3	permute	permute	VERB
ejpam-1951	246	4	the	the	DET
ejpam-1951	246	5	edges	edge	NOUN
ejpam-1951	246	6	incident	incident	NOUN
ejpam-1951	246	7	to	to	ADP
ejpam-1951	246	8	that	that	DET
ejpam-1951	246	9	corner	corner	NOUN
ejpam-1951	246	10	and	and	CCONJ
ejpam-1951	246	11	also	also	ADV
ejpam-1951	246	12	the	the	DET
ejpam-1951	246	13	edges	edge	NOUN
ejpam-1951	246	14	bounding	bound	VERB
ejpam-1951	246	15	the	the	DET
ejpam-1951	246	16	opposite	opposite	ADJ
ejpam-1951	246	17	face	face	NOUN
ejpam-1951	246	18	,	,	PUNCT
ejpam-1951	246	19	so	so	CCONJ
ejpam-1951	246	20	the	the	DET
ejpam-1951	246	21	cycle	cycle	NOUN
ejpam-1951	246	22	structure	structure	NOUN
ejpam-1951	246	23	representation	representation	NOUN
ejpam-1951	246	24	is	be	AUX
ejpam-1951	246	25	t2	t2	NOUN
ejpam-1951	246	26	3	3	NUM
ejpam-1951	246	27	.	.	PUNCT
ejpam-1951	247	1	(	(	PUNCT
ejpam-1951	247	2	iii	iii	X
ejpam-1951	247	3	)	)	PUNCT
ejpam-1951	247	4	there	there	PRON
ejpam-1951	247	5	are	be	VERB
ejpam-1951	247	6	four	four	NUM
ejpam-1951	247	7	240	240	NUM
ejpam-1951	247	8	◦	◦	NOUN
ejpam-1951	247	9	rotations	rotation	NOUN
ejpam-1951	247	10	as	as	ADP
ejpam-1951	247	11	like	like	ADP
ejpam-1951	247	12	the	the	DET
ejpam-1951	247	13	120	120	NUM
ejpam-1951	247	14	◦	◦	NOUN
ejpam-1951	247	15	rotations	rotation	NOUN
ejpam-1951	247	16	(	(	PUNCT
ejpam-1951	247	17	fig	fig	NOUN
ejpam-1951	247	18	.	.	PUNCT
ejpam-1951	248	1	3	3	NUM
ejpam-1951	248	2	)	)	PUNCT
ejpam-1951	248	3	.	.	PUNCT
ejpam-1951	249	1	so	so	ADV
ejpam-1951	249	2	the	the	DET
ejpam-1951	249	3	cycle	cycle	NOUN
ejpam-1951	249	4	structure	structure	NOUN
ejpam-1951	249	5	is	be	AUX
ejpam-1951	249	6	also	also	ADV
ejpam-1951	249	7	same	same	ADJ
ejpam-1951	249	8	.	.	PUNCT
ejpam-1951	250	1	(	(	PUNCT
ejpam-1951	250	2	iv	iv	X
ejpam-1951	250	3	)	)	PUNCT
ejpam-1951	250	4	there	there	PRON
ejpam-1951	250	5	are	be	VERB
ejpam-1951	250	6	three	three	NUM
ejpam-1951	250	7	180	180	NUM
ejpam-1951	250	8	◦	◦	NOUN
ejpam-1951	250	9	rotations	rotation	NOUN
ejpam-1951	250	10	about	about	ADP
ejpam-1951	250	11	opposite	opposite	ADJ
ejpam-1951	250	12	edges	edge	NOUN
ejpam-1951	250	13	leave	leave	VERB
ejpam-1951	250	14	the	the	DET
ejpam-1951	250	15	two	two	NUM
ejpam-1951	250	16	edges	edge	NOUN
ejpam-1951	250	17	fixed	fix	VERB
ejpam-1951	250	18	.	.	PUNCT
ejpam-1951	251	1	the	the	DET
ejpam-1951	251	2	other	other	ADJ
ejpam-1951	251	3	four	four	NUM
ejpam-1951	251	4	edges	edge	NOUN
ejpam-1951	251	5	are	be	AUX
ejpam-1951	251	6	left	leave	VERB
ejpam-1951	251	7	in	in	ADP
ejpam-1951	251	8	cycles	cycle	NOUN
ejpam-1951	251	9	of	of	ADP
ejpam-1951	251	10	length	length	NOUN
ejpam-1951	251	11	2	2	NUM
ejpam-1951	251	12	.	.	PUNCT
ejpam-1951	252	1	thus	thus	ADV
ejpam-1951	252	2	we	we	PRON
ejpam-1951	252	3	have	have	VERB
ejpam-1951	252	4	the	the	DET
ejpam-1951	252	5	cycle	cycle	NOUN
ejpam-1951	252	6	structure	structure	NOUN
ejpam-1951	252	7	t2	t2	NOUN
ejpam-1951	252	8	1	1	NUM
ejpam-1951	252	9	t2	t2	NOUN
ejpam-1951	252	10	2	2	NUM
ejpam-1951	253	1	[	[	X
ejpam-1951	253	2	7	7	NUM
ejpam-1951	253	3	]	]	PUNCT
ejpam-1951	253	4	.	.	PUNCT
ejpam-1951	254	1	figure	figure	VERB
ejpam-1951	254	2	3	3	NUM
ejpam-1951	254	3	:	:	PUNCT
ejpam-1951	254	4	rotation	rotation	NOUN
ejpam-1951	254	5	of	of	ADP
ejpam-1951	254	6	tetrahedron	tetrahedron	NOUN
ejpam-1951	254	7	by	by	ADP
ejpam-1951	254	8	120	120	NUM
ejpam-1951	254	9	◦	◦	NOUN
ejpam-1951	254	10	and	and	CCONJ
ejpam-1951	254	11	240	240	NUM
ejpam-1951	254	12	◦	◦	NOUN
ejpam-1951	254	13	t.	t.	NOUN
ejpam-1951	254	14	nasseef	nasseef	PROPN
ejpam-1951	254	15	/	/	SYM
ejpam-1951	254	16	eur	eur	PROPN
ejpam-1951	254	17	.	.	PUNCT
ejpam-1951	255	1	j.	j.	PROPN
ejpam-1951	255	2	pure	pure	PROPN
ejpam-1951	255	3	appl	appl	PROPN
ejpam-1951	255	4	.	.	PROPN
ejpam-1951	255	5	math	math	PROPN
ejpam-1951	255	6	,	,	PUNCT
ejpam-1951	255	7	9	9	NUM
ejpam-1951	255	8	(	(	PUNCT
ejpam-1951	255	9	2016	2016	NUM
ejpam-1951	255	10	)	)	PUNCT
ejpam-1951	255	11	,	,	PUNCT
ejpam-1951	255	12	84	84	NUM
ejpam-1951	255	13	-	-	SYM
ejpam-1951	255	14	113	113	NUM
ejpam-1951	255	15	94	94	NUM
ejpam-1951	255	16	then	then	ADV
ejpam-1951	255	17	by	by	ADP
ejpam-1951	255	18	burnside	burnside	PROPN
ejpam-1951	255	19	’s	’s	PART
ejpam-1951	255	20	lemma	lemma	PROPN
ejpam-1951	255	21	we	we	PRON
ejpam-1951	255	22	have	have	VERB
ejpam-1951	255	23	z(g	z(g	NOUN
ejpam-1951	255	24	,	,	PUNCT
ejpam-1951	255	25	t1	t1	NOUN
ejpam-1951	255	26	,	,	PUNCT
ejpam-1951	255	27	t2	t2	NOUN
ejpam-1951	255	28	,	,	PUNCT
ejpam-1951	255	29	.	.	PUNCT
ejpam-1951	255	30	.	.	PUNCT
ejpam-1951	256	1	.	.	PUNCT
ejpam-1951	257	1	,	,	PUNCT
ejpam-1951	257	2	t6	t6	PROPN
ejpam-1951	257	3	)	)	PUNCT
ejpam-1951	257	4	=	=	PUNCT
ejpam-1951	258	1	1	1	NUM
ejpam-1951	258	2	12	12	NUM
ejpam-1951	258	3	(	(	PUNCT
ejpam-1951	258	4	t6	t6	PROPN
ejpam-1951	258	5	1	1	NUM
ejpam-1951	258	6	+	+	CCONJ
ejpam-1951	258	7	8t2	8t2	NUM
ejpam-1951	258	8	3	3	NUM
ejpam-1951	258	9	+	+	SYM
ejpam-1951	258	10	3t2	3t2	NUM
ejpam-1951	258	11	1	1	NUM
ejpam-1951	258	12	t2	t2	NOUN
ejpam-1951	258	13	2	2	NUM
ejpam-1951	258	14	)	)	PUNCT
ejpam-1951	258	15	(	(	PUNCT
ejpam-1951	258	16	a	a	X
ejpam-1951	258	17	)	)	PUNCT
ejpam-1951	258	18	the	the	DET
ejpam-1951	258	19	number	number	NOUN
ejpam-1951	258	20	of	of	ADP
ejpam-1951	258	21	distinct	distinct	ADJ
ejpam-1951	258	22	2	2	NUM
ejpam-1951	258	23	colorings	coloring	NOUN
ejpam-1951	258	24	on	on	ADP
ejpam-1951	258	25	tetrahedron	tetrahedron	NOUN
ejpam-1951	258	26	edge	edge	NOUN
ejpam-1951	258	27	will	will	AUX
ejpam-1951	258	28	be	be	AUX
ejpam-1951	258	29	zg	zg	NOUN
ejpam-1951	258	30	=	=	SYM
ejpam-1951	258	31	1	1	NUM
ejpam-1951	258	32	12	12	NUM
ejpam-1951	258	33	(	(	PUNCT
ejpam-1951	258	34	26	26	NUM
ejpam-1951	258	35	+	+	NUM
ejpam-1951	258	36	8(22	8(22	NUM
ejpam-1951	258	37	)	)	PUNCT
ejpam-1951	259	1	+	+	CCONJ
ejpam-1951	259	2	3(22)(22	3(22)(22	NOUN
ejpam-1951	259	3	)	)	PUNCT
ejpam-1951	259	4	)	)	PUNCT
ejpam-1951	260	1	=	=	SYM
ejpam-1951	260	2	12	12	NUM
ejpam-1951	260	3	(	(	PUNCT
ejpam-1951	260	4	b	b	NOUN
ejpam-1951	260	5	)	)	PUNCT
ejpam-1951	260	6	now	now	ADV
ejpam-1951	260	7	we	we	PRON
ejpam-1951	260	8	will	will	AUX
ejpam-1951	260	9	apply	apply	VERB
ejpam-1951	260	10	pólya	pólya	NOUN
ejpam-1951	260	11	’s	’s	PART
ejpam-1951	260	12	substitution	substitution	NOUN
ejpam-1951	260	13	method	method	NOUN
ejpam-1951	260	14	.	.	PUNCT
ejpam-1951	261	1	let	let	VERB
ejpam-1951	261	2	the	the	DET
ejpam-1951	261	3	colors	color	NOUN
ejpam-1951	261	4	black	black	ADJ
ejpam-1951	261	5	and	and	CCONJ
ejpam-1951	261	6	yellow	yellow	ADJ
ejpam-1951	261	7	be	be	AUX
ejpam-1951	261	8	denoted	denote	VERB
ejpam-1951	261	9	by	by	ADP
ejpam-1951	261	10	x	x	PUNCT
ejpam-1951	261	11	and	and	CCONJ
ejpam-1951	261	12	y	y	PROPN
ejpam-1951	261	13	respectively	respectively	ADV
ejpam-1951	261	14	.	.	PUNCT
ejpam-1951	262	1	then	then	ADV
ejpam-1951	262	2	substituting	substitute	VERB
ejpam-1951	262	3	t	t	PROPN
ejpam-1951	262	4	i	i	PRON
ejpam-1951	262	5	→	→	PUNCT
ejpam-1951	262	6	(	(	PUNCT
ejpam-1951	262	7	x	x	X
ejpam-1951	262	8	i	i	PRON
ejpam-1951	262	9	+	+	NUM
ejpam-1951	262	10	y	y	PROPN
ejpam-1951	262	11	i	i	PROPN
ejpam-1951	262	12	)	)	PUNCT
ejpam-1951	262	13	for	for	ADP
ejpam-1951	262	14	each	each	DET
ejpam-1951	262	15	i	i	PRON
ejpam-1951	262	16	=	=	PUNCT
ejpam-1951	262	17	{	{	PUNCT
ejpam-1951	262	18	1,2,3,4,5,6	1,2,3,4,5,6	NUM
ejpam-1951	262	19	}	}	PUNCT
ejpam-1951	262	20	in	in	ADP
ejpam-1951	262	21	the	the	DET
ejpam-1951	262	22	previous	previous	ADJ
ejpam-1951	262	23	equation	equation	NOUN
ejpam-1951	262	24	,	,	PUNCT
ejpam-1951	262	25	we	we	PRON
ejpam-1951	262	26	get	get	VERB
ejpam-1951	262	27	zg	zg	NOUN
ejpam-1951	262	28	=	=	NOUN
ejpam-1951	262	29	1	1	NUM
ejpam-1951	262	30	12	12	NUM
ejpam-1951	262	31	(	(	PUNCT
ejpam-1951	262	32	(	(	PUNCT
ejpam-1951	262	33	x	x	SYM
ejpam-1951	262	34	+	+	PUNCT
ejpam-1951	262	35	y)6	y)6	PROPN
ejpam-1951	262	36	+	+	CCONJ
ejpam-1951	262	37	8(x3	8(x3	NUM
ejpam-1951	263	1	+	+	NUM
ejpam-1951	263	2	y3)2	y3)2	PROPN
ejpam-1951	263	3	+	+	NUM
ejpam-1951	263	4	3(x	3(x	NUM
ejpam-1951	263	5	+	+	CCONJ
ejpam-1951	263	6	y)2(x2	y)2(x2	NOUN
ejpam-1951	263	7	+	+	CCONJ
ejpam-1951	263	8	y2)2	y2)2	X
ejpam-1951	263	9	)	)	PUNCT
ejpam-1951	263	10	by	by	ADP
ejpam-1951	263	11	maple	maple	NOUN
ejpam-1951	263	12	we	we	PRON
ejpam-1951	263	13	get	get	VERB
ejpam-1951	263	14	,	,	PUNCT
ejpam-1951	264	1	zg	zg	PROPN
ejpam-1951	264	2	=	=	SYM
ejpam-1951	264	3	x6	x6	PROPN
ejpam-1951	264	4	+	+	CCONJ
ejpam-1951	264	5	x5	x5	PROPN
ejpam-1951	264	6	y	y	PROPN
ejpam-1951	264	7	+	+	CCONJ
ejpam-1951	264	8	2x4	2x4	NUM
ejpam-1951	264	9	y2	y2	NOUN
ejpam-1951	264	10	+	+	CCONJ
ejpam-1951	264	11	4x3	4x3	NUM
ejpam-1951	264	12	y3	y3	NOUN
ejpam-1951	264	13	+	+	CCONJ
ejpam-1951	264	14	2x2	2x2	NUM
ejpam-1951	264	15	y4	y4	ADJ
ejpam-1951	264	16	+	+	CCONJ
ejpam-1951	264	17	x	x	PUNCT
ejpam-1951	264	18	y5	y5	NOUN
ejpam-1951	264	19	+	+	CCONJ
ejpam-1951	264	20	y6	y6	ADJ
ejpam-1951	264	21	the	the	DET
ejpam-1951	264	22	term	term	NOUN
ejpam-1951	264	23	4x3	4x3	NUM
ejpam-1951	264	24	y3	y3	NOUN
ejpam-1951	264	25	contains	contain	VERB
ejpam-1951	264	26	tetrahedron	tetrahedron	NOUN
ejpam-1951	264	27	with	with	ADP
ejpam-1951	264	28	3	3	NUM
ejpam-1951	264	29	black	black	ADJ
ejpam-1951	264	30	and	and	CCONJ
ejpam-1951	264	31	3	3	NUM
ejpam-1951	264	32	yellow	yellow	ADJ
ejpam-1951	264	33	edges	edge	NOUN
ejpam-1951	264	34	.	.	PUNCT
ejpam-1951	265	1	the	the	DET
ejpam-1951	265	2	coefficient	coefficient	NOUN
ejpam-1951	265	3	of	of	ADP
ejpam-1951	265	4	this	this	DET
ejpam-1951	265	5	term	term	NOUN
ejpam-1951	265	6	is	be	AUX
ejpam-1951	265	7	4	4	NUM
ejpam-1951	265	8	.	.	PUNCT
ejpam-1951	266	1	hence	hence	ADV
ejpam-1951	266	2	there	there	PRON
ejpam-1951	266	3	are	be	VERB
ejpam-1951	266	4	4	4	NUM
ejpam-1951	266	5	ways	way	NOUN
ejpam-1951	266	6	to	to	PART
ejpam-1951	266	7	color	color	VERB
ejpam-1951	266	8	the	the	DET
ejpam-1951	266	9	edge	edge	NOUN
ejpam-1951	266	10	of	of	ADP
ejpam-1951	266	11	tetrahedron	tetrahedron	NOUN
ejpam-1951	266	12	.	.	PUNCT
ejpam-1951	267	1	2.4	2.4	NUM
ejpam-1951	267	2	.	.	PUNCT
ejpam-1951	268	1	pólya	pólya	NOUN
ejpam-1951	268	2	’s	’s	PART
ejpam-1951	268	3	fundamental	fundamental	ADJ
ejpam-1951	268	4	theorem	theorem	NOUN
ejpam-1951	268	5	theorem	theorem	NOUN
ejpam-1951	268	6	2	2	NUM
ejpam-1951	268	7	.	.	PUNCT
ejpam-1951	269	1	the	the	DET
ejpam-1951	269	2	pattern	pattern	NOUN
ejpam-1951	269	3	inventory	inventory	NOUN
ejpam-1951	269	4	is	be	AUX
ejpam-1951	269	5	p	p	PROPN
ejpam-1951	269	6	i	i	PROPN
ejpam-1951	269	7	=	=	PROPN
ejpam-1951	269	8	zg	zg	PROPN
ejpam-1951	269	9	(	(	PUNCT
ejpam-1951	269	10	∑	∑	PART
ejpam-1951	269	11	c∈c	c∈c	PROPN
ejpam-1951	269	12	wc	wc	PROPN
ejpam-1951	269	13	,	,	PUNCT
ejpam-1951	269	14	∑	∑	PART
ejpam-1951	269	15	c∈c	c∈c	NOUN
ejpam-1951	269	16	w2	w2	PROPN
ejpam-1951	269	17	c	c	PROPN
ejpam-1951	269	18	,	,	PUNCT
ejpam-1951	269	19	∑	∑	PART
ejpam-1951	269	20	c∈c	c∈c	PROPN
ejpam-1951	269	21	w3	w3	PROPN
ejpam-1951	269	22	c	c	PROPN
ejpam-1951	269	23	,	,	PUNCT
ejpam-1951	269	24	.	.	PUNCT
ejpam-1951	269	25	.	.	PUNCT
ejpam-1951	269	26	.	.	PUNCT
ejpam-1951	270	1	,	,	PUNCT
ejpam-1951	270	2	∑	∑	PUNCT
ejpam-1951	270	3	c∈c	c∈c	VERB
ejpam-1951	270	4	wp	wp	PROPN
ejpam-1951	270	5	c	c	PROPN
ejpam-1951	270	6	)	)	PUNCT
ejpam-1951	270	7	where	where	SCONJ
ejpam-1951	270	8	zg	zg	PROPN
ejpam-1951	270	9	is	be	AUX
ejpam-1951	270	10	the	the	DET
ejpam-1951	270	11	cycle	cycle	NOUN
ejpam-1951	270	12	index	index	NOUN
ejpam-1951	270	13	and	and	CCONJ
ejpam-1951	270	14	p	p	NOUN
ejpam-1951	270	15	=	=	PROPN
ejpam-1951	270	16	|d|	|d|	PROPN
ejpam-1951	271	1	[	[	X
ejpam-1951	271	2	2	2	NUM
ejpam-1951	271	3	]	]	PUNCT
ejpam-1951	271	4	.	.	PUNCT
ejpam-1951	272	1	proof	proof	NOUN
ejpam-1951	272	2	.	.	PUNCT
ejpam-1951	273	1	let	let	VERB
ejpam-1951	273	2	x	x	PUNCT
ejpam-1951	274	1	=	=	SYM
ejpam-1951	274	2	x1	x1	PROPN
ejpam-1951	274	3	∪	∪	VERB
ejpam-1951	274	4	x2	x2	NOUN
ejpam-1951	274	5	∪	∪	NOUN
ejpam-1951	274	6	.	.	PUNCT
ejpam-1951	274	7	.	.	PUNCT
ejpam-1951	275	1	.∪	.∪	PROPN
ejpam-1951	276	1	xm	xm	PROPN
ejpam-1951	276	2	be	be	AUX
ejpam-1951	276	3	the	the	DET
ejpam-1951	276	4	equivalence	equivalence	NOUN
ejpam-1951	276	5	classes	class	NOUN
ejpam-1951	276	6	of	of	ADP
ejpam-1951	276	7	x	x	PUNCT
ejpam-1951	276	8	under	under	ADP
ejpam-1951	276	9	the	the	DET
ejpam-1951	276	10	relation	relation	NOUN
ejpam-1951	276	11	x	x	PUNCT
ejpam-1951	276	12	∼	∼	NOUN
ejpam-1951	276	13	y	y	NOUN
ejpam-1951	276	14	if	if	SCONJ
ejpam-1951	276	15	and	and	CCONJ
ejpam-1951	276	16	only	only	ADV
ejpam-1951	276	17	if	if	SCONJ
ejpam-1951	276	18	w	w	PROPN
ejpam-1951	276	19	(	(	PUNCT
ejpam-1951	276	20	x	x	NOUN
ejpam-1951	276	21	)	)	PUNCT
ejpam-1951	277	1	=	=	NOUN
ejpam-1951	277	2	w	w	PROPN
ejpam-1951	277	3	(	(	PUNCT
ejpam-1951	277	4	y	y	NOUN
ejpam-1951	277	5	)	)	PUNCT
ejpam-1951	277	6	by	by	ADP
ejpam-1951	277	7	orbit	orbit	NOUN
ejpam-1951	277	8	-	-	PUNCT
ejpam-1951	277	9	stabilizer	stabilizer	NOUN
ejpam-1951	277	10	formula	formula	NOUN
ejpam-1951	277	11	,	,	PUNCT
ejpam-1951	277	12	g	g	NOUN
ejpam-1951	277	13	∗	∗	NOUN
ejpam-1951	277	14	x	x	PUNCT
ejpam-1951	277	15	∼	∼	NOUN
ejpam-1951	277	16	x	x	PUNCT
ejpam-1951	277	17	for	for	ADP
ejpam-1951	277	18	all	all	DET
ejpam-1951	277	19	x	x	SYM
ejpam-1951	277	20	∈	∈	PROPN
ejpam-1951	277	21	x	x	X
ejpam-1951	277	22	,	,	PUNCT
ejpam-1951	277	23	g	g	PROPN
ejpam-1951	277	24	∈	∈	PROPN
ejpam-1951	277	25	g	g	PROPN
ejpam-1951	278	1	and	and	CCONJ
ejpam-1951	278	2	so	so	ADV
ejpam-1951	278	3	we	we	PRON
ejpam-1951	278	4	can	can	AUX
ejpam-1951	278	5	think	think	VERB
ejpam-1951	278	6	of	of	ADP
ejpam-1951	278	7	g	g	NOUN
ejpam-1951	278	8	acting	act	VERB
ejpam-1951	278	9	on	on	ADP
ejpam-1951	278	10	each	each	PRON
ejpam-1951	278	11	x	x	NOUN
ejpam-1951	279	1	i	i	PRON
ejpam-1951	279	2	individually	individually	ADV
ejpam-1951	279	3	.	.	PUNCT
ejpam-1951	280	1	we	we	PRON
ejpam-1951	280	2	use	use	VERB
ejpam-1951	280	3	the	the	DET
ejpam-1951	280	4	fact	fact	NOUN
ejpam-1951	280	5	that	that	SCONJ
ejpam-1951	280	6	x	x	PUNCT
ejpam-1951	280	7	∈	∈	NOUN
ejpam-1951	280	8	x	x	PUNCT
ejpam-1951	280	9	i	i	PRON
ejpam-1951	280	10	implies	imply	VERB
ejpam-1951	280	11	g	g	PROPN
ejpam-1951	280	12	∗	∗	NOUN
ejpam-1951	280	13	x	x	PUNCT
ejpam-1951	280	14	∈	∈	NOUN
ejpam-1951	280	15	x	x	PUNCT
ejpam-1951	280	16	i	i	PRON
ejpam-1951	280	17	for	for	ADP
ejpam-1951	280	18	all	all	PRON
ejpam-1951	280	19	i	i	PRON
ejpam-1951	280	20	∈	∈	PROPN
ejpam-1951	281	1	[	[	X
ejpam-1951	281	2	m	m	X
ejpam-1951	281	3	]	]	X
ejpam-1951	281	4	,	,	PUNCT
ejpam-1951	281	5	g	g	PROPN
ejpam-1951	281	6	∈	∈	PROPN
ejpam-1951	281	7	g.	g.	NOUN
ejpam-1951	281	8	we	we	PRON
ejpam-1951	281	9	use	use	VERB
ejpam-1951	281	10	the	the	DET
ejpam-1951	281	11	notation	notation	NOUN
ejpam-1951	281	12	g(i	g(i	PROPN
ejpam-1951	281	13	)	)	PUNCT
ejpam-1951	281	14	∈	∈	PROPN
ejpam-1951	281	15	g(i	g(i	PROPN
ejpam-1951	281	16	)	)	PUNCT
ejpam-1951	281	17	when	when	SCONJ
ejpam-1951	281	18	we	we	PRON
ejpam-1951	281	19	restrict	restrict	VERB
ejpam-1951	281	20	attention	attention	NOUN
ejpam-1951	281	21	to	to	ADP
ejpam-1951	281	22	x	x	PROPN
ejpam-1951	281	23	i	i	PRON
ejpam-1951	281	24	.	.	PUNCT
ejpam-1951	282	1	let	let	VERB
ejpam-1951	282	2	mi	mi	PROPN
ejpam-1951	282	3	denote	denote	VERB
ejpam-1951	282	4	the	the	DET
ejpam-1951	282	5	number	number	NOUN
ejpam-1951	282	6	of	of	ADP
ejpam-1951	282	7	orbits	orbit	NOUN
ejpam-1951	282	8	.	.	PUNCT
ejpam-1951	283	1	then	then	ADV
ejpam-1951	283	2	pi	pi	NOUN
ejpam-1951	283	3	=	=	PUNCT
ejpam-1951	283	4	m	m	VERB
ejpam-1951	283	5	∑	∑	PROPN
ejpam-1951	283	6	i=1	i=1	PROPN
ejpam-1951	283	7	miwi	miwi	NOUN
ejpam-1951	283	8	=	=	SYM
ejpam-1951	284	1	m	m	VERB
ejpam-1951	284	2	∑	∑	PROPN
ejpam-1951	284	3	i=1	i=1	PROPN
ejpam-1951	284	4	wi	wi	PROPN
ejpam-1951	284	5	(	(	PUNCT
ejpam-1951	284	6	1	1	NUM
ejpam-1951	284	7	|g|	|g|	PROPN
ejpam-1951	284	8	∑	∑	PROPN
ejpam-1951	284	9	g∈g	g∈g	PROPN
ejpam-1951	284	10	|f	|f	PROPN
ejpam-1951	284	11	ix(g(i))|	ix(g(i))|	PROPN
ejpam-1951	284	12	)	)	PUNCT
ejpam-1951	284	13	,	,	PUNCT
ejpam-1951	284	14	by	by	ADP
ejpam-1951	284	15	burnside	burnside	PROPN
ejpam-1951	284	16	’s	’s	PART
ejpam-1951	284	17	lemma	lemma	PROPN
ejpam-1951	284	18	,	,	PUNCT
ejpam-1951	284	19	we	we	PRON
ejpam-1951	284	20	have	have	VERB
ejpam-1951	284	21	pi	pi	NOUN
ejpam-1951	284	22	=	=	SYM
ejpam-1951	284	23	1	1	NUM
ejpam-1951	284	24	|g|	|g|	PROPN
ejpam-1951	284	25	∑	∑	PROPN
ejpam-1951	284	26	g∈g	g∈g	PROPN
ejpam-1951	284	27	m	m	PRON
ejpam-1951	284	28	∑	∑	ADV
ejpam-1951	284	29	i=1	i=1	PROPN
ejpam-1951	284	30	|f	|f	PROPN
ejpam-1951	284	31	ix(g(i))|wi	ix(g(i))|wi	NOUN
ejpam-1951	284	32	=	=	NOUN
ejpam-1951	284	33	1	1	NUM
ejpam-1951	284	34	|g|	|g|	PROPN
ejpam-1951	284	35	∑	∑	PROPN
ejpam-1951	284	36	g∈g	g∈g	PROPN
ejpam-1951	284	37	w	w	PROPN
ejpam-1951	284	38	(	(	PUNCT
ejpam-1951	284	39	f	f	PROPN
ejpam-1951	284	40	ix(g	ix(g	NOUN
ejpam-1951	284	41	)	)	PUNCT
ejpam-1951	284	42	)	)	PUNCT
ejpam-1951	285	1	(	(	PUNCT
ejpam-1951	285	2	2	2	X
ejpam-1951	285	3	)	)	PUNCT
ejpam-1951	285	4	t.	t.	NOUN
ejpam-1951	285	5	nasseef	nasseef	PROPN
ejpam-1951	285	6	/	/	SYM
ejpam-1951	285	7	eur	eur	PROPN
ejpam-1951	285	8	.	.	PUNCT
ejpam-1951	286	1	j.	j.	PROPN
ejpam-1951	286	2	pure	pure	PROPN
ejpam-1951	286	3	appl	appl	PROPN
ejpam-1951	286	4	.	.	PROPN
ejpam-1951	286	5	math	math	PROPN
ejpam-1951	286	6	,	,	PUNCT
ejpam-1951	286	7	9	9	NUM
ejpam-1951	286	8	(	(	PUNCT
ejpam-1951	286	9	2016	2016	NUM
ejpam-1951	286	10	)	)	PUNCT
ejpam-1951	286	11	,	,	PUNCT
ejpam-1951	286	12	84	84	NUM
ejpam-1951	286	13	-	-	SYM
ejpam-1951	286	14	113	113	NUM
ejpam-1951	286	15	95	95	NUM
ejpam-1951	286	16	note	note	NOUN
ejpam-1951	286	17	that	that	SCONJ
ejpam-1951	286	18	(	(	PUNCT
ejpam-1951	286	19	1	1	X
ejpam-1951	286	20	)	)	PUNCT
ejpam-1951	286	21	follows	follow	VERB
ejpam-1951	286	22	f	f	PROPN
ejpam-1951	286	23	ix(g	ix(g	NOUN
ejpam-1951	286	24	)	)	PUNCT
ejpam-1951	286	25	=	=	PUNCT
ejpam-1951	286	26	⋃m	⋃m	NOUN
ejpam-1951	286	27	i=1	i=1	PROPN
ejpam-1951	286	28	f	f	PROPN
ejpam-1951	286	29	ix(g(i	ix(g(i	PROPN
ejpam-1951	286	30	)	)	PUNCT
ejpam-1951	286	31	)	)	PUNCT
ejpam-1951	286	32	since	since	SCONJ
ejpam-1951	286	33	x	x	PROPN
ejpam-1951	286	34	∈	∈	PROPN
ejpam-1951	286	35	f	f	PROPN
ejpam-1951	286	36	ix(g(i	ix(g(i	PROPN
ejpam-1951	286	37	)	)	PUNCT
ejpam-1951	286	38	)	)	PUNCT
ejpam-1951	287	1	if	if	SCONJ
ejpam-1951	287	2	and	and	CCONJ
ejpam-1951	287	3	only	only	ADV
ejpam-1951	287	4	if	if	SCONJ
ejpam-1951	287	5	x	x	PROPN
ejpam-1951	287	6	∈	∈	PROPN
ejpam-1951	287	7	wi	wi	PROPN
ejpam-1951	287	8	and	and	CCONJ
ejpam-1951	287	9	g	g	NOUN
ejpam-1951	287	10	∗	∗	NOUN
ejpam-1951	287	11	x	x	PUNCT
ejpam-1951	287	12	=	=	PUNCT
ejpam-1951	287	13	x	x	X
ejpam-1951	287	14	.	.	PUNCT
ejpam-1951	287	15	suppose	suppose	VERB
ejpam-1951	287	16	that	that	SCONJ
ejpam-1951	287	17	zg	zg	PROPN
ejpam-1951	287	18	=	=	PUNCT
ejpam-1951	287	19	x	x	SYM
ejpam-1951	287	20	k1	k1	PROPN
ejpam-1951	287	21	1	1	NUM
ejpam-1951	287	22	x	x	SYM
ejpam-1951	287	23	k2	k2	PROPN
ejpam-1951	287	24	2	2	NUM
ejpam-1951	287	25	.	.	PUNCT
ejpam-1951	287	26	.	.	PUNCT
ejpam-1951	287	27	.	.	PUNCT
ejpam-1951	288	1	x	x	X
ejpam-1951	288	2	kp	kp	PROPN
ejpam-1951	288	3	p	p	PROPN
ejpam-1951	288	4	.	.	PUNCT
ejpam-1951	289	1	then	then	ADV
ejpam-1951	289	2	we	we	PRON
ejpam-1951	289	3	can	can	AUX
ejpam-1951	289	4	claim	claim	VERB
ejpam-1951	289	5	that	that	SCONJ
ejpam-1951	289	6	w	w	INTJ
ejpam-1951	289	7	(	(	PUNCT
ejpam-1951	289	8	f	f	PROPN
ejpam-1951	289	9	ix(g	ix(g	NOUN
ejpam-1951	289	10	)	)	PUNCT
ejpam-1951	289	11	)	)	PUNCT
ejpam-1951	290	1	=	=	PRON
ejpam-1951	290	2	(	(	PUNCT
ejpam-1951	290	3	∑	∑	PUNCT
ejpam-1951	290	4	c∈c	c∈c	PROPN
ejpam-1951	290	5	wc	wc	PROPN
ejpam-1951	290	6	)	)	PUNCT
ejpam-1951	290	7	k1	k1	PROPN
ejpam-1951	290	8	(	(	PUNCT
ejpam-1951	290	9	∑	∑	PART
ejpam-1951	290	10	c∈c	c∈c	PROPN
ejpam-1951	290	11	wc	wc	PROPN
ejpam-1951	290	12	)	)	PUNCT
ejpam-1951	290	13	k2	k2	PROPN
ejpam-1951	290	14	.	.	PUNCT
ejpam-1951	290	15	.	.	PUNCT
ejpam-1951	290	16	.	.	PUNCT
ejpam-1951	291	1	(	(	PUNCT
ejpam-1951	291	2	∑	∑	PUNCT
ejpam-1951	291	3	c∈c	c∈c	PROPN
ejpam-1951	291	4	wc	wc	PROPN
ejpam-1951	291	5	)	)	PUNCT
ejpam-1951	291	6	kp	kp	PROPN
ejpam-1951	291	7	(	(	PUNCT
ejpam-1951	291	8	3	3	X
ejpam-1951	291	9	)	)	PUNCT
ejpam-1951	291	10	substituting	substitute	VERB
ejpam-1951	291	11	(	(	PUNCT
ejpam-1951	291	12	2	2	NUM
ejpam-1951	291	13	)	)	PUNCT
ejpam-1951	291	14	and	and	CCONJ
ejpam-1951	291	15	(	(	PUNCT
ejpam-1951	291	16	3	3	X
ejpam-1951	291	17	)	)	PUNCT
ejpam-1951	291	18	yields	yield	VERB
ejpam-1951	291	19	the	the	DET
ejpam-1951	291	20	theorem	theorem	NOUN
ejpam-1951	291	21	.	.	PROPN
ejpam-1951	291	22	to	to	PART
ejpam-1951	291	23	verify	verify	VERB
ejpam-1951	291	24	(	(	PUNCT
ejpam-1951	291	25	2	2	X
ejpam-1951	291	26	)	)	PUNCT
ejpam-1951	291	27	we	we	PRON
ejpam-1951	291	28	use	use	VERB
ejpam-1951	291	29	the	the	DET
ejpam-1951	291	30	fact	fact	NOUN
ejpam-1951	291	31	that	that	SCONJ
ejpam-1951	291	32	if	if	SCONJ
ejpam-1951	291	33	x	x	PROPN
ejpam-1951	291	34	∈	∈	PROPN
ejpam-1951	291	35	f	f	NOUN
ejpam-1951	291	36	ix(g	ix(g	NOUN
ejpam-1951	291	37	)	)	PUNCT
ejpam-1951	291	38	)	)	PUNCT
ejpam-1951	291	39	,	,	PUNCT
ejpam-1951	291	40	then	then	ADV
ejpam-1951	291	41	the	the	DET
ejpam-1951	291	42	elements	element	NOUN
ejpam-1951	291	43	of	of	ADP
ejpam-1951	291	44	a	a	DET
ejpam-1951	291	45	cycle	cycle	NOUN
ejpam-1951	291	46	of	of	ADP
ejpam-1951	291	47	g	g	NOUN
ejpam-1951	291	48	must	must	AUX
ejpam-1951	291	49	be	be	AUX
ejpam-1951	291	50	given	give	VERB
ejpam-1951	291	51	the	the	DET
ejpam-1951	291	52	same	same	ADJ
ejpam-1951	291	53	color	color	NOUN
ejpam-1951	291	54	.	.	PUNCT
ejpam-1951	292	1	a	a	DET
ejpam-1951	292	2	cycle	cycle	NOUN
ejpam-1951	292	3	of	of	ADP
ejpam-1951	292	4	length	length	NOUN
ejpam-1951	292	5	i	i	PRON
ejpam-1951	292	6	will	will	AUX
ejpam-1951	292	7	then	then	ADV
ejpam-1951	292	8	contribute	contribute	VERB
ejpam-1951	292	9	a	a	DET
ejpam-1951	292	10	factor	factor	NOUN
ejpam-1951	292	11	∑	∑	PUNCT
ejpam-1951	292	12	c∈c	c∈c	NOUN
ejpam-1951	292	13	wi	wi	PROPN
ejpam-1951	292	14	c	c	PROPN
ejpam-1951	292	15	where	where	SCONJ
ejpam-1951	292	16	the	the	DET
ejpam-1951	292	17	term	term	NOUN
ejpam-1951	292	18	wi	wi	PROPN
ejpam-1951	292	19	c	c	PROPN
ejpam-1951	292	20	comes	come	VERB
ejpam-1951	292	21	from	from	ADP
ejpam-1951	292	22	the	the	DET
ejpam-1951	292	23	choice	choice	NOUN
ejpam-1951	292	24	of	of	ADP
ejpam-1951	292	25	c	c	NOUN
ejpam-1951	292	26	for	for	ADP
ejpam-1951	292	27	every	every	DET
ejpam-1951	292	28	element	element	NOUN
ejpam-1951	292	29	of	of	ADP
ejpam-1951	292	30	the	the	DET
ejpam-1951	292	31	cycle	cycle	NOUN
ejpam-1951	292	32	[	[	X
ejpam-1951	292	33	8	8	NUM
ejpam-1951	292	34	]	]	PUNCT
ejpam-1951	292	35	.	.	PUNCT
ejpam-1951	293	1	example	example	NOUN
ejpam-1951	293	2	13	13	NUM
ejpam-1951	293	3	.	.	PUNCT
ejpam-1951	294	1	let	let	VERB
ejpam-1951	294	2	a=	a=	VERB
ejpam-1951	294	3	{	{	PUNCT
ejpam-1951	294	4	1,2,3,4,5,6	1,2,3,4,5,6	NUM
ejpam-1951	294	5	}	}	PUNCT
ejpam-1951	294	6	and	and	CCONJ
ejpam-1951	294	7	b	b	X
ejpam-1951	294	8	=	=	SYM
ejpam-1951	294	9	{	{	PUNCT
ejpam-1951	294	10	white	white	ADJ
ejpam-1951	294	11	,	,	PUNCT
ejpam-1951	294	12	black	black	ADJ
ejpam-1951	294	13	,	,	PUNCT
ejpam-1951	294	14	gra	gra	PROPN
ejpam-1951	294	15	y	y	PROPN
ejpam-1951	294	16	}	}	PUNCT
ejpam-1951	294	17	.	.	PUNCT
ejpam-1951	295	1	consider	consider	VERB
ejpam-1951	295	2	a	a	DET
ejpam-1951	295	3	function	function	NOUN
ejpam-1951	295	4	f	f	PROPN
ejpam-1951	295	5	∈	∈	PROPN
ejpam-1951	295	6	ba	ba	PROPN
ejpam-1951	295	7	which	which	PRON
ejpam-1951	295	8	is	be	AUX
ejpam-1951	295	9	a	a	DET
ejpam-1951	295	10	6	6	NUM
ejpam-1951	295	11	-	-	PUNCT
ejpam-1951	295	12	tuple	tuple	NOUN
ejpam-1951	295	13	of	of	ADP
ejpam-1951	295	14	colors	color	NOUN
ejpam-1951	295	15	and	and	CCONJ
ejpam-1951	295	16	can	can	AUX
ejpam-1951	295	17	be	be	AUX
ejpam-1951	295	18	viewed	view	VERB
ejpam-1951	295	19	as	as	ADP
ejpam-1951	295	20	necklace	necklace	NOUN
ejpam-1951	295	21	representation	representation	NOUN
ejpam-1951	295	22	.	.	PUNCT
ejpam-1951	296	1	w1	w1	PROPN
ejpam-1951	296	2	w	w	PROPN
ejpam-1951	296	3	2	2	NUM
ejpam-1951	296	4	b	b	SYM
ejpam-1951	296	5	3	3	NUM
ejpam-1951	296	6	b	b	SYM
ejpam-1951	296	7	4	4	NUM
ejpam-1951	296	8	g	g	NOUN
ejpam-1951	296	9	5	5	NUM
ejpam-1951	296	10	b6	b6	NOUN
ejpam-1951	296	11	figure	figure	NOUN
ejpam-1951	296	12	4	4	NUM
ejpam-1951	296	13	:	:	PUNCT
ejpam-1951	296	14	colored	colored	ADJ
ejpam-1951	296	15	necklace	necklace	NOUN
ejpam-1951	296	16	now	now	ADV
ejpam-1951	296	17	we	we	PRON
ejpam-1951	296	18	are	be	AUX
ejpam-1951	296	19	interested	interested	ADJ
ejpam-1951	296	20	to	to	PART
ejpam-1951	296	21	assign	assign	VERB
ejpam-1951	296	22	different	different	ADJ
ejpam-1951	296	23	weights	weight	NOUN
ejpam-1951	296	24	to	to	ADP
ejpam-1951	296	25	the	the	DET
ejpam-1951	296	26	beads	bead	NOUN
ejpam-1951	296	27	.	.	PUNCT
ejpam-1951	297	1	suppose	suppose	VERB
ejpam-1951	297	2	that	that	SCONJ
ejpam-1951	297	3	black(b	black(b	NOUN
ejpam-1951	297	4	)	)	PUNCT
ejpam-1951	297	5	=	=	SYM
ejpam-1951	298	1	1	1	NUM
ejpam-1951	298	2	,	,	PUNCT
ejpam-1951	298	3	white(w	white(w	NOUN
ejpam-1951	298	4	)	)	PUNCT
ejpam-1951	298	5	=	=	SYM
ejpam-1951	298	6	10	10	NUM
ejpam-1951	298	7	and	and	CCONJ
ejpam-1951	298	8	gra	gra	PROPN
ejpam-1951	298	9	y(g	y(g	PROPN
ejpam-1951	298	10	)	)	PUNCT
ejpam-1951	298	11	=	=	PUNCT
ejpam-1951	299	1	100	100	NUM
ejpam-1951	299	2	.	.	PUNCT
ejpam-1951	300	1	then	then	ADV
ejpam-1951	300	2	the	the	DET
ejpam-1951	300	3	weight	weight	NOUN
ejpam-1951	300	4	of	of	ADP
ejpam-1951	300	5	the	the	DET
ejpam-1951	300	6	necklace	necklace	NOUN
ejpam-1951	300	7	is	be	AUX
ejpam-1951	300	8	w	w	PROPN
ejpam-1951	300	9	(	(	PUNCT
ejpam-1951	300	10	f	f	NOUN
ejpam-1951	300	11	)	)	PUNCT
ejpam-1951	300	12	=	=	SYM
ejpam-1951	300	13	10×	10×	NUM
ejpam-1951	300	14	10×	10×	NUM
ejpam-1951	300	15	1×	1×	NUM
ejpam-1951	300	16	1×	1×	NUM
ejpam-1951	300	17	100=	100=	PROPN
ejpam-1951	300	18	104	104	NUM
ejpam-1951	300	19	note	note	NOUN
ejpam-1951	300	20	that	that	SCONJ
ejpam-1951	300	21	rotation	rotation	NOUN
ejpam-1951	300	22	does	do	AUX
ejpam-1951	300	23	not	not	PART
ejpam-1951	300	24	change	change	VERB
ejpam-1951	300	25	the	the	DET
ejpam-1951	300	26	weight	weight	NOUN
ejpam-1951	300	27	.	.	PUNCT
ejpam-1951	301	1	to	to	PART
ejpam-1951	301	2	count	count	VERB
ejpam-1951	301	3	the	the	DET
ejpam-1951	301	4	necklaces	necklace	NOUN
ejpam-1951	301	5	(	(	PUNCT
ejpam-1951	301	6	without	without	ADP
ejpam-1951	301	7	weight	weight	NOUN
ejpam-1951	301	8	)	)	PUNCT
ejpam-1951	301	9	,	,	PUNCT
ejpam-1951	301	10	we	we	PRON
ejpam-1951	301	11	have	have	VERB
ejpam-1951	301	12	to	to	PART
ejpam-1951	301	13	calculate	calculate	VERB
ejpam-1951	301	14	the	the	DET
ejpam-1951	301	15	number	number	NOUN
ejpam-1951	301	16	of	of	ADP
ejpam-1951	301	17	fixed	fix	VERB
ejpam-1951	301	18	points	point	NOUN
ejpam-1951	301	19	for	for	ADP
ejpam-1951	301	20	each	each	DET
ejpam-1951	301	21	element	element	NOUN
ejpam-1951	301	22	of	of	ADP
ejpam-1951	301	23	c6	c6	PROPN
ejpam-1951	301	24	.	.	PUNCT
ejpam-1951	302	1	t.	t.	PROPN
ejpam-1951	302	2	nasseef	nasseef	PROPN
ejpam-1951	302	3	/	/	SYM
ejpam-1951	302	4	eur	eur	PROPN
ejpam-1951	302	5	.	.	PUNCT
ejpam-1951	303	1	j.	j.	PROPN
ejpam-1951	303	2	pure	pure	PROPN
ejpam-1951	303	3	appl	appl	PROPN
ejpam-1951	303	4	.	.	PROPN
ejpam-1951	303	5	math	math	PROPN
ejpam-1951	303	6	,	,	PUNCT
ejpam-1951	303	7	9	9	NUM
ejpam-1951	303	8	(	(	PUNCT
ejpam-1951	303	9	2016	2016	NUM
ejpam-1951	303	10	)	)	PUNCT
ejpam-1951	303	11	,	,	PUNCT
ejpam-1951	303	12	84	84	NUM
ejpam-1951	303	13	-	-	SYM
ejpam-1951	303	14	113	113	NUM
ejpam-1951	303	15	96	96	NUM
ejpam-1951	303	16	table	table	NOUN
ejpam-1951	303	17	1	1	NUM
ejpam-1951	303	18	:	:	PUNCT
ejpam-1951	303	19	fixed	fix	VERB
ejpam-1951	303	20	points	point	NOUN
ejpam-1951	303	21	element	element	NOUN
ejpam-1951	303	22	g	g	PROPN
ejpam-1951	304	1	|	|	ADV
ejpam-1951	304	2	f	f	PROPN
ejpam-1951	305	1	i	i	PRON
ejpam-1951	305	2	x(g)|	x(g)|	PUNCT
ejpam-1951	306	1	e	e	X
ejpam-1951	306	2	36	36	NUM
ejpam-1951	306	3	(	(	PUNCT
ejpam-1951	306	4	1,2,3,4,5,6	1,2,3,4,5,6	NUM
ejpam-1951	306	5	)	)	PUNCT
ejpam-1951	306	6	3	3	NUM
ejpam-1951	306	7	(	(	PUNCT
ejpam-1951	306	8	1,3,5)(2,4,6	1,3,5)(2,4,6	NUM
ejpam-1951	306	9	)	)	PUNCT
ejpam-1951	306	10	32	32	NUM
ejpam-1951	306	11	(	(	PUNCT
ejpam-1951	306	12	1,4)(2,5)(3,6	1,4)(2,5)(3,6	NUM
ejpam-1951	306	13	)	)	PUNCT
ejpam-1951	306	14	33	33	NUM
ejpam-1951	306	15	(	(	PUNCT
ejpam-1951	306	16	1,5,3)(2,6,4	1,5,3)(2,6,4	NUM
ejpam-1951	306	17	)	)	PUNCT
ejpam-1951	306	18	32	32	NUM
ejpam-1951	306	19	(	(	PUNCT
ejpam-1951	306	20	1,6,5,4,3,2	1,6,5,4,3,2	NUM
ejpam-1951	306	21	)	)	PUNCT
ejpam-1951	306	22	3	3	NUM
ejpam-1951	306	23	now	now	ADV
ejpam-1951	306	24	we	we	PRON
ejpam-1951	306	25	have	have	VERB
ejpam-1951	306	26	to	to	PART
ejpam-1951	306	27	consider	consider	VERB
ejpam-1951	306	28	counting	count	VERB
ejpam-1951	306	29	the	the	DET
ejpam-1951	306	30	sums	sum	NOUN
ejpam-1951	306	31	of	of	ADP
ejpam-1951	306	32	the	the	DET
ejpam-1951	306	33	weights	weight	NOUN
ejpam-1951	306	34	of	of	ADP
ejpam-1951	306	35	the	the	DET
ejpam-1951	306	36	fixed	fix	VERB
ejpam-1951	306	37	points	point	NOUN
ejpam-1951	306	38	of	of	ADP
ejpam-1951	306	39	each	each	DET
ejpam-1951	306	40	element	element	NOUN
ejpam-1951	306	41	of	of	ADP
ejpam-1951	306	42	c6	c6	PROPN
ejpam-1951	306	43	.	.	PUNCT
ejpam-1951	307	1	let	let	VERB
ejpam-1951	307	2	us	we	PRON
ejpam-1951	307	3	calculate	calculate	VERB
ejpam-1951	307	4	wfix(g	wfix(g	PROPN
ejpam-1951	307	5	)	)	PUNCT
ejpam-1951	307	6	for	for	ADP
ejpam-1951	307	7	the	the	DET
ejpam-1951	307	8	element	element	NOUN
ejpam-1951	307	9	g	g	PROPN
ejpam-1951	307	10	=	=	SYM
ejpam-1951	307	11	(	(	PUNCT
ejpam-1951	307	12	1,4)(2,5)(3,6	1,4)(2,5)(3,6	NUM
ejpam-1951	307	13	)	)	PUNCT
ejpam-1951	307	14	.	.	PUNCT
ejpam-1951	308	1	for	for	ADP
ejpam-1951	308	2	a	a	DET
ejpam-1951	308	3	function	function	NOUN
ejpam-1951	308	4	f	f	X
ejpam-1951	308	5	to	to	PART
ejpam-1951	308	6	be	be	AUX
ejpam-1951	308	7	fixed	fix	VERB
ejpam-1951	308	8	by	by	ADP
ejpam-1951	308	9	g	g	PROPN
ejpam-1951	308	10	we	we	PRON
ejpam-1951	308	11	must	must	AUX
ejpam-1951	308	12	have	have	VERB
ejpam-1951	308	13	f	f	X
ejpam-1951	308	14	(	(	PUNCT
ejpam-1951	308	15	1	1	NUM
ejpam-1951	308	16	)	)	PUNCT
ejpam-1951	309	1	=	=	SYM
ejpam-1951	309	2	f	f	PROPN
ejpam-1951	309	3	(	(	PUNCT
ejpam-1951	309	4	4	4	NUM
ejpam-1951	309	5	)	)	PUNCT
ejpam-1951	309	6	f	f	NOUN
ejpam-1951	309	7	(	(	PUNCT
ejpam-1951	309	8	2	2	NUM
ejpam-1951	309	9	)	)	PUNCT
ejpam-1951	309	10	=	=	SYM
ejpam-1951	309	11	f	f	PROPN
ejpam-1951	309	12	(	(	PUNCT
ejpam-1951	309	13	5	5	NUM
ejpam-1951	309	14	)	)	PUNCT
ejpam-1951	309	15	f	f	NOUN
ejpam-1951	309	16	(	(	PUNCT
ejpam-1951	309	17	3	3	NUM
ejpam-1951	309	18	)	)	PUNCT
ejpam-1951	309	19	=	=	SYM
ejpam-1951	309	20	f	f	PROPN
ejpam-1951	309	21	(	(	PUNCT
ejpam-1951	309	22	6	6	NUM
ejpam-1951	309	23	)	)	PUNCT
ejpam-1951	309	24	and	and	CCONJ
ejpam-1951	309	25	hence	hence	ADV
ejpam-1951	309	26	w	w	PROPN
ejpam-1951	309	27	(	(	PUNCT
ejpam-1951	309	28	f	f	X
ejpam-1951	309	29	)	)	PUNCT
ejpam-1951	310	1	=	=	NOUN
ejpam-1951	310	2	w	w	PROPN
ejpam-1951	310	3	(	(	PUNCT
ejpam-1951	310	4	f	f	X
ejpam-1951	310	5	(	(	PUNCT
ejpam-1951	310	6	1))2w	1))2w	NUM
ejpam-1951	310	7	(	(	PUNCT
ejpam-1951	310	8	f	f	X
ejpam-1951	310	9	(	(	PUNCT
ejpam-1951	310	10	2))2w	2))2w	NUM
ejpam-1951	310	11	(	(	PUNCT
ejpam-1951	310	12	f	f	X
ejpam-1951	310	13	(	(	PUNCT
ejpam-1951	310	14	3))2	3))2	NUM
ejpam-1951	310	15	now	now	ADV
ejpam-1951	310	16	f	f	X
ejpam-1951	310	17	(	(	PUNCT
ejpam-1951	310	18	1	1	NUM
ejpam-1951	310	19	)	)	PUNCT
ejpam-1951	310	20	,	,	PUNCT
ejpam-1951	310	21	f	f	PROPN
ejpam-1951	310	22	(	(	PUNCT
ejpam-1951	310	23	2	2	NUM
ejpam-1951	310	24	)	)	PUNCT
ejpam-1951	310	25	and	and	CCONJ
ejpam-1951	310	26	f	f	PROPN
ejpam-1951	310	27	(	(	PUNCT
ejpam-1951	310	28	3	3	X
ejpam-1951	310	29	)	)	PUNCT
ejpam-1951	310	30	can	can	AUX
ejpam-1951	310	31	be	be	AUX
ejpam-1951	310	32	any	any	DET
ejpam-1951	310	33	white	white	ADJ
ejpam-1951	310	34	,	,	PUNCT
ejpam-1951	310	35	black	black	ADJ
ejpam-1951	310	36	or	or	CCONJ
ejpam-1951	310	37	gray	gray	ADJ
ejpam-1951	310	38	and	and	CCONJ
ejpam-1951	310	39	that	that	PRON
ejpam-1951	310	40	is	be	AUX
ejpam-1951	310	41	why	why	SCONJ
ejpam-1951	310	42	w	w	PROPN
ejpam-1951	310	43	f	f	PROPN
ejpam-1951	310	44	ix(g	ix(g	NOUN
ejpam-1951	310	45	)	)	PUNCT
ejpam-1951	310	46	=	=	SYM
ejpam-1951	311	1	(	(	PUNCT
ejpam-1951	311	2	w	w	NOUN
ejpam-1951	311	3	(	(	PUNCT
ejpam-1951	311	4	white)2	white)2	X
ejpam-1951	311	5	+	+	NOUN
ejpam-1951	311	6	w	w	NOUN
ejpam-1951	311	7	(	(	PUNCT
ejpam-1951	311	8	black)2	black)2	NOUN
ejpam-1951	311	9	+	+	NOUN
ejpam-1951	311	10	w	w	PROPN
ejpam-1951	311	11	(	(	PUNCT
ejpam-1951	311	12	gra	gra	PROPN
ejpam-1951	311	13	y)2)3	y)2)3	PROPN
ejpam-1951	311	14	.	.	PUNCT
ejpam-1951	312	1	by	by	ADP
ejpam-1951	312	2	repeating	repeat	VERB
ejpam-1951	312	3	this	this	DET
ejpam-1951	312	4	process	process	NOUN
ejpam-1951	312	5	we	we	PRON
ejpam-1951	312	6	can	can	AUX
ejpam-1951	312	7	find	find	VERB
ejpam-1951	312	8	out	out	ADP
ejpam-1951	312	9	the	the	DET
ejpam-1951	312	10	other	other	ADJ
ejpam-1951	312	11	elements	element	NOUN
ejpam-1951	312	12	of	of	ADP
ejpam-1951	312	13	c6	c6	PROPN
ejpam-1951	312	14	.	.	PUNCT
ejpam-1951	313	1	then	then	ADV
ejpam-1951	313	2	we	we	PRON
ejpam-1951	313	3	get	get	VERB
ejpam-1951	313	4	table	table	NOUN
ejpam-1951	313	5	2	2	NUM
ejpam-1951	313	6	:	:	PUNCT
ejpam-1951	313	7	weighted	weight	VERB
ejpam-1951	313	8	fixed	fix	VERB
ejpam-1951	313	9	points	point	NOUN
ejpam-1951	313	10	element	element	NOUN
ejpam-1951	313	11	g	g	PROPN
ejpam-1951	313	12	wfix(g	wfix(g	PROPN
ejpam-1951	313	13	)	)	PUNCT
ejpam-1951	313	14	e	e	NOUN
ejpam-1951	313	15	(	(	PUNCT
ejpam-1951	313	16	w	w	PROPN
ejpam-1951	313	17	(	(	PUNCT
ejpam-1951	313	18	white	white	ADJ
ejpam-1951	313	19	)	)	PUNCT
ejpam-1951	314	1	+	+	PROPN
ejpam-1951	314	2	w	w	ADJ
ejpam-1951	314	3	(	(	PUNCT
ejpam-1951	314	4	black	black	NOUN
ejpam-1951	314	5	)	)	PUNCT
ejpam-1951	314	6	+	+	PROPN
ejpam-1951	314	7	w	w	PROPN
ejpam-1951	314	8	(	(	PUNCT
ejpam-1951	314	9	gra	gra	PROPN
ejpam-1951	314	10	y))6	y))6	PROPN
ejpam-1951	314	11	(	(	PUNCT
ejpam-1951	314	12	1,2,3,4,5,6	1,2,3,4,5,6	NUM
ejpam-1951	314	13	)	)	PUNCT
ejpam-1951	314	14	w	w	NOUN
ejpam-1951	314	15	(	(	PUNCT
ejpam-1951	314	16	white)6	white)6	X
ejpam-1951	314	17	+	+	NOUN
ejpam-1951	314	18	w	w	NOUN
ejpam-1951	314	19	(	(	PUNCT
ejpam-1951	314	20	black)6	black)6	PROPN
ejpam-1951	314	21	+	+	PROPN
ejpam-1951	314	22	w	w	PROPN
ejpam-1951	314	23	(	(	PUNCT
ejpam-1951	314	24	gra	gra	PROPN
ejpam-1951	314	25	y)6	y)6	PROPN
ejpam-1951	314	26	(	(	PUNCT
ejpam-1951	314	27	1,3,5)(2,4,6	1,3,5)(2,4,6	NUM
ejpam-1951	314	28	)	)	PUNCT
ejpam-1951	314	29	(	(	PUNCT
ejpam-1951	314	30	w	w	NOUN
ejpam-1951	314	31	(	(	PUNCT
ejpam-1951	314	32	white)3	white)3	NUM
ejpam-1951	314	33	+	+	NOUN
ejpam-1951	314	34	w	w	PROPN
ejpam-1951	314	35	(	(	PUNCT
ejpam-1951	314	36	black)3	black)3	PROPN
ejpam-1951	314	37	+	+	PROPN
ejpam-1951	314	38	w	w	PROPN
ejpam-1951	314	39	(	(	PUNCT
ejpam-1951	314	40	gra	gra	PROPN
ejpam-1951	314	41	y)3)2	y)3)2	PROPN
ejpam-1951	314	42	(	(	PUNCT
ejpam-1951	314	43	1,4)(2,5)(3,6	1,4)(2,5)(3,6	NUM
ejpam-1951	314	44	)	)	PUNCT
ejpam-1951	314	45	(	(	PUNCT
ejpam-1951	314	46	w	w	NOUN
ejpam-1951	314	47	(	(	PUNCT
ejpam-1951	314	48	white)2	white)2	X
ejpam-1951	315	1	+	+	NOUN
ejpam-1951	315	2	w	w	NOUN
ejpam-1951	315	3	(	(	PUNCT
ejpam-1951	315	4	black)2	black)2	NOUN
ejpam-1951	315	5	+	+	NOUN
ejpam-1951	315	6	w	w	PROPN
ejpam-1951	315	7	(	(	PUNCT
ejpam-1951	315	8	gra	gra	PROPN
ejpam-1951	315	9	y)2)3	y)2)3	PROPN
ejpam-1951	315	10	(	(	PUNCT
ejpam-1951	315	11	1,5,3)(2,6,4	1,5,3)(2,6,4	NUM
ejpam-1951	315	12	)	)	PUNCT
ejpam-1951	315	13	(	(	PUNCT
ejpam-1951	315	14	w	w	NOUN
ejpam-1951	315	15	(	(	PUNCT
ejpam-1951	315	16	white)3	white)3	NUM
ejpam-1951	315	17	+	+	NOUN
ejpam-1951	315	18	w	w	PROPN
ejpam-1951	315	19	(	(	PUNCT
ejpam-1951	315	20	black)3	black)3	PROPN
ejpam-1951	315	21	+	+	PROPN
ejpam-1951	315	22	w	w	PROPN
ejpam-1951	315	23	(	(	PUNCT
ejpam-1951	315	24	gra	gra	PROPN
ejpam-1951	315	25	y)3)2	y)3)2	PROPN
ejpam-1951	315	26	(	(	PUNCT
ejpam-1951	315	27	1,6,5,4,3,2	1,6,5,4,3,2	NUM
ejpam-1951	315	28	)	)	PUNCT
ejpam-1951	315	29	w	w	NOUN
ejpam-1951	315	30	(	(	PUNCT
ejpam-1951	315	31	white)6	white)6	X
ejpam-1951	315	32	+	+	NOUN
ejpam-1951	315	33	w	w	NOUN
ejpam-1951	315	34	(	(	PUNCT
ejpam-1951	315	35	black)6	black)6	PROPN
ejpam-1951	315	36	+	+	PROPN
ejpam-1951	315	37	w	w	PROPN
ejpam-1951	315	38	(	(	PUNCT
ejpam-1951	315	39	gra	gra	PROPN
ejpam-1951	315	40	y)6	y)6	PROPN
ejpam-1951	315	41	for	for	ADP
ejpam-1951	315	42	any	any	DET
ejpam-1951	315	43	given	give	VERB
ejpam-1951	315	44	values	value	NOUN
ejpam-1951	315	45	of	of	ADP
ejpam-1951	315	46	w	w	PROPN
ejpam-1951	315	47	(	(	PUNCT
ejpam-1951	315	48	white),w	white),w	NOUN
ejpam-1951	315	49	(	(	PUNCT
ejpam-1951	315	50	black	black	ADJ
ejpam-1951	315	51	)	)	PUNCT
ejpam-1951	315	52	and	and	CCONJ
ejpam-1951	315	53	w	w	PROPN
ejpam-1951	315	54	(	(	PUNCT
ejpam-1951	315	55	gra	gra	PROPN
ejpam-1951	315	56	y	y	PROPN
ejpam-1951	315	57	)	)	PUNCT
ejpam-1951	315	58	we	we	PRON
ejpam-1951	315	59	can	can	AUX
ejpam-1951	315	60	calculate	calculate	VERB
ejpam-1951	315	61	this	this	DET
ejpam-1951	315	62	sum	sum	NOUN
ejpam-1951	315	63	and	and	CCONJ
ejpam-1951	315	64	find	find	VERB
ejpam-1951	315	65	the	the	DET
ejpam-1951	315	66	sum	sum	NOUN
ejpam-1951	315	67	of	of	ADP
ejpam-1951	315	68	the	the	DET
ejpam-1951	315	69	weights	weight	NOUN
ejpam-1951	315	70	of	of	ADP
ejpam-1951	315	71	the	the	DET
ejpam-1951	315	72	weighted	weight	VERB
ejpam-1951	315	73	(	(	PUNCT
ejpam-1951	315	74	6,3)−	6,3)−	NOUN
ejpam-1951	315	75	necklaces	necklace	NOUN
ejpam-1951	315	76	.	.	PUNCT
ejpam-1951	316	1	at	at	ADP
ejpam-1951	316	2	this	this	DET
ejpam-1951	316	3	moment	moment	NOUN
ejpam-1951	316	4	we	we	PRON
ejpam-1951	316	5	would	would	AUX
ejpam-1951	316	6	like	like	VERB
ejpam-1951	316	7	to	to	PART
ejpam-1951	316	8	apply	apply	VERB
ejpam-1951	316	9	pólya	pólya	NOUN
ejpam-1951	316	10	’s	’s	PART
ejpam-1951	316	11	fundamental	fundamental	ADJ
ejpam-1951	316	12	theorem	theorem	NOUN
ejpam-1951	316	13	.	.	PUNCT
ejpam-1951	317	1	first	first	ADV
ejpam-1951	317	2	we	we	PRON
ejpam-1951	317	3	need	need	VERB
ejpam-1951	317	4	to	to	PART
ejpam-1951	317	5	assign	assign	VERB
ejpam-1951	317	6	the	the	DET
ejpam-1951	317	7	weights	weight	NOUN
ejpam-1951	317	8	of	of	ADP
ejpam-1951	317	9	the	the	DET
ejpam-1951	317	10	three	three	NUM
ejpam-1951	317	11	colors	color	NOUN
ejpam-1951	317	12	.	.	PUNCT
ejpam-1951	318	1	let	let	VERB
ejpam-1951	318	2	w	w	NOUN
ejpam-1951	318	3	(	(	PUNCT
ejpam-1951	318	4	white	white	ADJ
ejpam-1951	318	5	)	)	PUNCT
ejpam-1951	318	6	=	=	SYM
ejpam-1951	319	1	x	x	X
ejpam-1951	319	2	,	,	PUNCT
ejpam-1951	319	3	w	w	PROPN
ejpam-1951	319	4	(	(	PUNCT
ejpam-1951	319	5	black	black	ADJ
ejpam-1951	319	6	)	)	PUNCT
ejpam-1951	319	7	=	=	SYM
ejpam-1951	319	8	y	y	PROPN
ejpam-1951	319	9	and	and	CCONJ
ejpam-1951	319	10	w	w	PROPN
ejpam-1951	319	11	(	(	PUNCT
ejpam-1951	319	12	gra	gra	PROPN
ejpam-1951	319	13	y	y	PROPN
ejpam-1951	319	14	)	)	PUNCT
ejpam-1951	319	15	=	=	PUNCT
ejpam-1951	320	1	z.	z.	PROPN
ejpam-1951	320	2	then	then	ADV
ejpam-1951	320	3	the	the	DET
ejpam-1951	320	4	weight	weight	NOUN
ejpam-1951	320	5	of	of	ADP
ejpam-1951	320	6	a	a	DET
ejpam-1951	320	7	necklace	necklace	NOUN
ejpam-1951	320	8	representative	representative	NOUN
ejpam-1951	320	9	is	be	AUX
ejpam-1951	320	10	not	not	PART
ejpam-1951	320	11	a	a	DET
ejpam-1951	320	12	number	number	NOUN
ejpam-1951	320	13	,	,	PUNCT
ejpam-1951	320	14	but	but	CCONJ
ejpam-1951	320	15	a	a	DET
ejpam-1951	320	16	multivariate	multivariate	NOUN
ejpam-1951	320	17	polynomial	polynomial	NOUN
ejpam-1951	320	18	in	in	ADP
ejpam-1951	320	19	the	the	DET
ejpam-1951	320	20	variables	variable	NOUN
ejpam-1951	320	21	x	x	NOUN
ejpam-1951	320	22	,	,	PUNCT
ejpam-1951	320	23	y	y	PROPN
ejpam-1951	320	24	and	and	CCONJ
ejpam-1951	320	25	z	z	NOUN
ejpam-1951	321	1	[	[	X
ejpam-1951	321	2	8	8	NUM
ejpam-1951	321	3	]	]	PUNCT
ejpam-1951	321	4	.	.	PUNCT
ejpam-1951	322	1	w	w	PROPN
ejpam-1951	322	2	(	(	PUNCT
ejpam-1951	322	3	f	f	PROPN
ejpam-1951	322	4	)	)	PUNCT
ejpam-1951	322	5	=	=	PUNCT
ejpam-1951	323	1	x	x	SYM
ejpam-1951	323	2	×	×	NOUN
ejpam-1951	323	3	x	x	SYM
ejpam-1951	323	4	×	×	NOUN
ejpam-1951	323	5	y	y	PROPN
ejpam-1951	323	6	×	×	NOUN
ejpam-1951	323	7	y	y	PROPN
ejpam-1951	323	8	×	×	PROPN
ejpam-1951	323	9	z	z	NOUN
ejpam-1951	323	10	×	×	NOUN
ejpam-1951	323	11	y	y	PROPN
ejpam-1951	323	12	=	=	SYM
ejpam-1951	323	13	x2	x2	PROPN
ejpam-1951	323	14	y3z	y3z	PROPN
ejpam-1951	323	15	.	.	PUNCT
ejpam-1951	324	1	t.	t.	PROPN
ejpam-1951	324	2	nasseef	nasseef	PROPN
ejpam-1951	324	3	/	/	SYM
ejpam-1951	324	4	eur	eur	PROPN
ejpam-1951	324	5	.	.	PUNCT
ejpam-1951	325	1	j.	j.	PROPN
ejpam-1951	325	2	pure	pure	PROPN
ejpam-1951	325	3	appl	appl	PROPN
ejpam-1951	325	4	.	.	PROPN
ejpam-1951	325	5	math	math	PROPN
ejpam-1951	325	6	,	,	PUNCT
ejpam-1951	325	7	9	9	NUM
ejpam-1951	325	8	(	(	PUNCT
ejpam-1951	325	9	2016	2016	NUM
ejpam-1951	325	10	)	)	PUNCT
ejpam-1951	325	11	,	,	PUNCT
ejpam-1951	325	12	84	84	NUM
ejpam-1951	325	13	-	-	SYM
ejpam-1951	325	14	113	113	NUM
ejpam-1951	325	15	97	97	NUM
ejpam-1951	325	16	x1	x1	NUM
ejpam-1951	325	17	x	x	SYM
ejpam-1951	325	18	2	2	NUM
ejpam-1951	325	19	y	y	PROPN
ejpam-1951	325	20	3	3	NUM
ejpam-1951	325	21	y	y	PROPN
ejpam-1951	325	22	4	4	NUM
ejpam-1951	325	23	z	z	SYM
ejpam-1951	325	24	5	5	NUM
ejpam-1951	325	25	y6	y6	ADJ
ejpam-1951	325	26	figure	figure	NOUN
ejpam-1951	325	27	5	5	NUM
ejpam-1951	325	28	:	:	PUNCT
ejpam-1951	325	29	weighted	weight	VERB
ejpam-1951	325	30	necklace	necklace	NOUN
ejpam-1951	325	31	by	by	ADP
ejpam-1951	325	32	using	use	VERB
ejpam-1951	325	33	burnside	burnside	PROPN
ejpam-1951	325	34	’s	’s	PART
ejpam-1951	325	35	lemma	lemma	PROPN
ejpam-1951	325	36	we	we	PRON
ejpam-1951	325	37	get	get	VERB
ejpam-1951	325	38	that	that	DET
ejpam-1951	325	39	z(c6	z(c6	NOUN
ejpam-1951	325	40	,	,	PUNCT
ejpam-1951	325	41	t1	t1	NOUN
ejpam-1951	325	42	,	,	PUNCT
ejpam-1951	325	43	t2	t2	NOUN
ejpam-1951	325	44	,	,	PUNCT
ejpam-1951	325	45	.	.	PUNCT
ejpam-1951	325	46	.	.	PUNCT
ejpam-1951	326	1	.	.	PUNCT
ejpam-1951	327	1	,	,	PUNCT
ejpam-1951	327	2	t6	t6	PROPN
ejpam-1951	327	3	)	)	PUNCT
ejpam-1951	327	4	=	=	PUNCT
ejpam-1951	328	1	1	1	NUM
ejpam-1951	328	2	6	6	NUM
ejpam-1951	328	3	(	(	PUNCT
ejpam-1951	328	4	t6	t6	PROPN
ejpam-1951	328	5	1	1	NUM
ejpam-1951	328	6	+	+	CCONJ
ejpam-1951	328	7	t3	t3	PROPN
ejpam-1951	328	8	2	2	NUM
ejpam-1951	328	9	+	+	CCONJ
ejpam-1951	328	10	2t2	2t2	NUM
ejpam-1951	328	11	3	3	NUM
ejpam-1951	328	12	+	+	NUM
ejpam-1951	328	13	2t6	2t6	NUM
ejpam-1951	328	14	)	)	PUNCT
ejpam-1951	328	15	according	accord	VERB
ejpam-1951	328	16	to	to	ADP
ejpam-1951	328	17	pólya	pólya	PROPN
ejpam-1951	328	18	’s	’s	PART
ejpam-1951	328	19	substitution	substitution	NOUN
ejpam-1951	328	20	we	we	PRON
ejpam-1951	328	21	have	have	VERB
ejpam-1951	328	22	t1	t1	NOUN
ejpam-1951	328	23	7−→	7−→	NOUN
ejpam-1951	328	24	x	x	PUNCT
ejpam-1951	329	1	+	+	CCONJ
ejpam-1951	329	2	y	y	PROPN
ejpam-1951	330	1	+	+	CCONJ
ejpam-1951	330	2	z	z	PROPN
ejpam-1951	330	3	,	,	PUNCT
ejpam-1951	330	4	t2	t2	NOUN
ejpam-1951	330	5	7−→	7−→	NOUN
ejpam-1951	331	1	x2	x2	PROPN
ejpam-1951	332	1	+	+	CCONJ
ejpam-1951	332	2	y2	y2	PROPN
ejpam-1951	332	3	+	+	CCONJ
ejpam-1951	332	4	z2	z2	PROPN
ejpam-1951	332	5	,	,	PUNCT
ejpam-1951	332	6	t3	t3	PROPN
ejpam-1951	332	7	7−→	7−→	NOUN
ejpam-1951	332	8	x3	x3	VERB
ejpam-1951	332	9	+	+	CCONJ
ejpam-1951	332	10	y3	y3	NOUN
ejpam-1951	332	11	+	+	CCONJ
ejpam-1951	332	12	z3	z3	PROPN
ejpam-1951	332	13	,	,	PUNCT
ejpam-1951	332	14	t4	t4	PROPN
ejpam-1951	332	15	7−→	7−→	PROPN
ejpam-1951	332	16	x4	x4	PROPN
ejpam-1951	333	1	+	+	CCONJ
ejpam-1951	333	2	y4	y4	PROPN
ejpam-1951	333	3	+	+	CCONJ
ejpam-1951	333	4	z4	z4	PROPN
ejpam-1951	333	5	,	,	PUNCT
ejpam-1951	333	6	t5	t5	PROPN
ejpam-1951	333	7	7−→	7−→	PROPN
ejpam-1951	333	8	x5	x5	NOUN
ejpam-1951	333	9	+	+	CCONJ
ejpam-1951	333	10	y5	y5	NOUN
ejpam-1951	333	11	+	+	X
ejpam-1951	333	12	z5	z5	NOUN
ejpam-1951	333	13	,	,	PUNCT
ejpam-1951	333	14	t6	t6	PROPN
ejpam-1951	333	15	7−→	7−→	PROPN
ejpam-1951	333	16	x6	x6	PROPN
ejpam-1951	333	17	+	+	CCONJ
ejpam-1951	333	18	y6	y6	PROPN
ejpam-1951	333	19	+	+	CCONJ
ejpam-1951	333	20	z6	z6	NOUN
ejpam-1951	333	21	,	,	PUNCT
ejpam-1951	333	22	now	now	ADV
ejpam-1951	333	23	pi	pi	NOUN
ejpam-1951	333	24	=	=	SYM
ejpam-1951	333	25	1	1	NUM
ejpam-1951	333	26	6	6	NUM
ejpam-1951	333	27	(	(	PUNCT
ejpam-1951	333	28	(	(	PUNCT
ejpam-1951	333	29	x	x	SYM
ejpam-1951	333	30	+	+	NUM
ejpam-1951	333	31	y	y	PROPN
ejpam-1951	333	32	+	+	CCONJ
ejpam-1951	333	33	z)6	z)6	PROPN
ejpam-1951	333	34	+	+	CCONJ
ejpam-1951	334	1	(	(	PUNCT
ejpam-1951	334	2	x2	x2	PROPN
ejpam-1951	334	3	+	+	CCONJ
ejpam-1951	335	1	y2	y2	PROPN
ejpam-1951	336	1	+	+	CCONJ
ejpam-1951	336	2	z2)3	z2)3	NUM
ejpam-1951	337	1	+	+	NUM
ejpam-1951	337	2	2(x3	2(x3	NUM
ejpam-1951	338	1	+	+	CCONJ
ejpam-1951	338	2	y3	y3	NOUN
ejpam-1951	338	3	+	+	CCONJ
ejpam-1951	338	4	z3)2	z3)2	PROPN
ejpam-1951	339	1	+	+	NUM
ejpam-1951	339	2	2(x6	2(x6	NUM
ejpam-1951	339	3	+	+	CCONJ
ejpam-1951	339	4	y6	y6	ADJ
ejpam-1951	339	5	+	+	CCONJ
ejpam-1951	339	6	z6	z6	NOUN
ejpam-1951	339	7	)	)	PUNCT
ejpam-1951	339	8	)	)	PUNCT
ejpam-1951	340	1	using	use	VERB
ejpam-1951	340	2	maple	maple	NOUN
ejpam-1951	340	3	the	the	DET
ejpam-1951	340	4	result	result	NOUN
ejpam-1951	340	5	becomes	become	VERB
ejpam-1951	340	6	p	p	PROPN
ejpam-1951	340	7	i	i	PRON
ejpam-1951	340	8	=	=	NOUN
ejpam-1951	340	9	16x2	16x2	NUM
ejpam-1951	340	10	y2z2	y2z2	X
ejpam-1951	341	1	+	+	CCONJ
ejpam-1951	341	2	10x3	10x3	NUM
ejpam-1951	341	3	y2z	y2z	X
ejpam-1951	341	4	+	+	NUM
ejpam-1951	341	5	5x4	5x4	NUM
ejpam-1951	341	6	yz	yz	NOUN
ejpam-1951	341	7	+	+	NOUN
ejpam-1951	341	8	10x3	10x3	NUM
ejpam-1951	341	9	yz2	yz2	NOUN
ejpam-1951	342	1	+	+	CCONJ
ejpam-1951	342	2	10x2	10x2	NUM
ejpam-1951	342	3	y3z	y3z	PROPN
ejpam-1951	342	4	+	+	PROPN
ejpam-1951	342	5	10x	10x	PROPN
ejpam-1951	342	6	y3z2	y3z2	PROPN
ejpam-1951	342	7	+	+	X
ejpam-1951	342	8	10x	10x	X
ejpam-1951	342	9	y2z3	y2z3	ADP
ejpam-1951	343	1	+	+	PUNCT
ejpam-1951	343	2	5x	5x	NUM
ejpam-1951	343	3	y4z	y4z	NOUN
ejpam-1951	344	1	+	+	CCONJ
ejpam-1951	344	2	x5	x5	PROPN
ejpam-1951	344	3	y	y	PROPN
ejpam-1951	344	4	+	+	PROPN
ejpam-1951	344	5	x5z	x5z	PUNCT
ejpam-1951	345	1	+	+	CCONJ
ejpam-1951	345	2	3x4	3x4	NUM
ejpam-1951	346	1	y2	y2	NOUN
ejpam-1951	346	2	+	+	CCONJ
ejpam-1951	346	3	3x4z2	3x4z2	NUM
ejpam-1951	346	4	+	+	CCONJ
ejpam-1951	346	5	4x3	4x3	NUM
ejpam-1951	346	6	y3	y3	NOUN
ejpam-1951	346	7	+	+	NUM
ejpam-1951	346	8	4x3z3	4x3z3	NUM
ejpam-1951	347	1	+	+	CCONJ
ejpam-1951	347	2	3x2y4	3x2y4	NUM
ejpam-1951	347	3	+	+	SYM
ejpam-1951	347	4	3x2z4	3x2z4	NUM
ejpam-1951	347	5	+	+	CCONJ
ejpam-1951	347	6	x	x	PUNCT
ejpam-1951	347	7	y5	y5	NOUN
ejpam-1951	347	8	+	+	NUM
ejpam-1951	347	9	xz5	xz5	NOUN
ejpam-1951	347	10	+	+	CCONJ
ejpam-1951	347	11	y5z	y5z	X
ejpam-1951	347	12	+	+	PUNCT
ejpam-1951	347	13	3y4z2	3y4z2	NUM
ejpam-1951	347	14	+	+	NUM
ejpam-1951	347	15	4y3z3	4y3z3	NUM
ejpam-1951	347	16	+	+	CCONJ
ejpam-1951	347	17	3y2z4	3y2z4	NUM
ejpam-1951	348	1	+	+	CCONJ
ejpam-1951	349	1	yz5	yz5	PROPN
ejpam-1951	349	2	+	+	CCONJ
ejpam-1951	349	3	10x2	10x2	NUM
ejpam-1951	349	4	yz3	yz3	PROPN
ejpam-1951	349	5	+	+	CCONJ
ejpam-1951	349	6	5x	5x	NUM
ejpam-1951	349	7	yz4	yz4	NOUN
ejpam-1951	350	1	+	+	CCONJ
ejpam-1951	350	2	x6	x6	PROPN
ejpam-1951	350	3	+	+	CCONJ
ejpam-1951	350	4	y6	y6	ADJ
ejpam-1951	350	5	+	+	CCONJ
ejpam-1951	350	6	z6	z6	NOUN
ejpam-1951	350	7	each	each	DET
ejpam-1951	350	8	term	term	NOUN
ejpam-1951	350	9	of	of	ADP
ejpam-1951	350	10	this	this	DET
ejpam-1951	350	11	expression	expression	NOUN
ejpam-1951	350	12	corresponds	correspond	VERB
ejpam-1951	350	13	to	to	ADP
ejpam-1951	350	14	necklaces	necklace	NOUN
ejpam-1951	350	15	with	with	ADP
ejpam-1951	350	16	a	a	DET
ejpam-1951	350	17	fixed	fix	VERB
ejpam-1951	350	18	number	number	NOUN
ejpam-1951	350	19	of	of	ADP
ejpam-1951	350	20	red	red	ADJ
ejpam-1951	350	21	,	,	PUNCT
ejpam-1951	350	22	green	green	ADJ
ejpam-1951	350	23	and	and	CCONJ
ejpam-1951	350	24	blue	blue	ADJ
ejpam-1951	350	25	beads	bead	NOUN
ejpam-1951	350	26	.	.	PUNCT
ejpam-1951	351	1	for	for	ADP
ejpam-1951	351	2	example	example	NOUN
ejpam-1951	351	3	,	,	PUNCT
ejpam-1951	351	4	the	the	DET
ejpam-1951	351	5	term	term	NOUN
ejpam-1951	351	6	3x2	3x2	NUM
ejpam-1951	351	7	y4	y4	PROPN
ejpam-1951	351	8	says	say	VERB
ejpam-1951	351	9	that	that	SCONJ
ejpam-1951	351	10	there	there	PRON
ejpam-1951	351	11	are	be	VERB
ejpam-1951	351	12	3	3	NUM
ejpam-1951	351	13	orbits	orbit	NOUN
ejpam-1951	351	14	with	with	ADP
ejpam-1951	351	15	weight	weight	NOUN
ejpam-1951	351	16	x	x	PUNCT
ejpam-1951	351	17	y4z	y4z	NOUN
ejpam-1951	351	18	or	or	CCONJ
ejpam-1951	351	19	in	in	ADP
ejpam-1951	351	20	other	other	ADJ
ejpam-1951	351	21	words	word	NOUN
ejpam-1951	351	22	3	3	NUM
ejpam-1951	351	23	necklaces	necklace	NOUN
ejpam-1951	351	24	with	with	ADP
ejpam-1951	351	25	2	2	NUM
ejpam-1951	351	26	white	white	ADJ
ejpam-1951	351	27	beads	bead	NOUN
ejpam-1951	351	28	,	,	PUNCT
ejpam-1951	351	29	4	4	NUM
ejpam-1951	351	30	black	black	ADJ
ejpam-1951	351	31	beads	bead	NOUN
ejpam-1951	351	32	and	and	CCONJ
ejpam-1951	351	33	0	0	NUM
ejpam-1951	351	34	gray	gray	ADJ
ejpam-1951	351	35	.	.	PUNCT
ejpam-1951	352	1	they	they	PRON
ejpam-1951	352	2	are	be	AUX
ejpam-1951	352	3	t.	t.	PROPN
ejpam-1951	352	4	nasseef	nasseef	PROPN
ejpam-1951	352	5	/	/	SYM
ejpam-1951	352	6	eur	eur	PROPN
ejpam-1951	352	7	.	.	PUNCT
ejpam-1951	353	1	j.	j.	PROPN
ejpam-1951	353	2	pure	pure	PROPN
ejpam-1951	353	3	appl	appl	PROPN
ejpam-1951	353	4	.	.	PROPN
ejpam-1951	353	5	math	math	PROPN
ejpam-1951	353	6	,	,	PUNCT
ejpam-1951	353	7	9	9	NUM
ejpam-1951	353	8	(	(	PUNCT
ejpam-1951	353	9	2016	2016	NUM
ejpam-1951	353	10	)	)	PUNCT
ejpam-1951	353	11	,	,	PUNCT
ejpam-1951	353	12	84	84	NUM
ejpam-1951	353	13	-	-	SYM
ejpam-1951	353	14	113	113	NUM
ejpam-1951	353	15	98	98	NUM
ejpam-1951	353	16	x1	x1	NUM
ejpam-1951	353	17	y	y	NOUN
ejpam-1951	353	18	2	2	NUM
ejpam-1951	353	19	y	y	PROPN
ejpam-1951	353	20	3	3	NUM
ejpam-1951	353	21	y	y	PROPN
ejpam-1951	353	22	4	4	NUM
ejpam-1951	353	23	x	x	SYM
ejpam-1951	353	24	5	5	NUM
ejpam-1951	353	25	y6	y6	ADJ
ejpam-1951	353	26	(	(	PUNCT
ejpam-1951	353	27	a	a	NOUN
ejpam-1951	353	28	)	)	PUNCT
ejpam-1951	353	29	y1	y1	NOUN
ejpam-1951	353	30	x	x	SYM
ejpam-1951	353	31	2	2	NUM
ejpam-1951	353	32	y	y	PROPN
ejpam-1951	353	33	3	3	NUM
ejpam-1951	353	34	y	y	PROPN
ejpam-1951	353	35	4	4	NUM
ejpam-1951	353	36	x	x	SYM
ejpam-1951	353	37	5	5	NUM
ejpam-1951	353	38	y6	y6	ADJ
ejpam-1951	353	39	(	(	PUNCT
ejpam-1951	353	40	b	b	NOUN
ejpam-1951	353	41	)	)	PUNCT
ejpam-1951	353	42	x1	x1	NOUN
ejpam-1951	353	43	x	x	SYM
ejpam-1951	353	44	2	2	NUM
ejpam-1951	353	45	y	y	PROPN
ejpam-1951	353	46	3	3	NUM
ejpam-1951	353	47	y	y	NOUN
ejpam-1951	353	48	4	4	NUM
ejpam-1951	353	49	y	y	SYM
ejpam-1951	353	50	5	5	NUM
ejpam-1951	353	51	y6	y6	ADJ
ejpam-1951	353	52	(	(	PUNCT
ejpam-1951	353	53	c	c	NOUN
ejpam-1951	353	54	)	)	PUNCT
ejpam-1951	353	55	figure	figure	NOUN
ejpam-1951	353	56	6	6	NUM
ejpam-1951	353	57	:	:	SYM
ejpam-1951	353	58	3	3	NUM
ejpam-1951	353	59	necklaces	necklace	NOUN
ejpam-1951	353	60	with	with	ADP
ejpam-1951	353	61	2	2	NUM
ejpam-1951	353	62	white	white	ADJ
ejpam-1951	353	63	beads	bead	NOUN
ejpam-1951	353	64	and	and	CCONJ
ejpam-1951	353	65	4	4	NUM
ejpam-1951	353	66	black	black	ADJ
ejpam-1951	353	67	beads	bead	NOUN
ejpam-1951	353	68	problem	problem	NOUN
ejpam-1951	353	69	2	2	NUM
ejpam-1951	353	70	(	(	PUNCT
ejpam-1951	353	71	face	face	NOUN
ejpam-1951	353	72	coloring	coloring	NOUN
ejpam-1951	353	73	of	of	ADP
ejpam-1951	353	74	a	a	DET
ejpam-1951	353	75	cube	cube	NOUN
ejpam-1951	353	76	)	)	PUNCT
ejpam-1951	353	77	.	.	PUNCT
ejpam-1951	354	1	a	a	DET
ejpam-1951	354	2	cube	cube	NOUN
ejpam-1951	354	3	has	have	VERB
ejpam-1951	354	4	6	6	NUM
ejpam-1951	354	5	faces	face	NOUN
ejpam-1951	354	6	and	and	CCONJ
ejpam-1951	354	7	the	the	DET
ejpam-1951	354	8	faces	face	NOUN
ejpam-1951	354	9	are	be	AUX
ejpam-1951	354	10	to	to	PART
ejpam-1951	354	11	be	be	AUX
ejpam-1951	354	12	colored	color	VERB
ejpam-1951	354	13	.	.	PUNCT
ejpam-1951	355	1	how	how	SCONJ
ejpam-1951	355	2	many	many	ADJ
ejpam-1951	355	3	inequivalent	inequivalent	NOUN
ejpam-1951	355	4	ways	way	NOUN
ejpam-1951	355	5	are	be	AUX
ejpam-1951	355	6	there	there	ADV
ejpam-1951	355	7	to	to	PART
ejpam-1951	355	8	color	color	VERB
ejpam-1951	355	9	it	it	PRON
ejpam-1951	355	10	with	with	ADP
ejpam-1951	355	11	namely	namely	ADV
ejpam-1951	355	12	(	(	PUNCT
ejpam-1951	355	13	a	a	X
ejpam-1951	355	14	)	)	PUNCT
ejpam-1951	355	15	4	4	NUM
ejpam-1951	355	16	red	red	ADJ
ejpam-1951	355	17	and	and	CCONJ
ejpam-1951	355	18	2	2	NUM
ejpam-1951	355	19	green	green	ADJ
ejpam-1951	355	20	faces	face	NOUN
ejpam-1951	355	21	?	?	PUNCT
ejpam-1951	356	1	(	(	PUNCT
ejpam-1951	356	2	b	b	X
ejpam-1951	356	3	)	)	PUNCT
ejpam-1951	356	4	3	3	NUM
ejpam-1951	356	5	red	red	ADJ
ejpam-1951	356	6	,	,	PUNCT
ejpam-1951	356	7	2	2	NUM
ejpam-1951	356	8	green	green	ADJ
ejpam-1951	356	9	and	and	CCONJ
ejpam-1951	356	10	1	1	NUM
ejpam-1951	356	11	blue	blue	ADJ
ejpam-1951	356	12	faces	face	NOUN
ejpam-1951	356	13	?	?	PUNCT
ejpam-1951	357	1	(	(	PUNCT
ejpam-1951	357	2	c	c	X
ejpam-1951	357	3	)	)	PUNCT
ejpam-1951	357	4	2	2	NUM
ejpam-1951	357	5	red	red	ADJ
ejpam-1951	357	6	,	,	PUNCT
ejpam-1951	357	7	1	1	NUM
ejpam-1951	357	8	green	green	ADJ
ejpam-1951	357	9	,	,	PUNCT
ejpam-1951	357	10	1	1	NUM
ejpam-1951	357	11	blue	blue	ADJ
ejpam-1951	357	12	and	and	CCONJ
ejpam-1951	357	13	2	2	NUM
ejpam-1951	357	14	yellow	yellow	ADJ
ejpam-1951	357	15	faces	face	NOUN
ejpam-1951	357	16	?	?	PUNCT
ejpam-1951	358	1	solution	solution	NOUN
ejpam-1951	358	2	:	:	PUNCT
ejpam-1951	358	3	we	we	PRON
ejpam-1951	358	4	have	have	VERB
ejpam-1951	358	5	to	to	PART
ejpam-1951	358	6	color	color	VERB
ejpam-1951	358	7	the	the	DET
ejpam-1951	358	8	faces	face	NOUN
ejpam-1951	358	9	of	of	ADP
ejpam-1951	358	10	the	the	DET
ejpam-1951	358	11	cube	cube	NOUN
ejpam-1951	358	12	.	.	PUNCT
ejpam-1951	359	1	so	so	ADV
ejpam-1951	359	2	recall	recall	VERB
ejpam-1951	359	3	example	example	NOUN
ejpam-1951	359	4	11	11	NUM
ejpam-1951	359	5	.	.	PUNCT
ejpam-1951	360	1	then	then	ADV
ejpam-1951	360	2	the	the	DET
ejpam-1951	360	3	cycle	cycle	NOUN
ejpam-1951	360	4	index	index	NOUN
ejpam-1951	360	5	is	be	AUX
ejpam-1951	360	6	z(g	z(g	NOUN
ejpam-1951	360	7	,	,	PUNCT
ejpam-1951	360	8	t1	t1	NOUN
ejpam-1951	360	9	,	,	PUNCT
ejpam-1951	360	10	t2	t2	NOUN
ejpam-1951	360	11	,	,	PUNCT
ejpam-1951	360	12	.	.	PUNCT
ejpam-1951	360	13	.	.	PUNCT
ejpam-1951	361	1	.	.	PUNCT
ejpam-1951	362	1	,	,	PUNCT
ejpam-1951	362	2	t6	t6	PROPN
ejpam-1951	362	3	)	)	PUNCT
ejpam-1951	363	1	=	=	SYM
ejpam-1951	363	2	1	1	NUM
ejpam-1951	363	3	24	24	NUM
ejpam-1951	363	4	(	(	PUNCT
ejpam-1951	363	5	6t2	6t2	NUM
ejpam-1951	363	6	1	1	NUM
ejpam-1951	363	7	t4	t4	PROPN
ejpam-1951	363	8	+	+	NUM
ejpam-1951	363	9	3t2	3t2	NUM
ejpam-1951	363	10	1	1	NUM
ejpam-1951	363	11	t2	t2	NOUN
ejpam-1951	363	12	2	2	NUM
ejpam-1951	363	13	+	+	CCONJ
ejpam-1951	363	14	8t2	8t2	NUM
ejpam-1951	363	15	3	3	NUM
ejpam-1951	363	16	+	+	SYM
ejpam-1951	363	17	6t3	6t3	NUM
ejpam-1951	363	18	2	2	NUM
ejpam-1951	363	19	+	+	CCONJ
ejpam-1951	363	20	t6	t6	PROPN
ejpam-1951	363	21	1	1	NUM
ejpam-1951	363	22	)	)	PUNCT
ejpam-1951	363	23	now	now	ADV
ejpam-1951	363	24	we	we	PRON
ejpam-1951	363	25	will	will	AUX
ejpam-1951	363	26	apply	apply	VERB
ejpam-1951	363	27	pólya	pólya	NOUN
ejpam-1951	363	28	’s	’s	PART
ejpam-1951	363	29	substitution	substitution	NOUN
ejpam-1951	363	30	method	method	NOUN
ejpam-1951	363	31	.	.	PUNCT
ejpam-1951	364	1	let	let	VERB
ejpam-1951	364	2	the	the	DET
ejpam-1951	364	3	colors	color	NOUN
ejpam-1951	364	4	red	red	ADJ
ejpam-1951	364	5	,	,	PUNCT
ejpam-1951	364	6	green	green	ADJ
ejpam-1951	364	7	,	,	PUNCT
ejpam-1951	364	8	blue	blue	ADJ
ejpam-1951	364	9	and	and	CCONJ
ejpam-1951	364	10	yellow	yellow	NOUN
ejpam-1951	364	11	be	be	AUX
ejpam-1951	364	12	denoted	denote	VERB
ejpam-1951	364	13	by	by	ADP
ejpam-1951	364	14	x	x	SYM
ejpam-1951	364	15	,	,	PUNCT
ejpam-1951	364	16	y	y	PROPN
ejpam-1951	364	17	,	,	PUNCT
ejpam-1951	364	18	z	z	PROPN
ejpam-1951	364	19	and	and	CCONJ
ejpam-1951	364	20	p	p	NOUN
ejpam-1951	364	21	respectively	respectively	ADV
ejpam-1951	364	22	.	.	PUNCT
ejpam-1951	365	1	then	then	ADV
ejpam-1951	365	2	substituting	substitute	VERB
ejpam-1951	365	3	t	t	PROPN
ejpam-1951	365	4	i	i	PRON
ejpam-1951	365	5	→	→	PUNCT
ejpam-1951	365	6	(	(	PUNCT
ejpam-1951	365	7	x	x	X
ejpam-1951	365	8	i	i	PRON
ejpam-1951	365	9	+	+	NOUN
ejpam-1951	365	10	y	y	NOUN
ejpam-1951	365	11	i	i	PRON
ejpam-1951	366	1	+	+	CCONJ
ejpam-1951	366	2	z	z	NOUN
ejpam-1951	367	1	i	i	PRON
ejpam-1951	367	2	+	+	CCONJ
ejpam-1951	367	3	pi	pi	NOUN
ejpam-1951	367	4	)	)	PUNCT
ejpam-1951	367	5	for	for	ADP
ejpam-1951	367	6	each	each	DET
ejpam-1951	367	7	i	i	PRON
ejpam-1951	367	8	=	=	PUNCT
ejpam-1951	367	9	{	{	PUNCT
ejpam-1951	367	10	1,2,3,4,5,6	1,2,3,4,5,6	NUM
ejpam-1951	367	11	}	}	PUNCT
ejpam-1951	367	12	in	in	ADP
ejpam-1951	367	13	the	the	DET
ejpam-1951	367	14	previous	previous	ADJ
ejpam-1951	367	15	equation	equation	NOUN
ejpam-1951	367	16	,	,	PUNCT
ejpam-1951	367	17	we	we	PRON
ejpam-1951	367	18	get	get	VERB
ejpam-1951	367	19	zg	zg	NOUN
ejpam-1951	367	20	=	=	SYM
ejpam-1951	367	21	1	1	NUM
ejpam-1951	367	22	24	24	NUM
ejpam-1951	367	23	(	(	PUNCT
ejpam-1951	367	24	6(x	6(x	NUM
ejpam-1951	367	25	+	+	CCONJ
ejpam-1951	367	26	y	y	PROPN
ejpam-1951	367	27	+	+	NOUN
ejpam-1951	367	28	z	z	NOUN
ejpam-1951	367	29	+	+	CCONJ
ejpam-1951	367	30	p)2(x4	p)2(x4	VERB
ejpam-1951	367	31	+	+	CCONJ
ejpam-1951	367	32	y4	y4	ADJ
ejpam-1951	367	33	+	+	CCONJ
ejpam-1951	367	34	z4	z4	PROPN
ejpam-1951	367	35	+	+	CCONJ
ejpam-1951	367	36	p4	p4	ADJ
ejpam-1951	367	37	)	)	PUNCT
ejpam-1951	368	1	+	+	CCONJ
ejpam-1951	368	2	3(x	3(x	NUM
ejpam-1951	368	3	+	+	CCONJ
ejpam-1951	368	4	y	y	PROPN
ejpam-1951	368	5	+	+	CCONJ
ejpam-1951	368	6	z	z	NOUN
ejpam-1951	368	7	+	+	CCONJ
ejpam-1951	368	8	p)2(x2	p)2(x2	NOUN
ejpam-1951	368	9	+	+	CCONJ
ejpam-1951	368	10	y2	y2	PROPN
ejpam-1951	368	11	+	+	CCONJ
ejpam-1951	368	12	z2	z2	PROPN
ejpam-1951	368	13	+	+	CCONJ
ejpam-1951	368	14	p2)2	p2)2	ADP
ejpam-1951	368	15	+	+	NOUN
ejpam-1951	368	16	8(x3	8(x3	NUM
ejpam-1951	368	17	+	+	NUM
ejpam-1951	368	18	y3	y3	NOUN
ejpam-1951	368	19	+	+	CCONJ
ejpam-1951	368	20	z3	z3	PROPN
ejpam-1951	368	21	+	+	CCONJ
ejpam-1951	368	22	p3)2	p3)2	PROPN
ejpam-1951	368	23	+	+	CCONJ
ejpam-1951	368	24	6(x2	6(x2	NUM
ejpam-1951	368	25	+	+	CCONJ
ejpam-1951	368	26	y2	y2	NOUN
ejpam-1951	368	27	+	+	CCONJ
ejpam-1951	368	28	z2	z2	PROPN
ejpam-1951	368	29	+	+	CCONJ
ejpam-1951	368	30	p2)3	p2)3	PUNCT
ejpam-1951	368	31	+	+	X
ejpam-1951	368	32	(	(	PUNCT
ejpam-1951	368	33	x	x	X
ejpam-1951	368	34	+	+	NUM
ejpam-1951	368	35	y	y	PROPN
ejpam-1951	368	36	+	+	CCONJ
ejpam-1951	368	37	z	z	NOUN
ejpam-1951	368	38	+	+	CCONJ
ejpam-1951	368	39	p)6	p)6	NOUN
ejpam-1951	368	40	)	)	PUNCT
ejpam-1951	368	41	using	use	VERB
ejpam-1951	368	42	maple	maple	NOUN
ejpam-1951	368	43	we	we	PRON
ejpam-1951	368	44	find	find	VERB
ejpam-1951	368	45	that	that	SCONJ
ejpam-1951	368	46	,	,	PUNCT
ejpam-1951	368	47	zg	zg	PROPN
ejpam-1951	368	48	=	=	NOUN
ejpam-1951	368	49	3y3px2	3y3px2	NUM
ejpam-1951	368	50	+	+	SYM
ejpam-1951	368	51	3y3zp2	3y3zp2	NUM
ejpam-1951	369	1	+	+	CCONJ
ejpam-1951	369	2	3yz3p2	3yz3p2	NUM
ejpam-1951	369	3	+	+	NUM
ejpam-1951	369	4	3y3pz2	3y3pz2	NUM
ejpam-1951	369	5	+	+	CCONJ
ejpam-1951	369	6	3yp3z2	3yp3z2	NUM
ejpam-1951	369	7	+	+	CCONJ
ejpam-1951	369	8	3x	3x	NUM
ejpam-1951	369	9	p3	p3	PROPN
ejpam-1951	369	10	y2	y2	PROPN
ejpam-1951	369	11	+	+	CCONJ
ejpam-1951	369	12	3x3p	3x3p	ADJ
ejpam-1951	369	13	y2	y2	NOUN
ejpam-1951	370	1	+	+	CCONJ
ejpam-1951	371	1	3x3pz2	3x3pz2	NUM
ejpam-1951	371	2	+	+	SYM
ejpam-1951	371	3	3x	3x	NUM
ejpam-1951	371	4	p3z2	p3z2	NOUN
ejpam-1951	371	5	+	+	CCONJ
ejpam-1951	372	1	6x2z2p2	6x2z2p2	NUM
ejpam-1951	372	2	+	+	NUM
ejpam-1951	372	3	2ypx4	2ypx4	NUM
ejpam-1951	372	4	+	+	NUM
ejpam-1951	372	5	2zpx4	2zpx4	NUM
ejpam-1951	372	6	+	+	CCONJ
ejpam-1951	372	7	2yzp4	2yzp4	NUM
ejpam-1951	372	8	+	+	NUM
ejpam-1951	372	9	2x	2x	NUM
ejpam-1951	372	10	pz4	pz4	NOUN
ejpam-1951	372	11	+	+	CCONJ
ejpam-1951	372	12	3zp3	3zp3	NUM
ejpam-1951	372	13	y2	y2	NOUN
ejpam-1951	372	14	+	+	CCONJ
ejpam-1951	372	15	2yzx4	2yzx4	NUM
ejpam-1951	373	1	+	+	NUM
ejpam-1951	373	2	8x	8x	PROPN
ejpam-1951	373	3	yz2p2	yz2p2	PROPN
ejpam-1951	373	4	+	+	CCONJ
ejpam-1951	373	5	8xz	8xz	ADJ
ejpam-1951	373	6	y2p2	y2p2	NOUN
ejpam-1951	374	1	+	+	CCONJ
ejpam-1951	374	2	8x	8x	PROPN
ejpam-1951	374	3	p	p	X
ejpam-1951	374	4	y2z2	y2z2	PROPN
ejpam-1951	374	5	+	+	NUM
ejpam-1951	374	6	8yzx2p2	8yzx2p2	NUM
ejpam-1951	374	7	+	+	NUM
ejpam-1951	374	8	8ypx2z2	8ypx2z2	NUM
ejpam-1951	374	9	+	+	CCONJ
ejpam-1951	374	10	8zpx2	8zpx2	NUM
ejpam-1951	374	11	y2	y2	NOUN
ejpam-1951	374	12	+	+	CCONJ
ejpam-1951	374	13	5x3	5x3	NUM
ejpam-1951	374	14	yzp	yzp	NOUN
ejpam-1951	374	15	+	+	CCONJ
ejpam-1951	374	16	5x	5x	NUM
ejpam-1951	374	17	y3zp+	y3zp+	NOUN
ejpam-1951	374	18	5x	5x	NUM
ejpam-1951	374	19	yzp3	yzp3	NOUN
ejpam-1951	374	20	+	+	CCONJ
ejpam-1951	374	21	5x	5x	NUM
ejpam-1951	374	22	yz3p+	yz3p+	NOUN
ejpam-1951	374	23	3yz3	3yz3	NUM
ejpam-1951	374	24	x2	x2	NOUN
ejpam-1951	375	1	+	+	CCONJ
ejpam-1951	375	2	3yp3	3yp3	NUM
ejpam-1951	375	3	x2	x2	NOUN
ejpam-1951	376	1	+	+	CCONJ
ejpam-1951	376	2	3x	3x	NUM
ejpam-1951	376	3	y3z2	y3z2	NOUN
ejpam-1951	376	4	+	+	CCONJ
ejpam-1951	376	5	2x	2x	NUM
ejpam-1951	376	6	yz4	yz4	X
ejpam-1951	377	1	+	+	CCONJ
ejpam-1951	377	2	6x2	6x2	NUM
ejpam-1951	377	3	y2z2	y2z2	X
ejpam-1951	377	4	+	+	CCONJ
ejpam-1951	377	5	6x2	6x2	NUM
ejpam-1951	377	6	y2p2	y2p2	NOUN
ejpam-1951	377	7	+	+	CCONJ
ejpam-1951	377	8	2ypz4	2ypz4	NUM
ejpam-1951	377	9	+	+	NUM
ejpam-1951	377	10	2x	2x	NUM
ejpam-1951	377	11	p	p	VERB
ejpam-1951	377	12	y4	y4	PROPN
ejpam-1951	378	1	+	+	CCONJ
ejpam-1951	378	2	2x	2x	NUM
ejpam-1951	378	3	yp4	yp4	NOUN
ejpam-1951	379	1	+	+	CCONJ
ejpam-1951	379	2	3xz3p2	3xz3p2	NUM
ejpam-1951	380	1	+	+	NUM
ejpam-1951	380	2	3x3zp2	3x3zp2	NUM
ejpam-1951	381	1	+	+	CCONJ
ejpam-1951	381	2	2xzp4	2xzp4	NUM
ejpam-1951	381	3	+	+	SYM
ejpam-1951	381	4	3x3	3x3	NUM
ejpam-1951	381	5	yp2	yp2	NOUN
ejpam-1951	381	6	t.	t.	PROPN
ejpam-1951	381	7	nasseef	nasseef	PROPN
ejpam-1951	381	8	/	/	SYM
ejpam-1951	381	9	eur	eur	PROPN
ejpam-1951	381	10	.	.	PUNCT
ejpam-1951	382	1	j.	j.	PROPN
ejpam-1951	382	2	pure	pure	PROPN
ejpam-1951	382	3	appl	appl	PROPN
ejpam-1951	382	4	.	.	PROPN
ejpam-1951	382	5	math	math	PROPN
ejpam-1951	382	6	,	,	PUNCT
ejpam-1951	382	7	9	9	NUM
ejpam-1951	382	8	(	(	PUNCT
ejpam-1951	382	9	2016	2016	NUM
ejpam-1951	382	10	)	)	PUNCT
ejpam-1951	382	11	,	,	PUNCT
ejpam-1951	382	12	84	84	NUM
ejpam-1951	382	13	-	-	SYM
ejpam-1951	382	14	113	113	NUM
ejpam-1951	382	15	99	99	NUM
ejpam-1951	382	16	+	+	CCONJ
ejpam-1951	382	17	3x3	3x3	NUM
ejpam-1951	382	18	yz2	yz2	ADJ
ejpam-1951	383	1	+	+	NUM
ejpam-1951	383	2	3x	3x	NUM
ejpam-1951	383	3	y3p2	y3p2	NOUN
ejpam-1951	383	4	+	+	X
ejpam-1951	383	5	2zp	2zp	ADJ
ejpam-1951	383	6	y4	y4	NOUN
ejpam-1951	383	7	+	+	CCONJ
ejpam-1951	383	8	2xz	2xz	ADJ
ejpam-1951	383	9	y4	y4	NOUN
ejpam-1951	384	1	+	+	CCONJ
ejpam-1951	385	1	3y3zx2	3y3zx2	NUM
ejpam-1951	385	2	+	+	NUM
ejpam-1951	385	3	3x3zy2	3x3zy2	NUM
ejpam-1951	385	4	+	+	SYM
ejpam-1951	385	5	3z3px2	3z3px2	NUM
ejpam-1951	385	6	+	+	CCONJ
ejpam-1951	385	7	6y2z2p2	6y2z2p2	NUM
ejpam-1951	385	8	+	+	CCONJ
ejpam-1951	385	9	3z3p	3z3p	NOUN
ejpam-1951	385	10	y2	y2	NOUN
ejpam-1951	385	11	+	+	CCONJ
ejpam-1951	385	12	3zp3	3zp3	NUM
ejpam-1951	385	13	x2	x2	NOUN
ejpam-1951	386	1	+	+	X
ejpam-1951	386	2	3xz3	3xz3	NUM
ejpam-1951	386	3	y2	y2	NOUN
ejpam-1951	386	4	+	+	CCONJ
ejpam-1951	386	5	2y2z4	2y2z4	NUM
ejpam-1951	386	6	+	+	CCONJ
ejpam-1951	386	7	y5z	y5z	X
ejpam-1951	386	8	+	+	CCONJ
ejpam-1951	386	9	yz5	yz5	PROPN
ejpam-1951	386	10	+	+	CCONJ
ejpam-1951	386	11	2z2	2z2	NUM
ejpam-1951	386	12	x4	x4	PROPN
ejpam-1951	386	13	+	+	CCONJ
ejpam-1951	386	14	2z2	2z2	NUM
ejpam-1951	386	15	y4	y4	NOUN
ejpam-1951	386	16	+	+	CCONJ
ejpam-1951	386	17	x5z	x5z	PUNCT
ejpam-1951	387	1	+	+	PUNCT
ejpam-1951	387	2	xz5	xz5	NOUN
ejpam-1951	387	3	+	+	CCONJ
ejpam-1951	387	4	2y2x4	2y2x4	NUM
ejpam-1951	387	5	+	+	SYM
ejpam-1951	387	6	2x2	2x2	NUM
ejpam-1951	387	7	y4	y4	ADJ
ejpam-1951	387	8	+	+	NOUN
ejpam-1951	387	9	2x2z4	2x2z4	NUM
ejpam-1951	387	10	+	+	CCONJ
ejpam-1951	387	11	x5	x5	PROPN
ejpam-1951	387	12	y	y	PROPN
ejpam-1951	387	13	+	+	NOUN
ejpam-1951	387	14	x	x	PUNCT
ejpam-1951	387	15	y5	y5	NOUN
ejpam-1951	387	16	+	+	CCONJ
ejpam-1951	387	17	x6	x6	PROPN
ejpam-1951	387	18	+	+	CCONJ
ejpam-1951	387	19	y6	y6	ADJ
ejpam-1951	387	20	+	+	CCONJ
ejpam-1951	387	21	z6	z6	NOUN
ejpam-1951	387	22	+	+	CCONJ
ejpam-1951	387	23	p6	p6	ADJ
ejpam-1951	387	24	+	+	CCONJ
ejpam-1951	387	25	2x3	2x3	NUM
ejpam-1951	387	26	y3	y3	NOUN
ejpam-1951	387	27	+	+	NUM
ejpam-1951	387	28	2x3z3	2x3z3	NUM
ejpam-1951	387	29	+	+	CCONJ
ejpam-1951	387	30	2y3z3	2y3z3	NUM
ejpam-1951	387	31	+	+	CCONJ
ejpam-1951	387	32	2x2p4	2x2p4	NUM
ejpam-1951	387	33	+	+	CCONJ
ejpam-1951	387	34	x5p+	x5p+	PROPN
ejpam-1951	387	35	x	x	X
ejpam-1951	387	36	p5	p5	ADJ
ejpam-1951	387	37	+	+	CCONJ
ejpam-1951	387	38	2y2p4	2y2p4	NOUN
ejpam-1951	387	39	+	+	CCONJ
ejpam-1951	387	40	y5p+	y5p+	ADJ
ejpam-1951	387	41	yp5	yp5	NOUN
ejpam-1951	387	42	+	+	CCONJ
ejpam-1951	387	43	2z2p4	2z2p4	NUM
ejpam-1951	387	44	+	+	CCONJ
ejpam-1951	387	45	z5p+	z5p+	PROPN
ejpam-1951	387	46	zp5	zp5	PROPN
ejpam-1951	388	1	+	+	CCONJ
ejpam-1951	388	2	2p2	2p2	NUM
ejpam-1951	388	3	x4	x4	PROPN
ejpam-1951	388	4	+	+	CCONJ
ejpam-1951	388	5	2p2	2p2	NUM
ejpam-1951	388	6	y4	y4	ADJ
ejpam-1951	388	7	+	+	CCONJ
ejpam-1951	388	8	2p2z4	2p2z4	NUM
ejpam-1951	388	9	+	+	CCONJ
ejpam-1951	388	10	2x3p3	2x3p3	NOUN
ejpam-1951	389	1	+	+	CCONJ
ejpam-1951	389	2	2y3p3	2y3p3	PRON
ejpam-1951	389	3	+	+	NOUN
ejpam-1951	389	4	2z3p3	2z3p3	NUM
ejpam-1951	389	5	each	each	DET
ejpam-1951	389	6	term	term	NOUN
ejpam-1951	389	7	of	of	ADP
ejpam-1951	389	8	this	this	DET
ejpam-1951	389	9	expression	expression	NOUN
ejpam-1951	389	10	on	on	ADP
ejpam-1951	389	11	the	the	DET
ejpam-1951	389	12	right	right	ADJ
ejpam-1951	389	13	hand	hand	NOUN
ejpam-1951	389	14	side	side	NOUN
ejpam-1951	389	15	corresponds	correspond	VERB
ejpam-1951	389	16	to	to	ADP
ejpam-1951	389	17	a	a	DET
ejpam-1951	389	18	fixed	fix	VERB
ejpam-1951	389	19	number	number	NOUN
ejpam-1951	389	20	of	of	ADP
ejpam-1951	389	21	red	red	ADJ
ejpam-1951	389	22	,	,	PUNCT
ejpam-1951	389	23	green	green	ADJ
ejpam-1951	389	24	,	,	PUNCT
ejpam-1951	389	25	blue	blue	ADJ
ejpam-1951	389	26	and	and	CCONJ
ejpam-1951	389	27	yellow	yellow	ADJ
ejpam-1951	389	28	colors	color	NOUN
ejpam-1951	389	29	.	.	PUNCT
ejpam-1951	390	1	(	(	PUNCT
ejpam-1951	390	2	a	a	X
ejpam-1951	390	3	)	)	PUNCT
ejpam-1951	390	4	the	the	DET
ejpam-1951	390	5	term	term	NOUN
ejpam-1951	390	6	2x4	2x4	NUM
ejpam-1951	390	7	y2	y2	NOUN
ejpam-1951	390	8	says	say	VERB
ejpam-1951	390	9	that	that	SCONJ
ejpam-1951	390	10	there	there	PRON
ejpam-1951	390	11	are	be	VERB
ejpam-1951	390	12	2	2	NUM
ejpam-1951	390	13	possible	possible	ADJ
ejpam-1951	390	14	ways	way	NOUN
ejpam-1951	390	15	to	to	PART
ejpam-1951	390	16	color	color	VERB
ejpam-1951	390	17	the	the	DET
ejpam-1951	390	18	cube	cube	NOUN
ejpam-1951	390	19	with	with	ADP
ejpam-1951	390	20	4	4	NUM
ejpam-1951	390	21	red	red	ADJ
ejpam-1951	390	22	and	and	CCONJ
ejpam-1951	390	23	2	2	NUM
ejpam-1951	390	24	green	green	ADJ
ejpam-1951	390	25	faces	face	NOUN
ejpam-1951	390	26	.	.	PUNCT
ejpam-1951	391	1	(	(	PUNCT
ejpam-1951	391	2	b	b	X
ejpam-1951	391	3	)	)	PUNCT
ejpam-1951	391	4	the	the	DET
ejpam-1951	391	5	term	term	NOUN
ejpam-1951	391	6	3x3	3x3	NUM
ejpam-1951	391	7	y2z	y2z	NOUN
ejpam-1951	391	8	says	say	VERB
ejpam-1951	391	9	that	that	SCONJ
ejpam-1951	391	10	there	there	PRON
ejpam-1951	391	11	are	be	VERB
ejpam-1951	391	12	3	3	NUM
ejpam-1951	391	13	possible	possible	ADJ
ejpam-1951	391	14	ways	way	NOUN
ejpam-1951	391	15	to	to	PART
ejpam-1951	391	16	color	color	VERB
ejpam-1951	391	17	the	the	DET
ejpam-1951	391	18	cube	cube	NOUN
ejpam-1951	391	19	with	with	ADP
ejpam-1951	391	20	3	3	NUM
ejpam-1951	391	21	red	red	ADJ
ejpam-1951	391	22	,	,	PUNCT
ejpam-1951	391	23	2	2	NUM
ejpam-1951	391	24	green	green	ADJ
ejpam-1951	391	25	and	and	CCONJ
ejpam-1951	391	26	1	1	NUM
ejpam-1951	391	27	blue	blue	ADJ
ejpam-1951	391	28	faces	face	NOUN
ejpam-1951	391	29	.	.	PUNCT
ejpam-1951	392	1	(	(	PUNCT
ejpam-1951	392	2	c	c	X
ejpam-1951	392	3	)	)	PUNCT
ejpam-1951	392	4	the	the	DET
ejpam-1951	392	5	term	term	NOUN
ejpam-1951	392	6	8x2	8x2	NUM
ejpam-1951	392	7	yzp2	yzp2	PROPN
ejpam-1951	392	8	says	say	VERB
ejpam-1951	392	9	that	that	SCONJ
ejpam-1951	392	10	there	there	PRON
ejpam-1951	392	11	are	be	VERB
ejpam-1951	392	12	8	8	NUM
ejpam-1951	392	13	possible	possible	ADJ
ejpam-1951	392	14	ways	way	NOUN
ejpam-1951	392	15	to	to	PART
ejpam-1951	392	16	color	color	VERB
ejpam-1951	392	17	the	the	DET
ejpam-1951	392	18	cube	cube	NOUN
ejpam-1951	392	19	with	with	ADP
ejpam-1951	392	20	2	2	NUM
ejpam-1951	392	21	red	red	ADJ
ejpam-1951	392	22	,	,	PUNCT
ejpam-1951	392	23	1	1	NUM
ejpam-1951	392	24	green	green	ADJ
ejpam-1951	392	25	,	,	PUNCT
ejpam-1951	392	26	1	1	NUM
ejpam-1951	392	27	blue	blue	ADJ
ejpam-1951	392	28	and	and	CCONJ
ejpam-1951	392	29	2	2	NUM
ejpam-1951	392	30	yellow	yellow	ADJ
ejpam-1951	392	31	faces	face	NOUN
ejpam-1951	392	32	.	.	PUNCT
ejpam-1951	393	1	problem	problem	NOUN
ejpam-1951	393	2	3	3	NUM
ejpam-1951	393	3	(	(	PUNCT
ejpam-1951	393	4	vertex	vertex	NOUN
ejpam-1951	393	5	coloring	coloring	NOUN
ejpam-1951	393	6	of	of	ADP
ejpam-1951	393	7	a	a	DET
ejpam-1951	393	8	cube	cube	NOUN
ejpam-1951	393	9	)	)	PUNCT
ejpam-1951	393	10	.	.	PUNCT
ejpam-1951	394	1	a	a	DET
ejpam-1951	394	2	cube	cube	NOUN
ejpam-1951	394	3	has	have	VERB
ejpam-1951	394	4	8	8	NUM
ejpam-1951	394	5	vertices	vertex	NOUN
ejpam-1951	394	6	and	and	CCONJ
ejpam-1951	394	7	the	the	DET
ejpam-1951	394	8	vertices	vertex	NOUN
ejpam-1951	394	9	are	be	AUX
ejpam-1951	394	10	to	to	PART
ejpam-1951	394	11	be	be	AUX
ejpam-1951	394	12	colored	color	VERB
ejpam-1951	394	13	.	.	PUNCT
ejpam-1951	395	1	how	how	SCONJ
ejpam-1951	395	2	many	many	ADJ
ejpam-1951	395	3	inequivalent	inequivalent	NOUN
ejpam-1951	395	4	ways	way	NOUN
ejpam-1951	395	5	are	be	AUX
ejpam-1951	395	6	there	there	ADV
ejpam-1951	395	7	to	to	PART
ejpam-1951	395	8	color	color	VERB
ejpam-1951	395	9	it	it	PRON
ejpam-1951	395	10	with	with	ADP
ejpam-1951	395	11	(	(	PUNCT
ejpam-1951	395	12	a	a	X
ejpam-1951	395	13	)	)	PUNCT
ejpam-1951	395	14	6	6	NUM
ejpam-1951	395	15	black	black	ADJ
ejpam-1951	395	16	,	,	PUNCT
ejpam-1951	395	17	1	1	NUM
ejpam-1951	395	18	yellow	yellow	ADJ
ejpam-1951	395	19	and	and	CCONJ
ejpam-1951	395	20	1	1	NUM
ejpam-1951	395	21	green	green	ADJ
ejpam-1951	395	22	vertices	vertex	NOUN
ejpam-1951	395	23	?	?	PUNCT
ejpam-1951	396	1	(	(	PUNCT
ejpam-1951	396	2	b	b	X
ejpam-1951	396	3	)	)	PUNCT
ejpam-1951	396	4	1	1	NUM
ejpam-1951	396	5	black	black	ADJ
ejpam-1951	396	6	,	,	PUNCT
ejpam-1951	396	7	1	1	NUM
ejpam-1951	396	8	red	red	ADJ
ejpam-1951	396	9	,	,	PUNCT
ejpam-1951	396	10	4	4	NUM
ejpam-1951	396	11	blue	blue	ADJ
ejpam-1951	396	12	and	and	CCONJ
ejpam-1951	396	13	2	2	NUM
ejpam-1951	396	14	yellow	yellow	ADJ
ejpam-1951	396	15	vertices	vertex	NOUN
ejpam-1951	396	16	?	?	PUNCT
ejpam-1951	397	1	(	(	PUNCT
ejpam-1951	397	2	c	c	X
ejpam-1951	397	3	)	)	PUNCT
ejpam-1951	397	4	3	3	NUM
ejpam-1951	397	5	black	black	ADJ
ejpam-1951	397	6	,	,	PUNCT
ejpam-1951	397	7	1	1	NUM
ejpam-1951	397	8	red	red	ADJ
ejpam-1951	397	9	,	,	PUNCT
ejpam-1951	397	10	1	1	NUM
ejpam-1951	397	11	green	green	ADJ
ejpam-1951	397	12	1	1	NUM
ejpam-1951	397	13	blue	blue	ADJ
ejpam-1951	397	14	and	and	CCONJ
ejpam-1951	397	15	2	2	NUM
ejpam-1951	397	16	yellow	yellow	ADJ
ejpam-1951	397	17	vertices	vertex	NOUN
ejpam-1951	397	18	?	?	PUNCT
ejpam-1951	398	1	solution	solution	NOUN
ejpam-1951	398	2	:	:	PUNCT
ejpam-1951	398	3	we	we	PRON
ejpam-1951	398	4	have	have	VERB
ejpam-1951	398	5	to	to	PART
ejpam-1951	398	6	color	color	VERB
ejpam-1951	398	7	the	the	DET
ejpam-1951	398	8	vertices	vertex	NOUN
ejpam-1951	398	9	of	of	ADP
ejpam-1951	398	10	the	the	DET
ejpam-1951	398	11	cube	cube	NOUN
ejpam-1951	398	12	.	.	PUNCT
ejpam-1951	399	1	so	so	ADV
ejpam-1951	399	2	recall	recall	VERB
ejpam-1951	399	3	example	example	NOUN
ejpam-1951	399	4	12	12	NUM
ejpam-1951	399	5	.	.	PUNCT
ejpam-1951	400	1	then	then	ADV
ejpam-1951	400	2	the	the	DET
ejpam-1951	400	3	cycle	cycle	NOUN
ejpam-1951	400	4	index	index	NOUN
ejpam-1951	400	5	is	be	AUX
ejpam-1951	400	6	z(g	z(g	NOUN
ejpam-1951	400	7	,	,	PUNCT
ejpam-1951	400	8	t1	t1	NOUN
ejpam-1951	400	9	,	,	PUNCT
ejpam-1951	400	10	t2	t2	NOUN
ejpam-1951	400	11	,	,	PUNCT
ejpam-1951	400	12	.	.	PUNCT
ejpam-1951	400	13	.	.	PUNCT
ejpam-1951	401	1	.	.	PUNCT
ejpam-1951	402	1	,	,	PUNCT
ejpam-1951	402	2	t8	t8	NOUN
ejpam-1951	402	3	)	)	PUNCT
ejpam-1951	402	4	=	=	SYM
ejpam-1951	402	5	1	1	NUM
ejpam-1951	402	6	24	24	NUM
ejpam-1951	402	7	(	(	PUNCT
ejpam-1951	402	8	6t2	6t2	NUM
ejpam-1951	402	9	4	4	NUM
ejpam-1951	402	10	+	+	NOUN
ejpam-1951	402	11	9t4	9t4	NUM
ejpam-1951	402	12	2	2	NUM
ejpam-1951	402	13	+	+	CCONJ
ejpam-1951	402	14	8t2	8t2	NUM
ejpam-1951	402	15	1	1	NUM
ejpam-1951	402	16	t2	t2	NOUN
ejpam-1951	402	17	3	3	NUM
ejpam-1951	402	18	+	+	SYM
ejpam-1951	402	19	6t3	6t3	NUM
ejpam-1951	402	20	2	2	NUM
ejpam-1951	402	21	+	+	CCONJ
ejpam-1951	402	22	t8	t8	NOUN
ejpam-1951	402	23	1	1	NUM
ejpam-1951	402	24	)	)	PUNCT
ejpam-1951	402	25	.	.	PUNCT
ejpam-1951	403	1	now	now	ADV
ejpam-1951	403	2	we	we	PRON
ejpam-1951	403	3	will	will	AUX
ejpam-1951	403	4	apply	apply	VERB
ejpam-1951	403	5	pólya	pólya	NOUN
ejpam-1951	403	6	’s	’s	PART
ejpam-1951	403	7	substitution	substitution	NOUN
ejpam-1951	403	8	method	method	NOUN
ejpam-1951	403	9	.	.	PUNCT
ejpam-1951	404	1	let	let	VERB
ejpam-1951	404	2	the	the	DET
ejpam-1951	404	3	colors	color	NOUN
ejpam-1951	404	4	black	black	ADJ
ejpam-1951	404	5	,	,	PUNCT
ejpam-1951	404	6	red	red	ADJ
ejpam-1951	404	7	,	,	PUNCT
ejpam-1951	404	8	green	green	ADJ
ejpam-1951	404	9	,	,	PUNCT
ejpam-1951	404	10	blue	blue	ADJ
ejpam-1951	404	11	and	and	CCONJ
ejpam-1951	404	12	yellow	yellow	NOUN
ejpam-1951	404	13	be	be	AUX
ejpam-1951	404	14	denoted	denote	VERB
ejpam-1951	404	15	by	by	ADP
ejpam-1951	404	16	x	x	SYM
ejpam-1951	404	17	,	,	PUNCT
ejpam-1951	404	18	y	y	PROPN
ejpam-1951	404	19	,	,	PUNCT
ejpam-1951	404	20	z	z	PROPN
ejpam-1951	404	21	,	,	PUNCT
ejpam-1951	404	22	p	p	NOUN
ejpam-1951	404	23	and	and	CCONJ
ejpam-1951	404	24	v	v	ADP
ejpam-1951	404	25	respectively.then	respectively.then	ADJ
ejpam-1951	404	26	substituting	substitute	VERB
ejpam-1951	404	27	t	t	NOUN
ejpam-1951	405	1	i	i	PRON
ejpam-1951	405	2	→	→	PUNCT
ejpam-1951	405	3	(	(	PUNCT
ejpam-1951	405	4	x	x	X
ejpam-1951	405	5	i+	i+	PUNCT
ejpam-1951	405	6	y	y	PROPN
ejpam-1951	405	7	i+z	i+z	PROPN
ejpam-1951	405	8	i+	i+	NUM
ejpam-1951	405	9	pi+	pi+	PROPN
ejpam-1951	405	10	v	v	NUM
ejpam-1951	405	11	i	i	PROPN
ejpam-1951	405	12	)	)	PUNCT
ejpam-1951	405	13	for	for	ADP
ejpam-1951	405	14	each	each	DET
ejpam-1951	405	15	i	i	PRON
ejpam-1951	405	16	=	=	PUNCT
ejpam-1951	405	17	{	{	PUNCT
ejpam-1951	405	18	1,2,3,4,5,6,7,8	1,2,3,4,5,6,7,8	NUM
ejpam-1951	405	19	}	}	PUNCT
ejpam-1951	405	20	in	in	ADP
ejpam-1951	405	21	the	the	DET
ejpam-1951	405	22	previous	previous	ADJ
ejpam-1951	405	23	equation	equation	NOUN
ejpam-1951	405	24	,	,	PUNCT
ejpam-1951	405	25	we	we	PRON
ejpam-1951	405	26	get	get	VERB
ejpam-1951	405	27	zg	zg	NOUN
ejpam-1951	405	28	=	=	SYM
ejpam-1951	405	29	1	1	NUM
ejpam-1951	405	30	24	24	NUM
ejpam-1951	405	31	(	(	PUNCT
ejpam-1951	405	32	6(x4	6(x4	NUM
ejpam-1951	405	33	+	+	CCONJ
ejpam-1951	405	34	y4	y4	PROPN
ejpam-1951	405	35	+	+	CCONJ
ejpam-1951	405	36	z4	z4	PROPN
ejpam-1951	405	37	+	+	CCONJ
ejpam-1951	405	38	p4	p4	ADJ
ejpam-1951	405	39	+	+	CCONJ
ejpam-1951	405	40	v4)2	v4)2	PUNCT
ejpam-1951	406	1	+	+	NUM
ejpam-1951	406	2	9(x2	9(x2	NOUN
ejpam-1951	407	1	+	+	CCONJ
ejpam-1951	407	2	y2	y2	PROPN
ejpam-1951	407	3	+	+	CCONJ
ejpam-1951	407	4	z2	z2	NOUN
ejpam-1951	407	5	+	+	CCONJ
ejpam-1951	407	6	p2	p2	PROPN
ejpam-1951	407	7	+	+	CCONJ
ejpam-1951	407	8	v2)4	v2)4	X
ejpam-1951	407	9	+	+	NUM
ejpam-1951	407	10	8(x	8(x	NUM
ejpam-1951	408	1	+	+	CCONJ
ejpam-1951	408	2	y	y	PROPN
ejpam-1951	408	3	+	+	CCONJ
ejpam-1951	408	4	z	z	PROPN
ejpam-1951	408	5	+	+	X
ejpam-1951	408	6	p+	p+	VERB
ejpam-1951	408	7	v)2(x3	v)2(x3	NOUN
ejpam-1951	408	8	+	+	CCONJ
ejpam-1951	408	9	y3	y3	NOUN
ejpam-1951	408	10	+	+	CCONJ
ejpam-1951	408	11	z3	z3	PROPN
ejpam-1951	408	12	+	+	CCONJ
ejpam-1951	408	13	p3	p3	PROPN
ejpam-1951	408	14	+	+	CCONJ
ejpam-1951	408	15	v3)2	v3)2	PROPN
ejpam-1951	409	1	+	+	NUM
ejpam-1951	409	2	6(x2	6(x2	NUM
ejpam-1951	410	1	+	+	CCONJ
ejpam-1951	410	2	y2	y2	PROPN
ejpam-1951	410	3	+	+	CCONJ
ejpam-1951	410	4	z2	z2	NOUN
ejpam-1951	410	5	+	+	CCONJ
ejpam-1951	410	6	p2	p2	PROPN
ejpam-1951	410	7	+	+	CCONJ
ejpam-1951	410	8	v2)3	v2)3	X
ejpam-1951	411	1	+	+	NOUN
ejpam-1951	411	2	(	(	PUNCT
ejpam-1951	411	3	x	x	X
ejpam-1951	411	4	+	+	NUM
ejpam-1951	411	5	y	y	PROPN
ejpam-1951	412	1	+	+	CCONJ
ejpam-1951	412	2	z	z	PROPN
ejpam-1951	412	3	+	+	PROPN
ejpam-1951	412	4	p+	p+	X
ejpam-1951	412	5	v)8	v)8	NOUN
ejpam-1951	412	6	)	)	PUNCT
ejpam-1951	412	7	.	.	PUNCT
ejpam-1951	413	1	we	we	PRON
ejpam-1951	413	2	use	use	VERB
ejpam-1951	413	3	maple	maple	NOUN
ejpam-1951	413	4	to	to	PART
ejpam-1951	413	5	expand	expand	VERB
ejpam-1951	413	6	and	and	CCONJ
ejpam-1951	413	7	find	find	VERB
ejpam-1951	413	8	that	that	SCONJ
ejpam-1951	413	9	the	the	DET
ejpam-1951	413	10	expression	expression	NOUN
ejpam-1951	413	11	on	on	ADP
ejpam-1951	413	12	the	the	DET
ejpam-1951	413	13	right	right	ADJ
ejpam-1951	413	14	hand	hand	NOUN
ejpam-1951	413	15	side	side	NOUN
ejpam-1951	413	16	is	be	AUX
ejpam-1951	413	17	very	very	ADV
ejpam-1951	413	18	long	long	ADJ
ejpam-1951	413	19	.	.	PUNCT
ejpam-1951	414	1	each	each	DET
ejpam-1951	414	2	term	term	NOUN
ejpam-1951	414	3	of	of	ADP
ejpam-1951	414	4	this	this	DET
ejpam-1951	414	5	expression	expression	NOUN
ejpam-1951	414	6	corresponds	correspond	VERB
ejpam-1951	414	7	to	to	ADP
ejpam-1951	414	8	a	a	DET
ejpam-1951	414	9	fixed	fix	VERB
ejpam-1951	414	10	number	number	NOUN
ejpam-1951	414	11	of	of	ADP
ejpam-1951	414	12	black	black	ADJ
ejpam-1951	414	13	,	,	PUNCT
ejpam-1951	414	14	red	red	ADJ
ejpam-1951	414	15	,	,	PUNCT
ejpam-1951	414	16	green	green	ADJ
ejpam-1951	414	17	,	,	PUNCT
ejpam-1951	414	18	blue	blue	ADJ
ejpam-1951	414	19	and	and	CCONJ
ejpam-1951	414	20	yellow	yellow	ADJ
ejpam-1951	414	21	colors	color	NOUN
ejpam-1951	414	22	.	.	PUNCT
ejpam-1951	415	1	(	(	PUNCT
ejpam-1951	415	2	a	a	X
ejpam-1951	415	3	)	)	PUNCT
ejpam-1951	415	4	the	the	DET
ejpam-1951	415	5	term	term	NOUN
ejpam-1951	415	6	3x6zv	3x6zv	NUM
ejpam-1951	415	7	contains	contain	VERB
ejpam-1951	415	8	cube	cube	NOUN
ejpam-1951	415	9	with	with	ADP
ejpam-1951	415	10	6	6	NUM
ejpam-1951	415	11	black	black	ADJ
ejpam-1951	415	12	,	,	PUNCT
ejpam-1951	415	13	1	1	NUM
ejpam-1951	415	14	green	green	ADJ
ejpam-1951	415	15	and	and	CCONJ
ejpam-1951	415	16	1	1	NUM
ejpam-1951	415	17	yellow	yellow	ADJ
ejpam-1951	415	18	vertices	vertex	NOUN
ejpam-1951	415	19	.	.	PUNCT
ejpam-1951	416	1	the	the	DET
ejpam-1951	416	2	coefficient	coefficient	NOUN
ejpam-1951	416	3	of	of	ADP
ejpam-1951	416	4	this	this	DET
ejpam-1951	416	5	term	term	NOUN
ejpam-1951	416	6	is	be	AUX
ejpam-1951	416	7	3	3	NUM
ejpam-1951	416	8	.	.	PUNCT
ejpam-1951	417	1	hence	hence	ADV
ejpam-1951	417	2	there	there	PRON
ejpam-1951	417	3	are	be	VERB
ejpam-1951	417	4	3	3	NUM
ejpam-1951	417	5	possible	possible	ADJ
ejpam-1951	417	6	ways	way	NOUN
ejpam-1951	417	7	to	to	PART
ejpam-1951	417	8	color	color	VERB
ejpam-1951	417	9	the	the	DET
ejpam-1951	417	10	cube	cube	NOUN
ejpam-1951	417	11	.	.	PUNCT
ejpam-1951	418	1	t.	t.	PROPN
ejpam-1951	418	2	nasseef	nasseef	PROPN
ejpam-1951	418	3	/	/	SYM
ejpam-1951	418	4	eur	eur	PROPN
ejpam-1951	418	5	.	.	PUNCT
ejpam-1951	419	1	j.	j.	PROPN
ejpam-1951	419	2	pure	pure	PROPN
ejpam-1951	419	3	appl	appl	PROPN
ejpam-1951	419	4	.	.	PROPN
ejpam-1951	419	5	math	math	PROPN
ejpam-1951	419	6	,	,	PUNCT
ejpam-1951	419	7	9	9	NUM
ejpam-1951	419	8	(	(	PUNCT
ejpam-1951	419	9	2016	2016	NUM
ejpam-1951	419	10	)	)	PUNCT
ejpam-1951	419	11	,	,	PUNCT
ejpam-1951	419	12	84	84	NUM
ejpam-1951	419	13	-	-	SYM
ejpam-1951	419	14	113	113	NUM
ejpam-1951	419	15	100	100	NUM
ejpam-1951	419	16	(	(	PUNCT
ejpam-1951	419	17	b	b	NOUN
ejpam-1951	419	18	)	)	PUNCT
ejpam-1951	419	19	in	in	ADP
ejpam-1951	419	20	this	this	DET
ejpam-1951	419	21	case	case	NOUN
ejpam-1951	419	22	the	the	DET
ejpam-1951	419	23	term	term	NOUN
ejpam-1951	419	24	is	be	AUX
ejpam-1951	419	25	35p4v2	35p4v2	NOUN
ejpam-1951	419	26	x	x	PUNCT
ejpam-1951	419	27	y	y	NOUN
ejpam-1951	419	28	which	which	PRON
ejpam-1951	419	29	contains	contain	VERB
ejpam-1951	419	30	cube	cube	NOUN
ejpam-1951	419	31	1	1	NUM
ejpam-1951	419	32	black	black	ADJ
ejpam-1951	419	33	,	,	PUNCT
ejpam-1951	419	34	1	1	NUM
ejpam-1951	419	35	red	red	ADJ
ejpam-1951	419	36	,	,	PUNCT
ejpam-1951	419	37	4	4	NUM
ejpam-1951	419	38	blue	blue	ADJ
ejpam-1951	419	39	and	and	CCONJ
ejpam-1951	419	40	2	2	NUM
ejpam-1951	419	41	yellow	yellow	ADJ
ejpam-1951	419	42	vertices	vertex	NOUN
ejpam-1951	419	43	.	.	PUNCT
ejpam-1951	420	1	so	so	ADV
ejpam-1951	420	2	there	there	PRON
ejpam-1951	420	3	are	be	VERB
ejpam-1951	420	4	35	35	NUM
ejpam-1951	420	5	ways	way	NOUN
ejpam-1951	420	6	to	to	PART
ejpam-1951	420	7	color	color	VERB
ejpam-1951	420	8	the	the	DET
ejpam-1951	420	9	cube	cube	NOUN
ejpam-1951	420	10	.	.	PUNCT
ejpam-1951	421	1	(	(	PUNCT
ejpam-1951	421	2	c	c	X
ejpam-1951	421	3	)	)	PUNCT
ejpam-1951	421	4	for	for	ADP
ejpam-1951	421	5	this	this	PRON
ejpam-1951	421	6	we	we	PRON
ejpam-1951	421	7	need	need	VERB
ejpam-1951	421	8	to	to	PART
ejpam-1951	421	9	find	find	VERB
ejpam-1951	421	10	out	out	ADP
ejpam-1951	421	11	the	the	DET
ejpam-1951	421	12	coefficient	coefficient	NOUN
ejpam-1951	421	13	of	of	ADP
ejpam-1951	421	14	the	the	DET
ejpam-1951	421	15	term	term	NOUN
ejpam-1951	422	1	140pv2	140pv2	NUM
ejpam-1951	422	2	x3	x3	NOUN
ejpam-1951	422	3	yz	yz	NUM
ejpam-1951	422	4	which	which	PRON
ejpam-1951	422	5	contains	contain	VERB
ejpam-1951	422	6	cube	cube	NOUN
ejpam-1951	422	7	with	with	ADP
ejpam-1951	422	8	3	3	NUM
ejpam-1951	422	9	black	black	ADJ
ejpam-1951	422	10	,	,	PUNCT
ejpam-1951	422	11	1	1	NUM
ejpam-1951	422	12	red	red	ADJ
ejpam-1951	422	13	,	,	PUNCT
ejpam-1951	422	14	1	1	NUM
ejpam-1951	422	15	green	green	ADJ
ejpam-1951	422	16	1	1	NUM
ejpam-1951	422	17	blue	blue	ADJ
ejpam-1951	422	18	and	and	CCONJ
ejpam-1951	422	19	2	2	NUM
ejpam-1951	422	20	yellow	yellow	ADJ
ejpam-1951	422	21	vertices	vertex	NOUN
ejpam-1951	422	22	.	.	PUNCT
ejpam-1951	423	1	there	there	PRON
ejpam-1951	423	2	are	be	VERB
ejpam-1951	423	3	140	140	NUM
ejpam-1951	423	4	ways	way	NOUN
ejpam-1951	423	5	to	to	PART
ejpam-1951	423	6	color	color	VERB
ejpam-1951	423	7	the	the	DET
ejpam-1951	423	8	cube	cube	NOUN
ejpam-1951	423	9	.	.	PUNCT
ejpam-1951	424	1	problem	problem	NOUN
ejpam-1951	424	2	4	4	NUM
ejpam-1951	424	3	(	(	PUNCT
ejpam-1951	424	4	16	16	NUM
ejpam-1951	424	5	bead	bead	NOUN
ejpam-1951	424	6	necklace	necklace	NOUN
ejpam-1951	424	7	)	)	PUNCT
ejpam-1951	424	8	.	.	PUNCT
ejpam-1951	425	1	count	count	VERB
ejpam-1951	425	2	the	the	DET
ejpam-1951	425	3	number	number	NOUN
ejpam-1951	425	4	of	of	ADP
ejpam-1951	425	5	ways	way	NOUN
ejpam-1951	425	6	to	to	PART
ejpam-1951	425	7	arrange	arrange	VERB
ejpam-1951	425	8	beads	bead	NOUN
ejpam-1951	425	9	on	on	ADP
ejpam-1951	425	10	a	a	DET
ejpam-1951	425	11	necklace	necklace	NOUN
ejpam-1951	425	12	,	,	PUNCT
ejpam-1951	425	13	where	where	SCONJ
ejpam-1951	425	14	16	16	NUM
ejpam-1951	425	15	total	total	ADJ
ejpam-1951	425	16	beads	bead	NOUN
ejpam-1951	425	17	arranged	arrange	VERB
ejpam-1951	425	18	on	on	ADP
ejpam-1951	425	19	the	the	DET
ejpam-1951	425	20	necklace	necklace	NOUN
ejpam-1951	425	21	with	with	ADP
ejpam-1951	425	22	(	(	PUNCT
ejpam-1951	425	23	a	a	X
ejpam-1951	425	24	)	)	PUNCT
ejpam-1951	425	25	2	2	NUM
ejpam-1951	425	26	different	different	ADJ
ejpam-1951	425	27	colors	color	NOUN
ejpam-1951	425	28	;	;	PUNCT
ejpam-1951	425	29	(	(	PUNCT
ejpam-1951	425	30	b	b	X
ejpam-1951	425	31	)	)	PUNCT
ejpam-1951	425	32	14	14	NUM
ejpam-1951	425	33	red	red	ADJ
ejpam-1951	425	34	and	and	CCONJ
ejpam-1951	425	35	2	2	NUM
ejpam-1951	425	36	black	black	ADJ
ejpam-1951	425	37	colors	color	NOUN
ejpam-1951	425	38	;	;	PUNCT
ejpam-1951	425	39	(	(	PUNCT
ejpam-1951	425	40	c	c	X
ejpam-1951	425	41	)	)	PUNCT
ejpam-1951	425	42	4	4	NUM
ejpam-1951	425	43	different	different	ADJ
ejpam-1951	425	44	colors	color	NOUN
ejpam-1951	425	45	;	;	PUNCT
ejpam-1951	425	46	solution	solution	NOUN
ejpam-1951	425	47	:	:	PUNCT
ejpam-1951	425	48	with	with	ADP
ejpam-1951	425	49	a	a	DET
ejpam-1951	425	50	necklace	necklace	NOUN
ejpam-1951	425	51	,	,	PUNCT
ejpam-1951	425	52	we	we	PRON
ejpam-1951	425	53	will	will	AUX
ejpam-1951	425	54	obviously	obviously	ADV
ejpam-1951	425	55	rotate	rotate	VERB
ejpam-1951	425	56	it	it	PRON
ejpam-1951	425	57	around	around	ADV
ejpam-1951	425	58	and	and	CCONJ
ejpam-1951	425	59	flip	flip	VERB
ejpam-1951	425	60	over	over	ADP
ejpam-1951	425	61	it	it	PRON
ejpam-1951	425	62	.	.	PUNCT
ejpam-1951	426	1	we	we	PRON
ejpam-1951	426	2	will	will	AUX
ejpam-1951	426	3	also	also	ADV
ejpam-1951	426	4	use	use	VERB
ejpam-1951	426	5	the	the	DET
ejpam-1951	426	6	definition	definition	NOUN
ejpam-1951	426	7	2	2	NUM
ejpam-1951	426	8	with	with	ADP
ejpam-1951	426	9	the	the	DET
ejpam-1951	426	10	formula	formula	NOUN
ejpam-1951	426	11	for	for	ADP
ejpam-1951	426	12	the	the	DET
ejpam-1951	426	13	cyclic	cyclic	ADJ
ejpam-1951	426	14	and	and	CCONJ
ejpam-1951	426	15	dihedral	dihedral	ADJ
ejpam-1951	426	16	groups	group	NOUN
ejpam-1951	426	17	to	to	PART
ejpam-1951	426	18	solve	solve	VERB
ejpam-1951	426	19	this	this	DET
ejpam-1951	426	20	problem	problem	NOUN
ejpam-1951	426	21	.	.	PUNCT
ejpam-1951	427	1	the	the	DET
ejpam-1951	427	2	cycle	cycle	NOUN
ejpam-1951	427	3	index	index	NOUN
ejpam-1951	427	4	of	of	ADP
ejpam-1951	427	5	this	this	DET
ejpam-1951	427	6	group	group	NOUN
ejpam-1951	427	7	c16	c16	PROPN
ejpam-1951	427	8	from	from	ADP
ejpam-1951	427	9	(	(	PUNCT
ejpam-1951	427	10	1	1	NUM
ejpam-1951	427	11	)	)	PUNCT
ejpam-1951	427	12	is	be	AUX
ejpam-1951	427	13	z(c16	z(c16	NOUN
ejpam-1951	427	14	,	,	PUNCT
ejpam-1951	427	15	t1	t1	NOUN
ejpam-1951	427	16	,	,	PUNCT
ejpam-1951	427	17	.	.	PUNCT
ejpam-1951	427	18	.	.	PUNCT
ejpam-1951	428	1	.	.	PUNCT
ejpam-1951	429	1	,	,	PUNCT
ejpam-1951	429	2	t16	t16	PROPN
ejpam-1951	429	3	)	)	PUNCT
ejpam-1951	429	4	=	=	SYM
ejpam-1951	430	1	1	1	NUM
ejpam-1951	430	2	16	16	NUM
ejpam-1951	430	3	∑	∑	ADP
ejpam-1951	430	4	l/16	l/16	PROPN
ejpam-1951	430	5	φ(l)t	φ(l)t	PROPN
ejpam-1951	430	6	16	16	NUM
ejpam-1951	430	7	/	/	SYM
ejpam-1951	430	8	l	l	NOUN
ejpam-1951	430	9	l	l	NOUN
ejpam-1951	431	1	=	=	SYM
ejpam-1951	432	1	1	1	NUM
ejpam-1951	432	2	16	16	NUM
ejpam-1951	432	3	(	(	PUNCT
ejpam-1951	432	4	φ(1)t	φ(1)t	PROPN
ejpam-1951	432	5	16/1	16/1	NUM
ejpam-1951	432	6	1	1	NUM
ejpam-1951	432	7	+	+	ADJ
ejpam-1951	432	8	φ(2)t	φ(2)t	PRON
ejpam-1951	433	1	16/2	16/2	NUM
ejpam-1951	433	2	2	2	NUM
ejpam-1951	433	3	+	+	NOUN
ejpam-1951	433	4	φ(4)t	φ(4)t	PROPN
ejpam-1951	433	5	16/4	16/4	VERB
ejpam-1951	433	6	4	4	NUM
ejpam-1951	434	1	+	+	NOUN
ejpam-1951	434	2	φ(8)t	φ(8)t	NOUN
ejpam-1951	434	3	16/8	16/8	NOUN
ejpam-1951	434	4	8	8	NUM
ejpam-1951	435	1	+	+	NOUN
ejpam-1951	435	2	φ(16)t	φ(16)t	PROPN
ejpam-1951	435	3	16/16	16/16	NUM
ejpam-1951	435	4	16	16	NUM
ejpam-1951	435	5	)	)	PUNCT
ejpam-1951	435	6	=	=	SYM
ejpam-1951	435	7	1	1	NUM
ejpam-1951	435	8	16	16	NUM
ejpam-1951	435	9	(	(	PUNCT
ejpam-1951	435	10	t16	t16	PROPN
ejpam-1951	435	11	1	1	NUM
ejpam-1951	435	12	+	+	CCONJ
ejpam-1951	435	13	t8	t8	VERB
ejpam-1951	435	14	2	2	NUM
ejpam-1951	435	15	+	+	CCONJ
ejpam-1951	435	16	2t4	2t4	NUM
ejpam-1951	435	17	4	4	NUM
ejpam-1951	435	18	+	+	NUM
ejpam-1951	435	19	4t2	4t2	NUM
ejpam-1951	435	20	8	8	NUM
ejpam-1951	435	21	+	+	CCONJ
ejpam-1951	435	22	8t1	8t1	NUM
ejpam-1951	435	23	16	16	NUM
ejpam-1951	435	24	)	)	PUNCT
ejpam-1951	435	25	now	now	ADV
ejpam-1951	435	26	we	we	PRON
ejpam-1951	435	27	will	will	AUX
ejpam-1951	435	28	illustrate	illustrate	VERB
ejpam-1951	435	29	the	the	DET
ejpam-1951	435	30	formula	formula	NOUN
ejpam-1951	435	31	by	by	ADP
ejpam-1951	435	32	computing	compute	VERB
ejpam-1951	435	33	the	the	DET
ejpam-1951	435	34	cycle	cycle	NOUN
ejpam-1951	435	35	index	index	NOUN
ejpam-1951	435	36	of	of	ADP
ejpam-1951	435	37	d16	d16	PROPN
ejpam-1951	435	38	z(d16	z(d16	PROPN
ejpam-1951	435	39	,	,	PUNCT
ejpam-1951	435	40	t1	t1	PROPN
ejpam-1951	435	41	,	,	PUNCT
ejpam-1951	435	42	.	.	PUNCT
ejpam-1951	435	43	.	.	PUNCT
ejpam-1951	436	1	.	.	PUNCT
ejpam-1951	437	1	,	,	PUNCT
ejpam-1951	437	2	t16	t16	PROPN
ejpam-1951	437	3	)	)	PUNCT
ejpam-1951	437	4	=	=	SYM
ejpam-1951	437	5	1	1	NUM
ejpam-1951	437	6	2	2	NUM
ejpam-1951	437	7	z(c16	z(c16	NOUN
ejpam-1951	437	8	,	,	PUNCT
ejpam-1951	437	9	t1	t1	NOUN
ejpam-1951	437	10	,	,	PUNCT
ejpam-1951	437	11	.	.	PUNCT
ejpam-1951	437	12	.	.	PUNCT
ejpam-1951	438	1	.	.	PUNCT
ejpam-1951	439	1	,	,	PUNCT
ejpam-1951	439	2	t16	t16	PROPN
ejpam-1951	439	3	)	)	PUNCT
ejpam-1951	440	1	+	+	CCONJ
ejpam-1951	440	2	1	1	NUM
ejpam-1951	440	3	4	4	NUM
ejpam-1951	440	4	(	(	PUNCT
ejpam-1951	440	5	t8	t8	NOUN
ejpam-1951	440	6	2	2	NUM
ejpam-1951	440	7	+	+	CCONJ
ejpam-1951	440	8	t2	t2	PROPN
ejpam-1951	440	9	1	1	NUM
ejpam-1951	440	10	t7	t7	PROPN
ejpam-1951	440	11	2	2	NUM
ejpam-1951	440	12	)	)	PUNCT
ejpam-1951	440	13	=	=	SYM
ejpam-1951	440	14	1	1	NUM
ejpam-1951	440	15	2	2	NUM
ejpam-1951	440	16	(	(	PUNCT
ejpam-1951	440	17	1	1	NUM
ejpam-1951	440	18	16	16	NUM
ejpam-1951	440	19	(	(	PUNCT
ejpam-1951	440	20	t16	t16	PROPN
ejpam-1951	440	21	1	1	NUM
ejpam-1951	440	22	+	+	CCONJ
ejpam-1951	440	23	t8	t8	VERB
ejpam-1951	440	24	2	2	NUM
ejpam-1951	440	25	+	+	CCONJ
ejpam-1951	440	26	2t4	2t4	NUM
ejpam-1951	440	27	4	4	NUM
ejpam-1951	440	28	+	+	NUM
ejpam-1951	440	29	4t2	4t2	NUM
ejpam-1951	440	30	8	8	NUM
ejpam-1951	440	31	+	+	CCONJ
ejpam-1951	440	32	8t1	8t1	NUM
ejpam-1951	440	33	16	16	NUM
ejpam-1951	440	34	)	)	PUNCT
ejpam-1951	440	35	)	)	PUNCT
ejpam-1951	441	1	+	+	CCONJ
ejpam-1951	441	2	1	1	NUM
ejpam-1951	441	3	4	4	NUM
ejpam-1951	441	4	(	(	PUNCT
ejpam-1951	441	5	t8	t8	NOUN
ejpam-1951	441	6	2	2	NUM
ejpam-1951	441	7	+	+	CCONJ
ejpam-1951	441	8	t2	t2	PROPN
ejpam-1951	441	9	1	1	NUM
ejpam-1951	441	10	t7	t7	PROPN
ejpam-1951	441	11	2	2	NUM
ejpam-1951	441	12	)	)	PUNCT
ejpam-1951	441	13	=	=	SYM
ejpam-1951	441	14	1	1	NUM
ejpam-1951	441	15	32	32	NUM
ejpam-1951	441	16	(	(	PUNCT
ejpam-1951	441	17	t16	t16	PROPN
ejpam-1951	441	18	1	1	NUM
ejpam-1951	441	19	+	+	CCONJ
ejpam-1951	441	20	9t8	9t8	NUM
ejpam-1951	441	21	2	2	NUM
ejpam-1951	441	22	+	+	CCONJ
ejpam-1951	441	23	8t2	8t2	NUM
ejpam-1951	441	24	1	1	NUM
ejpam-1951	441	25	t7	t7	PROPN
ejpam-1951	441	26	2	2	NUM
ejpam-1951	441	27	+	+	CCONJ
ejpam-1951	441	28	2t4	2t4	NUM
ejpam-1951	441	29	4	4	NUM
ejpam-1951	441	30	+	+	NUM
ejpam-1951	441	31	4t2	4t2	NUM
ejpam-1951	441	32	8	8	NUM
ejpam-1951	441	33	+	+	CCONJ
ejpam-1951	441	34	8t1	8t1	NUM
ejpam-1951	441	35	16	16	NUM
ejpam-1951	441	36	)	)	PUNCT
ejpam-1951	441	37	(	(	PUNCT
ejpam-1951	441	38	4	4	X
ejpam-1951	441	39	)	)	PUNCT
ejpam-1951	441	40	let	let	VERB
ejpam-1951	441	41	us	we	PRON
ejpam-1951	441	42	consider	consider	VERB
ejpam-1951	441	43	2	2	NUM
ejpam-1951	441	44	colors	color	NOUN
ejpam-1951	441	45	red	red	ADJ
ejpam-1951	441	46	and	and	CCONJ
ejpam-1951	441	47	black	black	ADJ
ejpam-1951	441	48	denoted	denote	VERB
ejpam-1951	441	49	by	by	ADP
ejpam-1951	441	50	x	x	PUNCT
ejpam-1951	441	51	and	and	CCONJ
ejpam-1951	441	52	y	y	PROPN
ejpam-1951	441	53	respectively	respectively	ADV
ejpam-1951	441	54	.	.	PUNCT
ejpam-1951	442	1	now	now	ADV
ejpam-1951	442	2	we	we	PRON
ejpam-1951	442	3	will	will	AUX
ejpam-1951	442	4	apply	apply	VERB
ejpam-1951	442	5	pólya	pólya	NOUN
ejpam-1951	442	6	’s	’s	PART
ejpam-1951	442	7	substitution	substitution	NOUN
ejpam-1951	442	8	method	method	NOUN
ejpam-1951	442	9	.	.	PUNCT
ejpam-1951	443	1	substituting	substitute	VERB
ejpam-1951	443	2	t	t	PROPN
ejpam-1951	443	3	i	i	PRON
ejpam-1951	443	4	→	→	PUNCT
ejpam-1951	443	5	(	(	PUNCT
ejpam-1951	443	6	x	x	X
ejpam-1951	443	7	i	i	PRON
ejpam-1951	443	8	+	+	NUM
ejpam-1951	443	9	y	y	PROPN
ejpam-1951	443	10	i	i	PROPN
ejpam-1951	443	11	)	)	PUNCT
ejpam-1951	443	12	for	for	ADP
ejpam-1951	443	13	each	each	DET
ejpam-1951	443	14	i	i	PRON
ejpam-1951	443	15	=	=	PUNCT
ejpam-1951	443	16	{	{	PUNCT
ejpam-1951	443	17	1,2,3	1,2,3	NUM
ejpam-1951	443	18	,	,	PUNCT
ejpam-1951	443	19	.	.	PUNCT
ejpam-1951	443	20	.	.	PUNCT
ejpam-1951	444	1	.	.	PUNCT
ejpam-1951	445	1	,	,	PUNCT
ejpam-1951	445	2	16	16	NUM
ejpam-1951	445	3	}	}	PUNCT
ejpam-1951	445	4	in	in	ADP
ejpam-1951	445	5	equation	equation	NOUN
ejpam-1951	445	6	(	(	PUNCT
ejpam-1951	445	7	4	4	NUM
ejpam-1951	445	8	)	)	PUNCT
ejpam-1951	445	9	,	,	PUNCT
ejpam-1951	445	10	we	we	PRON
ejpam-1951	445	11	get	get	VERB
ejpam-1951	445	12	z(d16	z(d16	NUM
ejpam-1951	445	13	,	,	PUNCT
ejpam-1951	445	14	t1	t1	NOUN
ejpam-1951	445	15	,	,	PUNCT
ejpam-1951	445	16	.	.	PUNCT
ejpam-1951	445	17	.	.	PUNCT
ejpam-1951	446	1	.	.	PUNCT
ejpam-1951	447	1	,	,	PUNCT
ejpam-1951	447	2	t16	t16	PROPN
ejpam-1951	447	3	)	)	PUNCT
ejpam-1951	447	4	=	=	PUNCT
ejpam-1951	448	1	1	1	NUM
ejpam-1951	448	2	32	32	NUM
ejpam-1951	448	3	(	(	PUNCT
ejpam-1951	448	4	(	(	PUNCT
ejpam-1951	448	5	x	x	SYM
ejpam-1951	448	6	+	+	NUM
ejpam-1951	448	7	y+)16	y+)16	NOUN
ejpam-1951	448	8	+	+	CCONJ
ejpam-1951	448	9	9(x2	9(x2	NUM
ejpam-1951	449	1	+	+	CCONJ
ejpam-1951	449	2	y2)8	y2)8	PROPN
ejpam-1951	449	3	+	+	NOUN
ejpam-1951	449	4	8(x	8(x	NUM
ejpam-1951	449	5	+	+	CCONJ
ejpam-1951	449	6	y)2(x2	y)2(x2	PRON
ejpam-1951	450	1	+	+	CCONJ
ejpam-1951	450	2	y2)7	y2)7	PROPN
ejpam-1951	451	1	+	+	CCONJ
ejpam-1951	451	2	2(x4	2(x4	NUM
ejpam-1951	451	3	+	+	PUNCT
ejpam-1951	451	4	y4)4	y4)4	X
ejpam-1951	452	1	+	+	NUM
ejpam-1951	452	2	4(x8	4(x8	NUM
ejpam-1951	453	1	+	+	CCONJ
ejpam-1951	453	2	y8)2	y8)2	NUM
ejpam-1951	453	3	+	+	NUM
ejpam-1951	453	4	8(x16	8(x16	NUM
ejpam-1951	453	5	+	+	CCONJ
ejpam-1951	453	6	y16)1	y16)1	NUM
ejpam-1951	453	7	)	)	PUNCT
ejpam-1951	453	8	(	(	PUNCT
ejpam-1951	453	9	i	i	NOUN
ejpam-1951	453	10	)	)	PUNCT
ejpam-1951	453	11	let	let	VERB
ejpam-1951	453	12	x	x	SYM
ejpam-1951	454	1	=	=	PUNCT
ejpam-1951	454	2	y	y	NOUN
ejpam-1951	454	3	=	=	SYM
ejpam-1951	454	4	1	1	X
ejpam-1951	454	5	.	.	PUNCT
ejpam-1951	454	6	then	then	ADV
ejpam-1951	454	7	using	use	VERB
ejpam-1951	454	8	maple	maple	NOUN
ejpam-1951	454	9	by	by	ADP
ejpam-1951	454	10	the	the	DET
ejpam-1951	454	11	above	above	ADJ
ejpam-1951	454	12	equation	equation	NOUN
ejpam-1951	454	13	we	we	PRON
ejpam-1951	454	14	get	get	VERB
ejpam-1951	454	15	the	the	DET
ejpam-1951	454	16	total	total	ADJ
ejpam-1951	454	17	count	count	NOUN
ejpam-1951	454	18	2250	2250	NUM
ejpam-1951	454	19	.	.	PUNCT
ejpam-1951	455	1	t.	t.	PROPN
ejpam-1951	455	2	nasseef	nasseef	PROPN
ejpam-1951	455	3	/	/	SYM
ejpam-1951	455	4	eur	eur	PROPN
ejpam-1951	455	5	.	.	PUNCT
ejpam-1951	456	1	j.	j.	PROPN
ejpam-1951	456	2	pure	pure	PROPN
ejpam-1951	456	3	appl	appl	PROPN
ejpam-1951	456	4	.	.	PROPN
ejpam-1951	456	5	math	math	PROPN
ejpam-1951	456	6	,	,	PUNCT
ejpam-1951	456	7	9	9	NUM
ejpam-1951	456	8	(	(	PUNCT
ejpam-1951	456	9	2016	2016	NUM
ejpam-1951	456	10	)	)	PUNCT
ejpam-1951	456	11	,	,	PUNCT
ejpam-1951	456	12	84	84	NUM
ejpam-1951	456	13	-	-	SYM
ejpam-1951	456	14	113	113	NUM
ejpam-1951	456	15	101	101	NUM
ejpam-1951	456	16	(	(	PUNCT
ejpam-1951	456	17	ii	ii	NOUN
ejpam-1951	456	18	)	)	PUNCT
ejpam-1951	456	19	expanding	expand	VERB
ejpam-1951	456	20	the	the	DET
ejpam-1951	456	21	same	same	ADJ
ejpam-1951	456	22	equation	equation	NOUN
ejpam-1951	456	23	we	we	PRON
ejpam-1951	456	24	have	have	VERB
ejpam-1951	456	25	by	by	ADP
ejpam-1951	456	26	maple	maple	NOUN
ejpam-1951	456	27	zd16	zd16	PROPN
ejpam-1951	456	28	=	=	SYM
ejpam-1951	456	29	x15	x15	PROPN
ejpam-1951	456	30	+	+	X
ejpam-1951	456	31	8x14y2	8x14y2	ADJ
ejpam-1951	456	32	+	+	CCONJ
ejpam-1951	456	33	21x13	21x13	NUM
ejpam-1951	456	34	y3	y3	NOUN
ejpam-1951	456	35	+	+	CCONJ
ejpam-1951	456	36	72x12	72x12	NUM
ejpam-1951	456	37	y4	y4	ADJ
ejpam-1951	456	38	+	+	CCONJ
ejpam-1951	456	39	147x11	147x11	NUM
ejpam-1951	456	40	y5	y5	NOUN
ejpam-1951	456	41	+	+	CCONJ
ejpam-1951	456	42	280x10	280x10	NUM
ejpam-1951	456	43	y6	y6	ADJ
ejpam-1951	457	1	+	+	CCONJ
ejpam-1951	457	2	375x9	375x9	NUM
ejpam-1951	457	3	y7	y7	ADJ
ejpam-1951	457	4	+	+	CCONJ
ejpam-1951	457	5	440x8	440x8	NUM
ejpam-1951	457	6	y8	y8	ADJ
ejpam-1951	457	7	+	+	CCONJ
ejpam-1951	457	8	375x7	375x7	NUM
ejpam-1951	457	9	y9	y9	NOUN
ejpam-1951	457	10	+	+	CCONJ
ejpam-1951	457	11	280x6	280x6	NUM
ejpam-1951	457	12	y10	y10	NOUN
ejpam-1951	458	1	+	+	NOUN
ejpam-1951	458	2	147x5	147x5	NUM
ejpam-1951	458	3	y11	y11	NOUN
ejpam-1951	458	4	+	+	CCONJ
ejpam-1951	458	5	72x4	72x4	NUM
ejpam-1951	458	6	y12	y12	NOUN
ejpam-1951	458	7	+	+	CCONJ
ejpam-1951	459	1	21x3	21x3	NUM
ejpam-1951	459	2	y13	y13	NOUN
ejpam-1951	459	3	+	+	CCONJ
ejpam-1951	459	4	8x2	8x2	NUM
ejpam-1951	459	5	y14	y14	VERB
ejpam-1951	460	1	+	+	CCONJ
ejpam-1951	460	2	x	x	SYM
ejpam-1951	460	3	y15	y15	NOUN
ejpam-1951	460	4	+	+	CCONJ
ejpam-1951	460	5	x16	x16	NOUN
ejpam-1951	461	1	+	+	CCONJ
ejpam-1951	461	2	y16	y16	ADJ
ejpam-1951	461	3	the	the	DET
ejpam-1951	461	4	term	term	NOUN
ejpam-1951	461	5	8x14	8x14	PROPN
ejpam-1951	461	6	y2	y2	PROPN
ejpam-1951	461	7	contains	contain	VERB
ejpam-1951	461	8	14	14	NUM
ejpam-1951	461	9	red	red	ADJ
ejpam-1951	461	10	and	and	CCONJ
ejpam-1951	461	11	2	2	NUM
ejpam-1951	461	12	black	black	ADJ
ejpam-1951	461	13	colors	color	NOUN
ejpam-1951	461	14	.	.	PUNCT
ejpam-1951	462	1	the	the	DET
ejpam-1951	462	2	coefficient	coefficient	NOUN
ejpam-1951	462	3	of	of	ADP
ejpam-1951	462	4	this	this	DET
ejpam-1951	462	5	term	term	NOUN
ejpam-1951	462	6	is	be	AUX
ejpam-1951	462	7	8	8	NUM
ejpam-1951	462	8	.	.	PUNCT
ejpam-1951	463	1	so	so	ADV
ejpam-1951	463	2	there	there	PRON
ejpam-1951	463	3	are	be	VERB
ejpam-1951	463	4	8	8	NUM
ejpam-1951	463	5	ways	way	NOUN
ejpam-1951	463	6	to	to	PART
ejpam-1951	463	7	decorate	decorate	VERB
ejpam-1951	463	8	a	a	DET
ejpam-1951	463	9	16	16	NUM
ejpam-1951	463	10	beaded	beaded	ADJ
ejpam-1951	463	11	necklace	necklace	NOUN
ejpam-1951	463	12	with	with	ADP
ejpam-1951	463	13	14	14	NUM
ejpam-1951	463	14	red	red	ADJ
ejpam-1951	463	15	and	and	CCONJ
ejpam-1951	463	16	2	2	NUM
ejpam-1951	463	17	black	black	ADJ
ejpam-1951	463	18	colors	color	NOUN
ejpam-1951	463	19	.	.	PUNCT
ejpam-1951	464	1	(	(	PUNCT
ejpam-1951	464	2	iii	iii	NOUN
ejpam-1951	464	3	)	)	PUNCT
ejpam-1951	464	4	for	for	ADP
ejpam-1951	464	5	this	this	DET
ejpam-1951	464	6	case	case	NOUN
ejpam-1951	464	7	consider	consider	VERB
ejpam-1951	464	8	4	4	NUM
ejpam-1951	464	9	colors	color	NOUN
ejpam-1951	464	10	x	x	SYM
ejpam-1951	464	11	,	,	PUNCT
ejpam-1951	464	12	y	y	PROPN
ejpam-1951	464	13	,	,	PUNCT
ejpam-1951	464	14	z	z	NOUN
ejpam-1951	464	15	,	,	PUNCT
ejpam-1951	464	16	and	and	CCONJ
ejpam-1951	464	17	p.	p.	NOUN
ejpam-1951	464	18	we	we	PRON
ejpam-1951	464	19	will	will	AUX
ejpam-1951	464	20	again	again	ADV
ejpam-1951	464	21	apply	apply	VERB
ejpam-1951	464	22	pólya	pólya	NOUN
ejpam-1951	464	23	’s	’s	PART
ejpam-1951	464	24	substitution	substitution	NOUN
ejpam-1951	464	25	method	method	NOUN
ejpam-1951	464	26	.	.	PUNCT
ejpam-1951	465	1	substituting	substitute	VERB
ejpam-1951	465	2	t	t	PROPN
ejpam-1951	465	3	i	i	PRON
ejpam-1951	465	4	→	→	PUNCT
ejpam-1951	465	5	(	(	PUNCT
ejpam-1951	465	6	x	x	X
ejpam-1951	465	7	i	i	PRON
ejpam-1951	465	8	+	+	NOUN
ejpam-1951	465	9	y	y	NOUN
ejpam-1951	465	10	i	i	PRON
ejpam-1951	466	1	+	+	CCONJ
ejpam-1951	466	2	z	z	NOUN
ejpam-1951	467	1	i	i	PRON
ejpam-1951	467	2	+	+	CCONJ
ejpam-1951	467	3	pi	pi	NOUN
ejpam-1951	467	4	)	)	PUNCT
ejpam-1951	467	5	for	for	ADP
ejpam-1951	467	6	each	each	DET
ejpam-1951	467	7	i	i	PRON
ejpam-1951	467	8	=	=	PUNCT
ejpam-1951	467	9	{	{	PUNCT
ejpam-1951	467	10	1,2,3	1,2,3	NUM
ejpam-1951	467	11	,	,	PUNCT
ejpam-1951	467	12	.	.	PUNCT
ejpam-1951	467	13	.	.	PUNCT
ejpam-1951	467	14	.	.	PUNCT
ejpam-1951	468	1	,	,	PUNCT
ejpam-1951	468	2	16	16	NUM
ejpam-1951	468	3	}	}	PUNCT
ejpam-1951	468	4	in	in	ADP
ejpam-1951	468	5	equation	equation	NOUN
ejpam-1951	468	6	(	(	PUNCT
ejpam-1951	468	7	4	4	NUM
ejpam-1951	468	8	)	)	PUNCT
ejpam-1951	468	9	,	,	PUNCT
ejpam-1951	468	10	we	we	PRON
ejpam-1951	468	11	get	get	VERB
ejpam-1951	468	12	z(d16	z(d16	NUM
ejpam-1951	468	13	,	,	PUNCT
ejpam-1951	468	14	t1	t1	NOUN
ejpam-1951	468	15	,	,	PUNCT
ejpam-1951	468	16	.	.	PUNCT
ejpam-1951	468	17	.	.	PUNCT
ejpam-1951	469	1	.	.	PUNCT
ejpam-1951	470	1	,	,	PUNCT
ejpam-1951	470	2	t16	t16	PROPN
ejpam-1951	470	3	)	)	PUNCT
ejpam-1951	470	4	=	=	PUNCT
ejpam-1951	471	1	1	1	NUM
ejpam-1951	471	2	32	32	NUM
ejpam-1951	471	3	(	(	PUNCT
ejpam-1951	471	4	(	(	PUNCT
ejpam-1951	471	5	x	x	SYM
ejpam-1951	471	6	+	+	NUM
ejpam-1951	471	7	y	y	PROPN
ejpam-1951	471	8	+	+	NUM
ejpam-1951	471	9	z	z	NOUN
ejpam-1951	471	10	+	+	CCONJ
ejpam-1951	471	11	p)16	p)16	NOUN
ejpam-1951	471	12	+	+	CCONJ
ejpam-1951	471	13	9(x2	9(x2	NUM
ejpam-1951	471	14	+	+	CCONJ
ejpam-1951	471	15	y2	y2	PROPN
ejpam-1951	471	16	+	+	CCONJ
ejpam-1951	471	17	z2	z2	PROPN
ejpam-1951	471	18	+	+	CCONJ
ejpam-1951	471	19	p2)8	p2)8	PROPN
ejpam-1951	471	20	+	+	NUM
ejpam-1951	471	21	8(x	8(x	NUM
ejpam-1951	471	22	+	+	CCONJ
ejpam-1951	471	23	y	y	PROPN
ejpam-1951	471	24	+	+	CCONJ
ejpam-1951	471	25	z	z	NOUN
ejpam-1951	471	26	+	+	CCONJ
ejpam-1951	471	27	p)2(x2	p)2(x2	NOUN
ejpam-1951	471	28	+	+	CCONJ
ejpam-1951	471	29	y2	y2	PROPN
ejpam-1951	471	30	+	+	CCONJ
ejpam-1951	471	31	z2	z2	PROPN
ejpam-1951	471	32	+	+	CCONJ
ejpam-1951	471	33	p2)7	p2)7	PROPN
ejpam-1951	471	34	+	+	CCONJ
ejpam-1951	471	35	2(x4	2(x4	NUM
ejpam-1951	471	36	+	+	CCONJ
ejpam-1951	471	37	y4	y4	ADJ
ejpam-1951	471	38	+	+	CCONJ
ejpam-1951	471	39	z4	z4	PROPN
ejpam-1951	471	40	+	+	CCONJ
ejpam-1951	471	41	p4)4	p4)4	X
ejpam-1951	471	42	+	+	NUM
ejpam-1951	471	43	4(x8	4(x8	NOUN
ejpam-1951	472	1	+	+	CCONJ
ejpam-1951	472	2	y8	y8	PROPN
ejpam-1951	472	3	+	+	NUM
ejpam-1951	472	4	z8	z8	NOUN
ejpam-1951	472	5	+	+	CCONJ
ejpam-1951	473	1	p4)2	p4)2	PROPN
ejpam-1951	473	2	+	+	NUM
ejpam-1951	473	3	8(x16	8(x16	NUM
ejpam-1951	473	4	+	+	CCONJ
ejpam-1951	473	5	y16	y16	NOUN
ejpam-1951	473	6	+	+	CCONJ
ejpam-1951	473	7	z16	z16	ADJ
ejpam-1951	473	8	+	+	CCONJ
ejpam-1951	473	9	p16)1	p16)1	NOUN
ejpam-1951	473	10	)	)	PUNCT
ejpam-1951	473	11	let	let	VERB
ejpam-1951	473	12	x	x	SYM
ejpam-1951	473	13	=	=	PUNCT
ejpam-1951	473	14	y	y	NOUN
ejpam-1951	473	15	=	=	PUNCT
ejpam-1951	473	16	z	z	NOUN
ejpam-1951	474	1	=	=	PUNCT
ejpam-1951	474	2	p	p	NOUN
ejpam-1951	474	3	=	=	NOUN
ejpam-1951	474	4	1	1	X
ejpam-1951	474	5	.	.	PUNCT
ejpam-1951	474	6	then	then	ADV
ejpam-1951	474	7	using	use	VERB
ejpam-1951	474	8	maple	maple	NOUN
ejpam-1951	474	9	by	by	ADP
ejpam-1951	474	10	the	the	DET
ejpam-1951	474	11	above	above	ADJ
ejpam-1951	474	12	equation	equation	NOUN
ejpam-1951	474	13	we	we	PRON
ejpam-1951	474	14	get	get	VERB
ejpam-1951	474	15	the	the	DET
ejpam-1951	474	16	total	total	ADJ
ejpam-1951	474	17	count	count	NOUN
ejpam-1951	474	18	134301715	134301715	NUM
ejpam-1951	474	19	.	.	PUNCT
ejpam-1951	475	1	3	3	X
ejpam-1951	475	2	.	.	X
ejpam-1951	475	3	generalization	generalization	NOUN
ejpam-1951	475	4	of	of	ADP
ejpam-1951	475	5	pólya	pólya	NOUN
ejpam-1951	475	6	’s	’s	PART
ejpam-1951	475	7	theorem	theorem	NOUN
ejpam-1951	475	8	in	in	ADP
ejpam-1951	475	9	the	the	DET
ejpam-1951	475	10	preceding	precede	VERB
ejpam-1951	475	11	sections	section	NOUN
ejpam-1951	475	12	we	we	PRON
ejpam-1951	475	13	considered	consider	VERB
ejpam-1951	475	14	mappings	mapping	NOUN
ejpam-1951	475	15	of	of	ADP
ejpam-1951	475	16	x	x	PUNCT
ejpam-1951	475	17	into	into	ADP
ejpam-1951	475	18	y	y	PROPN
ejpam-1951	475	19	,	,	PUNCT
ejpam-1951	475	20	introduced	introduce	VERB
ejpam-1951	475	21	by	by	ADP
ejpam-1951	475	22	a	a	DET
ejpam-1951	475	23	permutation	permutation	NOUN
ejpam-1951	475	24	group	group	NOUN
ejpam-1951	475	25	g	g	PROPN
ejpam-1951	475	26	of	of	ADP
ejpam-1951	475	27	x	x	INTJ
ejpam-1951	475	28	.	.	PUNCT
ejpam-1951	476	1	we	we	PRON
ejpam-1951	476	2	are	be	AUX
ejpam-1951	476	3	now	now	ADV
ejpam-1951	476	4	going	go	VERB
ejpam-1951	476	5	to	to	PART
ejpam-1951	476	6	move	move	VERB
ejpam-1951	476	7	on	on	ADP
ejpam-1951	476	8	more	more	ADJ
ejpam-1951	476	9	general	general	ADJ
ejpam-1951	476	10	situation	situation	NOUN
ejpam-1951	476	11	.	.	PUNCT
ejpam-1951	477	1	let	let	VERB
ejpam-1951	477	2	us	we	PRON
ejpam-1951	477	3	consider	consider	VERB
ejpam-1951	477	4	two	two	NUM
ejpam-1951	477	5	mappings	mapping	NOUN
ejpam-1951	477	6	f1	f1	NOUN
ejpam-1951	477	7	∈	∈	PROPN
ejpam-1951	478	1	y	y	PROPN
ejpam-1951	478	2	x	x	X
ejpam-1951	478	3	and	and	CCONJ
ejpam-1951	478	4	f2	f2	PROPN
ejpam-1951	478	5	∈	∈	PROPN
ejpam-1951	478	6	y	y	PROPN
ejpam-1951	478	7	x	x	X
ejpam-1951	478	8	.	.	PUNCT
ejpam-1951	479	1	they	they	PRON
ejpam-1951	479	2	are	be	AUX
ejpam-1951	479	3	equivalent	equivalent	ADJ
ejpam-1951	479	4	if	if	SCONJ
ejpam-1951	479	5	there	there	PRON
ejpam-1951	479	6	exist	exist	VERB
ejpam-1951	479	7	elements	element	NOUN
ejpam-1951	479	8	g	g	PROPN
ejpam-1951	479	9	∈	∈	PROPN
ejpam-1951	479	10	g	g	PROPN
ejpam-1951	479	11	and	and	CCONJ
ejpam-1951	479	12	h	h	NOUN
ejpam-1951	479	13	∈	∈	PROPN
ejpam-1951	479	14	h	h	NOUN
ejpam-1951	479	15	such	such	ADJ
ejpam-1951	479	16	that	that	DET
ejpam-1951	479	17	f1	f1	PROPN
ejpam-1951	479	18	g	g	PROPN
ejpam-1951	479	19	=	=	PUNCT
ejpam-1951	479	20	hf2	hf2	PROPN
ejpam-1951	479	21	,	,	PUNCT
ejpam-1951	479	22	that	that	PRON
ejpam-1951	479	23	is	be	AUX
ejpam-1951	479	24	f1(g	f1(g	ADJ
ejpam-1951	479	25	x	x	NOUN
ejpam-1951	479	26	)	)	PUNCT
ejpam-1951	480	1	=	=	SYM
ejpam-1951	480	2	hf2(x	hf2(x	NOUN
ejpam-1951	480	3	)	)	PUNCT
ejpam-1951	480	4	for	for	ADP
ejpam-1951	480	5	all	all	DET
ejpam-1951	480	6	x	x	SYM
ejpam-1951	480	7	∈	∈	NOUN
ejpam-1951	480	8	x	x	X
ejpam-1951	480	9	.	.	PUNCT
ejpam-1951	481	1	next	next	ADV
ejpam-1951	481	2	we	we	PRON
ejpam-1951	481	3	assume	assume	VERB
ejpam-1951	481	4	that	that	SCONJ
ejpam-1951	481	5	each	each	DET
ejpam-1951	481	6	f	f	PROPN
ejpam-1951	481	7	∈	∈	PROPN
ejpam-1951	481	8	y	y	PROPN
ejpam-1951	481	9	x	x	PUNCT
ejpam-1951	481	10	has	have	VERB
ejpam-1951	481	11	a	a	DET
ejpam-1951	481	12	certain	certain	ADJ
ejpam-1951	481	13	weight	weight	NOUN
ejpam-1951	481	14	w	w	NOUN
ejpam-1951	481	15	(	(	PUNCT
ejpam-1951	481	16	f	f	PROPN
ejpam-1951	481	17	)	)	PUNCT
ejpam-1951	481	18	.	.	PUNCT
ejpam-1951	482	1	then	then	ADV
ejpam-1951	482	2	we	we	PRON
ejpam-1951	482	3	can	can	AUX
ejpam-1951	482	4	also	also	ADV
ejpam-1951	482	5	assume	assume	VERB
ejpam-1951	482	6	that	that	SCONJ
ejpam-1951	482	7	equivalence	equivalence	NOUN
ejpam-1951	482	8	functions	function	NOUN
ejpam-1951	482	9	have	have	VERB
ejpam-1951	482	10	the	the	DET
ejpam-1951	482	11	same	same	ADJ
ejpam-1951	482	12	weight	weight	NOUN
ejpam-1951	482	13	:	:	PUNCT
ejpam-1951	482	14	f1	f1	NOUN
ejpam-1951	482	15	∼	∼	NOUN
ejpam-1951	482	16	f2	f2	PROPN
ejpam-1951	482	17	implies	imply	VERB
ejpam-1951	482	18	w	w	PROPN
ejpam-1951	482	19	(	(	PUNCT
ejpam-1951	482	20	f1	f1	NOUN
ejpam-1951	482	21	)	)	PUNCT
ejpam-1951	483	1	=	=	NOUN
ejpam-1951	483	2	w	w	PROPN
ejpam-1951	483	3	(	(	PUNCT
ejpam-1951	483	4	f2	f2	PROPN
ejpam-1951	483	5	)	)	PUNCT
ejpam-1951	483	6	.	.	PUNCT
ejpam-1951	484	1	if	if	SCONJ
ejpam-1951	484	2	f	f	PROPN
ejpam-1951	484	3	denotes	denote	VERB
ejpam-1951	484	4	a	a	DET
ejpam-1951	484	5	pattern	pattern	NOUN
ejpam-1951	484	6	,	,	PUNCT
ejpam-1951	484	7	we	we	PRON
ejpam-1951	484	8	define	define	VERB
ejpam-1951	484	9	its	its	PRON
ejpam-1951	484	10	weight	weight	NOUN
ejpam-1951	484	11	w	w	NOUN
ejpam-1951	484	12	(	(	PUNCT
ejpam-1951	484	13	f	f	X
ejpam-1951	484	14	)	)	PUNCT
ejpam-1951	484	15	as	as	ADP
ejpam-1951	484	16	the	the	DET
ejpam-1951	484	17	common	common	ADJ
ejpam-1951	484	18	value	value	NOUN
ejpam-1951	484	19	of	of	ADP
ejpam-1951	484	20	all	all	DET
ejpam-1951	484	21	w	w	NOUN
ejpam-1951	484	22	(	(	PUNCT
ejpam-1951	484	23	f	f	PROPN
ejpam-1951	484	24	)	)	PUNCT
ejpam-1951	484	25	with	with	ADP
ejpam-1951	484	26	f	f	PROPN
ejpam-1951	484	27	∈	∈	PROPN
ejpam-1951	484	28	f	f	PROPN
ejpam-1951	485	1	[	[	X
ejpam-1951	485	2	2	2	NUM
ejpam-1951	485	3	]	]	PUNCT
ejpam-1951	485	4	.	.	PUNCT
ejpam-1951	486	1	lemma	lemma	PROPN
ejpam-1951	486	2	2	2	NUM
ejpam-1951	486	3	.	.	PUNCT
ejpam-1951	487	1	the	the	DET
ejpam-1951	487	2	pattern	pattern	NOUN
ejpam-1951	487	3	inventory	inventory	NOUN
ejpam-1951	487	4	is	be	AUX
ejpam-1951	487	5	∑	∑	PROPN
ejpam-1951	487	6	w	w	PROPN
ejpam-1951	487	7	(	(	PUNCT
ejpam-1951	487	8	f	f	X
ejpam-1951	487	9	)	)	PUNCT
ejpam-1951	487	10	=	=	SYM
ejpam-1951	488	1	1	1	NUM
ejpam-1951	488	2	|g|	|g|	PROPN
ejpam-1951	488	3	1	1	NUM
ejpam-1951	488	4	|h|	|h|	NOUN
ejpam-1951	488	5	∑	∑	PUNCT
ejpam-1951	488	6	g∈g	g∈g	PROPN
ejpam-1951	488	7	∑	∑	PROPN
ejpam-1951	488	8	h∈h	h∈h	PROPN
ejpam-1951	488	9	(	(	PUNCT
ejpam-1951	488	10	g	g	NOUN
ejpam-1951	488	11	,	,	PUNCT
ejpam-1951	488	12	h	h	NOUN
ejpam-1951	488	13	)	)	PUNCT
ejpam-1951	488	14	∑	∑	PROPN
ejpam-1951	488	15	f	f	PROPN
ejpam-1951	489	1	w	w	PROPN
ejpam-1951	489	2	(	(	PUNCT
ejpam-1951	489	3	f	f	PROPN
ejpam-1951	489	4	)	)	PUNCT
ejpam-1951	489	5	where	where	SCONJ
ejpam-1951	489	6	∑(g	∑(g	PROPN
ejpam-1951	489	7	,	,	PUNCT
ejpam-1951	489	8	h	h	NOUN
ejpam-1951	489	9	)	)	PUNCT
ejpam-1951	489	10	f	f	PROPN
ejpam-1951	490	1	w	w	PROPN
ejpam-1951	490	2	(	(	PUNCT
ejpam-1951	490	3	f	f	PROPN
ejpam-1951	490	4	)	)	PUNCT
ejpam-1951	490	5	means	mean	VERB
ejpam-1951	490	6	the	the	DET
ejpam-1951	490	7	sum	sum	NOUN
ejpam-1951	490	8	of	of	ADP
ejpam-1951	490	9	w	w	PROPN
ejpam-1951	490	10	(	(	PUNCT
ejpam-1951	490	11	f	f	PROPN
ejpam-1951	490	12	)	)	PUNCT
ejpam-1951	490	13	extended	extend	VERB
ejpam-1951	490	14	over	over	ADP
ejpam-1951	490	15	all	all	DET
ejpam-1951	490	16	f	f	PROPN
ejpam-1951	490	17	that	that	PRON
ejpam-1951	490	18	satisfy	satisfy	VERB
ejpam-1951	491	1	f	f	PROPN
ejpam-1951	491	2	g	g	PROPN
ejpam-1951	491	3	=	=	PUNCT
ejpam-1951	491	4	hf	hf	PROPN
ejpam-1951	492	1	[	[	X
ejpam-1951	492	2	2	2	NUM
ejpam-1951	492	3	]	]	PUNCT
ejpam-1951	492	4	.	.	PUNCT
ejpam-1951	493	1	t.	t.	PROPN
ejpam-1951	493	2	nasseef	nasseef	PROPN
ejpam-1951	493	3	/	/	SYM
ejpam-1951	493	4	eur	eur	PROPN
ejpam-1951	493	5	.	.	PUNCT
ejpam-1951	494	1	j.	j.	PROPN
ejpam-1951	494	2	pure	pure	PROPN
ejpam-1951	494	3	appl	appl	PROPN
ejpam-1951	494	4	.	.	PROPN
ejpam-1951	494	5	math	math	PROPN
ejpam-1951	494	6	,	,	PUNCT
ejpam-1951	494	7	9	9	NUM
ejpam-1951	494	8	(	(	PUNCT
ejpam-1951	494	9	2016	2016	NUM
ejpam-1951	494	10	)	)	PUNCT
ejpam-1951	494	11	,	,	PUNCT
ejpam-1951	494	12	84	84	NUM
ejpam-1951	494	13	-	-	SYM
ejpam-1951	494	14	113	113	NUM
ejpam-1951	494	15	102	102	NUM
ejpam-1951	494	16	3.1	3.1	NUM
ejpam-1951	494	17	.	.	PUNCT
ejpam-1951	495	1	patterns	pattern	NOUN
ejpam-1951	495	2	of	of	ADP
ejpam-1951	495	3	one	one	NUM
ejpam-1951	495	4	-	-	PUNCT
ejpam-1951	495	5	to	to	ADP
ejpam-1951	495	6	-	-	PUNCT
ejpam-1951	495	7	one	one	NUM
ejpam-1951	495	8	mappings	mapping	NOUN
ejpam-1951	495	9	we	we	PRON
ejpam-1951	495	10	already	already	ADV
ejpam-1951	495	11	have	have	VERB
ejpam-1951	495	12	the	the	DET
ejpam-1951	495	13	finite	finite	ADJ
ejpam-1951	495	14	sets	set	NOUN
ejpam-1951	495	15	x	x	PUNCT
ejpam-1951	495	16	and	and	CCONJ
ejpam-1951	495	17	y	y	PROPN
ejpam-1951	495	18	,	,	PUNCT
ejpam-1951	495	19	subject	subject	ADJ
ejpam-1951	495	20	to	to	ADP
ejpam-1951	495	21	the	the	DET
ejpam-1951	495	22	permutation	permutation	NOUN
ejpam-1951	495	23	groups	group	NOUN
ejpam-1951	495	24	g	g	PROPN
ejpam-1951	495	25	and	and	CCONJ
ejpam-1951	495	26	h.	h.	PROPN
ejpam-1951	496	1	now	now	ADV
ejpam-1951	496	2	we	we	PRON
ejpam-1951	496	3	define	define	VERB
ejpam-1951	496	4	the	the	DET
ejpam-1951	496	5	weight	weight	NOUN
ejpam-1951	496	6	w	w	NOUN
ejpam-1951	496	7	(	(	PUNCT
ejpam-1951	496	8	f	f	PROPN
ejpam-1951	496	9	)	)	PUNCT
ejpam-1951	496	10	of	of	ADP
ejpam-1951	496	11	any	any	DET
ejpam-1951	496	12	f	f	PROPN
ejpam-1951	496	13	∈	∈	PROPN
ejpam-1951	496	14	y	y	PROPN
ejpam-1951	496	15	x	x	VERB
ejpam-1951	496	16	by	by	ADP
ejpam-1951	496	17	w	w	PROPN
ejpam-1951	496	18	(	(	PUNCT
ejpam-1951	496	19	f	f	PROPN
ejpam-1951	496	20	)	)	PUNCT
ejpam-1951	497	1	=	=	PUNCT
ejpam-1951	497	2	¨	¨	NOUN
ejpam-1951	497	3	1	1	NUM
ejpam-1951	497	4	if	if	SCONJ
ejpam-1951	497	5	f	f	PROPN
ejpam-1951	497	6	is	be	AUX
ejpam-1951	497	7	a	a	DET
ejpam-1951	497	8	one	one	NUM
ejpam-1951	497	9	-	-	PUNCT
ejpam-1951	497	10	to	to	ADP
ejpam-1951	497	11	-	-	PUNCT
ejpam-1951	497	12	one	one	NUM
ejpam-1951	497	13	mapping	mapping	NOUN
ejpam-1951	497	14	0	0	PUNCT
ejpam-1951	497	15	otherwise	otherwise	ADV
ejpam-1951	497	16	if	if	SCONJ
ejpam-1951	497	17	g	g	PROPN
ejpam-1951	497	18	∈	∈	PROPN
ejpam-1951	497	19	g	g	PROPN
ejpam-1951	497	20	and	and	CCONJ
ejpam-1951	497	21	h	h	NOUN
ejpam-1951	497	22	∈	∈	PROPN
ejpam-1951	497	23	h	h	NOUN
ejpam-1951	497	24	,	,	PUNCT
ejpam-1951	497	25	then	then	ADV
ejpam-1951	497	26	the	the	DET
ejpam-1951	497	27	mapping	mapping	NOUN
ejpam-1951	497	28	hf	hf	ADP
ejpam-1951	497	29	g−1	g−1	PROPN
ejpam-1951	497	30	is	be	AUX
ejpam-1951	497	31	one	one	NUM
ejpam-1951	497	32	-	-	PUNCT
ejpam-1951	497	33	to	to	ADP
ejpam-1951	497	34	-	-	PUNCT
ejpam-1951	497	35	one	one	NOUN
ejpam-1951	497	36	if	if	SCONJ
ejpam-1951	497	37	and	and	CCONJ
ejpam-1951	497	38	only	only	ADV
ejpam-1951	497	39	if	if	SCONJ
ejpam-1951	497	40	f	f	PROPN
ejpam-1951	497	41	is	be	AUX
ejpam-1951	497	42	one	one	NUM
ejpam-1951	497	43	-	-	PUNCT
ejpam-1951	497	44	to	to	ADP
ejpam-1951	497	45	-	-	PUNCT
ejpam-1951	497	46	one	one	NUM
ejpam-1951	497	47	and	and	CCONJ
ejpam-1951	497	48	thus	thus	ADV
ejpam-1951	497	49	w	w	PROPN
ejpam-1951	497	50	(	(	PUNCT
ejpam-1951	497	51	f1	f1	NOUN
ejpam-1951	497	52	)	)	PUNCT
ejpam-1951	498	1	=	=	NOUN
ejpam-1951	498	2	w	w	PROPN
ejpam-1951	498	3	(	(	PUNCT
ejpam-1951	498	4	f2	f2	PROPN
ejpam-1951	498	5	)	)	PUNCT
ejpam-1951	498	6	.	.	PUNCT
ejpam-1951	499	1	the	the	DET
ejpam-1951	499	2	inventory	inventory	NOUN
ejpam-1951	499	3	∑	∑	PROPN
ejpam-1951	499	4	w	w	PROPN
ejpam-1951	499	5	(	(	PUNCT
ejpam-1951	499	6	f	f	X
ejpam-1951	499	7	)	)	PUNCT
ejpam-1951	499	8	is	be	AUX
ejpam-1951	499	9	just	just	ADV
ejpam-1951	499	10	the	the	DET
ejpam-1951	499	11	number	number	NOUN
ejpam-1951	499	12	of	of	ADP
ejpam-1951	499	13	patterns	pattern	NOUN
ejpam-1951	499	14	of	of	ADP
ejpam-1951	499	15	one	one	NUM
ejpam-1951	499	16	-	-	PUNCT
ejpam-1951	499	17	to	to	ADP
ejpam-1951	499	18	-	-	PUNCT
ejpam-1951	499	19	one	one	NUM
ejpam-1951	499	20	function	function	NOUN
ejpam-1951	499	21	.	.	PUNCT
ejpam-1951	500	1	now	now	ADV
ejpam-1951	500	2	let	let	VERB
ejpam-1951	500	3	g	g	PRON
ejpam-1951	500	4	be	be	AUX
ejpam-1951	500	5	of	of	ADP
ejpam-1951	500	6	type	type	NOUN
ejpam-1951	500	7	{	{	PUNCT
ejpam-1951	500	8	g1	g1	PROPN
ejpam-1951	500	9	,	,	PUNCT
ejpam-1951	500	10	g2	g2	PROPN
ejpam-1951	500	11	,	,	PUNCT
ejpam-1951	500	12	.	.	PUNCT
ejpam-1951	500	13	.	.	PUNCT
ejpam-1951	501	1	.}where	.}where	PUNCT
ejpam-1951	502	1	gi	gi	PROPN
ejpam-1951	502	2	shows	show	VERB
ejpam-1951	502	3	the	the	DET
ejpam-1951	502	4	number	number	NOUN
ejpam-1951	502	5	of	of	ADP
ejpam-1951	502	6	cycles	cycle	NOUN
ejpam-1951	502	7	of	of	ADP
ejpam-1951	502	8	length	length	NOUN
ejpam-1951	502	9	i.	i.	PROPN
ejpam-1951	502	10	similarly	similarly	ADV
ejpam-1951	502	11	let	let	VERB
ejpam-1951	502	12	h	h	NOUN
ejpam-1951	502	13	be	be	AUX
ejpam-1951	502	14	of	of	ADP
ejpam-1951	502	15	type	type	NOUN
ejpam-1951	502	16	{	{	PUNCT
ejpam-1951	502	17	h1,h2	h1,h2	PROPN
ejpam-1951	502	18	,	,	PUNCT
ejpam-1951	502	19	.	.	PUNCT
ejpam-1951	502	20	.	.	PUNCT
ejpam-1951	502	21	.	.	PUNCT
ejpam-1951	502	22	}	}	PUNCT
ejpam-1951	502	23	.	.	PUNCT
ejpam-1951	503	1	we	we	PRON
ejpam-1951	503	2	will	will	AUX
ejpam-1951	503	3	find	find	VERB
ejpam-1951	503	4	the	the	DET
ejpam-1951	503	5	number	number	NOUN
ejpam-1951	503	6	of	of	ADP
ejpam-1951	503	7	one	one	NUM
ejpam-1951	503	8	-	-	PUNCT
ejpam-1951	503	9	to	to	ADP
ejpam-1951	503	10	-	-	PUNCT
ejpam-1951	503	11	one	one	NUM
ejpam-1951	503	12	mappings	mapping	NOUN
ejpam-1951	503	13	f	f	NOUN
ejpam-1951	503	14	of	of	ADP
ejpam-1951	503	15	y	y	PROPN
ejpam-1951	503	16	into	into	ADP
ejpam-1951	503	17	x	x	PRON
ejpam-1951	503	18	that	that	SCONJ
ejpam-1951	503	19	satisfies	satisfy	VERB
ejpam-1951	503	20	f	f	PROPN
ejpam-1951	503	21	g	g	PROPN
ejpam-1951	503	22	=	=	SYM
ejpam-1951	503	23	hf	hf	PROPN
ejpam-1951	503	24	.	.	PUNCT
ejpam-1951	504	1	let	let	VERB
ejpam-1951	504	2	x	x	PRON
ejpam-1951	504	3	be	be	AUX
ejpam-1951	504	4	any	any	DET
ejpam-1951	504	5	element	element	NOUN
ejpam-1951	504	6	in	in	ADP
ejpam-1951	504	7	x	x	X
ejpam-1951	504	8	,	,	PUNCT
ejpam-1951	504	9	belonging	belong	VERB
ejpam-1951	504	10	to	to	ADP
ejpam-1951	504	11	a	a	DET
ejpam-1951	504	12	cycle	cycle	NOUN
ejpam-1951	504	13	of	of	ADP
ejpam-1951	504	14	length	length	NOUN
ejpam-1951	504	15	j.	j.	PROPN
ejpam-1951	504	16	this	this	DET
ejpam-1951	504	17	cycle	cycle	NOUN
ejpam-1951	504	18	consists	consist	VERB
ejpam-1951	504	19	of	of	ADP
ejpam-1951	504	20	elements	element	NOUN
ejpam-1951	504	21	x	x	SYM
ejpam-1951	504	22	,	,	PUNCT
ejpam-1951	504	23	g	g	PROPN
ejpam-1951	504	24	x	x	X
ejpam-1951	504	25	,	,	PUNCT
ejpam-1951	504	26	g2	g2	PROPN
ejpam-1951	504	27	x	x	X
ejpam-1951	504	28	,	,	PUNCT
ejpam-1951	504	29	.	.	PUNCT
ejpam-1951	504	30	.	.	PUNCT
ejpam-1951	505	1	.	.	PUNCT
ejpam-1951	506	1	,	,	PUNCT
ejpam-1951	506	2	g	g	PROPN
ejpam-1951	506	3	j−1	j−1	PROPN
ejpam-1951	506	4	x	x	PUNCT
ejpam-1951	506	5	and	and	CCONJ
ejpam-1951	506	6	we	we	PRON
ejpam-1951	506	7	have	have	VERB
ejpam-1951	506	8	g	g	PROPN
ejpam-1951	506	9	j	j	PROPN
ejpam-1951	506	10	x	x	X
ejpam-1951	507	1	=	=	PUNCT
ejpam-1951	507	2	x	x	X
ejpam-1951	507	3	.	.	PUNCT
ejpam-1951	508	1	now	now	ADV
ejpam-1951	508	2	f	f	X
ejpam-1951	508	3	g	g	PROPN
ejpam-1951	508	4	=	=	PUNCT
ejpam-1951	508	5	hf	hf	PROPN
ejpam-1951	508	6	implies	imply	VERB
ejpam-1951	508	7	f	f	PROPN
ejpam-1951	508	8	g2	g2	PROPN
ejpam-1951	508	9	=	=	PUNCT
ejpam-1951	509	1	f	f	PROPN
ejpam-1951	509	2	g	g	NOUN
ejpam-1951	509	3	g	g	PROPN
ejpam-1951	509	4	=	=	NOUN
ejpam-1951	509	5	hf	hf	NOUN
ejpam-1951	509	6	g	g	NOUN
ejpam-1951	509	7	=	=	PUNCT
ejpam-1951	509	8	hhf	hhf	NOUN
ejpam-1951	510	1	=	=	SYM
ejpam-1951	510	2	h2	h2	PROPN
ejpam-1951	510	3	f	f	PROPN
ejpam-1951	510	4	,	,	PUNCT
ejpam-1951	510	5	f	f	PROPN
ejpam-1951	510	6	g3	g3	PROPN
ejpam-1951	510	7	=	=	PROPN
ejpam-1951	510	8	h3	h3	PROPN
ejpam-1951	510	9	f	f	PROPN
ejpam-1951	510	10	,	,	PUNCT
ejpam-1951	510	11	.	.	PUNCT
ejpam-1951	510	12	.	.	PUNCT
ejpam-1951	510	13	.	.	PUNCT
ejpam-1951	511	1	hence	hence	ADV
ejpam-1951	511	2	we	we	PRON
ejpam-1951	511	3	have	have	VERB
ejpam-1951	511	4	h	h	PROPN
ejpam-1951	512	1	j	j	PROPN
ejpam-1951	512	2	f	f	PROPN
ejpam-1951	512	3	x	x	PROPN
ejpam-1951	513	1	=	=	SYM
ejpam-1951	513	2	f	f	PROPN
ejpam-1951	513	3	g	g	PROPN
ejpam-1951	513	4	j	j	PROPN
ejpam-1951	513	5	x	x	X
ejpam-1951	513	6	=	=	PUNCT
ejpam-1951	513	7	f	f	PROPN
ejpam-1951	513	8	x	x	X
ejpam-1951	513	9	.	.	PUNCT
ejpam-1951	514	1	it	it	PRON
ejpam-1951	514	2	follows	follow	VERB
ejpam-1951	514	3	that	that	SCONJ
ejpam-1951	514	4	the	the	DET
ejpam-1951	514	5	length	length	NOUN
ejpam-1951	514	6	of	of	ADP
ejpam-1951	514	7	cycle	cycle	NOUN
ejpam-1951	514	8	of	of	ADP
ejpam-1951	514	9	y	y	PROPN
ejpam-1951	514	10	to	to	PART
ejpam-1951	514	11	which	which	PRON
ejpam-1951	514	12	f	f	AUX
ejpam-1951	514	13	x	x	AUX
ejpam-1951	514	14	belongs	belong	VERB
ejpam-1951	514	15	is	be	AUX
ejpam-1951	514	16	a	a	DET
ejpam-1951	514	17	divisor	divisor	NOUN
ejpam-1951	514	18	of	of	ADP
ejpam-1951	514	19	j.	j.	PROPN
ejpam-1951	514	20	the	the	DET
ejpam-1951	514	21	number	number	NOUN
ejpam-1951	514	22	of	of	ADP
ejpam-1951	514	23	elements	element	NOUN
ejpam-1951	514	24	of	of	ADP
ejpam-1951	514	25	one	one	NUM
ejpam-1951	514	26	-	-	PUNCT
ejpam-1951	514	27	to	to	ADP
ejpam-1951	514	28	-	-	PUNCT
ejpam-1951	514	29	one	one	NUM
ejpam-1951	514	30	mappings	mapping	NOUN
ejpam-1951	514	31	of	of	ADP
ejpam-1951	514	32	a	a	DET
ejpam-1951	514	33	set	set	NOUN
ejpam-1951	514	34	g	g	PROPN
ejpam-1951	514	35	j	j	PROPN
ejpam-1951	514	36	elements	element	NOUN
ejpam-1951	514	37	into	into	ADP
ejpam-1951	514	38	a	a	DET
ejpam-1951	514	39	set	set	NOUN
ejpam-1951	514	40	of	of	ADP
ejpam-1951	514	41	h	h	NOUN
ejpam-1951	514	42	j	j	PROPN
ejpam-1951	514	43	elements	element	NOUN
ejpam-1951	514	44	equals	equal	VERB
ejpam-1951	514	45	h	h	PROPN
ejpam-1951	514	46	j(h	j(h	PROPN
ejpam-1951	514	47	j	j	PROPN
ejpam-1951	515	1	−	−	PROPN
ejpam-1951	515	2	1)(h	1)(h	NUM
ejpam-1951	515	3	j	j	NOUN
ejpam-1951	515	4	−	−	PROPN
ejpam-1951	515	5	2	2	NUM
ejpam-1951	515	6	)	)	PUNCT
ejpam-1951	515	7	.	.	PUNCT
ejpam-1951	515	8	.	.	PUNCT
ejpam-1951	516	1	.	.	PUNCT
ejpam-1951	517	1	(	(	PUNCT
ejpam-1951	517	2	h	h	NOUN
ejpam-1951	517	3	j	j	PROPN
ejpam-1951	517	4	−	−	PROPN
ejpam-1951	518	1	g	g	PROPN
ejpam-1951	518	2	j	j	PROPN
ejpam-1951	518	3	+	+	CCONJ
ejpam-1951	518	4	1	1	X
ejpam-1951	518	5	)	)	PUNCT
ejpam-1951	518	6	which	which	PRON
ejpam-1951	518	7	is	be	AUX
ejpam-1951	518	8	zero	zero	NUM
ejpam-1951	519	1	if	if	SCONJ
ejpam-1951	519	2	h	h	NOUN
ejpam-1951	519	3	j	j	PROPN
ejpam-1951	519	4	<	<	X
ejpam-1951	519	5	g	g	PROPN
ejpam-1951	519	6	j	j	PROPN
ejpam-1951	519	7	.	.	PUNCT
ejpam-1951	520	1	therefore	therefore	ADV
ejpam-1951	520	2	we	we	PRON
ejpam-1951	520	3	have	have	VERB
ejpam-1951	520	4	(	(	PUNCT
ejpam-1951	520	5	g	g	NOUN
ejpam-1951	520	6	,	,	PUNCT
ejpam-1951	520	7	h	h	NOUN
ejpam-1951	520	8	)	)	PUNCT
ejpam-1951	520	9	∑	∑	PROPN
ejpam-1951	521	1	f	f	PROPN
ejpam-1951	521	2	w	w	PROPN
ejpam-1951	521	3	(	(	PUNCT
ejpam-1951	521	4	f	f	PROPN
ejpam-1951	521	5	)	)	PUNCT
ejpam-1951	522	1	=	=	SYM
ejpam-1951	522	2	∏	∏	PROPN
ejpam-1951	522	3	j	j	PROPN
ejpam-1951	523	1	jg	jg	PROPN
ejpam-1951	523	2	j	j	PROPN
ejpam-1951	523	3	h	h	PROPN
ejpam-1951	523	4	j(h	j(h	PROPN
ejpam-1951	523	5	j	j	PROPN
ejpam-1951	524	1	−	−	PROPN
ejpam-1951	524	2	1)(h	1)(h	NUM
ejpam-1951	524	3	j	j	NOUN
ejpam-1951	524	4	−	−	PROPN
ejpam-1951	524	5	2	2	NUM
ejpam-1951	524	6	)	)	PUNCT
ejpam-1951	524	7	.	.	PUNCT
ejpam-1951	524	8	.	.	PUNCT
ejpam-1951	525	1	.	.	PUNCT
ejpam-1951	526	1	(	(	PUNCT
ejpam-1951	526	2	h	h	NOUN
ejpam-1951	526	3	j	j	PROPN
ejpam-1951	526	4	−	−	PROPN
ejpam-1951	527	1	g	g	PROPN
ejpam-1951	527	2	j	j	PROPN
ejpam-1951	527	3	+	+	CCONJ
ejpam-1951	527	4	1	1	NUM
ejpam-1951	527	5	)	)	PUNCT
ejpam-1951	527	6	.	.	PUNCT
ejpam-1951	528	1	this	this	DET
ejpam-1951	528	2	product	product	NOUN
ejpam-1951	528	3	runs	run	VERB
ejpam-1951	528	4	over	over	ADP
ejpam-1951	528	5	all	all	DET
ejpam-1951	528	6	j	j	PROPN
ejpam-1951	528	7	for	for	ADP
ejpam-1951	528	8	g	g	PROPN
ejpam-1951	528	9	j	j	PROPN
ejpam-1951	528	10	>	>	X
ejpam-1951	528	11	0	0	NUM
ejpam-1951	528	12	;	;	PUNCT
ejpam-1951	528	13	but	but	CCONJ
ejpam-1951	528	14	if	if	SCONJ
ejpam-1951	528	15	g	g	PROPN
ejpam-1951	528	16	j	j	PROPN
ejpam-1951	528	17	=	=	SYM
ejpam-1951	528	18	0	0	PROPN
ejpam-1951	528	19	we	we	PRON
ejpam-1951	528	20	can	can	AUX
ejpam-1951	528	21	take	take	VERB
ejpam-1951	528	22	the	the	PRON
ejpam-1951	528	23	over	over	ADP
ejpam-1951	528	24	all	all	DET
ejpam-1951	528	25	values	value	NOUN
ejpam-1951	528	26	j	j	PROPN
ejpam-1951	528	27	=	=	SYM
ejpam-1951	528	28	1,2,3	1,2,3	NUM
ejpam-1951	528	29	,	,	PUNCT
ejpam-1951	528	30	.	.	PUNCT
ejpam-1951	528	31	.	.	PUNCT
ejpam-1951	529	1	.	.	PUNCT
ejpam-1951	530	1	as	as	ADV
ejpam-1951	530	2	well	well	ADV
ejpam-1951	530	3	.	.	PUNCT
ejpam-1951	531	1	next	next	ADV
ejpam-1951	531	2	we	we	PRON
ejpam-1951	531	3	can	can	AUX
ejpam-1951	531	4	write	write	VERB
ejpam-1951	531	5	jgh(h−1)(h−2	jgh(h−1)(h−2	PROPN
ejpam-1951	531	6	)	)	PUNCT
ejpam-1951	531	7	.	.	PUNCT
ejpam-1951	531	8	.	.	PUNCT
ejpam-1951	531	9	.	.	PUNCT
ejpam-1951	532	1	(	(	PUNCT
ejpam-1951	532	2	h−	h−	NOUN
ejpam-1951	532	3	g+1	g+1	NOUN
ejpam-1951	532	4	)	)	PUNCT
ejpam-1951	532	5	as	as	ADP
ejpam-1951	532	6	gth	gth	PROPN
ejpam-1951	532	7	derivative	derivative	NOUN
ejpam-1951	532	8	of	of	ADP
ejpam-1951	532	9	(	(	PUNCT
ejpam-1951	532	10	1	1	NUM
ejpam-1951	532	11	+	+	NUM
ejpam-1951	532	12	jz)h	jz)h	NOUN
ejpam-1951	532	13	at	at	ADP
ejpam-1951	532	14	the	the	DET
ejpam-1951	532	15	point	point	NOUN
ejpam-1951	532	16	z	z	NOUN
ejpam-1951	532	17	=	=	NOUN
ejpam-1951	532	18	0	0	X
ejpam-1951	532	19	.	.	PUNCT
ejpam-1951	533	1	as	as	ADP
ejpam-1951	533	2	the	the	DET
ejpam-1951	533	3	result	result	NOUN
ejpam-1951	533	4	of	of	ADP
ejpam-1951	533	5	a	a	DET
ejpam-1951	533	6	number	number	NOUN
ejpam-1951	533	7	of	of	ADP
ejpam-1951	533	8	partial	partial	ADJ
ejpam-1951	533	9	differentiations	differentiation	NOUN
ejpam-1951	533	10	with	with	ADP
ejpam-1951	533	11	respect	respect	NOUN
ejpam-1951	533	12	to	to	ADP
ejpam-1951	533	13	variables	variable	NOUN
ejpam-1951	533	14	z1	z1	PROPN
ejpam-1951	533	15	,	,	PUNCT
ejpam-1951	533	16	z2	z2	PROPN
ejpam-1951	533	17	,	,	PUNCT
ejpam-1951	533	18	.	.	PUNCT
ejpam-1951	533	19	.	.	PUNCT
ejpam-1951	534	1	.	.	PUNCT
ejpam-1951	535	1	at	at	ADP
ejpam-1951	535	2	the	the	DET
ejpam-1951	535	3	points	point	NOUN
ejpam-1951	535	4	z1	z1	PROPN
ejpam-1951	535	5	=	=	SYM
ejpam-1951	535	6	z2	z2	PROPN
ejpam-1951	535	7	=	=	PUNCT
ejpam-1951	535	8	.	.	PUNCT
ejpam-1951	535	9	.	.	PUNCT
ejpam-1951	536	1	.=	.=	NOUN
ejpam-1951	536	2	0	0	NUM
ejpam-1951	536	3	,	,	PUNCT
ejpam-1951	536	4	we	we	PRON
ejpam-1951	536	5	have	have	VERB
ejpam-1951	536	6	�	�	PROPN
ejpam-1951	536	7	∂	∂	NUM
ejpam-1951	536	8	∂	∂	NUM
ejpam-1951	536	9	z1	z1	PROPN
ejpam-1951	536	10	�	�	PROPN
ejpam-1951	536	11	g1	g1	PROPN
ejpam-1951	536	12	�	�	PROPN
ejpam-1951	536	13	∂	∂	NUM
ejpam-1951	536	14	∂	∂	NUM
ejpam-1951	536	15	z2	z2	PROPN
ejpam-1951	536	16	�	�	PROPN
ejpam-1951	536	17	g2	g2	PROPN
ejpam-1951	536	18	�	�	PROPN
ejpam-1951	536	19	∂	∂	NUM
ejpam-1951	536	20	∂	∂	NUM
ejpam-1951	536	21	z3	z3	PROPN
ejpam-1951	536	22	�	�	PROPN
ejpam-1951	536	23	g3	g3	PROPN
ejpam-1951	536	24	.	.	PUNCT
ejpam-1951	536	25	.	.	PUNCT
ejpam-1951	536	26	.	.	PUNCT
ejpam-1951	537	1	(	(	PUNCT
ejpam-1951	537	2	1	1	NUM
ejpam-1951	537	3	+	+	X
ejpam-1951	537	4	z1	z1	ADJ
ejpam-1951	537	5	)	)	PUNCT
ejpam-1951	537	6	h1(1	h1(1	PROPN
ejpam-1951	537	7	+	+	NOUN
ejpam-1951	537	8	2z2	2z2	NUM
ejpam-1951	537	9	)	)	PUNCT
ejpam-1951	537	10	h2(1	h2(1	PROPN
ejpam-1951	537	11	+	+	SYM
ejpam-1951	537	12	3z3	3z3	NUM
ejpam-1951	537	13	)	)	PUNCT
ejpam-1951	537	14	h3	h3	NOUN
ejpam-1951	537	15	.	.	PUNCT
ejpam-1951	537	16	.	.	PUNCT
ejpam-1951	537	17	.	.	PUNCT
ejpam-1951	538	1	the	the	DET
ejpam-1951	538	2	differential	differential	ADJ
ejpam-1951	538	3	operator	operator	NOUN
ejpam-1951	538	4	is	be	AUX
ejpam-1951	538	5	obtained	obtain	VERB
ejpam-1951	538	6	from	from	ADP
ejpam-1951	538	7	a	a	DET
ejpam-1951	538	8	term	term	NOUN
ejpam-1951	538	9	of	of	ADP
ejpam-1951	538	10	cycle	cycle	NOUN
ejpam-1951	538	11	index	index	NOUN
ejpam-1951	538	12	zg(t1	zg(t1	NOUN
ejpam-1951	538	13	,	,	PUNCT
ejpam-1951	538	14	t2	t2	NOUN
ejpam-1951	538	15	,	,	PUNCT
ejpam-1951	538	16	.	.	PUNCT
ejpam-1951	538	17	.	.	PUNCT
ejpam-1951	539	1	.	.	PUNCT
ejpam-1951	539	2	)	)	PUNCT
ejpam-1951	540	1	of	of	ADP
ejpam-1951	540	2	g	g	PROPN
ejpam-1951	540	3	upon	upon	SCONJ
ejpam-1951	540	4	substitution	substitution	NOUN
ejpam-1951	540	5	of	of	ADP
ejpam-1951	540	6	t1	t1	NOUN
ejpam-1951	540	7	=	=	SYM
ejpam-1951	540	8	∂	∂	NUM
ejpam-1951	540	9	∂	∂	NOUN
ejpam-1951	540	10	z1	z1	NOUN
ejpam-1951	540	11	,	,	PUNCT
ejpam-1951	540	12	t2	t2	NOUN
ejpam-1951	540	13	=	=	SYM
ejpam-1951	540	14	∂	∂	NUM
ejpam-1951	540	15	∂	∂	NUM
ejpam-1951	540	16	z2	z2	PROPN
ejpam-1951	540	17	,	,	PUNCT
ejpam-1951	540	18	.	.	PUNCT
ejpam-1951	540	19	.	.	PUNCT
ejpam-1951	540	20	.	.	PUNCT
ejpam-1951	541	1	and	and	CCONJ
ejpam-1951	541	2	the	the	DET
ejpam-1951	541	3	operand	operand	NOUN
ejpam-1951	541	4	is	be	AUX
ejpam-1951	541	5	obtained	obtain	VERB
ejpam-1951	541	6	upon	upon	SCONJ
ejpam-1951	541	7	substitution	substitution	NOUN
ejpam-1951	541	8	of	of	ADP
ejpam-1951	541	9	t1	t1	NOUN
ejpam-1951	541	10	=	=	SYM
ejpam-1951	541	11	1+z1	1+z1	NUM
ejpam-1951	541	12	,	,	PUNCT
ejpam-1951	541	13	t2	t2	NOUN
ejpam-1951	541	14	=	=	PUNCT
ejpam-1951	541	15	1	1	NUM
ejpam-1951	541	16	+	+	NUM
ejpam-1951	541	17	2z2	2z2	NUM
ejpam-1951	541	18	,	,	PUNCT
ejpam-1951	541	19	.	.	PUNCT
ejpam-1951	541	20	.	.	PUNCT
ejpam-1951	542	1	.	.	PUNCT
ejpam-1951	543	1	into	into	ADP
ejpam-1951	543	2	a	a	DET
ejpam-1951	543	3	term	term	NOUN
ejpam-1951	543	4	of	of	ADP
ejpam-1951	543	5	the	the	DET
ejpam-1951	543	6	index	index	NOUN
ejpam-1951	543	7	zh(t1	zh(t1	PROPN
ejpam-1951	543	8	,	,	PUNCT
ejpam-1951	543	9	t2	t2	NOUN
ejpam-1951	543	10	,	,	PUNCT
ejpam-1951	543	11	..	..	PUNCT
ejpam-1951	543	12	)	)	PUNCT
ejpam-1951	543	13	of	of	ADP
ejpam-1951	543	14	h	h	NOUN
ejpam-1951	544	1	[	[	X
ejpam-1951	544	2	2	2	NUM
ejpam-1951	544	3	]	]	PUNCT
ejpam-1951	544	4	.	.	PUNCT
ejpam-1951	545	1	theorem	theorem	NOUN
ejpam-1951	545	2	3	3	NUM
ejpam-1951	545	3	.	.	PUNCT
ejpam-1951	546	1	the	the	DET
ejpam-1951	546	2	number	number	NOUN
ejpam-1951	546	3	of	of	ADP
ejpam-1951	546	4	patterns	pattern	NOUN
ejpam-1951	546	5	of	of	ADP
ejpam-1951	546	6	one	one	NUM
ejpam-1951	546	7	-	-	PUNCT
ejpam-1951	546	8	to	to	ADP
ejpam-1951	546	9	-	-	PUNCT
ejpam-1951	546	10	one	one	NUM
ejpam-1951	546	11	mappings	mapping	NOUN
ejpam-1951	546	12	of	of	ADP
ejpam-1951	546	13	x	x	PUNCT
ejpam-1951	546	14	into	into	ADP
ejpam-1951	546	15	y	y	PROPN
ejpam-1951	546	16	equals	equal	VERB
ejpam-1951	546	17	zg	zg	PROPN
ejpam-1951	546	18	�	�	PROPN
ejpam-1951	546	19	∂	∂	NUM
ejpam-1951	546	20	∂	∂	NOUN
ejpam-1951	546	21	z1	z1	NOUN
ejpam-1951	546	22	,	,	PUNCT
ejpam-1951	546	23	∂	∂	NUM
ejpam-1951	546	24	∂	∂	NOUN
ejpam-1951	546	25	z2	z2	PROPN
ejpam-1951	546	26	,	,	PUNCT
ejpam-1951	546	27	∂	∂	NUM
ejpam-1951	546	28	∂	∂	NUM
ejpam-1951	546	29	z3	z3	PROPN
ejpam-1951	546	30	,	,	PUNCT
ejpam-1951	546	31	.	.	PUNCT
ejpam-1951	546	32	.	.	PUNCT
ejpam-1951	546	33	.	.	PUNCT
ejpam-1951	547	1	�	�	PROPN
ejpam-1951	547	2	zh(1	zh(1	NOUN
ejpam-1951	547	3	+	+	X
ejpam-1951	547	4	z1	z1	VERB
ejpam-1951	547	5	,	,	PUNCT
ejpam-1951	547	6	1	1	NUM
ejpam-1951	547	7	+	+	NUM
ejpam-1951	547	8	2z2	2z2	NUM
ejpam-1951	547	9	,	,	PUNCT
ejpam-1951	547	10	1	1	NUM
ejpam-1951	547	11	+	+	NUM
ejpam-1951	547	12	3z3	3z3	NUM
ejpam-1951	547	13	,	,	PUNCT
ejpam-1951	547	14	.	.	PUNCT
ejpam-1951	547	15	.	.	PUNCT
ejpam-1951	547	16	.	.	PUNCT
ejpam-1951	547	17	)	)	PUNCT
ejpam-1951	548	1	evaluated	evaluate	VERB
ejpam-1951	548	2	at	at	ADP
ejpam-1951	548	3	z1	z1	ADJ
ejpam-1951	548	4	=	=	SYM
ejpam-1951	548	5	z2	z2	PROPN
ejpam-1951	548	6	=	=	SYM
ejpam-1951	548	7	z3	z3	PROPN
ejpam-1951	548	8	=	=	PUNCT
ejpam-1951	548	9	.	.	PUNCT
ejpam-1951	548	10	.	.	PUNCT
ejpam-1951	549	1	.=	.=	VERB
ejpam-1951	550	1	0	0	X
ejpam-1951	550	2	.	.	PUNCT
ejpam-1951	551	1	t.	t.	PROPN
ejpam-1951	551	2	nasseef	nasseef	PROPN
ejpam-1951	551	3	/	/	SYM
ejpam-1951	551	4	eur	eur	PROPN
ejpam-1951	551	5	.	.	PUNCT
ejpam-1951	552	1	j.	j.	PROPN
ejpam-1951	552	2	pure	pure	PROPN
ejpam-1951	552	3	appl	appl	PROPN
ejpam-1951	552	4	.	.	PROPN
ejpam-1951	552	5	math	math	PROPN
ejpam-1951	552	6	,	,	PUNCT
ejpam-1951	552	7	9	9	NUM
ejpam-1951	552	8	(	(	PUNCT
ejpam-1951	552	9	2016	2016	NUM
ejpam-1951	552	10	)	)	PUNCT
ejpam-1951	552	11	,	,	PUNCT
ejpam-1951	552	12	84	84	NUM
ejpam-1951	552	13	-	-	SYM
ejpam-1951	552	14	113	113	NUM
ejpam-1951	552	15	103	103	NUM
ejpam-1951	552	16	if	if	SCONJ
ejpam-1951	552	17	|x	|x	NOUN
ejpam-1951	552	18	|=	|=	PUNCT
ejpam-1951	552	19	|y	|y	NOUN
ejpam-1951	552	20	|	|	ADV
ejpam-1951	552	21	,	,	PUNCT
ejpam-1951	552	22	then	then	ADV
ejpam-1951	552	23	we	we	PRON
ejpam-1951	552	24	always	always	ADV
ejpam-1951	552	25	have	have	VERB
ejpam-1951	552	26	∑	∑	PROPN
ejpam-1951	552	27	j	j	PROPN
ejpam-1951	552	28	g	g	PROPN
ejpam-1951	552	29	j	j	PROPN
ejpam-1951	553	1	=	=	PUNCT
ejpam-1951	553	2	∑	∑	PUNCT
ejpam-1951	553	3	j	j	PROPN
ejpam-1951	553	4	h	h	PROPN
ejpam-1951	553	5	j	j	PROPN
ejpam-1951	553	6	.	.	PUNCT
ejpam-1951	554	1	so	so	ADV
ejpam-1951	554	2	that	that	SCONJ
ejpam-1951	554	3	we	we	PRON
ejpam-1951	554	4	have	have	VERB
ejpam-1951	554	5	either	either	CCONJ
ejpam-1951	554	6	g1	g1	PROPN
ejpam-1951	554	7	=	=	SYM
ejpam-1951	554	8	h1	h1	PROPN
ejpam-1951	554	9	,	,	PUNCT
ejpam-1951	554	10	g2	g2	PROPN
ejpam-1951	554	11	=	=	SYM
ejpam-1951	554	12	h2	h2	PROPN
ejpam-1951	554	13	,	,	PUNCT
ejpam-1951	554	14	.	.	PUNCT
ejpam-1951	554	15	.	.	PUNCT
ejpam-1951	555	1	.	.	PUNCT
ejpam-1951	556	1	or	or	CCONJ
ejpam-1951	556	2	at	at	ADV
ejpam-1951	556	3	least	least	ADJ
ejpam-1951	556	4	once	once	ADV
ejpam-1951	556	5	g	g	PROPN
ejpam-1951	556	6	j	j	PROPN
ejpam-1951	556	7	>	>	X
ejpam-1951	556	8	h	h	PROPN
ejpam-1951	556	9	j	j	PROPN
ejpam-1951	556	10	.	.	PUNCT
ejpam-1951	557	1	thus	thus	ADV
ejpam-1951	557	2	we	we	PRON
ejpam-1951	557	3	have	have	VERB
ejpam-1951	557	4	[	[	X
ejpam-1951	557	5	2	2	NUM
ejpam-1951	557	6	]	]	PUNCT
ejpam-1951	557	7	�	�	PROPN
ejpam-1951	557	8	∂	∂	NUM
ejpam-1951	557	9	∂	∂	NUM
ejpam-1951	557	10	z1	z1	PROPN
ejpam-1951	557	11	�	�	PROPN
ejpam-1951	557	12	g1	g1	PROPN
ejpam-1951	557	13	�	�	PROPN
ejpam-1951	557	14	∂	∂	NUM
ejpam-1951	557	15	∂	∂	NUM
ejpam-1951	557	16	z2	z2	PROPN
ejpam-1951	557	17	�	�	PROPN
ejpam-1951	557	18	g2	g2	PROPN
ejpam-1951	557	19	�	�	PROPN
ejpam-1951	557	20	∂	∂	NUM
ejpam-1951	557	21	∂	∂	NUM
ejpam-1951	557	22	z3	z3	PROPN
ejpam-1951	557	23	�	�	PROPN
ejpam-1951	557	24	g3	g3	PROPN
ejpam-1951	557	25	.	.	PUNCT
ejpam-1951	557	26	.	.	PUNCT
ejpam-1951	557	27	.	.	PUNCT
ejpam-1951	558	1	(	(	PUNCT
ejpam-1951	558	2	z1	z1	NOUN
ejpam-1951	558	3	)	)	PUNCT
ejpam-1951	558	4	h1(2z2	h1(2z2	NUM
ejpam-1951	558	5	)	)	PUNCT
ejpam-1951	558	6	h2(3z3	h2(3z3	NUM
ejpam-1951	558	7	)	)	PUNCT
ejpam-1951	558	8	h3	h3	NOUN
ejpam-1951	558	9	.	.	PUNCT
ejpam-1951	558	10	.	.	PUNCT
ejpam-1951	558	11	.	.	PUNCT
ejpam-1951	558	12	.	.	PUNCT
ejpam-1951	559	1	.	.	PUNCT
ejpam-1951	560	1	theorem	theorem	VERB
ejpam-1951	560	2	4	4	NUM
ejpam-1951	560	3	.	.	PUNCT
ejpam-1951	561	1	if	if	SCONJ
ejpam-1951	561	2	|x	|x	NOUN
ejpam-1951	561	3	|=	|=	PUNCT
ejpam-1951	561	4	|y	|y	NOUN
ejpam-1951	561	5	|	|	ADV
ejpam-1951	561	6	,	,	PUNCT
ejpam-1951	561	7	then	then	ADV
ejpam-1951	561	8	the	the	DET
ejpam-1951	561	9	number	number	NOUN
ejpam-1951	561	10	of	of	ADP
ejpam-1951	561	11	patterns	pattern	NOUN
ejpam-1951	561	12	is	be	AUX
ejpam-1951	561	13	equal	equal	ADJ
ejpam-1951	561	14	to	to	ADP
ejpam-1951	561	15	zg	zg	PROPN
ejpam-1951	561	16	�	�	PROPN
ejpam-1951	561	17	∂	∂	NUM
ejpam-1951	561	18	∂	∂	NOUN
ejpam-1951	561	19	z1	z1	NOUN
ejpam-1951	561	20	,	,	PUNCT
ejpam-1951	561	21	∂	∂	NUM
ejpam-1951	561	22	∂	∂	NOUN
ejpam-1951	561	23	z2	z2	PROPN
ejpam-1951	561	24	,	,	PUNCT
ejpam-1951	561	25	∂	∂	NUM
ejpam-1951	561	26	∂	∂	NUM
ejpam-1951	561	27	z3	z3	PROPN
ejpam-1951	561	28	,	,	PUNCT
ejpam-1951	561	29	.	.	PUNCT
ejpam-1951	561	30	.	.	PUNCT
ejpam-1951	562	1	.	.	PUNCT
ejpam-1951	563	1	�	�	PROPN
ejpam-1951	563	2	zh(z1	zh(z1	PROPN
ejpam-1951	563	3	,	,	PUNCT
ejpam-1951	563	4	2z2	2z2	NUM
ejpam-1951	563	5	,	,	PUNCT
ejpam-1951	563	6	3z3	3z3	NUM
ejpam-1951	563	7	,	,	PUNCT
ejpam-1951	563	8	.	.	PUNCT
ejpam-1951	563	9	.	.	PUNCT
ejpam-1951	563	10	.	.	PUNCT
ejpam-1951	563	11	)	)	PUNCT
ejpam-1951	563	12	evaluated	evaluate	VERB
ejpam-1951	563	13	at	at	ADP
ejpam-1951	563	14	z1	z1	ADJ
ejpam-1951	563	15	=	=	SYM
ejpam-1951	563	16	z2	z2	PROPN
ejpam-1951	563	17	=	=	SYM
ejpam-1951	563	18	z3	z3	PROPN
ejpam-1951	563	19	=	=	PUNCT
ejpam-1951	563	20	.	.	PUNCT
ejpam-1951	563	21	.	.	PUNCT
ejpam-1951	564	1	.=	.=	VERB
ejpam-1951	565	1	0	0	X
ejpam-1951	565	2	.	.	PUNCT
ejpam-1951	566	1	the	the	DET
ejpam-1951	566	2	inverse	inverse	NOUN
ejpam-1951	566	3	mappings	mapping	NOUN
ejpam-1951	566	4	are	be	AUX
ejpam-1951	566	5	one	one	NUM
ejpam-1951	566	6	-	-	PUNCT
ejpam-1951	566	7	to	to	ADP
ejpam-1951	566	8	-	-	PUNCT
ejpam-1951	566	9	one	one	NUM
ejpam-1951	566	10	mappings	mapping	NOUN
ejpam-1951	566	11	of	of	ADP
ejpam-1951	566	12	y	y	PRON
ejpam-1951	566	13	onto	onto	ADP
ejpam-1951	566	14	x	x	X
ejpam-1951	566	15	.	.	PUNCT
ejpam-1951	567	1	in	in	ADP
ejpam-1951	567	2	this	this	DET
ejpam-1951	567	3	case	case	NOUN
ejpam-1951	567	4	we	we	PRON
ejpam-1951	567	5	can	can	AUX
ejpam-1951	567	6	easily	easily	ADV
ejpam-1951	567	7	find	find	VERB
ejpam-1951	567	8	that	that	SCONJ
ejpam-1951	567	9	the	the	DET
ejpam-1951	567	10	number	number	NOUN
ejpam-1951	567	11	of	of	ADP
ejpam-1951	567	12	patterns	pattern	NOUN
ejpam-1951	567	13	is	be	AUX
ejpam-1951	567	14	equal	equal	ADJ
ejpam-1951	567	15	to	to	ADP
ejpam-1951	567	16	zh	zh	PROPN
ejpam-1951	567	17	�	�	PROPN
ejpam-1951	567	18	∂	∂	NUM
ejpam-1951	567	19	∂	∂	NUM
ejpam-1951	567	20	z1	z1	NOUN
ejpam-1951	567	21	,	,	PUNCT
ejpam-1951	567	22	∂	∂	NUM
ejpam-1951	567	23	∂	∂	NOUN
ejpam-1951	567	24	z2	z2	PROPN
ejpam-1951	567	25	,	,	PUNCT
ejpam-1951	567	26	∂	∂	NUM
ejpam-1951	567	27	∂	∂	NUM
ejpam-1951	567	28	z3	z3	PROPN
ejpam-1951	567	29	,	,	PUNCT
ejpam-1951	567	30	.	.	PUNCT
ejpam-1951	567	31	.	.	PUNCT
ejpam-1951	567	32	.	.	PUNCT
ejpam-1951	568	1	�	�	PROPN
ejpam-1951	568	2	zg(z1	zg(z1	PROPN
ejpam-1951	568	3	,	,	PUNCT
ejpam-1951	568	4	2z2	2z2	NUM
ejpam-1951	568	5	,	,	PUNCT
ejpam-1951	568	6	3z3	3z3	NUM
ejpam-1951	568	7	,	,	PUNCT
ejpam-1951	568	8	.	.	PUNCT
ejpam-1951	568	9	.	.	PUNCT
ejpam-1951	568	10	.	.	PUNCT
ejpam-1951	568	11	)	)	PUNCT
ejpam-1951	569	1	evaluated	evaluate	VERB
ejpam-1951	569	2	at	at	ADP
ejpam-1951	569	3	z1	z1	ADJ
ejpam-1951	569	4	=	=	SYM
ejpam-1951	569	5	z2	z2	PROPN
ejpam-1951	569	6	=	=	SYM
ejpam-1951	569	7	z3	z3	PROPN
ejpam-1951	569	8	=	=	PUNCT
ejpam-1951	569	9	.	.	PUNCT
ejpam-1951	569	10	.	.	PUNCT
ejpam-1951	570	1	.=	.=	VERB
ejpam-1951	570	2	0	0	PUNCT
ejpam-1951	571	1	[	[	X
ejpam-1951	571	2	2	2	NUM
ejpam-1951	571	3	]	]	PUNCT
ejpam-1951	571	4	.	.	PUNCT
ejpam-1951	572	1	problem	problem	NOUN
ejpam-1951	572	2	5	5	NUM
ejpam-1951	572	3	.	.	PUNCT
ejpam-1951	572	4	how	how	SCONJ
ejpam-1951	572	5	many	many	ADJ
ejpam-1951	572	6	geometrically	geometrically	ADV
ejpam-1951	572	7	different	different	ADJ
ejpam-1951	572	8	ways	way	NOUN
ejpam-1951	572	9	can	can	AUX
ejpam-1951	572	10	the	the	DET
ejpam-1951	572	11	faces	face	NOUN
ejpam-1951	572	12	of	of	ADP
ejpam-1951	572	13	a	a	DET
ejpam-1951	572	14	cube	cube	NOUN
ejpam-1951	572	15	be	be	AUX
ejpam-1951	572	16	arranged	arrange	VERB
ejpam-1951	572	17	in	in	ADP
ejpam-1951	572	18	cyclic	cyclic	ADJ
ejpam-1951	572	19	order	order	NOUN
ejpam-1951	573	1	[	[	X
ejpam-1951	573	2	2	2	NUM
ejpam-1951	573	3	]	]	PUNCT
ejpam-1951	573	4	?	?	PUNCT
ejpam-1951	574	1	solution	solution	NOUN
ejpam-1951	574	2	:	:	PUNCT
ejpam-1951	574	3	we	we	PRON
ejpam-1951	574	4	need	need	VERB
ejpam-1951	574	5	to	to	PART
ejpam-1951	574	6	find	find	VERB
ejpam-1951	574	7	out	out	ADP
ejpam-1951	574	8	the	the	DET
ejpam-1951	574	9	number	number	NOUN
ejpam-1951	574	10	of	of	ADP
ejpam-1951	574	11	patterns	pattern	NOUN
ejpam-1951	574	12	of	of	ADP
ejpam-1951	574	13	one	one	NUM
ejpam-1951	574	14	-	-	PUNCT
ejpam-1951	574	15	to	to	ADP
ejpam-1951	574	16	-	-	PUNCT
ejpam-1951	574	17	one	one	NUM
ejpam-1951	574	18	mappings	mapping	NOUN
ejpam-1951	574	19	.	.	PUNCT
ejpam-1951	575	1	let	let	VERB
ejpam-1951	575	2	x	x	PRON
ejpam-1951	575	3	be	be	AUX
ejpam-1951	575	4	the	the	DET
ejpam-1951	575	5	set	set	NOUN
ejpam-1951	575	6	of	of	ADP
ejpam-1951	575	7	faces	face	NOUN
ejpam-1951	575	8	of	of	ADP
ejpam-1951	575	9	a	a	DET
ejpam-1951	575	10	cube	cube	NOUN
ejpam-1951	575	11	and	and	CCONJ
ejpam-1951	575	12	g	g	NOUN
ejpam-1951	575	13	be	be	AUX
ejpam-1951	575	14	the	the	DET
ejpam-1951	575	15	cube	cube	NOUN
ejpam-1951	575	16	induced	induce	VERB
ejpam-1951	575	17	by	by	ADP
ejpam-1951	575	18	rotations(example	rotations(example	PROPN
ejpam-1951	575	19	11	11	NUM
ejpam-1951	575	20	)	)	PUNCT
ejpam-1951	575	21	;	;	PUNCT
ejpam-1951	575	22	y	y	PROPN
ejpam-1951	575	23	be	be	AUX
ejpam-1951	575	24	the	the	DET
ejpam-1951	575	25	6th	6th	ADJ
ejpam-1951	575	26	roots	root	NOUN
ejpam-1951	575	27	of	of	ADP
ejpam-1951	575	28	unity	unity	NOUN
ejpam-1951	575	29	and	and	CCONJ
ejpam-1951	575	30	again	again	ADV
ejpam-1951	575	31	h	h	NOUN
ejpam-1951	575	32	is	be	AUX
ejpam-1951	575	33	the	the	DET
ejpam-1951	575	34	group	group	NOUN
ejpam-1951	575	35	of	of	ADP
ejpam-1951	575	36	permutation	permutation	NOUN
ejpam-1951	575	37	induced	induce	VERB
ejpam-1951	575	38	by	by	ADP
ejpam-1951	575	39	the	the	DET
ejpam-1951	575	40	rotations	rotation	NOUN
ejpam-1951	575	41	in	in	ADP
ejpam-1951	575	42	the	the	DET
ejpam-1951	575	43	complex	complex	ADJ
ejpam-1951	575	44	plane	plane	NOUN
ejpam-1951	575	45	(	(	PUNCT
ejpam-1951	575	46	definition	definition	NOUN
ejpam-1951	575	47	2	2	NUM
ejpam-1951	575	48	with	with	ADP
ejpam-1951	575	49	cycle	cycle	NOUN
ejpam-1951	575	50	index	index	NOUN
ejpam-1951	575	51	formula	formula	NOUN
ejpam-1951	575	52	z(cn	z(cn	PROPN
ejpam-1951	575	53	)	)	PUNCT
ejpam-1951	575	54	)	)	PUNCT
ejpam-1951	575	55	.	.	PUNCT
ejpam-1951	576	1	then	then	ADV
ejpam-1951	576	2	|x	|x	NOUN
ejpam-1951	576	3	|=	|=	PUNCT
ejpam-1951	576	4	|y	|y	NOUN
ejpam-1951	576	5	|	|	ADV
ejpam-1951	576	6	.	.	PUNCT
ejpam-1951	577	1	the	the	DET
ejpam-1951	577	2	cycle	cycle	NOUN
ejpam-1951	577	3	indexes	index	NOUN
ejpam-1951	577	4	are	be	AUX
ejpam-1951	577	5	zg	zg	NOUN
ejpam-1951	577	6	=	=	SYM
ejpam-1951	577	7	1	1	NUM
ejpam-1951	577	8	24	24	NUM
ejpam-1951	577	9	(	(	PUNCT
ejpam-1951	577	10	t6	t6	PROPN
ejpam-1951	577	11	1	1	NUM
ejpam-1951	577	12	+	+	NUM
ejpam-1951	577	13	6t3	6t3	NUM
ejpam-1951	577	14	2	2	NUM
ejpam-1951	577	15	+	+	CCONJ
ejpam-1951	577	16	8t2	8t2	NUM
ejpam-1951	577	17	3	3	NUM
ejpam-1951	577	18	+	+	SYM
ejpam-1951	577	19	3t2	3t2	NUM
ejpam-1951	577	20	1	1	NUM
ejpam-1951	577	21	t2	t2	NOUN
ejpam-1951	577	22	2	2	NUM
ejpam-1951	577	23	+	+	CCONJ
ejpam-1951	577	24	6t2	6t2	NUM
ejpam-1951	577	25	1	1	NUM
ejpam-1951	577	26	t4	t4	PROPN
ejpam-1951	577	27	)	)	PUNCT
ejpam-1951	577	28	zh	zh	NOUN
ejpam-1951	578	1	=	=	SYM
ejpam-1951	578	2	1	1	NUM
ejpam-1951	578	3	6	6	NUM
ejpam-1951	578	4	(	(	PUNCT
ejpam-1951	578	5	t6	t6	PROPN
ejpam-1951	578	6	1	1	NUM
ejpam-1951	578	7	+	+	CCONJ
ejpam-1951	578	8	t3	t3	PROPN
ejpam-1951	578	9	2	2	NUM
ejpam-1951	578	10	+	+	CCONJ
ejpam-1951	578	11	2t2	2t2	NUM
ejpam-1951	578	12	3	3	NUM
ejpam-1951	578	13	+	+	NUM
ejpam-1951	578	14	2t6	2t6	NUM
ejpam-1951	578	15	)	)	PUNCT
ejpam-1951	578	16	the	the	DET
ejpam-1951	578	17	number	number	NOUN
ejpam-1951	578	18	of	of	ADP
ejpam-1951	578	19	patterns	pattern	NOUN
ejpam-1951	578	20	is	be	AUX
ejpam-1951	578	21	equal	equal	ADJ
ejpam-1951	578	22	to	to	ADP
ejpam-1951	578	23	zg	zg	PROPN
ejpam-1951	578	24	�	�	PROPN
ejpam-1951	578	25	∂	∂	NUM
ejpam-1951	578	26	∂	∂	NOUN
ejpam-1951	578	27	z1	z1	NOUN
ejpam-1951	578	28	,	,	PUNCT
ejpam-1951	578	29	∂	∂	NUM
ejpam-1951	578	30	∂	∂	NOUN
ejpam-1951	578	31	z2	z2	PROPN
ejpam-1951	578	32	,	,	PUNCT
ejpam-1951	578	33	∂	∂	NUM
ejpam-1951	578	34	∂	∂	NUM
ejpam-1951	578	35	z3	z3	PROPN
ejpam-1951	578	36	�	�	PROPN
ejpam-1951	578	37	zh(z1	zh(z1	PROPN
ejpam-1951	578	38	,	,	PUNCT
ejpam-1951	578	39	2z2	2z2	NUM
ejpam-1951	578	40	,	,	PUNCT
ejpam-1951	578	41	3z3	3z3	NUM
ejpam-1951	578	42	)	)	PUNCT
ejpam-1951	578	43	=	=	SYM
ejpam-1951	579	1	1	1	NUM
ejpam-1951	579	2	24	24	NUM
ejpam-1951	579	3	·	·	SYM
ejpam-1951	579	4	1	1	NUM
ejpam-1951	579	5	6	6	NUM
ejpam-1951	579	6	�	�	PROPN
ejpam-1951	579	7	�	�	PROPN
ejpam-1951	579	8	∂	∂	NUM
ejpam-1951	579	9	∂	∂	NUM
ejpam-1951	579	10	z1	z1	PROPN
ejpam-1951	579	11	�	�	PROPN
ejpam-1951	579	12	6	6	NUM
ejpam-1951	579	13	(	(	PUNCT
ejpam-1951	579	14	z1	z1	NOUN
ejpam-1951	579	15	)	)	PUNCT
ejpam-1951	579	16	6	6	NUM
ejpam-1951	579	17	+	+	SYM
ejpam-1951	579	18	�	�	PROPN
ejpam-1951	579	19	∂	∂	NUM
ejpam-1951	579	20	∂	∂	NUM
ejpam-1951	579	21	z2	z2	PROPN
ejpam-1951	579	22	�	�	PROPN
ejpam-1951	579	23	3	3	NUM
ejpam-1951	579	24	(	(	PUNCT
ejpam-1951	579	25	2z2	2z2	NUM
ejpam-1951	579	26	)	)	PUNCT
ejpam-1951	579	27	3	3	NUM
ejpam-1951	579	28	+	+	PROPN
ejpam-1951	579	29	�	�	PROPN
ejpam-1951	579	30	∂	∂	NUM
ejpam-1951	579	31	∂	∂	NUM
ejpam-1951	579	32	z3	z3	PROPN
ejpam-1951	579	33	�	�	PROPN
ejpam-1951	579	34	2	2	NUM
ejpam-1951	579	35	(	(	PUNCT
ejpam-1951	579	36	3z3	3z3	NUM
ejpam-1951	579	37	)	)	PUNCT
ejpam-1951	579	38	2	2	NUM
ejpam-1951	579	39	�	�	NOUN
ejpam-1951	579	40	=	=	SYM
ejpam-1951	579	41	1	1	NUM
ejpam-1951	579	42	24	24	NUM
ejpam-1951	579	43	·	·	SYM
ejpam-1951	579	44	1	1	NUM
ejpam-1951	579	45	6	6	NUM
ejpam-1951	579	46	(	(	PUNCT
ejpam-1951	579	47	6!+	6!+	NUM
ejpam-1951	579	48	6	6	NUM
ejpam-1951	579	49	·	·	SYM
ejpam-1951	579	50	23	23	NUM
ejpam-1951	579	51	·	·	SYM
ejpam-1951	579	52	3!+	3!+	NUM
ejpam-1951	579	53	16	16	NUM
ejpam-1951	579	54	·	·	SYM
ejpam-1951	579	55	32	32	NUM
ejpam-1951	579	56	·	·	PUNCT
ejpam-1951	579	57	2	2	NUM
ejpam-1951	579	58	!	!	PUNCT
ejpam-1951	579	59	)	)	PUNCT
ejpam-1951	580	1	=	=	SYM
ejpam-1951	580	2	9	9	NUM
ejpam-1951	580	3	problem	problem	NOUN
ejpam-1951	580	4	6	6	NUM
ejpam-1951	580	5	.	.	PUNCT
ejpam-1951	580	6	how	how	SCONJ
ejpam-1951	580	7	many	many	ADJ
ejpam-1951	580	8	geometrically	geometrically	ADV
ejpam-1951	580	9	different	different	ADJ
ejpam-1951	580	10	ways	way	NOUN
ejpam-1951	580	11	can	can	AUX
ejpam-1951	580	12	the	the	DET
ejpam-1951	580	13	edges	edge	NOUN
ejpam-1951	580	14	of	of	ADP
ejpam-1951	580	15	a	a	DET
ejpam-1951	580	16	tetrahedron	tetrahedron	NOUN
ejpam-1951	580	17	be	be	AUX
ejpam-1951	580	18	arranged	arrange	VERB
ejpam-1951	580	19	in	in	ADP
ejpam-1951	580	20	cyclic	cyclic	ADJ
ejpam-1951	580	21	order	order	NOUN
ejpam-1951	580	22	?	?	PUNCT
ejpam-1951	581	1	t.	t.	PROPN
ejpam-1951	581	2	nasseef	nasseef	PROPN
ejpam-1951	581	3	/	/	SYM
ejpam-1951	581	4	eur	eur	PROPN
ejpam-1951	581	5	.	.	PUNCT
ejpam-1951	582	1	j.	j.	PROPN
ejpam-1951	582	2	pure	pure	PROPN
ejpam-1951	582	3	appl	appl	PROPN
ejpam-1951	582	4	.	.	PROPN
ejpam-1951	582	5	math	math	PROPN
ejpam-1951	582	6	,	,	PUNCT
ejpam-1951	582	7	9	9	NUM
ejpam-1951	582	8	(	(	PUNCT
ejpam-1951	582	9	2016	2016	NUM
ejpam-1951	582	10	)	)	PUNCT
ejpam-1951	582	11	,	,	PUNCT
ejpam-1951	582	12	84	84	NUM
ejpam-1951	582	13	-	-	SYM
ejpam-1951	582	14	113	113	NUM
ejpam-1951	582	15	104	104	NUM
ejpam-1951	582	16	solution	solution	NOUN
ejpam-1951	582	17	:	:	PUNCT
ejpam-1951	582	18	here	here	ADV
ejpam-1951	582	19	we	we	PRON
ejpam-1951	582	20	also	also	ADV
ejpam-1951	582	21	need	need	VERB
ejpam-1951	582	22	to	to	PART
ejpam-1951	582	23	find	find	VERB
ejpam-1951	582	24	out	out	ADP
ejpam-1951	582	25	the	the	DET
ejpam-1951	582	26	number	number	NOUN
ejpam-1951	582	27	of	of	ADP
ejpam-1951	582	28	patterns	pattern	NOUN
ejpam-1951	582	29	of	of	ADP
ejpam-1951	582	30	one	one	NUM
ejpam-1951	582	31	-	-	PUNCT
ejpam-1951	582	32	to	to	ADP
ejpam-1951	582	33	-	-	PUNCT
ejpam-1951	582	34	one	one	NUM
ejpam-1951	582	35	mappings	mapping	NOUN
ejpam-1951	582	36	.	.	PUNCT
ejpam-1951	583	1	again	again	ADV
ejpam-1951	583	2	let	let	VERB
ejpam-1951	583	3	x	x	PRON
ejpam-1951	583	4	be	be	AUX
ejpam-1951	583	5	the	the	DET
ejpam-1951	583	6	set	set	NOUN
ejpam-1951	583	7	of	of	ADP
ejpam-1951	583	8	edges	edge	NOUN
ejpam-1951	583	9	of	of	ADP
ejpam-1951	583	10	a	a	DET
ejpam-1951	583	11	tetrahedron	tetrahedron	NOUN
ejpam-1951	583	12	and	and	CCONJ
ejpam-1951	583	13	g	g	PROPN
ejpam-1951	583	14	be	be	VERB
ejpam-1951	583	15	the	the	DET
ejpam-1951	583	16	tetrahedron	tetrahedron	NOUN
ejpam-1951	583	17	induced	induce	VERB
ejpam-1951	583	18	by	by	ADP
ejpam-1951	583	19	rotations;y	rotations;y	NOUN
ejpam-1951	583	20	be	be	AUX
ejpam-1951	583	21	the	the	DET
ejpam-1951	583	22	6th	6th	ADJ
ejpam-1951	583	23	roots	root	NOUN
ejpam-1951	583	24	of	of	ADP
ejpam-1951	583	25	unity	unity	NOUN
ejpam-1951	583	26	and	and	CCONJ
ejpam-1951	583	27	again	again	ADV
ejpam-1951	583	28	h	h	NOUN
ejpam-1951	583	29	is	be	AUX
ejpam-1951	583	30	the	the	DET
ejpam-1951	583	31	group	group	NOUN
ejpam-1951	583	32	of	of	ADP
ejpam-1951	583	33	permutation	permutation	NOUN
ejpam-1951	583	34	induced	induce	VERB
ejpam-1951	583	35	by	by	ADP
ejpam-1951	583	36	the	the	DET
ejpam-1951	583	37	rotations	rotation	NOUN
ejpam-1951	583	38	in	in	ADP
ejpam-1951	583	39	the	the	DET
ejpam-1951	583	40	complex	complex	ADJ
ejpam-1951	583	41	plane	plane	NOUN
ejpam-1951	583	42	(	(	PUNCT
ejpam-1951	583	43	definition	definition	NOUN
ejpam-1951	583	44	2	2	NUM
ejpam-1951	583	45	with	with	ADP
ejpam-1951	583	46	cycle	cycle	NOUN
ejpam-1951	583	47	index	index	NOUN
ejpam-1951	583	48	formula	formula	NOUN
ejpam-1951	583	49	z(cn	z(cn	PROPN
ejpam-1951	583	50	)	)	PUNCT
ejpam-1951	583	51	)	)	PUNCT
ejpam-1951	583	52	.	.	PUNCT
ejpam-1951	584	1	then	then	ADV
ejpam-1951	584	2	|x	|x	NOUN
ejpam-1951	584	3	|=	|=	PUNCT
ejpam-1951	584	4	|y	|y	NOUN
ejpam-1951	584	5	|	|	ADV
ejpam-1951	584	6	.	.	PUNCT
ejpam-1951	585	1	the	the	DET
ejpam-1951	585	2	cycle	cycle	NOUN
ejpam-1951	585	3	indexes	index	NOUN
ejpam-1951	585	4	are	be	AUX
ejpam-1951	585	5	zg	zg	NOUN
ejpam-1951	585	6	=	=	SYM
ejpam-1951	585	7	1	1	NUM
ejpam-1951	585	8	12	12	NUM
ejpam-1951	585	9	(	(	PUNCT
ejpam-1951	585	10	t6	t6	PROPN
ejpam-1951	585	11	1	1	NUM
ejpam-1951	585	12	+	+	CCONJ
ejpam-1951	585	13	8t2	8t2	NUM
ejpam-1951	585	14	3	3	NUM
ejpam-1951	585	15	+	+	SYM
ejpam-1951	585	16	3t2	3t2	NUM
ejpam-1951	585	17	1	1	NUM
ejpam-1951	585	18	t2	t2	NOUN
ejpam-1951	585	19	2	2	NUM
ejpam-1951	585	20	)	)	PUNCT
ejpam-1951	585	21	zh	zh	NOUN
ejpam-1951	586	1	=	=	SYM
ejpam-1951	586	2	1	1	NUM
ejpam-1951	586	3	6	6	NUM
ejpam-1951	586	4	(	(	PUNCT
ejpam-1951	586	5	t6	t6	PROPN
ejpam-1951	586	6	1	1	NUM
ejpam-1951	586	7	+	+	CCONJ
ejpam-1951	586	8	t3	t3	PROPN
ejpam-1951	586	9	2	2	NUM
ejpam-1951	586	10	+	+	CCONJ
ejpam-1951	586	11	2t2	2t2	NUM
ejpam-1951	586	12	3	3	NUM
ejpam-1951	586	13	+	+	NUM
ejpam-1951	586	14	2t6	2t6	NUM
ejpam-1951	586	15	)	)	PUNCT
ejpam-1951	586	16	the	the	DET
ejpam-1951	586	17	number	number	NOUN
ejpam-1951	586	18	of	of	ADP
ejpam-1951	586	19	patterns	pattern	NOUN
ejpam-1951	586	20	is	be	AUX
ejpam-1951	586	21	equal	equal	ADJ
ejpam-1951	586	22	to	to	ADP
ejpam-1951	586	23	zg	zg	PROPN
ejpam-1951	586	24	�	�	PROPN
ejpam-1951	586	25	∂	∂	NUM
ejpam-1951	586	26	∂	∂	NOUN
ejpam-1951	586	27	z1	z1	NOUN
ejpam-1951	586	28	,	,	PUNCT
ejpam-1951	586	29	∂	∂	NUM
ejpam-1951	586	30	∂	∂	NUM
ejpam-1951	586	31	z3	z3	PROPN
ejpam-1951	586	32	�	�	PROPN
ejpam-1951	586	33	zh(z1	zh(z1	PROPN
ejpam-1951	586	34	,	,	PUNCT
ejpam-1951	586	35	2z2	2z2	NUM
ejpam-1951	586	36	)	)	PUNCT
ejpam-1951	586	37	=	=	SYM
ejpam-1951	587	1	1	1	NUM
ejpam-1951	587	2	12	12	NUM
ejpam-1951	587	3	·	·	SYM
ejpam-1951	587	4	1	1	NUM
ejpam-1951	587	5	6	6	NUM
ejpam-1951	587	6	�	�	PROPN
ejpam-1951	587	7	�	�	PROPN
ejpam-1951	587	8	∂	∂	NUM
ejpam-1951	587	9	∂	∂	NUM
ejpam-1951	587	10	z1	z1	PROPN
ejpam-1951	587	11	�	�	PROPN
ejpam-1951	587	12	6	6	NUM
ejpam-1951	587	13	(	(	PUNCT
ejpam-1951	587	14	z1	z1	NOUN
ejpam-1951	587	15	)	)	PUNCT
ejpam-1951	587	16	6	6	NUM
ejpam-1951	587	17	+	+	PROPN
ejpam-1951	587	18	�	�	PROPN
ejpam-1951	587	19	∂	∂	NUM
ejpam-1951	587	20	∂	∂	NUM
ejpam-1951	587	21	z3	z3	PROPN
ejpam-1951	587	22	�	�	PROPN
ejpam-1951	587	23	2	2	NUM
ejpam-1951	587	24	(	(	PUNCT
ejpam-1951	587	25	3z3	3z3	NUM
ejpam-1951	587	26	)	)	PUNCT
ejpam-1951	587	27	2	2	NUM
ejpam-1951	587	28	�	�	NOUN
ejpam-1951	587	29	=	=	NOUN
ejpam-1951	587	30	1	1	NUM
ejpam-1951	587	31	12	12	NUM
ejpam-1951	587	32	·	·	SYM
ejpam-1951	587	33	1	1	NUM
ejpam-1951	587	34	6	6	NUM
ejpam-1951	587	35	(	(	PUNCT
ejpam-1951	587	36	6!+	6!+	NUM
ejpam-1951	587	37	16	16	NUM
ejpam-1951	587	38	·	·	SYM
ejpam-1951	587	39	32	32	NUM
ejpam-1951	587	40	·	·	PUNCT
ejpam-1951	587	41	2	2	NUM
ejpam-1951	587	42	!	!	PUNCT
ejpam-1951	587	43	)	)	PUNCT
ejpam-1951	588	1	=	=	SYM
ejpam-1951	588	2	14	14	NUM
ejpam-1951	588	3	example	example	NOUN
ejpam-1951	588	4	14	14	NUM
ejpam-1951	588	5	.	.	PUNCT
ejpam-1951	589	1	we	we	PRON
ejpam-1951	589	2	have	have	VERB
ejpam-1951	589	3	6	6	NUM
ejpam-1951	589	4	colored	colored	ADJ
ejpam-1951	589	5	labels	label	NOUN
ejpam-1951	589	6	l1	l1	PROPN
ejpam-1951	589	7	,	,	PUNCT
ejpam-1951	589	8	l2	l2	NOUN
ejpam-1951	589	9	,	,	PUNCT
ejpam-1951	589	10	l3	l3	PROPN
ejpam-1951	589	11	,	,	PUNCT
ejpam-1951	589	12	l4	l4	PROPN
ejpam-1951	589	13	,	,	PUNCT
ejpam-1951	589	14	l5	l5	PROPN
ejpam-1951	589	15	,	,	PUNCT
ejpam-1951	589	16	l6	l6	ADJ
ejpam-1951	589	17	to	to	PART
ejpam-1951	589	18	be	be	AUX
ejpam-1951	589	19	pasted	paste	VERB
ejpam-1951	589	20	on	on	ADP
ejpam-1951	589	21	the	the	DET
ejpam-1951	589	22	faces	face	NOUN
ejpam-1951	589	23	of	of	ADP
ejpam-1951	589	24	a	a	DET
ejpam-1951	589	25	cube	cube	NOUN
ejpam-1951	589	26	,	,	PUNCT
ejpam-1951	589	27	one	one	NUM
ejpam-1951	589	28	on	on	ADP
ejpam-1951	589	29	each	each	DET
ejpam-1951	589	30	side	side	NOUN
ejpam-1951	589	31	.	.	PUNCT
ejpam-1951	590	1	label	label	NOUN
ejpam-1951	590	2	l1	l1	PROPN
ejpam-1951	590	3	and	and	CCONJ
ejpam-1951	590	4	l2	l2	NOUN
ejpam-1951	590	5	are	be	AUX
ejpam-1951	590	6	yellow	yellow	ADJ
ejpam-1951	590	7	and	and	CCONJ
ejpam-1951	590	8	black	black	ADJ
ejpam-1951	590	9	respectively	respectively	ADV
ejpam-1951	590	10	.	.	PUNCT
ejpam-1951	591	1	the	the	DET
ejpam-1951	591	2	labels	label	NOUN
ejpam-1951	591	3	l3	l3	PROPN
ejpam-1951	591	4	and	and	CCONJ
ejpam-1951	591	5	l4	l4	PROPN
ejpam-1951	591	6	are	be	AUX
ejpam-1951	591	7	both	both	PRON
ejpam-1951	591	8	violet	violet	ADJ
ejpam-1951	591	9	and	and	CCONJ
ejpam-1951	591	10	can	can	AUX
ejpam-1951	591	11	not	not	PART
ejpam-1951	591	12	be	be	AUX
ejpam-1951	591	13	distinguished	distinguish	VERB
ejpam-1951	591	14	from	from	ADP
ejpam-1951	591	15	each	each	DET
ejpam-1951	591	16	other	other	ADJ
ejpam-1951	591	17	.	.	PUNCT
ejpam-1951	592	1	the	the	DET
ejpam-1951	592	2	same	same	ADJ
ejpam-1951	592	3	condition	condition	NOUN
ejpam-1951	592	4	holds	hold	VERB
ejpam-1951	592	5	for	for	ADP
ejpam-1951	592	6	l5	l5	ADJ
ejpam-1951	592	7	and	and	CCONJ
ejpam-1951	592	8	l6	l6	PROPN
ejpam-1951	592	9	which	which	PRON
ejpam-1951	592	10	are	be	AUX
ejpam-1951	592	11	both	both	ADV
ejpam-1951	592	12	purple	purple	ADJ
ejpam-1951	592	13	.	.	PUNCT
ejpam-1951	593	1	we	we	PRON
ejpam-1951	593	2	are	be	AUX
ejpam-1951	593	3	interested	interested	ADJ
ejpam-1951	593	4	to	to	PART
ejpam-1951	593	5	find	find	VERB
ejpam-1951	593	6	out	out	ADP
ejpam-1951	593	7	the	the	DET
ejpam-1951	593	8	number	number	NOUN
ejpam-1951	593	9	of	of	ADP
ejpam-1951	593	10	patterns	pattern	NOUN
ejpam-1951	593	11	.	.	PUNCT
ejpam-1951	594	1	now	now	ADV
ejpam-1951	594	2	x	x	AUX
ejpam-1951	594	3	be	be	AUX
ejpam-1951	594	4	set	set	VERB
ejpam-1951	594	5	of	of	ADP
ejpam-1951	594	6	6	6	NUM
ejpam-1951	594	7	labels	label	NOUN
ejpam-1951	594	8	and	and	CCONJ
ejpam-1951	594	9	y	y	PROPN
ejpam-1951	594	10	is	be	AUX
ejpam-1951	594	11	the	the	DET
ejpam-1951	594	12	set	set	NOUN
ejpam-1951	594	13	of	of	ADP
ejpam-1951	594	14	6	6	NUM
ejpam-1951	594	15	faces	face	NOUN
ejpam-1951	594	16	.	.	PUNCT
ejpam-1951	595	1	the	the	DET
ejpam-1951	595	2	group	group	NOUN
ejpam-1951	595	3	g	g	PROPN
ejpam-1951	595	4	consists	consist	VERB
ejpam-1951	595	5	of	of	ADP
ejpam-1951	595	6	8	8	NUM
ejpam-1951	595	7	permutations	permutation	NOUN
ejpam-1951	595	8	,	,	PUNCT
ejpam-1951	595	9	characterized	characterize	VERB
ejpam-1951	595	10	by	by	ADP
ejpam-1951	595	11	the	the	DET
ejpam-1951	595	12	conditions	condition	NOUN
ejpam-1951	595	13	that	that	PRON
ejpam-1951	595	14	l1	l1	PROPN
ejpam-1951	595	15	and	and	CCONJ
ejpam-1951	595	16	l2	l2	NOUN
ejpam-1951	595	17	are	be	AUX
ejpam-1951	595	18	fixed	fix	VERB
ejpam-1951	595	19	and	and	CCONJ
ejpam-1951	595	20	the	the	DET
ejpam-1951	595	21	subset	subset	NOUN
ejpam-1951	595	22	{	{	PUNCT
ejpam-1951	595	23	l3	l3	PROPN
ejpam-1951	595	24	,	,	PUNCT
ejpam-1951	595	25	l4	l4	PROPN
ejpam-1951	595	26	}	}	PUNCT
ejpam-1951	595	27	mapped	map	VERB
ejpam-1951	595	28	onto	onto	ADP
ejpam-1951	595	29	either	either	DET
ejpam-1951	595	30	itself	itself	PRON
ejpam-1951	595	31	or	or	CCONJ
ejpam-1951	595	32	the	the	DET
ejpam-1951	595	33	set	set	NOUN
ejpam-1951	595	34	{	{	PUNCT
ejpam-1951	595	35	l5	l5	PROPN
ejpam-1951	595	36	,	,	PUNCT
ejpam-1951	595	37	l6	l6	NOUN
ejpam-1951	595	38	}	}	PUNCT
ejpam-1951	595	39	[	[	X
ejpam-1951	595	40	2	2	NUM
ejpam-1951	595	41	]	]	PUNCT
ejpam-1951	595	42	.	.	PUNCT
ejpam-1951	596	1	the	the	DET
ejpam-1951	596	2	cycle	cycle	NOUN
ejpam-1951	596	3	index	index	NOUN
ejpam-1951	596	4	of	of	ADP
ejpam-1951	596	5	this	this	DET
ejpam-1951	596	6	group	group	NOUN
ejpam-1951	596	7	is	be	AUX
ejpam-1951	596	8	zg	zg	NOUN
ejpam-1951	596	9	=	=	SYM
ejpam-1951	596	10	1	1	NUM
ejpam-1951	596	11	8	8	NUM
ejpam-1951	596	12	(	(	PUNCT
ejpam-1951	596	13	t6	t6	PROPN
ejpam-1951	596	14	1	1	NUM
ejpam-1951	596	15	+	+	NUM
ejpam-1951	596	16	2t4	2t4	NUM
ejpam-1951	596	17	1	1	NUM
ejpam-1951	596	18	t2	t2	NOUN
ejpam-1951	596	19	+	+	CCONJ
ejpam-1951	596	20	3t2	3t2	NUM
ejpam-1951	596	21	1t2	1t2	NUM
ejpam-1951	596	22	2	2	NUM
ejpam-1951	596	23	+	+	NUM
ejpam-1951	596	24	2t2	2t2	NUM
ejpam-1951	596	25	1t4	1t4	NUM
ejpam-1951	596	26	)	)	PUNCT
ejpam-1951	596	27	and	and	CCONJ
ejpam-1951	596	28	also	also	ADV
ejpam-1951	596	29	given	give	VERB
ejpam-1951	596	30	by	by	ADP
ejpam-1951	596	31	zh	zh	X
ejpam-1951	596	32	=	=	SYM
ejpam-1951	596	33	1	1	NUM
ejpam-1951	596	34	24	24	NUM
ejpam-1951	596	35	(	(	PUNCT
ejpam-1951	596	36	t6	t6	PROPN
ejpam-1951	596	37	1	1	NUM
ejpam-1951	596	38	+	+	NUM
ejpam-1951	596	39	6t3	6t3	NUM
ejpam-1951	596	40	2	2	NUM
ejpam-1951	596	41	+	+	CCONJ
ejpam-1951	596	42	8t2	8t2	NUM
ejpam-1951	596	43	3	3	NUM
ejpam-1951	596	44	+	+	SYM
ejpam-1951	596	45	3t2	3t2	NUM
ejpam-1951	596	46	1t2	1t2	NUM
ejpam-1951	596	47	2	2	NUM
ejpam-1951	596	48	+	+	CCONJ
ejpam-1951	596	49	6t2	6t2	NUM
ejpam-1951	596	50	1t4	1t4	NUM
ejpam-1951	596	51	)	)	PUNCT
ejpam-1951	596	52	for	for	ADP
ejpam-1951	596	53	the	the	DET
ejpam-1951	596	54	number	number	NOUN
ejpam-1951	596	55	of	of	ADP
ejpam-1951	596	56	patterns	pattern	NOUN
ejpam-1951	596	57	we	we	PRON
ejpam-1951	596	58	obtain	obtain	VERB
ejpam-1951	596	59	zh	zh	PROPN
ejpam-1951	596	60	�	�	PROPN
ejpam-1951	596	61	∂	∂	NUM
ejpam-1951	596	62	∂	∂	NUM
ejpam-1951	596	63	z1	z1	NOUN
ejpam-1951	596	64	,	,	PUNCT
ejpam-1951	596	65	∂	∂	NUM
ejpam-1951	596	66	2	2	NUM
ejpam-1951	596	67	∂	∂	NUM
ejpam-1951	596	68	z1∂	z1∂	PROPN
ejpam-1951	596	69	z2	z2	PROPN
ejpam-1951	596	70	,	,	PUNCT
ejpam-1951	596	71	∂	∂	NUM
ejpam-1951	596	72	2	2	NUM
ejpam-1951	596	73	∂	∂	NUM
ejpam-1951	596	74	z1∂	z1∂	PROPN
ejpam-1951	596	75	z4	z4	PROPN
ejpam-1951	596	76	�	�	PROPN
ejpam-1951	596	77	zg(z1	zg(z1	PROPN
ejpam-1951	596	78	,	,	PUNCT
ejpam-1951	596	79	2z2	2z2	NUM
ejpam-1951	596	80	,	,	PUNCT
ejpam-1951	596	81	4z4	4z4	NUM
ejpam-1951	596	82	)	)	PUNCT
ejpam-1951	596	83	=	=	SYM
ejpam-1951	596	84	1	1	NUM
ejpam-1951	596	85	24	24	NUM
ejpam-1951	596	86	·	·	SYM
ejpam-1951	596	87	1	1	NUM
ejpam-1951	596	88	8	8	NUM
ejpam-1951	596	89	�	�	PROPN
ejpam-1951	596	90	�	�	PROPN
ejpam-1951	596	91	∂	∂	NUM
ejpam-1951	596	92	∂	∂	NUM
ejpam-1951	596	93	z1	z1	PROPN
ejpam-1951	596	94	�	�	PROPN
ejpam-1951	596	95	6	6	NUM
ejpam-1951	596	96	(	(	PUNCT
ejpam-1951	596	97	z1	z1	NOUN
ejpam-1951	596	98	)	)	PUNCT
ejpam-1951	596	99	6	6	NUM
ejpam-1951	596	100	+	+	SYM
ejpam-1951	596	101	�	�	PROPN
ejpam-1951	596	102	∂	∂	NUM
ejpam-1951	596	103	2	2	NUM
ejpam-1951	596	104	∂	∂	NUM
ejpam-1951	597	1	z1∂	z1∂	PROPN
ejpam-1951	597	2	z2	z2	PROPN
ejpam-1951	597	3	�	�	PROPN
ejpam-1951	597	4	2	2	NUM
ejpam-1951	597	5	(	(	PUNCT
ejpam-1951	597	6	z12z2	z12z2	X
ejpam-1951	597	7	)	)	PUNCT
ejpam-1951	597	8	2	2	NUM
ejpam-1951	597	9	+	+	CCONJ
ejpam-1951	597	10	�	�	PROPN
ejpam-1951	597	11	�	�	PROPN
ejpam-1951	597	12	∂	∂	NUM
ejpam-1951	597	13	∂	∂	NUM
ejpam-1951	597	14	z1	z1	VERB
ejpam-1951	597	15	�	�	PROPN
ejpam-1951	597	16	2	2	NUM
ejpam-1951	597	17	�	�	PROPN
ejpam-1951	597	18	∂	∂	NUM
ejpam-1951	597	19	∂	∂	NUM
ejpam-1951	597	20	z1	z1	PROPN
ejpam-1951	597	21	�	�	PROPN
ejpam-1951	597	22	�	�	PROPN
ejpam-1951	597	23	(	(	PUNCT
ejpam-1951	597	24	z2	z2	PROPN
ejpam-1951	597	25	14z4	14z4	NUM
ejpam-1951	597	26	)	)	PUNCT
ejpam-1951	597	27	�	�	PROPN
ejpam-1951	597	28	=	=	NOUN
ejpam-1951	597	29	1	1	NUM
ejpam-1951	597	30	24	24	NUM
ejpam-1951	597	31	·	·	SYM
ejpam-1951	597	32	1	1	NUM
ejpam-1951	597	33	8	8	NUM
ejpam-1951	597	34	(	(	PUNCT
ejpam-1951	597	35	6!+	6!+	NOUN
ejpam-1951	597	36	3	3	NUM
ejpam-1951	597	37	·	·	SYM
ejpam-1951	597	38	3	3	NUM
ejpam-1951	597	39	·	·	SYM
ejpam-1951	597	40	2!22	2!22	X
ejpam-1951	597	41	·	·	PUNCT
ejpam-1951	597	42	2!+	2!+	NOUN
ejpam-1951	597	43	6	6	NUM
ejpam-1951	597	44	·	·	SYM
ejpam-1951	597	45	2	2	NUM
ejpam-1951	597	46	·	·	PUNCT
ejpam-1951	597	47	2!4	2!4	NUM
ejpam-1951	597	48	·	·	PUNCT
ejpam-1951	597	49	1	1	NUM
ejpam-1951	597	50	!	!	PUNCT
ejpam-1951	597	51	)	)	PUNCT
ejpam-1951	598	1	=	=	SYM
ejpam-1951	598	2	5	5	NUM
ejpam-1951	598	3	t.	t.	NOUN
ejpam-1951	598	4	nasseef	nasseef	PROPN
ejpam-1951	598	5	/	/	SYM
ejpam-1951	598	6	eur	eur	PROPN
ejpam-1951	598	7	.	.	PUNCT
ejpam-1951	599	1	j.	j.	PROPN
ejpam-1951	599	2	pure	pure	PROPN
ejpam-1951	599	3	appl	appl	PROPN
ejpam-1951	599	4	.	.	PROPN
ejpam-1951	599	5	math	math	PROPN
ejpam-1951	599	6	,	,	PUNCT
ejpam-1951	599	7	9	9	NUM
ejpam-1951	599	8	(	(	PUNCT
ejpam-1951	599	9	2016	2016	NUM
ejpam-1951	599	10	)	)	PUNCT
ejpam-1951	599	11	,	,	PUNCT
ejpam-1951	599	12	84	84	NUM
ejpam-1951	599	13	-	-	SYM
ejpam-1951	599	14	113	113	NUM
ejpam-1951	599	15	105	105	NUM
ejpam-1951	599	16	example	example	NOUN
ejpam-1951	599	17	15	15	NUM
ejpam-1951	599	18	.	.	PUNCT
ejpam-1951	600	1	consider	consider	VERB
ejpam-1951	600	2	6	6	NUM
ejpam-1951	600	3	colors	color	NOUN
ejpam-1951	600	4	l1	l1	PROPN
ejpam-1951	600	5	,	,	PUNCT
ejpam-1951	600	6	l2	l2	NOUN
ejpam-1951	600	7	,	,	PUNCT
ejpam-1951	600	8	l3	l3	PROPN
ejpam-1951	600	9	,	,	PUNCT
ejpam-1951	600	10	l4	l4	PROPN
ejpam-1951	600	11	,	,	PUNCT
ejpam-1951	600	12	l5	l5	PROPN
ejpam-1951	600	13	,	,	PUNCT
ejpam-1951	600	14	l6	l6	ADJ
ejpam-1951	600	15	to	to	PART
ejpam-1951	600	16	be	be	AUX
ejpam-1951	600	17	colored	color	VERB
ejpam-1951	600	18	on	on	ADP
ejpam-1951	600	19	the	the	DET
ejpam-1951	600	20	edges	edge	NOUN
ejpam-1951	600	21	of	of	ADP
ejpam-1951	600	22	a	a	DET
ejpam-1951	600	23	tetrahedron	tetrahedron	NOUN
ejpam-1951	600	24	,	,	PUNCT
ejpam-1951	600	25	one	one	NUM
ejpam-1951	600	26	on	on	ADP
ejpam-1951	600	27	each	each	DET
ejpam-1951	600	28	edge	edge	NOUN
ejpam-1951	600	29	by	by	ADP
ejpam-1951	600	30	following	follow	VERB
ejpam-1951	600	31	the	the	DET
ejpam-1951	600	32	same	same	ADJ
ejpam-1951	600	33	conditions	condition	NOUN
ejpam-1951	600	34	with	with	ADP
ejpam-1951	600	35	example	example	NOUN
ejpam-1951	600	36	14	14	NUM
ejpam-1951	600	37	.	.	PUNCT
ejpam-1951	601	1	then	then	ADV
ejpam-1951	601	2	the	the	DET
ejpam-1951	601	3	cycle	cycle	NOUN
ejpam-1951	601	4	index	index	NOUN
ejpam-1951	601	5	of	of	ADP
ejpam-1951	601	6	this	this	DET
ejpam-1951	601	7	group	group	NOUN
ejpam-1951	601	8	is	be	AUX
ejpam-1951	601	9	zg	zg	NOUN
ejpam-1951	601	10	=	=	SYM
ejpam-1951	601	11	1	1	NUM
ejpam-1951	601	12	8	8	NUM
ejpam-1951	601	13	(	(	PUNCT
ejpam-1951	601	14	t6	t6	PROPN
ejpam-1951	601	15	1	1	NUM
ejpam-1951	601	16	+	+	NUM
ejpam-1951	601	17	2t4	2t4	NUM
ejpam-1951	601	18	1	1	NUM
ejpam-1951	601	19	t2	t2	NOUN
ejpam-1951	601	20	+	+	CCONJ
ejpam-1951	601	21	3t2	3t2	NUM
ejpam-1951	601	22	1t2	1t2	NUM
ejpam-1951	601	23	2	2	NUM
ejpam-1951	601	24	+	+	CCONJ
ejpam-1951	601	25	2t2	2t2	NUM
ejpam-1951	601	26	1	1	NUM
ejpam-1951	601	27	t4	t4	PROPN
ejpam-1951	601	28	)	)	PUNCT
ejpam-1951	601	29	and	and	CCONJ
ejpam-1951	601	30	also	also	ADV
ejpam-1951	601	31	given	give	VERB
ejpam-1951	601	32	by	by	ADP
ejpam-1951	601	33	zh	zh	X
ejpam-1951	601	34	=	=	SYM
ejpam-1951	601	35	1	1	NUM
ejpam-1951	601	36	12	12	NUM
ejpam-1951	601	37	(	(	PUNCT
ejpam-1951	601	38	t6	t6	PROPN
ejpam-1951	601	39	1	1	NUM
ejpam-1951	601	40	+	+	CCONJ
ejpam-1951	601	41	8t2	8t2	NUM
ejpam-1951	601	42	3	3	NUM
ejpam-1951	601	43	+	+	NUM
ejpam-1951	601	44	3t2	3t2	NUM
ejpam-1951	601	45	1t2	1t2	NUM
ejpam-1951	601	46	2	2	NUM
ejpam-1951	601	47	)	)	PUNCT
ejpam-1951	601	48	for	for	ADP
ejpam-1951	601	49	the	the	DET
ejpam-1951	601	50	number	number	NOUN
ejpam-1951	601	51	of	of	ADP
ejpam-1951	601	52	patterns	pattern	NOUN
ejpam-1951	601	53	we	we	PRON
ejpam-1951	601	54	obtain	obtain	VERB
ejpam-1951	601	55	zh	zh	PROPN
ejpam-1951	601	56	�	�	PROPN
ejpam-1951	601	57	∂	∂	NUM
ejpam-1951	601	58	∂	∂	NUM
ejpam-1951	601	59	z1	z1	NOUN
ejpam-1951	601	60	,	,	PUNCT
ejpam-1951	601	61	∂	∂	NUM
ejpam-1951	601	62	2	2	NUM
ejpam-1951	601	63	∂	∂	NUM
ejpam-1951	601	64	z1∂	z1∂	PROPN
ejpam-1951	601	65	z2	z2	PROPN
ejpam-1951	601	66	�	�	PROPN
ejpam-1951	601	67	zg(z1	zg(z1	PROPN
ejpam-1951	601	68	,	,	PUNCT
ejpam-1951	601	69	2z2	2z2	NUM
ejpam-1951	601	70	)	)	PUNCT
ejpam-1951	601	71	=	=	SYM
ejpam-1951	601	72	1	1	NUM
ejpam-1951	601	73	12	12	NUM
ejpam-1951	601	74	·	·	SYM
ejpam-1951	601	75	1	1	NUM
ejpam-1951	601	76	8	8	NUM
ejpam-1951	601	77	�	�	PROPN
ejpam-1951	601	78	�	�	PROPN
ejpam-1951	601	79	∂	∂	NUM
ejpam-1951	601	80	∂	∂	NUM
ejpam-1951	601	81	z1	z1	PROPN
ejpam-1951	601	82	�	�	PROPN
ejpam-1951	601	83	6	6	NUM
ejpam-1951	601	84	(	(	PUNCT
ejpam-1951	601	85	z1	z1	NOUN
ejpam-1951	601	86	)	)	PUNCT
ejpam-1951	601	87	6	6	NUM
ejpam-1951	601	88	+	+	SYM
ejpam-1951	601	89	�	�	PROPN
ejpam-1951	601	90	∂	∂	NUM
ejpam-1951	601	91	2	2	NUM
ejpam-1951	601	92	∂	∂	NUM
ejpam-1951	601	93	z1∂	z1∂	PROPN
ejpam-1951	601	94	z2	z2	PROPN
ejpam-1951	601	95	�	�	PROPN
ejpam-1951	601	96	2	2	NUM
ejpam-1951	601	97	(	(	PUNCT
ejpam-1951	601	98	z12z2	z12z2	X
ejpam-1951	601	99	)	)	PUNCT
ejpam-1951	601	100	2	2	NUM
ejpam-1951	601	101	�	�	NOUN
ejpam-1951	601	102	=	=	NOUN
ejpam-1951	601	103	1	1	NUM
ejpam-1951	601	104	12	12	NUM
ejpam-1951	601	105	·	·	SYM
ejpam-1951	601	106	1	1	NUM
ejpam-1951	601	107	8	8	NUM
ejpam-1951	601	108	(	(	PUNCT
ejpam-1951	601	109	6!+	6!+	NOUN
ejpam-1951	601	110	3	3	NUM
ejpam-1951	601	111	·	·	SYM
ejpam-1951	601	112	3	3	NUM
ejpam-1951	601	113	·	·	SYM
ejpam-1951	601	114	2!22	2!22	X
ejpam-1951	601	115	·	·	PUNCT
ejpam-1951	601	116	2	2	X
ejpam-1951	601	117	!	!	PUNCT
ejpam-1951	601	118	)	)	PUNCT
ejpam-1951	602	1	=	=	NOUN
ejpam-1951	602	2	9	9	NUM
ejpam-1951	602	3	3.2	3.2	NUM
ejpam-1951	602	4	.	.	PUNCT
ejpam-1951	603	1	the	the	DET
ejpam-1951	603	2	total	total	ADJ
ejpam-1951	603	3	number	number	NOUN
ejpam-1951	603	4	of	of	ADP
ejpam-1951	603	5	patterns	pattern	NOUN
ejpam-1951	603	6	again	again	ADV
ejpam-1951	603	7	consider	consider	VERB
ejpam-1951	603	8	finite	finite	NOUN
ejpam-1951	603	9	sets	set	NOUN
ejpam-1951	603	10	x	x	PUNCT
ejpam-1951	603	11	and	and	CCONJ
ejpam-1951	603	12	y	y	PROPN
ejpam-1951	603	13	with	with	ADP
ejpam-1951	603	14	permutation	permutation	NOUN
ejpam-1951	603	15	groups	group	NOUN
ejpam-1951	603	16	g	g	PROPN
ejpam-1951	603	17	and	and	CCONJ
ejpam-1951	603	18	h	h	NOUN
ejpam-1951	603	19	of	of	ADP
ejpam-1951	603	20	x	x	X
ejpam-1951	603	21	and	and	CCONJ
ejpam-1951	603	22	y	y	PROPN
ejpam-1951	603	23	respectively	respectively	ADV
ejpam-1951	603	24	.	.	PUNCT
ejpam-1951	604	1	we	we	PRON
ejpam-1951	604	2	will	will	AUX
ejpam-1951	604	3	find	find	VERB
ejpam-1951	604	4	the	the	DET
ejpam-1951	604	5	number	number	NOUN
ejpam-1951	604	6	of	of	ADP
ejpam-1951	604	7	patterns	pattern	NOUN
ejpam-1951	604	8	.	.	PUNCT
ejpam-1951	605	1	again	again	ADV
ejpam-1951	605	2	we	we	PRON
ejpam-1951	605	3	will	will	AUX
ejpam-1951	605	4	apply	apply	VERB
ejpam-1951	605	5	lemma	lemma	PROPN
ejpam-1951	605	6	2	2	NUM
ejpam-1951	605	7	to	to	PART
ejpam-1951	605	8	evaluate	evaluate	VERB
ejpam-1951	605	9	∑(g	∑(g	PROPN
ejpam-1951	605	10	,	,	PUNCT
ejpam-1951	605	11	h	h	NOUN
ejpam-1951	605	12	)	)	PUNCT
ejpam-1951	606	1	f	f	PROPN
ejpam-1951	606	2	w	w	PROPN
ejpam-1951	606	3	(	(	PUNCT
ejpam-1951	606	4	f	f	PROPN
ejpam-1951	606	5	)	)	PUNCT
ejpam-1951	606	6	.	.	PUNCT
ejpam-1951	607	1	we	we	PRON
ejpam-1951	607	2	will	will	AUX
ejpam-1951	607	3	use	use	VERB
ejpam-1951	607	4	the	the	DET
ejpam-1951	607	5	subsection	subsection	NOUN
ejpam-1951	607	6	3.1	3.1	NUM
ejpam-1951	607	7	.	.	PUNCT
ejpam-1951	608	1	so	so	ADV
ejpam-1951	608	2	we	we	PRON
ejpam-1951	608	3	can	can	AUX
ejpam-1951	608	4	easily	easily	ADV
ejpam-1951	608	5	compute	compute	VERB
ejpam-1951	608	6	the	the	DET
ejpam-1951	608	7	number	number	NOUN
ejpam-1951	608	8	of	of	ADP
ejpam-1951	608	9	possibilities	possibility	NOUN
ejpam-1951	608	10	for	for	ADP
ejpam-1951	608	11	f	f	PROPN
ejpam-1951	608	12	.	.	PUNCT
ejpam-1951	609	1	for	for	ADP
ejpam-1951	609	2	each	each	DET
ejpam-1951	609	3	cycle	cycle	NOUN
ejpam-1951	609	4	of	of	ADP
ejpam-1951	609	5	x	x	PUNCT
ejpam-1951	609	6	we	we	PRON
ejpam-1951	609	7	will	will	AUX
ejpam-1951	609	8	select	select	VERB
ejpam-1951	609	9	an	an	DET
ejpam-1951	609	10	element	element	NOUN
ejpam-1951	609	11	,	,	PUNCT
ejpam-1951	609	12	called	call	VERB
ejpam-1951	609	13	the	the	DET
ejpam-1951	609	14	selected	select	VERB
ejpam-1951	609	15	element	element	NOUN
ejpam-1951	609	16	.	.	PUNCT
ejpam-1951	610	1	the	the	DET
ejpam-1951	610	2	number	number	NOUN
ejpam-1951	610	3	of	of	ADP
ejpam-1951	610	4	possibilities	possibility	NOUN
ejpam-1951	610	5	for	for	ADP
ejpam-1951	610	6	the	the	DET
ejpam-1951	610	7	element	element	NOUN
ejpam-1951	610	8	of	of	ADP
ejpam-1951	610	9	y	y	PROPN
ejpam-1951	610	10	onto	onto	ADP
ejpam-1951	610	11	which	which	PRON
ejpam-1951	610	12	is	be	AUX
ejpam-1951	610	13	selected	select	VERB
ejpam-1951	610	14	element	element	NOUN
ejpam-1951	610	15	can	can	AUX
ejpam-1951	610	16	be	be	AUX
ejpam-1951	610	17	mapped	map	VERB
ejpam-1951	610	18	by	by	ADP
ejpam-1951	610	19	an	an	DET
ejpam-1951	610	20	f	f	PROPN
ejpam-1951	610	21	is	be	AUX
ejpam-1951	610	22	∑	∑	PROPN
ejpam-1951	610	23	j	j	PROPN
ejpam-1951	610	24	/	/	SYM
ejpam-1951	610	25	i	i	PROPN
ejpam-1951	610	26	jc	jc	PROPN
ejpam-1951	610	27	j	j	PROPN
ejpam-1951	610	28	,	,	PUNCT
ejpam-1951	610	29	where	where	SCONJ
ejpam-1951	610	30	i	i	PRON
ejpam-1951	610	31	is	be	AUX
ejpam-1951	610	32	the	the	DET
ejpam-1951	610	33	length	length	NOUN
ejpam-1951	610	34	of	of	ADP
ejpam-1951	610	35	the	the	DET
ejpam-1951	610	36	cycle	cycle	NOUN
ejpam-1951	610	37	of	of	ADP
ejpam-1951	610	38	x	x	PART
ejpam-1951	610	39	to	to	PART
ejpam-1951	610	40	which	which	PRON
ejpam-1951	610	41	the	the	DET
ejpam-1951	610	42	selected	select	VERB
ejpam-1951	610	43	item	item	NOUN
ejpam-1951	610	44	belongs	belong	VERB
ejpam-1951	610	45	,	,	PUNCT
ejpam-1951	610	46	c′s	c′s	ADJ
ejpam-1951	610	47	are	be	AUX
ejpam-1951	610	48	of	of	ADP
ejpam-1951	610	49	type	type	NOUN
ejpam-1951	610	50	{	{	PUNCT
ejpam-1951	610	51	c1	c1	NOUN
ejpam-1951	610	52	,	,	PUNCT
ejpam-1951	610	53	c2	c2	PROPN
ejpam-1951	610	54	,	,	PUNCT
ejpam-1951	610	55	.	.	PUNCT
ejpam-1951	610	56	.	.	PUNCT
ejpam-1951	611	1	.	.	PUNCT
ejpam-1951	612	1	}	}	PUNCT
ejpam-1951	612	2	of	of	ADP
ejpam-1951	612	3	h	h	NOUN
ejpam-1951	613	1	and	and	CCONJ
ejpam-1951	613	2	the	the	DET
ejpam-1951	613	3	sum	sum	NOUN
ejpam-1951	613	4	is	be	AUX
ejpam-1951	613	5	over	over	ADP
ejpam-1951	613	6	all	all	DET
ejpam-1951	613	7	divisors	divisor	NOUN
ejpam-1951	613	8	j	j	PROPN
ejpam-1951	613	9	of	of	ADP
ejpam-1951	613	10	i.	i.	PROPN
ejpam-1951	613	11	because	because	SCONJ
ejpam-1951	613	12	the	the	DET
ejpam-1951	613	13	choices	choice	NOUN
ejpam-1951	613	14	of	of	ADP
ejpam-1951	613	15	function	function	NOUN
ejpam-1951	613	16	values	value	NOUN
ejpam-1951	613	17	for	for	ADP
ejpam-1951	613	18	the	the	DET
ejpam-1951	613	19	various	various	ADJ
ejpam-1951	613	20	selected	select	VERB
ejpam-1951	613	21	elements	element	NOUN
ejpam-1951	613	22	are	be	AUX
ejpam-1951	613	23	independent	independent	ADJ
ejpam-1951	613	24	and	and	CCONJ
ejpam-1951	613	25	determine	determine	VERB
ejpam-1951	613	26	f	f	NOUN
ejpam-1951	613	27	completely	completely	ADV
ejpam-1951	613	28	.	.	PUNCT
ejpam-1951	614	1	the	the	DET
ejpam-1951	614	2	number	number	NOUN
ejpam-1951	614	3	of	of	ADP
ejpam-1951	614	4	f	f	PROPN
ejpam-1951	614	5	equals	equal	VERB
ejpam-1951	614	6	the	the	DET
ejpam-1951	614	7	product	product	NOUN
ejpam-1951	614	8	of	of	ADP
ejpam-1951	614	9	∑	∑	PROPN
ejpam-1951	614	10	j	j	PROPN
ejpam-1951	614	11	/	/	SYM
ejpam-1951	614	12	i	i	PROPN
ejpam-1951	614	13	jc	jc	PROPN
ejpam-1951	614	14	j	j	PROPN
ejpam-1951	614	15	taken	take	VERB
ejpam-1951	614	16	over	over	ADP
ejpam-1951	614	17	all	all	DET
ejpam-1951	614	18	selected	select	VERB
ejpam-1951	614	19	elements	element	NOUN
ejpam-1951	614	20	.	.	PUNCT
ejpam-1951	615	1	since	since	SCONJ
ejpam-1951	615	2	there	there	PRON
ejpam-1951	615	3	are	be	VERB
ejpam-1951	615	4	gi	gi	X
ejpam-1951	615	5	cycles	cycle	NOUN
ejpam-1951	615	6	of	of	ADP
ejpam-1951	615	7	length	length	NOUN
ejpam-1951	615	8	i	i	PRON
ejpam-1951	615	9	,	,	PUNCT
ejpam-1951	615	10	then	then	ADV
ejpam-1951	615	11	we	we	PRON
ejpam-1951	615	12	get	get	VERB
ejpam-1951	615	13	(	(	PUNCT
ejpam-1951	615	14	g	g	NOUN
ejpam-1951	615	15	,	,	PUNCT
ejpam-1951	615	16	h	h	NOUN
ejpam-1951	615	17	)	)	PUNCT
ejpam-1951	615	18	∑	∑	PROPN
ejpam-1951	616	1	f	f	PROPN
ejpam-1951	616	2	w	w	PROPN
ejpam-1951	616	3	(	(	PUNCT
ejpam-1951	616	4	f	f	PROPN
ejpam-1951	616	5	)	)	PUNCT
ejpam-1951	616	6	=	=	SYM
ejpam-1951	616	7	∏	∏	PROPN
ejpam-1951	616	8	(	(	PUNCT
ejpam-1951	616	9	∑	∑	INTJ
ejpam-1951	616	10	j	j	PROPN
ejpam-1951	616	11	/	/	SYM
ejpam-1951	616	12	i	i	PROPN
ejpam-1951	616	13	jc	jc	PROPN
ejpam-1951	616	14	j	j	PROPN
ejpam-1951	616	15	)	)	PUNCT
ejpam-1951	616	16	gi	gi	PROPN
ejpam-1951	616	17	=(	=(	PROPN
ejpam-1951	616	18	c1	c1	PROPN
ejpam-1951	616	19	)	)	PUNCT
ejpam-1951	616	20	g1(c1	g1(c1	PROPN
ejpam-1951	616	21	+	+	CCONJ
ejpam-1951	616	22	2c2	2c2	NUM
ejpam-1951	616	23	)	)	PUNCT
ejpam-1951	616	24	g2(c1	g2(c1	NOUN
ejpam-1951	616	25	+	+	CCONJ
ejpam-1951	616	26	3c3	3c3	NUM
ejpam-1951	616	27	)	)	PUNCT
ejpam-1951	616	28	g3(c1	g3(c1	NOUN
ejpam-1951	616	29	+	+	NUM
ejpam-1951	616	30	2c2	2c2	NUM
ejpam-1951	616	31	+	+	CCONJ
ejpam-1951	616	32	4c4	4c4	X
ejpam-1951	616	33	)	)	PUNCT
ejpam-1951	616	34	g4	g4	NOUN
ejpam-1951	616	35	.	.	PUNCT
ejpam-1951	616	36	.	.	PUNCT
ejpam-1951	616	37	.	.	PUNCT
ejpam-1951	617	1	(	(	PUNCT
ejpam-1951	617	2	5	5	X
ejpam-1951	617	3	)	)	PUNCT
ejpam-1951	617	4	note	note	NOUN
ejpam-1951	617	5	that	that	SCONJ
ejpam-1951	617	6	a	a	DET
ejpam-1951	617	7	power	power	NOUN
ejpam-1951	617	8	with	with	ADP
ejpam-1951	617	9	exponent	exponent	PROPN
ejpam-1951	617	10	0	0	NUM
ejpam-1951	617	11	has	have	VERB
ejpam-1951	617	12	to	to	PART
ejpam-1951	617	13	be	be	AUX
ejpam-1951	617	14	interpreted	interpret	VERB
ejpam-1951	617	15	as	as	ADP
ejpam-1951	617	16	1	1	NUM
ejpam-1951	617	17	in	in	ADP
ejpam-1951	617	18	this	this	DET
ejpam-1951	617	19	context	context	NOUN
ejpam-1951	617	20	even	even	ADV
ejpam-1951	617	21	if	if	SCONJ
ejpam-1951	617	22	the	the	DET
ejpam-1951	617	23	base	base	NOUN
ejpam-1951	617	24	is	be	AUX
ejpam-1951	617	25	zero	zero	NUM
ejpam-1951	617	26	.	.	PUNCT
ejpam-1951	618	1	therefore	therefore	ADV
ejpam-1951	618	2	is	be	AUX
ejpam-1951	618	3	no	no	DET
ejpam-1951	618	4	difficulty	difficulty	NOUN
ejpam-1951	618	5	about	about	ADP
ejpam-1951	618	6	the	the	DET
ejpam-1951	618	7	interpretation	interpretation	NOUN
ejpam-1951	618	8	of	of	ADP
ejpam-1951	618	9	the	the	DET
ejpam-1951	618	10	infinite	infinite	ADJ
ejpam-1951	618	11	product	product	NOUN
ejpam-1951	618	12	.	.	PUNCT
ejpam-1951	619	1	as	as	ADP
ejpam-1951	619	2	in	in	ADP
ejpam-1951	619	3	subsection	subsection	NOUN
ejpam-1951	619	4	3.1	3.1	NUM
ejpam-1951	619	5	,	,	PUNCT
ejpam-1951	619	6	we	we	PRON
ejpam-1951	619	7	can	can	AUX
ejpam-1951	619	8	interpret	interpret	VERB
ejpam-1951	619	9	the	the	DET
ejpam-1951	619	10	previous	previous	ADJ
ejpam-1951	619	11	equation	equation	NOUN
ejpam-1951	619	12	as	as	ADP
ejpam-1951	619	13	a	a	DET
ejpam-1951	619	14	derivative	derivative	NOUN
ejpam-1951	619	15	.	.	PUNCT
ejpam-1951	620	1	a	a	DET
ejpam-1951	620	2	power	power	NOUN
ejpam-1951	620	3	ab	ab	PROPN
ejpam-1951	620	4	can	can	AUX
ejpam-1951	620	5	be	be	AUX
ejpam-1951	620	6	written	write	VERB
ejpam-1951	620	7	as	as	ADP
ejpam-1951	620	8	the	the	DET
ejpam-1951	620	9	bth	bth	NOUN
ejpam-1951	620	10	derivative	derivative	NOUN
ejpam-1951	620	11	of	of	ADP
ejpam-1951	620	12	eaz	eaz	PROPN
ejpam-1951	620	13	at	at	ADP
ejpam-1951	620	14	z	z	PROPN
ejpam-1951	620	15	=	=	SYM
ejpam-1951	620	16	0	0	NUM
ejpam-1951	620	17	;	;	PUNCT
ejpam-1951	620	18	if	if	SCONJ
ejpam-1951	620	19	a	a	DET
ejpam-1951	620	20	=	=	SYM
ejpam-1951	620	21	b	b	NOUN
ejpam-1951	620	22	=	=	SYM
ejpam-1951	620	23	0	0	PROPN
ejpam-1951	620	24	,	,	PUNCT
ejpam-1951	620	25	this	this	PRON
ejpam-1951	620	26	still	still	ADV
ejpam-1951	620	27	gives	give	VERB
ejpam-1951	620	28	the	the	DET
ejpam-1951	620	29	desired	desire	VERB
ejpam-1951	620	30	value	value	NOUN
ejpam-1951	620	31	0	0	NUM
ejpam-1951	620	32	◦	◦	NOUN
ejpam-1951	620	33	=	=	SYM
ejpam-1951	620	34	1	1	X
ejpam-1951	620	35	.	.	PUNCT
ejpam-1951	621	1	so	so	ADV
ejpam-1951	621	2	the	the	DET
ejpam-1951	621	3	previous	previous	ADJ
ejpam-1951	621	4	expression	expression	NOUN
ejpam-1951	621	5	can	can	AUX
ejpam-1951	621	6	be	be	AUX
ejpam-1951	621	7	written	write	VERB
ejpam-1951	621	8	as	as	ADP
ejpam-1951	621	9	�	�	PROPN
ejpam-1951	621	10	∂	∂	NUM
ejpam-1951	621	11	∂	∂	NUM
ejpam-1951	621	12	z1	z1	PROPN
ejpam-1951	621	13	�	�	PROPN
ejpam-1951	621	14	g1	g1	PROPN
ejpam-1951	621	15	�	�	PROPN
ejpam-1951	621	16	∂	∂	NUM
ejpam-1951	621	17	∂	∂	NUM
ejpam-1951	621	18	z2	z2	PROPN
ejpam-1951	621	19	�	�	PROPN
ejpam-1951	621	20	g2	g2	PROPN
ejpam-1951	621	21	�	�	PROPN
ejpam-1951	621	22	∂	∂	NUM
ejpam-1951	621	23	∂	∂	NUM
ejpam-1951	621	24	z3	z3	PROPN
ejpam-1951	621	25	�	�	PROPN
ejpam-1951	621	26	g3	g3	PROPN
ejpam-1951	621	27	.	.	PUNCT
ejpam-1951	621	28	.	.	PUNCT
ejpam-1951	621	29	.	.	PUNCT
ejpam-1951	622	1	ex	ex	PRON
ejpam-1951	623	1	p	p	X
ejpam-1951	623	2	(	(	PUNCT
ejpam-1951	623	3	∑	∑	PROPN
ejpam-1951	623	4	i	i	PROPN
ejpam-1951	623	5	zi	zi	VERB
ejpam-1951	623	6	∑	∑	PROPN
ejpam-1951	623	7	j	j	PROPN
ejpam-1951	623	8	/	/	SYM
ejpam-1951	623	9	i	i	PROPN
ejpam-1951	623	10	jc	jc	PROPN
ejpam-1951	623	11	j	j	PROPN
ejpam-1951	623	12	)	)	PUNCT
ejpam-1951	623	13	,	,	PUNCT
ejpam-1951	623	14	t.	t.	PROPN
ejpam-1951	623	15	nasseef	nasseef	PROPN
ejpam-1951	623	16	/	/	SYM
ejpam-1951	623	17	eur	eur	PROPN
ejpam-1951	623	18	.	.	PUNCT
ejpam-1951	624	1	j.	j.	PROPN
ejpam-1951	624	2	pure	pure	PROPN
ejpam-1951	624	3	appl	appl	PROPN
ejpam-1951	624	4	.	.	PROPN
ejpam-1951	624	5	math	math	PROPN
ejpam-1951	624	6	,	,	PUNCT
ejpam-1951	624	7	9	9	NUM
ejpam-1951	624	8	(	(	PUNCT
ejpam-1951	624	9	2016	2016	NUM
ejpam-1951	624	10	)	)	PUNCT
ejpam-1951	624	11	,	,	PUNCT
ejpam-1951	624	12	84	84	NUM
ejpam-1951	624	13	-	-	SYM
ejpam-1951	624	14	113	113	NUM
ejpam-1951	624	15	106	106	NUM
ejpam-1951	624	16	evaluated	evaluate	VERB
ejpam-1951	624	17	at	at	ADP
ejpam-1951	624	18	z1	z1	ADJ
ejpam-1951	624	19	=	=	SYM
ejpam-1951	624	20	z2	z2	PROPN
ejpam-1951	624	21	=	=	PUNCT
ejpam-1951	624	22	.	.	PUNCT
ejpam-1951	624	23	.	.	PUNCT
ejpam-1951	625	1	.=	.=	VERB
ejpam-1951	626	1	0	0	X
ejpam-1951	626	2	.	.	PUNCT
ejpam-1951	627	1	the	the	DET
ejpam-1951	627	2	exponent	exponent	NOUN
ejpam-1951	627	3	can	can	AUX
ejpam-1951	627	4	be	be	AUX
ejpam-1951	627	5	expressed	express	VERB
ejpam-1951	627	6	as	as	ADP
ejpam-1951	627	7	(	(	PUNCT
ejpam-1951	627	8	∑	∑	PROPN
ejpam-1951	627	9	i	i	PROPN
ejpam-1951	627	10	zi	zi	VERB
ejpam-1951	627	11	∑	∑	PROPN
ejpam-1951	627	12	j	j	PROPN
ejpam-1951	627	13	/	/	SYM
ejpam-1951	627	14	i	i	PROPN
ejpam-1951	627	15	jc	jc	PROPN
ejpam-1951	627	16	j	j	PROPN
ejpam-1951	627	17	)	)	PUNCT
ejpam-1951	628	1	=	=	PUNCT
ejpam-1951	628	2	∑	∑	PUNCT
ejpam-1951	629	1	j	j	PROPN
ejpam-1951	629	2	jc	jc	PROPN
ejpam-1951	629	3	j(z	j(z	PROPN
ejpam-1951	629	4	j	j	PROPN
ejpam-1951	629	5	+	+	CCONJ
ejpam-1951	629	6	z2	z2	PROPN
ejpam-1951	629	7	j	j	PROPN
ejpam-1951	629	8	+	+	CCONJ
ejpam-1951	629	9	z3	z3	PROPN
ejpam-1951	629	10	j	j	PROPN
ejpam-1951	630	1	+	+	CCONJ
ejpam-1951	630	2	.	.	PUNCT
ejpam-1951	630	3	.	.	PUNCT
ejpam-1951	630	4	.	.	PUNCT
ejpam-1951	630	5	)	)	PUNCT
ejpam-1951	630	6	.	.	PUNCT
ejpam-1951	631	1	now	now	ADV
ejpam-1951	631	2	the	the	DET
ejpam-1951	631	3	differential	differential	ADJ
ejpam-1951	631	4	operator	operator	NOUN
ejpam-1951	631	5	is	be	AUX
ejpam-1951	631	6	obtained	obtain	VERB
ejpam-1951	631	7	from	from	ADP
ejpam-1951	631	8	t	t	PROPN
ejpam-1951	631	9	g1	g1	PROPN
ejpam-1951	631	10	1	1	NUM
ejpam-1951	631	11	t	t	NOUN
ejpam-1951	631	12	g2	g2	PROPN
ejpam-1951	631	13	2	2	NUM
ejpam-1951	631	14	t	t	NOUN
ejpam-1951	631	15	g3	g3	NOUN
ejpam-1951	631	16	3	3	NUM
ejpam-1951	631	17	.	.	PUNCT
ejpam-1951	631	18	.	.	PUNCT
ejpam-1951	631	19	.	.	PUNCT
ejpam-1951	632	1	on	on	ADP
ejpam-1951	632	2	substitution	substitution	NOUN
ejpam-1951	632	3	of	of	ADP
ejpam-1951	632	4	t1	t1	NOUN
ejpam-1951	632	5	=	=	SYM
ejpam-1951	632	6	∂	∂	NUM
ejpam-1951	632	7	∂	∂	NOUN
ejpam-1951	632	8	z1	z1	NOUN
ejpam-1951	632	9	,	,	PUNCT
ejpam-1951	632	10	t2	t2	NOUN
ejpam-1951	632	11	=	=	SYM
ejpam-1951	632	12	∂	∂	NUM
ejpam-1951	632	13	∂	∂	NOUN
ejpam-1951	632	14	z2	z2	PROPN
ejpam-1951	632	15	,	,	PUNCT
ejpam-1951	632	16	t3	t3	PROPN
ejpam-1951	632	17	=	=	SYM
ejpam-1951	632	18	∂	∂	NUM
ejpam-1951	632	19	∂	∂	NUM
ejpam-1951	632	20	z3	z3	PROPN
ejpam-1951	632	21	4	4	NUM
ejpam-1951	632	22	,	,	PUNCT
ejpam-1951	632	23	.	.	PUNCT
ejpam-1951	632	24	.	.	PUNCT
ejpam-1951	633	1	.	.	PUNCT
ejpam-1951	634	1	and	and	CCONJ
ejpam-1951	634	2	the	the	DET
ejpam-1951	634	3	operand	operand	NOUN
ejpam-1951	634	4	is	be	AUX
ejpam-1951	634	5	obtained	obtain	VERB
ejpam-1951	634	6	from	from	ADP
ejpam-1951	634	7	t	t	PROPN
ejpam-1951	634	8	c1	c1	PROPN
ejpam-1951	634	9	1	1	NUM
ejpam-1951	635	1	t	t	PROPN
ejpam-1951	635	2	c2	c2	PROPN
ejpam-1951	635	3	2	2	NUM
ejpam-1951	635	4	t	t	NOUN
ejpam-1951	635	5	c3	c3	NOUN
ejpam-1951	635	6	3	3	NUM
ejpam-1951	635	7	.	.	PUNCT
ejpam-1951	635	8	.	.	PUNCT
ejpam-1951	635	9	.	.	PUNCT
ejpam-1951	636	1	on	on	ADP
ejpam-1951	636	2	substitution	substitution	NOUN
ejpam-1951	636	3	of	of	ADP
ejpam-1951	636	4	[	[	X
ejpam-1951	636	5	2	2	NUM
ejpam-1951	636	6	]	]	PUNCT
ejpam-1951	636	7	t1	t1	NOUN
ejpam-1951	636	8	=	=	PUNCT
ejpam-1951	636	9	ez1+z2+z3	ez1+z2+z3	X
ejpam-1951	636	10	+	+	NOUN
ejpam-1951	636	11	...	...	PUNCT
ejpam-1951	636	12	,	,	PUNCT
ejpam-1951	636	13	t2	t2	NOUN
ejpam-1951	636	14	=	=	NUM
ejpam-1951	636	15	e2(z2+z4+z6	e2(z2+z4+z6	VERB
ejpam-1951	636	16	+	+	NUM
ejpam-1951	636	17	...	...	PUNCT
ejpam-1951	636	18	)	)	PUNCT
ejpam-1951	636	19	,	,	PUNCT
ejpam-1951	636	20	t3	t3	NOUN
ejpam-1951	636	21	=	=	PUNCT
ejpam-1951	636	22	e3(z3+z6+z9	e3(z3+z6+z9	NOUN
ejpam-1951	636	23	+	+	NOUN
ejpam-1951	636	24	...	...	PUNCT
ejpam-1951	636	25	)	)	PUNCT
ejpam-1951	636	26	,	,	PUNCT
ejpam-1951	636	27	.	.	PUNCT
ejpam-1951	636	28	.	.	PUNCT
ejpam-1951	636	29	.	.	PUNCT
ejpam-1951	636	30	.	.	PUNCT
ejpam-1951	637	1	theorem	theorem	ADJ
ejpam-1951	637	2	5	5	NUM
ejpam-1951	637	3	.	.	PUNCT
ejpam-1951	638	1	the	the	DET
ejpam-1951	638	2	total	total	ADJ
ejpam-1951	638	3	number	number	NOUN
ejpam-1951	638	4	of	of	ADP
ejpam-1951	638	5	patterns	pattern	NOUN
ejpam-1951	638	6	of	of	ADP
ejpam-1951	638	7	mapping	mapping	NOUN
ejpam-1951	638	8	of	of	ADP
ejpam-1951	638	9	x	x	PUNCT
ejpam-1951	638	10	into	into	ADP
ejpam-1951	638	11	y	y	PROPN
ejpam-1951	638	12	equals	equal	VERB
ejpam-1951	638	13	zg	zg	PROPN
ejpam-1951	638	14	�	�	PROPN
ejpam-1951	638	15	∂	∂	NUM
ejpam-1951	638	16	∂	∂	NOUN
ejpam-1951	638	17	z1	z1	NOUN
ejpam-1951	638	18	,	,	PUNCT
ejpam-1951	638	19	∂	∂	NUM
ejpam-1951	638	20	∂	∂	NOUN
ejpam-1951	638	21	z2	z2	PROPN
ejpam-1951	638	22	,	,	PUNCT
ejpam-1951	638	23	∂	∂	NUM
ejpam-1951	638	24	∂	∂	NUM
ejpam-1951	638	25	z3	z3	PROPN
ejpam-1951	638	26	,	,	PUNCT
ejpam-1951	638	27	.	.	PUNCT
ejpam-1951	638	28	.	.	PUNCT
ejpam-1951	638	29	.	.	PUNCT
ejpam-1951	639	1	�	�	PROPN
ejpam-1951	639	2	zh[e	zh[e	PROPN
ejpam-1951	639	3	z1+z2+z3	z1+z2+z3	PROPN
ejpam-1951	639	4	+	+	PROPN
ejpam-1951	639	5	...	...	PUNCT
ejpam-1951	639	6	,	,	PUNCT
ejpam-1951	639	7	e2(z2+z4+z6	e2(z2+z4+z6	VERB
ejpam-1951	639	8	+	+	NOUN
ejpam-1951	639	9	...	...	PUNCT
ejpam-1951	639	10	)	)	PUNCT
ejpam-1951	639	11	,	,	PUNCT
ejpam-1951	639	12	e3(z3+z6+z9	e3(z3+z6+z9	NOUN
ejpam-1951	639	13	+	+	NOUN
ejpam-1951	639	14	...	...	PUNCT
ejpam-1951	639	15	)	)	PUNCT
ejpam-1951	639	16	,	,	PUNCT
ejpam-1951	639	17	.	.	PUNCT
ejpam-1951	639	18	.	.	PUNCT
ejpam-1951	640	1	.	.	PUNCT
ejpam-1951	640	2	]	]	PUNCT
ejpam-1951	641	1	evaluated	evaluate	VERB
ejpam-1951	641	2	at	at	ADP
ejpam-1951	641	3	z1	z1	ADJ
ejpam-1951	641	4	=	=	SYM
ejpam-1951	641	5	z2	z2	PROPN
ejpam-1951	641	6	=	=	SYM
ejpam-1951	641	7	z3	z3	PROPN
ejpam-1951	641	8	=	=	PUNCT
ejpam-1951	641	9	.	.	PUNCT
ejpam-1951	641	10	.	.	PUNCT
ejpam-1951	642	1	.=	.=	VERB
ejpam-1951	643	1	0	0	X
ejpam-1951	643	2	.	.	PUNCT
ejpam-1951	644	1	there	there	PRON
ejpam-1951	644	2	is	be	VERB
ejpam-1951	644	3	a	a	DET
ejpam-1951	644	4	second	second	ADJ
ejpam-1951	644	5	expression	expression	NOUN
ejpam-1951	644	6	for	for	ADP
ejpam-1951	644	7	the	the	DET
ejpam-1951	644	8	number	number	NOUN
ejpam-1951	644	9	of	of	ADP
ejpam-1951	644	10	patterns	pattern	NOUN
ejpam-1951	644	11	,	,	PUNCT
ejpam-1951	644	12	which	which	PRON
ejpam-1951	644	13	sometimes	sometimes	ADV
ejpam-1951	644	14	may	may	AUX
ejpam-1951	644	15	turn	turn	VERB
ejpam-1951	644	16	out	out	ADP
ejpam-1951	644	17	to	to	PART
ejpam-1951	644	18	be	be	AUX
ejpam-1951	644	19	simpler	simple	ADJ
ejpam-1951	644	20	to	to	PART
ejpam-1951	644	21	handle	handle	VERB
ejpam-1951	644	22	.	.	PUNCT
ejpam-1951	645	1	note	note	VERB
ejpam-1951	645	2	that	that	SCONJ
ejpam-1951	645	3	(	(	PUNCT
ejpam-1951	645	4	5	5	X
ejpam-1951	645	5	)	)	PUNCT
ejpam-1951	645	6	is	be	AUX
ejpam-1951	645	7	obtained	obtain	VERB
ejpam-1951	645	8	by	by	ADP
ejpam-1951	645	9	substituting	substitute	VERB
ejpam-1951	645	10	t1	t1	PROPN
ejpam-1951	645	11	=	=	SYM
ejpam-1951	645	12	c1	c1	PROPN
ejpam-1951	645	13	,	,	PUNCT
ejpam-1951	645	14	t2	t2	PROPN
ejpam-1951	645	15	=	=	PROPN
ejpam-1951	645	16	c1	c1	PROPN
ejpam-1951	645	17	+	+	CCONJ
ejpam-1951	645	18	2c2	2c2	NUM
ejpam-1951	645	19	,	,	PUNCT
ejpam-1951	645	20	.	.	PUNCT
ejpam-1951	645	21	.	.	PUNCT
ejpam-1951	646	1	.	.	PUNCT
ejpam-1951	647	1	into	into	ADP
ejpam-1951	647	2	t	t	PROPN
ejpam-1951	647	3	g1	g1	PROPN
ejpam-1951	647	4	1	1	NUM
ejpam-1951	647	5	t	t	NOUN
ejpam-1951	647	6	g2	g2	PROPN
ejpam-1951	647	7	2	2	NUM
ejpam-1951	647	8	.	.	PUNCT
ejpam-1951	647	9	.	.	PUNCT
ejpam-1951	648	1	..	..	PUNCT
ejpam-1951	648	2	summing	sum	VERB
ejpam-1951	648	3	for	for	ADP
ejpam-1951	648	4	g	g	NOUN
ejpam-1951	648	5	and	and	CCONJ
ejpam-1951	648	6	dividing	divide	VERB
ejpam-1951	648	7	by	by	ADP
ejpam-1951	648	8	|g|	|g|	PROPN
ejpam-1951	648	9	,	,	PUNCT
ejpam-1951	648	10	we	we	PRON
ejpam-1951	648	11	obtain	obtain	VERB
ejpam-1951	648	12	zg(c1	zg(c1	NOUN
ejpam-1951	648	13	,	,	PUNCT
ejpam-1951	648	14	c1	c1	PROPN
ejpam-1951	648	15	+	+	CCONJ
ejpam-1951	648	16	2c2	2c2	NUM
ejpam-1951	648	17	,	,	PUNCT
ejpam-1951	648	18	c1	c1	NOUN
ejpam-1951	648	19	+	+	CCONJ
ejpam-1951	648	20	3c3	3c3	NUM
ejpam-1951	648	21	,	,	PUNCT
ejpam-1951	648	22	c1	c1	NOUN
ejpam-1951	648	23	+	+	CCONJ
ejpam-1951	648	24	2c2	2c2	NUM
ejpam-1951	648	25	+	+	CCONJ
ejpam-1951	648	26	4c4	4c4	NUM
ejpam-1951	648	27	,	,	PUNCT
ejpam-1951	648	28	.	.	PUNCT
ejpam-1951	648	29	.	.	PUNCT
ejpam-1951	649	1	.	.	PUNCT
ejpam-1951	649	2	)	)	PUNCT
ejpam-1951	649	3	,	,	PUNCT
ejpam-1951	649	4	in	in	ADP
ejpam-1951	649	5	which	which	PRON
ejpam-1951	649	6	the	the	DET
ejpam-1951	649	7	ith	ith	ADJ
ejpam-1951	649	8	argument	argument	NOUN
ejpam-1951	649	9	is	be	AUX
ejpam-1951	649	10	∑	∑	PROPN
ejpam-1951	649	11	j	j	PROPN
ejpam-1951	649	12	/	/	SYM
ejpam-1951	649	13	i	i	PROPN
ejpam-1951	649	14	jc	jc	PROPN
ejpam-1951	649	15	j	j	PROPN
ejpam-1951	649	16	.	.	PUNCT
ejpam-1951	650	1	thus	thus	ADV
ejpam-1951	650	2	again	again	ADV
ejpam-1951	650	3	using	use	VERB
ejpam-1951	650	4	lemma	lemma	PROPN
ejpam-1951	650	5	2	2	NUM
ejpam-1951	650	6	for	for	ADP
ejpam-1951	650	7	the	the	DET
ejpam-1951	650	8	number	number	NOUN
ejpam-1951	650	9	of	of	ADP
ejpam-1951	650	10	patterns	pattern	NOUN
ejpam-1951	650	11	we	we	PRON
ejpam-1951	650	12	have	have	VERB
ejpam-1951	650	13	|h|−1	|h|−1	VERB
ejpam-1951	650	14	∑	∑	X
ejpam-1951	650	15	h∈h	h∈h	PROPN
ejpam-1951	650	16	zg(c1	zg(c1	PROPN
ejpam-1951	650	17	,	,	PUNCT
ejpam-1951	650	18	c1	c1	PROPN
ejpam-1951	650	19	+	+	CCONJ
ejpam-1951	650	20	2c2	2c2	NUM
ejpam-1951	650	21	,	,	PUNCT
ejpam-1951	650	22	c1	c1	NOUN
ejpam-1951	650	23	+	+	CCONJ
ejpam-1951	650	24	3c3	3c3	NUM
ejpam-1951	650	25	,	,	PUNCT
ejpam-1951	650	26	c1	c1	NOUN
ejpam-1951	650	27	+	+	CCONJ
ejpam-1951	650	28	2c2	2c2	NUM
ejpam-1951	650	29	+	+	CCONJ
ejpam-1951	650	30	4c4	4c4	NUM
ejpam-1951	650	31	,	,	PUNCT
ejpam-1951	650	32	.	.	PUNCT
ejpam-1951	650	33	.	.	PUNCT
ejpam-1951	650	34	.	.	PUNCT
ejpam-1951	650	35	)	)	PUNCT
ejpam-1951	651	1	here	here	ADV
ejpam-1951	651	2	it	it	PRON
ejpam-1951	651	3	has	have	VERB
ejpam-1951	651	4	to	to	PART
ejpam-1951	651	5	be	be	AUX
ejpam-1951	651	6	remembered	remember	VERB
ejpam-1951	651	7	that	that	SCONJ
ejpam-1951	651	8	{	{	PUNCT
ejpam-1951	651	9	c1	c1	PROPN
ejpam-1951	651	10	,	,	PUNCT
ejpam-1951	651	11	c2	c2	PROPN
ejpam-1951	651	12	,	,	PUNCT
ejpam-1951	651	13	c3	c3	PROPN
ejpam-1951	651	14	,	,	PUNCT
ejpam-1951	651	15	.	.	PUNCT
ejpam-1951	651	16	.	.	PUNCT
ejpam-1951	652	1	.	.	PUNCT
ejpam-1951	652	2	}	}	PUNCT
ejpam-1951	652	3	is	be	AUX
ejpam-1951	652	4	of	of	ADP
ejpam-1951	652	5	type	type	NOUN
ejpam-1951	652	6	h	h	NOUN
ejpam-1951	653	1	[	[	X
ejpam-1951	653	2	2	2	NUM
ejpam-1951	653	3	]	]	PUNCT
ejpam-1951	653	4	.	.	PUNCT
ejpam-1951	654	1	now	now	ADV
ejpam-1951	654	2	we	we	PRON
ejpam-1951	654	3	are	be	AUX
ejpam-1951	654	4	going	go	VERB
ejpam-1951	654	5	to	to	PART
ejpam-1951	654	6	discuss	discuss	VERB
ejpam-1951	654	7	some	some	PRON
ejpam-1951	654	8	of	of	ADP
ejpam-1951	654	9	the	the	DET
ejpam-1951	654	10	examples	example	NOUN
ejpam-1951	654	11	.	.	PUNCT
ejpam-1951	655	1	in	in	ADP
ejpam-1951	655	2	all	all	DET
ejpam-1951	655	3	cases	case	NOUN
ejpam-1951	655	4	,	,	PUNCT
ejpam-1951	655	5	m	m	VERB
ejpam-1951	655	6	and	and	CCONJ
ejpam-1951	655	7	n	n	ADV
ejpam-1951	655	8	stand	stand	VERB
ejpam-1951	655	9	for	for	ADP
ejpam-1951	655	10	the	the	DET
ejpam-1951	655	11	number	number	NOUN
ejpam-1951	655	12	of	of	ADP
ejpam-1951	655	13	elements	element	NOUN
ejpam-1951	655	14	of	of	ADP
ejpam-1951	655	15	x	x	X
ejpam-1951	655	16	and	and	CCONJ
ejpam-1951	655	17	y	y	PROPN
ejpam-1951	655	18	respectively	respectively	ADV
ejpam-1951	655	19	.	.	PUNCT
ejpam-1951	655	20	example	example	NOUN
ejpam-1951	656	1	16	16	NUM
ejpam-1951	656	2	.	.	PUNCT
ejpam-1951	657	1	let	let	VERB
ejpam-1951	657	2	g	g	PRON
ejpam-1951	657	3	be	be	AUX
ejpam-1951	657	4	a	a	DET
ejpam-1951	657	5	group	group	NOUN
ejpam-1951	657	6	consisting	consist	VERB
ejpam-1951	657	7	of	of	ADP
ejpam-1951	657	8	the	the	DET
ejpam-1951	657	9	identity	identity	NOUN
ejpam-1951	657	10	only	only	ADV
ejpam-1951	657	11	,	,	PUNCT
ejpam-1951	657	12	where	where	SCONJ
ejpam-1951	657	13	zg	zg	PROPN
ejpam-1951	657	14	=	=	PUNCT
ejpam-1951	657	15	tm	tm	PROPN
ejpam-1951	657	16	1	1	NUM
ejpam-1951	657	17	.	.	PUNCT
ejpam-1951	658	1	then	then	ADV
ejpam-1951	658	2	the	the	DET
ejpam-1951	658	3	patterns	pattern	NOUN
ejpam-1951	658	4	are	be	AUX
ejpam-1951	658	5	called	call	VERB
ejpam-1951	658	6	patterns	pattern	NOUN
ejpam-1951	658	7	of	of	ADP
ejpam-1951	658	8	variation	variation	NOUN
ejpam-1951	658	9	with	with	ADP
ejpam-1951	658	10	repetition	repetition	NOUN
ejpam-1951	658	11	.	.	PUNCT
ejpam-1951	659	1	now	now	ADV
ejpam-1951	659	2	let	let	VERB
ejpam-1951	659	3	{	{	PUNCT
ejpam-1951	659	4	1,2	1,2	NUM
ejpam-1951	659	5	,	,	PUNCT
ejpam-1951	659	6	.	.	PUNCT
ejpam-1951	659	7	.	.	PUNCT
ejpam-1951	659	8	.	.	PUNCT
ejpam-1951	660	1	,	,	PUNCT
ejpam-1951	660	2	m	m	AUX
ejpam-1951	660	3	}	}	PUNCT
ejpam-1951	660	4	be	be	AUX
ejpam-1951	660	5	a	a	DET
ejpam-1951	660	6	sequence	sequence	NOUN
ejpam-1951	660	7	of	of	ADP
ejpam-1951	660	8	x	x	PUNCT
ejpam-1951	660	9	then	then	ADV
ejpam-1951	660	10	for	for	ADP
ejpam-1951	660	11	each	each	DET
ejpam-1951	660	12	f	f	PROPN
ejpam-1951	660	13	∈	∈	PROPN
ejpam-1951	660	14	x	x	SYM
ejpam-1951	660	15	y	y	PROPN
ejpam-1951	660	16	,	,	PUNCT
ejpam-1951	660	17	the	the	DET
ejpam-1951	660	18	sequence	sequence	NOUN
ejpam-1951	660	19	{	{	PUNCT
ejpam-1951	660	20	f	f	X
ejpam-1951	660	21	(	(	PUNCT
ejpam-1951	660	22	1	1	NUM
ejpam-1951	660	23	)	)	PUNCT
ejpam-1951	660	24	,	,	PUNCT
ejpam-1951	660	25	f	f	PROPN
ejpam-1951	660	26	(	(	PUNCT
ejpam-1951	660	27	2	2	NUM
ejpam-1951	660	28	)	)	PUNCT
ejpam-1951	660	29	,	,	PUNCT
ejpam-1951	660	30	.	.	PUNCT
ejpam-1951	660	31	.	.	PUNCT
ejpam-1951	661	1	.	.	PUNCT
ejpam-1951	662	1	,	,	PUNCT
ejpam-1951	662	2	f	f	PROPN
ejpam-1951	662	3	(	(	PUNCT
ejpam-1951	662	4	m	m	NOUN
ejpam-1951	662	5	)	)	PUNCT
ejpam-1951	662	6	}	}	PUNCT
ejpam-1951	662	7	shows	show	VERB
ejpam-1951	662	8	repetitions	repetition	NOUN
ejpam-1951	662	9	.	.	PUNCT
ejpam-1951	663	1	for	for	ADP
ejpam-1951	663	2	the	the	DET
ejpam-1951	663	3	number	number	NOUN
ejpam-1951	663	4	of	of	ADP
ejpam-1951	663	5	patterns	pattern	NOUN
ejpam-1951	663	6	,	,	PUNCT
ejpam-1951	663	7	theorem	theorem	VERB
ejpam-1951	663	8	4	4	NUM
ejpam-1951	663	9	gives	give	VERB
ejpam-1951	663	10	the	the	DET
ejpam-1951	663	11	expression	expression	NOUN
ejpam-1951	663	12	�	�	NOUN
ejpam-1951	663	13	�	�	PROPN
ejpam-1951	663	14	d	d	PROPN
ejpam-1951	663	15	dz	dz	PROPN
ejpam-1951	663	16	�	�	PROPN
ejpam-1951	663	17	m	m	PROPN
ejpam-1951	663	18	zh(e	zh(e	PROPN
ejpam-1951	663	19	z	z	PROPN
ejpam-1951	663	20	,	,	PUNCT
ejpam-1951	663	21	1	1	NUM
ejpam-1951	663	22	,	,	PUNCT
ejpam-1951	663	23	1	1	NUM
ejpam-1951	663	24	,	,	PUNCT
ejpam-1951	663	25	.	.	PUNCT
ejpam-1951	663	26	.	.	PUNCT
ejpam-1951	664	1	.	.	PUNCT
ejpam-1951	664	2	)	)	PUNCT
ejpam-1951	665	1	�	�	PROPN
ejpam-1951	665	2	z=0	z=0	PROPN
ejpam-1951	665	3	(	(	PUNCT
ejpam-1951	665	4	6	6	NUM
ejpam-1951	665	5	)	)	PUNCT
ejpam-1951	665	6	a	a	DET
ejpam-1951	665	7	second	second	ADJ
ejpam-1951	665	8	specialization	specialization	NOUN
ejpam-1951	665	9	of	of	ADP
ejpam-1951	665	10	(	(	PUNCT
ejpam-1951	665	11	6	6	NUM
ejpam-1951	665	12	)	)	PUNCT
ejpam-1951	665	13	can	can	AUX
ejpam-1951	665	14	be	be	AUX
ejpam-1951	665	15	obtained	obtain	VERB
ejpam-1951	665	16	by	by	ADP
ejpam-1951	665	17	keeping	keep	VERB
ejpam-1951	665	18	y	y	PROPN
ejpam-1951	665	19	and	and	CCONJ
ejpam-1951	665	20	h	h	PROPN
ejpam-1951	665	21	general	general	ADJ
ejpam-1951	665	22	but	but	CCONJ
ejpam-1951	665	23	x	x	PRON
ejpam-1951	665	24	has	have	VERB
ejpam-1951	665	25	only	only	ADV
ejpam-1951	665	26	one	one	NUM
ejpam-1951	665	27	element	element	NOUN
ejpam-1951	665	28	d1	d1	NOUN
ejpam-1951	665	29	.	.	PUNCT
ejpam-1951	666	1	now	now	ADV
ejpam-1951	666	2	two	two	NUM
ejpam-1951	666	3	functions	function	NOUN
ejpam-1951	666	4	f1	f1	NOUN
ejpam-1951	666	5	and	and	CCONJ
ejpam-1951	666	6	f2	f2	PROPN
ejpam-1951	666	7	are	be	AUX
ejpam-1951	666	8	equivalent	equivalent	ADJ
ejpam-1951	666	9	if	if	SCONJ
ejpam-1951	666	10	and	and	CCONJ
ejpam-1951	666	11	only	only	ADV
ejpam-1951	666	12	if	if	SCONJ
ejpam-1951	666	13	f1(d1	f1(d1	ADJ
ejpam-1951	666	14	)	)	PUNCT
ejpam-1951	666	15	are	be	AUX
ejpam-1951	666	16	mapped	map	VERB
ejpam-1951	666	17	to	to	ADP
ejpam-1951	666	18	f2(d1	f2(d1	NOUN
ejpam-1951	666	19	)	)	PUNCT
ejpam-1951	666	20	.	.	PUNCT
ejpam-1951	667	1	so	so	ADV
ejpam-1951	667	2	the	the	DET
ejpam-1951	667	3	number	number	NOUN
ejpam-1951	667	4	of	of	ADP
ejpam-1951	667	5	patterns	pattern	NOUN
ejpam-1951	667	6	is	be	AUX
ejpam-1951	667	7	the	the	DET
ejpam-1951	667	8	number	number	NOUN
ejpam-1951	667	9	of	of	ADP
ejpam-1951	667	10	transitive	transitive	ADJ
ejpam-1951	667	11	sets	set	NOUN
ejpam-1951	667	12	.	.	PUNCT
ejpam-1951	668	1	if	if	SCONJ
ejpam-1951	668	2	we	we	PRON
ejpam-1951	668	3	take	take	VERB
ejpam-1951	668	4	m	m	VERB
ejpam-1951	668	5	=	=	NOUN
ejpam-1951	668	6	1	1	NUM
ejpam-1951	668	7	in	in	ADP
ejpam-1951	668	8	(	(	PUNCT
ejpam-1951	668	9	6	6	NUM
ejpam-1951	668	10	)	)	PUNCT
ejpam-1951	668	11	then	then	ADV
ejpam-1951	668	12	we	we	PRON
ejpam-1951	668	13	get	get	VERB
ejpam-1951	668	14	|h|−1c1	|h|−1c1	NOUN
ejpam-1951	668	15	and	and	CCONJ
ejpam-1951	668	16	c1	c1	NOUN
ejpam-1951	668	17	is	be	AUX
ejpam-1951	668	18	the	the	DET
ejpam-1951	668	19	number	number	NOUN
ejpam-1951	668	20	of	of	ADP
ejpam-1951	668	21	elements	element	NOUN
ejpam-1951	668	22	of	of	ADP
ejpam-1951	668	23	y	y	PRON
ejpam-1951	668	24	that	that	PRON
ejpam-1951	668	25	are	be	AUX
ejpam-1951	668	26	invariant	invariant	ADJ
ejpam-1951	668	27	under	under	ADP
ejpam-1951	668	28	the	the	DET
ejpam-1951	668	29	permutation	permutation	NOUN
ejpam-1951	668	30	h	h	NOUN
ejpam-1951	669	1	[	[	X
ejpam-1951	669	2	2	2	NUM
ejpam-1951	669	3	]	]	PUNCT
ejpam-1951	669	4	.	.	PUNCT
ejpam-1951	670	1	example	example	NOUN
ejpam-1951	670	2	17	17	NUM
ejpam-1951	670	3	.	.	PUNCT
ejpam-1951	671	1	again	again	ADV
ejpam-1951	671	2	let	let	VERB
ejpam-1951	671	3	g	g	NOUN
ejpam-1951	671	4	be	be	AUX
ejpam-1951	671	5	the	the	DET
ejpam-1951	671	6	symmetric	symmetric	ADJ
ejpam-1951	671	7	group	group	NOUN
ejpam-1951	671	8	of	of	ADP
ejpam-1951	671	9	x	x	PUNCT
ejpam-1951	671	10	with	with	SCONJ
ejpam-1951	671	11	h	h	NOUN
ejpam-1951	671	12	not	not	PART
ejpam-1951	671	13	specified	specify	VERB
ejpam-1951	671	14	.	.	PUNCT
ejpam-1951	672	1	we	we	PRON
ejpam-1951	672	2	are	be	AUX
ejpam-1951	672	3	only	only	ADV
ejpam-1951	672	4	interested	interested	ADJ
ejpam-1951	672	5	in	in	ADP
ejpam-1951	672	6	the	the	DET
ejpam-1951	672	7	number	number	NOUN
ejpam-1951	672	8	of	of	ADP
ejpam-1951	672	9	elements	element	NOUN
ejpam-1951	672	10	of	of	ADP
ejpam-1951	672	11	x	x	PUNCT
ejpam-1951	672	12	that	that	SCONJ
ejpam-1951	672	13	a	a	DET
ejpam-1951	672	14	function	function	NOUN
ejpam-1951	672	15	f	f	PROPN
ejpam-1951	672	16	maps	map	NOUN
ejpam-1951	672	17	onto	onto	ADP
ejpam-1951	672	18	a	a	DET
ejpam-1951	672	19	given	give	VERB
ejpam-1951	672	20	element	element	NOUN
ejpam-1951	672	21	of	of	ADP
ejpam-1951	672	22	y	y	PROPN
ejpam-1951	672	23	.	.	PUNCT
ejpam-1951	673	1	thus	thus	ADV
ejpam-1951	673	2	our	our	PRON
ejpam-1951	673	3	patterns	pattern	NOUN
ejpam-1951	673	4	of	of	ADP
ejpam-1951	673	5	mappings	mapping	NOUN
ejpam-1951	673	6	ψ	ψ	X
ejpam-1951	673	7	of	of	ADP
ejpam-1951	673	8	y	y	PROPN
ejpam-1951	673	9	into	into	ADP
ejpam-1951	673	10	the	the	DET
ejpam-1951	673	11	set	set	NOUN
ejpam-1951	673	12	p	p	X
ejpam-1951	673	13	=	=	X
ejpam-1951	673	14	{	{	PUNCT
ejpam-1951	673	15	0,1,2	0,1,2	NOUN
ejpam-1951	673	16	,	,	PUNCT
ejpam-1951	673	17	.	.	PUNCT
ejpam-1951	673	18	.	.	PUNCT
ejpam-1951	674	1	.	.	PUNCT
ejpam-1951	674	2	}	}	PUNCT
ejpam-1951	675	1	,	,	PUNCT
ejpam-1951	675	2	with	with	ADP
ejpam-1951	675	3	restriction	restriction	NOUN
ejpam-1951	675	4	∑	∑	PUNCT
ejpam-1951	675	5	r∈rψ(r	r∈rψ(r	PROPN
ejpam-1951	675	6	)	)	PUNCT
ejpam-1951	675	7	=	=	SYM
ejpam-1951	675	8	m	m	PROPN
ejpam-1951	675	9	,	,	PUNCT
ejpam-1951	675	10	t.	t.	PROPN
ejpam-1951	675	11	nasseef	nasseef	PROPN
ejpam-1951	675	12	/	/	SYM
ejpam-1951	675	13	eur	eur	PROPN
ejpam-1951	675	14	.	.	PUNCT
ejpam-1951	676	1	j.	j.	PROPN
ejpam-1951	676	2	pure	pure	PROPN
ejpam-1951	676	3	appl	appl	PROPN
ejpam-1951	676	4	.	.	PROPN
ejpam-1951	676	5	math	math	PROPN
ejpam-1951	676	6	,	,	PUNCT
ejpam-1951	676	7	9	9	NUM
ejpam-1951	676	8	(	(	PUNCT
ejpam-1951	676	9	2016	2016	NUM
ejpam-1951	676	10	)	)	PUNCT
ejpam-1951	676	11	,	,	PUNCT
ejpam-1951	676	12	84	84	NUM
ejpam-1951	676	13	-	-	SYM
ejpam-1951	676	14	113	113	NUM
ejpam-1951	676	15	107	107	NUM
ejpam-1951	676	16	whereas	whereas	SCONJ
ejpam-1951	676	17	patterns	pattern	NOUN
ejpam-1951	676	18	are	be	AUX
ejpam-1951	676	19	formed	form	VERB
ejpam-1951	676	20	with	with	ADP
ejpam-1951	676	21	respect	respect	NOUN
ejpam-1951	676	22	to	to	ADP
ejpam-1951	676	23	h	h	NOUN
ejpam-1951	676	24	acting	act	VERB
ejpam-1951	676	25	on	on	ADP
ejpam-1951	676	26	y	y	PROPN
ejpam-1951	676	27	.	.	PUNCT
ejpam-1951	677	1	let	let	VERB
ejpam-1951	677	2	the	the	DET
ejpam-1951	677	3	weights	weight	NOUN
ejpam-1951	677	4	of	of	ADP
ejpam-1951	677	5	p	p	NOUN
ejpam-1951	677	6	be	be	AUX
ejpam-1951	677	7	1	1	NUM
ejpam-1951	677	8	,	,	PUNCT
ejpam-1951	677	9	w1	w1	NOUN
ejpam-1951	677	10	,	,	PUNCT
ejpam-1951	677	11	w2	w2	NOUN
ejpam-1951	677	12	,	,	PUNCT
ejpam-1951	677	13	.	.	PUNCT
ejpam-1951	677	14	.	.	PUNCT
ejpam-1951	678	1	..	..	PUNCT
ejpam-1951	679	1	if	if	SCONJ
ejpam-1951	679	2	we	we	PRON
ejpam-1951	679	3	apply	apply	VERB
ejpam-1951	679	4	theorem	theorem	NOUN
ejpam-1951	679	5	4	4	NUM
ejpam-1951	679	6	,	,	PUNCT
ejpam-1951	679	7	we	we	PRON
ejpam-1951	679	8	have	have	VERB
ejpam-1951	679	9	as	as	ADP
ejpam-1951	679	10	differential	differential	ADJ
ejpam-1951	679	11	operator	operator	NOUN
ejpam-1951	679	12	the	the	DET
ejpam-1951	679	13	coefficient	coefficient	NOUN
ejpam-1951	679	14	of	of	ADP
ejpam-1951	679	15	wm	wm	PROPN
ejpam-1951	679	16	in	in	ADP
ejpam-1951	679	17	ex	ex	X
ejpam-1951	679	18	p(w	p(w	PROPN
ejpam-1951	679	19	∂	∂	NUM
ejpam-1951	679	20	∂	∂	NOUN
ejpam-1951	680	1	z1	z1	NOUN
ejpam-1951	681	1	+	+	CCONJ
ejpam-1951	681	2	1	1	NUM
ejpam-1951	681	3	2	2	NUM
ejpam-1951	681	4	w2	w2	NOUN
ejpam-1951	681	5	∂	∂	NUM
ejpam-1951	681	6	∂	∂	NOUN
ejpam-1951	681	7	z2	z2	PROPN
ejpam-1951	681	8	+	+	PUNCT
ejpam-1951	681	9	.	.	PUNCT
ejpam-1951	681	10	.	.	PUNCT
ejpam-1951	681	11	.	.	PUNCT
ejpam-1951	681	12	)	)	PUNCT
ejpam-1951	682	1	by	by	ADP
ejpam-1951	682	2	example	example	NOUN
ejpam-1951	682	3	5	5	NUM
ejpam-1951	682	4	.	.	PUNCT
ejpam-1951	683	1	the	the	DET
ejpam-1951	683	2	effect	effect	NOUN
ejpam-1951	683	3	of	of	ADP
ejpam-1951	683	4	this	this	DET
ejpam-1951	683	5	operator	operator	NOUN
ejpam-1951	683	6	on	on	ADP
ejpam-1951	683	7	a	a	DET
ejpam-1951	683	8	function	function	NOUN
ejpam-1951	683	9	ψ(z1	ψ(z1	NOUN
ejpam-1951	683	10	,	,	PUNCT
ejpam-1951	683	11	z2	z2	PROPN
ejpam-1951	683	12	,	,	PUNCT
ejpam-1951	683	13	.	.	PUNCT
ejpam-1951	683	14	.	.	PUNCT
ejpam-1951	683	15	.	.	PUNCT
ejpam-1951	683	16	)	)	PUNCT
ejpam-1951	684	1	at	at	ADP
ejpam-1951	684	2	z1	z1	NOUN
ejpam-1951	684	3	=	=	SYM
ejpam-1951	684	4	z2	z2	PROPN
ejpam-1951	684	5	=	=	PUNCT
ejpam-1951	684	6	.	.	PUNCT
ejpam-1951	684	7	.	.	PUNCT
ejpam-1951	684	8	.	.	PUNCT
ejpam-1951	685	1	=	=	PUNCT
ejpam-1951	685	2	0	0	NUM
ejpam-1951	685	3	is	be	AUX
ejpam-1951	685	4	ψ(w	ψ(w	PROPN
ejpam-1951	685	5	,	,	PUNCT
ejpam-1951	685	6	1	1	NUM
ejpam-1951	685	7	2	2	NUM
ejpam-1951	685	8	w2	w2	NOUN
ejpam-1951	685	9	,	,	PUNCT
ejpam-1951	685	10	1	1	NUM
ejpam-1951	685	11	3	3	NUM
ejpam-1951	685	12	w3	w3	NOUN
ejpam-1951	685	13	,	,	PUNCT
ejpam-1951	685	14	.	.	PUNCT
ejpam-1951	685	15	.	.	PUNCT
ejpam-1951	685	16	.	.	PUNCT
ejpam-1951	685	17	)	)	PUNCT
ejpam-1951	685	18	.	.	PUNCT
ejpam-1951	686	1	now	now	ADV
ejpam-1951	686	2	by	by	ADP
ejpam-1951	686	3	substituting	substitute	VERB
ejpam-1951	686	4	z1	z1	PROPN
ejpam-1951	686	5	=	=	SYM
ejpam-1951	686	6	w	w	PROPN
ejpam-1951	686	7	,	,	PUNCT
ejpam-1951	686	8	z2	z2	NOUN
ejpam-1951	686	9	=	=	SYM
ejpam-1951	686	10	1	1	NUM
ejpam-1951	686	11	2	2	NUM
ejpam-1951	686	12	w2	w2	NOUN
ejpam-1951	686	13	,	,	PUNCT
ejpam-1951	686	14	z3	z3	PROPN
ejpam-1951	686	15	=	=	SYM
ejpam-1951	686	16	1	1	NUM
ejpam-1951	686	17	3	3	NUM
ejpam-1951	686	18	w3	w3	NOUN
ejpam-1951	686	19	,	,	PUNCT
ejpam-1951	686	20	.	.	PUNCT
ejpam-1951	686	21	.	.	PUNCT
ejpam-1951	686	22	.	.	PUNCT
ejpam-1951	687	1	in	in	ADP
ejpam-1951	687	2	theorem	theorem	NOUN
ejpam-1951	687	3	4	4	NUM
ejpam-1951	687	4	we	we	PRON
ejpam-1951	687	5	get	get	VERB
ejpam-1951	687	6	ex	ex	PRON
ejpam-1951	687	7	p(z1	p(z1	ADJ
ejpam-1951	687	8	+	+	CCONJ
ejpam-1951	687	9	z2	z2	PROPN
ejpam-1951	687	10	+	+	CCONJ
ejpam-1951	687	11	.	.	PUNCT
ejpam-1951	687	12	.	.	PUNCT
ejpam-1951	687	13	.	.	PUNCT
ejpam-1951	687	14	)	)	PUNCT
ejpam-1951	688	1	=	=	PRON
ejpam-1951	688	2	ex	ex	X
ejpam-1951	688	3	p(w+	p(w+	NOUN
ejpam-1951	688	4	1	1	NUM
ejpam-1951	688	5	2	2	NUM
ejpam-1951	688	6	w2	w2	NOUN
ejpam-1951	688	7	+	+	CCONJ
ejpam-1951	688	8	1	1	NUM
ejpam-1951	688	9	3	3	NUM
ejpam-1951	688	10	w3	w3	NOUN
ejpam-1951	688	11	+	+	X
ejpam-1951	688	12	.	.	PUNCT
ejpam-1951	688	13	.	.	PUNCT
ejpam-1951	688	14	.	.	PUNCT
ejpam-1951	688	15	)	)	PUNCT
ejpam-1951	689	1	=	=	PUNCT
ejpam-1951	689	2	(	(	PUNCT
ejpam-1951	689	3	1−	1−	NUM
ejpam-1951	689	4	w)−1	w)−1	NOUN
ejpam-1951	689	5	ex	ex	X
ejpam-1951	689	6	p(2(z2	p(2(z2	NOUN
ejpam-1951	689	7	+	+	CCONJ
ejpam-1951	689	8	z4	z4	PROPN
ejpam-1951	689	9	+	+	CCONJ
ejpam-1951	689	10	.	.	PUNCT
ejpam-1951	689	11	.	.	PUNCT
ejpam-1951	689	12	.	.	PUNCT
ejpam-1951	689	13	)	)	PUNCT
ejpam-1951	689	14	)	)	PUNCT
ejpam-1951	690	1	=	=	PRON
ejpam-1951	690	2	ex	ex	NOUN
ejpam-1951	690	3	p(w2	p(w2	NOUN
ejpam-1951	690	4	+	+	CCONJ
ejpam-1951	690	5	1	1	NUM
ejpam-1951	690	6	2	2	NUM
ejpam-1951	690	7	w4	w4	NOUN
ejpam-1951	690	8	+	+	CCONJ
ejpam-1951	690	9	1	1	NUM
ejpam-1951	690	10	3	3	NUM
ejpam-1951	690	11	w6	w6	PROPN
ejpam-1951	690	12	+	+	CCONJ
ejpam-1951	690	13	.	.	PUNCT
ejpam-1951	690	14	.	.	PUNCT
ejpam-1951	690	15	.	.	PUNCT
ejpam-1951	690	16	)	)	PUNCT
ejpam-1951	691	1	=	=	PUNCT
ejpam-1951	691	2	(	(	PUNCT
ejpam-1951	691	3	1−	1−	NUM
ejpam-1951	691	4	w2)−1	w2)−1	X
ejpam-1951	691	5	etc	etc	X
ejpam-1951	691	6	.	.	X
ejpam-1951	692	1	thus	thus	ADV
ejpam-1951	692	2	we	we	PRON
ejpam-1951	692	3	obtain	obtain	VERB
ejpam-1951	692	4	zh[(1−w)−1	zh[(1−w)−1	NUM
ejpam-1951	692	5	,	,	PUNCT
ejpam-1951	692	6	(	(	PUNCT
ejpam-1951	692	7	1−	1−	NUM
ejpam-1951	692	8	w2)−1	w2)−1	NOUN
ejpam-1951	692	9	,	,	PUNCT
ejpam-1951	692	10	.	.	PUNCT
ejpam-1951	692	11	.	.	PUNCT
ejpam-1951	692	12	.	.	PUNCT
ejpam-1951	692	13	]	]	X
ejpam-1951	693	1	[	[	X
ejpam-1951	693	2	2	2	NUM
ejpam-1951	693	3	]	]	PUNCT
ejpam-1951	693	4	.	.	PUNCT
ejpam-1951	693	5	example	example	NOUN
ejpam-1951	694	1	18	18	NUM
ejpam-1951	694	2	.	.	PUNCT
ejpam-1951	695	1	next	next	ADV
ejpam-1951	695	2	let	let	VERB
ejpam-1951	695	3	us	we	PRON
ejpam-1951	695	4	take	take	VERB
ejpam-1951	695	5	for	for	ADP
ejpam-1951	695	6	h	h	NOUN
ejpam-1951	695	7	the	the	DET
ejpam-1951	695	8	symmetric	symmetric	ADJ
ejpam-1951	695	9	group	group	NOUN
ejpam-1951	695	10	of	of	ADP
ejpam-1951	695	11	all	all	DET
ejpam-1951	695	12	permutations	permutation	NOUN
ejpam-1951	695	13	of	of	ADP
ejpam-1951	695	14	y	y	PROPN
ejpam-1951	695	15	and	and	CCONJ
ejpam-1951	695	16	for	for	ADP
ejpam-1951	695	17	g	g	NOUN
ejpam-1951	695	18	take	take	VERB
ejpam-1951	695	19	the	the	DET
ejpam-1951	695	20	identity	identity	NOUN
ejpam-1951	695	21	only	only	ADV
ejpam-1951	695	22	.	.	PUNCT
ejpam-1951	696	1	now	now	ADV
ejpam-1951	696	2	the	the	DET
ejpam-1951	696	3	patterns	pattern	NOUN
ejpam-1951	696	4	turn	turn	VERB
ejpam-1951	696	5	out	out	ADP
ejpam-1951	696	6	to	to	PART
ejpam-1951	696	7	be	be	AUX
ejpam-1951	696	8	class	class	NOUN
ejpam-1951	696	9	partition	partition	NOUN
ejpam-1951	696	10	of	of	ADP
ejpam-1951	696	11	x	x	PUNCT
ejpam-1951	696	12	into	into	ADP
ejpam-1951	696	13	at	at	ADP
ejpam-1951	696	14	most	most	ADJ
ejpam-1951	696	15	m	m	NOUN
ejpam-1951	696	16	parts	part	NOUN
ejpam-1951	696	17	,	,	PUNCT
ejpam-1951	696	18	where	where	SCONJ
ejpam-1951	696	19	a	a	DET
ejpam-1951	696	20	class	class	NOUN
ejpam-1951	696	21	partition	partition	NOUN
ejpam-1951	696	22	is	be	AUX
ejpam-1951	696	23	defined	define	VERB
ejpam-1951	696	24	as	as	ADP
ejpam-1951	696	25	a	a	DET
ejpam-1951	696	26	set	set	NOUN
ejpam-1951	696	27	of	of	ADP
ejpam-1951	696	28	disjoint	disjoint	NOUN
ejpam-1951	696	29	subsets(classes	subsets(classe	NOUN
ejpam-1951	696	30	)	)	PUNCT
ejpam-1951	696	31	of	of	ADP
ejpam-1951	696	32	x	x	X
ejpam-1951	696	33	whose	whose	DET
ejpam-1951	696	34	union	union	NOUN
ejpam-1951	696	35	is	be	AUX
ejpam-1951	696	36	x	x	X
ejpam-1951	696	37	.	.	PUNCT
ejpam-1951	697	1	the	the	DET
ejpam-1951	697	2	previous	previous	ADJ
ejpam-1951	697	3	result	result	NOUN
ejpam-1951	697	4	follows	follow	VERB
ejpam-1951	697	5	from	from	ADP
ejpam-1951	697	6	the	the	DET
ejpam-1951	697	7	fact	fact	NOUN
ejpam-1951	697	8	that	that	SCONJ
ejpam-1951	697	9	if	if	SCONJ
ejpam-1951	697	10	f	f	PROPN
ejpam-1951	697	11	∈	∈	PROPN
ejpam-1951	697	12	y	y	PROPN
ejpam-1951	697	13	x	x	INTJ
ejpam-1951	697	14	,	,	PUNCT
ejpam-1951	697	15	then	then	ADV
ejpam-1951	697	16	f	f	PROPN
ejpam-1951	697	17	defines	define	VERB
ejpam-1951	697	18	a	a	DET
ejpam-1951	697	19	class	class	NOUN
ejpam-1951	697	20	partition	partition	NOUN
ejpam-1951	697	21	by	by	ADP
ejpam-1951	697	22	putting	put	VERB
ejpam-1951	697	23	into	into	ADP
ejpam-1951	697	24	one	one	NUM
ejpam-1951	697	25	class	class	NOUN
ejpam-1951	697	26	all	all	DET
ejpam-1951	697	27	d	d	PROPN
ejpam-1951	697	28	that	that	PRON
ejpam-1951	697	29	are	be	AUX
ejpam-1951	697	30	mapped	map	VERB
ejpam-1951	697	31	by	by	ADP
ejpam-1951	697	32	f	f	PROPN
ejpam-1951	697	33	onto	onto	ADP
ejpam-1951	697	34	one	one	NUM
ejpam-1951	697	35	and	and	CCONJ
ejpam-1951	697	36	the	the	DET
ejpam-1951	697	37	same	same	ADJ
ejpam-1951	697	38	element	element	NOUN
ejpam-1951	697	39	of	of	ADP
ejpam-1951	697	40	y	y	PROPN
ejpam-1951	697	41	.	.	PUNCT
ejpam-1951	698	1	according	accord	VERB
ejpam-1951	698	2	to	to	ADP
ejpam-1951	698	3	(	(	PUNCT
ejpam-1951	698	4	a	a	NOUN
ejpam-1951	698	5	)	)	PUNCT
ejpam-1951	698	6	and	and	CCONJ
ejpam-1951	698	7	example	example	NOUN
ejpam-1951	698	8	5	5	NUM
ejpam-1951	698	9	we	we	PRON
ejpam-1951	698	10	find	find	VERB
ejpam-1951	698	11	that	that	SCONJ
ejpam-1951	698	12	the	the	DET
ejpam-1951	698	13	number	number	NOUN
ejpam-1951	698	14	of	of	ADP
ejpam-1951	698	15	patterns	pattern	NOUN
ejpam-1951	698	16	is	be	AUX
ejpam-1951	698	17	the	the	DET
ejpam-1951	698	18	coefficient	coefficient	NOUN
ejpam-1951	698	19	of	of	ADP
ejpam-1951	698	20	wm	wm	PROPN
ejpam-1951	698	21	in	in	ADP
ejpam-1951	698	22	�	�	PROPN
ejpam-1951	698	23	�	�	PROPN
ejpam-1951	698	24	d	d	PROPN
ejpam-1951	698	25	dz	dz	PROPN
ejpam-1951	698	26	�	�	PROPN
ejpam-1951	698	27	m	m	VERB
ejpam-1951	698	28	ex	ex	NOUN
ejpam-1951	698	29	p(wez	p(wez	NOUN
ejpam-1951	699	1	+	+	CCONJ
ejpam-1951	699	2	1	1	NUM
ejpam-1951	699	3	2	2	NUM
ejpam-1951	699	4	w2	w2	NOUN
ejpam-1951	699	5	+	+	CCONJ
ejpam-1951	699	6	1	1	NUM
ejpam-1951	699	7	3	3	NUM
ejpam-1951	699	8	w3	w3	NOUN
ejpam-1951	699	9	+	+	X
ejpam-1951	699	10	.	.	PUNCT
ejpam-1951	699	11	.	.	PUNCT
ejpam-1951	699	12	.	.	PUNCT
ejpam-1951	699	13	)	)	PUNCT
ejpam-1951	700	1	�	�	PROPN
ejpam-1951	700	2	z=0	z=0	PROPN
ejpam-1951	701	1	and	and	CCONJ
ejpam-1951	701	2	we	we	PRON
ejpam-1951	701	3	can	can	AUX
ejpam-1951	701	4	easily	easily	ADV
ejpam-1951	701	5	find	find	VERB
ejpam-1951	701	6	to	to	PART
ejpam-1951	701	7	be	be	AUX
ejpam-1951	701	8	m	m	PROPN
ejpam-1951	701	9	!	!	PUNCT
ejpam-1951	701	10	times	time	NOUN
ejpam-1951	701	11	the	the	DET
ejpam-1951	701	12	coefficient	coefficient	NOUN
ejpam-1951	701	13	of	of	ADP
ejpam-1951	701	14	zmwn	zmwn	PROPN
ejpam-1951	701	15	in	in	ADP
ejpam-1951	701	16	the	the	DET
ejpam-1951	701	17	expression	expression	NOUN
ejpam-1951	701	18	of	of	ADP
ejpam-1951	701	19	(	(	PUNCT
ejpam-1951	701	20	1−w)−1ew(ez−1	1−w)−1ew(ez−1	NUM
ejpam-1951	701	21	)	)	PUNCT
ejpam-1951	701	22	.	.	PUNCT
ejpam-1951	702	1	here	here	ADV
ejpam-1951	702	2	the	the	DET
ejpam-1951	702	3	number	number	NOUN
ejpam-1951	702	4	of	of	ADP
ejpam-1951	702	5	partitions	partition	NOUN
ejpam-1951	702	6	can	can	AUX
ejpam-1951	702	7	be	be	AUX
ejpam-1951	702	8	at	at	ADP
ejpam-1951	702	9	most	most	ADJ
ejpam-1951	702	10	n	n	PRON
ejpam-1951	702	11	parts	part	NOUN
ejpam-1951	702	12	.	.	PUNCT
ejpam-1951	703	1	so	so	ADV
ejpam-1951	703	2	the	the	DET
ejpam-1951	703	3	total	total	ADJ
ejpam-1951	703	4	number	number	NOUN
ejpam-1951	703	5	of	of	ADP
ejpam-1951	703	6	patterns	pattern	NOUN
ejpam-1951	703	7	equals	equal	VERB
ejpam-1951	703	8	m	m	PROPN
ejpam-1951	703	9	!	!	PROPN
ejpam-1951	703	10	times	time	NOUN
ejpam-1951	704	1	the	the	DET
ejpam-1951	704	2	coefficients	coefficient	NOUN
ejpam-1951	704	3	of	of	ADP
ejpam-1951	704	4	zm	zm	PROPN
ejpam-1951	704	5	in	in	ADP
ejpam-1951	704	6	eez−1	eez−1	NOUN
ejpam-1951	704	7	[	[	X
ejpam-1951	704	8	2	2	NUM
ejpam-1951	704	9	]	]	PUNCT
ejpam-1951	704	10	.	.	PUNCT
ejpam-1951	705	1	example	example	NOUN
ejpam-1951	706	1	19	19	NUM
ejpam-1951	706	2	.	.	PUNCT
ejpam-1951	707	1	now	now	ADV
ejpam-1951	707	2	we	we	PRON
ejpam-1951	707	3	are	be	AUX
ejpam-1951	707	4	interested	interested	ADJ
ejpam-1951	707	5	for	for	ADP
ejpam-1951	707	6	h	h	NOUN
ejpam-1951	707	7	the	the	DET
ejpam-1951	707	8	symmetric	symmetric	ADJ
ejpam-1951	707	9	group	group	NOUN
ejpam-1951	707	10	of	of	ADP
ejpam-1951	707	11	x	x	PRON
ejpam-1951	707	12	without	without	ADP
ejpam-1951	707	13	any	any	DET
ejpam-1951	707	14	specialization	specialization	NOUN
ejpam-1951	707	15	of	of	ADP
ejpam-1951	707	16	g.	g.	PROPN
ejpam-1951	707	17	we	we	PRON
ejpam-1951	707	18	get	get	VERB
ejpam-1951	707	19	partitions	partition	NOUN
ejpam-1951	707	20	of	of	ADP
ejpam-1951	707	21	class	class	NOUN
ejpam-1951	707	22	partitions	partition	NOUN
ejpam-1951	707	23	of	of	ADP
ejpam-1951	707	24	x	x	X
ejpam-1951	707	25	.	.	PUNCT
ejpam-1951	708	1	it	it	PRON
ejpam-1951	708	2	seems	seem	VERB
ejpam-1951	708	3	to	to	ADP
ejpam-1951	708	4	us	we	PRON
ejpam-1951	708	5	impossible	impossible	ADJ
ejpam-1951	708	6	to	to	PART
ejpam-1951	708	7	simplify	simplify	VERB
ejpam-1951	708	8	the	the	DET
ejpam-1951	708	9	result	result	NOUN
ejpam-1951	708	10	of	of	ADP
ejpam-1951	708	11	theorem	theorem	NOUN
ejpam-1951	708	12	4	4	NUM
ejpam-1951	708	13	.	.	PUNCT
ejpam-1951	709	1	if	if	SCONJ
ejpam-1951	709	2	we	we	PRON
ejpam-1951	709	3	take	take	VERB
ejpam-1951	709	4	g	g	NOUN
ejpam-1951	709	5	to	to	ADP
ejpam-1951	709	6	the	the	DET
ejpam-1951	709	7	symmetric	symmetric	ADJ
ejpam-1951	709	8	group	group	NOUN
ejpam-1951	709	9	of	of	ADP
ejpam-1951	709	10	x	x	PRON
ejpam-1951	709	11	,	,	PUNCT
ejpam-1951	709	12	the	the	DET
ejpam-1951	709	13	partitions	partition	NOUN
ejpam-1951	709	14	become	become	VERB
ejpam-1951	709	15	class	class	NOUN
ejpam-1951	709	16	partitions	partition	NOUN
ejpam-1951	709	17	of	of	ADP
ejpam-1951	709	18	a	a	DET
ejpam-1951	709	19	set	set	NOUN
ejpam-1951	709	20	of	of	ADP
ejpam-1951	709	21	unidentifiable	unidentifiable	ADJ
ejpam-1951	709	22	objects	object	NOUN
ejpam-1951	709	23	.	.	PUNCT
ejpam-1951	710	1	so	so	ADV
ejpam-1951	710	2	we	we	PRON
ejpam-1951	710	3	are	be	AUX
ejpam-1951	710	4	only	only	ADV
ejpam-1951	710	5	concern	concern	NOUN
ejpam-1951	710	6	about	about	ADP
ejpam-1951	710	7	the	the	DET
ejpam-1951	710	8	size	size	NOUN
ejpam-1951	710	9	of	of	ADP
ejpam-1951	710	10	the	the	DET
ejpam-1951	710	11	classes	class	NOUN
ejpam-1951	710	12	.	.	PUNCT
ejpam-1951	711	1	our	our	PRON
ejpam-1951	711	2	patterns	pattern	NOUN
ejpam-1951	711	3	can	can	AUX
ejpam-1951	711	4	be	be	AUX
ejpam-1951	711	5	brought	bring	VERB
ejpam-1951	711	6	into	into	ADP
ejpam-1951	711	7	one	one	NUM
ejpam-1951	711	8	-	-	PUNCT
ejpam-1951	711	9	to	to	ADP
ejpam-1951	711	10	-	-	PUNCT
ejpam-1951	711	11	one	one	NUM
ejpam-1951	711	12	correspondence	correspondence	NOUN
ejpam-1951	711	13	with	with	ADP
ejpam-1951	711	14	the	the	DET
ejpam-1951	711	15	partitions	partition	NOUN
ejpam-1951	711	16	of	of	ADP
ejpam-1951	711	17	m	m	NOUN
ejpam-1951	711	18	into	into	ADP
ejpam-1951	711	19	at	at	ADP
ejpam-1951	711	20	most	most	ADJ
ejpam-1951	711	21	n	n	PRON
ejpam-1951	711	22	parts	part	NOUN
ejpam-1951	711	23	.	.	PUNCT
ejpam-1951	712	1	a	a	DET
ejpam-1951	712	2	partition	partition	NOUN
ejpam-1951	712	3	of	of	ADP
ejpam-1951	712	4	m	m	PROPN
ejpam-1951	712	5	is	be	AUX
ejpam-1951	712	6	a	a	DET
ejpam-1951	712	7	solution	solution	NOUN
ejpam-1951	712	8	{	{	PUNCT
ejpam-1951	712	9	g1	g1	PROPN
ejpam-1951	712	10	,	,	PUNCT
ejpam-1951	712	11	g2	g2	PROPN
ejpam-1951	712	12	,	,	PUNCT
ejpam-1951	712	13	.	.	PUNCT
ejpam-1951	712	14	.	.	PUNCT
ejpam-1951	713	1	.	.	PUNCT
ejpam-1951	713	2	}	}	PUNCT
ejpam-1951	714	1	of	of	ADP
ejpam-1951	714	2	the	the	DET
ejpam-1951	714	3	equation	equation	NOUN
ejpam-1951	714	4	g1	g1	NOUN
ejpam-1951	714	5	+	+	CCONJ
ejpam-1951	714	6	2g2	2g2	NUM
ejpam-1951	714	7	+	+	CCONJ
ejpam-1951	714	8	3g3	3g3	NUM
ejpam-1951	714	9	+	+	NUM
ejpam-1951	714	10	.	.	PUNCT
ejpam-1951	714	11	.	.	PUNCT
ejpam-1951	715	1	.=	.=	VERB
ejpam-1951	715	2	m	m	VERB
ejpam-1951	715	3	in	in	ADP
ejpam-1951	715	4	nonnegative	nonnegative	ADJ
ejpam-1951	715	5	integers	integer	NOUN
ejpam-1951	715	6	g1	g1	NOUN
ejpam-1951	715	7	,	,	PUNCT
ejpam-1951	715	8	g2	g2	PROPN
ejpam-1951	715	9	,	,	PUNCT
ejpam-1951	715	10	.	.	PUNCT
ejpam-1951	715	11	.	.	PUNCT
ejpam-1951	716	1	.	.	PUNCT
ejpam-1951	717	1	so	so	ADV
ejpam-1951	717	2	m	m	PROPN
ejpam-1951	717	3	has	have	AUX
ejpam-1951	717	4	been	be	AUX
ejpam-1951	717	5	partitioned	partition	VERB
ejpam-1951	717	6	into	into	ADP
ejpam-1951	717	7	g1	g1	PROPN
ejpam-1951	717	8	1	1	NUM
ejpam-1951	717	9	’s	’s	PART
ejpam-1951	717	10	,	,	PUNCT
ejpam-1951	717	11	g2	g2	PROPN
ejpam-1951	717	12	2	2	NUM
ejpam-1951	717	13	’s	’s	ADV
ejpam-1951	717	14	,	,	PUNCT
ejpam-1951	717	15	.	.	PUNCT
ejpam-1951	717	16	.	.	PUNCT
ejpam-1951	717	17	.	.	PUNCT
ejpam-1951	718	1	and	and	CCONJ
ejpam-1951	718	2	accordingly	accordingly	ADV
ejpam-1951	718	3	g1	g1	VERB
ejpam-1951	718	4	+	+	CCONJ
ejpam-1951	718	5	g2	g2	PROPN
ejpam-1951	718	6	+	+	CCONJ
ejpam-1951	718	7	g3	g3	PROPN
ejpam-1951	718	8	+	+	CCONJ
ejpam-1951	718	9	.	.	PUNCT
ejpam-1951	718	10	.	.	PUNCT
ejpam-1951	718	11	.	.	PUNCT
ejpam-1951	719	1	is	be	AUX
ejpam-1951	719	2	called	call	VERB
ejpam-1951	719	3	the	the	DET
ejpam-1951	719	4	number	number	NOUN
ejpam-1951	719	5	of	of	ADP
ejpam-1951	719	6	parts	part	NOUN
ejpam-1951	719	7	of	of	ADP
ejpam-1951	719	8	the	the	DET
ejpam-1951	719	9	partition	partition	NOUN
ejpam-1951	719	10	.	.	PUNCT
ejpam-1951	720	1	the	the	DET
ejpam-1951	720	2	number	number	NOUN
ejpam-1951	720	3	of	of	ADP
ejpam-1951	720	4	partitions	partition	NOUN
ejpam-1951	720	5	can	can	AUX
ejpam-1951	720	6	be	be	AUX
ejpam-1951	720	7	obtained	obtain	VERB
ejpam-1951	720	8	from	from	ADP
ejpam-1951	720	9	example	example	NOUN
ejpam-1951	720	10	17	17	NUM
ejpam-1951	720	11	by	by	ADP
ejpam-1951	720	12	specializing	specialize	VERB
ejpam-1951	720	13	h	h	NOUN
ejpam-1951	720	14	to	to	PART
ejpam-1951	720	15	be	be	AUX
ejpam-1951	720	16	the	the	DET
ejpam-1951	720	17	symmetric	symmetric	ADJ
ejpam-1951	720	18	group	group	NOUN
ejpam-1951	720	19	.	.	PUNCT
ejpam-1951	721	1	we	we	PRON
ejpam-1951	721	2	obtain	obtain	VERB
ejpam-1951	721	3	the	the	DET
ejpam-1951	721	4	coefficient	coefficient	NOUN
ejpam-1951	721	5	of	of	ADP
ejpam-1951	721	6	zm	zm	PROPN
ejpam-1951	721	7	in	in	ADP
ejpam-1951	721	8	zh[(1−	zh[(1−	PROPN
ejpam-1951	721	9	z)−1	z)−1	NUM
ejpam-1951	721	10	,	,	PUNCT
ejpam-1951	721	11	(	(	PUNCT
ejpam-1951	721	12	1−	1−	NUM
ejpam-1951	721	13	z2)−1	z2)−1	NOUN
ejpam-1951	721	14	,	,	PUNCT
ejpam-1951	721	15	.	.	PUNCT
ejpam-1951	721	16	.	.	PUNCT
ejpam-1951	721	17	.	.	PUNCT
ejpam-1951	721	18	]	]	PUNCT
ejpam-1951	722	1	t.	t.	PROPN
ejpam-1951	722	2	nasseef	nasseef	PROPN
ejpam-1951	722	3	/	/	SYM
ejpam-1951	722	4	eur	eur	PROPN
ejpam-1951	722	5	.	.	PUNCT
ejpam-1951	723	1	j.	j.	PROPN
ejpam-1951	723	2	pure	pure	PROPN
ejpam-1951	723	3	appl	appl	PROPN
ejpam-1951	723	4	.	.	PROPN
ejpam-1951	723	5	math	math	PROPN
ejpam-1951	723	6	,	,	PUNCT
ejpam-1951	723	7	9	9	NUM
ejpam-1951	723	8	(	(	PUNCT
ejpam-1951	723	9	2016	2016	NUM
ejpam-1951	723	10	)	)	PUNCT
ejpam-1951	723	11	,	,	PUNCT
ejpam-1951	723	12	84	84	NUM
ejpam-1951	723	13	-	-	SYM
ejpam-1951	723	14	113	113	NUM
ejpam-1951	723	15	108	108	NUM
ejpam-1951	723	16	which	which	PRON
ejpam-1951	723	17	becomes	become	VERB
ejpam-1951	723	18	in	in	ADP
ejpam-1951	723	19	this	this	DET
ejpam-1951	723	20	case	case	NOUN
ejpam-1951	723	21	,	,	PUNCT
ejpam-1951	723	22	the	the	DET
ejpam-1951	723	23	coefficient	coefficient	NOUN
ejpam-1951	723	24	of	of	ADP
ejpam-1951	723	25	zmwn	zmwn	PROPN
ejpam-1951	723	26	in	in	ADP
ejpam-1951	723	27	ex	ex	X
ejpam-1951	723	28	p[w(1−	p[w(1−	PROPN
ejpam-1951	723	29	z)−1	z)−1	PROPN
ejpam-1951	723	30	+	+	CCONJ
ejpam-1951	723	31	1	1	NUM
ejpam-1951	723	32	2	2	NUM
ejpam-1951	723	33	w2(1−	w2(1−	NOUN
ejpam-1951	723	34	z2)−1	z2)−1	NOUN
ejpam-1951	723	35	+	+	CCONJ
ejpam-1951	723	36	1	1	NUM
ejpam-1951	723	37	3	3	NUM
ejpam-1951	723	38	w3(1−	w3(1−	NOUN
ejpam-1951	723	39	z3)−1	z3)−1	NOUN
ejpam-1951	723	40	+	+	CCONJ
ejpam-1951	723	41	.	.	PUNCT
ejpam-1951	723	42	.	.	PUNCT
ejpam-1951	723	43	.	.	PUNCT
ejpam-1951	724	1	]	]	X
ejpam-1951	724	2	,	,	PUNCT
ejpam-1951	724	3	and	and	CCONJ
ejpam-1951	724	4	this	this	DET
ejpam-1951	724	5	expression	expression	NOUN
ejpam-1951	724	6	can	can	AUX
ejpam-1951	724	7	be	be	AUX
ejpam-1951	724	8	reduced	reduce	VERB
ejpam-1951	724	9	to	to	ADP
ejpam-1951	724	10	ex	ex	ADJ
ejpam-1951	724	11	p[log(1−w)−1	p[log(1−w)−1	NOUN
ejpam-1951	724	12	+	+	CCONJ
ejpam-1951	724	13	log(1−wz)−1	log(1−wz)−1	VERB
ejpam-1951	724	14	+	+	CCONJ
ejpam-1951	724	15	log(1−wz2)−1	log(1−wz2)−1	NOUN
ejpam-1951	724	16	+	+	X
ejpam-1951	724	17	.	.	PUNCT
ejpam-1951	724	18	.	.	PUNCT
ejpam-1951	724	19	.	.	PUNCT
ejpam-1951	724	20	]	]	PUNCT
ejpam-1951	725	1	=	=	PUNCT
ejpam-1951	726	1	∞	∞	NUM
ejpam-1951	726	2	∏	∏	NUM
ejpam-1951	726	3	k=1	k=1	NOUN
ejpam-1951	726	4	1	1	NUM
ejpam-1951	726	5	1−	1−	NUM
ejpam-1951	726	6	wzk	wzk	NOUN
ejpam-1951	726	7	.	.	PUNCT
ejpam-1951	727	1	this	this	PRON
ejpam-1951	727	2	is	be	AUX
ejpam-1951	727	3	a	a	DET
ejpam-1951	727	4	well	well	ADV
ejpam-1951	727	5	-	-	PUNCT
ejpam-1951	727	6	know	know	NOUN
ejpam-1951	727	7	result	result	NOUN
ejpam-1951	727	8	for	for	ADP
ejpam-1951	727	9	the	the	DET
ejpam-1951	727	10	generating	generate	VERB
ejpam-1951	727	11	function	function	NOUN
ejpam-1951	727	12	of	of	ADP
ejpam-1951	727	13	the	the	DET
ejpam-1951	727	14	number	number	NOUN
ejpam-1951	727	15	of	of	ADP
ejpam-1951	727	16	partitions	partition	NOUN
ejpam-1951	727	17	of	of	ADP
ejpam-1951	727	18	a	a	DET
ejpam-1951	727	19	given	give	VERB
ejpam-1951	727	20	number	number	NOUN
ejpam-1951	727	21	into	into	ADP
ejpam-1951	727	22	a	a	DET
ejpam-1951	727	23	given	give	VERB
ejpam-1951	727	24	number	number	NOUN
ejpam-1951	727	25	of	of	ADP
ejpam-1951	727	26	components	component	NOUN
ejpam-1951	727	27	[	[	X
ejpam-1951	727	28	2	2	NUM
ejpam-1951	727	29	]	]	PUNCT
ejpam-1951	727	30	.	.	PUNCT
ejpam-1951	728	1	example	example	NOUN
ejpam-1951	728	2	20	20	NUM
ejpam-1951	728	3	.	.	PUNCT
ejpam-1951	729	1	let	let	VERB
ejpam-1951	729	2	h	h	PRON
ejpam-1951	729	3	be	be	AUX
ejpam-1951	729	4	a	a	DET
ejpam-1951	729	5	symmetric	symmetric	ADJ
ejpam-1951	729	6	group	group	NOUN
ejpam-1951	729	7	and	and	CCONJ
ejpam-1951	729	8	let	let	VERB
ejpam-1951	729	9	g	g	NOUN
ejpam-1951	729	10	be	be	AUX
ejpam-1951	729	11	specialized	specialize	VERB
ejpam-1951	729	12	by	by	ADP
ejpam-1951	729	13	taking	take	VERB
ejpam-1951	729	14	n	n	X
ejpam-1951	729	15	=	=	SYM
ejpam-1951	729	16	2	2	NUM
ejpam-1951	729	17	.	.	PUNCT
ejpam-1951	730	1	so	so	ADV
ejpam-1951	730	2	the	the	DET
ejpam-1951	730	3	patterns	pattern	NOUN
ejpam-1951	730	4	of	of	ADP
ejpam-1951	730	5	class	class	NOUN
ejpam-1951	730	6	partitions	partition	NOUN
ejpam-1951	730	7	into	into	ADP
ejpam-1951	730	8	at	at	ADP
ejpam-1951	730	9	most	most	ADV
ejpam-1951	730	10	two	two	NUM
ejpam-1951	730	11	parts	part	NOUN
ejpam-1951	730	12	.	.	PUNCT
ejpam-1951	731	1	by	by	ADP
ejpam-1951	731	2	(	(	PUNCT
ejpam-1951	731	3	5	5	X
ejpam-1951	731	4	)	)	PUNCT
ejpam-1951	731	5	the	the	DET
ejpam-1951	731	6	number	number	NOUN
ejpam-1951	731	7	of	of	ADP
ejpam-1951	731	8	these	these	PRON
ejpam-1951	731	9	is	be	AUX
ejpam-1951	731	10	1	1	NUM
ejpam-1951	731	11	2	2	NUM
ejpam-1951	731	12	zg(2,2,2	zg(2,2,2	PROPN
ejpam-1951	731	13	,	,	PUNCT
ejpam-1951	731	14	.	.	PUNCT
ejpam-1951	731	15	.	.	PUNCT
ejpam-1951	731	16	.	.	PUNCT
ejpam-1951	731	17	)	)	PUNCT
ejpam-1951	732	1	+	+	CCONJ
ejpam-1951	732	2	1	1	NUM
ejpam-1951	732	3	2	2	NUM
ejpam-1951	732	4	zg(0,2,0,2	zg(0,2,0,2	NOUN
ejpam-1951	732	5	,	,	PUNCT
ejpam-1951	732	6	.	.	PUNCT
ejpam-1951	732	7	.	.	PUNCT
ejpam-1951	732	8	.	.	PUNCT
ejpam-1951	732	9	)	)	PUNCT
ejpam-1951	732	10	,	,	PUNCT
ejpam-1951	732	11	since	since	SCONJ
ejpam-1951	732	12	zh	zh	PROPN
ejpam-1951	732	13	=	=	SYM
ejpam-1951	732	14	1	1	NUM
ejpam-1951	732	15	2	2	NUM
ejpam-1951	732	16	t2	t2	NOUN
ejpam-1951	732	17	1	1	NUM
ejpam-1951	732	18	+	+	CCONJ
ejpam-1951	732	19	1	1	NUM
ejpam-1951	732	20	2	2	NUM
ejpam-1951	732	21	t2	t2	NOUN
ejpam-1951	732	22	.	.	PUNCT
ejpam-1951	733	1	if	if	SCONJ
ejpam-1951	733	2	we	we	PRON
ejpam-1951	733	3	compare	compare	VERB
ejpam-1951	733	4	this	this	PRON
ejpam-1951	733	5	to	to	ADP
ejpam-1951	733	6	the	the	DET
ejpam-1951	733	7	number	number	NOUN
ejpam-1951	733	8	of	of	ADP
ejpam-1951	733	9	patterns	pattern	NOUN
ejpam-1951	733	10	of	of	ADP
ejpam-1951	733	11	partitions	partition	NOUN
ejpam-1951	733	12	into	into	ADP
ejpam-1951	733	13	two	two	NUM
ejpam-1951	733	14	labeled	label	VERB
ejpam-1951	733	15	classes	class	NOUN
ejpam-1951	733	16	,	,	PUNCT
ejpam-1951	733	17	zg(2,2,2	zg(2,2,2	PROPN
ejpam-1951	733	18	,	,	PUNCT
ejpam-1951	733	19	.	.	PUNCT
ejpam-1951	733	20	.	.	PUNCT
ejpam-1951	734	1	.	.	PUNCT
ejpam-1951	734	2	)	)	PUNCT
ejpam-1951	735	1	,	,	PUNCT
ejpam-1951	735	2	we	we	PRON
ejpam-1951	735	3	observe	observe	VERB
ejpam-1951	735	4	that	that	SCONJ
ejpam-1951	735	5	the	the	DET
ejpam-1951	735	6	term	term	NOUN
ejpam-1951	735	7	zg(0,2,0,2	zg(0,2,0,2	NOUN
ejpam-1951	735	8	,	,	PUNCT
ejpam-1951	735	9	.	.	PUNCT
ejpam-1951	735	10	.	.	PUNCT
ejpam-1951	735	11	.	.	PUNCT
ejpam-1951	735	12	)	)	PUNCT
ejpam-1951	736	1	represents	represent	VERB
ejpam-1951	736	2	the	the	DET
ejpam-1951	736	3	number	number	NOUN
ejpam-1951	736	4	of	of	ADP
ejpam-1951	736	5	symmetric	symmetric	ADJ
ejpam-1951	736	6	patterns	pattern	NOUN
ejpam-1951	736	7	of	of	ADP
ejpam-1951	736	8	x	x	PUNCT
ejpam-1951	736	9	into	into	ADP
ejpam-1951	736	10	two	two	NUM
ejpam-1951	736	11	classes	class	NOUN
ejpam-1951	736	12	x1	x1	NUM
ejpam-1951	736	13	and	and	CCONJ
ejpam-1951	736	14	x2	x2	NOUN
ejpam-1951	736	15	.	.	PUNCT
ejpam-1951	737	1	that	that	PRON
ejpam-1951	737	2	is	be	AUX
ejpam-1951	737	3	,	,	PUNCT
ejpam-1951	737	4	zg(0,2,0,2	zg(0,2,0,2	NOUN
ejpam-1951	737	5	,	,	PUNCT
ejpam-1951	737	6	.	.	PUNCT
ejpam-1951	737	7	.	.	PUNCT
ejpam-1951	737	8	.	.	PUNCT
ejpam-1951	737	9	)	)	PUNCT
ejpam-1951	738	1	represents	represent	VERB
ejpam-1951	738	2	the	the	DET
ejpam-1951	738	3	number	number	NOUN
ejpam-1951	738	4	of	of	ADP
ejpam-1951	738	5	symmetric	symmetric	ADJ
ejpam-1951	738	6	patterns	pattern	NOUN
ejpam-1951	738	7	of	of	ADP
ejpam-1951	738	8	subsets	subset	NOUN
ejpam-1951	738	9	x1	x1	PROPN
ejpam-1951	738	10	that	that	PRON
ejpam-1951	738	11	are	be	AUX
ejpam-1951	738	12	equivalent	equivalent	ADJ
ejpam-1951	738	13	to	to	ADP
ejpam-1951	738	14	there	there	PRON
ejpam-1951	738	15	complement	complement	NOUN
ejpam-1951	738	16	,	,	PUNCT
ejpam-1951	738	17	where	where	SCONJ
ejpam-1951	738	18	equivalence	equivalence	NOUN
ejpam-1951	738	19	is	be	AUX
ejpam-1951	738	20	defined	define	VERB
ejpam-1951	738	21	by	by	ADP
ejpam-1951	738	22	the	the	DET
ejpam-1951	738	23	permutations	permutation	NOUN
ejpam-1951	738	24	of	of	ADP
ejpam-1951	738	25	g	g	NOUN
ejpam-1951	738	26	and	and	CCONJ
ejpam-1951	738	27	patterns	pattern	NOUN
ejpam-1951	738	28	are	be	AUX
ejpam-1951	738	29	defined	define	VERB
ejpam-1951	738	30	by	by	ADP
ejpam-1951	738	31	this	this	DET
ejpam-1951	738	32	equivalence	equivalence	NOUN
ejpam-1951	738	33	.	.	PUNCT
ejpam-1951	739	1	let	let	VERB
ejpam-1951	739	2	x	x	PRON
ejpam-1951	739	3	be	be	AUX
ejpam-1951	739	4	the	the	DET
ejpam-1951	739	5	set	set	NOUN
ejpam-1951	739	6	of	of	ADP
ejpam-1951	739	7	10	10	NUM
ejpam-1951	739	8	roots	root	NOUN
ejpam-1951	739	9	of	of	ADP
ejpam-1951	739	10	unity	unity	NOUN
ejpam-1951	739	11	and	and	CCONJ
ejpam-1951	739	12	g	g	NOUN
ejpam-1951	739	13	be	be	AUX
ejpam-1951	739	14	the	the	DET
ejpam-1951	739	15	group	group	NOUN
ejpam-1951	739	16	of	of	ADP
ejpam-1951	739	17	10	10	NUM
ejpam-1951	739	18	rotations	rotation	NOUN
ejpam-1951	739	19	.	.	PUNCT
ejpam-1951	740	1	the	the	DET
ejpam-1951	740	2	cycle	cycle	NOUN
ejpam-1951	740	3	index	index	NOUN
ejpam-1951	740	4	(	(	PUNCT
ejpam-1951	740	5	see	see	VERB
ejpam-1951	740	6	definition	definition	NOUN
ejpam-1951	740	7	2	2	NUM
ejpam-1951	740	8	with	with	ADP
ejpam-1951	740	9	cyclic	cyclic	ADJ
ejpam-1951	740	10	groups	group	NOUN
ejpam-1951	740	11	formula	formula	NOUN
ejpam-1951	740	12	(	(	PUNCT
ejpam-1951	740	13	1	1	NUM
ejpam-1951	740	14	)	)	PUNCT
ejpam-1951	740	15	)	)	PUNCT
ejpam-1951	740	16	is	be	AUX
ejpam-1951	740	17	zg	zg	PROPN
ejpam-1951	740	18	=	=	SYM
ejpam-1951	740	19	1	1	NUM
ejpam-1951	740	20	10	10	NUM
ejpam-1951	740	21	(	(	PUNCT
ejpam-1951	740	22	t10	t10	NUM
ejpam-1951	740	23	1	1	NUM
ejpam-1951	740	24	+	+	CCONJ
ejpam-1951	740	25	t5	t5	PROPN
ejpam-1951	740	26	2	2	NUM
ejpam-1951	740	27	+	+	NUM
ejpam-1951	740	28	4t2	4t2	NUM
ejpam-1951	740	29	5	5	NUM
ejpam-1951	740	30	+	+	NUM
ejpam-1951	740	31	4t10	4t10	NOUN
ejpam-1951	740	32	)	)	PUNCT
ejpam-1951	740	33	and	and	CCONJ
ejpam-1951	740	34	therefore	therefore	ADV
ejpam-1951	740	35	[	[	X
ejpam-1951	740	36	2	2	NUM
ejpam-1951	740	37	]	]	PUNCT
ejpam-1951	740	38	zg(0,2,0,2	zg(0,2,0,2	NOUN
ejpam-1951	740	39	,	,	PUNCT
ejpam-1951	740	40	.	.	PUNCT
ejpam-1951	740	41	.	.	PUNCT
ejpam-1951	740	42	.	.	PUNCT
ejpam-1951	740	43	)	)	PUNCT
ejpam-1951	741	1	=	=	PUNCT
ejpam-1951	741	2	1	1	NUM
ejpam-1951	741	3	10	10	NUM
ejpam-1951	741	4	(	(	PUNCT
ejpam-1951	741	5	(	(	PUNCT
ejpam-1951	741	6	2)5	2)5	NUM
ejpam-1951	741	7	+	+	NOUN
ejpam-1951	741	8	4.2	4.2	NUM
ejpam-1951	741	9	)	)	PUNCT
ejpam-1951	741	10	=	=	SYM
ejpam-1951	741	11	4	4	X
ejpam-1951	741	12	.	.	X
ejpam-1951	741	13	theorem	theorem	VERB
ejpam-1951	741	14	6	6	NUM
ejpam-1951	741	15	(	(	PUNCT
ejpam-1951	741	16	pólya	pólya	NOUN
ejpam-1951	741	17	)	)	PUNCT
ejpam-1951	741	18	.	.	PUNCT
ejpam-1951	742	1	we	we	PRON
ejpam-1951	742	2	have	have	VERB
ejpam-1951	742	3	zg[h](t1	zg[h](t1	NUM
ejpam-1951	742	4	,	,	PUNCT
ejpam-1951	742	5	t2	t2	NOUN
ejpam-1951	742	6	,	,	PUNCT
ejpam-1951	742	7	.	.	PUNCT
ejpam-1951	742	8	.	.	PUNCT
ejpam-1951	742	9	.	.	PUNCT
ejpam-1951	742	10	)	)	PUNCT
ejpam-1951	743	1	=	=	PUNCT
ejpam-1951	743	2	zg[zh(t1	zg[zh(t1	NUM
ejpam-1951	743	3	,	,	PUNCT
ejpam-1951	743	4	t2	t2	NOUN
ejpam-1951	743	5	,	,	PUNCT
ejpam-1951	743	6	t3	t3	PROPN
ejpam-1951	743	7	,	,	PUNCT
ejpam-1951	743	8	.	.	PUNCT
ejpam-1951	743	9	.	.	PUNCT
ejpam-1951	744	1	.	.	PUNCT
ejpam-1951	744	2	)	)	PUNCT
ejpam-1951	745	1	,	,	PUNCT
ejpam-1951	745	2	zh(t2	zh(t2	PROPN
ejpam-1951	745	3	,	,	PUNCT
ejpam-1951	745	4	t4	t4	PROPN
ejpam-1951	745	5	,	,	PUNCT
ejpam-1951	745	6	t6	t6	PROPN
ejpam-1951	745	7	,	,	PUNCT
ejpam-1951	745	8	.	.	PUNCT
ejpam-1951	745	9	.	.	PUNCT
ejpam-1951	745	10	.	.	PUNCT
ejpam-1951	745	11	)	)	PUNCT
ejpam-1951	745	12	,	,	PUNCT
ejpam-1951	745	13	.	.	PUNCT
ejpam-1951	745	14	.	.	PUNCT
ejpam-1951	746	1	.	.	PUNCT
ejpam-1951	746	2	]	]	PUNCT
ejpam-1951	747	1	where	where	SCONJ
ejpam-1951	747	2	zg[h	zg[h	PROPN
ejpam-1951	747	3	]	]	X
ejpam-1951	747	4	is	be	AUX
ejpam-1951	747	5	in	in	ADP
ejpam-1951	747	6	kranz	kranz	PROPN
ejpam-1951	747	7	group	group	NOUN
ejpam-1951	747	8	and	and	CCONJ
ejpam-1951	747	9	the	the	DET
ejpam-1951	747	10	the	the	DET
ejpam-1951	747	11	right	right	ADJ
ejpam-1951	747	12	hand	hand	NOUN
ejpam-1951	747	13	side	side	NOUN
ejpam-1951	747	14	is	be	AUX
ejpam-1951	747	15	obtained	obtain	VERB
ejpam-1951	747	16	on	on	ADP
ejpam-1951	747	17	substitution	substitution	NOUN
ejpam-1951	747	18	of	of	ADP
ejpam-1951	747	19	x	x	PUNCT
ejpam-1951	747	20	j	j	PROPN
ejpam-1951	747	21	=	=	SYM
ejpam-1951	747	22	zh(t	zh(t	NUM
ejpam-1951	747	23	j	j	PROPN
ejpam-1951	747	24	,	,	PUNCT
ejpam-1951	747	25	t2	t2	PROPN
ejpam-1951	747	26	j	j	PROPN
ejpam-1951	747	27	,	,	PUNCT
ejpam-1951	747	28	t3	t3	PROPN
ejpam-1951	747	29	j	j	PROPN
ejpam-1951	747	30	,	,	PUNCT
ejpam-1951	747	31	.	.	PUNCT
ejpam-1951	747	32	.	.	PUNCT
ejpam-1951	748	1	.	.	PUNCT
ejpam-1951	748	2	)	)	PUNCT
ejpam-1951	749	1	into	into	ADP
ejpam-1951	749	2	zg(x1	zg(x1	PROPN
ejpam-1951	749	3	,	,	PUNCT
ejpam-1951	749	4	x2	x2	PROPN
ejpam-1951	749	5	,	,	PUNCT
ejpam-1951	749	6	x3	x3	ADJ
ejpam-1951	749	7	,	,	PUNCT
ejpam-1951	749	8	...	...	PUNCT
ejpam-1951	749	9	)	)	PUNCT
ejpam-1951	750	1	[	[	X
ejpam-1951	750	2	2	2	NUM
ejpam-1951	750	3	]	]	PUNCT
ejpam-1951	750	4	.	.	PUNCT
ejpam-1951	750	5	example	example	NOUN
ejpam-1951	750	6	21	21	NUM
ejpam-1951	750	7	.	.	PUNCT
ejpam-1951	751	1	consider	consider	VERB
ejpam-1951	751	2	n	n	PRON
ejpam-1951	751	3	cubes	cube	NOUN
ejpam-1951	751	4	and	and	CCONJ
ejpam-1951	751	5	we	we	PRON
ejpam-1951	751	6	want	want	VERB
ejpam-1951	751	7	to	to	PART
ejpam-1951	751	8	color	color	VERB
ejpam-1951	751	9	the	the	DET
ejpam-1951	751	10	faces	face	NOUN
ejpam-1951	751	11	with	with	ADP
ejpam-1951	751	12	red	red	ADJ
ejpam-1951	751	13	and	and	CCONJ
ejpam-1951	751	14	yellow	yellow	ADJ
ejpam-1951	751	15	.	.	PUNCT
ejpam-1951	752	1	we	we	PRON
ejpam-1951	752	2	are	be	AUX
ejpam-1951	752	3	interested	interested	ADJ
ejpam-1951	752	4	for	for	ADP
ejpam-1951	752	5	the	the	DET
ejpam-1951	752	6	number	number	NOUN
ejpam-1951	752	7	of	of	ADP
ejpam-1951	752	8	ways	way	NOUN
ejpam-1951	752	9	to	to	PART
ejpam-1951	752	10	do	do	VERB
ejpam-1951	752	11	this	this	PRON
ejpam-1951	752	12	when	when	SCONJ
ejpam-1951	752	13	equivalences	equivalence	NOUN
ejpam-1951	752	14	are	be	AUX
ejpam-1951	752	15	defined	define	VERB
ejpam-1951	752	16	by	by	ADP
ejpam-1951	752	17	permutations	permutation	NOUN
ejpam-1951	752	18	of	of	ADP
ejpam-1951	752	19	the	the	DET
ejpam-1951	752	20	sets	set	NOUN
ejpam-1951	752	21	of	of	ADP
ejpam-1951	752	22	cubes	cube	NOUN
ejpam-1951	752	23	and	and	CCONJ
ejpam-1951	752	24	rotations	rotation	NOUN
ejpam-1951	752	25	of	of	ADP
ejpam-1951	752	26	the	the	DET
ejpam-1951	752	27	separate	separate	ADJ
ejpam-1951	752	28	cubes	cube	NOUN
ejpam-1951	752	29	.	.	PUNCT
ejpam-1951	753	1	the	the	DET
ejpam-1951	753	2	group	group	NOUN
ejpam-1951	753	3	is	be	AUX
ejpam-1951	753	4	considered	consider	VERB
ejpam-1951	753	5	as	as	ADP
ejpam-1951	753	6	sn[g	sn[g	NOUN
ejpam-1951	753	7	]	]	PUNCT
ejpam-1951	753	8	where	where	SCONJ
ejpam-1951	753	9	sn	sn	PROPN
ejpam-1951	753	10	is	be	AUX
ejpam-1951	753	11	the	the	DET
ejpam-1951	753	12	symmetric	symmetric	ADJ
ejpam-1951	753	13	group	group	NOUN
ejpam-1951	753	14	of	of	ADP
ejpam-1951	753	15	degree	degree	NOUN
ejpam-1951	753	16	n	n	PROPN
ejpam-1951	753	17	and	and	CCONJ
ejpam-1951	753	18	g	g	PROPN
ejpam-1951	753	19	is	be	AUX
ejpam-1951	753	20	the	the	DET
ejpam-1951	753	21	cube	cube	NOUN
ejpam-1951	753	22	-	-	PUNCT
ejpam-1951	753	23	face	face	NOUN
ejpam-1951	753	24	group	group	NOUN
ejpam-1951	753	25	of	of	ADP
ejpam-1951	753	26	example	example	NOUN
ejpam-1951	753	27	11	11	NUM
ejpam-1951	753	28	.	.	PUNCT
ejpam-1951	754	1	then	then	ADV
ejpam-1951	754	2	we	we	PRON
ejpam-1951	754	3	have	have	VERB
ejpam-1951	754	4	to	to	PART
ejpam-1951	754	5	substitute	substitute	VERB
ejpam-1951	754	6	t1	t1	NOUN
ejpam-1951	754	7	=	=	SYM
ejpam-1951	754	8	t2	t2	PROPN
ejpam-1951	754	9	=	=	PUNCT
ejpam-1951	754	10	.	.	PUNCT
ejpam-1951	754	11	.	.	PUNCT
ejpam-1951	754	12	.	.	PUNCT
ejpam-1951	755	1	=	=	PUNCT
ejpam-1951	755	2	2	2	NUM
ejpam-1951	755	3	in	in	ADP
ejpam-1951	755	4	to	to	ADP
ejpam-1951	755	5	its	its	PRON
ejpam-1951	755	6	cycle	cycle	NOUN
ejpam-1951	755	7	index	index	NOUN
ejpam-1951	755	8	to	to	PART
ejpam-1951	755	9	find	find	VERB
ejpam-1951	755	10	the	the	DET
ejpam-1951	755	11	required	required	ADJ
ejpam-1951	755	12	number	number	NOUN
ejpam-1951	755	13	.	.	PUNCT
ejpam-1951	756	1	if	if	SCONJ
ejpam-1951	756	2	we	we	PRON
ejpam-1951	756	3	make	make	VERB
ejpam-1951	756	4	this	this	DET
ejpam-1951	756	5	substitution	substitution	NOUN
ejpam-1951	756	6	in	in	ADP
ejpam-1951	756	7	any	any	PRON
ejpam-1951	756	8	of	of	ADP
ejpam-1951	756	9	the	the	DET
ejpam-1951	756	10	polynomials	polynomial	NOUN
ejpam-1951	756	11	zg(t1	zg(t1	NUM
ejpam-1951	756	12	,	,	PUNCT
ejpam-1951	756	13	t2	t2	NOUN
ejpam-1951	756	14	,	,	PUNCT
ejpam-1951	756	15	t3	t3	PROPN
ejpam-1951	756	16	,	,	PUNCT
ejpam-1951	756	17	.	.	PUNCT
ejpam-1951	756	18	.	.	PUNCT
ejpam-1951	757	1	.	.	PUNCT
ejpam-1951	757	2	)	)	PUNCT
ejpam-1951	758	1	,	,	PUNCT
ejpam-1951	758	2	zg(t2	zg(t2	PROPN
ejpam-1951	758	3	,	,	PUNCT
ejpam-1951	758	4	t4	t4	PROPN
ejpam-1951	758	5	,	,	PUNCT
ejpam-1951	758	6	t6	t6	PROPN
ejpam-1951	758	7	,	,	PUNCT
ejpam-1951	758	8	.	.	PUNCT
ejpam-1951	758	9	.	.	PUNCT
ejpam-1951	759	1	.	.	PUNCT
ejpam-1951	759	2	)	)	PUNCT
ejpam-1951	759	3	,	,	PUNCT
ejpam-1951	759	4	zg(t3	zg(t3	PROPN
ejpam-1951	759	5	,	,	PUNCT
ejpam-1951	759	6	t6	t6	PROPN
ejpam-1951	759	7	,	,	PUNCT
ejpam-1951	759	8	t9	t9	PROPN
ejpam-1951	759	9	,	,	PUNCT
ejpam-1951	759	10	.	.	PUNCT
ejpam-1951	759	11	.	.	PUNCT
ejpam-1951	759	12	.	.	PUNCT
ejpam-1951	759	13	)	)	PUNCT
ejpam-1951	759	14	,	,	PUNCT
ejpam-1951	759	15	.	.	PUNCT
ejpam-1951	759	16	.	.	PUNCT
ejpam-1951	759	17	.	.	PUNCT
ejpam-1951	760	1	,	,	PUNCT
ejpam-1951	760	2	(	(	PUNCT
ejpam-1951	760	3	7	7	X
ejpam-1951	760	4	)	)	PUNCT
ejpam-1951	760	5	t.	t.	NOUN
ejpam-1951	760	6	nasseef	nasseef	PROPN
ejpam-1951	760	7	/	/	SYM
ejpam-1951	760	8	eur	eur	PROPN
ejpam-1951	760	9	.	.	PUNCT
ejpam-1951	761	1	j.	j.	PROPN
ejpam-1951	761	2	pure	pure	PROPN
ejpam-1951	761	3	appl	appl	PROPN
ejpam-1951	761	4	.	.	PROPN
ejpam-1951	761	5	math	math	PROPN
ejpam-1951	761	6	,	,	PUNCT
ejpam-1951	761	7	9	9	NUM
ejpam-1951	761	8	(	(	PUNCT
ejpam-1951	761	9	2016	2016	NUM
ejpam-1951	761	10	)	)	PUNCT
ejpam-1951	761	11	,	,	PUNCT
ejpam-1951	761	12	84	84	NUM
ejpam-1951	761	13	-	-	SYM
ejpam-1951	761	14	113	113	NUM
ejpam-1951	761	15	109	109	NUM
ejpam-1951	761	16	we	we	PRON
ejpam-1951	761	17	always	always	ADV
ejpam-1951	761	18	get	get	VERB
ejpam-1951	761	19	zg(2,2,2	zg(2,2,2	PROPN
ejpam-1951	761	20	,	,	PUNCT
ejpam-1951	761	21	.	.	PUNCT
ejpam-1951	761	22	.	.	PUNCT
ejpam-1951	762	1	.	.	PUNCT
ejpam-1951	762	2	)	)	PUNCT
ejpam-1951	763	1	and	and	CCONJ
ejpam-1951	763	2	hence	hence	ADV
ejpam-1951	763	3	zg(2,2,2	zg(2,2,2	PROPN
ejpam-1951	763	4	,	,	PUNCT
ejpam-1951	763	5	.	.	PUNCT
ejpam-1951	763	6	.	.	PUNCT
ejpam-1951	763	7	.	.	PUNCT
ejpam-1951	763	8	)	)	PUNCT
ejpam-1951	764	1	=	=	SYM
ejpam-1951	765	1	1	1	NUM
ejpam-1951	765	2	24	24	NUM
ejpam-1951	765	3	(	(	PUNCT
ejpam-1951	765	4	6(2)2(2	6(2)2(2	NOUN
ejpam-1951	765	5	)	)	PUNCT
ejpam-1951	765	6	+	+	NUM
ejpam-1951	765	7	3(2)2(2)2	3(2)2(2)2	NUM
ejpam-1951	765	8	+	+	NUM
ejpam-1951	765	9	8(2)2	8(2)2	NUM
ejpam-1951	765	10	+	+	CCONJ
ejpam-1951	765	11	6(2)3	6(2)3	NUM
ejpam-1951	766	1	+	+	CCONJ
ejpam-1951	766	2	26	26	NUM
ejpam-1951	766	3	)	)	PUNCT
ejpam-1951	766	4	=	=	PUNCT
ejpam-1951	767	1	10	10	NUM
ejpam-1951	767	2	thus	thus	ADV
ejpam-1951	767	3	the	the	DET
ejpam-1951	767	4	answer	answer	NOUN
ejpam-1951	767	5	of	of	ADP
ejpam-1951	767	6	the	the	DET
ejpam-1951	767	7	question	question	NOUN
ejpam-1951	767	8	is	be	AUX
ejpam-1951	767	9	sn(10,10,10	sn(10,10,10	ADJ
ejpam-1951	767	10	,	,	PUNCT
ejpam-1951	767	11	.	.	PUNCT
ejpam-1951	767	12	.	.	PUNCT
ejpam-1951	767	13	.	.	PUNCT
ejpam-1951	767	14	)	)	PUNCT
ejpam-1951	767	15	.	.	PUNCT
ejpam-1951	768	1	this	this	DET
ejpam-1951	768	2	number	number	NOUN
ejpam-1951	768	3	equals	equal	VERB
ejpam-1951	768	4	the	the	DET
ejpam-1951	768	5	coefficient	coefficient	NOUN
ejpam-1951	768	6	of	of	ADP
ejpam-1951	768	7	wn	wn	PROPN
ejpam-1951	768	8	in	in	ADP
ejpam-1951	768	9	the	the	DET
ejpam-1951	768	10	development	development	NOUN
ejpam-1951	768	11	of	of	ADP
ejpam-1951	768	12	ex	ex	ADJ
ejpam-1951	768	13	p(10w+	p(10w+	PROPN
ejpam-1951	768	14	1	1	NUM
ejpam-1951	768	15	2	2	NUM
ejpam-1951	768	16	10w2	10w2	NUM
ejpam-1951	768	17	+	+	CCONJ
ejpam-1951	768	18	1	1	NUM
ejpam-1951	768	19	3	3	NUM
ejpam-1951	768	20	10w3	10w3	NUM
ejpam-1951	768	21	+	+	PUNCT
ejpam-1951	768	22	.	.	PUNCT
ejpam-1951	768	23	.	.	PUNCT
ejpam-1951	768	24	.	.	PUNCT
ejpam-1951	768	25	)	)	PUNCT
ejpam-1951	769	1	=	=	PUNCT
ejpam-1951	769	2	(	(	PUNCT
ejpam-1951	769	3	1−w)−10	1−w)−10	NUM
ejpam-1951	769	4	therefore	therefore	ADV
ejpam-1951	769	5	sn(10,10,10	sn(10,10,10	X
ejpam-1951	769	6	,	,	PUNCT
ejpam-1951	769	7	.	.	PUNCT
ejpam-1951	769	8	.	.	PUNCT
ejpam-1951	769	9	.	.	PUNCT
ejpam-1951	769	10	)	)	PUNCT
ejpam-1951	770	1	=	=	PUNCT
ejpam-1951	770	2	(	(	PUNCT
ejpam-1951	770	3	n+	n+	NOUN
ejpam-1951	770	4	9	9	NUM
ejpam-1951	770	5	)	)	PUNCT
ejpam-1951	770	6	!	!	PUNCT
ejpam-1951	771	1	n!9	n!9	X
ejpam-1951	771	2	!	!	PUNCT
ejpam-1951	772	1	how	how	SCONJ
ejpam-1951	772	2	many	many	ADJ
ejpam-1951	772	3	of	of	ADP
ejpam-1951	772	4	the	the	DET
ejpam-1951	772	5	preceding	precede	VERB
ejpam-1951	772	6	patterns	pattern	NOUN
ejpam-1951	772	7	have	have	VERB
ejpam-1951	772	8	the	the	DET
ejpam-1951	772	9	property	property	NOUN
ejpam-1951	772	10	that	that	PRON
ejpam-1951	772	11	they	they	PRON
ejpam-1951	772	12	do	do	AUX
ejpam-1951	772	13	not	not	PART
ejpam-1951	772	14	change	change	VERB
ejpam-1951	772	15	if	if	SCONJ
ejpam-1951	772	16	we	we	PRON
ejpam-1951	772	17	interchange	interchange	VERB
ejpam-1951	772	18	the	the	DET
ejpam-1951	772	19	color	color	NOUN
ejpam-1951	772	20	?	?	PUNCT
ejpam-1951	773	1	according	accord	VERB
ejpam-1951	773	2	to	to	ADP
ejpam-1951	773	3	example	example	NOUN
ejpam-1951	773	4	20	20	NUM
ejpam-1951	773	5	this	this	DET
ejpam-1951	773	6	number	number	NOUN
ejpam-1951	773	7	is	be	AUX
ejpam-1951	773	8	found	find	VERB
ejpam-1951	773	9	by	by	ADP
ejpam-1951	773	10	substituting	substitute	VERB
ejpam-1951	773	11	t1	t1	NOUN
ejpam-1951	773	12	=	=	NOUN
ejpam-1951	773	13	t3	t3	PROPN
ejpam-1951	773	14	=	=	PUNCT
ejpam-1951	773	15	t5	t5	PROPN
ejpam-1951	773	16	=	=	PUNCT
ejpam-1951	773	17	....	....	PUNCT
ejpam-1951	774	1	=	=	SYM
ejpam-1951	774	2	0	0	PROPN
ejpam-1951	774	3	,	,	PUNCT
ejpam-1951	774	4	t2	t2	PROPN
ejpam-1951	774	5	=	=	SYM
ejpam-1951	774	6	t4	t4	PROPN
ejpam-1951	774	7	=	=	PROPN
ejpam-1951	774	8	t6	t6	PROPN
ejpam-1951	774	9	=	=	PUNCT
ejpam-1951	774	10	...	...	PUNCT
ejpam-1951	775	1	=	=	SYM
ejpam-1951	775	2	2	2	NUM
ejpam-1951	775	3	into	into	ADP
ejpam-1951	775	4	the	the	DET
ejpam-1951	775	5	cycle	cycle	NOUN
ejpam-1951	775	6	index	index	NOUN
ejpam-1951	775	7	.	.	PUNCT
ejpam-1951	776	1	under	under	ADP
ejpam-1951	776	2	the	the	DET
ejpam-1951	776	3	substitution	substitution	NOUN
ejpam-1951	776	4	the	the	DET
ejpam-1951	776	5	polynomials	polynomial	NOUN
ejpam-1951	776	6	(	(	PUNCT
ejpam-1951	776	7	7	7	X
ejpam-1951	776	8	)	)	PUNCT
ejpam-1951	776	9	become	become	VERB
ejpam-1951	776	10	zg(0,2,0,2	zg(0,2,0,2	NOUN
ejpam-1951	776	11	,	,	PUNCT
ejpam-1951	776	12	.	.	PUNCT
ejpam-1951	776	13	.	.	PUNCT
ejpam-1951	776	14	.	.	PUNCT
ejpam-1951	776	15	)	)	PUNCT
ejpam-1951	777	1	and	and	CCONJ
ejpam-1951	777	2	zg(2,2,2	zg(2,2,2	PROPN
ejpam-1951	777	3	,	,	PUNCT
ejpam-1951	777	4	.	.	PUNCT
ejpam-1951	777	5	.	.	PUNCT
ejpam-1951	777	6	.	.	PUNCT
ejpam-1951	777	7	)	)	PUNCT
ejpam-1951	777	8	,	,	PUNCT
ejpam-1951	777	9	alternately	alternately	ADV
ejpam-1951	777	10	.	.	PUNCT
ejpam-1951	778	1	as	as	ADP
ejpam-1951	778	2	zg(0,2,0,2	zg(0,2,0,2	NOUN
ejpam-1951	778	3	,	,	PUNCT
ejpam-1951	778	4	.	.	PUNCT
ejpam-1951	778	5	.	.	PUNCT
ejpam-1951	778	6	.	.	PUNCT
ejpam-1951	778	7	)	)	PUNCT
ejpam-1951	779	1	=	=	PUNCT
ejpam-1951	780	1	2	2	X
ejpam-1951	780	2	.	.	X
ejpam-1951	780	3	we	we	PRON
ejpam-1951	780	4	obtain	obtain	VERB
ejpam-1951	780	5	zsn[g	zsn[g	PROPN
ejpam-1951	780	6	]	]	X
ejpam-1951	780	7	(	(	PUNCT
ejpam-1951	780	8	0,2,0,2	0,2,0,2	NUM
ejpam-1951	780	9	,	,	PUNCT
ejpam-1951	780	10	.	.	PUNCT
ejpam-1951	780	11	.	.	PUNCT
ejpam-1951	780	12	.	.	PUNCT
ejpam-1951	780	13	)	)	PUNCT
ejpam-1951	781	1	=	=	PUNCT
ejpam-1951	781	2	zsn	zsn	X
ejpam-1951	781	3	(	(	PUNCT
ejpam-1951	781	4	2,10,2,10	2,10,2,10	NUM
ejpam-1951	781	5	,	,	PUNCT
ejpam-1951	781	6	.	.	PUNCT
ejpam-1951	781	7	.	.	PUNCT
ejpam-1951	781	8	.	.	PUNCT
ejpam-1951	781	9	)	)	PUNCT
ejpam-1951	782	1	this	this	PRON
ejpam-1951	782	2	is	be	AUX
ejpam-1951	782	3	the	the	DET
ejpam-1951	782	4	coefficient	coefficient	NOUN
ejpam-1951	782	5	of	of	ADP
ejpam-1951	782	6	wn	wn	PROPN
ejpam-1951	782	7	in	in	ADP
ejpam-1951	782	8	ex	ex	X
ejpam-1951	782	9	p(2w+	p(2w+	PROPN
ejpam-1951	782	10	1	1	NUM
ejpam-1951	782	11	2	2	NUM
ejpam-1951	782	12	10w2	10w2	NUM
ejpam-1951	782	13	+	+	CCONJ
ejpam-1951	782	14	1	1	NUM
ejpam-1951	782	15	3	3	NUM
ejpam-1951	782	16	2w3	2w3	NUM
ejpam-1951	782	17	+	+	CCONJ
ejpam-1951	782	18	1	1	NUM
ejpam-1951	782	19	4	4	NUM
ejpam-1951	782	20	10w4	10w4	NUM
ejpam-1951	782	21	+	+	CCONJ
ejpam-1951	782	22	.	.	PUNCT
ejpam-1951	782	23	.	.	PUNCT
ejpam-1951	782	24	.	.	PUNCT
ejpam-1951	782	25	.	.	PUNCT
ejpam-1951	782	26	)	)	PUNCT
ejpam-1951	783	1	=	=	X
ejpam-1951	783	2	ex	ex	X
ejpam-1951	783	3	p[2log(1−w)−1	p[2log(1−w)−1	NOUN
ejpam-1951	783	4	+	+	CCONJ
ejpam-1951	783	5	8log(1−w2)−1/2	8log(1−w2)−1/2	NOUN
ejpam-1951	783	6	]	]	X
ejpam-1951	784	1	=	=	X
ejpam-1951	784	2	(	(	PUNCT
ejpam-1951	784	3	1−w)−2(1−w2)−4	1−w)−2(1−w2)−4	NUM
ejpam-1951	784	4	=(	=(	NOUN
ejpam-1951	784	5	1	1	NUM
ejpam-1951	784	6	+	+	NUM
ejpam-1951	784	7	2w+w2)(1−w2)−6	2w+w2)(1−w2)−6	NOUN
ejpam-1951	784	8	=	=	SYM
ejpam-1951	784	9	1	1	NUM
ejpam-1951	784	10	+	+	NUM
ejpam-1951	784	11	2w+	2w+	NUM
ejpam-1951	784	12	7w2	7w2	NUM
ejpam-1951	784	13	+	+	CCONJ
ejpam-1951	784	14	12w3	12w3	NUM
ejpam-1951	784	15	+	+	CCONJ
ejpam-1951	784	16	27w4	27w4	NUM
ejpam-1951	785	1	+	+	CCONJ
ejpam-1951	785	2	42w5	42w5	NUM
ejpam-1951	786	1	+	+	NUM
ejpam-1951	786	2	77w6	77w6	NUM
ejpam-1951	786	3	+	+	CCONJ
ejpam-1951	786	4	112w7	112w7	NUM
ejpam-1951	786	5	+	+	CCONJ
ejpam-1951	786	6	182w8	182w8	NUM
ejpam-1951	786	7	+	+	NUM
ejpam-1951	786	8	252w9	252w9	NUM
ejpam-1951	786	9	+	+	PUNCT
ejpam-1951	786	10	.	.	PUNCT
ejpam-1951	786	11	.	.	PUNCT
ejpam-1951	786	12	.	.	PUNCT
ejpam-1951	787	1	for	for	ADP
ejpam-1951	787	2	example	example	NOUN
ejpam-1951	787	3	if	if	SCONJ
ejpam-1951	787	4	n=	n=	ADJ
ejpam-1951	787	5	9	9	NUM
ejpam-1951	787	6	the	the	DET
ejpam-1951	787	7	required	require	VERB
ejpam-1951	787	8	number	number	NOUN
ejpam-1951	787	9	of	of	ADP
ejpam-1951	787	10	patterns	pattern	NOUN
ejpam-1951	787	11	is	be	AUX
ejpam-1951	787	12	252	252	NUM
ejpam-1951	787	13	[	[	X
ejpam-1951	787	14	2	2	NUM
ejpam-1951	787	15	]	]	PUNCT
ejpam-1951	787	16	.	.	PUNCT
ejpam-1951	788	1	example	example	NOUN
ejpam-1951	788	2	22	22	NUM
ejpam-1951	788	3	.	.	PUNCT
ejpam-1951	789	1	consider	consider	VERB
ejpam-1951	789	2	n	n	PRON
ejpam-1951	789	3	tetrahedrons	tetrahedron	NOUN
ejpam-1951	789	4	and	and	CCONJ
ejpam-1951	789	5	we	we	PRON
ejpam-1951	789	6	want	want	VERB
ejpam-1951	789	7	to	to	PART
ejpam-1951	789	8	color	color	VERB
ejpam-1951	789	9	the	the	DET
ejpam-1951	789	10	edges	edge	NOUN
ejpam-1951	789	11	with	with	ADP
ejpam-1951	789	12	red	red	ADJ
ejpam-1951	789	13	and	and	CCONJ
ejpam-1951	789	14	yellow	yellow	ADJ
ejpam-1951	789	15	.	.	PUNCT
ejpam-1951	790	1	by	by	ADP
ejpam-1951	790	2	following	follow	VERB
ejpam-1951	790	3	problem	problem	NOUN
ejpam-1951	790	4	1	1	NUM
ejpam-1951	790	5	we	we	PRON
ejpam-1951	790	6	get	get	VERB
ejpam-1951	790	7	from	from	ADP
ejpam-1951	790	8	edge	edge	NOUN
ejpam-1951	790	9	coloring	coloring	NOUN
ejpam-1951	790	10	of	of	ADP
ejpam-1951	790	11	a	a	DET
ejpam-1951	790	12	tetrahedron	tetrahedron	NOUN
ejpam-1951	790	13	zg(2,2,2	zg(2,2,2	PROPN
ejpam-1951	790	14	,	,	PUNCT
ejpam-1951	790	15	.	.	PUNCT
ejpam-1951	790	16	.	.	PUNCT
ejpam-1951	790	17	.	.	PUNCT
ejpam-1951	790	18	)	)	PUNCT
ejpam-1951	791	1	=	=	PUNCT
ejpam-1951	791	2	12	12	NUM
ejpam-1951	791	3	thus	thus	ADV
ejpam-1951	791	4	the	the	DET
ejpam-1951	791	5	answer	answer	NOUN
ejpam-1951	791	6	of	of	ADP
ejpam-1951	791	7	this	this	DET
ejpam-1951	791	8	question	question	NOUN
ejpam-1951	791	9	is	be	AUX
ejpam-1951	791	10	sn(12,12,12	sn(12,12,12	NOUN
ejpam-1951	791	11	,	,	PUNCT
ejpam-1951	791	12	.	.	PUNCT
ejpam-1951	791	13	.	.	PUNCT
ejpam-1951	791	14	.	.	PUNCT
ejpam-1951	791	15	)	)	PUNCT
ejpam-1951	791	16	.	.	PUNCT
ejpam-1951	792	1	this	this	DET
ejpam-1951	792	2	number	number	NOUN
ejpam-1951	792	3	equals	equal	VERB
ejpam-1951	792	4	the	the	DET
ejpam-1951	792	5	coefficient	coefficient	NOUN
ejpam-1951	792	6	of	of	ADP
ejpam-1951	792	7	wn	wn	PROPN
ejpam-1951	792	8	in	in	ADP
ejpam-1951	792	9	the	the	DET
ejpam-1951	792	10	development	development	NOUN
ejpam-1951	792	11	of	of	ADP
ejpam-1951	792	12	ex	ex	PRON
ejpam-1951	792	13	p(12w+	p(12w+	NUM
ejpam-1951	792	14	1	1	NUM
ejpam-1951	792	15	2	2	NUM
ejpam-1951	792	16	12w2	12w2	NUM
ejpam-1951	792	17	+	+	NUM
ejpam-1951	792	18	1	1	NUM
ejpam-1951	792	19	3	3	NUM
ejpam-1951	792	20	12w3	12w3	NUM
ejpam-1951	792	21	+	+	PUNCT
ejpam-1951	792	22	.	.	PUNCT
ejpam-1951	792	23	.	.	PUNCT
ejpam-1951	792	24	.	.	PUNCT
ejpam-1951	792	25	)	)	PUNCT
ejpam-1951	793	1	=	=	PRON
ejpam-1951	793	2	(	(	PUNCT
ejpam-1951	793	3	1−w)−12	1−w)−12	NUM
ejpam-1951	793	4	t.	t.	NOUN
ejpam-1951	793	5	nasseef	nasseef	PROPN
ejpam-1951	793	6	/	/	SYM
ejpam-1951	793	7	eur	eur	PROPN
ejpam-1951	793	8	.	.	PUNCT
ejpam-1951	794	1	j.	j.	PROPN
ejpam-1951	794	2	pure	pure	PROPN
ejpam-1951	794	3	appl	appl	PROPN
ejpam-1951	794	4	.	.	PROPN
ejpam-1951	794	5	math	math	PROPN
ejpam-1951	794	6	,	,	PUNCT
ejpam-1951	794	7	9	9	NUM
ejpam-1951	794	8	(	(	PUNCT
ejpam-1951	794	9	2016	2016	NUM
ejpam-1951	794	10	)	)	PUNCT
ejpam-1951	794	11	,	,	PUNCT
ejpam-1951	794	12	84	84	NUM
ejpam-1951	794	13	-	-	SYM
ejpam-1951	794	14	113	113	NUM
ejpam-1951	794	15	110	110	NUM
ejpam-1951	794	16	therefore	therefore	ADV
ejpam-1951	794	17	sn(12,12,12	sn(12,12,12	NOUN
ejpam-1951	794	18	,	,	PUNCT
ejpam-1951	794	19	.	.	PUNCT
ejpam-1951	794	20	.	.	PUNCT
ejpam-1951	794	21	.	.	PUNCT
ejpam-1951	794	22	)	)	PUNCT
ejpam-1951	795	1	=	=	PUNCT
ejpam-1951	795	2	(	(	PUNCT
ejpam-1951	795	3	n+	n+	NOUN
ejpam-1951	795	4	11	11	NUM
ejpam-1951	795	5	)	)	PUNCT
ejpam-1951	795	6	!	!	PUNCT
ejpam-1951	796	1	n!11	n!11	PROPN
ejpam-1951	796	2	!	!	NOUN
ejpam-1951	797	1	now	now	ADV
ejpam-1951	797	2	we	we	PRON
ejpam-1951	797	3	want	want	VERB
ejpam-1951	797	4	to	to	PART
ejpam-1951	797	5	find	find	VERB
ejpam-1951	797	6	the	the	DET
ejpam-1951	797	7	number	number	NOUN
ejpam-1951	797	8	of	of	ADP
ejpam-1951	797	9	the	the	DET
ejpam-1951	797	10	preceding	precede	VERB
ejpam-1951	797	11	patterns	pattern	NOUN
ejpam-1951	797	12	having	have	VERB
ejpam-1951	797	13	the	the	DET
ejpam-1951	797	14	property	property	NOUN
ejpam-1951	797	15	that	that	PRON
ejpam-1951	797	16	they	they	PRON
ejpam-1951	797	17	do	do	AUX
ejpam-1951	797	18	not	not	PART
ejpam-1951	797	19	change	change	VERB
ejpam-1951	797	20	if	if	SCONJ
ejpam-1951	797	21	we	we	PRON
ejpam-1951	797	22	interchange	interchange	VERB
ejpam-1951	797	23	the	the	DET
ejpam-1951	797	24	color	color	NOUN
ejpam-1951	797	25	.	.	PUNCT
ejpam-1951	798	1	again	again	ADV
ejpam-1951	798	2	following	follow	VERB
ejpam-1951	798	3	problem	problem	NOUN
ejpam-1951	798	4	1	1	NUM
ejpam-1951	798	5	we	we	PRON
ejpam-1951	798	6	get	get	VERB
ejpam-1951	798	7	zsn[g	zsn[g	NUM
ejpam-1951	798	8	]	]	X
ejpam-1951	798	9	(	(	PUNCT
ejpam-1951	798	10	0,2,0,2	0,2,0,2	NUM
ejpam-1951	798	11	,	,	PUNCT
ejpam-1951	798	12	.	.	PUNCT
ejpam-1951	798	13	.	.	PUNCT
ejpam-1951	798	14	.	.	PUNCT
ejpam-1951	798	15	)	)	PUNCT
ejpam-1951	799	1	=	=	PUNCT
ejpam-1951	799	2	zsn	zsn	X
ejpam-1951	799	3	(	(	PUNCT
ejpam-1951	799	4	2,12,2,12	2,12,2,12	NUM
ejpam-1951	799	5	,	,	PUNCT
ejpam-1951	799	6	.	.	PUNCT
ejpam-1951	799	7	.	.	PUNCT
ejpam-1951	799	8	.	.	PUNCT
ejpam-1951	799	9	)	)	PUNCT
ejpam-1951	800	1	this	this	PRON
ejpam-1951	800	2	is	be	AUX
ejpam-1951	800	3	the	the	DET
ejpam-1951	800	4	coefficient	coefficient	NOUN
ejpam-1951	800	5	of	of	ADP
ejpam-1951	800	6	wn	wn	PROPN
ejpam-1951	800	7	in	in	ADP
ejpam-1951	800	8	ex	ex	X
ejpam-1951	800	9	p(2w+	p(2w+	PROPN
ejpam-1951	800	10	1	1	NUM
ejpam-1951	800	11	2	2	NUM
ejpam-1951	800	12	12w2	12w2	NUM
ejpam-1951	800	13	+	+	NUM
ejpam-1951	800	14	1	1	NUM
ejpam-1951	800	15	3	3	NUM
ejpam-1951	800	16	2w3	2w3	NUM
ejpam-1951	800	17	+	+	CCONJ
ejpam-1951	800	18	1	1	NUM
ejpam-1951	800	19	4	4	NUM
ejpam-1951	800	20	12w4	12w4	NUM
ejpam-1951	800	21	+	+	CCONJ
ejpam-1951	800	22	.	.	PUNCT
ejpam-1951	800	23	.	.	PUNCT
ejpam-1951	800	24	.	.	PUNCT
ejpam-1951	800	25	.	.	PUNCT
ejpam-1951	800	26	)	)	PUNCT
ejpam-1951	801	1	=	=	X
ejpam-1951	801	2	ex	ex	PRON
ejpam-1951	801	3	p[2log(1−w)−1	p[2log(1−w)−1	NOUN
ejpam-1951	801	4	+	+	CCONJ
ejpam-1951	801	5	10log(1−w2)−1/2	10log(1−w2)−1/2	NUM
ejpam-1951	801	6	]	]	X
ejpam-1951	801	7	=	=	X
ejpam-1951	801	8	(	(	PUNCT
ejpam-1951	801	9	1−w)−2(1−w2)−5	1−w)−2(1−w2)−5	NUM
ejpam-1951	801	10	=(	=(	NOUN
ejpam-1951	801	11	1	1	NUM
ejpam-1951	801	12	+	+	NOUN
ejpam-1951	801	13	2w+w2)(1−w2)−7	2w+w2)(1−w2)−7	NUM
ejpam-1951	801	14	=(	=(	NOUN
ejpam-1951	801	15	1	1	NUM
ejpam-1951	801	16	+	+	NUM
ejpam-1951	801	17	2w+w2)(1	2w+w2)(1	NUM
ejpam-1951	801	18	+	+	NOUN
ejpam-1951	801	19	7w2	7w2	NUM
ejpam-1951	801	20	+	+	SYM
ejpam-1951	801	21	28w4	28w4	NUM
ejpam-1951	801	22	+	+	CCONJ
ejpam-1951	801	23	.	.	PUNCT
ejpam-1951	801	24	.	.	PUNCT
ejpam-1951	801	25	.	.	PUNCT
ejpam-1951	801	26	)	)	PUNCT
ejpam-1951	802	1	=	=	PUNCT
ejpam-1951	803	1	1	1	NUM
ejpam-1951	803	2	+	+	NUM
ejpam-1951	803	3	2w+	2w+	NUM
ejpam-1951	803	4	8w2	8w2	NUM
ejpam-1951	803	5	+	+	SYM
ejpam-1951	803	6	14w3	14w3	NUM
ejpam-1951	803	7	+	+	NUM
ejpam-1951	803	8	35w4	35w4	NUM
ejpam-1951	803	9	+	+	NUM
ejpam-1951	803	10	.	.	PUNCT
ejpam-1951	803	11	.	.	PUNCT
ejpam-1951	803	12	.	.	PUNCT
ejpam-1951	804	1	for	for	ADP
ejpam-1951	804	2	example	example	NOUN
ejpam-1951	804	3	if	if	SCONJ
ejpam-1951	804	4	n=	n=	ADJ
ejpam-1951	804	5	4	4	NUM
ejpam-1951	804	6	the	the	DET
ejpam-1951	804	7	required	require	VERB
ejpam-1951	804	8	number	number	NOUN
ejpam-1951	804	9	of	of	ADP
ejpam-1951	804	10	patterns	pattern	NOUN
ejpam-1951	804	11	is	be	AUX
ejpam-1951	804	12	35	35	NUM
ejpam-1951	804	13	.	.	PUNCT
ejpam-1951	805	1	problem	problem	NOUN
ejpam-1951	805	2	7	7	NUM
ejpam-1951	805	3	.	.	PUNCT
ejpam-1951	806	1	let	let	VERB
ejpam-1951	806	2	us	we	PRON
ejpam-1951	806	3	take	take	VERB
ejpam-1951	806	4	n	n	PRON
ejpam-1951	806	5	cubes	cube	NOUN
ejpam-1951	806	6	and	and	CCONJ
ejpam-1951	806	7	we	we	PRON
ejpam-1951	806	8	want	want	VERB
ejpam-1951	806	9	to	to	PART
ejpam-1951	806	10	color	color	VERB
ejpam-1951	806	11	the	the	DET
ejpam-1951	806	12	faces	face	NOUN
ejpam-1951	806	13	with	with	ADP
ejpam-1951	806	14	red	red	ADJ
ejpam-1951	806	15	,	,	PUNCT
ejpam-1951	806	16	yellow	yellow	ADJ
ejpam-1951	806	17	and	and	CCONJ
ejpam-1951	806	18	green	green	ADJ
ejpam-1951	806	19	.	.	PUNCT
ejpam-1951	807	1	we	we	PRON
ejpam-1951	807	2	are	be	AUX
ejpam-1951	807	3	interested	interested	ADJ
ejpam-1951	807	4	for	for	ADP
ejpam-1951	807	5	the	the	DET
ejpam-1951	807	6	number	number	NOUN
ejpam-1951	807	7	of	of	ADP
ejpam-1951	807	8	ways	way	NOUN
ejpam-1951	807	9	to	to	PART
ejpam-1951	807	10	do	do	VERB
ejpam-1951	807	11	this	this	PRON
ejpam-1951	807	12	when	when	SCONJ
ejpam-1951	807	13	equivalences	equivalence	NOUN
ejpam-1951	807	14	are	be	AUX
ejpam-1951	807	15	defined	define	VERB
ejpam-1951	807	16	by	by	ADP
ejpam-1951	807	17	permutations	permutation	NOUN
ejpam-1951	807	18	of	of	ADP
ejpam-1951	807	19	the	the	DET
ejpam-1951	807	20	sets	set	NOUN
ejpam-1951	807	21	of	of	ADP
ejpam-1951	807	22	cubes	cube	NOUN
ejpam-1951	807	23	and	and	CCONJ
ejpam-1951	807	24	rotations	rotation	NOUN
ejpam-1951	807	25	of	of	ADP
ejpam-1951	807	26	the	the	DET
ejpam-1951	807	27	separate	separate	ADJ
ejpam-1951	807	28	cubes	cube	NOUN
ejpam-1951	807	29	.	.	PUNCT
ejpam-1951	808	1	solution	solution	NOUN
ejpam-1951	808	2	:	:	PUNCT
ejpam-1951	808	3	the	the	DET
ejpam-1951	808	4	group	group	NOUN
ejpam-1951	808	5	is	be	AUX
ejpam-1951	808	6	considered	consider	VERB
ejpam-1951	808	7	as	as	ADP
ejpam-1951	808	8	sn[g	sn[g	NOUN
ejpam-1951	808	9	]	]	PUNCT
ejpam-1951	808	10	where	where	SCONJ
ejpam-1951	808	11	sn	sn	PROPN
ejpam-1951	808	12	is	be	AUX
ejpam-1951	808	13	the	the	DET
ejpam-1951	808	14	symmetric	symmetric	ADJ
ejpam-1951	808	15	group	group	NOUN
ejpam-1951	808	16	of	of	ADP
ejpam-1951	808	17	degree	degree	NOUN
ejpam-1951	808	18	n	n	PROPN
ejpam-1951	808	19	and	and	CCONJ
ejpam-1951	808	20	g	g	PROPN
ejpam-1951	808	21	is	be	AUX
ejpam-1951	808	22	the	the	DET
ejpam-1951	808	23	cube	cube	NOUN
ejpam-1951	808	24	-	-	PUNCT
ejpam-1951	808	25	face	face	NOUN
ejpam-1951	808	26	group	group	NOUN
ejpam-1951	808	27	of	of	ADP
ejpam-1951	808	28	example	example	NOUN
ejpam-1951	808	29	11	11	NUM
ejpam-1951	808	30	.	.	PUNCT
ejpam-1951	809	1	then	then	ADV
ejpam-1951	809	2	we	we	PRON
ejpam-1951	809	3	have	have	VERB
ejpam-1951	809	4	to	to	PART
ejpam-1951	809	5	substitute	substitute	VERB
ejpam-1951	809	6	t1	t1	NOUN
ejpam-1951	809	7	=	=	SYM
ejpam-1951	809	8	t2	t2	PROPN
ejpam-1951	809	9	=	=	PUNCT
ejpam-1951	809	10	.	.	PUNCT
ejpam-1951	809	11	.	.	PUNCT
ejpam-1951	810	1	.=	.=	VERB
ejpam-1951	810	2	3	3	NUM
ejpam-1951	810	3	in	in	ADP
ejpam-1951	810	4	to	to	ADP
ejpam-1951	810	5	its	its	PRON
ejpam-1951	810	6	cycle	cycle	NOUN
ejpam-1951	810	7	index	index	NOUN
ejpam-1951	810	8	to	to	PART
ejpam-1951	810	9	find	find	VERB
ejpam-1951	810	10	the	the	DET
ejpam-1951	810	11	required	required	ADJ
ejpam-1951	810	12	number	number	NOUN
ejpam-1951	810	13	.	.	PUNCT
ejpam-1951	811	1	if	if	SCONJ
ejpam-1951	811	2	we	we	PRON
ejpam-1951	811	3	make	make	VERB
ejpam-1951	811	4	this	this	DET
ejpam-1951	811	5	substitution	substitution	NOUN
ejpam-1951	811	6	in	in	ADP
ejpam-1951	811	7	any	any	PRON
ejpam-1951	811	8	of	of	ADP
ejpam-1951	811	9	the	the	DET
ejpam-1951	811	10	polynomials	polynomial	NOUN
ejpam-1951	811	11	zg(t1	zg(t1	NUM
ejpam-1951	811	12	,	,	PUNCT
ejpam-1951	811	13	t2	t2	NOUN
ejpam-1951	811	14	,	,	PUNCT
ejpam-1951	811	15	t3	t3	PROPN
ejpam-1951	811	16	,	,	PUNCT
ejpam-1951	811	17	]	]	PUNCT
ejpam-1951	811	18	.	.	PUNCT
ejpam-1951	811	19	.	.	PUNCT
ejpam-1951	812	1	.	.	PUNCT
ejpam-1951	812	2	)	)	PUNCT
ejpam-1951	813	1	,	,	PUNCT
ejpam-1951	813	2	zg(t2	zg(t2	PROPN
ejpam-1951	813	3	,	,	PUNCT
ejpam-1951	813	4	t4	t4	PROPN
ejpam-1951	813	5	,	,	PUNCT
ejpam-1951	813	6	t6	t6	PROPN
ejpam-1951	813	7	,	,	PUNCT
ejpam-1951	813	8	.	.	PUNCT
ejpam-1951	813	9	.	.	PUNCT
ejpam-1951	814	1	.	.	PUNCT
ejpam-1951	814	2	)	)	PUNCT
ejpam-1951	814	3	,	,	PUNCT
ejpam-1951	814	4	zg(t3	zg(t3	PROPN
ejpam-1951	814	5	,	,	PUNCT
ejpam-1951	814	6	t6	t6	PROPN
ejpam-1951	814	7	,	,	PUNCT
ejpam-1951	814	8	t9	t9	PROPN
ejpam-1951	814	9	,	,	PUNCT
ejpam-1951	814	10	.	.	PUNCT
ejpam-1951	814	11	.	.	PUNCT
ejpam-1951	814	12	.	.	PUNCT
ejpam-1951	814	13	)	)	PUNCT
ejpam-1951	814	14	,	,	PUNCT
ejpam-1951	814	15	.	.	PUNCT
ejpam-1951	814	16	.	.	PUNCT
ejpam-1951	815	1	.	.	PUNCT
ejpam-1951	816	1	,	,	PUNCT
ejpam-1951	816	2	we	we	PRON
ejpam-1951	816	3	always	always	ADV
ejpam-1951	816	4	get	get	VERB
ejpam-1951	816	5	zg(3,3,3	zg(3,3,3	PROPN
ejpam-1951	816	6	,	,	PUNCT
ejpam-1951	816	7	.	.	PUNCT
ejpam-1951	816	8	.	.	PUNCT
ejpam-1951	816	9	.	.	PUNCT
ejpam-1951	816	10	)	)	PUNCT
ejpam-1951	817	1	and	and	CCONJ
ejpam-1951	817	2	hence	hence	ADV
ejpam-1951	817	3	zg(3,3,3	zg(3,3,3	PROPN
ejpam-1951	817	4	,	,	PUNCT
ejpam-1951	817	5	.	.	PUNCT
ejpam-1951	817	6	.	.	PUNCT
ejpam-1951	817	7	.	.	PUNCT
ejpam-1951	817	8	)	)	PUNCT
ejpam-1951	818	1	=	=	SYM
ejpam-1951	818	2	1	1	NUM
ejpam-1951	818	3	24	24	NUM
ejpam-1951	818	4	(	(	PUNCT
ejpam-1951	818	5	6(3)2(2	6(3)2(2	NUM
ejpam-1951	818	6	)	)	PUNCT
ejpam-1951	818	7	+	+	CCONJ
ejpam-1951	818	8	3(3)2(3)2	3(3)2(3)2	NUM
ejpam-1951	818	9	+	+	CCONJ
ejpam-1951	818	10	8(3)2	8(3)2	ADJ
ejpam-1951	818	11	+	+	CCONJ
ejpam-1951	818	12	6(3)3	6(3)3	NUM
ejpam-1951	818	13	+	+	NOUN
ejpam-1951	818	14	36	36	NUM
ejpam-1951	818	15	)	)	PUNCT
ejpam-1951	818	16	=	=	SYM
ejpam-1951	818	17	57	57	NUM
ejpam-1951	818	18	thus	thus	ADV
ejpam-1951	818	19	the	the	DET
ejpam-1951	818	20	answer	answer	NOUN
ejpam-1951	818	21	of	of	ADP
ejpam-1951	818	22	the	the	DET
ejpam-1951	818	23	question	question	NOUN
ejpam-1951	818	24	is	be	AUX
ejpam-1951	818	25	sn(57,57,57	sn(57,57,57	NOUN
ejpam-1951	818	26	,	,	PUNCT
ejpam-1951	818	27	.	.	PUNCT
ejpam-1951	818	28	.	.	PUNCT
ejpam-1951	818	29	.	.	PUNCT
ejpam-1951	818	30	)	)	PUNCT
ejpam-1951	818	31	.	.	PUNCT
ejpam-1951	819	1	this	this	DET
ejpam-1951	819	2	number	number	NOUN
ejpam-1951	819	3	equals	equal	VERB
ejpam-1951	819	4	the	the	DET
ejpam-1951	819	5	coefficient	coefficient	NOUN
ejpam-1951	819	6	of	of	ADP
ejpam-1951	819	7	wn	wn	PROPN
ejpam-1951	819	8	in	in	ADP
ejpam-1951	819	9	the	the	DET
ejpam-1951	819	10	development	development	NOUN
ejpam-1951	819	11	of	of	ADP
ejpam-1951	819	12	ex	ex	ADJ
ejpam-1951	819	13	p(57w+	p(57w+	NOUN
ejpam-1951	819	14	1	1	NUM
ejpam-1951	819	15	2	2	NUM
ejpam-1951	819	16	57w2	57w2	NUM
ejpam-1951	819	17	+	+	CCONJ
ejpam-1951	819	18	1	1	NUM
ejpam-1951	819	19	3	3	NUM
ejpam-1951	819	20	57w3	57w3	NUM
ejpam-1951	819	21	+	+	CCONJ
ejpam-1951	819	22	.	.	PUNCT
ejpam-1951	819	23	.	.	PUNCT
ejpam-1951	819	24	.	.	PUNCT
ejpam-1951	819	25	)	)	PUNCT
ejpam-1951	820	1	=	=	PUNCT
ejpam-1951	820	2	(	(	PUNCT
ejpam-1951	820	3	1−w)−57	1−w)−57	NOUN
ejpam-1951	820	4	therefore	therefore	ADV
ejpam-1951	820	5	sn(57,57,57	sn(57,57,57	NOUN
ejpam-1951	820	6	,	,	PUNCT
ejpam-1951	820	7	.	.	PUNCT
ejpam-1951	820	8	.	.	PUNCT
ejpam-1951	820	9	.	.	PUNCT
ejpam-1951	820	10	)	)	PUNCT
ejpam-1951	821	1	=	=	PUNCT
ejpam-1951	821	2	(	(	PUNCT
ejpam-1951	821	3	n+	n+	NOUN
ejpam-1951	821	4	56	56	NUM
ejpam-1951	821	5	)	)	PUNCT
ejpam-1951	821	6	!	!	PUNCT
ejpam-1951	822	1	n!(56	n!(56	PROPN
ejpam-1951	822	2	)	)	PUNCT
ejpam-1951	822	3	!	!	PUNCT
ejpam-1951	823	1	how	how	SCONJ
ejpam-1951	823	2	many	many	ADJ
ejpam-1951	823	3	of	of	ADP
ejpam-1951	823	4	the	the	DET
ejpam-1951	823	5	preceding	precede	VERB
ejpam-1951	823	6	patterns	pattern	NOUN
ejpam-1951	823	7	have	have	VERB
ejpam-1951	823	8	the	the	DET
ejpam-1951	823	9	property	property	NOUN
ejpam-1951	823	10	that	that	PRON
ejpam-1951	823	11	they	they	PRON
ejpam-1951	823	12	do	do	AUX
ejpam-1951	823	13	not	not	PART
ejpam-1951	823	14	change	change	VERB
ejpam-1951	823	15	if	if	SCONJ
ejpam-1951	823	16	we	we	PRON
ejpam-1951	823	17	interchange	interchange	VERB
ejpam-1951	823	18	the	the	DET
ejpam-1951	823	19	color	color	NOUN
ejpam-1951	823	20	?	?	PUNCT
ejpam-1951	824	1	t.	t.	PROPN
ejpam-1951	824	2	nasseef	nasseef	PROPN
ejpam-1951	824	3	/	/	SYM
ejpam-1951	824	4	eur	eur	PROPN
ejpam-1951	824	5	.	.	PUNCT
ejpam-1951	825	1	j.	j.	PROPN
ejpam-1951	825	2	pure	pure	PROPN
ejpam-1951	825	3	appl	appl	PROPN
ejpam-1951	825	4	.	.	PROPN
ejpam-1951	825	5	math	math	PROPN
ejpam-1951	825	6	,	,	PUNCT
ejpam-1951	825	7	9	9	NUM
ejpam-1951	825	8	(	(	PUNCT
ejpam-1951	825	9	2016	2016	NUM
ejpam-1951	825	10	)	)	PUNCT
ejpam-1951	825	11	,	,	PUNCT
ejpam-1951	825	12	84	84	NUM
ejpam-1951	825	13	-	-	SYM
ejpam-1951	825	14	113	113	NUM
ejpam-1951	825	15	111	111	NUM
ejpam-1951	825	16	by	by	ADP
ejpam-1951	825	17	(	(	PUNCT
ejpam-1951	825	18	5	5	NUM
ejpam-1951	825	19	)	)	PUNCT
ejpam-1951	825	20	,	,	PUNCT
ejpam-1951	825	21	this	this	DET
ejpam-1951	825	22	number	number	NOUN
ejpam-1951	825	23	is	be	AUX
ejpam-1951	825	24	found	find	VERB
ejpam-1951	825	25	by	by	ADP
ejpam-1951	825	26	substituting	substitute	VERB
ejpam-1951	825	27	t1	t1	NOUN
ejpam-1951	825	28	=	=	NOUN
ejpam-1951	825	29	t2	t2	NOUN
ejpam-1951	825	30	=	=	SYM
ejpam-1951	825	31	t4	t4	PROPN
ejpam-1951	825	32	=	=	PROPN
ejpam-1951	825	33	t5	t5	PROPN
ejpam-1951	825	34	.	.	PUNCT
ejpam-1951	825	35	.	.	PUNCT
ejpam-1951	826	1	.=	.=	PROPN
ejpam-1951	826	2	0	0	NUM
ejpam-1951	826	3	,	,	PUNCT
ejpam-1951	826	4	t3	t3	PROPN
ejpam-1951	826	5	=	=	PROPN
ejpam-1951	826	6	t6	t6	PROPN
ejpam-1951	826	7	=	=	SYM
ejpam-1951	826	8	t9	t9	PROPN
ejpam-1951	826	9	=	=	PRON
ejpam-1951	826	10	.	.	PUNCT
ejpam-1951	826	11	.	.	PUNCT
ejpam-1951	827	1	.=	.=	VERB
ejpam-1951	827	2	3	3	NUM
ejpam-1951	827	3	into	into	ADP
ejpam-1951	827	4	the	the	DET
ejpam-1951	827	5	cycle	cycle	NOUN
ejpam-1951	827	6	index	index	NOUN
ejpam-1951	827	7	.	.	PUNCT
ejpam-1951	828	1	under	under	ADP
ejpam-1951	828	2	the	the	DET
ejpam-1951	828	3	substitution	substitution	NOUN
ejpam-1951	828	4	the	the	DET
ejpam-1951	828	5	polynomials	polynomial	NOUN
ejpam-1951	828	6	become	become	VERB
ejpam-1951	828	7	zg(0,0,3,0,0,3	zg(0,0,3,0,0,3	PROPN
ejpam-1951	828	8	,	,	PUNCT
ejpam-1951	828	9	.	.	PUNCT
ejpam-1951	828	10	.	.	PUNCT
ejpam-1951	828	11	.	.	PUNCT
ejpam-1951	828	12	)	)	PUNCT
ejpam-1951	829	1	and	and	CCONJ
ejpam-1951	829	2	zg(3,3,3	zg(3,3,3	PROPN
ejpam-1951	829	3	,	,	PUNCT
ejpam-1951	829	4	.	.	PUNCT
ejpam-1951	829	5	.	.	PUNCT
ejpam-1951	829	6	.	.	PUNCT
ejpam-1951	829	7	)	)	PUNCT
ejpam-1951	829	8	,	,	PUNCT
ejpam-1951	829	9	alternately	alternately	ADV
ejpam-1951	829	10	.	.	PUNCT
ejpam-1951	830	1	as	as	ADP
ejpam-1951	830	2	zg(0,0,3,0,0,3	zg(0,0,3,0,0,3	NUM
ejpam-1951	830	3	,	,	PUNCT
ejpam-1951	830	4	.	.	PUNCT
ejpam-1951	830	5	.	.	PUNCT
ejpam-1951	830	6	.	.	PUNCT
ejpam-1951	830	7	)	)	PUNCT
ejpam-1951	831	1	=	=	PUNCT
ejpam-1951	832	1	3	3	X
ejpam-1951	832	2	.	.	X
ejpam-1951	832	3	we	we	PRON
ejpam-1951	832	4	obtain	obtain	VERB
ejpam-1951	832	5	zsn[g	zsn[g	PROPN
ejpam-1951	832	6	]	]	X
ejpam-1951	832	7	(	(	PUNCT
ejpam-1951	832	8	0,0,3,0,0,3	0,0,3,0,0,3	NUM
ejpam-1951	832	9	,	,	PUNCT
ejpam-1951	832	10	.	.	PUNCT
ejpam-1951	832	11	.	.	PUNCT
ejpam-1951	832	12	.	.	PUNCT
ejpam-1951	832	13	)	)	PUNCT
ejpam-1951	833	1	=	=	PUNCT
ejpam-1951	833	2	zsn	zsn	X
ejpam-1951	833	3	(	(	PUNCT
ejpam-1951	833	4	3,3,57,3,3,57	3,3,57,3,3,57	NOUN
ejpam-1951	833	5	,	,	PUNCT
ejpam-1951	833	6	.	.	PUNCT
ejpam-1951	833	7	.	.	PUNCT
ejpam-1951	833	8	.	.	PUNCT
ejpam-1951	833	9	)	)	PUNCT
ejpam-1951	834	1	this	this	PRON
ejpam-1951	834	2	is	be	AUX
ejpam-1951	834	3	the	the	DET
ejpam-1951	834	4	coefficient	coefficient	NOUN
ejpam-1951	834	5	of	of	ADP
ejpam-1951	834	6	wn	wn	PROPN
ejpam-1951	834	7	in	in	ADP
ejpam-1951	834	8	ex	ex	X
ejpam-1951	834	9	p(3w+	p(3w+	NOUN
ejpam-1951	834	10	1	1	NUM
ejpam-1951	834	11	2	2	NUM
ejpam-1951	834	12	3w2	3w2	NUM
ejpam-1951	834	13	+	+	CCONJ
ejpam-1951	834	14	1	1	NUM
ejpam-1951	834	15	3	3	NUM
ejpam-1951	834	16	57w3	57w3	NUM
ejpam-1951	834	17	+	+	CCONJ
ejpam-1951	834	18	1	1	NUM
ejpam-1951	834	19	4	4	NUM
ejpam-1951	834	20	3w4	3w4	NUM
ejpam-1951	834	21	+	+	NUM
ejpam-1951	834	22	....	....	PUNCT
ejpam-1951	834	23	)	)	PUNCT
ejpam-1951	835	1	=	=	X
ejpam-1951	835	2	ex	ex	X
ejpam-1951	835	3	p[3log(1−w)−1	p[3log(1−w)−1	NOUN
ejpam-1951	835	4	+	+	CCONJ
ejpam-1951	836	1	54log(1−w3)−1/3	54log(1−w3)−1/3	NUM
ejpam-1951	836	2	]	]	X
ejpam-1951	837	1	=	=	NOUN
ejpam-1951	837	2	(	(	PUNCT
ejpam-1951	837	3	1−w)−3(1−w3)−18	1−w)−3(1−w3)−18	NUM
ejpam-1951	837	4	=(	=(	NOUN
ejpam-1951	837	5	1	1	NUM
ejpam-1951	837	6	+	+	NUM
ejpam-1951	837	7	3w+	3w+	NUM
ejpam-1951	837	8	6w2	6w2	NUM
ejpam-1951	837	9	+	+	CCONJ
ejpam-1951	837	10	10w3	10w3	NUM
ejpam-1951	837	11	.	.	PUNCT
ejpam-1951	837	12	.	.	PUNCT
ejpam-1951	838	1	.)(1	.)(1	PROPN
ejpam-1951	839	1	+	+	CCONJ
ejpam-1951	839	2	18w3	18w3	NUM
ejpam-1951	839	3	+	+	NUM
ejpam-1951	839	4	171w6	171w6	NUM
ejpam-1951	839	5	+	+	NUM
ejpam-1951	839	6	.	.	PUNCT
ejpam-1951	839	7	.	.	PUNCT
ejpam-1951	839	8	.	.	PUNCT
ejpam-1951	839	9	)	)	PUNCT
ejpam-1951	840	1	=	=	PUNCT
ejpam-1951	840	2	1	1	NUM
ejpam-1951	840	3	+	+	NUM
ejpam-1951	840	4	3w+	3w+	NUM
ejpam-1951	840	5	6w2	6w2	NUM
ejpam-1951	840	6	+	+	CCONJ
ejpam-1951	840	7	28w3	28w3	NUM
ejpam-1951	840	8	+	+	CCONJ
ejpam-1951	840	9	.	.	PUNCT
ejpam-1951	840	10	.	.	PUNCT
ejpam-1951	840	11	.	.	PUNCT
ejpam-1951	841	1	for	for	ADP
ejpam-1951	841	2	example	example	NOUN
ejpam-1951	841	3	if	if	SCONJ
ejpam-1951	841	4	n=	n=	ADJ
ejpam-1951	841	5	3	3	NUM
ejpam-1951	841	6	the	the	DET
ejpam-1951	841	7	required	require	VERB
ejpam-1951	841	8	number	number	NOUN
ejpam-1951	841	9	of	of	ADP
ejpam-1951	841	10	patterns	pattern	NOUN
ejpam-1951	841	11	is	be	AUX
ejpam-1951	841	12	28	28	NUM
ejpam-1951	841	13	.	.	PUNCT
ejpam-1951	842	1	problem	problem	NOUN
ejpam-1951	842	2	8	8	NUM
ejpam-1951	842	3	.	.	PUNCT
ejpam-1951	843	1	let	let	VERB
ejpam-1951	843	2	us	we	PRON
ejpam-1951	843	3	take	take	VERB
ejpam-1951	843	4	n	n	PRON
ejpam-1951	843	5	cubes	cube	NOUN
ejpam-1951	843	6	and	and	CCONJ
ejpam-1951	843	7	we	we	PRON
ejpam-1951	843	8	want	want	VERB
ejpam-1951	843	9	to	to	PART
ejpam-1951	843	10	color	color	VERB
ejpam-1951	843	11	the	the	DET
ejpam-1951	843	12	faces	face	NOUN
ejpam-1951	843	13	with	with	ADP
ejpam-1951	843	14	red	red	ADJ
ejpam-1951	843	15	,	,	PUNCT
ejpam-1951	843	16	black	black	ADJ
ejpam-1951	843	17	,	,	PUNCT
ejpam-1951	843	18	yellow	yellow	ADJ
ejpam-1951	843	19	and	and	CCONJ
ejpam-1951	843	20	green	green	ADJ
ejpam-1951	843	21	.	.	PUNCT
ejpam-1951	844	1	how	how	SCONJ
ejpam-1951	844	2	many	many	ADJ
ejpam-1951	844	3	of	of	ADP
ejpam-1951	844	4	the	the	DET
ejpam-1951	844	5	patterns	pattern	NOUN
ejpam-1951	844	6	have	have	VERB
ejpam-1951	844	7	the	the	DET
ejpam-1951	844	8	property	property	NOUN
ejpam-1951	844	9	that	that	PRON
ejpam-1951	844	10	they	they	PRON
ejpam-1951	844	11	do	do	AUX
ejpam-1951	844	12	not	not	PART
ejpam-1951	844	13	change	change	VERB
ejpam-1951	844	14	if	if	SCONJ
ejpam-1951	844	15	we	we	PRON
ejpam-1951	844	16	interchange	interchange	VERB
ejpam-1951	844	17	the	the	DET
ejpam-1951	844	18	color	color	NOUN
ejpam-1951	844	19	?	?	PUNCT
ejpam-1951	845	1	solution	solution	NOUN
ejpam-1951	845	2	:	:	PUNCT
ejpam-1951	845	3	with	with	ADP
ejpam-1951	845	4	the	the	DET
ejpam-1951	845	5	help	help	NOUN
ejpam-1951	845	6	of	of	ADP
ejpam-1951	845	7	(	(	PUNCT
ejpam-1951	845	8	5	5	NUM
ejpam-1951	845	9	)	)	PUNCT
ejpam-1951	845	10	,	,	PUNCT
ejpam-1951	845	11	this	this	DET
ejpam-1951	845	12	number	number	NOUN
ejpam-1951	845	13	is	be	AUX
ejpam-1951	845	14	found	find	VERB
ejpam-1951	845	15	by	by	ADP
ejpam-1951	845	16	substituting	substitute	VERB
ejpam-1951	845	17	t1	t1	NOUN
ejpam-1951	845	18	=	=	NOUN
ejpam-1951	845	19	t3	t3	PROPN
ejpam-1951	845	20	=	=	PROPN
ejpam-1951	845	21	t5	t5	PROPN
ejpam-1951	845	22	=	=	PROPN
ejpam-1951	845	23	t7	t7	PROPN
ejpam-1951	845	24	.	.	PUNCT
ejpam-1951	845	25	.	.	PUNCT
ejpam-1951	846	1	.=	.=	PROPN
ejpam-1951	847	1	0	0	NUM
ejpam-1951	847	2	,	,	PUNCT
ejpam-1951	847	3	t2	t2	PROPN
ejpam-1951	847	4	=	=	SYM
ejpam-1951	847	5	t6	t6	PROPN
ejpam-1951	847	6	=	=	SYM
ejpam-1951	847	7	t10	t10	PROPN
ejpam-1951	847	8	=	=	NOUN
ejpam-1951	847	9	.	.	PUNCT
ejpam-1951	847	10	.	.	PUNCT
ejpam-1951	848	1	.=	.=	VERB
ejpam-1951	849	1	4	4	NUM
ejpam-1951	849	2	,	,	PUNCT
ejpam-1951	849	3	t4	t4	PROPN
ejpam-1951	849	4	=	=	PROPN
ejpam-1951	849	5	t8	t8	PROPN
ejpam-1951	849	6	=	=	X
ejpam-1951	849	7	.	.	PUNCT
ejpam-1951	849	8	.	.	PUNCT
ejpam-1951	850	1	.=	.=	VERB
ejpam-1951	850	2	4	4	NUM
ejpam-1951	850	3	into	into	ADP
ejpam-1951	850	4	the	the	DET
ejpam-1951	850	5	cycle	cycle	NOUN
ejpam-1951	850	6	index	index	NOUN
ejpam-1951	850	7	.	.	PUNCT
ejpam-1951	851	1	under	under	ADP
ejpam-1951	851	2	the	the	DET
ejpam-1951	851	3	substitution	substitution	NOUN
ejpam-1951	851	4	the	the	DET
ejpam-1951	851	5	polynomials	polynomial	NOUN
ejpam-1951	851	6	become	become	VERB
ejpam-1951	851	7	zg(0,0,0,4,0,0,0,4	zg(0,0,0,4,0,0,0,4	NOUN
ejpam-1951	851	8	,	,	PUNCT
ejpam-1951	851	9	.	.	PUNCT
ejpam-1951	851	10	.	.	PUNCT
ejpam-1951	852	1	.	.	PUNCT
ejpam-1951	852	2	)	)	PUNCT
ejpam-1951	853	1	,	,	PUNCT
ejpam-1951	853	2	zg(0,4,0,4,0,4,0,4	zg(0,4,0,4,0,4,0,4	PROPN
ejpam-1951	853	3	,	,	PUNCT
ejpam-1951	853	4	.	.	PUNCT
ejpam-1951	853	5	.	.	PUNCT
ejpam-1951	853	6	.	.	PUNCT
ejpam-1951	853	7	)	)	PUNCT
ejpam-1951	854	1	and	and	CCONJ
ejpam-1951	854	2	zg(4,4,4	zg(4,4,4	PROPN
ejpam-1951	854	3	,	,	PUNCT
ejpam-1951	854	4	.	.	PUNCT
ejpam-1951	854	5	.	.	PUNCT
ejpam-1951	854	6	.	.	PUNCT
ejpam-1951	854	7	)	)	PUNCT
ejpam-1951	854	8	,	,	PUNCT
ejpam-1951	854	9	alternately	alternately	ADV
ejpam-1951	854	10	.	.	PUNCT
ejpam-1951	855	1	now	now	ADV
ejpam-1951	855	2	zg(4,4,4	zg(4,4,4	PROPN
ejpam-1951	855	3	,	,	PUNCT
ejpam-1951	855	4	.	.	PUNCT
ejpam-1951	855	5	.	.	PUNCT
ejpam-1951	855	6	.	.	PUNCT
ejpam-1951	855	7	)	)	PUNCT
ejpam-1951	856	1	=	=	SYM
ejpam-1951	856	2	1	1	NUM
ejpam-1951	856	3	24	24	NUM
ejpam-1951	856	4	(	(	PUNCT
ejpam-1951	856	5	6(4)2(4	6(4)2(4	NOUN
ejpam-1951	856	6	)	)	PUNCT
ejpam-1951	856	7	+	+	CCONJ
ejpam-1951	856	8	3(4)2(4)2	3(4)2(4)2	NUM
ejpam-1951	856	9	+	+	SYM
ejpam-1951	856	10	8(4)2	8(4)2	NUM
ejpam-1951	857	1	+	+	CCONJ
ejpam-1951	857	2	6(4)3	6(4)3	ADJ
ejpam-1951	857	3	+	+	NUM
ejpam-1951	857	4	46	46	NUM
ejpam-1951	857	5	)	)	PUNCT
ejpam-1951	857	6	=	=	SYM
ejpam-1951	857	7	240	240	NUM
ejpam-1951	857	8	and	and	CCONJ
ejpam-1951	857	9	zg(0,4,0,4	zg(0,4,0,4	NOUN
ejpam-1951	857	10	,	,	PUNCT
ejpam-1951	857	11	.	.	PUNCT
ejpam-1951	857	12	.	.	PUNCT
ejpam-1951	858	1	.	.	PUNCT
ejpam-1951	858	2	)	)	PUNCT
ejpam-1951	859	1	=	=	SYM
ejpam-1951	859	2	1	1	NUM
ejpam-1951	859	3	24	24	NUM
ejpam-1951	859	4	(	(	PUNCT
ejpam-1951	859	5	6(0)2(4	6(0)2(4	PROPN
ejpam-1951	859	6	)	)	PUNCT
ejpam-1951	859	7	+	+	CCONJ
ejpam-1951	859	8	3(0)2(4)2	3(0)2(4)2	NUM
ejpam-1951	860	1	+	+	NUM
ejpam-1951	860	2	8(0)2	8(0)2	NUM
ejpam-1951	860	3	+	+	CCONJ
ejpam-1951	860	4	6(4)3	6(4)3	ADJ
ejpam-1951	860	5	+	+	NUM
ejpam-1951	860	6	06	06	NUM
ejpam-1951	860	7	)	)	PUNCT
ejpam-1951	860	8	=	=	SYM
ejpam-1951	860	9	16	16	NUM
ejpam-1951	860	10	as	as	ADP
ejpam-1951	860	11	zg(0,0,0,4,0,0,0,4	zg(0,0,0,4,0,0,0,4	NOUN
ejpam-1951	860	12	,	,	PUNCT
ejpam-1951	860	13	.	.	PUNCT
ejpam-1951	860	14	.	.	PUNCT
ejpam-1951	860	15	.	.	PUNCT
ejpam-1951	860	16	)	)	PUNCT
ejpam-1951	861	1	=	=	PUNCT
ejpam-1951	862	1	0	0	X
ejpam-1951	862	2	.	.	PUNCT
ejpam-1951	863	1	we	we	PRON
ejpam-1951	863	2	obtain	obtain	VERB
ejpam-1951	863	3	zsn[g	zsn[g	PROPN
ejpam-1951	863	4	]	]	X
ejpam-1951	863	5	(	(	PUNCT
ejpam-1951	863	6	0,0,0,4,0,0	0,0,0,4,0,0	NOUN
ejpam-1951	863	7	,	,	PUNCT
ejpam-1951	863	8	.	.	PUNCT
ejpam-1951	863	9	.	.	PUNCT
ejpam-1951	863	10	.	.	PUNCT
ejpam-1951	863	11	)	)	PUNCT
ejpam-1951	864	1	=	=	PUNCT
ejpam-1951	864	2	zsn	zsn	X
ejpam-1951	864	3	(	(	PUNCT
ejpam-1951	864	4	0,16,0,240,0,16,0,240	0,16,0,240,0,16,0,240	NOUN
ejpam-1951	864	5	,	,	PUNCT
ejpam-1951	864	6	.	.	PUNCT
ejpam-1951	864	7	.	.	PUNCT
ejpam-1951	864	8	.	.	PUNCT
ejpam-1951	864	9	)	)	PUNCT
ejpam-1951	865	1	this	this	PRON
ejpam-1951	865	2	is	be	AUX
ejpam-1951	865	3	the	the	DET
ejpam-1951	865	4	coefficient	coefficient	NOUN
ejpam-1951	865	5	of	of	ADP
ejpam-1951	865	6	wn	wn	PROPN
ejpam-1951	865	7	in	in	ADP
ejpam-1951	865	8	ex	ex	ADJ
ejpam-1951	865	9	p(0w+	p(0w+	NOUN
ejpam-1951	865	10	1	1	NUM
ejpam-1951	865	11	2	2	NUM
ejpam-1951	865	12	16w2	16w2	NUM
ejpam-1951	865	13	+	+	NUM
ejpam-1951	865	14	1	1	NUM
ejpam-1951	865	15	3	3	NUM
ejpam-1951	865	16	0w3	0w3	NUM
ejpam-1951	865	17	+	+	CCONJ
ejpam-1951	865	18	1	1	NUM
ejpam-1951	865	19	4	4	NUM
ejpam-1951	865	20	240w4	240w4	NUM
ejpam-1951	865	21	+	+	SYM
ejpam-1951	865	22	.	.	PUNCT
ejpam-1951	865	23	.	.	PUNCT
ejpam-1951	865	24	.	.	PUNCT
ejpam-1951	865	25	)	)	PUNCT
ejpam-1951	866	1	references	reference	VERB
ejpam-1951	866	2	112	112	NUM
ejpam-1951	866	3	=	=	ADJ
ejpam-1951	866	4	ex	ex	X
ejpam-1951	866	5	p	p	X
ejpam-1951	866	6	(	(	PUNCT
ejpam-1951	866	7	1	1	NUM
ejpam-1951	866	8	2	2	NUM
ejpam-1951	866	9	16w2	16w2	NUM
ejpam-1951	866	10	+	+	NUM
ejpam-1951	866	11	1	1	NUM
ejpam-1951	866	12	4	4	NUM
ejpam-1951	866	13	240w4	240w4	NUM
ejpam-1951	866	14	+	+	CCONJ
ejpam-1951	866	15	1	1	NUM
ejpam-1951	866	16	6	6	NUM
ejpam-1951	866	17	16w6	16w6	NUM
ejpam-1951	866	18	+	+	CCONJ
ejpam-1951	866	19	1	1	NUM
ejpam-1951	866	20	8	8	NUM
ejpam-1951	866	21	240w8	240w8	NUM
ejpam-1951	866	22	.	.	PUNCT
ejpam-1951	866	23	.	.	PUNCT
ejpam-1951	866	24	.	.	PUNCT
ejpam-1951	866	25	)	)	PUNCT
ejpam-1951	867	1	=	=	PRON
ejpam-1951	867	2	ex	ex	X
ejpam-1951	867	3	p[16log(1−w2)−1/2	p[16log(1−w2)−1/2	NOUN
ejpam-1951	867	4	+	+	CCONJ
ejpam-1951	867	5	224log(1−w4)−1/4	224log(1−w4)−1/4	NUM
ejpam-1951	867	6	]	]	X
ejpam-1951	868	1	=	=	X
ejpam-1951	868	2	(	(	PUNCT
ejpam-1951	868	3	1−w2)−8(1−w4)−56	1−w2)−8(1−w4)−56	NUM
ejpam-1951	868	4	=(	=(	NOUN
ejpam-1951	868	5	1	1	NUM
ejpam-1951	868	6	+	+	NUM
ejpam-1951	868	7	8w2	8w2	NUM
ejpam-1951	868	8	+	+	CCONJ
ejpam-1951	868	9	36w4	36w4	NUM
ejpam-1951	868	10	+	+	NUM
ejpam-1951	868	11	.	.	PUNCT
ejpam-1951	868	12	.	.	PUNCT
ejpam-1951	869	1	.)(1	.)(1	PUNCT
ejpam-1951	870	1	+	+	CCONJ
ejpam-1951	870	2	56w4	56w4	NUM
ejpam-1951	870	3	+	+	NUM
ejpam-1951	870	4	1596w8	1596w8	NUM
ejpam-1951	871	1	+	+	X
ejpam-1951	871	2	.	.	PUNCT
ejpam-1951	871	3	.	.	PUNCT
ejpam-1951	871	4	.	.	PUNCT
ejpam-1951	871	5	)	)	PUNCT
ejpam-1951	872	1	=	=	PUNCT
ejpam-1951	873	1	1	1	NUM
ejpam-1951	873	2	+	+	NUM
ejpam-1951	873	3	8w2	8w2	NUM
ejpam-1951	873	4	+	+	CCONJ
ejpam-1951	873	5	92w4	92w4	NUM
ejpam-1951	873	6	+	+	NOUN
ejpam-1951	873	7	.	.	PUNCT
ejpam-1951	873	8	.	.	PUNCT
ejpam-1951	873	9	.	.	PUNCT
ejpam-1951	874	1	for	for	ADP
ejpam-1951	874	2	example	example	NOUN
ejpam-1951	874	3	if	if	SCONJ
ejpam-1951	874	4	n=	n=	ADJ
ejpam-1951	874	5	4	4	NUM
ejpam-1951	874	6	the	the	DET
ejpam-1951	874	7	required	require	VERB
ejpam-1951	874	8	number	number	NOUN
ejpam-1951	874	9	of	of	ADP
ejpam-1951	874	10	patterns	pattern	NOUN
ejpam-1951	874	11	is	be	AUX
ejpam-1951	874	12	92	92	NUM
ejpam-1951	874	13	.	.	PUNCT
ejpam-1951	875	1	4	4	X
ejpam-1951	875	2	.	.	X
ejpam-1951	875	3	conclusion	conclusion	NOUN
ejpam-1951	875	4	counting	count	VERB
ejpam-1951	875	5	symmetries	symmetry	NOUN
ejpam-1951	875	6	is	be	AUX
ejpam-1951	875	7	a	a	DET
ejpam-1951	875	8	vast	vast	ADJ
ejpam-1951	875	9	and	and	CCONJ
ejpam-1951	875	10	challenging	challenging	ADJ
ejpam-1951	875	11	topic	topic	NOUN
ejpam-1951	875	12	.	.	PUNCT
ejpam-1951	876	1	many	many	ADJ
ejpam-1951	876	2	mathematicians	mathematician	NOUN
ejpam-1951	876	3	have	have	AUX
ejpam-1951	876	4	already	already	ADV
ejpam-1951	876	5	researched	research	VERB
ejpam-1951	876	6	on	on	ADP
ejpam-1951	876	7	it	it	PRON
ejpam-1951	876	8	.	.	PUNCT
ejpam-1951	877	1	in	in	ADP
ejpam-1951	877	2	this	this	DET
ejpam-1951	877	3	study	study	NOUN
ejpam-1951	877	4	it	it	PRON
ejpam-1951	877	5	has	have	AUX
ejpam-1951	877	6	already	already	ADV
ejpam-1951	877	7	observed	observe	VERB
ejpam-1951	877	8	that	that	PRON
ejpam-1951	877	9	pólya	pólya	NOUN
ejpam-1951	877	10	’s	’s	PART
ejpam-1951	877	11	theory	theory	NOUN
ejpam-1951	877	12	has	have	VERB
ejpam-1951	877	13	remarkable	remarkable	ADJ
ejpam-1951	877	14	and	and	CCONJ
ejpam-1951	877	15	numerous	numerous	ADJ
ejpam-1951	877	16	applications	application	NOUN
ejpam-1951	877	17	in	in	ADP
ejpam-1951	877	18	counting	count	VERB
ejpam-1951	877	19	symmetries	symmetry	NOUN
ejpam-1951	877	20	.	.	PUNCT
ejpam-1951	878	1	this	this	DET
ejpam-1951	878	2	theory	theory	NOUN
ejpam-1951	878	3	has	have	AUX
ejpam-1951	878	4	been	be	AUX
ejpam-1951	878	5	used	use	VERB
ejpam-1951	878	6	on	on	ADP
ejpam-1951	878	7	colorings	coloring	NOUN
ejpam-1951	878	8	on	on	ADP
ejpam-1951	878	9	cube	cube	NOUN
ejpam-1951	878	10	(	(	PUNCT
ejpam-1951	878	11	faces	face	NOUN
ejpam-1951	878	12	and	and	CCONJ
ejpam-1951	878	13	vertices	vertex	NOUN
ejpam-1951	878	14	)	)	PUNCT
ejpam-1951	878	15	and	and	CCONJ
ejpam-1951	878	16	tetrahedron	tetrahedron	NOUN
ejpam-1951	878	17	.	.	PUNCT
ejpam-1951	879	1	furthermore	furthermore	ADV
ejpam-1951	879	2	we	we	PRON
ejpam-1951	879	3	have	have	AUX
ejpam-1951	879	4	also	also	ADV
ejpam-1951	879	5	discussed	discuss	VERB
ejpam-1951	879	6	on	on	ADP
ejpam-1951	879	7	generalization	generalization	NOUN
ejpam-1951	879	8	of	of	ADP
ejpam-1951	879	9	pólya	pólya	NOUN
ejpam-1951	879	10	’s	’s	PART
ejpam-1951	879	11	theorem	theorem	NOUN
ejpam-1951	879	12	with	with	ADP
ejpam-1951	879	13	some	some	DET
ejpam-1951	879	14	problems	problem	NOUN
ejpam-1951	879	15	and	and	CCONJ
ejpam-1951	879	16	examples	example	NOUN
ejpam-1951	879	17	;	;	PUNCT
ejpam-1951	879	18	but	but	CCONJ
ejpam-1951	879	19	there	there	PRON
ejpam-1951	879	20	are	be	VERB
ejpam-1951	879	21	penalty	penalty	NOUN
ejpam-1951	879	22	of	of	ADP
ejpam-1951	879	23	other	other	ADJ
ejpam-1951	879	24	uses	use	NOUN
ejpam-1951	879	25	as	as	ADV
ejpam-1951	879	26	well	well	ADV
ejpam-1951	879	27	.	.	PUNCT
ejpam-1951	880	1	pólya	pólya	NOUN
ejpam-1951	880	2	and	and	CCONJ
ejpam-1951	880	3	reade[9	reade[9	PRON
ejpam-1951	880	4	]	]	PUNCT
ejpam-1951	880	5	mentioned	mention	VERB
ejpam-1951	880	6	the	the	DET
ejpam-1951	880	7	other	other	ADJ
ejpam-1951	880	8	following	follow	VERB
ejpam-1951	880	9	applications	application	NOUN
ejpam-1951	880	10	without	without	ADP
ejpam-1951	880	11	exploring	explore	VERB
ejpam-1951	880	12	the	the	DET
ejpam-1951	880	13	details	detail	NOUN
ejpam-1951	880	14	(	(	PUNCT
ejpam-1951	880	15	i	i	NOUN
ejpam-1951	880	16	)	)	PUNCT
ejpam-1951	880	17	counting	count	VERB
ejpam-1951	880	18	latin	latin	ADJ
ejpam-1951	880	19	squares	square	NOUN
ejpam-1951	880	20	,	,	PUNCT
ejpam-1951	880	21	which	which	PRON
ejpam-1951	880	22	are	be	AUX
ejpam-1951	880	23	n	n	PRON
ejpam-1951	880	24	×	×	NOUN
ejpam-1951	880	25	n	n	PRON
ejpam-1951	880	26	arrays	array	VERB
ejpam-1951	880	27	filled	fill	VERB
ejpam-1951	880	28	with	with	ADP
ejpam-1951	880	29	n	n	CCONJ
ejpam-1951	880	30	different	different	ADJ
ejpam-1951	880	31	symbols	symbol	NOUN
ejpam-1951	880	32	,	,	PUNCT
ejpam-1951	880	33	each	each	PRON
ejpam-1951	880	34	occurring	occur	VERB
ejpam-1951	880	35	exactly	exactly	ADV
ejpam-1951	880	36	once	once	ADV
ejpam-1951	880	37	in	in	ADP
ejpam-1951	880	38	each	each	DET
ejpam-1951	880	39	row	row	NOUN
ejpam-1951	880	40	and	and	CCONJ
ejpam-1951	880	41	exactly	exactly	ADV
ejpam-1951	880	42	once	once	ADV
ejpam-1951	880	43	in	in	ADP
ejpam-1951	880	44	each	each	DET
ejpam-1951	880	45	column	column	NOUN
ejpam-1951	880	46	.	.	PUNCT
ejpam-1951	881	1	(	(	PUNCT
ejpam-1951	881	2	ii	ii	NOUN
ejpam-1951	881	3	)	)	PUNCT
ejpam-1951	881	4	counting	count	VERB
ejpam-1951	881	5	the	the	DET
ejpam-1951	881	6	number	number	NOUN
ejpam-1951	881	7	of	of	ADP
ejpam-1951	881	8	essentially	essentially	ADV
ejpam-1951	881	9	different	different	ADJ
ejpam-1951	881	10	propositions	proposition	NOUN
ejpam-1951	881	11	of	of	ADP
ejpam-1951	881	12	n	n	PRON
ejpam-1951	881	13	statements	statement	NOUN
ejpam-1951	881	14	,	,	PUNCT
ejpam-1951	881	15	and	and	CCONJ
ejpam-1951	881	16	showing	show	VERB
ejpam-1951	881	17	that	that	SCONJ
ejpam-1951	881	18	the	the	DET
ejpam-1951	881	19	problem	problem	NOUN
ejpam-1951	881	20	is	be	AUX
ejpam-1951	881	21	equivalent	equivalent	ADJ
ejpam-1951	881	22	to	to	ADP
ejpam-1951	881	23	coloring	color	VERB
ejpam-1951	881	24	the	the	DET
ejpam-1951	881	25	vertices	vertex	NOUN
ejpam-1951	881	26	of	of	ADP
ejpam-1951	881	27	a	a	DET
ejpam-1951	881	28	hypercube	hypercube	NOUN
ejpam-1951	881	29	.	.	PUNCT
ejpam-1951	882	1	(	(	PUNCT
ejpam-1951	882	2	iii	iii	X
ejpam-1951	882	3	)	)	PUNCT
ejpam-1951	882	4	counting	count	VERB
ejpam-1951	882	5	finite	finite	ADJ
ejpam-1951	882	6	automata	automata	NOUN
ejpam-1951	882	7	and	and	CCONJ
ejpam-1951	882	8	certain	certain	ADJ
ejpam-1951	882	9	binary	binary	ADJ
ejpam-1951	882	10	matrices	matrix	NOUN
ejpam-1951	882	11	.	.	PUNCT
ejpam-1951	883	1	(	(	PUNCT
ejpam-1951	883	2	iv	iv	X
ejpam-1951	883	3	)	)	PUNCT
ejpam-1951	883	4	counting	counting	NOUN
ejpam-1951	883	5	graphs	graph	NOUN
ejpam-1951	883	6	in	in	ADP
ejpam-1951	883	7	statistical	statistical	ADJ
ejpam-1951	883	8	mechanics	mechanic	NOUN
ejpam-1951	883	9	.	.	PUNCT
ejpam-1951	884	1	there	there	PRON
ejpam-1951	884	2	are	be	VERB
ejpam-1951	884	3	certainly	certainly	ADV
ejpam-1951	884	4	more	more	ADJ
ejpam-1951	884	5	which	which	PRON
ejpam-1951	884	6	have	have	AUX
ejpam-1951	884	7	not	not	PART
ejpam-1951	884	8	been	be	AUX
ejpam-1951	884	9	mentioned	mention	VERB
ejpam-1951	884	10	.	.	PUNCT
ejpam-1951	885	1	hence	hence	ADV
ejpam-1951	885	2	we	we	PRON
ejpam-1951	885	3	can	can	AUX
ejpam-1951	885	4	conclude	conclude	VERB
ejpam-1951	885	5	that	that	DET
ejpam-1951	885	6	pólya	pólya	NOUN
ejpam-1951	885	7	’s	’s	PART
ejpam-1951	885	8	theory	theory	NOUN
ejpam-1951	885	9	is	be	AUX
ejpam-1951	885	10	one	one	NUM
ejpam-1951	885	11	of	of	ADP
ejpam-1951	885	12	the	the	DET
ejpam-1951	885	13	most	most	ADV
ejpam-1951	885	14	powerful	powerful	ADJ
ejpam-1951	885	15	and	and	CCONJ
ejpam-1951	885	16	useful	useful	ADJ
ejpam-1951	885	17	tools	tool	NOUN
ejpam-1951	885	18	in	in	ADP
ejpam-1951	885	19	counting	count	VERB
ejpam-1951	885	20	symmetries	symmetry	NOUN
ejpam-1951	885	21	.	.	PUNCT
ejpam-1951	886	1	acknowledgements	acknowledgement	VERB
ejpam-1951	886	2	the	the	DET
ejpam-1951	886	3	authors	author	NOUN
ejpam-1951	886	4	thank	thank	VERB
ejpam-1951	886	5	the	the	DET
ejpam-1951	886	6	readers	reader	NOUN
ejpam-1951	886	7	of	of	ADP
ejpam-1951	886	8	european	european	PROPN
ejpam-1951	886	9	journal	journal	PROPN
ejpam-1951	886	10	of	of	ADP
ejpam-1951	886	11	pure	pure	ADJ
ejpam-1951	886	12	and	and	CCONJ
ejpam-1951	886	13	applied	applied	ADJ
ejpam-1951	886	14	mathematics	mathematic	NOUN
ejpam-1951	886	15	,	,	PUNCT
ejpam-1951	886	16	for	for	ADP
ejpam-1951	886	17	making	make	VERB
ejpam-1951	886	18	our	our	PRON
ejpam-1951	886	19	journal	journal	NOUN
ejpam-1951	886	20	successful	successful	ADJ
ejpam-1951	886	21	.	.	PUNCT
ejpam-1951	887	1	references	reference	NOUN
ejpam-1951	887	2	[	[	X
ejpam-1951	887	3	1	1	NUM
ejpam-1951	887	4	]	]	PUNCT
ejpam-1951	887	5	a.	a.	NOUN
ejpam-1951	887	6	n.	n.	NOUN
ejpam-1951	887	7	bjørge	bjørge	NOUN
ejpam-1951	887	8	.	.	PUNCT
ejpam-1951	888	1	counting	counting	NOUN
ejpam-1951	888	2	and	and	CCONJ
ejpam-1951	888	3	coloring	color	VERB
ejpam-1951	888	4	with	with	ADP
ejpam-1951	888	5	symmetry	symmetry	NOUN
ejpam-1951	888	6	,	,	PUNCT
ejpam-1951	888	7	m.sc	m.sc	PROPN
ejpam-1951	888	8	thesis	thesis	NOUN
ejpam-1951	888	9	,	,	PUNCT
ejpam-1951	888	10	ntnu	ntnu	INTJ
ejpam-1951	888	11	,	,	PUNCT
ejpam-1951	888	12	may	may	AUX
ejpam-1951	888	13	,	,	PUNCT
ejpam-1951	888	14	2009	2009	NUM
ejpam-1951	888	15	.	.	PUNCT
ejpam-1951	889	1	[	[	X
ejpam-1951	889	2	2	2	NUM
ejpam-1951	889	3	]	]	PUNCT
ejpam-1951	889	4	n.	n.	NOUN
ejpam-1951	889	5	g.	g.	PROPN
ejpam-1951	889	6	d.	d.	PROPN
ejpam-1951	889	7	bruijn	bruijn	PROPN
ejpam-1951	889	8	.	.	PUNCT
ejpam-1951	890	1	counting	counting	NOUN
ejpam-1951	890	2	and	and	CCONJ
ejpam-1951	890	3	enumeration	enumeration	NOUN
ejpam-1951	890	4	,	,	PUNCT
ejpam-1951	890	5	pólya	pólya	NOUN
ejpam-1951	890	6	’s	’s	PART
ejpam-1951	890	7	theory	theory	NOUN
ejpam-1951	890	8	of	of	ADP
ejpam-1951	890	9	counting	counting	NOUN
ejpam-1951	890	10	,	,	PUNCT
ejpam-1951	890	11	page	page	NOUN
ejpam-1951	890	12	144	144	NUM
ejpam-1951	890	13	-	-	SYM
ejpam-1951	890	14	183	183	NUM
ejpam-1951	890	15	,	,	PUNCT
ejpam-1951	890	16	1964	1964	NUM
ejpam-1951	890	17	.	.	PUNCT
ejpam-1951	891	1	[	[	X
ejpam-1951	891	2	3	3	X
ejpam-1951	891	3	]	]	X
ejpam-1951	891	4	p.	p.	NOUN
ejpam-1951	891	5	fleischmann	fleischmann	PROPN
ejpam-1951	891	6	.	.	PUNCT
ejpam-1951	892	1	groups	group	NOUN
ejpam-1951	892	2	and	and	CCONJ
ejpam-1951	892	3	symmetries	symmetry	NOUN
ejpam-1951	892	4	,	,	PUNCT
ejpam-1951	892	5	institute	institute	NOUN
ejpam-1951	892	6	of	of	ADP
ejpam-1951	892	7	mathematics	mathematics	PROPN
ejpam-1951	892	8	and	and	CCONJ
ejpam-1951	892	9	statistics	statistic	NOUN
ejpam-1951	892	10	,	,	PUNCT
ejpam-1951	892	11	university	university	NOUN
ejpam-1951	892	12	of	of	ADP
ejpam-1951	892	13	kent	kent	PROPN
ejpam-1951	892	14	at	at	ADP
ejpam-1951	892	15	canterbury	canterbury	PROPN
ejpam-1951	892	16	,	,	PUNCT
ejpam-1951	892	17	u.k	u.k	PROPN
ejpam-1951	892	18	.	.	PROPN
ejpam-1951	892	19	,	,	PUNCT
ejpam-1951	892	20	2011	2011	NUM
ejpam-1951	892	21	.	.	PUNCT
ejpam-1951	893	1	references	reference	NOUN
ejpam-1951	893	2	113	113	NUM
ejpam-1951	893	3	[	[	SYM
ejpam-1951	893	4	4	4	NUM
ejpam-1951	893	5	]	]	PUNCT
ejpam-1951	893	6	harary	harary	NOUN
ejpam-1951	893	7	,	,	PUNCT
ejpam-1951	893	8	frank	frank	PROPN
ejpam-1951	893	9	,	,	PUNCT
ejpam-1951	893	10	palmer	palmer	PROPN
ejpam-1951	893	11	,	,	PUNCT
ejpam-1951	893	12	and	and	CCONJ
ejpam-1951	893	13	m.	m.	NOUN
ejpam-1951	893	14	edgar	edgar	PROPN
ejpam-1951	893	15	.	.	PUNCT
ejpam-1951	894	1	graphical	graphical	ADJ
ejpam-1951	894	2	enumeration	enumeration	NOUN
ejpam-1951	894	3	,	,	PUNCT
ejpam-1951	894	4	new	new	PROPN
ejpam-1951	894	5	york	york	PROPN
ejpam-1951	894	6	:	:	PUNCT
ejpam-1951	894	7	academic	academic	ADJ
ejpam-1951	894	8	press	press	NOUN
ejpam-1951	894	9	,	,	PUNCT
ejpam-1951	894	10	1973	1973	NUM
ejpam-1951	894	11	.	.	PUNCT
ejpam-1951	895	1	[	[	X
ejpam-1951	895	2	5	5	X
ejpam-1951	895	3	]	]	PUNCT
ejpam-1951	895	4	p.	p.	NOUN
ejpam-1951	895	5	m.	m.	PROPN
ejpam-1951	895	6	neumann	neumann	PROPN
ejpam-1951	895	7	.	.	PUNCT
ejpam-1951	896	1	a	a	DET
ejpam-1951	896	2	lemma	lemma	PROPN
ejpam-1951	896	3	that	that	PRON
ejpam-1951	896	4	is	be	AUX
ejpam-1951	896	5	not	not	PART
ejpam-1951	896	6	burnside	burnside	NOUN
ejpam-1951	896	7	’s	’s	NOUN
ejpam-1951	896	8	,	,	PUNCT
ejpam-1951	896	9	the	the	DET
ejpam-1951	896	10	mathematical	mathematical	ADJ
ejpam-1951	896	11	scientist	scientist	NOUN
ejpam-1951	896	12	4(2	4(2	NUM
ejpam-1951	896	13	):	):	PUNCT
ejpam-1951	896	14	133	133	NUM
ejpam-1951	896	15	–	–	SYM
ejpam-1951	896	16	141	141	NUM
ejpam-1951	896	17	,	,	PUNCT
ejpam-1951	896	18	issn	issn	PROPN
ejpam-1951	896	19	0312	0312	NUM
ejpam-1951	896	20	-	-	SYM
ejpam-1951	896	21	3685	3685	NUM
ejpam-1951	896	22	,	,	PUNCT
ejpam-1951	896	23	mr562002	mr562002	NOUN
ejpam-1951	896	24	,	,	PUNCT
ejpam-1951	896	25	1979	1979	NUM
ejpam-1951	896	26	.	.	PUNCT
ejpam-1951	897	1	[	[	X
ejpam-1951	897	2	6	6	NUM
ejpam-1951	897	3	]	]	PUNCT
ejpam-1951	897	4	f.	f.	PROPN
ejpam-1951	897	5	y.	y.	PROPN
ejpam-1951	897	6	tomakin	tomakin	PROPN
ejpam-1951	897	7	.	.	PUNCT
ejpam-1951	898	1	the	the	DET
ejpam-1951	898	2	pólya	pólya	NOUN
ejpam-1951	898	3	theory	theory	NOUN
ejpam-1951	898	4	and	and	CCONJ
ejpam-1951	898	5	permutation	permutation	NOUN
ejpam-1951	898	6	groups	group	NOUN
ejpam-1951	898	7	,	,	PUNCT
ejpam-1951	898	8	chamchuri	chamchuri	PROPN
ejpam-1951	898	9	journal	journal	PROPN
ejpam-1951	898	10	of	of	ADP
ejpam-1951	898	11	mathematics	mathematics	PROPN
ejpam-1951	898	12	,	,	PUNCT
ejpam-1951	898	13	vol	vol	NOUN
ejpam-1951	898	14	.	.	PUNCT
ejpam-1951	898	15	1(2	1(2	NUM
ejpam-1951	898	16	)	)	PUNCT
ejpam-1951	898	17	,	,	PUNCT
ejpam-1951	898	18	page	page	NOUN
ejpam-1951	898	19	1	1	NUM
ejpam-1951	898	20	-	-	SYM
ejpam-1951	898	21	23	23	NUM
ejpam-1951	898	22	,	,	PUNCT
ejpam-1951	898	23	2000	2000	NUM
ejpam-1951	898	24	.	.	PUNCT
ejpam-1951	899	1	[	[	X
ejpam-1951	899	2	7	7	NUM
ejpam-1951	899	3	]	]	SYM
ejpam-1951	899	4	a.	a.	NOUN
ejpam-1951	899	5	tucker	tucker	PROPN
ejpam-1951	899	6	.	.	PUNCT
ejpam-1951	900	1	applied	apply	VERB
ejpam-1951	900	2	combinatorics	combinatoric	NOUN
ejpam-1951	900	3	,	,	PUNCT
ejpam-1951	900	4	4th	4th	ADJ
ejpam-1951	900	5	edition	edition	NOUN
ejpam-1951	900	6	,	,	PUNCT
ejpam-1951	900	7	john	john	PROPN
ejpam-1951	900	8	wiley	wiley	PROPN
ejpam-1951	900	9	and	and	CCONJ
ejpam-1951	900	10	sons	son	NOUN
ejpam-1951	900	11	,	,	PUNCT
ejpam-1951	900	12	new	new	PROPN
ejpam-1951	900	13	york	york	PROPN
ejpam-1951	900	14	.	.	PUNCT
ejpam-1951	901	1	2002	2002	NUM
ejpam-1951	902	1	[	[	X
ejpam-1951	902	2	8	8	X
ejpam-1951	902	3	]	]	X
ejpam-1951	902	4	v.	v.	PROPN
ejpam-1951	902	5	c.	c.	PROPN
ejpam-1951	902	6	venkaiah	venkaiah	PROPN
ejpam-1951	902	7	,	,	PUNCT
ejpam-1951	902	8	t.	t.	PROPN
ejpam-1951	902	9	a.	a.	NOUN
ejpam-1951	902	10	gulliver	gulliver	PROPN
ejpam-1951	902	11	.	.	PUNCT
ejpam-1951	903	1	quasi	quasi	ADJ
ejpam-1951	903	2	-	-	ADJ
ejpam-1951	903	3	cyclic	cyclic	ADJ
ejpam-1951	903	4	codes	code	NOUN
ejpam-1951	903	5	over	over	ADP
ejpam-1951	903	6	f13	f13	PROPN
ejpam-1951	903	7	and	and	CCONJ
ejpam-1951	903	8	enumeration	enumeration	NOUN
ejpam-1951	903	9	of	of	ADP
ejpam-1951	903	10	defining	define	VERB
ejpam-1951	903	11	polynomials	polynomial	NOUN
ejpam-1951	903	12	,	,	PUNCT
ejpam-1951	903	13	journal	journal	NOUN
ejpam-1951	903	14	of	of	ADP
ejpam-1951	903	15	discrete	discrete	ADJ
ejpam-1951	903	16	algorithms	algorithm	NOUN
ejpam-1951	903	17	,	,	PUNCT
ejpam-1951	903	18	vol	vol	NOUN
ejpam-1951	903	19	.	.	PROPN
ejpam-1951	903	20	16	16	NUM
ejpam-1951	903	21	,	,	PUNCT
ejpam-1951	903	22	pages	page	NOUN
ejpam-1951	903	23	249âăş257	249âăş257	NOUN
ejpam-1951	903	24	.	.	PUNCT
ejpam-1951	903	25	2012	2012	NUM
ejpam-1951	903	26	.	.	PUNCT