id	sid	tid	token	lemma	pos
ejpam-2339	1	1	compile	compile	NOUN
ejpam-2339	1	2	/	/	SYM
ejpam-2339	1	3	output.dvi	output.dvi	NOUN
ejpam-2339	1	4	european	european	ADJ
ejpam-2339	1	5	journal	journal	NOUN
ejpam-2339	1	6	of	of	ADP
ejpam-2339	1	7	pure	pure	ADJ
ejpam-2339	1	8	and	and	CCONJ
ejpam-2339	1	9	applied	apply	VERB
ejpam-2339	1	10	mathematics	mathematic	NOUN
ejpam-2339	1	11	vol	vol	NOUN
ejpam-2339	1	12	.	.	PROPN
ejpam-2339	1	13	8	8	NUM
ejpam-2339	1	14	,	,	PUNCT
ejpam-2339	1	15	no	no	INTJ
ejpam-2339	1	16	.	.	NOUN
ejpam-2339	1	17	4	4	NUM
ejpam-2339	1	18	,	,	PUNCT
ejpam-2339	1	19	2015	2015	NUM
ejpam-2339	1	20	,	,	PUNCT
ejpam-2339	1	21	450	450	NUM
ejpam-2339	1	22	-	-	SYM
ejpam-2339	1	23	457	457	NUM
ejpam-2339	1	24	issn	issn	PROPN
ejpam-2339	1	25	1307	1307	NUM
ejpam-2339	1	26	-	-	SYM
ejpam-2339	1	27	5543	5543	NUM
ejpam-2339	1	28	–	–	PUNCT
ejpam-2339	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2339	1	30	on	on	ADP
ejpam-2339	1	31	hadamard	hadamard	ADJ
ejpam-2339	1	32	groups	group	NOUN
ejpam-2339	1	33	with	with	ADP
ejpam-2339	1	34	relatively	relatively	ADV
ejpam-2339	1	35	large	large	ADJ
ejpam-2339	1	36	2	2	NUM
ejpam-2339	1	37	-	-	PUNCT
ejpam-2339	1	38	subgroup	subgroup	NOUN
ejpam-2339	1	39	kristijan	kristijan	PROPN
ejpam-2339	1	40	tabak	tabak	PROPN
ejpam-2339	1	41	rochester	rochester	PROPN
ejpam-2339	1	42	institute	institute	PROPN
ejpam-2339	1	43	of	of	ADP
ejpam-2339	1	44	technology	technology	PROPN
ejpam-2339	1	45	,	,	PUNCT
ejpam-2339	1	46	zagreb	zagreb	PROPN
ejpam-2339	1	47	campus	campus	PROPN
ejpam-2339	1	48	,	,	PUNCT
ejpam-2339	1	49	d.t	d.t	PROPN
ejpam-2339	1	50	.	.	PUNCT
ejpam-2339	2	1	gavrana	gavrana	PROPN
ejpam-2339	2	2	15	15	NUM
ejpam-2339	2	3	,	,	PUNCT
ejpam-2339	2	4	10000	10000	NUM
ejpam-2339	2	5	zagreb	zagreb	PROPN
ejpam-2339	2	6	,	,	PUNCT
ejpam-2339	2	7	croatia	croatia	PROPN
ejpam-2339	2	8	abstract	abstract	NOUN
ejpam-2339	2	9	.	.	PUNCT
ejpam-2339	3	1	a	a	DET
ejpam-2339	3	2	hadamard	hadamard	ADJ
ejpam-2339	3	3	group	group	NOUN
ejpam-2339	3	4	is	be	AUX
ejpam-2339	3	5	any	any	DET
ejpam-2339	3	6	group	group	NOUN
ejpam-2339	3	7	of	of	ADP
ejpam-2339	3	8	order	order	NOUN
ejpam-2339	3	9	4u2	4u2	NUM
ejpam-2339	3	10	that	that	PRON
ejpam-2339	3	11	contain	contain	VERB
ejpam-2339	3	12	a	a	DET
ejpam-2339	3	13	difference	difference	NOUN
ejpam-2339	3	14	set	set	NOUN
ejpam-2339	3	15	.	.	PUNCT
ejpam-2339	4	1	in	in	ADP
ejpam-2339	4	2	this	this	DET
ejpam-2339	4	3	paper	paper	NOUN
ejpam-2339	4	4	we	we	PRON
ejpam-2339	4	5	obtain	obtain	VERB
ejpam-2339	4	6	some	some	DET
ejpam-2339	4	7	new	new	ADJ
ejpam-2339	4	8	conditions	condition	NOUN
ejpam-2339	4	9	for	for	ADP
ejpam-2339	4	10	hadamard	hadamard	ADJ
ejpam-2339	4	11	groups	group	NOUN
ejpam-2339	4	12	with	with	ADP
ejpam-2339	4	13	relatively	relatively	ADV
ejpam-2339	4	14	large	large	ADJ
ejpam-2339	4	15	2	2	NUM
ejpam-2339	4	16	-	-	PUNCT
ejpam-2339	4	17	subgroup	subgroup	NOUN
ejpam-2339	4	18	.	.	PUNCT
ejpam-2339	5	1	we	we	PRON
ejpam-2339	5	2	use	use	VERB
ejpam-2339	5	3	norm	norm	NOUN
ejpam-2339	5	4	invariant	invariant	ADJ
ejpam-2339	5	5	polynomials	polynomial	NOUN
ejpam-2339	5	6	f	f	X
ejpam-2339	5	7	(	(	PUNCT
ejpam-2339	5	8	ǫ	ǫ	NOUN
ejpam-2339	5	9	)	)	PUNCT
ejpam-2339	5	10	∈	∈	PROPN
ejpam-2339	5	11	z[ǫ	z[ǫ	PROPN
ejpam-2339	5	12	]	]	PUNCT
ejpam-2339	5	13	,	,	PUNCT
ejpam-2339	5	14	|	|	ADV
ejpam-2339	5	15	f	f	X
ejpam-2339	5	16	(	(	PUNCT
ejpam-2339	5	17	ǫ	ǫ	NOUN
ejpam-2339	5	18	t)|	t)|	NOUN
ejpam-2339	5	19	=	=	SYM
ejpam-2339	5	20	const	const	NOUN
ejpam-2339	5	21	.	.	PUNCT
ejpam-2339	5	22	,	,	PUNCT
ejpam-2339	5	23	where	where	SCONJ
ejpam-2339	5	24	ǫ	ǫ	NOUN
ejpam-2339	5	25	is	be	AUX
ejpam-2339	5	26	root	root	NOUN
ejpam-2339	5	27	of	of	ADP
ejpam-2339	5	28	unity	unity	NOUN
ejpam-2339	5	29	of	of	ADP
ejpam-2339	5	30	order	order	NOUN
ejpam-2339	5	31	2n	2n	NUM
ejpam-2339	5	32	.	.	PUNCT
ejpam-2339	6	1	necessary	necessary	ADJ
ejpam-2339	6	2	condition	condition	NOUN
ejpam-2339	6	3	on	on	ADP
ejpam-2339	6	4	a	a	DET
ejpam-2339	6	5	size	size	NOUN
ejpam-2339	6	6	of	of	ADP
ejpam-2339	6	7	normal	normal	ADJ
ejpam-2339	6	8	cyclic	cyclic	ADJ
ejpam-2339	6	9	2	2	NUM
ejpam-2339	6	10	-	-	PUNCT
ejpam-2339	6	11	subgroup	subgroup	NOUN
ejpam-2339	6	12	are	be	AUX
ejpam-2339	6	13	given	give	VERB
ejpam-2339	6	14	.	.	PUNCT
ejpam-2339	7	1	also	also	ADV
ejpam-2339	7	2	,	,	PUNCT
ejpam-2339	7	3	we	we	PRON
ejpam-2339	7	4	have	have	AUX
ejpam-2339	7	5	covered	cover	VERB
ejpam-2339	7	6	cases	case	NOUN
ejpam-2339	7	7	when	when	SCONJ
ejpam-2339	7	8	2	2	NUM
ejpam-2339	7	9	-	-	PUNCT
ejpam-2339	7	10	subgroup	subgroup	NOUN
ejpam-2339	7	11	has	have	VERB
ejpam-2339	7	12	generators	generator	NOUN
ejpam-2339	7	13	similar	similar	ADJ
ejpam-2339	7	14	to	to	ADP
ejpam-2339	7	15	a	a	DET
ejpam-2339	7	16	modular	modular	ADJ
ejpam-2339	7	17	or	or	CCONJ
ejpam-2339	7	18	dihedral	dihedral	ADJ
ejpam-2339	7	19	2	2	NUM
ejpam-2339	7	20	-	-	PUNCT
ejpam-2339	7	21	group	group	NOUN
ejpam-2339	7	22	.	.	PUNCT
ejpam-2339	8	1	additionally	additionally	ADV
ejpam-2339	8	2	,	,	PUNCT
ejpam-2339	8	3	we	we	PRON
ejpam-2339	8	4	construct	construct	VERB
ejpam-2339	8	5	such	such	ADJ
ejpam-2339	8	6	two	two	NUM
ejpam-2339	8	7	infinite	infinite	ADJ
ejpam-2339	8	8	series	series	NOUN
ejpam-2339	8	9	of	of	ADP
ejpam-2339	8	10	groups	group	NOUN
ejpam-2339	8	11	.	.	PUNCT
ejpam-2339	9	1	obtained	obtain	VERB
ejpam-2339	9	2	results	result	NOUN
ejpam-2339	9	3	are	be	AUX
ejpam-2339	9	4	natural	natural	ADJ
ejpam-2339	9	5	generalization	generalization	NOUN
ejpam-2339	9	6	of	of	ADP
ejpam-2339	9	7	a	a	DET
ejpam-2339	9	8	case	case	NOUN
ejpam-2339	9	9	when	when	SCONJ
ejpam-2339	9	10	entire	entire	ADJ
ejpam-2339	9	11	group	group	NOUN
ejpam-2339	9	12	is	be	AUX
ejpam-2339	9	13	2	2	NUM
ejpam-2339	9	14	-	-	PUNCT
ejpam-2339	9	15	group	group	NOUN
ejpam-2339	9	16	.	.	PUNCT
ejpam-2339	10	1	2010	2010	NUM
ejpam-2339	10	2	mathematics	mathematic	NOUN
ejpam-2339	10	3	subject	subject	NOUN
ejpam-2339	10	4	classifications	classification	NOUN
ejpam-2339	10	5	:	:	PUNCT
ejpam-2339	10	6	05b10	05b10	NUM
ejpam-2339	10	7	,	,	PUNCT
ejpam-2339	10	8	20e07	20e07	NUM
ejpam-2339	10	9	,	,	PUNCT
ejpam-2339	10	10	20e28	20e28	NUM
ejpam-2339	10	11	key	key	ADJ
ejpam-2339	10	12	words	word	NOUN
ejpam-2339	10	13	and	and	CCONJ
ejpam-2339	10	14	phrases	phrase	NOUN
ejpam-2339	10	15	:	:	PUNCT
ejpam-2339	10	16	difference	difference	NOUN
ejpam-2339	10	17	set	set	NOUN
ejpam-2339	10	18	,	,	PUNCT
ejpam-2339	10	19	norm	norm	NOUN
ejpam-2339	10	20	invariance	invariance	NOUN
ejpam-2339	10	21	,	,	PUNCT
ejpam-2339	10	22	hadamard	hadamard	ADJ
ejpam-2339	10	23	group	group	NOUN
ejpam-2339	10	24	,	,	PUNCT
ejpam-2339	10	25	group	group	NOUN
ejpam-2339	10	26	representation	representation	NOUN
ejpam-2339	10	27	1	1	NUM
ejpam-2339	10	28	.	.	PUNCT
ejpam-2339	11	1	introduction	introduction	NOUN
ejpam-2339	11	2	and	and	CCONJ
ejpam-2339	11	3	known	know	VERB
ejpam-2339	11	4	results	result	NOUN
ejpam-2339	11	5	we	we	PRON
ejpam-2339	11	6	start	start	VERB
ejpam-2339	11	7	by	by	ADP
ejpam-2339	11	8	introducing	introduce	VERB
ejpam-2339	11	9	a	a	DET
ejpam-2339	11	10	standard	standard	ADJ
ejpam-2339	11	11	definition	definition	NOUN
ejpam-2339	11	12	of	of	ADP
ejpam-2339	11	13	a	a	DET
ejpam-2339	11	14	difference	difference	NOUN
ejpam-2339	11	15	set	set	NOUN
ejpam-2339	11	16	.	.	PUNCT
ejpam-2339	12	1	let	let	VERB
ejpam-2339	12	2	g	g	PRON
ejpam-2339	12	3	be	be	AUX
ejpam-2339	12	4	a	a	DET
ejpam-2339	12	5	group	group	NOUN
ejpam-2339	12	6	where	where	SCONJ
ejpam-2339	12	7	|g|=	|g|=	VERB
ejpam-2339	12	8	4u2	4u2	PROPN
ejpam-2339	12	9	.	.	PUNCT
ejpam-2339	13	1	if	if	SCONJ
ejpam-2339	13	2	d	d	PROPN
ejpam-2339	13	3	⊆	⊆	NUM
ejpam-2339	13	4	g	g	NOUN
ejpam-2339	13	5	,	,	PUNCT
ejpam-2339	13	6	where	where	SCONJ
ejpam-2339	13	7	|d|=	|d|=	NOUN
ejpam-2339	13	8	2u2	2u2	NUM
ejpam-2339	13	9	−	−	PROPN
ejpam-2339	13	10	u	u	NOUN
ejpam-2339	13	11	,	,	PUNCT
ejpam-2339	13	12	is	be	AUX
ejpam-2339	13	13	such	such	ADJ
ejpam-2339	13	14	that	that	SCONJ
ejpam-2339	13	15	{	{	PUNCT
ejpam-2339	13	16	d1d−1	d1d−1	PROPN
ejpam-2339	13	17	2	2	PROPN
ejpam-2339	13	18	|	|	ADV
ejpam-2339	13	19	d1	d1	PROPN
ejpam-2339	13	20	,	,	PUNCT
ejpam-2339	13	21	d2	d2	PROPN
ejpam-2339	13	22	∈	∈	PROPN
ejpam-2339	13	23	d}=	d}=	PROPN
ejpam-2339	13	24	{	{	PUNCT
ejpam-2339	13	25	(	(	PUNCT
ejpam-2339	13	26	u2	u2	PROPN
ejpam-2339	13	27	−	−	PROPN
ejpam-2339	13	28	u	u	NOUN
ejpam-2339	13	29	)	)	PUNCT
ejpam-2339	13	30	·	·	PUNCT
ejpam-2339	14	1	g	g	ADP
ejpam-2339	14	2	|	|	ADV
ejpam-2339	14	3	g	g	PROPN
ejpam-2339	14	4	∈	∈	PROPN
ejpam-2339	14	5	g	g	PROPN
ejpam-2339	14	6	\	\	PROPN
ejpam-2339	14	7	{	{	PUNCT
ejpam-2339	14	8	1	1	NUM
ejpam-2339	14	9	g	g	NOUN
ejpam-2339	14	10	}	}	PUNCT
ejpam-2339	14	11	}	}	PUNCT
ejpam-2339	14	12	,	,	PUNCT
ejpam-2339	14	13	then	then	ADV
ejpam-2339	14	14	we	we	PRON
ejpam-2339	14	15	call	call	VERB
ejpam-2339	14	16	d	d	NOUN
ejpam-2339	14	17	a	a	DET
ejpam-2339	14	18	difference	difference	NOUN
ejpam-2339	14	19	set	set	NOUN
ejpam-2339	14	20	.	.	PUNCT
ejpam-2339	15	1	in	in	ADP
ejpam-2339	15	2	that	that	DET
ejpam-2339	15	3	case	case	NOUN
ejpam-2339	15	4	group	group	NOUN
ejpam-2339	15	5	g	g	PROPN
ejpam-2339	15	6	is	be	AUX
ejpam-2339	15	7	called	call	VERB
ejpam-2339	15	8	a	a	DET
ejpam-2339	15	9	hadamard	hadamard	ADJ
ejpam-2339	15	10	group	group	NOUN
ejpam-2339	15	11	(	(	PUNCT
ejpam-2339	15	12	see	see	VERB
ejpam-2339	15	13	[	[	X
ejpam-2339	15	14	1	1	NUM
ejpam-2339	15	15	,	,	PUNCT
ejpam-2339	15	16	2	2	NUM
ejpam-2339	15	17	]	]	PUNCT
ejpam-2339	15	18	)	)	PUNCT
ejpam-2339	15	19	.	.	PUNCT
ejpam-2339	16	1	in	in	ADP
ejpam-2339	16	2	difference	difference	NOUN
ejpam-2339	16	3	set	set	NOUN
ejpam-2339	16	4	theory	theory	NOUN
ejpam-2339	16	5	is	be	AUX
ejpam-2339	16	6	usual	usual	ADJ
ejpam-2339	16	7	to	to	PART
ejpam-2339	16	8	deal	deal	VERB
ejpam-2339	16	9	with	with	ADP
ejpam-2339	16	10	linear	linear	ADJ
ejpam-2339	16	11	combinations	combination	NOUN
ejpam-2339	16	12	of	of	ADP
ejpam-2339	16	13	some	some	DET
ejpam-2339	16	14	roots	root	NOUN
ejpam-2339	16	15	of	of	ADP
ejpam-2339	16	16	unity	unity	NOUN
ejpam-2339	16	17	.	.	PUNCT
ejpam-2339	17	1	good	good	ADJ
ejpam-2339	17	2	example	example	NOUN
ejpam-2339	17	3	is	be	AUX
ejpam-2339	17	4	classical	classical	ADJ
ejpam-2339	17	5	paper	paper	NOUN
ejpam-2339	18	1	[	[	X
ejpam-2339	18	2	6	6	NUM
ejpam-2339	18	3	]	]	PUNCT
ejpam-2339	18	4	.	.	PUNCT
ejpam-2339	19	1	we	we	PRON
ejpam-2339	19	2	will	will	AUX
ejpam-2339	19	3	analyze	analyze	VERB
ejpam-2339	19	4	polynomials	polynomial	NOUN
ejpam-2339	19	5	like	like	ADP
ejpam-2339	19	6	f	f	PROPN
ejpam-2339	19	7	(	(	PUNCT
ejpam-2339	19	8	ǫ	ǫ	NOUN
ejpam-2339	19	9	)	)	PUNCT
ejpam-2339	19	10	=	=	PUNCT
ejpam-2339	20	1	∑w	∑w	PROPN
ejpam-2339	20	2	j=1	j=1	PROPN
ejpam-2339	20	3	k	k	PROPN
ejpam-2339	21	1	jǫ	jǫ	INTJ
ejpam-2339	21	2	r	r	PROPN
ejpam-2339	21	3	j	j	PROPN
ejpam-2339	21	4	,	,	PUNCT
ejpam-2339	21	5	where	where	SCONJ
ejpam-2339	21	6	ki	ki	PROPN
ejpam-2339	21	7	∈	∈	PROPN
ejpam-2339	21	8	z	z	PROPN
ejpam-2339	21	9	and	and	CCONJ
ejpam-2339	21	10	ǫ	ǫ	PRON
ejpam-2339	21	11	is	be	AUX
ejpam-2339	21	12	some	some	DET
ejpam-2339	21	13	root	root	NOUN
ejpam-2339	21	14	of	of	ADP
ejpam-2339	21	15	unity	unity	NOUN
ejpam-2339	21	16	.	.	PUNCT
ejpam-2339	22	1	as	as	SCONJ
ejpam-2339	22	2	it	it	PRON
ejpam-2339	22	3	can	can	AUX
ejpam-2339	22	4	be	be	AUX
ejpam-2339	22	5	seen	see	VERB
ejpam-2339	22	6	from	from	ADP
ejpam-2339	22	7	some	some	DET
ejpam-2339	22	8	publications	publication	NOUN
ejpam-2339	22	9	(	(	PUNCT
ejpam-2339	22	10	i.e.	i.e.	X
ejpam-2339	22	11	[	[	X
ejpam-2339	22	12	5	5	NUM
ejpam-2339	22	13	]	]	NUM
ejpam-2339	22	14	)	)	PUNCT
ejpam-2339	22	15	,	,	PUNCT
ejpam-2339	22	16	algebraic	algebraic	ADJ
ejpam-2339	22	17	approach	approach	NOUN
ejpam-2339	22	18	to	to	ADP
ejpam-2339	22	19	difference	difference	NOUN
ejpam-2339	22	20	set	set	NOUN
ejpam-2339	22	21	problems	problem	NOUN
ejpam-2339	22	22	induce	induce	VERB
ejpam-2339	22	23	a	a	DET
ejpam-2339	22	24	significant	significant	ADJ
ejpam-2339	22	25	progress	progress	NOUN
ejpam-2339	22	26	.	.	PUNCT
ejpam-2339	23	1	elements	element	NOUN
ejpam-2339	23	2	of	of	ADP
ejpam-2339	23	3	representation	representation	NOUN
ejpam-2339	23	4	theory	theory	NOUN
ejpam-2339	23	5	played	play	VERB
ejpam-2339	23	6	important	important	ADJ
ejpam-2339	23	7	role	role	NOUN
ejpam-2339	23	8	in	in	ADP
ejpam-2339	23	9	this	this	DET
ejpam-2339	23	10	paper	paper	NOUN
ejpam-2339	23	11	.	.	PUNCT
ejpam-2339	24	1	the	the	DET
ejpam-2339	24	2	main	main	ADJ
ejpam-2339	24	3	theoretical	theoretical	ADJ
ejpam-2339	24	4	result	result	NOUN
ejpam-2339	24	5	which	which	PRON
ejpam-2339	24	6	served	serve	VERB
ejpam-2339	24	7	as	as	ADP
ejpam-2339	24	8	technical	technical	ADJ
ejpam-2339	24	9	tool	tool	NOUN
ejpam-2339	24	10	in	in	ADP
ejpam-2339	24	11	difference	difference	NOUN
ejpam-2339	24	12	set	set	NOUN
ejpam-2339	24	13	theory	theory	NOUN
ejpam-2339	24	14	is	be	AUX
ejpam-2339	24	15	theorem	theorem	VERB
ejpam-2339	24	16	1	1	X
ejpam-2339	24	17	.	.	PUNCT
ejpam-2339	25	1	let	let	VERB
ejpam-2339	25	2	d	d	PRON
ejpam-2339	25	3	be	be	AUX
ejpam-2339	25	4	a	a	DET
ejpam-2339	25	5	subset	subset	NOUN
ejpam-2339	25	6	of	of	ADP
ejpam-2339	25	7	size	size	NOUN
ejpam-2339	25	8	k	k	PROPN
ejpam-2339	25	9	of	of	ADP
ejpam-2339	25	10	a	a	DET
ejpam-2339	25	11	group	group	NOUN
ejpam-2339	25	12	g	g	NOUN
ejpam-2339	25	13	of	of	ADP
ejpam-2339	25	14	order	order	NOUN
ejpam-2339	26	1	v.	v.	ADV
ejpam-2339	26	2	let	let	VERB
ejpam-2339	26	3	s	s	PRON
ejpam-2339	26	4	be	be	AUX
ejpam-2339	26	5	a	a	DET
ejpam-2339	26	6	complete	complete	ADJ
ejpam-2339	26	7	set	set	NOUN
ejpam-2339	26	8	of	of	ADP
ejpam-2339	26	9	distinct	distinct	ADJ
ejpam-2339	26	10	,	,	PUNCT
ejpam-2339	26	11	inequivalent	inequivalent	NOUN
ejpam-2339	26	12	,	,	PUNCT
ejpam-2339	26	13	nontrivial	nontrivial	NOUN
ejpam-2339	26	14	,	,	PUNCT
ejpam-2339	26	15	irreducible	irreducible	ADJ
ejpam-2339	26	16	representations	representation	NOUN
ejpam-2339	26	17	for	for	ADP
ejpam-2339	26	18	g.	g.	PROPN
ejpam-2339	26	19	if	if	SCONJ
ejpam-2339	26	20	φ(d)φ(d(−1	φ(d)φ(d(−1	X
ejpam-2339	26	21	)	)	PUNCT
ejpam-2339	26	22	)	)	PUNCT
ejpam-2339	27	1	=	=	SYM
ejpam-2339	27	2	(	(	PUNCT
ejpam-2339	27	3	k	k	NOUN
ejpam-2339	27	4	−	−	PROPN
ejpam-2339	27	5	λ)i	λ)i	PUNCT
ejpam-2339	27	6	for	for	ADP
ejpam-2339	27	7	all	all	DET
ejpam-2339	27	8	φ	φ	PROPN
ejpam-2339	27	9	∈	∈	PROPN
ejpam-2339	27	10	s	s	PROPN
ejpam-2339	27	11	,	,	PUNCT
ejpam-2339	27	12	then	then	ADV
ejpam-2339	27	13	d	d	PROPN
ejpam-2339	27	14	is	be	AUX
ejpam-2339	27	15	a	a	DET
ejpam-2339	27	16	(	(	PUNCT
ejpam-2339	27	17	v	v	NOUN
ejpam-2339	27	18	,	,	PUNCT
ejpam-2339	27	19	k	k	NOUN
ejpam-2339	27	20	,	,	PUNCT
ejpam-2339	27	21	λ	λ	NOUN
ejpam-2339	27	22	)	)	PUNCT
ejpam-2339	27	23	difference	difference	NOUN
ejpam-2339	27	24	set	set	VERB
ejpam-2339	27	25	in	in	ADP
ejpam-2339	27	26	g.	g.	PROPN
ejpam-2339	27	27	email	email	NOUN
ejpam-2339	27	28	address	address	NOUN
ejpam-2339	27	29	:	:	PUNCT
ejpam-2339	27	30	kxtcad@rit.edu	kxtcad@rit.edu	PROPN
ejpam-2339	27	31	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2339	28	1	450	450	NUM
ejpam-2339	28	2	c	c	NOUN
ejpam-2339	28	3	©	©	PROPN
ejpam-2339	28	4	2015	2015	NUM
ejpam-2339	28	5	ejpam	ejpam	NOUN
ejpam-2339	28	6	all	all	DET
ejpam-2339	28	7	rights	right	NOUN
ejpam-2339	28	8	reserved	reserve	VERB
ejpam-2339	28	9	.	.	PUNCT
ejpam-2339	29	1	k.tabak	k.tabak	ADJ
ejpam-2339	29	2	/	/	SYM
ejpam-2339	29	3	eur	eur	PROPN
ejpam-2339	29	4	.	.	PUNCT
ejpam-2339	30	1	j.	j.	PROPN
ejpam-2339	30	2	pure	pure	PROPN
ejpam-2339	30	3	appl	appl	PROPN
ejpam-2339	30	4	.	.	PROPN
ejpam-2339	30	5	math	math	PROPN
ejpam-2339	30	6	,	,	PUNCT
ejpam-2339	30	7	8	8	NUM
ejpam-2339	30	8	(	(	PUNCT
ejpam-2339	30	9	2015	2015	NUM
ejpam-2339	30	10	)	)	PUNCT
ejpam-2339	30	11	,	,	PUNCT
ejpam-2339	30	12	450	450	NUM
ejpam-2339	30	13	-	-	SYM
ejpam-2339	30	14	457	457	NUM
ejpam-2339	30	15	451	451	NUM
ejpam-2339	30	16	if	if	SCONJ
ejpam-2339	30	17	hypothesized	hypothesize	VERB
ejpam-2339	30	18	hadamard	hadamard	ADJ
ejpam-2339	30	19	group	group	NOUN
ejpam-2339	30	20	has	have	VERB
ejpam-2339	30	21	some	some	DET
ejpam-2339	30	22	cyclic	cyclic	ADJ
ejpam-2339	30	23	image	image	NOUN
ejpam-2339	30	24	of	of	ADP
ejpam-2339	30	25	order	order	NOUN
ejpam-2339	30	26	equal	equal	ADJ
ejpam-2339	30	27	to	to	ADP
ejpam-2339	30	28	the	the	DET
ejpam-2339	30	29	order	order	NOUN
ejpam-2339	30	30	of	of	ADP
ejpam-2339	30	31	ǫ	ǫ	PRON
ejpam-2339	30	32	,	,	PUNCT
ejpam-2339	30	33	then	then	ADV
ejpam-2339	30	34	using	use	VERB
ejpam-2339	30	35	representation	representation	NOUN
ejpam-2339	30	36	theory	theory	NOUN
ejpam-2339	30	37	tools	tool	NOUN
ejpam-2339	30	38	it	it	PRON
ejpam-2339	30	39	can	can	AUX
ejpam-2339	30	40	be	be	AUX
ejpam-2339	30	41	shown	show	VERB
ejpam-2339	30	42	that	that	SCONJ
ejpam-2339	30	43	there	there	PRON
ejpam-2339	30	44	is	be	VERB
ejpam-2339	30	45	some	some	DET
ejpam-2339	30	46	polynomial	polynomial	ADJ
ejpam-2339	30	47	f	f	NOUN
ejpam-2339	30	48	(	(	PUNCT
ejpam-2339	30	49	ǫ	ǫ	NOUN
ejpam-2339	30	50	)	)	PUNCT
ejpam-2339	30	51	such	such	ADJ
ejpam-2339	30	52	that	that	SCONJ
ejpam-2339	30	53	|	|	ADV
ejpam-2339	30	54	f	f	X
ejpam-2339	30	55	(	(	PUNCT
ejpam-2339	30	56	ǫp)|	ǫp)|	NOUN
ejpam-2339	30	57	is	be	AUX
ejpam-2339	30	58	constant	constant	ADJ
ejpam-2339	30	59	for	for	ADP
ejpam-2339	30	60	every	every	DET
ejpam-2339	30	61	p	p	PROPN
ejpam-2339	30	62	∈	∈	PROPN
ejpam-2339	30	63	z	z	NOUN
ejpam-2339	30	64	(	(	PUNCT
ejpam-2339	30	65	assuming	assume	VERB
ejpam-2339	30	66	f	f	PROPN
ejpam-2339	30	67	(	(	PUNCT
ejpam-2339	30	68	ǫp	ǫp	NOUN
ejpam-2339	30	69	)	)	PUNCT
ejpam-2339	30	70	is	be	AUX
ejpam-2339	30	71	nontrivial	nontrivial	ADJ
ejpam-2339	30	72	)	)	PUNCT
ejpam-2339	30	73	.	.	PUNCT
ejpam-2339	31	1	in	in	ADP
ejpam-2339	31	2	paper	paper	NOUN
ejpam-2339	31	3	[	[	X
ejpam-2339	31	4	3	3	X
ejpam-2339	31	5	]	]	X
ejpam-2339	31	6	hadamard	hadamard	ADJ
ejpam-2339	31	7	groups	group	NOUN
ejpam-2339	31	8	of	of	ADP
ejpam-2339	31	9	order	order	NOUN
ejpam-2339	31	10	22d+2	22d+2	NUM
ejpam-2339	31	11	were	be	AUX
ejpam-2339	31	12	considered	consider	VERB
ejpam-2339	31	13	.	.	PUNCT
ejpam-2339	32	1	consequent	consequent	ADJ
ejpam-2339	32	2	polynomials	polynomial	NOUN
ejpam-2339	32	3	were	be	AUX
ejpam-2339	32	4	fully	fully	ADV
ejpam-2339	32	5	described	describe	VERB
ejpam-2339	32	6	,	,	PUNCT
ejpam-2339	32	7	after	after	ADP
ejpam-2339	32	8	which	which	PRON
ejpam-2339	32	9	new	new	ADJ
ejpam-2339	32	10	necessary	necessary	ADJ
ejpam-2339	32	11	conditions	condition	NOUN
ejpam-2339	32	12	have	have	AUX
ejpam-2339	32	13	been	be	AUX
ejpam-2339	32	14	proven	prove	VERB
ejpam-2339	32	15	.	.	PUNCT
ejpam-2339	33	1	pairwise	pairwise	NOUN
ejpam-2339	33	2	abbreviation	abbreviation	NOUN
ejpam-2339	33	3	theorem	theorem	VERB
ejpam-2339	33	4	[	[	X
ejpam-2339	33	5	3	3	NUM
ejpam-2339	33	6	]	]	PUNCT
ejpam-2339	33	7	is	be	AUX
ejpam-2339	33	8	also	also	ADV
ejpam-2339	33	9	used	use	VERB
ejpam-2339	33	10	in	in	ADP
ejpam-2339	33	11	this	this	DET
ejpam-2339	33	12	paper	paper	NOUN
ejpam-2339	33	13	.	.	PUNCT
ejpam-2339	34	1	results	result	NOUN
ejpam-2339	34	2	that	that	PRON
ejpam-2339	34	3	follow	follow	VERB
ejpam-2339	34	4	will	will	AUX
ejpam-2339	34	5	show	show	VERB
ejpam-2339	34	6	us	we	PRON
ejpam-2339	34	7	again	again	ADV
ejpam-2339	34	8	that	that	SCONJ
ejpam-2339	34	9	’	'	PUNCT
ejpam-2339	34	10	fourier	fouri	ADJ
ejpam-2339	34	11	type	type	NOUN
ejpam-2339	34	12	’	'	PUNCT
ejpam-2339	34	13	approach	approach	NOUN
ejpam-2339	34	14	,	,	PUNCT
ejpam-2339	34	15	by	by	ADP
ejpam-2339	34	16	comparing	compare	VERB
ejpam-2339	34	17	coefficients	coefficient	NOUN
ejpam-2339	34	18	of	of	ADP
ejpam-2339	34	19	respective	respective	ADJ
ejpam-2339	34	20	powers	power	NOUN
ejpam-2339	34	21	,	,	PUNCT
ejpam-2339	34	22	can	can	AUX
ejpam-2339	34	23	lead	lead	VERB
ejpam-2339	34	24	us	we	PRON
ejpam-2339	34	25	to	to	ADP
ejpam-2339	34	26	some	some	DET
ejpam-2339	34	27	new	new	ADJ
ejpam-2339	34	28	conditions	condition	NOUN
ejpam-2339	34	29	.	.	PUNCT
ejpam-2339	35	1	main	main	ADJ
ejpam-2339	35	2	goal	goal	NOUN
ejpam-2339	35	3	of	of	ADP
ejpam-2339	35	4	this	this	DET
ejpam-2339	35	5	paper	paper	NOUN
ejpam-2339	35	6	is	be	AUX
ejpam-2339	35	7	to	to	PART
ejpam-2339	35	8	offer	offer	VERB
ejpam-2339	35	9	generalization	generalization	NOUN
ejpam-2339	35	10	of	of	ADP
ejpam-2339	35	11	results	result	NOUN
ejpam-2339	35	12	in	in	ADP
ejpam-2339	35	13	[	[	X
ejpam-2339	35	14	3	3	NUM
ejpam-2339	35	15	]	]	PUNCT
ejpam-2339	35	16	.	.	PUNCT
ejpam-2339	36	1	that	that	PRON
ejpam-2339	36	2	will	will	AUX
ejpam-2339	36	3	be	be	AUX
ejpam-2339	36	4	provided	provide	VERB
ejpam-2339	36	5	by	by	ADP
ejpam-2339	36	6	proving	prove	VERB
ejpam-2339	36	7	result	result	NOUN
ejpam-2339	36	8	where	where	SCONJ
ejpam-2339	36	9	norm	norm	NOUN
ejpam-2339	36	10	of	of	ADP
ejpam-2339	36	11	polynomials	polynomial	NOUN
ejpam-2339	36	12	is	be	AUX
ejpam-2339	36	13	not	not	PART
ejpam-2339	36	14	necessary	necessary	ADJ
ejpam-2339	36	15	some	some	DET
ejpam-2339	36	16	power	power	NOUN
ejpam-2339	36	17	of	of	ADP
ejpam-2339	36	18	2	2	NUM
ejpam-2339	36	19	.	.	PUNCT
ejpam-2339	37	1	we	we	PRON
ejpam-2339	37	2	will	will	AUX
ejpam-2339	37	3	denote	denote	VERB
ejpam-2339	37	4	f	f	PROPN
ejpam-2339	37	5	(	(	PUNCT
ejpam-2339	37	6	ǫ	ǫ	NOUN
ejpam-2339	37	7	)	)	PUNCT
ejpam-2339	37	8	as	as	ADP
ejpam-2339	37	9	nontrivial	nontrivial	ADJ
ejpam-2339	37	10	if	if	SCONJ
ejpam-2339	37	11	it	it	PRON
ejpam-2339	37	12	has	have	VERB
ejpam-2339	37	13	some	some	DET
ejpam-2339	37	14	nonzero	nonzero	ADJ
ejpam-2339	37	15	coefficient	coefficient	NOUN
ejpam-2339	37	16	next	next	ADV
ejpam-2339	37	17	to	to	ADP
ejpam-2339	37	18	some	some	PRON
ejpam-2339	37	19	ǫi	ǫi	ADP
ejpam-2339	37	20	6=	6=	NUM
ejpam-2339	37	21	1	1	NUM
ejpam-2339	37	22	.	.	PUNCT
ejpam-2339	37	23	definition	definition	NOUN
ejpam-2339	37	24	1	1	NUM
ejpam-2339	37	25	.	.	PUNCT
ejpam-2339	38	1	let	let	VERB
ejpam-2339	38	2	ǫ	ǫ	PRON
ejpam-2339	38	3	be	be	AUX
ejpam-2339	38	4	a	a	DET
ejpam-2339	38	5	root	root	NOUN
ejpam-2339	38	6	of	of	ADP
ejpam-2339	38	7	unity	unity	NOUN
ejpam-2339	38	8	and	and	CCONJ
ejpam-2339	38	9	f	f	PROPN
ejpam-2339	38	10	(	(	PUNCT
ejpam-2339	38	11	ǫ	ǫ	NOUN
ejpam-2339	38	12	)	)	PUNCT
ejpam-2339	38	13	∈	∈	PROPN
ejpam-2339	38	14	z[ǫ	z[ǫ	PROPN
ejpam-2339	38	15	]	]	PUNCT
ejpam-2339	38	16	is	be	AUX
ejpam-2339	38	17	nontrivial	nontrivial	ADJ
ejpam-2339	38	18	.	.	PUNCT
ejpam-2339	39	1	if	if	SCONJ
ejpam-2339	39	2	there	there	PRON
ejpam-2339	39	3	is	be	VERB
ejpam-2339	39	4	some	some	DET
ejpam-2339	39	5	c	c	NOUN
ejpam-2339	39	6	,	,	PUNCT
ejpam-2339	39	7	such	such	ADJ
ejpam-2339	39	8	that	that	SCONJ
ejpam-2339	39	9	|	|	NOUN
ejpam-2339	39	10	f	f	X
ejpam-2339	39	11	(	(	PUNCT
ejpam-2339	39	12	ǫp)|=	ǫp)|=	PROPN
ejpam-2339	39	13	c	c	AUX
ejpam-2339	39	14	,	,	PUNCT
ejpam-2339	39	15	for	for	ADP
ejpam-2339	39	16	all	all	DET
ejpam-2339	39	17	p	p	NOUN
ejpam-2339	39	18	∈	∈	PROPN
ejpam-2339	39	19	z	z	NOUN
ejpam-2339	39	20	such	such	ADJ
ejpam-2339	39	21	that	that	SCONJ
ejpam-2339	39	22	f	f	PROPN
ejpam-2339	39	23	(	(	PUNCT
ejpam-2339	39	24	ǫp	ǫp	NOUN
ejpam-2339	39	25	)	)	PUNCT
ejpam-2339	39	26	is	be	AUX
ejpam-2339	39	27	nontrivial	nontrivial	ADJ
ejpam-2339	39	28	,	,	PUNCT
ejpam-2339	39	29	then	then	ADV
ejpam-2339	39	30	we	we	PRON
ejpam-2339	39	31	shall	shall	AUX
ejpam-2339	39	32	say	say	VERB
ejpam-2339	39	33	f	f	PROPN
ejpam-2339	39	34	(	(	PUNCT
ejpam-2339	39	35	ǫ	ǫ	NOUN
ejpam-2339	39	36	)	)	PUNCT
ejpam-2339	39	37	is	be	AUX
ejpam-2339	39	38	norm	norm	NOUN
ejpam-2339	39	39	invariant	invariant	ADJ
ejpam-2339	39	40	.	.	PUNCT
ejpam-2339	40	1	following	follow	VERB
ejpam-2339	40	2	result	result	NOUN
ejpam-2339	40	3	describes	describe	VERB
ejpam-2339	40	4	pairwise	pairwise	PROPN
ejpam-2339	40	5	abbreviation	abbreviation	NOUN
ejpam-2339	40	6	.	.	PUNCT
ejpam-2339	41	1	theorem	theorem	NOUN
ejpam-2339	41	2	2	2	NUM
ejpam-2339	41	3	.	.	PUNCT
ejpam-2339	42	1	let	let	AUX
ejpam-2339	42	2	ǫ	ǫ	PRON
ejpam-2339	42	3	be	be	AUX
ejpam-2339	42	4	a	a	DET
ejpam-2339	42	5	root	root	NOUN
ejpam-2339	42	6	of	of	ADP
ejpam-2339	42	7	unity	unity	NOUN
ejpam-2339	42	8	of	of	ADP
ejpam-2339	42	9	order	order	NOUN
ejpam-2339	42	10	2k	2k	NUM
ejpam-2339	42	11	,	,	PUNCT
ejpam-2339	42	12	k	k	PROPN
ejpam-2339	42	13	≥	≥	NUM
ejpam-2339	42	14	1	1	NUM
ejpam-2339	42	15	.	.	PUNCT
ejpam-2339	42	16	suppose	suppose	VERB
ejpam-2339	43	1	that	that	SCONJ
ejpam-2339	43	2	ǫα1	ǫα1	PROPN
ejpam-2339	44	1	+	+	NUM
ejpam-2339	44	2	ǫα2	ǫα2	PROPN
ejpam-2339	44	3	+	+	X
ejpam-2339	44	4	·	·	PUNCT
ejpam-2339	44	5	·	·	PUNCT
ejpam-2339	44	6	·	·	PUNCT
ejpam-2339	45	1	+	+	NUM
ejpam-2339	45	2	ǫαl	ǫαl	NOUN
ejpam-2339	45	3	=	=	SYM
ejpam-2339	45	4	0	0	NUM
ejpam-2339	45	5	,	,	PUNCT
ejpam-2339	45	6	where	where	SCONJ
ejpam-2339	45	7	αi	αi	PROPN
ejpam-2339	45	8	’s	’	VERB
ejpam-2339	45	9	need	need	VERB
ejpam-2339	45	10	not	not	PART
ejpam-2339	45	11	to	to	PART
ejpam-2339	45	12	be	be	AUX
ejpam-2339	45	13	mutually	mutually	ADV
ejpam-2339	45	14	different	different	ADJ
ejpam-2339	45	15	.	.	PUNCT
ejpam-2339	46	1	then	then	ADV
ejpam-2339	46	2	l	l	NOUN
ejpam-2339	46	3	is	be	AUX
ejpam-2339	46	4	even	even	ADV
ejpam-2339	46	5	and	and	CCONJ
ejpam-2339	46	6	there	there	PRON
ejpam-2339	46	7	is	be	VERB
ejpam-2339	46	8	a	a	DET
ejpam-2339	46	9	partition	partition	NOUN
ejpam-2339	46	10	of	of	ADP
ejpam-2339	46	11	the	the	DET
ejpam-2339	46	12	multiset	multiset	NOUN
ejpam-2339	46	13	{	{	PUNCT
ejpam-2339	46	14	α1,α2	α1,α2	PROPN
ejpam-2339	46	15	,	,	PUNCT
ejpam-2339	46	16	.	.	PUNCT
ejpam-2339	46	17	.	.	PUNCT
ejpam-2339	46	18	.	.	PUNCT
ejpam-2339	47	1	,	,	PUNCT
ejpam-2339	47	2	αl	αl	ADP
ejpam-2339	47	3	}	}	PUNCT
ejpam-2339	47	4	in	in	ADP
ejpam-2339	47	5	2	2	NUM
ejpam-2339	47	6	-	-	PUNCT
ejpam-2339	47	7	element	element	NOUN
ejpam-2339	47	8	subsets	subset	NOUN
ejpam-2339	47	9	{	{	PUNCT
ejpam-2339	47	10	αi	αi	INTJ
ejpam-2339	47	11	,	,	PUNCT
ejpam-2339	47	12	α	α	PROPN
ejpam-2339	47	13	j	j	PROPN
ejpam-2339	47	14	}	}	PUNCT
ejpam-2339	47	15	such	such	ADJ
ejpam-2339	47	16	that	that	SCONJ
ejpam-2339	47	17	ǫαi	ǫαi	PRON
ejpam-2339	48	1	+	+	NOUN
ejpam-2339	48	2	ǫα	ǫα	PROPN
ejpam-2339	48	3	j	j	NOUN
ejpam-2339	48	4	=	=	PROPN
ejpam-2339	48	5	0	0	PROPN
ejpam-2339	48	6	.	.	PUNCT
ejpam-2339	49	1	next	next	ADJ
ejpam-2339	49	2	result	result	NOUN
ejpam-2339	49	3	(	(	PUNCT
ejpam-2339	49	4	see	see	VERB
ejpam-2339	49	5	[	[	X
ejpam-2339	49	6	3	3	NUM
ejpam-2339	49	7	]	]	PUNCT
ejpam-2339	49	8	)	)	PUNCT
ejpam-2339	49	9	gives	give	VERB
ejpam-2339	49	10	a	a	DET
ejpam-2339	49	11	characterization	characterization	NOUN
ejpam-2339	49	12	of	of	ADP
ejpam-2339	49	13	norm	norm	ADJ
ejpam-2339	49	14	invariant	invariant	ADJ
ejpam-2339	49	15	polynomials	polynomial	NOUN
ejpam-2339	49	16	of	of	ADP
ejpam-2339	49	17	norm	norm	NOUN
ejpam-2339	49	18	2d	2d	NOUN
ejpam-2339	49	19	.	.	PUNCT
ejpam-2339	50	1	theorem	theorem	NOUN
ejpam-2339	50	2	3	3	X
ejpam-2339	50	3	.	.	PUNCT
ejpam-2339	51	1	let	let	VERB
ejpam-2339	51	2	f	f	PROPN
ejpam-2339	51	3	(	(	PUNCT
ejpam-2339	51	4	ǫ	ǫ	NOUN
ejpam-2339	51	5	)	)	PUNCT
ejpam-2339	51	6	=	=	SYM
ejpam-2339	52	1	ǫr1	ǫr1	PROPN
ejpam-2339	53	1	+	+	NUM
ejpam-2339	53	2	·	·	PUNCT
ejpam-2339	53	3	·	·	PUNCT
ejpam-2339	53	4	·	·	PUNCT
ejpam-2339	53	5	+	+	CCONJ
ejpam-2339	53	6	ǫrq	ǫrq	NOUN
ejpam-2339	53	7	be	be	AUX
ejpam-2339	53	8	a	a	DET
ejpam-2339	53	9	norm	norm	NOUN
ejpam-2339	53	10	invariant	invariant	ADJ
ejpam-2339	53	11	polynomial	polynomial	NOUN
ejpam-2339	53	12	of	of	ADP
ejpam-2339	53	13	norm	norm	NOUN
ejpam-2339	53	14	2d	2d	NUM
ejpam-2339	53	15	where	where	SCONJ
ejpam-2339	53	16	q	q	NOUN
ejpam-2339	53	17	=	=	SYM
ejpam-2339	53	18	2d(2d+1	2d(2d+1	NUM
ejpam-2339	53	19	−	−	NOUN
ejpam-2339	53	20	1	1	NUM
ejpam-2339	53	21	)	)	PUNCT
ejpam-2339	53	22	and	and	CCONJ
ejpam-2339	53	23	ǫ	ǫ	PRON
ejpam-2339	53	24	is	be	AUX
ejpam-2339	53	25	a	a	DET
ejpam-2339	53	26	root	root	NOUN
ejpam-2339	53	27	of	of	ADP
ejpam-2339	53	28	unity	unity	NOUN
ejpam-2339	53	29	of	of	ADP
ejpam-2339	53	30	order	order	NOUN
ejpam-2339	53	31	22d+2	22d+2	NUM
ejpam-2339	53	32	.	.	PUNCT
ejpam-2339	54	1	let	let	VERB
ejpam-2339	54	2	2n	2n	NUM
ejpam-2339	54	3	=	=	SYM
ejpam-2339	54	4	max{o(ǫri	max{o(ǫri	NOUN
ejpam-2339	54	5	)	)	PUNCT
ejpam-2339	54	6	}	}	PUNCT
ejpam-2339	54	7	.	.	PUNCT
ejpam-2339	55	1	then	then	ADV
ejpam-2339	55	2	for	for	ADP
ejpam-2339	55	3	every	every	DET
ejpam-2339	55	4	k	k	NOUN
ejpam-2339	55	5	=	=	SYM
ejpam-2339	55	6	0,1,2	0,1,2	NUM
ejpam-2339	55	7	,	,	PUNCT
ejpam-2339	55	8	.	.	PUNCT
ejpam-2339	55	9	.	.	PUNCT
ejpam-2339	55	10	.	.	PUNCT
ejpam-2339	56	1	,	,	PUNCT
ejpam-2339	56	2	n	n	CCONJ
ejpam-2339	56	3	−	−	PROPN
ejpam-2339	56	4	1	1	NUM
ejpam-2339	56	5	there	there	PRON
ejpam-2339	56	6	is	be	VERB
ejpam-2339	56	7	an	an	DET
ejpam-2339	56	8	r(k	r(k	PROPN
ejpam-2339	56	9	)	)	PUNCT
ejpam-2339	56	10	∈	∈	PROPN
ejpam-2339	56	11	z	z	NOUN
ejpam-2339	56	12	such	such	ADJ
ejpam-2339	57	1	that	that	SCONJ
ejpam-2339	57	2	f	f	PROPN
ejpam-2339	57	3	(	(	PUNCT
ejpam-2339	57	4	ǫ2k	ǫ2k	NOUN
ejpam-2339	57	5	)	)	PUNCT
ejpam-2339	57	6	=	=	SYM
ejpam-2339	57	7	2dǫr(k	2dǫr(k	NUM
ejpam-2339	57	8	)	)	PUNCT
ejpam-2339	57	9	.	.	PUNCT
ejpam-2339	58	1	we	we	PRON
ejpam-2339	58	2	call	call	VERB
ejpam-2339	58	3	such	such	ADJ
ejpam-2339	58	4	polynomials	polynomial	NOUN
ejpam-2339	58	5	f	f	X
ejpam-2339	58	6	(	(	PUNCT
ejpam-2339	58	7	ǫ2k	ǫ2k	NOUN
ejpam-2339	58	8	)	)	PUNCT
ejpam-2339	58	9	maximally	maximally	ADV
ejpam-2339	58	10	abbreviated	abbreviate	VERB
ejpam-2339	58	11	.	.	PUNCT
ejpam-2339	59	1	2	2	X
ejpam-2339	59	2	.	.	X
ejpam-2339	59	3	some	some	DET
ejpam-2339	59	4	algebraic	algebraic	ADJ
ejpam-2339	59	5	tools	tool	NOUN
ejpam-2339	59	6	let	let	VERB
ejpam-2339	59	7	us	we	PRON
ejpam-2339	59	8	introduce	introduce	VERB
ejpam-2339	59	9	some	some	DET
ejpam-2339	59	10	notation	notation	NOUN
ejpam-2339	59	11	.	.	PUNCT
ejpam-2339	60	1	for	for	ADP
ejpam-2339	60	2	n	n	PRON
ejpam-2339	60	3	∈	∈	NOUN
ejpam-2339	60	4	n	n	CCONJ
ejpam-2339	60	5	we	we	PRON
ejpam-2339	60	6	denote	denote	VERB
ejpam-2339	60	7	[	[	X
ejpam-2339	60	8	n	n	X
ejpam-2339	60	9	]	]	X
ejpam-2339	60	10	=	=	PUNCT
ejpam-2339	60	11	{	{	PUNCT
ejpam-2339	60	12	1,2	1,2	NUM
ejpam-2339	60	13	,	,	PUNCT
ejpam-2339	60	14	.	.	PUNCT
ejpam-2339	60	15	.	.	PUNCT
ejpam-2339	61	1	.	.	PUNCT
ejpam-2339	62	1	,	,	PUNCT
ejpam-2339	62	2	n	n	CCONJ
ejpam-2339	62	3	}	}	PUNCT
ejpam-2339	63	1	and	and	CCONJ
ejpam-2339	64	1	[	[	X
ejpam-2339	64	2	n]0	n]0	ADJ
ejpam-2339	64	3	=	=	PUNCT
ejpam-2339	64	4	{	{	PUNCT
ejpam-2339	64	5	0,1,2	0,1,2	NOUN
ejpam-2339	64	6	,	,	PUNCT
ejpam-2339	64	7	.	.	PUNCT
ejpam-2339	64	8	.	.	PUNCT
ejpam-2339	65	1	.	.	PUNCT
ejpam-2339	65	2	,	,	PUNCT
ejpam-2339	65	3	n	n	CCONJ
ejpam-2339	65	4	}	}	PUNCT
ejpam-2339	65	5	.	.	PUNCT
ejpam-2339	66	1	next	next	ADJ
ejpam-2339	66	2	result	result	NOUN
ejpam-2339	66	3	describes	describe	VERB
ejpam-2339	66	4	distribution	distribution	NOUN
ejpam-2339	66	5	of	of	ADP
ejpam-2339	66	6	coefficients	coefficient	NOUN
ejpam-2339	66	7	standing	stand	VERB
ejpam-2339	66	8	by	by	ADP
ejpam-2339	66	9	ǫ0	ǫ0	PROPN
ejpam-2339	66	10	in	in	ADP
ejpam-2339	66	11	norm	norm	NOUN
ejpam-2339	66	12	invariant	invariant	ADJ
ejpam-2339	66	13	polynomial	polynomial	NOUN
ejpam-2339	66	14	from	from	ADP
ejpam-2339	66	15	z[ǫ	z[ǫ	PROPN
ejpam-2339	66	16	]	]	PUNCT
ejpam-2339	66	17	,	,	PUNCT
ejpam-2339	66	18	where	where	SCONJ
ejpam-2339	66	19	ǫ2	ǫ2	NOUN
ejpam-2339	66	20	t	t	NOUN
ejpam-2339	66	21	=	=	SYM
ejpam-2339	66	22	1	1	X
ejpam-2339	66	23	.	.	PUNCT
ejpam-2339	66	24	theorem	theorem	NOUN
ejpam-2339	66	25	4	4	NUM
ejpam-2339	66	26	.	.	PUNCT
ejpam-2339	67	1	let	let	VERB
ejpam-2339	67	2	ǫ	ǫ	PRON
ejpam-2339	67	3	be	be	AUX
ejpam-2339	67	4	root	root	NOUN
ejpam-2339	67	5	of	of	ADP
ejpam-2339	67	6	unity	unity	NOUN
ejpam-2339	67	7	of	of	ADP
ejpam-2339	67	8	order	order	NOUN
ejpam-2339	67	9	2	2	NUM
ejpam-2339	67	10	t	t	NOUN
ejpam-2339	67	11	and	and	CCONJ
ejpam-2339	67	12	f(ǫ	f(ǫ	PROPN
ejpam-2339	67	13	)	)	PUNCT
ejpam-2339	68	1	=	=	PUNCT
ejpam-2339	68	2	∑	∑	PUNCT
ejpam-2339	68	3	kiǫ	kiǫ	VERB
ejpam-2339	69	1	i	i	PROPN
ejpam-2339	69	2	,	,	PUNCT
ejpam-2339	69	3	k	k	PROPN
ejpam-2339	69	4	∈	∈	PROPN
ejpam-2339	69	5	n0	n0	PROPN
ejpam-2339	69	6	.	.	PUNCT
ejpam-2339	70	1	let	let	VERB
ejpam-2339	70	2	sum	sum	NOUN
ejpam-2339	70	3	of	of	ADP
ejpam-2339	70	4	coefficients	coefficient	NOUN
ejpam-2339	70	5	is	be	AUX
ejpam-2339	70	6	2u2	2u2	NUM
ejpam-2339	70	7	−	−	PROPN
ejpam-2339	70	8	u	u	NOUN
ejpam-2339	70	9	,	,	PUNCT
ejpam-2339	70	10	for	for	ADP
ejpam-2339	70	11	some	some	DET
ejpam-2339	70	12	u	u	PROPN
ejpam-2339	70	13	∈	∈	PROPN
ejpam-2339	70	14	n.	n.	NOUN
ejpam-2339	71	1	if	if	SCONJ
ejpam-2339	71	2	every	every	DET
ejpam-2339	71	3	nontrivial	nontrivial	NOUN
ejpam-2339	71	4	f(ǫ2s	f(ǫ2s	X
ejpam-2339	71	5	)	)	PUNCT
ejpam-2339	71	6	is	be	AUX
ejpam-2339	71	7	of	of	ADP
ejpam-2339	71	8	norm	norm	NOUN
ejpam-2339	71	9	u	u	NOUN
ejpam-2339	71	10	,	,	PUNCT
ejpam-2339	71	11	then	then	ADV
ejpam-2339	71	12	∑	∑	PUNCT
ejpam-2339	71	13	i∈a0	i∈a0	ADJ
ejpam-2339	71	14	k2	k2	PROPN
ejpam-2339	71	15	i	i	PROPN
ejpam-2339	71	16	+	+	CCONJ
ejpam-2339	71	17	2	2	NUM
ejpam-2339	71	18	s	s	PART
ejpam-2339	71	19	∑	∑	PROPN
ejpam-2339	71	20	j=1	j=1	NOUN
ejpam-2339	71	21	∑	∑	PROPN
ejpam-2339	71	22	(	(	PUNCT
ejpam-2339	71	23	a	a	PRON
ejpam-2339	71	24	,	,	PUNCT
ejpam-2339	71	25	b)∈a	b)∈a	SYM
ejpam-2339	71	26	j	j	PROPN
ejpam-2339	71	27	kakb	kakb	PROPN
ejpam-2339	71	28	−	−	PROPN
ejpam-2339	71	29	2	2	NUM
ejpam-2339	71	30	∑	∑	PUNCT
ejpam-2339	71	31	(	(	PUNCT
ejpam-2339	71	32	a	a	PRON
ejpam-2339	71	33	,	,	PUNCT
ejpam-2339	71	34	b)∈as+1	b)∈as+1	PROPN
ejpam-2339	71	35	kakb	kakb	PROPN
ejpam-2339	71	36	=	=	PROPN
ejpam-2339	71	37	u2	u2	PROPN
ejpam-2339	71	38	where	where	SCONJ
ejpam-2339	71	39	a0	a0	NOUN
ejpam-2339	72	1	=	=	PUNCT
ejpam-2339	73	1	[	[	X
ejpam-2339	73	2	2	2	NUM
ejpam-2339	73	3	t	t	NOUN
ejpam-2339	73	4	−	−	PROPN
ejpam-2339	73	5	1]0	1]0	PROPN
ejpam-2339	73	6	and	and	CCONJ
ejpam-2339	73	7	a	a	DET
ejpam-2339	73	8	j	j	NOUN
ejpam-2339	73	9	=	=	PRON
ejpam-2339	73	10	{	{	PUNCT
ejpam-2339	73	11	(	(	PUNCT
ejpam-2339	73	12	a	a	PRON
ejpam-2339	73	13	,	,	PUNCT
ejpam-2339	73	14	b	b	NOUN
ejpam-2339	73	15	)	)	PUNCT
ejpam-2339	73	16	∈	∈	PROPN
ejpam-2339	73	17	a2	a2	PROPN
ejpam-2339	73	18	0	0	PUNCT
ejpam-2339	74	1	|	|	ADV
ejpam-2339	74	2	a	a	DET
ejpam-2339	74	3	<	<	X
ejpam-2339	74	4	b	b	PROPN
ejpam-2339	74	5	,	,	PUNCT
ejpam-2339	74	6	2	2	NUM
ejpam-2339	74	7	j−1(a−	j−1(a−	X
ejpam-2339	74	8	b)≡	b)≡	NOUN
ejpam-2339	74	9	2t−1(mod	2t−1(mod	ADJ
ejpam-2339	74	10	2	2	NUM
ejpam-2339	74	11	t	t	NOUN
ejpam-2339	74	12	)	)	PUNCT
ejpam-2339	74	13	}	}	PUNCT
ejpam-2339	74	14	.	.	PUNCT
ejpam-2339	75	1	proof	proof	NOUN
ejpam-2339	75	2	.	.	PUNCT
ejpam-2339	76	1	we	we	PRON
ejpam-2339	76	2	start	start	VERB
ejpam-2339	76	3	by	by	ADP
ejpam-2339	76	4	taking	take	VERB
ejpam-2339	76	5	s	s	PART
ejpam-2339	76	6	=	=	NOUN
ejpam-2339	76	7	0	0	NUM
ejpam-2339	76	8	.	.	PUNCT
ejpam-2339	77	1	by	by	ADP
ejpam-2339	77	2	assumption	assumption	NOUN
ejpam-2339	77	3	we	we	PRON
ejpam-2339	77	4	have	have	VERB
ejpam-2339	77	5	|f(ǫ)|=	|f(ǫ)|=	PROPN
ejpam-2339	77	6	u.	u.	NOUN
ejpam-2339	77	7	then	then	ADV
ejpam-2339	77	8	u2	u2	NOUN
ejpam-2339	77	9	=	=	PUNCT
ejpam-2339	77	10	|f(ǫ)|2	|f(ǫ)|2	PUNCT
ejpam-2339	77	11	=	=	SYM
ejpam-2339	77	12	∑	∑	PUNCT
ejpam-2339	77	13	i	i	PROPN
ejpam-2339	77	14	,	,	PUNCT
ejpam-2339	77	15	j∈a0	j∈a0	PROPN
ejpam-2339	77	16	kik	kik	PROPN
ejpam-2339	77	17	jβ	jβ	PROPN
ejpam-2339	77	18	i−	i−	PROPN
ejpam-2339	77	19	j	j	PROPN
ejpam-2339	77	20	,	,	PUNCT
ejpam-2339	77	21	where	where	SCONJ
ejpam-2339	77	22	a0	a0	NOUN
ejpam-2339	77	23	=	=	PUNCT
ejpam-2339	78	1	[	[	X
ejpam-2339	78	2	2	2	NUM
ejpam-2339	78	3	t	t	NOUN
ejpam-2339	78	4	−	−	PROPN
ejpam-2339	78	5	1]0	1]0	PROPN
ejpam-2339	78	6	.	.	PUNCT
ejpam-2339	79	1	by	by	ADP
ejpam-2339	79	2	theorem	theorem	NOUN
ejpam-2339	79	3	2	2	NUM
ejpam-2339	79	4	,	,	PUNCT
ejpam-2339	79	5	after	after	ADP
ejpam-2339	79	6	comparing	compare	VERB
ejpam-2339	79	7	coefficients	coefficient	NOUN
ejpam-2339	79	8	next	next	ADV
ejpam-2339	79	9	to	to	ADP
ejpam-2339	79	10	1	1	NUM
ejpam-2339	79	11	,	,	PUNCT
ejpam-2339	79	12	we	we	PRON
ejpam-2339	79	13	get	get	VERB
ejpam-2339	79	14	∑	∑	PUNCT
ejpam-2339	79	15	ǫi−	ǫi−	NUM
ejpam-2339	79	16	j=1	j=1	ADJ
ejpam-2339	79	17	kik	kik	PROPN
ejpam-2339	79	18	jβ	jβ	PROPN
ejpam-2339	79	19	i−	i−	PROPN
ejpam-2339	79	20	j	j	PROPN
ejpam-2339	80	1	−	−	PROPN
ejpam-2339	80	2	∑	∑	PROPN
ejpam-2339	80	3	ǫi−	ǫi−	NUM
ejpam-2339	80	4	j=−1	j=−1	ADJ
ejpam-2339	80	5	kik	kik	NOUN
ejpam-2339	80	6	jβ	jβ	PROPN
ejpam-2339	80	7	i−	i−	PROPN
ejpam-2339	80	8	j	j	PROPN
ejpam-2339	80	9	=	=	PROPN
ejpam-2339	80	10	u2	u2	PROPN
ejpam-2339	80	11	.	.	PUNCT
ejpam-2339	81	1	(	(	PUNCT
ejpam-2339	81	2	1	1	X
ejpam-2339	81	3	)	)	PUNCT
ejpam-2339	81	4	k.tabak	k.tabak	ADJ
ejpam-2339	81	5	/	/	SYM
ejpam-2339	81	6	eur	eur	PROPN
ejpam-2339	81	7	.	.	PUNCT
ejpam-2339	82	1	j.	j.	PROPN
ejpam-2339	82	2	pure	pure	PROPN
ejpam-2339	82	3	appl	appl	PROPN
ejpam-2339	82	4	.	.	PROPN
ejpam-2339	82	5	math	math	PROPN
ejpam-2339	82	6	,	,	PUNCT
ejpam-2339	82	7	8	8	NUM
ejpam-2339	82	8	(	(	PUNCT
ejpam-2339	82	9	2015	2015	NUM
ejpam-2339	82	10	)	)	PUNCT
ejpam-2339	82	11	,	,	PUNCT
ejpam-2339	82	12	450	450	NUM
ejpam-2339	82	13	-	-	SYM
ejpam-2339	82	14	457	457	NUM
ejpam-2339	82	15	452	452	NUM
ejpam-2339	82	16	if	if	SCONJ
ejpam-2339	82	17	ǫi−	ǫi−	NUM
ejpam-2339	82	18	j	j	NOUN
ejpam-2339	82	19	=	=	SYM
ejpam-2339	82	20	1	1	NUM
ejpam-2339	82	21	,	,	PUNCT
ejpam-2339	82	22	then	then	ADV
ejpam-2339	82	23	ki	ki	PROPN
ejpam-2339	82	24	=	=	PUNCT
ejpam-2339	83	1	k	k	PROPN
ejpam-2339	83	2	j	j	PROPN
ejpam-2339	83	3	.	.	PUNCT
ejpam-2339	84	1	if	if	SCONJ
ejpam-2339	84	2	ǫi−	ǫi−	NUM
ejpam-2339	84	3	j	j	NOUN
ejpam-2339	84	4	=	=	SYM
ejpam-2339	84	5	−1	−1	NOUN
ejpam-2339	84	6	,	,	PUNCT
ejpam-2339	84	7	then	then	ADV
ejpam-2339	84	8	i	i	PRON
ejpam-2339	84	9	−	−	PROPN
ejpam-2339	84	10	j	j	PROPN
ejpam-2339	84	11	≡	≡	PROPN
ejpam-2339	84	12	2t−1(mod	2t−1(mod	ADJ
ejpam-2339	84	13	2	2	NUM
ejpam-2339	84	14	t	t	NOUN
ejpam-2339	84	15	)	)	PUNCT
ejpam-2339	84	16	.	.	PUNCT
ejpam-2339	85	1	it	it	PRON
ejpam-2339	85	2	is	be	AUX
ejpam-2339	85	3	clear	clear	ADJ
ejpam-2339	85	4	that	that	SCONJ
ejpam-2339	85	5	also	also	ADV
ejpam-2339	85	6	j	j	PROPN
ejpam-2339	86	1	−	−	NOUN
ejpam-2339	87	1	i	i	PRON
ejpam-2339	87	2	≡	≡	PROPN
ejpam-2339	87	3	2t−1(mod	2t−1(mod	ADJ
ejpam-2339	87	4	2	2	NUM
ejpam-2339	87	5	t	t	NOUN
ejpam-2339	87	6	)	)	PUNCT
ejpam-2339	87	7	.	.	PUNCT
ejpam-2339	88	1	therefore	therefore	ADV
ejpam-2339	88	2	,	,	PUNCT
ejpam-2339	88	3	it	it	PRON
ejpam-2339	88	4	is	be	AUX
ejpam-2339	88	5	natural	natural	ADJ
ejpam-2339	88	6	to	to	PART
ejpam-2339	88	7	introduce	introduce	VERB
ejpam-2339	88	8	a1	a1	NOUN
ejpam-2339	88	9	=	=	SYM
ejpam-2339	88	10	{	{	PUNCT
ejpam-2339	88	11	(	(	PUNCT
ejpam-2339	88	12	a	a	PRON
ejpam-2339	88	13	,	,	PUNCT
ejpam-2339	88	14	b	b	NOUN
ejpam-2339	88	15	)	)	PUNCT
ejpam-2339	88	16	∈	∈	PROPN
ejpam-2339	88	17	a2	a2	PROPN
ejpam-2339	88	18	0	0	PUNCT
ejpam-2339	89	1	|	|	ADV
ejpam-2339	89	2	a	a	DET
ejpam-2339	89	3	<	<	X
ejpam-2339	89	4	b	b	PROPN
ejpam-2339	89	5	,	,	PUNCT
ejpam-2339	89	6	a−	a−	PROPN
ejpam-2339	89	7	b	b	PROPN
ejpam-2339	89	8	≡	≡	PROPN
ejpam-2339	89	9	2t−1	2t−1	NUM
ejpam-2339	89	10	(	(	PUNCT
ejpam-2339	89	11	mod	mod	PROPN
ejpam-2339	89	12	2	2	NUM
ejpam-2339	89	13	t	t	NOUN
ejpam-2339	89	14	)	)	PUNCT
ejpam-2339	89	15	}	}	PUNCT
ejpam-2339	89	16	.	.	PUNCT
ejpam-2339	90	1	then	then	ADV
ejpam-2339	90	2	,	,	PUNCT
ejpam-2339	90	3	from	from	ADP
ejpam-2339	90	4	(	(	PUNCT
ejpam-2339	90	5	1	1	X
ejpam-2339	90	6	)	)	PUNCT
ejpam-2339	90	7	we	we	PRON
ejpam-2339	90	8	get	get	VERB
ejpam-2339	90	9	∑	∑	DET
ejpam-2339	90	10	i∈a0	i∈a0	ADJ
ejpam-2339	90	11	k2	k2	X
ejpam-2339	91	1	i	i	PROPN
ejpam-2339	91	2	−	−	PROPN
ejpam-2339	91	3	2	2	NUM
ejpam-2339	91	4	∑	∑	PUNCT
ejpam-2339	91	5	(	(	PUNCT
ejpam-2339	91	6	a	a	DET
ejpam-2339	91	7	,	,	PUNCT
ejpam-2339	91	8	b)∈a1	b)∈a1	NOUN
ejpam-2339	91	9	kakb	kakb	NOUN
ejpam-2339	91	10	=	=	NOUN
ejpam-2339	91	11	u2	u2	PROPN
ejpam-2339	91	12	.	.	PUNCT
ejpam-2339	92	1	(	(	PUNCT
ejpam-2339	92	2	2	2	X
ejpam-2339	92	3	)	)	PUNCT
ejpam-2339	92	4	now	now	ADV
ejpam-2339	92	5	in	in	ADP
ejpam-2339	92	6	next	next	ADJ
ejpam-2339	92	7	step	step	NOUN
ejpam-2339	92	8	,	,	PUNCT
ejpam-2339	92	9	let	let	VERB
ejpam-2339	92	10	’s	’s	PRON
ejpam-2339	92	11	take	take	VERB
ejpam-2339	92	12	|f(ǫ2)|	|f(ǫ2)|	PRON
ejpam-2339	92	13	.	.	PUNCT
ejpam-2339	93	1	after	after	ADP
ejpam-2339	93	2	expanding	expand	VERB
ejpam-2339	93	3	we	we	PRON
ejpam-2339	93	4	get	get	VERB
ejpam-2339	93	5	|f(ǫ2)|2	|f(ǫ2)|2	PROPN
ejpam-2339	93	6	=	=	PUNCT
ejpam-2339	93	7	∑	∑	PUNCT
ejpam-2339	93	8	i	i	PROPN
ejpam-2339	93	9	,	,	PUNCT
ejpam-2339	93	10	j∈a0	j∈a0	PROPN
ejpam-2339	93	11	kik	kik	PROPN
ejpam-2339	93	12	jǫ	jǫ	VERB
ejpam-2339	93	13	2(i−	2(i−	PROPN
ejpam-2339	93	14	j	j	PROPN
ejpam-2339	93	15	)	)	PUNCT
ejpam-2339	94	1	=	=	SYM
ejpam-2339	94	2	u2	u2	PROPN
ejpam-2339	94	3	.	.	PROPN
ejpam-2339	94	4	comparing	compare	VERB
ejpam-2339	94	5	coefficients	coefficient	NOUN
ejpam-2339	94	6	next	next	ADV
ejpam-2339	94	7	to	to	ADP
ejpam-2339	94	8	1	1	NUM
ejpam-2339	94	9	gives	give	VERB
ejpam-2339	94	10	∑	∑	PROPN
ejpam-2339	94	11	ǫ2(i−	ǫ2(i−	PROPN
ejpam-2339	94	12	j)=1	j)=1	PROPN
ejpam-2339	94	13	kik	kik	PROPN
ejpam-2339	95	1	jǫ	jǫ	VERB
ejpam-2339	95	2	2(i−	2(i−	PROPN
ejpam-2339	95	3	j	j	PROPN
ejpam-2339	95	4	)	)	PUNCT
ejpam-2339	95	5	−	−	PROPN
ejpam-2339	96	1	∑	∑	NOUN
ejpam-2339	96	2	ǫ2(i−	ǫ2(i−	NUM
ejpam-2339	96	3	j)=−1	j)=−1	NUM
ejpam-2339	96	4	kik	kik	PROPN
ejpam-2339	96	5	jǫ	jǫ	VERB
ejpam-2339	96	6	2(i−	2(i−	PROPN
ejpam-2339	96	7	j	j	PROPN
ejpam-2339	96	8	)	)	PUNCT
ejpam-2339	97	1	=	=	SYM
ejpam-2339	97	2	u2	u2	PROPN
ejpam-2339	97	3	.	.	PUNCT
ejpam-2339	98	1	(	(	PUNCT
ejpam-2339	98	2	3	3	X
ejpam-2339	98	3	)	)	PUNCT
ejpam-2339	98	4	if	if	SCONJ
ejpam-2339	98	5	ǫ2(i−	ǫ2(i−	NUM
ejpam-2339	98	6	j	j	NOUN
ejpam-2339	98	7	)	)	PUNCT
ejpam-2339	98	8	=	=	SYM
ejpam-2339	98	9	1	1	NUM
ejpam-2339	98	10	,	,	PUNCT
ejpam-2339	98	11	then	then	ADV
ejpam-2339	98	12	ǫi−	ǫi−	NUM
ejpam-2339	98	13	j	j	NOUN
ejpam-2339	98	14	=	=	SYM
ejpam-2339	98	15	1	1	NUM
ejpam-2339	98	16	or	or	CCONJ
ejpam-2339	98	17	ǫi−	ǫi−	NUM
ejpam-2339	98	18	j	j	NOUN
ejpam-2339	98	19	=	=	SYM
ejpam-2339	98	20	−1	−1	NOUN
ejpam-2339	98	21	.	.	PUNCT
ejpam-2339	99	1	hence	hence	ADV
ejpam-2339	99	2	∑	∑	NOUN
ejpam-2339	99	3	ǫ2(i−	ǫ2(i−	PROPN
ejpam-2339	99	4	j)=1	j)=1	PROPN
ejpam-2339	99	5	kik	kik	PROPN
ejpam-2339	99	6	jǫ	jǫ	VERB
ejpam-2339	99	7	2(i−	2(i−	PROPN
ejpam-2339	99	8	j	j	NOUN
ejpam-2339	99	9	)	)	PUNCT
ejpam-2339	100	1	=	=	PUNCT
ejpam-2339	100	2	∑	∑	PUNCT
ejpam-2339	100	3	i∈a0	i∈a0	PROPN
ejpam-2339	100	4	k2	k2	PROPN
ejpam-2339	100	5	i	i	PROPN
ejpam-2339	100	6	+	+	CCONJ
ejpam-2339	100	7	2	2	NUM
ejpam-2339	100	8	∑	∑	PUNCT
ejpam-2339	100	9	(	(	PUNCT
ejpam-2339	100	10	a	a	DET
ejpam-2339	100	11	,	,	PUNCT
ejpam-2339	100	12	b)∈a1	b)∈a1	NOUN
ejpam-2339	100	13	kakb	kakb	NOUN
ejpam-2339	100	14	.	.	PUNCT
ejpam-2339	101	1	(	(	PUNCT
ejpam-2339	101	2	4	4	NUM
ejpam-2339	101	3	)	)	PUNCT
ejpam-2339	101	4	on	on	ADP
ejpam-2339	101	5	the	the	DET
ejpam-2339	101	6	other	other	ADJ
ejpam-2339	101	7	hand	hand	NOUN
ejpam-2339	101	8	,	,	PUNCT
ejpam-2339	101	9	if	if	SCONJ
ejpam-2339	101	10	ǫ2(i−	ǫ2(i−	NUM
ejpam-2339	101	11	j	j	NOUN
ejpam-2339	101	12	)	)	PUNCT
ejpam-2339	101	13	=	=	SYM
ejpam-2339	101	14	−1	−1	NOUN
ejpam-2339	101	15	,	,	PUNCT
ejpam-2339	101	16	then	then	ADV
ejpam-2339	101	17	2(i−	2(i−	NUM
ejpam-2339	101	18	j)≡	j)≡	NOUN
ejpam-2339	101	19	2t−1(mod	2t−1(mod	NUM
ejpam-2339	101	20	2	2	NUM
ejpam-2339	101	21	t	t	NOUN
ejpam-2339	101	22	)	)	PUNCT
ejpam-2339	101	23	and	and	CCONJ
ejpam-2339	101	24	2	2	NUM
ejpam-2339	101	25	(	(	PUNCT
ejpam-2339	101	26	j−	j−	PROPN
ejpam-2339	101	27	i)≡	i)≡	PROPN
ejpam-2339	101	28	2t−1(mod	2t−1(mod	NUM
ejpam-2339	101	29	2	2	NUM
ejpam-2339	101	30	t	t	NOUN
ejpam-2339	101	31	)	)	PUNCT
ejpam-2339	101	32	.	.	PUNCT
ejpam-2339	102	1	thus	thus	ADV
ejpam-2339	102	2	∑	∑	NUM
ejpam-2339	102	3	ǫ2(i−	ǫ2(i−	NUM
ejpam-2339	102	4	j)=−1	j)=−1	NUM
ejpam-2339	102	5	kik	kik	PROPN
ejpam-2339	102	6	jǫ	jǫ	VERB
ejpam-2339	102	7	2(i−	2(i−	PROPN
ejpam-2339	102	8	j	j	NOUN
ejpam-2339	102	9	)	)	PUNCT
ejpam-2339	103	1	=	=	SYM
ejpam-2339	103	2	2	2	NUM
ejpam-2339	103	3	∑	∑	PUNCT
ejpam-2339	103	4	(	(	PUNCT
ejpam-2339	103	5	a	a	PRON
ejpam-2339	103	6	,	,	PUNCT
ejpam-2339	103	7	b)∈a2	b)∈a2	NOUN
ejpam-2339	103	8	kakb	kakb	NOUN
ejpam-2339	103	9	where	where	SCONJ
ejpam-2339	103	10	a2	a2	PROPN
ejpam-2339	103	11	=	=	PRON
ejpam-2339	103	12	{	{	PUNCT
ejpam-2339	103	13	(	(	PUNCT
ejpam-2339	103	14	a	a	PRON
ejpam-2339	103	15	,	,	PUNCT
ejpam-2339	103	16	b	b	NOUN
ejpam-2339	103	17	)	)	PUNCT
ejpam-2339	103	18	∈	∈	PROPN
ejpam-2339	103	19	a2	a2	PROPN
ejpam-2339	103	20	0	0	PUNCT
ejpam-2339	104	1	|	|	ADV
ejpam-2339	104	2	a	a	DET
ejpam-2339	104	3	<	<	X
ejpam-2339	104	4	b	b	PROPN
ejpam-2339	104	5	,	,	PUNCT
ejpam-2339	104	6	2(a−	2(a−	PROPN
ejpam-2339	104	7	b)≡	b)≡	VERB
ejpam-2339	104	8	2t−1(mod	2t−1(mod	NOUN
ejpam-2339	104	9	2	2	NUM
ejpam-2339	104	10	t	t	NOUN
ejpam-2339	104	11	)	)	PUNCT
ejpam-2339	104	12	}	}	PUNCT
ejpam-2339	104	13	.	.	PUNCT
ejpam-2339	105	1	if	if	SCONJ
ejpam-2339	105	2	we	we	PRON
ejpam-2339	105	3	continue	continue	VERB
ejpam-2339	105	4	in	in	ADP
ejpam-2339	105	5	similar	similar	ADJ
ejpam-2339	105	6	manner	manner	NOUN
ejpam-2339	105	7	,	,	PUNCT
ejpam-2339	105	8	for	for	ADP
ejpam-2339	105	9	every	every	DET
ejpam-2339	105	10	nontrivial	nontrivial	NOUN
ejpam-2339	105	11	f(ǫ2s	f(ǫ2	NOUN
ejpam-2339	105	12	)	)	PUNCT
ejpam-2339	105	13	we	we	PRON
ejpam-2339	105	14	get	get	VERB
ejpam-2339	105	15	∑	∑	ADV
ejpam-2339	105	16	i∈a0	i∈a0	ADJ
ejpam-2339	105	17	k2	k2	X
ejpam-2339	105	18	i	i	PROPN
ejpam-2339	106	1	+	+	CCONJ
ejpam-2339	106	2	2	2	NUM
ejpam-2339	106	3	s	s	PART
ejpam-2339	106	4	∑	∑	PROPN
ejpam-2339	106	5	j=1	j=1	NOUN
ejpam-2339	106	6	∑	∑	PROPN
ejpam-2339	106	7	(	(	PUNCT
ejpam-2339	106	8	a	a	PRON
ejpam-2339	106	9	,	,	PUNCT
ejpam-2339	106	10	b)∈a	b)∈a	SYM
ejpam-2339	106	11	j	j	PROPN
ejpam-2339	106	12	kakb	kakb	PROPN
ejpam-2339	106	13	−	−	PROPN
ejpam-2339	106	14	2	2	NUM
ejpam-2339	106	15	∑	∑	PUNCT
ejpam-2339	106	16	(	(	PUNCT
ejpam-2339	106	17	a	a	PRON
ejpam-2339	106	18	,	,	PUNCT
ejpam-2339	106	19	b)∈as+1	b)∈as+1	PROPN
ejpam-2339	106	20	kakb	kakb	PROPN
ejpam-2339	106	21	=	=	PROPN
ejpam-2339	106	22	u2	u2	PROPN
ejpam-2339	106	23	.	.	PUNCT
ejpam-2339	107	1	(	(	PUNCT
ejpam-2339	107	2	5	5	X
ejpam-2339	107	3	)	)	PUNCT
ejpam-2339	107	4	there	there	PRON
ejpam-2339	107	5	is	be	VERB
ejpam-2339	107	6	also	also	ADV
ejpam-2339	107	7	one	one	NUM
ejpam-2339	107	8	simple	simple	ADJ
ejpam-2339	107	9	question	question	NOUN
ejpam-2339	107	10	that	that	PRON
ejpam-2339	107	11	should	should	AUX
ejpam-2339	107	12	be	be	AUX
ejpam-2339	107	13	covered	cover	VERB
ejpam-2339	107	14	.	.	PUNCT
ejpam-2339	108	1	sometimes	sometimes	ADV
ejpam-2339	108	2	,	,	PUNCT
ejpam-2339	108	3	we	we	PRON
ejpam-2339	108	4	need	need	VERB
ejpam-2339	108	5	to	to	PART
ejpam-2339	108	6	know	know	VERB
ejpam-2339	108	7	how	how	SCONJ
ejpam-2339	108	8	many	many	ADJ
ejpam-2339	108	9	different	different	ADJ
ejpam-2339	108	10	powers	power	NOUN
ejpam-2339	108	11	we	we	PRON
ejpam-2339	108	12	have	have	VERB
ejpam-2339	108	13	such	such	ADJ
ejpam-2339	108	14	that	that	SCONJ
ejpam-2339	108	15	ǫ2s(i−	ǫ2s(i−	NUM
ejpam-2339	108	16	j	j	NOUN
ejpam-2339	108	17	)	)	PUNCT
ejpam-2339	108	18	is	be	AUX
ejpam-2339	108	19	an	an	DET
ejpam-2339	108	20	involution	involution	NOUN
ejpam-2339	108	21	.	.	PUNCT
ejpam-2339	109	1	next	next	ADJ
ejpam-2339	109	2	lemma	lemma	PROPN
ejpam-2339	109	3	gives	give	VERB
ejpam-2339	109	4	the	the	DET
ejpam-2339	109	5	answer	answer	NOUN
ejpam-2339	109	6	.	.	PUNCT
ejpam-2339	110	1	lemma	lemma	PROPN
ejpam-2339	110	2	1	1	X
ejpam-2339	110	3	.	.	PUNCT
ejpam-2339	111	1	let	let	VERB
ejpam-2339	111	2	(	(	PUNCT
ejpam-2339	111	3	i	i	NOUN
ejpam-2339	111	4	,	,	PUNCT
ejpam-2339	111	5	j	j	PROPN
ejpam-2339	111	6	)	)	PUNCT
ejpam-2339	111	7	∈	∈	PROPN
ejpam-2339	111	8	a2	a2	PROPN
ejpam-2339	111	9	0	0	NUM
ejpam-2339	111	10	,	,	PUNCT
ejpam-2339	111	11	where	where	SCONJ
ejpam-2339	111	12	i	i	PRON
ejpam-2339	111	13	<	<	X
ejpam-2339	111	14	j	j	PROPN
ejpam-2339	111	15	and	and	CCONJ
ejpam-2339	111	16	a0	a0	PROPN
ejpam-2339	111	17	=	=	PUNCT
ejpam-2339	112	1	[	[	X
ejpam-2339	112	2	2	2	NUM
ejpam-2339	112	3	t	t	NOUN
ejpam-2339	112	4	−	−	PROPN
ejpam-2339	112	5	1]0	1]0	PROPN
ejpam-2339	112	6	.	.	PUNCT
ejpam-2339	113	1	then	then	ADV
ejpam-2339	113	2	there	there	PRON
ejpam-2339	113	3	is	be	VERB
ejpam-2339	113	4	unique	unique	ADJ
ejpam-2339	113	5	s	s	X
ejpam-2339	113	6	∈	∈	X
ejpam-2339	113	7	{	{	PUNCT
ejpam-2339	113	8	1,2	1,2	NUM
ejpam-2339	113	9	,	,	PUNCT
ejpam-2339	113	10	.	.	PUNCT
ejpam-2339	113	11	.	.	PUNCT
ejpam-2339	114	1	.	.	PUNCT
ejpam-2339	115	1	,	,	PUNCT
ejpam-2339	115	2	t	t	X
ejpam-2339	115	3	}	}	PUNCT
ejpam-2339	115	4	such	such	ADJ
ejpam-2339	115	5	that	that	SCONJ
ejpam-2339	115	6	2s−1(i	2s−1(i	NUM
ejpam-2339	115	7	−	−	PROPN
ejpam-2339	115	8	j)≡	j)≡	NOUN
ejpam-2339	115	9	2t−1(mod	2t−1(mod	NUM
ejpam-2339	115	10	2	2	NUM
ejpam-2339	115	11	t	t	NOUN
ejpam-2339	115	12	)	)	PUNCT
ejpam-2339	115	13	.	.	PUNCT
ejpam-2339	116	1	proof	proof	NOUN
ejpam-2339	116	2	.	.	PUNCT
ejpam-2339	117	1	take	take	VERB
ejpam-2339	117	2	s1	s1	PROPN
ejpam-2339	117	3	6=	6=	NUM
ejpam-2339	117	4	s2	s2	PROPN
ejpam-2339	117	5	from	from	ADP
ejpam-2339	117	6	set	set	NOUN
ejpam-2339	117	7	[	[	X
ejpam-2339	117	8	t	t	X
ejpam-2339	117	9	]	]	PUNCT
ejpam-2339	117	10	.	.	PUNCT
ejpam-2339	118	1	let	let	VERB
ejpam-2339	118	2	as	as	SCONJ
ejpam-2339	118	3	assume	assume	VERB
ejpam-2339	118	4	that	that	SCONJ
ejpam-2339	118	5	2s1−1(i	2s1−1(i	NUM
ejpam-2339	118	6	−	−	PROPN
ejpam-2339	118	7	j	j	PROPN
ejpam-2339	118	8	)	)	PUNCT
ejpam-2339	118	9	≡	≡	PROPN
ejpam-2339	118	10	2t−1(mod	2t−1(mod	ADJ
ejpam-2339	118	11	2	2	NUM
ejpam-2339	118	12	t	t	NOUN
ejpam-2339	118	13	)	)	PUNCT
ejpam-2339	118	14	and	and	CCONJ
ejpam-2339	118	15	2s2−1(i	2s2−1(i	PROPN
ejpam-2339	118	16	−	−	PROPN
ejpam-2339	118	17	j	j	PROPN
ejpam-2339	118	18	)	)	PUNCT
ejpam-2339	118	19	≡	≡	PROPN
ejpam-2339	119	1	2t−1(mod	2t−1(mod	ADJ
ejpam-2339	119	2	2	2	NUM
ejpam-2339	119	3	t	t	NOUN
ejpam-2339	119	4	)	)	PUNCT
ejpam-2339	119	5	.	.	PUNCT
ejpam-2339	120	1	then	then	ADV
ejpam-2339	120	2	,	,	PUNCT
ejpam-2339	120	3	there	there	PRON
ejpam-2339	120	4	are	be	VERB
ejpam-2339	120	5	k1	k1	NOUN
ejpam-2339	120	6	,	,	PUNCT
ejpam-2339	120	7	k2	k2	PROPN
ejpam-2339	120	8	∈	∈	PROPN
ejpam-2339	120	9	z	z	NOUN
ejpam-2339	120	10	such	such	ADJ
ejpam-2339	120	11	that	that	DET
ejpam-2339	120	12	2s1−1(i	2s1−1(i	NUM
ejpam-2339	120	13	−	−	PROPN
ejpam-2339	120	14	j	j	NOUN
ejpam-2339	120	15	)	)	PUNCT
ejpam-2339	120	16	=	=	SYM
ejpam-2339	121	1	2t−1	2t−1	NUM
ejpam-2339	122	1	+	+	CCONJ
ejpam-2339	122	2	k1	k1	NOUN
ejpam-2339	122	3	·	·	PUNCT
ejpam-2339	122	4	2	2	NUM
ejpam-2339	122	5	t	t	NOUN
ejpam-2339	122	6	and	and	CCONJ
ejpam-2339	122	7	2s2−1(i	2s2−1(i	PROPN
ejpam-2339	122	8	−	−	PROPN
ejpam-2339	122	9	j	j	PROPN
ejpam-2339	122	10	)	)	PUNCT
ejpam-2339	122	11	=	=	SYM
ejpam-2339	123	1	2t−1	2t−1	NUM
ejpam-2339	124	1	+	+	CCONJ
ejpam-2339	124	2	k2	k2	X
ejpam-2339	124	3	·	·	PUNCT
ejpam-2339	124	4	2	2	NUM
ejpam-2339	124	5	t	t	NOUN
ejpam-2339	124	6	.	.	PUNCT
ejpam-2339	125	1	we	we	PRON
ejpam-2339	125	2	may	may	AUX
ejpam-2339	125	3	assume	assume	VERB
ejpam-2339	125	4	that	that	SCONJ
ejpam-2339	125	5	s1	s1	PROPN
ejpam-2339	125	6	>	>	X
ejpam-2339	125	7	s2	s2	PROPN
ejpam-2339	125	8	,	,	PUNCT
ejpam-2339	125	9	thus	thus	ADV
ejpam-2339	125	10	�	�	PROPN
ejpam-2339	125	11	2s1−s2	2s1−s2	NUM
ejpam-2339	125	12	−	−	NOUN
ejpam-2339	125	13	1	1	NUM
ejpam-2339	125	14	�	�	PROPN
ejpam-2339	126	1	2s2−1(i	2s2−1(i	PROPN
ejpam-2339	126	2	−	−	PROPN
ejpam-2339	126	3	j	j	PROPN
ejpam-2339	126	4	)	)	PUNCT
ejpam-2339	126	5	=	=	SYM
ejpam-2339	127	1	(	(	PUNCT
ejpam-2339	127	2	k1	k1	NOUN
ejpam-2339	127	3	−	−	PROPN
ejpam-2339	127	4	k2)2	k2)2	PROPN
ejpam-2339	127	5	t	t	PROPN
ejpam-2339	127	6	.	.	PUNCT
ejpam-2339	128	1	now	now	ADV
ejpam-2339	128	2	we	we	PRON
ejpam-2339	128	3	get	get	VERB
ejpam-2339	128	4	(	(	PUNCT
ejpam-2339	128	5	i−	i−	PROPN
ejpam-2339	128	6	j)≡	j)≡	PROPN
ejpam-2339	128	7	0(mod	0(mod	PROPN
ejpam-2339	128	8	2t+1−s2	2t+1−s2	NOUN
ejpam-2339	128	9	)	)	PUNCT
ejpam-2339	128	10	,	,	PUNCT
ejpam-2339	128	11	hence	hence	ADV
ejpam-2339	128	12	2s2−1(i−	2s2−1(i−	NUM
ejpam-2339	128	13	j)≡	j)≡	NOUN
ejpam-2339	128	14	0(mod	0(mod	NOUN
ejpam-2339	128	15	2	2	NUM
ejpam-2339	128	16	t	t	NOUN
ejpam-2339	128	17	)	)	PUNCT
ejpam-2339	128	18	.	.	PUNCT
ejpam-2339	129	1	but	but	CCONJ
ejpam-2339	129	2	,	,	PUNCT
ejpam-2339	129	3	using	use	VERB
ejpam-2339	129	4	first	first	ADJ
ejpam-2339	129	5	assumption	assumption	NOUN
ejpam-2339	129	6	we	we	PRON
ejpam-2339	129	7	would	would	AUX
ejpam-2339	129	8	have	have	VERB
ejpam-2339	129	9	2t−1	2t−1	NUM
ejpam-2339	129	10	≡	≡	PROPN
ejpam-2339	129	11	0(mod	0(mod	NOUN
ejpam-2339	129	12	2t+1−s2	2t+1−s2	NOUN
ejpam-2339	129	13	)	)	PUNCT
ejpam-2339	129	14	,	,	PUNCT
ejpam-2339	129	15	which	which	PRON
ejpam-2339	129	16	is	be	AUX
ejpam-2339	129	17	obvious	obvious	ADJ
ejpam-2339	129	18	contradiction	contradiction	NOUN
ejpam-2339	129	19	.	.	PUNCT
ejpam-2339	130	1	therefore	therefore	ADV
ejpam-2339	130	2	k1	k1	PROPN
ejpam-2339	130	3	=	=	SYM
ejpam-2339	130	4	k2	k2	PROPN
ejpam-2339	130	5	,	,	PUNCT
ejpam-2339	130	6	but	but	CCONJ
ejpam-2339	130	7	then	then	ADV
ejpam-2339	130	8	we	we	PRON
ejpam-2339	130	9	get	get	VERB
ejpam-2339	130	10	s1	s1	PROPN
ejpam-2339	130	11	=	=	SYM
ejpam-2339	130	12	s2	s2	PROPN
ejpam-2339	130	13	,	,	PUNCT
ejpam-2339	130	14	again	again	ADV
ejpam-2339	130	15	contradiction	contradiction	NOUN
ejpam-2339	130	16	.	.	PUNCT
ejpam-2339	131	1	thereby	thereby	ADV
ejpam-2339	131	2	,	,	PUNCT
ejpam-2339	131	3	we	we	PRON
ejpam-2339	131	4	have	have	AUX
ejpam-2339	131	5	proved	prove	VERB
ejpam-2339	131	6	the	the	DET
ejpam-2339	131	7	assertion	assertion	NOUN
ejpam-2339	131	8	.	.	PUNCT
ejpam-2339	132	1	next	next	ADJ
ejpam-2339	132	2	assertion	assertion	NOUN
ejpam-2339	132	3	rise	rise	VERB
ejpam-2339	132	4	from	from	ADP
ejpam-2339	132	5	norm	norm	NOUN
ejpam-2339	132	6	invariance	invariance	NOUN
ejpam-2339	132	7	analysis	analysis	NOUN
ejpam-2339	132	8	.	.	PUNCT
ejpam-2339	133	1	k.tabak	k.tabak	ADJ
ejpam-2339	133	2	/	/	SYM
ejpam-2339	133	3	eur	eur	PROPN
ejpam-2339	133	4	.	.	PUNCT
ejpam-2339	134	1	j.	j.	PROPN
ejpam-2339	134	2	pure	pure	PROPN
ejpam-2339	134	3	appl	appl	PROPN
ejpam-2339	134	4	.	.	PROPN
ejpam-2339	134	5	math	math	PROPN
ejpam-2339	134	6	,	,	PUNCT
ejpam-2339	134	7	8	8	NUM
ejpam-2339	134	8	(	(	PUNCT
ejpam-2339	134	9	2015	2015	NUM
ejpam-2339	134	10	)	)	PUNCT
ejpam-2339	134	11	,	,	PUNCT
ejpam-2339	134	12	450	450	NUM
ejpam-2339	134	13	-	-	SYM
ejpam-2339	134	14	457	457	NUM
ejpam-2339	134	15	453	453	NUM
ejpam-2339	134	16	lemma	lemma	PROPN
ejpam-2339	134	17	2	2	NUM
ejpam-2339	134	18	.	.	PUNCT
ejpam-2339	134	19	let	let	VERB
ejpam-2339	134	20	ω0	ω0	NOUN
ejpam-2339	134	21	,	,	PUNCT
ejpam-2339	134	22	.	.	PUNCT
ejpam-2339	134	23	.	.	PUNCT
ejpam-2339	135	1	.	.	PUNCT
ejpam-2339	136	1	,	,	PUNCT
ejpam-2339	136	2	ωt	ωt	PROPN
ejpam-2339	136	3	∈	∈	PROPN
ejpam-2339	136	4	n0	n0	NOUN
ejpam-2339	136	5	such	such	ADJ
ejpam-2339	136	6	that	that	SCONJ
ejpam-2339	136	7	where	where	SCONJ
ejpam-2339	136	8	t	t	PROPN
ejpam-2339	136	9	∈	∈	PROPN
ejpam-2339	136	10	n	n	CCONJ
ejpam-2339	136	11	(	(	PUNCT
ejpam-2339	136	12	i	i	NOUN
ejpam-2339	136	13	)	)	PUNCT
ejpam-2339	136	14	ω0	ω0	ADV
ejpam-2339	136	15	+	+	CCONJ
ejpam-2339	136	16	2	2	NUM
ejpam-2339	136	17	∑s	∑s	NOUN
ejpam-2339	136	18	i=1ωi	i=1ωi	PRON
ejpam-2339	136	19	−	−	PROPN
ejpam-2339	136	20	2ωs+1	2ωs+1	ADJ
ejpam-2339	136	21	=	=	SYM
ejpam-2339	136	22	u2	u2	PROPN
ejpam-2339	136	23	,	,	PUNCT
ejpam-2339	136	24	s	s	PART
ejpam-2339	136	25	∈	∈	PROPN
ejpam-2339	137	1	[	[	X
ejpam-2339	137	2	t	t	X
ejpam-2339	137	3	−	−	NUM
ejpam-2339	137	4	1	1	NUM
ejpam-2339	137	5	]	]	PUNCT
ejpam-2339	137	6	,	,	PUNCT
ejpam-2339	137	7	(	(	PUNCT
ejpam-2339	137	8	ii	ii	NOUN
ejpam-2339	137	9	)	)	PUNCT
ejpam-2339	137	10	ω0	ω0	PROPN
ejpam-2339	137	11	+	+	CCONJ
ejpam-2339	137	12	2	2	NUM
ejpam-2339	137	13	∑t	∑t	NOUN
ejpam-2339	137	14	i=1ωi	i=1ωi	NOUN
ejpam-2339	137	15	=	=	PUNCT
ejpam-2339	137	16	(	(	PUNCT
ejpam-2339	137	17	2u2	2u2	NUM
ejpam-2339	137	18	−	−	NOUN
ejpam-2339	137	19	u)2	u)2	ADJ
ejpam-2339	137	20	,	,	PUNCT
ejpam-2339	137	21	if	if	SCONJ
ejpam-2339	137	22	u1	u1	NOUN
ejpam-2339	137	23	is	be	AUX
ejpam-2339	137	24	maximal	maximal	ADJ
ejpam-2339	137	25	odd	odd	ADJ
ejpam-2339	137	26	divisor	divisor	NOUN
ejpam-2339	137	27	of	of	ADP
ejpam-2339	137	28	u	u	NOUN
ejpam-2339	137	29	,	,	PUNCT
ejpam-2339	137	30	then	then	ADV
ejpam-2339	137	31	ωi	ωi	PROPN
ejpam-2339	137	32	≡	≡	PROPN
ejpam-2339	137	33	0(mod	0(mod	X
ejpam-2339	137	34	u2	u2	PROPN
ejpam-2339	137	35	1	1	NUM
ejpam-2339	137	36	)	)	PUNCT
ejpam-2339	137	37	for	for	ADP
ejpam-2339	137	38	every	every	DET
ejpam-2339	137	39	i	i	NOUN
ejpam-2339	137	40	∈	∈	PROPN
ejpam-2339	138	1	[	[	X
ejpam-2339	138	2	t]0	t]0	NOUN
ejpam-2339	138	3	.	.	PUNCT
ejpam-2339	139	1	additionally	additionally	ADV
ejpam-2339	139	2	:	:	PUNCT
ejpam-2339	139	3	if	if	SCONJ
ejpam-2339	139	4	u	u	PROPN
ejpam-2339	139	5	∈	∈	PROPN
ejpam-2339	139	6	n	n	VERB
ejpam-2339	139	7	is	be	AUX
ejpam-2339	139	8	odd	odd	ADJ
ejpam-2339	139	9	,	,	PUNCT
ejpam-2339	139	10	then	then	ADV
ejpam-2339	139	11	ωi	ωi	PROPN
ejpam-2339	139	12	≡	≡	PROPN
ejpam-2339	139	13	0(mod	0(mod	X
ejpam-2339	139	14	u2	u2	PROPN
ejpam-2339	139	15	)	)	PUNCT
ejpam-2339	139	16	for	for	ADP
ejpam-2339	139	17	every	every	DET
ejpam-2339	139	18	i	i	NOUN
ejpam-2339	139	19	∈	∈	PROPN
ejpam-2339	140	1	[	[	X
ejpam-2339	140	2	t]0	t]0	NOUN
ejpam-2339	140	3	,	,	PUNCT
ejpam-2339	140	4	and	and	CCONJ
ejpam-2339	140	5	also	also	ADV
ejpam-2339	140	6	there	there	PRON
ejpam-2339	140	7	is	be	VERB
ejpam-2339	140	8	some	some	DET
ejpam-2339	140	9	integer	integer	NOUN
ejpam-2339	140	10	k	k	PROPN
ejpam-2339	140	11	such	such	ADJ
ejpam-2339	140	12	that	that	PRON
ejpam-2339	140	13	u=	u=	ADJ
ejpam-2339	140	14	1	1	NUM
ejpam-2339	140	15	+	+	NUM
ejpam-2339	140	16	2t−1k	2t−1k	NOUN
ejpam-2339	140	17	.	.	PUNCT
ejpam-2339	141	1	proof	proof	NOUN
ejpam-2339	141	2	.	.	PUNCT
ejpam-2339	142	1	solving	solve	VERB
ejpam-2339	142	2	system	system	NOUN
ejpam-2339	142	3	of	of	ADP
ejpam-2339	142	4	linear	linear	ADJ
ejpam-2339	142	5	equations	equation	NOUN
ejpam-2339	142	6	we	we	PRON
ejpam-2339	142	7	get	get	VERB
ejpam-2339	142	8	ωi	ωi	X
ejpam-2339	142	9	=	=	SYM
ejpam-2339	142	10	2i−2(ω0	2i−2(ω0	NUM
ejpam-2339	142	11	−	−	PROPN
ejpam-2339	142	12	u2	u2	PROPN
ejpam-2339	142	13	)	)	PUNCT
ejpam-2339	142	14	,	,	PUNCT
ejpam-2339	142	15	i	i	PRON
ejpam-2339	142	16	∈	∈	PROPN
ejpam-2339	143	1	[	[	X
ejpam-2339	143	2	t	t	X
ejpam-2339	143	3	]	]	PUNCT
ejpam-2339	143	4	.	.	PUNCT
ejpam-2339	144	1	now	now	ADV
ejpam-2339	144	2	,	,	PUNCT
ejpam-2339	144	3	using	use	VERB
ejpam-2339	144	4	this	this	PRON
ejpam-2339	144	5	and	and	CCONJ
ejpam-2339	144	6	second	second	ADJ
ejpam-2339	144	7	assumption	assumption	NOUN
ejpam-2339	144	8	in	in	ADP
ejpam-2339	144	9	our	our	PRON
ejpam-2339	144	10	statement	statement	NOUN
ejpam-2339	144	11	,	,	PUNCT
ejpam-2339	144	12	we	we	PRON
ejpam-2339	144	13	get	get	VERB
ejpam-2339	144	14	(	(	PUNCT
ejpam-2339	144	15	2u2−u)2	2u2−u)2	NUM
ejpam-2339	144	16	=	=	SYM
ejpam-2339	144	17	ω0+(ω0−u2)(2t−1	ω0+(ω0−u2)(2t−1	NUM
ejpam-2339	144	18	)	)	PUNCT
ejpam-2339	144	19	,	,	PUNCT
ejpam-2339	144	20	hence	hence	ADV
ejpam-2339	144	21	2t−2(ω0	2t−2(ω0	ADJ
ejpam-2339	144	22	−	−	PROPN
ejpam-2339	144	23	u2	u2	NOUN
ejpam-2339	144	24	)	)	PUNCT
ejpam-2339	144	25	=	=	PUNCT
ejpam-2339	145	1	u3(u−	u3(u−	X
ejpam-2339	145	2	1	1	NUM
ejpam-2339	145	3	)	)	PUNCT
ejpam-2339	145	4	.	.	PUNCT
ejpam-2339	146	1	(	(	PUNCT
ejpam-2339	146	2	6	6	NUM
ejpam-2339	146	3	)	)	PUNCT
ejpam-2339	146	4	firstly	firstly	ADV
ejpam-2339	146	5	,	,	PUNCT
ejpam-2339	146	6	let	let	AUX
ejpam-2339	146	7	assume	assume	VERB
ejpam-2339	146	8	that	that	SCONJ
ejpam-2339	146	9	u	u	PRON
ejpam-2339	146	10	is	be	AUX
ejpam-2339	146	11	odd	odd	ADJ
ejpam-2339	146	12	.	.	PUNCT
ejpam-2339	147	1	therefore	therefore	ADV
ejpam-2339	147	2	u−	u−	PROPN
ejpam-2339	147	3	1	1	NUM
ejpam-2339	147	4	is	be	AUX
ejpam-2339	147	5	divisible	divisible	ADJ
ejpam-2339	147	6	by	by	ADP
ejpam-2339	147	7	2t−2	2t−2	NUM
ejpam-2339	147	8	.	.	PUNCT
ejpam-2339	148	1	so	so	ADV
ejpam-2339	148	2	,	,	PUNCT
ejpam-2339	148	3	there	there	PRON
ejpam-2339	148	4	is	be	VERB
ejpam-2339	148	5	some	some	DET
ejpam-2339	148	6	integer	integer	NOUN
ejpam-2339	148	7	k1	k1	NOUN
ejpam-2339	148	8	such	such	ADJ
ejpam-2339	148	9	that	that	DET
ejpam-2339	148	10	u=	u=	ADJ
ejpam-2339	148	11	1	1	NUM
ejpam-2339	148	12	+	+	NUM
ejpam-2339	148	13	k1	k1	X
ejpam-2339	148	14	·	·	SYM
ejpam-2339	148	15	2	2	NUM
ejpam-2339	148	16	t−2	t−2	PROPN
ejpam-2339	148	17	.	.	PUNCT
ejpam-2339	149	1	therefore	therefore	ADV
ejpam-2339	149	2	,	,	PUNCT
ejpam-2339	149	3	ω0−	ω0−	NUM
ejpam-2339	149	4	u2	u2	NOUN
ejpam-2339	149	5	=	=	PUNCT
ejpam-2339	149	6	k1	k1	PROPN
ejpam-2339	149	7	·	·	PUNCT
ejpam-2339	149	8	u	u	NOUN
ejpam-2339	149	9	3	3	NUM
ejpam-2339	149	10	and	and	CCONJ
ejpam-2339	149	11	ω0	ω0	PROPN
ejpam-2339	149	12	=	=	SYM
ejpam-2339	149	13	u2(1	u2(1	PROPN
ejpam-2339	149	14	+	+	CCONJ
ejpam-2339	149	15	k1	k1	NOUN
ejpam-2339	149	16	·	·	PUNCT
ejpam-2339	149	17	u	u	NOUN
ejpam-2339	149	18	)	)	PUNCT
ejpam-2339	149	19	.	.	PUNCT
ejpam-2339	150	1	this	this	PRON
ejpam-2339	150	2	gives	give	VERB
ejpam-2339	150	3	us	we	PRON
ejpam-2339	150	4	ω0	ω0	PROPN
ejpam-2339	150	5	≡	≡	PROPN
ejpam-2339	150	6	0(mod	0(mod	X
ejpam-2339	150	7	u2	u2	NOUN
ejpam-2339	150	8	)	)	PUNCT
ejpam-2339	150	9	.	.	PUNCT
ejpam-2339	151	1	since	since	SCONJ
ejpam-2339	151	2	ω1	ω1	PROPN
ejpam-2339	151	3	=	=	PROPN
ejpam-2339	151	4	1	1	NUM
ejpam-2339	151	5	2(ω0−u2	2(ω0−u2	NUM
ejpam-2339	151	6	)	)	PUNCT
ejpam-2339	151	7	=	=	SYM
ejpam-2339	151	8	1	1	NUM
ejpam-2339	151	9	2	2	NUM
ejpam-2339	151	10	k1u3	k1u3	NOUN
ejpam-2339	151	11	∈	∈	PROPN
ejpam-2339	151	12	n0	n0	NOUN
ejpam-2339	151	13	and	and	CCONJ
ejpam-2339	151	14	u	u	NOUN
ejpam-2339	151	15	odd	odd	ADJ
ejpam-2339	151	16	,	,	PUNCT
ejpam-2339	151	17	we	we	PRON
ejpam-2339	151	18	get	get	VERB
ejpam-2339	151	19	k1	k1	NOUN
ejpam-2339	151	20	=	=	SYM
ejpam-2339	151	21	2k	2k	NUM
ejpam-2339	151	22	for	for	ADP
ejpam-2339	151	23	some	some	DET
ejpam-2339	151	24	integer	integer	NOUN
ejpam-2339	151	25	k	k	PROPN
ejpam-2339	151	26	.	.	PUNCT
ejpam-2339	152	1	finally	finally	ADV
ejpam-2339	152	2	,	,	PUNCT
ejpam-2339	152	3	u	u	NOUN
ejpam-2339	152	4	=	=	PROPN
ejpam-2339	152	5	1	1	NUM
ejpam-2339	152	6	+	+	CCONJ
ejpam-2339	152	7	k	k	PROPN
ejpam-2339	152	8	·	·	PUNCT
ejpam-2339	152	9	2t−1	2t−1	NUM
ejpam-2339	152	10	and	and	CCONJ
ejpam-2339	152	11	ω1	ω1	PROPN
ejpam-2339	152	12	≡	≡	PROPN
ejpam-2339	152	13	0(mod	0(mod	X
ejpam-2339	152	14	u2	u2	NOUN
ejpam-2339	152	15	)	)	PUNCT
ejpam-2339	152	16	.	.	PUNCT
ejpam-2339	153	1	we	we	PRON
ejpam-2339	153	2	already	already	ADV
ejpam-2339	153	3	proved	prove	VERB
ejpam-2339	153	4	that	that	SCONJ
ejpam-2339	153	5	ωi+1	ωi+1	NUM
ejpam-2339	153	6	=	=	NOUN
ejpam-2339	153	7	2ωi	2ωi	NOUN
ejpam-2339	153	8	,	,	PUNCT
ejpam-2339	153	9	i	i	PRON
ejpam-2339	153	10	≥	≥	VERB
ejpam-2339	153	11	1	1	NUM
ejpam-2339	153	12	.	.	PUNCT
ejpam-2339	154	1	this	this	PRON
ejpam-2339	154	2	gives	give	VERB
ejpam-2339	154	3	us	we	PRON
ejpam-2339	154	4	ωi	ωi	X
ejpam-2339	154	5	≡	≡	PROPN
ejpam-2339	154	6	0(mod	0(mod	X
ejpam-2339	154	7	u2	u2	PROPN
ejpam-2339	154	8	)	)	PUNCT
ejpam-2339	154	9	.	.	PUNCT
ejpam-2339	155	1	now	now	ADV
ejpam-2339	155	2	,	,	PUNCT
ejpam-2339	155	3	if	if	SCONJ
ejpam-2339	155	4	u=	u=	NOUN
ejpam-2339	155	5	2ru1	2ru1	NUM
ejpam-2339	155	6	where	where	SCONJ
ejpam-2339	155	7	u1	u1	NOUN
ejpam-2339	155	8	is	be	AUX
ejpam-2339	155	9	odd	odd	ADJ
ejpam-2339	155	10	,	,	PUNCT
ejpam-2339	155	11	using	use	VERB
ejpam-2339	155	12	(	(	PUNCT
ejpam-2339	155	13	6	6	NUM
ejpam-2339	155	14	)	)	PUNCT
ejpam-2339	155	15	we	we	PRON
ejpam-2339	155	16	getω0	getω0	PUNCT
ejpam-2339	156	1	≡	≡	PROPN
ejpam-2339	156	2	0(mod	0(mod	X
ejpam-2339	156	3	u2	u2	PROPN
ejpam-2339	156	4	1	1	NUM
ejpam-2339	156	5	)	)	PUNCT
ejpam-2339	156	6	,	,	PUNCT
ejpam-2339	156	7	henceω1	henceω1	NOUN
ejpam-2339	156	8	≡	≡	PROPN
ejpam-2339	156	9	0(mod	0(mod	X
ejpam-2339	156	10	u2	u2	PROPN
ejpam-2339	156	11	1	1	NUM
ejpam-2339	156	12	)	)	PUNCT
ejpam-2339	156	13	.	.	PUNCT
ejpam-2339	157	1	therefore	therefore	ADV
ejpam-2339	157	2	,	,	PUNCT
ejpam-2339	157	3	ωi	ωi	PROPN
ejpam-2339	157	4	≡	≡	PROPN
ejpam-2339	157	5	0(mod	0(mod	X
ejpam-2339	157	6	u2	u2	PROPN
ejpam-2339	157	7	1	1	NUM
ejpam-2339	157	8	)	)	PUNCT
ejpam-2339	157	9	,	,	PUNCT
ejpam-2339	157	10	i	i	PRON
ejpam-2339	157	11	∈	∈	PROPN
ejpam-2339	158	1	[	[	X
ejpam-2339	158	2	t	t	X
ejpam-2339	158	3	]	]	PUNCT
ejpam-2339	158	4	.	.	PUNCT
ejpam-2339	159	1	now	now	ADV
ejpam-2339	159	2	,	,	PUNCT
ejpam-2339	159	3	we	we	PRON
ejpam-2339	159	4	are	be	AUX
ejpam-2339	159	5	going	go	VERB
ejpam-2339	159	6	to	to	PART
ejpam-2339	159	7	need	need	VERB
ejpam-2339	159	8	one	one	NUM
ejpam-2339	159	9	classical	classical	ADJ
ejpam-2339	159	10	result	result	NOUN
ejpam-2339	159	11	(	(	PUNCT
ejpam-2339	159	12	for	for	ADP
ejpam-2339	159	13	example	example	NOUN
ejpam-2339	159	14	see	see	VERB
ejpam-2339	159	15	[	[	X
ejpam-2339	159	16	4	4	NUM
ejpam-2339	159	17	]	]	NUM
ejpam-2339	159	18	)	)	PUNCT
ejpam-2339	159	19	.	.	PUNCT
ejpam-2339	160	1	lemma	lemma	PROPN
ejpam-2339	160	2	3	3	X
ejpam-2339	160	3	.	.	PUNCT
ejpam-2339	161	1	let	let	VERB
ejpam-2339	161	2	a	a	PRON
ejpam-2339	161	3	be	be	AUX
ejpam-2339	161	4	an	an	DET
ejpam-2339	161	5	element	element	NOUN
ejpam-2339	161	6	of	of	ADP
ejpam-2339	161	7	the	the	DET
ejpam-2339	161	8	group	group	NOUN
ejpam-2339	161	9	ring	ring	NOUN
ejpam-2339	161	10	z[g	z[g	PROPN
ejpam-2339	161	11	]	]	PUNCT
ejpam-2339	161	12	,	,	PUNCT
ejpam-2339	161	13	where	where	SCONJ
ejpam-2339	161	14	g	g	PROPN
ejpam-2339	161	15	is	be	AUX
ejpam-2339	161	16	an	an	DET
ejpam-2339	161	17	abelian	abelian	ADJ
ejpam-2339	161	18	group	group	NOUN
ejpam-2339	161	19	.	.	PUNCT
ejpam-2339	162	1	let	let	VERB
ejpam-2339	162	2	χ	χ	PRON
ejpam-2339	162	3	be	be	AUX
ejpam-2339	162	4	a	a	DET
ejpam-2339	162	5	character	character	NOUN
ejpam-2339	162	6	of	of	ADP
ejpam-2339	162	7	g	g	NOUN
ejpam-2339	162	8	of	of	ADP
ejpam-2339	162	9	order	order	NOUN
ejpam-2339	162	10	w.	w.	NOUN
ejpam-2339	162	11	let	let	VERB
ejpam-2339	162	12	a	a	DET
ejpam-2339	162	13	prime	prime	NOUN
ejpam-2339	162	14	p	p	NOUN
ejpam-2339	162	15	be	be	AUX
ejpam-2339	162	16	self	self	NOUN
ejpam-2339	162	17	-	-	PUNCT
ejpam-2339	162	18	conjugated	conjugate	VERB
ejpam-2339	162	19	modulo	modulo	PROPN
ejpam-2339	162	20	w	w	PROPN
ejpam-2339	162	21	,	,	PUNCT
ejpam-2339	162	22	i.e.	i.e.	X
ejpam-2339	162	23	p	p	PRON
ejpam-2339	162	24	j	j	PROPN
ejpam-2339	162	25	≡	≡	PROPN
ejpam-2339	162	26	−1(mod	−1(mod	PROPN
ejpam-2339	162	27	w′	w′	NOUN
ejpam-2339	162	28	)	)	PUNCT
ejpam-2339	162	29	for	for	ADP
ejpam-2339	162	30	some	some	DET
ejpam-2339	162	31	j	j	PROPN
ejpam-2339	162	32	∈	∈	PROPN
ejpam-2339	162	33	n	n	CCONJ
ejpam-2339	162	34	where	where	SCONJ
ejpam-2339	162	35	m=	m=	X
ejpam-2339	162	36	paw′	paw′	NOUN
ejpam-2339	162	37	,	,	PUNCT
ejpam-2339	162	38	w′	w′	VERB
ejpam-2339	162	39	not	not	PART
ejpam-2339	162	40	divisible	divisible	ADJ
ejpam-2339	162	41	by	by	ADP
ejpam-2339	162	42	p.	p.	NOUN
ejpam-2339	162	43	if	if	SCONJ
ejpam-2339	162	44	χ(a)χ(a)≡	χ(a)χ(a)≡	PROPN
ejpam-2339	162	45	0(mod	0(mod	X
ejpam-2339	162	46	p2i	p2i	ADJ
ejpam-2339	162	47	)	)	PUNCT
ejpam-2339	162	48	,	,	PUNCT
ejpam-2339	162	49	then	then	ADV
ejpam-2339	162	50	χ(a)≡	χ(a)≡	X
ejpam-2339	162	51	0(mod	0(mod	ADJ
ejpam-2339	162	52	pi	pi	NOUN
ejpam-2339	162	53	)	)	PUNCT
ejpam-2339	162	54	.	.	PUNCT
ejpam-2339	163	1	we	we	PRON
ejpam-2339	163	2	present	present	VERB
ejpam-2339	163	3	helpful	helpful	ADJ
ejpam-2339	163	4	algebraic	algebraic	ADJ
ejpam-2339	163	5	claim	claim	NOUN
ejpam-2339	163	6	that	that	PRON
ejpam-2339	163	7	is	be	AUX
ejpam-2339	163	8	most	most	ADV
ejpam-2339	163	9	critical	critical	ADJ
ejpam-2339	163	10	for	for	ADP
ejpam-2339	163	11	proving	prove	VERB
ejpam-2339	163	12	main	main	ADJ
ejpam-2339	163	13	results	result	NOUN
ejpam-2339	163	14	of	of	ADP
ejpam-2339	163	15	this	this	DET
ejpam-2339	163	16	paper	paper	NOUN
ejpam-2339	163	17	.	.	PUNCT
ejpam-2339	164	1	theorem	theorem	NOUN
ejpam-2339	164	2	5	5	NUM
ejpam-2339	164	3	.	.	PUNCT
ejpam-2339	165	1	let	let	VERB
ejpam-2339	165	2	ǫ	ǫ	PRON
ejpam-2339	165	3	be	be	AUX
ejpam-2339	165	4	a	a	DET
ejpam-2339	165	5	root	root	NOUN
ejpam-2339	165	6	of	of	ADP
ejpam-2339	165	7	unity	unity	NOUN
ejpam-2339	165	8	of	of	ADP
ejpam-2339	165	9	order	order	NOUN
ejpam-2339	165	10	2	2	NUM
ejpam-2339	165	11	t	t	NOUN
ejpam-2339	165	12	.	.	PUNCT
ejpam-2339	166	1	let	let	VERB
ejpam-2339	166	2	f(ǫ	f(ǫ	PROPN
ejpam-2339	166	3	)	)	PUNCT
ejpam-2339	166	4	∈	∈	PROPN
ejpam-2339	166	5	z[ǫ	z[ǫ	PROPN
ejpam-2339	166	6	]	]	PUNCT
ejpam-2339	166	7	with	with	ADP
ejpam-2339	166	8	nonnegative	nonnegative	ADJ
ejpam-2339	166	9	coefficients	coefficient	NOUN
ejpam-2339	166	10	whose	whose	DET
ejpam-2339	166	11	sum	sum	NOUN
ejpam-2339	166	12	is	be	AUX
ejpam-2339	166	13	2u2	2u2	NUM
ejpam-2339	166	14	−	−	PROPN
ejpam-2339	166	15	u	u	NOUN
ejpam-2339	166	16	,	,	PUNCT
ejpam-2339	166	17	for	for	ADP
ejpam-2339	166	18	some	some	DET
ejpam-2339	166	19	u	u	PROPN
ejpam-2339	166	20	∈	∈	PROPN
ejpam-2339	166	21	n.	n.	NOUN
ejpam-2339	166	22	if	if	SCONJ
ejpam-2339	166	23	f(ǫ	f(ǫ	NOUN
ejpam-2339	166	24	)	)	PUNCT
ejpam-2339	166	25	is	be	AUX
ejpam-2339	166	26	norm	norm	NOUN
ejpam-2339	166	27	invariant	invariant	ADJ
ejpam-2339	166	28	of	of	ADP
ejpam-2339	166	29	the	the	DET
ejpam-2339	166	30	norm	norm	NOUN
ejpam-2339	166	31	u	u	NOUN
ejpam-2339	166	32	,	,	PUNCT
ejpam-2339	166	33	then	then	ADV
ejpam-2339	166	34	for	for	ADP
ejpam-2339	166	35	every	every	DET
ejpam-2339	166	36	nontrivial	nontrivial	NOUN
ejpam-2339	166	37	f(ǫ2s	f(ǫ2	NOUN
ejpam-2339	166	38	)	)	PUNCT
ejpam-2339	166	39	there	there	PRON
ejpam-2339	166	40	is	be	VERB
ejpam-2339	166	41	some	some	DET
ejpam-2339	166	42	rs	rs	NOUN
ejpam-2339	166	43	∈	∈	PROPN
ejpam-2339	166	44	z	z	NOUN
ejpam-2339	167	1	such	such	ADJ
ejpam-2339	167	2	that	that	SCONJ
ejpam-2339	167	3	f(ǫ2s	f(ǫ2	NOUN
ejpam-2339	167	4	)	)	PUNCT
ejpam-2339	167	5	=	=	SYM
ejpam-2339	167	6	uǫrs	uǫrs	ADJ
ejpam-2339	167	7	.	.	PUNCT
ejpam-2339	168	1	proof	proof	NOUN
ejpam-2339	168	2	.	.	PUNCT
ejpam-2339	169	1	let	let	VERB
ejpam-2339	169	2	f(ǫ	f(ǫ	NOUN
ejpam-2339	169	3	)	)	PUNCT
ejpam-2339	170	1	=	=	PUNCT
ejpam-2339	170	2	∑	∑	PUNCT
ejpam-2339	170	3	i∈a0	i∈a0	PROPN
ejpam-2339	170	4	kiǫ	kiǫ	PROPN
ejpam-2339	170	5	i	i	PRON
ejpam-2339	170	6	,	,	PUNCT
ejpam-2339	170	7	where	where	SCONJ
ejpam-2339	170	8	a0	a0	NOUN
ejpam-2339	170	9	=	=	PUNCT
ejpam-2339	171	1	[	[	X
ejpam-2339	171	2	2	2	NUM
ejpam-2339	171	3	t	t	NOUN
ejpam-2339	171	4	−	−	PROPN
ejpam-2339	171	5	1]0	1]0	PROPN
ejpam-2339	171	6	.	.	PUNCT
ejpam-2339	171	7	motivated	motivate	VERB
ejpam-2339	171	8	by	by	ADP
ejpam-2339	171	9	previous	previous	ADJ
ejpam-2339	171	10	results	result	NOUN
ejpam-2339	171	11	,	,	PUNCT
ejpam-2339	171	12	we	we	PRON
ejpam-2339	171	13	introduce	introduce	VERB
ejpam-2339	171	14	notation	notation	NOUN
ejpam-2339	171	15	ω0	ω0	NOUN
ejpam-2339	171	16	=	=	PUNCT
ejpam-2339	171	17	∑	∑	PUNCT
ejpam-2339	171	18	i∈a0	i∈a0	PROPN
ejpam-2339	171	19	k2	k2	PROPN
ejpam-2339	171	20	i	i	PRON
ejpam-2339	171	21	,	,	PUNCT
ejpam-2339	171	22	ω	ω	PROPN
ejpam-2339	171	23	j	j	PROPN
ejpam-2339	172	1	=	=	PUNCT
ejpam-2339	172	2	∑	∑	PROPN
ejpam-2339	172	3	(	(	PUNCT
ejpam-2339	172	4	a	a	PRON
ejpam-2339	172	5	,	,	PUNCT
ejpam-2339	172	6	b)∈a	b)∈a	SYM
ejpam-2339	172	7	j	j	PROPN
ejpam-2339	172	8	kakb	kakb	NOUN
ejpam-2339	172	9	,	,	PUNCT
ejpam-2339	172	10	where	where	SCONJ
ejpam-2339	172	11	a	a	DET
ejpam-2339	172	12	j	j	NOUN
ejpam-2339	172	13	=	=	PRON
ejpam-2339	172	14	{	{	PUNCT
ejpam-2339	172	15	(	(	PUNCT
ejpam-2339	172	16	a	a	PRON
ejpam-2339	172	17	,	,	PUNCT
ejpam-2339	172	18	b	b	NOUN
ejpam-2339	172	19	)	)	PUNCT
ejpam-2339	172	20	∈	∈	PROPN
ejpam-2339	172	21	a2	a2	PROPN
ejpam-2339	172	22	0	0	PUNCT
ejpam-2339	173	1	|	|	ADV
ejpam-2339	173	2	a	a	DET
ejpam-2339	173	3	<	<	X
ejpam-2339	173	4	b	b	PROPN
ejpam-2339	173	5	,	,	PUNCT
ejpam-2339	173	6	2	2	NUM
ejpam-2339	173	7	j−1(a−	j−1(a−	X
ejpam-2339	173	8	b)≡	b)≡	NOUN
ejpam-2339	173	9	2t−1(mod	2t−1(mod	ADJ
ejpam-2339	173	10	2	2	NUM
ejpam-2339	173	11	t	t	NOUN
ejpam-2339	173	12	)	)	PUNCT
ejpam-2339	173	13	}	}	PUNCT
ejpam-2339	173	14	.	.	PUNCT
ejpam-2339	174	1	if	if	SCONJ
ejpam-2339	174	2	we	we	PRON
ejpam-2339	174	3	compare	compare	VERB
ejpam-2339	174	4	coefficients	coefficient	NOUN
ejpam-2339	174	5	next	next	ADV
ejpam-2339	174	6	to	to	ADP
ejpam-2339	174	7	1	1	NUM
ejpam-2339	174	8	in	in	ADP
ejpam-2339	174	9	|f(ǫ2s	|f(ǫ2s	ADJ
ejpam-2339	174	10	)	)	PUNCT
ejpam-2339	174	11	|2	|2	NUM
ejpam-2339	175	1	and	and	CCONJ
ejpam-2339	175	2	use	use	VERB
ejpam-2339	175	3	pairwise	pairwise	NOUN
ejpam-2339	175	4	abbreviation	abbreviation	NOUN
ejpam-2339	175	5	theorem	theorem	NOUN
ejpam-2339	175	6	,	,	PUNCT
ejpam-2339	175	7	we	we	PRON
ejpam-2339	175	8	get	get	VERB
ejpam-2339	175	9	ω0	ω0	ADV
ejpam-2339	175	10	+	+	CCONJ
ejpam-2339	175	11	2	2	NUM
ejpam-2339	175	12	∑s	∑s	NOUN
ejpam-2339	175	13	i=1ωi	i=1ωi	PRON
ejpam-2339	176	1	−	−	PROPN
ejpam-2339	176	2	2ωs+1	2ωs+1	NUM
ejpam-2339	176	3	=	=	SYM
ejpam-2339	176	4	u2	u2	PROPN
ejpam-2339	176	5	.	.	PROPN
ejpam-2339	176	6	assumption	assumption	NOUN
ejpam-2339	176	7	from	from	ADP
ejpam-2339	176	8	theorem	theorem	ADJ
ejpam-2339	176	9	claim	claim	NOUN
ejpam-2339	176	10	gives	give	VERB
ejpam-2339	176	11	us	we	PRON
ejpam-2339	176	12	|f(ǫ2	|f(ǫ2	PROPN
ejpam-2339	176	13	t	t	NOUN
ejpam-2339	176	14	)	)	PUNCT
ejpam-2339	176	15	|2	|2	NUM
ejpam-2339	177	1	=	=	SYM
ejpam-2339	177	2	ω0	ω0	NOUN
ejpam-2339	177	3	+	+	SYM
ejpam-2339	177	4	2	2	NUM
ejpam-2339	177	5	∑t	∑t	PROPN
ejpam-2339	177	6	i=1ωt	i=1ωt	NOUN
ejpam-2339	177	7	.	.	PUNCT
ejpam-2339	178	1	therefore	therefore	ADV
ejpam-2339	178	2	,	,	PUNCT
ejpam-2339	178	3	we	we	PRON
ejpam-2339	178	4	are	be	AUX
ejpam-2339	178	5	within	within	ADP
ejpam-2339	178	6	conditions	condition	NOUN
ejpam-2339	178	7	of	of	ADP
ejpam-2339	178	8	lemma	lemma	PROPN
ejpam-2339	178	9	2	2	NUM
ejpam-2339	178	10	.	.	PUNCT
ejpam-2339	179	1	in	in	ADP
ejpam-2339	179	2	the	the	DET
ejpam-2339	179	3	first	first	ADJ
ejpam-2339	179	4	case	case	NOUN
ejpam-2339	179	5	we	we	PRON
ejpam-2339	179	6	will	will	AUX
ejpam-2339	179	7	assume	assume	VERB
ejpam-2339	179	8	that	that	SCONJ
ejpam-2339	179	9	u	u	PRON
ejpam-2339	179	10	is	be	AUX
ejpam-2339	179	11	odd	odd	ADJ
ejpam-2339	179	12	.	.	PUNCT
ejpam-2339	180	1	then	then	ADV
ejpam-2339	180	2	ωi	ωi	PROPN
ejpam-2339	180	3	≡	≡	PROPN
ejpam-2339	180	4	0(mod	0(mod	X
ejpam-2339	180	5	u2	u2	PROPN
ejpam-2339	180	6	)	)	PUNCT
ejpam-2339	180	7	.	.	PUNCT
ejpam-2339	181	1	therefore	therefore	ADV
ejpam-2339	181	2	,	,	PUNCT
ejpam-2339	181	3	we	we	PRON
ejpam-2339	181	4	can	can	AUX
ejpam-2339	181	5	define	define	VERB
ejpam-2339	181	6	f	f	PROPN
ejpam-2339	181	7	′(ǫ	′(ǫ	NOUN
ejpam-2339	181	8	)	)	PUNCT
ejpam-2339	181	9	=	=	SYM
ejpam-2339	181	10	1	1	NUM
ejpam-2339	181	11	u	u	NOUN
ejpam-2339	181	12	f(ǫ	f(ǫ	PROPN
ejpam-2339	181	13	)	)	PUNCT
ejpam-2339	181	14	,	,	PUNCT
ejpam-2339	181	15	ω′	ω′	X
ejpam-2339	182	1	i	i	PRON
ejpam-2339	182	2	=	=	NOUN
ejpam-2339	182	3	1	1	NUM
ejpam-2339	182	4	u2ωi	u2ωi	PRON
ejpam-2339	182	5	.	.	PUNCT
ejpam-2339	183	1	notice	notice	VERB
ejpam-2339	183	2	that	that	SCONJ
ejpam-2339	183	3	for	for	ADP
ejpam-2339	183	4	every	every	DET
ejpam-2339	183	5	s	s	X
ejpam-2339	183	6	∈	∈	PROPN
ejpam-2339	183	7	[	[	X
ejpam-2339	183	8	t	t	X
ejpam-2339	183	9	−	−	NUM
ejpam-2339	183	10	1	1	NUM
ejpam-2339	183	11	]	]	X
ejpam-2339	183	12	we	we	PRON
ejpam-2339	183	13	get	get	VERB
ejpam-2339	183	14	the	the	DET
ejpam-2339	183	15	system	system	NOUN
ejpam-2339	183	16	ω′0	ω′0	X
ejpam-2339	184	1	+	+	CCONJ
ejpam-2339	184	2	2	2	NUM
ejpam-2339	184	3	∑s	∑s	NOUN
ejpam-2339	184	4	i=1ω	i=1ω	ADJ
ejpam-2339	184	5	′	′	NOUN
ejpam-2339	185	1	i	i	PRON
ejpam-2339	185	2	−	−	PROPN
ejpam-2339	185	3	2ω′s+1	2ω′s+1	NOUN
ejpam-2339	185	4	=	=	SYM
ejpam-2339	185	5	1	1	NUM
ejpam-2339	185	6	,	,	PUNCT
ejpam-2339	185	7	or	or	CCONJ
ejpam-2339	185	8	in	in	ADP
ejpam-2339	185	9	other	other	ADJ
ejpam-2339	185	10	words	word	NOUN
ejpam-2339	185	11	|f	|f	PUNCT
ejpam-2339	185	12	′(ǫ)|=	′(ǫ)|=	NOUN
ejpam-2339	185	13	1	1	NUM
ejpam-2339	185	14	.	.	X
ejpam-2339	186	1	k.tabak	k.tabak	ADJ
ejpam-2339	186	2	/	/	SYM
ejpam-2339	186	3	eur	eur	PROPN
ejpam-2339	186	4	.	.	PUNCT
ejpam-2339	187	1	j.	j.	PROPN
ejpam-2339	187	2	pure	pure	PROPN
ejpam-2339	187	3	appl	appl	PROPN
ejpam-2339	187	4	.	.	PROPN
ejpam-2339	187	5	math	math	PROPN
ejpam-2339	187	6	,	,	PUNCT
ejpam-2339	187	7	8	8	NUM
ejpam-2339	187	8	(	(	PUNCT
ejpam-2339	187	9	2015	2015	NUM
ejpam-2339	187	10	)	)	PUNCT
ejpam-2339	187	11	,	,	PUNCT
ejpam-2339	187	12	450	450	NUM
ejpam-2339	187	13	-	-	SYM
ejpam-2339	187	14	457	457	NUM
ejpam-2339	187	15	454	454	NUM
ejpam-2339	187	16	second	second	ADJ
ejpam-2339	187	17	case	case	NOUN
ejpam-2339	187	18	deals	deal	VERB
ejpam-2339	187	19	with	with	ADP
ejpam-2339	187	20	even	even	ADV
ejpam-2339	187	21	u.	u.	VERB
ejpam-2339	187	22	in	in	ADP
ejpam-2339	187	23	this	this	DET
ejpam-2339	187	24	one	one	NOUN
ejpam-2339	187	25	we	we	PRON
ejpam-2339	187	26	will	will	AUX
ejpam-2339	187	27	need	need	VERB
ejpam-2339	187	28	more	more	ADV
ejpam-2339	187	29	severe	severe	ADJ
ejpam-2339	187	30	tools	tool	NOUN
ejpam-2339	187	31	.	.	PUNCT
ejpam-2339	188	1	put	put	VERB
ejpam-2339	188	2	u	u	NOUN
ejpam-2339	188	3	=	=	NOUN
ejpam-2339	188	4	2ru1	2ru1	NUM
ejpam-2339	188	5	,	,	PUNCT
ejpam-2339	188	6	where	where	SCONJ
ejpam-2339	188	7	u1	u1	NOUN
ejpam-2339	188	8	is	be	AUX
ejpam-2339	188	9	odd	odd	ADJ
ejpam-2339	188	10	.	.	PUNCT
ejpam-2339	189	1	then	then	ADV
ejpam-2339	189	2	ωi	ωi	PROPN
ejpam-2339	189	3	≡	≡	PROPN
ejpam-2339	189	4	0(mod	0(mod	X
ejpam-2339	189	5	u2	u2	PROPN
ejpam-2339	189	6	1	1	NUM
ejpam-2339	189	7	)	)	PUNCT
ejpam-2339	189	8	.	.	PUNCT
ejpam-2339	190	1	we	we	PRON
ejpam-2339	190	2	will	will	AUX
ejpam-2339	190	3	use	use	VERB
ejpam-2339	190	4	lemma	lemma	PROPN
ejpam-2339	190	5	3	3	X
ejpam-2339	190	6	.	.	PUNCT
ejpam-2339	190	7	let	let	VERB
ejpam-2339	190	8	us	we	PRON
ejpam-2339	190	9	introduce	introduce	VERB
ejpam-2339	190	10	a=	a=	ADV
ejpam-2339	191	1	∑2t−1	∑2t−1	PUNCT
ejpam-2339	191	2	i=0	i=0	PROPN
ejpam-2339	191	3	ki	ki	PROPN
ejpam-2339	191	4	x	x	PUNCT
ejpam-2339	191	5	i	i	PRON
ejpam-2339	191	6	∈	∈	PROPN
ejpam-2339	191	7	z[x	z[x	NOUN
ejpam-2339	191	8	]	]	X
ejpam-2339	191	9	,	,	PUNCT
ejpam-2339	191	10	where	where	SCONJ
ejpam-2339	191	11	〈	〈	NOUN
ejpam-2339	191	12	x	x	X
ejpam-2339	191	13	〉	〉	NOUN
ejpam-2339	191	14	∼=	∼=	PART
ejpam-2339	191	15	〈	〈	NOUN
ejpam-2339	191	16	ǫ	ǫ	PRON
ejpam-2339	191	17	〉	〉	NOUN
ejpam-2339	191	18	∼=	∼=	PART
ejpam-2339	191	19	c2	c2	PROPN
ejpam-2339	191	20	t	t	PROPN
ejpam-2339	191	21	.	.	PUNCT
ejpam-2339	192	1	take	take	VERB
ejpam-2339	192	2	character	character	NOUN
ejpam-2339	192	3	χ	χ	X
ejpam-2339	192	4	:	:	PUNCT
ejpam-2339	192	5	a→	a→	PROPN
ejpam-2339	192	6	c	c	NOUN
ejpam-2339	192	7	given	give	VERB
ejpam-2339	192	8	by	by	ADP
ejpam-2339	192	9	χ(x	χ(x	PROPN
ejpam-2339	192	10	)	)	PUNCT
ejpam-2339	193	1	=	=	SYM
ejpam-2339	194	1	ǫ	ǫ	X
ejpam-2339	194	2	.	.	PUNCT
ejpam-2339	195	1	now	now	ADV
ejpam-2339	195	2	we	we	PRON
ejpam-2339	195	3	have	have	VERB
ejpam-2339	195	4	χ(a)χ(a	χ(a)χ(a	NOUN
ejpam-2339	195	5	)	)	PUNCT
ejpam-2339	195	6	=	=	NOUN
ejpam-2339	195	7	|f(ǫ)|2	|f(ǫ)|2	NUM
ejpam-2339	195	8	=	=	SYM
ejpam-2339	195	9	f(ǫ)f(ǫ	f(ǫ)f(ǫ	NOUN
ejpam-2339	195	10	)	)	PUNCT
ejpam-2339	195	11	=	=	PUNCT
ejpam-2339	196	1	22ru2	22ru2	NOUN
ejpam-2339	196	2	1	1	NUM
ejpam-2339	196	3	≡	≡	PROPN
ejpam-2339	196	4	0	0	NUM
ejpam-2339	196	5	(	(	PUNCT
ejpam-2339	196	6	mod	mod	PROPN
ejpam-2339	196	7	22r	22r	NOUN
ejpam-2339	196	8	)	)	PUNCT
ejpam-2339	196	9	.	.	PUNCT
ejpam-2339	197	1	using	use	VERB
ejpam-2339	197	2	the	the	DET
ejpam-2339	197	3	notation	notation	NOUN
ejpam-2339	197	4	from	from	ADP
ejpam-2339	197	5	lemma	lemma	PROPN
ejpam-2339	197	6	3	3	NUM
ejpam-2339	197	7	,	,	PUNCT
ejpam-2339	197	8	we	we	PRON
ejpam-2339	197	9	may	may	AUX
ejpam-2339	197	10	write	write	VERB
ejpam-2339	197	11	w	w	PROPN
ejpam-2339	197	12	=	=	SYM
ejpam-2339	197	13	2	2	NUM
ejpam-2339	197	14	t	t	NOUN
ejpam-2339	197	15	,	,	PUNCT
ejpam-2339	197	16	p	p	X
ejpam-2339	197	17	=	=	NOUN
ejpam-2339	197	18	2	2	X
ejpam-2339	197	19	.	.	PUNCT
ejpam-2339	198	1	furthermore	furthermore	ADV
ejpam-2339	198	2	w	w	NOUN
ejpam-2339	198	3	=	=	SYM
ejpam-2339	198	4	2	2	NUM
ejpam-2339	198	5	t	t	NOUN
ejpam-2339	198	6	w′	w′	NOUN
ejpam-2339	198	7	,	,	PUNCT
ejpam-2339	198	8	where	where	SCONJ
ejpam-2339	198	9	w′	w′	PROPN
ejpam-2339	198	10	=	=	SYM
ejpam-2339	199	1	1	1	X
ejpam-2339	199	2	.	.	PUNCT
ejpam-2339	199	3	it	it	PRON
ejpam-2339	199	4	is	be	AUX
ejpam-2339	199	5	obvious	obvious	ADJ
ejpam-2339	199	6	that	that	SCONJ
ejpam-2339	199	7	2	2	NUM
ejpam-2339	199	8	j	j	PROPN
ejpam-2339	199	9	≡	≡	PROPN
ejpam-2339	199	10	−1(mod	−1(mod	PROPN
ejpam-2339	199	11	w′	w′	NOUN
ejpam-2339	199	12	)	)	PUNCT
ejpam-2339	199	13	.	.	PUNCT
ejpam-2339	200	1	by	by	ADP
ejpam-2339	200	2	lemma	lemma	PROPN
ejpam-2339	200	3	3	3	NUM
ejpam-2339	200	4	,	,	PUNCT
ejpam-2339	200	5	we	we	PRON
ejpam-2339	200	6	have	have	VERB
ejpam-2339	200	7	f(ǫ	f(ǫ	NOUN
ejpam-2339	200	8	)	)	PUNCT
ejpam-2339	201	1	=	=	SYM
ejpam-2339	201	2	χ(a	χ(a	NOUN
ejpam-2339	201	3	)	)	PUNCT
ejpam-2339	202	1	≡	≡	PROPN
ejpam-2339	202	2	0(mod	0(mod	NOUN
ejpam-2339	202	3	2r	2r	NUM
ejpam-2339	202	4	)	)	PUNCT
ejpam-2339	202	5	.	.	PUNCT
ejpam-2339	203	1	therefore	therefore	ADV
ejpam-2339	203	2	,	,	PUNCT
ejpam-2339	203	3	|f(ǫ)|2	|f(ǫ)|2	NUM
ejpam-2339	203	4	≡	≡	PROPN
ejpam-2339	203	5	0(mod	0(mod	ADJ
ejpam-2339	203	6	u2	u2	PROPN
ejpam-2339	203	7	)	)	PUNCT
ejpam-2339	203	8	.	.	PUNCT
ejpam-2339	204	1	therefore	therefore	ADV
ejpam-2339	204	2	,	,	PUNCT
ejpam-2339	204	3	we	we	PRON
ejpam-2339	204	4	can	can	AUX
ejpam-2339	204	5	define	define	VERB
ejpam-2339	204	6	f	f	PROPN
ejpam-2339	204	7	′	′	NUM
ejpam-2339	204	8	and	and	CCONJ
ejpam-2339	204	9	ω′	ω′	NUM
ejpam-2339	204	10	i	i	PRON
ejpam-2339	204	11	as	as	ADP
ejpam-2339	204	12	in	in	ADP
ejpam-2339	204	13	previous	previous	ADJ
ejpam-2339	204	14	case	case	NOUN
ejpam-2339	204	15	.	.	PUNCT
ejpam-2339	205	1	so	so	ADV
ejpam-2339	205	2	,	,	PUNCT
ejpam-2339	205	3	both	both	DET
ejpam-2339	205	4	cases	case	NOUN
ejpam-2339	205	5	lead	lead	VERB
ejpam-2339	205	6	us	we	PRON
ejpam-2339	205	7	to	to	ADP
ejpam-2339	205	8	|f(ǫ)′|	|f(ǫ)′|	NOUN
ejpam-2339	205	9	=	=	SYM
ejpam-2339	205	10	1	1	X
ejpam-2339	205	11	.	.	PUNCT
ejpam-2339	206	1	it	it	PRON
ejpam-2339	206	2	is	be	AUX
ejpam-2339	206	3	clear	clear	ADJ
ejpam-2339	206	4	that	that	SCONJ
ejpam-2339	206	5	f	f	PROPN
ejpam-2339	206	6	′	′	NOUN
ejpam-2339	206	7	has	have	VERB
ejpam-2339	206	8	coefficients	coefficient	NOUN
ejpam-2339	206	9	from	from	ADP
ejpam-2339	206	10	q.	q.	NOUN
ejpam-2339	206	11	let	let	VERB
ejpam-2339	206	12	us	we	PRON
ejpam-2339	206	13	write	write	VERB
ejpam-2339	206	14	f(ǫ)′	f(ǫ)′	PROPN
ejpam-2339	206	15	=	=	PUNCT
ejpam-2339	206	16	(	(	PUNCT
ejpam-2339	206	17	ǫ′)i1	ǫ′)i1	X
ejpam-2339	206	18	+	+	CCONJ
ejpam-2339	206	19	.	.	PUNCT
ejpam-2339	206	20	.	.	PUNCT
ejpam-2339	207	1	.+(ǫ′)iq	.+(ǫ′)iq	INTJ
ejpam-2339	207	2	,	,	PUNCT
ejpam-2339	207	3	where	where	SCONJ
ejpam-2339	207	4	(	(	PUNCT
ejpam-2339	207	5	ǫ′)i	ǫ′)i	NUM
ejpam-2339	207	6	j	j	NOUN
ejpam-2339	207	7	=	=	SYM
ejpam-2339	207	8	1	1	NUM
ejpam-2339	207	9	uǫ	uǫ	VERB
ejpam-2339	208	1	i	i	PRON
ejpam-2339	208	2	j	j	PROPN
ejpam-2339	208	3	.	.	PUNCT
ejpam-2339	209	1	let	let	VERB
ejpam-2339	209	2	us	we	PRON
ejpam-2339	209	3	assume	assume	VERB
ejpam-2339	209	4	that	that	SCONJ
ejpam-2339	209	5	some	some	DET
ejpam-2339	209	6	two	two	NUM
ejpam-2339	209	7	(	(	PUNCT
ejpam-2339	209	8	ǫ′)i	ǫ′)i	NUM
ejpam-2339	209	9	j	j	NOUN
ejpam-2339	209	10	can	can	AUX
ejpam-2339	209	11	be	be	AUX
ejpam-2339	209	12	abbreviated	abbreviate	VERB
ejpam-2339	209	13	in	in	ADP
ejpam-2339	209	14	pairs	pair	NOUN
ejpam-2339	209	15	.	.	PUNCT
ejpam-2339	210	1	additionally	additionally	ADV
ejpam-2339	210	2	,	,	PUNCT
ejpam-2339	210	3	we	we	PRON
ejpam-2339	210	4	may	may	AUX
ejpam-2339	210	5	assume	assume	VERB
ejpam-2339	210	6	that	that	SCONJ
ejpam-2339	210	7	we	we	PRON
ejpam-2339	210	8	have	have	AUX
ejpam-2339	210	9	done	do	VERB
ejpam-2339	210	10	all	all	DET
ejpam-2339	210	11	possible	possible	ADJ
ejpam-2339	210	12	abbreviations	abbreviation	NOUN
ejpam-2339	210	13	in	in	ADP
ejpam-2339	210	14	f(ǫ)′.	f(ǫ)′.	PRON
ejpam-2339	210	15	therefore	therefore	ADV
ejpam-2339	210	16	,	,	PUNCT
ejpam-2339	210	17	for	for	ADP
ejpam-2339	210	18	roots	root	NOUN
ejpam-2339	210	19	that	that	PRON
ejpam-2339	210	20	’	'	PUNCT
ejpam-2339	210	21	survived	survive	VERB
ejpam-2339	210	22	’	'	PUNCT
ejpam-2339	210	23	abbreviations	abbreviation	NOUN
ejpam-2339	210	24	we	we	PRON
ejpam-2339	210	25	may	may	AUX
ejpam-2339	210	26	write	write	VERB
ejpam-2339	210	27	f(ǫ)′	f(ǫ)′	PROPN
ejpam-2339	210	28	=	=	SYM
ejpam-2339	210	29	(	(	PUNCT
ejpam-2339	210	30	ǫ′)s1	ǫ′)s1	NUM
ejpam-2339	210	31	+	+	CCONJ
ejpam-2339	210	32	.	.	PUNCT
ejpam-2339	210	33	.	.	PUNCT
ejpam-2339	211	1	.+	.+	NOUN
ejpam-2339	211	2	(	(	PUNCT
ejpam-2339	211	3	ǫ′)sq1	ǫ′)sq1	PROPN
ejpam-2339	211	4	.	.	PUNCT
ejpam-2339	212	1	hence	hence	ADV
ejpam-2339	212	2	,	,	PUNCT
ejpam-2339	212	3	∑q1	∑q1	PROPN
ejpam-2339	212	4	i	i	PROPN
ejpam-2339	212	5	,	,	PUNCT
ejpam-2339	212	6	j=1	j=1	PROPN
ejpam-2339	212	7	(	(	PUNCT
ejpam-2339	212	8	ǫ′)si−s	ǫ′)si−s	NOUN
ejpam-2339	212	9	j	j	NOUN
ejpam-2339	212	10	=	=	SYM
ejpam-2339	212	11	1	1	X
ejpam-2339	212	12	.	.	PUNCT
ejpam-2339	213	1	by	by	ADP
ejpam-2339	213	2	pairwise	pairwise	NOUN
ejpam-2339	213	3	abbreviation	abbreviation	NOUN
ejpam-2339	213	4	we	we	PRON
ejpam-2339	213	5	get	get	VERB
ejpam-2339	213	6	1=	1=	NUM
ejpam-2339	213	7	|f(ǫ)′|=	|f(ǫ)′|=	PUNCT
ejpam-2339	213	8	|	|	ADV
ejpam-2339	213	9	q1	q1	VERB
ejpam-2339	213	10	∑	∑	PROPN
ejpam-2339	213	11	i=1	i=1	PROPN
ejpam-2339	213	12	(	(	PUNCT
ejpam-2339	213	13	ǫ′)si	ǫ′)si	NUM
ejpam-2339	213	14	|	|	ADV
ejpam-2339	213	15	≤	≤	NUM
ejpam-2339	213	16	q1	q1	PROPN
ejpam-2339	213	17	∑	∑	PROPN
ejpam-2339	213	18	i=1	i=1	PROPN
ejpam-2339	213	19	|(ǫ′)si	|(ǫ′)si	ADJ
ejpam-2339	213	20	|=	|=	NUM
ejpam-2339	213	21	q1	q1	NOUN
ejpam-2339	213	22	u	u	NOUN
ejpam-2339	213	23	.	.	PUNCT
ejpam-2339	214	1	thus	thus	ADV
ejpam-2339	214	2	q1	q1	VERB
ejpam-2339	214	3	≥	≥	NOUN
ejpam-2339	214	4	u.	u.	PROPN
ejpam-2339	214	5	also	also	ADV
ejpam-2339	214	6	,	,	PUNCT
ejpam-2339	214	7	we	we	PRON
ejpam-2339	214	8	get	get	VERB
ejpam-2339	214	9	∑q1	∑q1	PROPN
ejpam-2339	214	10	i	i	PROPN
ejpam-2339	214	11	6=	6=	PROPN
ejpam-2339	214	12	j	j	PROPN
ejpam-2339	214	13	(	(	PUNCT
ejpam-2339	214	14	ǫ′)si−s	ǫ′)si−s	NOUN
ejpam-2339	214	15	j	j	PROPN
ejpam-2339	214	16	+	+	PROPN
ejpam-2339	214	17	q1	q1	PROPN
ejpam-2339	214	18	−	−	NOUN
ejpam-2339	214	19	1	1	NUM
ejpam-2339	214	20	=	=	SYM
ejpam-2339	214	21	0	0	NUM
ejpam-2339	214	22	.	.	PUNCT
ejpam-2339	215	1	the	the	DET
ejpam-2339	215	2	consequence	consequence	NOUN
ejpam-2339	215	3	is	be	AUX
ejpam-2339	215	4	that	that	SCONJ
ejpam-2339	215	5	,	,	PUNCT
ejpam-2339	215	6	in	in	ADP
ejpam-2339	215	7	previous	previous	ADJ
ejpam-2339	215	8	sum	sum	NOUN
ejpam-2339	215	9	,	,	PUNCT
ejpam-2339	215	10	we	we	PRON
ejpam-2339	215	11	must	must	AUX
ejpam-2339	215	12	have	have	VERB
ejpam-2339	215	13	at	at	ADV
ejpam-2339	215	14	least	least	ADV
ejpam-2339	215	15	one	one	NUM
ejpam-2339	215	16	term	term	NOUN
ejpam-2339	215	17	equal	equal	ADJ
ejpam-2339	215	18	to	to	ADP
ejpam-2339	215	19	(	(	PUNCT
ejpam-2339	215	20	−1	−1	NOUN
ejpam-2339	215	21	)	)	PUNCT
ejpam-2339	215	22	.	.	PUNCT
ejpam-2339	216	1	for	for	ADP
ejpam-2339	216	2	example	example	NOUN
ejpam-2339	216	3	(	(	PUNCT
ejpam-2339	216	4	ǫ′)s1−s2	ǫ′)s1−s2	NOUN
ejpam-2339	216	5	=	=	SYM
ejpam-2339	216	6	−1	−1	NOUN
ejpam-2339	216	7	.	.	PUNCT
ejpam-2339	217	1	it	it	PRON
ejpam-2339	217	2	is	be	AUX
ejpam-2339	217	3	clear	clear	ADJ
ejpam-2339	217	4	that	that	SCONJ
ejpam-2339	217	5	we	we	PRON
ejpam-2339	217	6	would	would	AUX
ejpam-2339	217	7	get	get	VERB
ejpam-2339	217	8	(	(	PUNCT
ejpam-2339	217	9	ǫ′)s1	ǫ′)s1	X
ejpam-2339	217	10	+	+	NOUN
ejpam-2339	217	11	(	(	PUNCT
ejpam-2339	217	12	ǫ′)s1	ǫ′)s1	NUM
ejpam-2339	217	13	=	=	SYM
ejpam-2339	217	14	0	0	NUM
ejpam-2339	217	15	,	,	PUNCT
ejpam-2339	217	16	contrary	contrary	ADJ
ejpam-2339	217	17	to	to	ADP
ejpam-2339	217	18	our	our	PRON
ejpam-2339	217	19	assumption	assumption	NOUN
ejpam-2339	217	20	about	about	ADP
ejpam-2339	217	21	maximal	maximal	ADJ
ejpam-2339	217	22	abbreviation	abbreviation	NOUN
ejpam-2339	217	23	.	.	PUNCT
ejpam-2339	218	1	therefore	therefore	ADV
ejpam-2339	218	2	,	,	PUNCT
ejpam-2339	218	3	the	the	DET
ejpam-2339	218	4	only	only	ADJ
ejpam-2339	218	5	option	option	NOUN
ejpam-2339	218	6	is	be	AUX
ejpam-2339	218	7	that	that	SCONJ
ejpam-2339	218	8	for	for	ADP
ejpam-2339	218	9	every	every	DET
ejpam-2339	218	10	ji	ji	PROPN
ejpam-2339	218	11	,	,	PUNCT
ejpam-2339	218	12	j2	j2	PROPN
ejpam-2339	218	13	∈	∈	PROPN
ejpam-2339	218	14	[	[	X
ejpam-2339	218	15	q1	q1	X
ejpam-2339	218	16	]	]	X
ejpam-2339	218	17	equation	equation	NOUN
ejpam-2339	218	18	(	(	PUNCT
ejpam-2339	218	19	ǫ′)s	ǫ′)s	NUM
ejpam-2339	218	20	j1	j1	PROPN
ejpam-2339	218	21	−s	−s	NOUN
ejpam-2339	218	22	j2	j2	NOUN
ejpam-2339	218	23	=	=	SYM
ejpam-2339	218	24	1	1	NUM
ejpam-2339	218	25	holds	hold	NOUN
ejpam-2339	218	26	.	.	PUNCT
ejpam-2339	219	1	now	now	ADV
ejpam-2339	219	2	,	,	PUNCT
ejpam-2339	219	3	it	it	PRON
ejpam-2339	219	4	is	be	AUX
ejpam-2339	219	5	straight	straight	ADV
ejpam-2339	219	6	forward	forward	ADV
ejpam-2339	219	7	q1	q1	PROPN
ejpam-2339	219	8	=	=	PUNCT
ejpam-2339	220	1	u.	u.	NOUN
ejpam-2339	220	2	thus	thus	ADV
ejpam-2339	220	3	f(ǫ)′	f(ǫ)′	PROPN
ejpam-2339	220	4	=	=	SYM
ejpam-2339	220	5	q1	q1	PROPN
ejpam-2339	220	6	u	u	NOUN
ejpam-2339	220	7	ǫ	ǫ	NOUN
ejpam-2339	220	8	r0	r0	NOUN
ejpam-2339	220	9	for	for	ADP
ejpam-2339	220	10	some	some	DET
ejpam-2339	220	11	r0	r0	NOUN
ejpam-2339	220	12	∈	∈	PROPN
ejpam-2339	220	13	z.	z.	PROPN
ejpam-2339	220	14	finally	finally	ADV
ejpam-2339	220	15	,	,	PUNCT
ejpam-2339	220	16	this	this	PRON
ejpam-2339	220	17	gives	give	VERB
ejpam-2339	220	18	us	we	PRON
ejpam-2339	220	19	f(ǫ	f(ǫ	NOUN
ejpam-2339	220	20	)	)	PUNCT
ejpam-2339	221	1	=	=	PUNCT
ejpam-2339	222	1	uf(ǫ)′	uf(ǫ)′	PROPN
ejpam-2339	222	2	=	=	SYM
ejpam-2339	222	3	uǫr0	uǫr0	ADJ
ejpam-2339	222	4	.	.	PUNCT
ejpam-2339	223	1	3	3	X
ejpam-2339	223	2	.	.	X
ejpam-2339	223	3	modular	modular	ADJ
ejpam-2339	223	4	case	case	NOUN
ejpam-2339	223	5	this	this	DET
ejpam-2339	223	6	section	section	NOUN
ejpam-2339	223	7	deals	deal	VERB
ejpam-2339	223	8	with	with	ADP
ejpam-2339	223	9	groups	group	NOUN
ejpam-2339	223	10	of	of	ADP
ejpam-2339	223	11	order	order	NOUN
ejpam-2339	223	12	4u2	4u2	NUM
ejpam-2339	223	13	with	with	ADP
ejpam-2339	223	14	maximal	maximal	ADJ
ejpam-2339	223	15	2	2	NUM
ejpam-2339	223	16	-	-	PUNCT
ejpam-2339	223	17	group	group	NOUN
ejpam-2339	223	18	of	of	ADP
ejpam-2339	223	19	modular	modular	ADJ
ejpam-2339	223	20	type	type	NOUN
ejpam-2339	223	21	.	.	PUNCT
ejpam-2339	224	1	by	by	ADP
ejpam-2339	224	2	that	that	PRON
ejpam-2339	224	3	we	we	PRON
ejpam-2339	224	4	mean	mean	VERB
ejpam-2339	224	5	that	that	SCONJ
ejpam-2339	224	6	generators	generator	NOUN
ejpam-2339	224	7	of	of	ADP
ejpam-2339	224	8	such	such	ADJ
ejpam-2339	224	9	2	2	NUM
ejpam-2339	224	10	-	-	PUNCT
ejpam-2339	224	11	group	group	NOUN
ejpam-2339	224	12	look	look	NOUN
ejpam-2339	224	13	like	like	ADP
ejpam-2339	224	14	those	those	PRON
ejpam-2339	224	15	in	in	ADP
ejpam-2339	224	16	2	2	NUM
ejpam-2339	224	17	-	-	PUNCT
ejpam-2339	224	18	generated	generate	VERB
ejpam-2339	224	19	modular	modular	ADJ
ejpam-2339	224	20	2	2	NUM
ejpam-2339	224	21	-	-	PUNCT
ejpam-2339	224	22	group	group	NOUN
ejpam-2339	224	23	.	.	PUNCT
ejpam-2339	225	1	we	we	PRON
ejpam-2339	225	2	will	will	AUX
ejpam-2339	225	3	use	use	VERB
ejpam-2339	225	4	o(g	o(g	NOUN
ejpam-2339	225	5	)	)	PUNCT
ejpam-2339	225	6	for	for	SCONJ
ejpam-2339	225	7	order	order	NOUN
ejpam-2339	225	8	of	of	ADP
ejpam-2339	225	9	element	element	NOUN
ejpam-2339	225	10	g.	g.	PROPN
ejpam-2339	225	11	theorem	theorem	VERB
ejpam-2339	225	12	6	6	NUM
ejpam-2339	225	13	.	.	PUNCT
ejpam-2339	226	1	let	let	VERB
ejpam-2339	226	2	g	g	NOUN
ejpam-2339	226	3	=	=	PUNCT
ejpam-2339	227	1	h	h	NOUN
ejpam-2339	227	2	×	×	PROPN
ejpam-2339	227	3	l	l	NOUN
ejpam-2339	227	4	be	be	VERB
ejpam-2339	227	5	a	a	DET
ejpam-2339	227	6	group	group	NOUN
ejpam-2339	227	7	of	of	ADP
ejpam-2339	227	8	4u2	4u2	NUM
ejpam-2339	228	1	where	where	SCONJ
ejpam-2339	228	2	|l|=	|l|=	NOUN
ejpam-2339	228	3	u2	u2	PROPN
ejpam-2339	228	4	1	1	NUM
ejpam-2339	228	5	.	.	PUNCT
ejpam-2339	228	6	let	let	VERB
ejpam-2339	228	7	h	h	NOUN
ejpam-2339	228	8	=	=	PUNCT
ejpam-2339	228	9	〈	〈	PROPN
ejpam-2339	228	10	x	x	SYM
ejpam-2339	228	11	,	,	PUNCT
ejpam-2339	228	12	y1	y1	PROPN
ejpam-2339	228	13	,	,	PUNCT
ejpam-2339	228	14	.	.	PUNCT
ejpam-2339	228	15	.	.	PUNCT
ejpam-2339	229	1	.	.	PUNCT
ejpam-2339	230	1	,	,	PUNCT
ejpam-2339	230	2	ys	ys	NOUN
ejpam-2339	230	3	〉	〉	NOUN
ejpam-2339	230	4	is	be	AUX
ejpam-2339	230	5	of	of	ADP
ejpam-2339	230	6	order	order	NOUN
ejpam-2339	230	7	22d+2	22d+2	NUM
ejpam-2339	230	8	and	and	CCONJ
ejpam-2339	230	9	o(x	o(x	PROPN
ejpam-2339	230	10	)	)	PUNCT
ejpam-2339	230	11	=	=	PUNCT
ejpam-2339	231	1	2	2	NUM
ejpam-2339	231	2	t	t	NOUN
ejpam-2339	231	3	where	where	SCONJ
ejpam-2339	231	4	x	x	PUNCT
ejpam-2339	231	5	yi	yi	PROPN
ejpam-2339	231	6	∈	∈	PROPN
ejpam-2339	231	7	{	{	PUNCT
ejpam-2339	231	8	x	x	NOUN
ejpam-2339	231	9	,	,	PUNCT
ejpam-2339	231	10	x2t−1	x2t−1	PROPN
ejpam-2339	231	11	+	+	NOUN
ejpam-2339	231	12	1	1	NUM
ejpam-2339	231	13	}	}	PUNCT
ejpam-2339	231	14	.	.	PUNCT
ejpam-2339	232	1	if	if	SCONJ
ejpam-2339	232	2	h	h	NOUN
ejpam-2339	232	3	′	′	NUM
ejpam-2339	232	4	∩	∩	PROPN
ejpam-2339	232	5	〈	〈	PROPN
ejpam-2339	232	6	x	x	X
ejpam-2339	232	7	〉	〉	NOUN
ejpam-2339	232	8	≤	≤	NUM
ejpam-2339	232	9	〈	〈	PROPN
ejpam-2339	232	10	x2t−p	x2t−p	PROPN
ejpam-2339	232	11	〉	〉	NOUN
ejpam-2339	232	12	and	and	CCONJ
ejpam-2339	232	13	o(x	o(x	PROPN
ejpam-2339	232	14	)	)	PUNCT
ejpam-2339	232	15	≥	≥	NOUN
ejpam-2339	232	16	2p+3u	2p+3u	NUM
ejpam-2339	232	17	,	,	PUNCT
ejpam-2339	232	18	then	then	ADV
ejpam-2339	232	19	g	g	PROPN
ejpam-2339	232	20	is	be	AUX
ejpam-2339	232	21	not	not	PART
ejpam-2339	232	22	a	a	DET
ejpam-2339	232	23	hadamard	hadamard	ADJ
ejpam-2339	232	24	group	group	NOUN
ejpam-2339	232	25	.	.	PUNCT
ejpam-2339	233	1	proof	proof	NOUN
ejpam-2339	233	2	.	.	PUNCT
ejpam-2339	234	1	let	let	VERB
ejpam-2339	234	2	us	we	PRON
ejpam-2339	234	3	assume	assume	VERB
ejpam-2339	234	4	that	that	SCONJ
ejpam-2339	234	5	g	g	PROPN
ejpam-2339	234	6	is	be	AUX
ejpam-2339	234	7	a	a	DET
ejpam-2339	234	8	hadamard	hadamard	ADJ
ejpam-2339	234	9	group	group	NOUN
ejpam-2339	234	10	.	.	PUNCT
ejpam-2339	235	1	then	then	ADV
ejpam-2339	235	2	g	g	PROPN
ejpam-2339	235	3	posses	posse	NOUN
ejpam-2339	235	4	a	a	DET
ejpam-2339	235	5	difference	difference	NOUN
ejpam-2339	235	6	set	set	VERB
ejpam-2339	235	7	d	d	NOUN
ejpam-2339	235	8	with	with	ADP
ejpam-2339	235	9	parameters	parameter	NOUN
ejpam-2339	235	10	(	(	PUNCT
ejpam-2339	235	11	4u2	4u2	NUM
ejpam-2339	235	12	,	,	PUNCT
ejpam-2339	235	13	2u2	2u2	NUM
ejpam-2339	235	14	−	−	PROPN
ejpam-2339	235	15	u	u	NOUN
ejpam-2339	235	16	,	,	PUNCT
ejpam-2339	235	17	u2	u2	PROPN
ejpam-2339	235	18	−	−	PROPN
ejpam-2339	235	19	u	u	NOUN
ejpam-2339	235	20	)	)	PUNCT
ejpam-2339	235	21	.	.	PUNCT
ejpam-2339	236	1	now	now	ADV
ejpam-2339	236	2	we	we	PRON
ejpam-2339	236	3	will	will	AUX
ejpam-2339	236	4	construct	construct	VERB
ejpam-2339	236	5	a	a	DET
ejpam-2339	236	6	1	1	NUM
ejpam-2339	236	7	-	-	PUNCT
ejpam-2339	236	8	dimensional	dimensional	ADJ
ejpam-2339	236	9	representations	representation	NOUN
ejpam-2339	236	10	on	on	ADP
ejpam-2339	236	11	h	h	NOUN
ejpam-2339	236	12	,	,	PUNCT
ejpam-2339	236	13	which	which	PRON
ejpam-2339	236	14	is	be	AUX
ejpam-2339	236	15	also	also	ADV
ejpam-2339	236	16	a	a	DET
ejpam-2339	236	17	representation	representation	NOUN
ejpam-2339	236	18	on	on	ADP
ejpam-2339	236	19	g.	g.	PROPN
ejpam-2339	236	20	notice	notice	VERB
ejpam-2339	236	21	that	that	SCONJ
ejpam-2339	236	22	u	u	NOUN
ejpam-2339	236	23	=	=	NOUN
ejpam-2339	236	24	2du1	2du1	NUM
ejpam-2339	236	25	.	.	PUNCT
ejpam-2339	237	1	condition	condition	NOUN
ejpam-2339	237	2	h	h	NOUN
ejpam-2339	237	3	′	′	NOUN
ejpam-2339	237	4	≤	≤	PUNCT
ejpam-2339	238	1	〈	〈	PROPN
ejpam-2339	238	2	x2t−p	x2t−p	PROPN
ejpam-2339	238	3	〉	〉	NOUN
ejpam-2339	238	4	is	be	AUX
ejpam-2339	238	5	needed	need	VERB
ejpam-2339	238	6	,	,	PUNCT
ejpam-2339	238	7	since	since	SCONJ
ejpam-2339	238	8	for	for	ADP
ejpam-2339	238	9	any	any	DET
ejpam-2339	238	10	homomorphism	homomorphism	NOUN
ejpam-2339	238	11	ϕ	ϕ	X
ejpam-2339	238	12	:	:	PUNCT
ejpam-2339	238	13	g→	g→	NOUN
ejpam-2339	238	14	c	c	VERB
ejpam-2339	238	15	we	we	PRON
ejpam-2339	238	16	also	also	ADV
ejpam-2339	238	17	have	have	VERB
ejpam-2339	238	18	g′	g′	NOUN
ejpam-2339	238	19	≤	≤	NUM
ejpam-2339	238	20	ker(ϕ	ker(ϕ	PROPN
ejpam-2339	238	21	)	)	PUNCT
ejpam-2339	238	22	.	.	PUNCT
ejpam-2339	239	1	now	now	ADV
ejpam-2339	239	2	,	,	PUNCT
ejpam-2339	239	3	we	we	PRON
ejpam-2339	239	4	take	take	VERB
ejpam-2339	239	5	difference	difference	NOUN
ejpam-2339	239	6	set	set	VERB
ejpam-2339	239	7	and	and	CCONJ
ejpam-2339	239	8	divide	divide	VERB
ejpam-2339	239	9	it	it	PRON
ejpam-2339	239	10	over	over	ADP
ejpam-2339	239	11	classes	class	NOUN
ejpam-2339	239	12	modulo	modulo	VERB
ejpam-2339	239	13	〈	〈	PROPN
ejpam-2339	239	14	x	x	X
ejpam-2339	239	15	〉	〉	NOUN
ejpam-2339	239	16	.	.	PUNCT
ejpam-2339	240	1	then	then	ADV
ejpam-2339	240	2	we	we	PRON
ejpam-2339	240	3	get	get	VERB
ejpam-2339	240	4	d	d	NOUN
ejpam-2339	240	5	=	=	PUNCT
ejpam-2339	240	6	a	a	PRON
ejpam-2339	240	7	∑	∑	PUNCT
ejpam-2339	240	8	i=1	i=1	PROPN
ejpam-2339	240	9	xni	xni	PROPN
ejpam-2339	241	1	+	+	CCONJ
ejpam-2339	241	2	r	r	NOUN
ejpam-2339	241	3	∑	∑	PROPN
ejpam-2339	241	4	j=1	j=1	PROPN
ejpam-2339	241	5	t	t	PROPN
ejpam-2339	241	6	j	j	PROPN
ejpam-2339	241	7	∑	∑	PUNCT
ejpam-2339	241	8	s=1	s=1	NOUN
ejpam-2339	241	9	xm	xm	NUM
ejpam-2339	241	10	js	js	INTJ
ejpam-2339	241	11	!	!	PUNCT
ejpam-2339	242	1	g	g	PROPN
ejpam-2339	242	2	j	j	PROPN
ejpam-2339	242	3	.	.	PUNCT
ejpam-2339	243	1	k.tabak	k.tabak	ADJ
ejpam-2339	243	2	/	/	SYM
ejpam-2339	243	3	eur	eur	PROPN
ejpam-2339	243	4	.	.	PUNCT
ejpam-2339	244	1	j.	j.	PROPN
ejpam-2339	244	2	pure	pure	PROPN
ejpam-2339	244	3	appl	appl	PROPN
ejpam-2339	244	4	.	.	PROPN
ejpam-2339	244	5	math	math	PROPN
ejpam-2339	244	6	,	,	PUNCT
ejpam-2339	244	7	8	8	NUM
ejpam-2339	244	8	(	(	PUNCT
ejpam-2339	244	9	2015	2015	NUM
ejpam-2339	244	10	)	)	PUNCT
ejpam-2339	244	11	,	,	PUNCT
ejpam-2339	244	12	450	450	NUM
ejpam-2339	244	13	-	-	SYM
ejpam-2339	244	14	457	457	NUM
ejpam-2339	244	15	455	455	NUM
ejpam-2339	244	16	every	every	DET
ejpam-2339	244	17	g	g	PROPN
ejpam-2339	244	18	∈	∈	PROPN
ejpam-2339	244	19	g	g	PROPN
ejpam-2339	244	20	can	can	AUX
ejpam-2339	244	21	be	be	AUX
ejpam-2339	244	22	written	write	VERB
ejpam-2339	244	23	in	in	ADP
ejpam-2339	244	24	a	a	DET
ejpam-2339	244	25	form	form	NOUN
ejpam-2339	244	26	g	g	NOUN
ejpam-2339	244	27	=	=	NOUN
ejpam-2339	244	28	x	x	PROPN
ejpam-2339	244	29	i	i	PRON
ejpam-2339	245	1	yi1	yi1	INTJ
ejpam-2339	245	2	yi2	yi2	INTJ
ejpam-2339	245	3	.	.	PUNCT
ejpam-2339	245	4	.	.	PUNCT
ejpam-2339	245	5	.	.	PUNCT
ejpam-2339	246	1	yin	yin	PROPN
ejpam-2339	246	2	,	,	PUNCT
ejpam-2339	246	3	where	where	SCONJ
ejpam-2339	246	4	yi	yi	PROPN
ejpam-2339	246	5	j	j	PROPN
ejpam-2339	246	6	∈	∈	PROPN
ejpam-2339	246	7	〈	〈	PROPN
ejpam-2339	246	8	y1	y1	PROPN
ejpam-2339	246	9	,	,	PUNCT
ejpam-2339	246	10	.	.	PUNCT
ejpam-2339	246	11	.	.	PUNCT
ejpam-2339	246	12	.	.	PUNCT
ejpam-2339	247	1	,	,	PUNCT
ejpam-2339	247	2	ys	ys	NOUN
ejpam-2339	247	3	〉	〉	NOUN
ejpam-2339	247	4	.	.	PUNCT
ejpam-2339	248	1	now	now	ADV
ejpam-2339	248	2	,	,	PUNCT
ejpam-2339	248	3	for	for	ADP
ejpam-2339	248	4	w	w	NOUN
ejpam-2339	248	5	=	=	SYM
ejpam-2339	248	6	1,2	1,2	NUM
ejpam-2339	248	7	,	,	PUNCT
ejpam-2339	248	8	.	.	PUNCT
ejpam-2339	248	9	.	.	PUNCT
ejpam-2339	248	10	.	.	PUNCT
ejpam-2339	249	1	,	,	PUNCT
ejpam-2339	249	2	2t−p	2t−p	INTJ
ejpam-2339	249	3	we	we	PRON
ejpam-2339	249	4	define	define	VERB
ejpam-2339	250	1	ϕw	ϕw	INTJ
ejpam-2339	250	2	:	:	PUNCT
ejpam-2339	250	3	g	g	PROPN
ejpam-2339	250	4	→	→	SYM
ejpam-2339	250	5	c	c	NOUN
ejpam-2339	250	6	by	by	ADV
ejpam-2339	250	7	ϕw(x	ϕw(x	ADP
ejpam-2339	251	1	i	i	PRON
ejpam-2339	252	1	yi1	yi1	INTJ
ejpam-2339	253	1	yi2	yi2	INTJ
ejpam-2339	253	2	.	.	PUNCT
ejpam-2339	253	3	.	.	PUNCT
ejpam-2339	253	4	.	.	PUNCT
ejpam-2339	254	1	yin	yin	PROPN
ejpam-2339	254	2	)	)	PUNCT
ejpam-2339	255	1	=	=	PUNCT
ejpam-2339	255	2	ǫ2pwi	ǫ2pwi	NOUN
ejpam-2339	255	3	,	,	PUNCT
ejpam-2339	255	4	where	where	SCONJ
ejpam-2339	255	5	ǫ	ǫ	PRON
ejpam-2339	255	6	is	be	AUX
ejpam-2339	255	7	a	a	DET
ejpam-2339	255	8	root	root	NOUN
ejpam-2339	255	9	of	of	ADP
ejpam-2339	255	10	unity	unity	NOUN
ejpam-2339	255	11	of	of	ADP
ejpam-2339	255	12	order	order	NOUN
ejpam-2339	255	13	2	2	NUM
ejpam-2339	255	14	t	t	NOUN
ejpam-2339	255	15	.	.	PUNCT
ejpam-2339	256	1	also	also	ADV
ejpam-2339	256	2	,	,	PUNCT
ejpam-2339	256	3	g′	g′	NOUN
ejpam-2339	256	4	=	=	PUNCT
ejpam-2339	256	5	h	h	NOUN
ejpam-2339	257	1	′	′	NUM
ejpam-2339	257	2	×	×	NOUN
ejpam-2339	257	3	l′.	l′.	NOUN
ejpam-2339	257	4	we	we	PRON
ejpam-2339	257	5	notice	notice	VERB
ejpam-2339	257	6	that	that	SCONJ
ejpam-2339	257	7	ϕw	ϕw	PRON
ejpam-2339	257	8	is	be	AUX
ejpam-2339	257	9	well	well	ADV
ejpam-2339	257	10	defined	define	VERB
ejpam-2339	257	11	,	,	PUNCT
ejpam-2339	257	12	since	since	SCONJ
ejpam-2339	257	13	g′∩	g′∩	PROPN
ejpam-2339	257	14	�	�	PROPN
ejpam-2339	257	15	〈	〈	NOUN
ejpam-2339	257	16	x	x	X
ejpam-2339	257	17	〉	〉	NOUN
ejpam-2339	257	18	×	×	NOUN
ejpam-2339	257	19	{	{	PUNCT
ejpam-2339	257	20	1l	1l	PROPN
ejpam-2339	257	21	}	}	PUNCT
ejpam-2339	257	22	�	�	PROPN
ejpam-2339	257	23	≤	≤	PUNCT
ejpam-2339	257	24	〈	〈	PROPN
ejpam-2339	257	25	x2t−p	x2t−p	PROPN
ejpam-2339	257	26	〉	〉	NOUN
ejpam-2339	257	27	and	and	CCONJ
ejpam-2339	257	28	〈	〈	NOUN
ejpam-2339	257	29	ϕw(x	ϕw(x	NUM
ejpam-2339	257	30	2t−p	2t−p	NOUN
ejpam-2339	257	31	)	)	PUNCT
ejpam-2339	257	32	〉	〉	NOUN
ejpam-2339	257	33	=	=	SYM
ejpam-2339	257	34	〈	〈	NOUN
ejpam-2339	257	35	1	1	NUM
ejpam-2339	257	36	〉	〉	NOUN
ejpam-2339	257	37	.	.	PUNCT
ejpam-2339	258	1	now	now	ADV
ejpam-2339	258	2	it	it	PRON
ejpam-2339	258	3	is	be	AUX
ejpam-2339	258	4	clear	clear	ADJ
ejpam-2339	258	5	that	that	SCONJ
ejpam-2339	258	6	g′	g′	NOUN
ejpam-2339	258	7	≤	≤	X
ejpam-2339	258	8	ker(ϕw	ker(ϕw	PRON
ejpam-2339	258	9	)	)	PUNCT
ejpam-2339	258	10	is	be	AUX
ejpam-2339	258	11	fulfilled	fulfil	VERB
ejpam-2339	258	12	.	.	PUNCT
ejpam-2339	259	1	by	by	ADP
ejpam-2339	259	2	theorem	theorem	NOUN
ejpam-2339	259	3	1	1	NUM
ejpam-2339	259	4	we	we	PRON
ejpam-2339	259	5	have	have	VERB
ejpam-2339	259	6	ϕw(d)ϕw(d	ϕw(d)ϕw(d	X
ejpam-2339	259	7	−1	−1	NOUN
ejpam-2339	259	8	)	)	PUNCT
ejpam-2339	259	9	=	=	NOUN
ejpam-2339	259	10	|ϕw(d)|	|ϕw(d)|	NOUN
ejpam-2339	259	11	2	2	NUM
ejpam-2339	259	12	=	=	SYM
ejpam-2339	259	13	u2	u2	NOUN
ejpam-2339	259	14	,	,	PUNCT
ejpam-2339	259	15	for	for	ADP
ejpam-2339	259	16	every	every	DET
ejpam-2339	259	17	nontrivial	nontrivial	NOUN
ejpam-2339	259	18	ϕw	ϕw	NOUN
ejpam-2339	259	19	,	,	PUNCT
ejpam-2339	259	20	i.e.	i.e.	X
ejpam-2339	259	21	for	for	ADP
ejpam-2339	259	22	w	w	NOUN
ejpam-2339	259	23	=	=	SYM
ejpam-2339	259	24	1,2	1,2	NUM
ejpam-2339	259	25	,	,	PUNCT
ejpam-2339	259	26	.	.	PUNCT
ejpam-2339	259	27	.	.	PUNCT
ejpam-2339	260	1	.	.	PUNCT
ejpam-2339	261	1	,	,	PUNCT
ejpam-2339	261	2	2t−p	2t−p	INTJ
ejpam-2339	261	3	−	−	NOUN
ejpam-2339	261	4	1	1	X
ejpam-2339	261	5	.	.	PUNCT
ejpam-2339	262	1	hence	hence	ADV
ejpam-2339	262	2	ϕw(d	ϕw(d	PUNCT
ejpam-2339	262	3	)	)	PUNCT
ejpam-2339	262	4	=	=	PUNCT
ejpam-2339	263	1	∑a	∑a	NOUN
ejpam-2339	263	2	i=1	i=1	PRON
ejpam-2339	264	1	ǫ	ǫ	DET
ejpam-2339	264	2	2pwni	2pwni	NUM
ejpam-2339	264	3	+	+	CCONJ
ejpam-2339	264	4	∑r	∑r	PROPN
ejpam-2339	264	5	j=1	j=1	PROPN
ejpam-2339	264	6	�	�	PROPN
ejpam-2339	265	1	∑t	∑t	PROPN
ejpam-2339	265	2	j	j	PROPN
ejpam-2339	266	1	s=1	s=1	PUNCT
ejpam-2339	266	2	ǫ2pwm	ǫ2pwm	NUM
ejpam-2339	266	3	j	j	PROPN
ejpam-2339	266	4	�	�	PROPN
ejpam-2339	266	5	is	be	AUX
ejpam-2339	266	6	norm	norm	ADJ
ejpam-2339	266	7	invariant	invariant	ADJ
ejpam-2339	266	8	polynomial	polynomial	NOUN
ejpam-2339	266	9	of	of	ADP
ejpam-2339	266	10	norm	norm	NOUN
ejpam-2339	267	1	u.	u.	PROPN
ejpam-2339	267	2	therefore	therefore	ADV
ejpam-2339	267	3	,	,	PUNCT
ejpam-2339	267	4	by	by	ADP
ejpam-2339	267	5	theorem	theorem	NOUN
ejpam-2339	267	6	5	5	NUM
ejpam-2339	267	7	,	,	PUNCT
ejpam-2339	267	8	for	for	ADP
ejpam-2339	267	9	every	every	DET
ejpam-2339	267	10	w=	w=	NOUN
ejpam-2339	267	11	1,2	1,2	NUM
ejpam-2339	267	12	,	,	PUNCT
ejpam-2339	267	13	.	.	PUNCT
ejpam-2339	267	14	.	.	PUNCT
ejpam-2339	268	1	.	.	PUNCT
ejpam-2339	269	1	,	,	PUNCT
ejpam-2339	269	2	2t−p−1	2t−p−1	NUM
ejpam-2339	269	3	there	there	PRON
ejpam-2339	269	4	is	be	VERB
ejpam-2339	269	5	some	some	DET
ejpam-2339	269	6	rw	rw	NOUN
ejpam-2339	269	7	∈	∈	PROPN
ejpam-2339	269	8	z	z	NOUN
ejpam-2339	269	9	such	such	ADJ
ejpam-2339	269	10	that	that	SCONJ
ejpam-2339	269	11	ϕw(d	ϕw(d	PUNCT
ejpam-2339	269	12	)	)	PUNCT
ejpam-2339	269	13	=	=	PUNCT
ejpam-2339	270	1	∑a	∑a	NOUN
ejpam-2339	270	2	i=1	i=1	PRON
ejpam-2339	271	1	ǫ	ǫ	DET
ejpam-2339	271	2	2pwni	2pwni	NUM
ejpam-2339	271	3	+	+	CCONJ
ejpam-2339	271	4	∑r	∑r	PROPN
ejpam-2339	271	5	j=1	j=1	PROPN
ejpam-2339	271	6	�	�	PROPN
ejpam-2339	272	1	∑t	∑t	PROPN
ejpam-2339	272	2	j	j	PROPN
ejpam-2339	273	1	s=1	s=1	X
ejpam-2339	273	2	ǫ2pwm	ǫ2pwm	NUM
ejpam-2339	273	3	j	j	PROPN
ejpam-2339	273	4	�	�	PROPN
ejpam-2339	273	5	=	=	SYM
ejpam-2339	273	6	uǫ2p	uǫ2p	PROPN
ejpam-2339	273	7	rw	rw	NOUN
ejpam-2339	273	8	.	.	PUNCT
ejpam-2339	274	1	then	then	ADV
ejpam-2339	274	2	,	,	PUNCT
ejpam-2339	274	3	by	by	ADP
ejpam-2339	274	4	theorem	theorem	NOUN
ejpam-2339	274	5	2	2	NUM
ejpam-2339	274	6	,	,	PUNCT
ejpam-2339	274	7	in	in	ADP
ejpam-2339	274	8	a	a	DET
ejpam-2339	274	9	sum	sum	NOUN
ejpam-2339	274	10	ϕ1(d	ϕ1(d	NOUN
ejpam-2339	274	11	)	)	PUNCT
ejpam-2339	274	12	=	=	SYM
ejpam-2339	275	1	∑r	∑r	PROPN
ejpam-2339	275	2	j=0ϕ1(d	j=0ϕ1(d	ADJ
ejpam-2339	275	3	∩	∩	NOUN
ejpam-2339	275	4	〈	〈	PROPN
ejpam-2339	275	5	x〉g	x〉g	PROPN
ejpam-2339	275	6	j	j	PROPN
ejpam-2339	275	7	)	)	PUNCT
ejpam-2339	276	1	we	we	PRON
ejpam-2339	276	2	must	must	AUX
ejpam-2339	276	3	have	have	VERB
ejpam-2339	276	4	u	u	PROPN
ejpam-2339	276	5	addends	addend	VERB
ejpam-2339	276	6	ǫ2p	ǫ2p	NUM
ejpam-2339	276	7	r1	r1	PROPN
ejpam-2339	276	8	distributed	distribute	VERB
ejpam-2339	276	9	over	over	ADP
ejpam-2339	276	10	r	r	NOUN
ejpam-2339	276	11	+	+	CCONJ
ejpam-2339	276	12	1	1	NUM
ejpam-2339	276	13	classes	class	NOUN
ejpam-2339	276	14	.	.	PUNCT
ejpam-2339	277	1	this	this	PRON
ejpam-2339	277	2	could	could	AUX
ejpam-2339	277	3	be	be	AUX
ejpam-2339	277	4	interpreted	interpret	VERB
ejpam-2339	277	5	is	be	AUX
ejpam-2339	277	6	of	of	ADP
ejpam-2339	277	7	u	u	NOUN
ejpam-2339	277	8	copies	copy	NOUN
ejpam-2339	277	9	(	(	PUNCT
ejpam-2339	277	10	items	item	NOUN
ejpam-2339	277	11	or	or	CCONJ
ejpam-2339	277	12	objects	object	NOUN
ejpam-2339	277	13	)	)	PUNCT
ejpam-2339	277	14	of	of	ADP
ejpam-2339	277	15	ǫ2p	ǫ2p	NUM
ejpam-2339	277	16	r1	r1	PROPN
ejpam-2339	277	17	are	be	AUX
ejpam-2339	277	18	distributed	distribute	VERB
ejpam-2339	277	19	over	over	ADP
ejpam-2339	277	20	r	r	NOUN
ejpam-2339	277	21	+	+	CCONJ
ejpam-2339	277	22	1	1	NUM
ejpam-2339	277	23	boxes	box	NOUN
ejpam-2339	277	24	.	.	PUNCT
ejpam-2339	278	1	then	then	ADV
ejpam-2339	278	2	we	we	PRON
ejpam-2339	278	3	can	can	AUX
ejpam-2339	278	4	use	use	VERB
ejpam-2339	278	5	dirichlet	dirichlet	PROPN
ejpam-2339	278	6	’s	’s	PART
ejpam-2339	278	7	principle	principle	NOUN
ejpam-2339	278	8	.	.	PUNCT
ejpam-2339	279	1	number	number	NOUN
ejpam-2339	279	2	of	of	ADP
ejpam-2339	279	3	boxes	box	NOUN
ejpam-2339	279	4	should	should	AUX
ejpam-2339	279	5	be	be	AUX
ejpam-2339	279	6	[	[	X
ejpam-2339	279	7	g	g	NOUN
ejpam-2339	279	8	:	:	PUNCT
ejpam-2339	279	9	〈	〈	NOUN
ejpam-2339	279	10	x	x	X
ejpam-2339	279	11	〉	〉	NOUN
ejpam-2339	279	12	]	]	PUNCT
ejpam-2339	279	13	=	=	SYM
ejpam-2339	279	14	22d+2−tu2	22d+2−tu2	NUM
ejpam-2339	279	15	1	1	NUM
ejpam-2339	279	16	.	.	PUNCT
ejpam-2339	279	17	by	by	ADP
ejpam-2339	279	18	dirichlet	dirichlet	PROPN
ejpam-2339	279	19	’s	’s	PART
ejpam-2339	279	20	principle	principle	NOUN
ejpam-2339	279	21	,	,	PUNCT
ejpam-2339	279	22	there	there	PRON
ejpam-2339	279	23	is	be	VERB
ejpam-2339	279	24	some	some	DET
ejpam-2339	279	25	j′	j′	NUM
ejpam-2339	279	26	∈	∈	PROPN
ejpam-2339	279	27	{	{	PUNCT
ejpam-2339	279	28	0,1	0,1	NOUN
ejpam-2339	279	29	,	,	PUNCT
ejpam-2339	279	30	.	.	PUNCT
ejpam-2339	279	31	.	.	PUNCT
ejpam-2339	280	1	.	.	PUNCT
ejpam-2339	281	1	,	,	PUNCT
ejpam-2339	281	2	r	r	X
ejpam-2339	281	3	}	}	PUNCT
ejpam-2339	281	4	such	such	ADJ
ejpam-2339	281	5	that	that	SCONJ
ejpam-2339	281	6	ϕ1(d∩	ϕ1(d∩	ADJ
ejpam-2339	281	7	〈	〈	PROPN
ejpam-2339	281	8	x〉g	x〉g	PROPN
ejpam-2339	281	9	j′	j′	PROPN
ejpam-2339	281	10	)	)	PUNCT
ejpam-2339	281	11	has	have	VERB
ejpam-2339	281	12	ω	ω	PROPN
ejpam-2339	281	13	copies	copy	NOUN
ejpam-2339	281	14	of	of	ADP
ejpam-2339	281	15	ǫ2p	ǫ2p	PROPN
ejpam-2339	281	16	r1	r1	PROPN
ejpam-2339	281	17	.	.	PUNCT
ejpam-2339	282	1	we	we	PRON
ejpam-2339	282	2	estimate	estimate	VERB
ejpam-2339	282	3	value	value	NOUN
ejpam-2339	282	4	for	for	ADP
ejpam-2339	282	5	ω	ω	NUM
ejpam-2339	282	6	as	as	SCONJ
ejpam-2339	282	7	follows	follow	VERB
ejpam-2339	282	8	:	:	PUNCT
ejpam-2339	282	9	ω	ω	NUM
ejpam-2339	282	10	=	=	SYM
ejpam-2339	282	11	�	�	PROPN
ejpam-2339	282	12	u−	u−	PROPN
ejpam-2339	282	13	1	1	NUM
ejpam-2339	282	14	22d+2−tu2	22d+2−tu2	NUM
ejpam-2339	282	15	1	1	NUM
ejpam-2339	282	16	�	�	PROPN
ejpam-2339	282	17	+	+	CCONJ
ejpam-2339	282	18	1=	1=	NUM
ejpam-2339	282	19	�	�	NOUN
ejpam-2339	282	20	2du1	2du1	NUM
ejpam-2339	282	21	−	−	NUM
ejpam-2339	282	22	1	1	NUM
ejpam-2339	282	23	22d+2−tu2	22d+2−tu2	NUM
ejpam-2339	282	24	1	1	NUM
ejpam-2339	282	25	�	�	PROPN
ejpam-2339	282	26	+	+	CCONJ
ejpam-2339	282	27	1≥	1≥	NUM
ejpam-2339	282	28	�	�	PROPN
ejpam-2339	282	29	2du1	2du1	NUM
ejpam-2339	282	30	22d+2−tu2	22d+2−tu2	NUM
ejpam-2339	282	31	1	1	NUM
ejpam-2339	282	32	�	�	NOUN
ejpam-2339	282	33	−	−	ADP
ejpam-2339	282	34	1	1	NUM
ejpam-2339	282	35	+	+	NUM
ejpam-2339	282	36	1	1	NUM
ejpam-2339	282	37	=	=	SYM
ejpam-2339	282	38	�	�	PROPN
ejpam-2339	282	39	2t−d−2	2t−d−2	NUM
ejpam-2339	282	40	u1	u1	NOUN
ejpam-2339	282	41	�	�	PROPN
ejpam-2339	282	42	=	=	PUNCT
ejpam-2339	282	43	{	{	PUNCT
ejpam-2339	282	44	since	since	SCONJ
ejpam-2339	282	45	2	2	NUM
ejpam-2339	282	46	t	t	NOUN
ejpam-2339	282	47	≥	≥	NOUN
ejpam-2339	282	48	2p+3u=	2p+3u=	NUM
ejpam-2339	282	49	2p+32du1}=	2p+32du1}=	NUM
ejpam-2339	282	50	�	�	PROPN
ejpam-2339	282	51	2	2	NUM
ejpam-2339	282	52	t	t	NOUN
ejpam-2339	282	53	·	·	PUNCT
ejpam-2339	282	54	2−d−2	2−d−2	NUM
ejpam-2339	282	55	u1	u1	PROPN
ejpam-2339	282	56	�	�	PROPN
ejpam-2339	282	57	≥	≥	NUM
ejpam-2339	282	58	�	�	PROPN
ejpam-2339	282	59	2p+32du12−d−2	2p+32du12−d−2	NUM
ejpam-2339	282	60	u1	u1	NOUN
ejpam-2339	282	61	�	�	PROPN
ejpam-2339	282	62	=	=	SYM
ejpam-2339	282	63	2p+1	2p+1	PROPN
ejpam-2339	282	64	.	.	PUNCT
ejpam-2339	283	1	therefore	therefore	ADV
ejpam-2339	283	2	,	,	PUNCT
ejpam-2339	283	3	ω	ω	PROPN
ejpam-2339	283	4	≥	≥	NOUN
ejpam-2339	283	5	2p+1	2p+1	NUM
ejpam-2339	283	6	.	.	PUNCT
ejpam-2339	284	1	before	before	SCONJ
ejpam-2339	284	2	we	we	PRON
ejpam-2339	284	3	get	get	VERB
ejpam-2339	284	4	a	a	DET
ejpam-2339	284	5	final	final	ADJ
ejpam-2339	284	6	contradiction	contradiction	NOUN
ejpam-2339	284	7	,	,	PUNCT
ejpam-2339	284	8	additional	additional	ADJ
ejpam-2339	284	9	observation	observation	NOUN
ejpam-2339	284	10	is	be	AUX
ejpam-2339	284	11	necessary	necessary	ADJ
ejpam-2339	284	12	.	.	PUNCT
ejpam-2339	285	1	we	we	PRON
ejpam-2339	285	2	have	have	VERB
ejpam-2339	285	3	(	(	PUNCT
ejpam-2339	285	4	ϕ1|〈x	ϕ1|〈x	NOUN
ejpam-2339	285	5	〉	〉	NOUN
ejpam-2339	285	6	)	)	PUNCT
ejpam-2339	285	7	−1(ǫ2p	−1(ǫ2p	NOUN
ejpam-2339	285	8	r1	r1	NOUN
ejpam-2339	285	9	)	)	PUNCT
ejpam-2339	285	10	=	=	PRON
ejpam-2339	286	1	{	{	PUNCT
ejpam-2339	286	2	x	x	INTJ
ejpam-2339	287	1	i	i	PRON
ejpam-2339	287	2	|	|	ADV
ejpam-2339	287	3	ϕ1(x	ϕ1(x	VERB
ejpam-2339	287	4	i	i	NOUN
ejpam-2339	287	5	)	)	PUNCT
ejpam-2339	287	6	=	=	SYM
ejpam-2339	287	7	ǫ2p	ǫ2p	NUM
ejpam-2339	287	8	r1}=	r1}=	NUM
ejpam-2339	287	9	{	{	PUNCT
ejpam-2339	287	10	x	x	NOUN
ejpam-2339	287	11	i	i	PRON
ejpam-2339	287	12	|	|	ADV
ejpam-2339	287	13	ǫ2p	ǫ2p	NUM
ejpam-2339	288	1	i	i	NOUN
ejpam-2339	288	2	=	=	PROPN
ejpam-2339	288	3	ǫ2p	ǫ2p	NUM
ejpam-2339	288	4	r1	r1	NOUN
ejpam-2339	288	5	}	}	PUNCT
ejpam-2339	288	6	=	=	NOUN
ejpam-2339	288	7	{	{	PUNCT
ejpam-2339	288	8	x	x	NOUN
ejpam-2339	288	9	i	i	PRON
ejpam-2339	288	10	|	|	ADV
ejpam-2339	288	11	ǫ2p(i−r1	ǫ2p(i−r1	X
ejpam-2339	288	12	)	)	PUNCT
ejpam-2339	288	13	=	=	SYM
ejpam-2339	289	1	1}=	1}=	NUM
ejpam-2339	289	2	{	{	PUNCT
ejpam-2339	289	3	x	x	NOUN
ejpam-2339	290	1	i	i	PRON
ejpam-2339	290	2	|	|	ADV
ejpam-2339	290	3	ϕ1(x	ϕ1(x	INTJ
ejpam-2339	290	4	i−r1	i−r1	NOUN
ejpam-2339	290	5	)	)	PUNCT
ejpam-2339	290	6	=	=	SYM
ejpam-2339	291	1	1}=	1}=	NUM
ejpam-2339	291	2	x	x	PROPN
ejpam-2339	291	3	r1	r1	PROPN
ejpam-2339	291	4	ker(ϕ1	ker(ϕ1	PROPN
ejpam-2339	291	5	)	)	PUNCT
ejpam-2339	291	6	.	.	PUNCT
ejpam-2339	292	1	hence	hence	ADV
ejpam-2339	292	2	,	,	PUNCT
ejpam-2339	292	3	2p+1	2p+1	PROPN
ejpam-2339	292	4	≤|{i	≤|{i	VERB
ejpam-2339	292	5	|	|	ADV
ejpam-2339	292	6	0≤	0≤	ADP
ejpam-2339	293	1	i	i	PRON
ejpam-2339	293	2	<	<	X
ejpam-2339	293	3	2	2	NUM
ejpam-2339	293	4	t	t	NOUN
ejpam-2339	293	5	,	,	PUNCT
ejpam-2339	293	6	ϕ1(x	ϕ1(x	VERB
ejpam-2339	294	1	i	i	PRON
ejpam-2339	294	2	g	g	PROPN
ejpam-2339	294	3	j′	j′	PROPN
ejpam-2339	294	4	)	)	PUNCT
ejpam-2339	295	1	=	=	PUNCT
ejpam-2339	295	2	ǫ	ǫ	DET
ejpam-2339	295	3	2p	2p	NUM
ejpam-2339	295	4	r1}|	r1}|	X
ejpam-2339	296	1	=	=	PRON
ejpam-2339	296	2	|{i	|{i	PUNCT
ejpam-2339	296	3	|	|	ADV
ejpam-2339	296	4	0≤	0≤	ADP
ejpam-2339	296	5	i	i	PRON
ejpam-2339	296	6	<	<	X
ejpam-2339	296	7	2	2	NUM
ejpam-2339	296	8	t	t	NOUN
ejpam-2339	296	9	,	,	PUNCT
ejpam-2339	296	10	ϕ1(x	ϕ1(x	PROPN
ejpam-2339	296	11	i	i	NOUN
ejpam-2339	296	12	)	)	PUNCT
ejpam-2339	296	13	=	=	PUNCT
ejpam-2339	297	1	ǫ2p	ǫ2p	NUM
ejpam-2339	297	2	r1}|	r1}|	NOUN
ejpam-2339	297	3	=	=	SYM
ejpam-2339	297	4	|(ϕ1|〈x	|(ϕ1|〈x	NOUN
ejpam-2339	297	5	〉	〉	NOUN
ejpam-2339	297	6	)	)	PUNCT
ejpam-2339	297	7	−1(ǫ2p	−1(ǫ2p	NOUN
ejpam-2339	297	8	r1)|	r1)|	PROPN
ejpam-2339	297	9	=	=	PROPN
ejpam-2339	297	10	|ker(ϕ1|〈x〉)|	|ker(ϕ1|〈x〉)|	X
ejpam-2339	297	11	=	=	NOUN
ejpam-2339	297	12	2p	2p	NOUN
ejpam-2339	297	13	,	,	PUNCT
ejpam-2339	297	14	which	which	PRON
ejpam-2339	297	15	is	be	AUX
ejpam-2339	297	16	an	an	DET
ejpam-2339	297	17	obvious	obvious	ADJ
ejpam-2339	297	18	contradiction	contradiction	NOUN
ejpam-2339	297	19	.	.	PUNCT
ejpam-2339	298	1	4	4	X
ejpam-2339	298	2	.	.	X
ejpam-2339	298	3	one	one	NUM
ejpam-2339	298	4	infinite	infinite	ADJ
ejpam-2339	298	5	series	series	NOUN
ejpam-2339	298	6	of	of	ADP
ejpam-2339	298	7	groups	group	NOUN
ejpam-2339	298	8	for	for	ADP
ejpam-2339	298	9	modular	modular	ADJ
ejpam-2339	298	10	case	case	NOUN
ejpam-2339	298	11	we	we	PRON
ejpam-2339	298	12	construct	construct	VERB
ejpam-2339	298	13	one	one	NUM
ejpam-2339	298	14	example	example	NOUN
ejpam-2339	298	15	of	of	ADP
ejpam-2339	298	16	infinite	infinite	ADJ
ejpam-2339	298	17	series	series	NOUN
ejpam-2339	298	18	of	of	ADP
ejpam-2339	298	19	groups	group	NOUN
ejpam-2339	298	20	that	that	PRON
ejpam-2339	298	21	can	can	AUX
ejpam-2339	298	22	be	be	AUX
ejpam-2339	298	23	covered	cover	VERB
ejpam-2339	298	24	by	by	ADP
ejpam-2339	298	25	previous	previous	ADJ
ejpam-2339	298	26	result	result	NOUN
ejpam-2339	298	27	.	.	PUNCT
ejpam-2339	299	1	take	take	VERB
ejpam-2339	299	2	g	g	NOUN
ejpam-2339	299	3	=	=	PUNCT
ejpam-2339	299	4	h	h	NOUN
ejpam-2339	299	5	×	×	PROPN
ejpam-2339	299	6	l	l	NOUN
ejpam-2339	299	7	,	,	PUNCT
ejpam-2339	299	8	where	where	SCONJ
ejpam-2339	299	9	h	h	NOUN
ejpam-2339	299	10	=	=	SYM
ejpam-2339	299	11	〈	〈	PROPN
ejpam-2339	299	12	x	x	SYM
ejpam-2339	299	13	,	,	PUNCT
ejpam-2339	299	14	y1	y1	PROPN
ejpam-2339	299	15	,	,	PUNCT
ejpam-2339	299	16	y2	y2	PROPN
ejpam-2339	299	17	|	|	ADV
ejpam-2339	299	18	x	x	SYM
ejpam-2339	299	19	22t1	22t1	NUM
ejpam-2339	299	20	=	=	NOUN
ejpam-2339	299	21	y23	y23	NOUN
ejpam-2339	299	22	=	=	NOUN
ejpam-2339	299	23	y23	y23	NOUN
ejpam-2339	299	24	2	2	NUM
ejpam-2339	299	25	=	=	SYM
ejpam-2339	299	26	1	1	NUM
ejpam-2339	299	27	,	,	PUNCT
ejpam-2339	299	28	x	x	PUNCT
ejpam-2339	299	29	y1	y1	NOUN
ejpam-2339	299	30	=	=	PUNCT
ejpam-2339	299	31	x	x	PUNCT
ejpam-2339	299	32	y2	y2	NOUN
ejpam-2339	299	33	=	=	SYM
ejpam-2339	300	1	x22t1−1	x22t1−1	PROPN
ejpam-2339	300	2	+	+	NOUN
ejpam-2339	300	3	1	1	NUM
ejpam-2339	300	4	,	,	PUNCT
ejpam-2339	300	5	[	[	X
ejpam-2339	300	6	y1	y1	X
ejpam-2339	300	7	,	,	PUNCT
ejpam-2339	300	8	y2	y2	NOUN
ejpam-2339	300	9	]	]	PUNCT
ejpam-2339	300	10	=	=	SYM
ejpam-2339	300	11	x22t1−4	x22t1−4	PROPN
ejpam-2339	300	12	〉	〉	NOUN
ejpam-2339	300	13	.	.	PUNCT
ejpam-2339	301	1	k.tabak	k.tabak	ADJ
ejpam-2339	301	2	/	/	SYM
ejpam-2339	301	3	eur	eur	PROPN
ejpam-2339	301	4	.	.	PUNCT
ejpam-2339	302	1	j.	j.	PROPN
ejpam-2339	302	2	pure	pure	PROPN
ejpam-2339	302	3	appl	appl	PROPN
ejpam-2339	302	4	.	.	PROPN
ejpam-2339	302	5	math	math	PROPN
ejpam-2339	302	6	,	,	PUNCT
ejpam-2339	302	7	8	8	NUM
ejpam-2339	302	8	(	(	PUNCT
ejpam-2339	302	9	2015	2015	NUM
ejpam-2339	302	10	)	)	PUNCT
ejpam-2339	302	11	,	,	PUNCT
ejpam-2339	302	12	450	450	NUM
ejpam-2339	302	13	-	-	SYM
ejpam-2339	302	14	457	457	NUM
ejpam-2339	302	15	456	456	NUM
ejpam-2339	302	16	l	l	NOUN
ejpam-2339	302	17	could	could	AUX
ejpam-2339	302	18	be	be	AUX
ejpam-2339	302	19	any	any	DET
ejpam-2339	302	20	group	group	NOUN
ejpam-2339	302	21	of	of	ADP
ejpam-2339	302	22	order	order	NOUN
ejpam-2339	302	23	u2	u2	PROPN
ejpam-2339	302	24	1	1	NUM
ejpam-2339	302	25	.	.	PUNCT
ejpam-2339	303	1	then	then	ADV
ejpam-2339	303	2	|h|=	|h|=	NOUN
ejpam-2339	303	3	22t1	22t1	NUM
ejpam-2339	303	4	+	+	NOUN
ejpam-2339	303	5	6	6	NUM
ejpam-2339	303	6	=	=	SYM
ejpam-2339	303	7	22d+2	22d+2	NUM
ejpam-2339	303	8	,	,	PUNCT
ejpam-2339	303	9	where	where	SCONJ
ejpam-2339	303	10	t1	t1	NOUN
ejpam-2339	303	11	=	=	SYM
ejpam-2339	304	1	d−2	d−2	PROPN
ejpam-2339	304	2	.	.	PUNCT
ejpam-2339	305	1	put	put	VERB
ejpam-2339	305	2	|g|=	|g|=	NOUN
ejpam-2339	305	3	4u2	4u2	PROPN
ejpam-2339	305	4	,	,	PUNCT
ejpam-2339	305	5	where	where	SCONJ
ejpam-2339	305	6	u	u	NOUN
ejpam-2339	305	7	=	=	NOUN
ejpam-2339	305	8	2du1	2du1	NUM
ejpam-2339	305	9	.	.	PUNCT
ejpam-2339	306	1	let	let	VERB
ejpam-2339	306	2	’s	’s	PRON
ejpam-2339	306	3	take	take	VERB
ejpam-2339	306	4	p	p	NOUN
ejpam-2339	306	5	=	=	NOUN
ejpam-2339	306	6	4	4	X
ejpam-2339	306	7	.	.	PUNCT
ejpam-2339	307	1	then	then	ADV
ejpam-2339	307	2	we	we	PRON
ejpam-2339	307	3	have	have	VERB
ejpam-2339	307	4	[	[	X
ejpam-2339	307	5	x	x	X
ejpam-2339	307	6	,	,	PUNCT
ejpam-2339	307	7	yi	yi	NOUN
ejpam-2339	307	8	]	]	X
ejpam-2339	308	1	=	=	PUNCT
ejpam-2339	308	2	x−1	x−1	PUNCT
ejpam-2339	308	3	x	x	PUNCT
ejpam-2339	308	4	yi	yi	PROPN
ejpam-2339	308	5	=	=	PUNCT
ejpam-2339	308	6	x22t1−1	x22t1−1	PROPN
ejpam-2339	308	7	∈	∈	PROPN
ejpam-2339	308	8	〈	〈	NOUN
ejpam-2339	308	9	x22t1−4	x22t1−4	PROPN
ejpam-2339	308	10	〉	〉	NOUN
ejpam-2339	308	11	.	.	PUNCT
ejpam-2339	309	1	therefore	therefore	ADV
ejpam-2339	309	2	h	h	NOUN
ejpam-2339	309	3	′	′	NOUN
ejpam-2339	309	4	≤	≤	PUNCT
ejpam-2339	310	1	〈	〈	ADP
ejpam-2339	310	2	x22t1−4	x22t1−4	NOUN
ejpam-2339	310	3	〉	〉	NOUN
ejpam-2339	310	4	=	=	SYM
ejpam-2339	310	5	〈	〈	PROPN
ejpam-2339	310	6	x22t1−p	x22t1−p	PUNCT
ejpam-2339	310	7	〉	〉	NOUN
ejpam-2339	310	8	.	.	PUNCT
ejpam-2339	311	1	additionally	additionally	ADV
ejpam-2339	311	2	,	,	PUNCT
ejpam-2339	311	3	if	if	SCONJ
ejpam-2339	311	4	we	we	PRON
ejpam-2339	311	5	put	put	VERB
ejpam-2339	311	6	2t1	2t1	NUM
ejpam-2339	311	7	≥	≥	NOUN
ejpam-2339	311	8	29u1	29u1	NUM
ejpam-2339	311	9	,	,	PUNCT
ejpam-2339	311	10	using	use	VERB
ejpam-2339	311	11	t1	t1	NOUN
ejpam-2339	311	12	=	=	PUNCT
ejpam-2339	312	1	d	d	NOUN
ejpam-2339	312	2	−	−	PROPN
ejpam-2339	312	3	2	2	NUM
ejpam-2339	312	4	,	,	PUNCT
ejpam-2339	312	5	we	we	PRON
ejpam-2339	312	6	get	get	VERB
ejpam-2339	312	7	22d−4	22d−4	NUM
ejpam-2339	312	8	≥	≥	NOUN
ejpam-2339	312	9	2d	2d	NUM
ejpam-2339	312	10	·	·	PUNCT
ejpam-2339	313	1	27u1	27u1	NUM
ejpam-2339	313	2	=	=	SYM
ejpam-2339	313	3	2p+3u	2p+3u	NUM
ejpam-2339	313	4	.	.	PUNCT
ejpam-2339	314	1	therefore	therefore	ADV
ejpam-2339	314	2	,	,	PUNCT
ejpam-2339	314	3	we	we	PRON
ejpam-2339	314	4	are	be	AUX
ejpam-2339	314	5	within	within	ADP
ejpam-2339	314	6	conditions	condition	NOUN
ejpam-2339	314	7	of	of	ADP
ejpam-2339	314	8	theorem	theorem	NOUN
ejpam-2339	314	9	6	6	NUM
ejpam-2339	314	10	.	.	PUNCT
ejpam-2339	315	1	for	for	ADP
ejpam-2339	315	2	example	example	NOUN
ejpam-2339	315	3	,	,	PUNCT
ejpam-2339	315	4	u1	u1	PROPN
ejpam-2339	315	5	=	=	SYM
ejpam-2339	315	6	36	36	NUM
ejpam-2339	315	7	,	,	PUNCT
ejpam-2339	315	8	t1	t1	NOUN
ejpam-2339	315	9	=	=	SYM
ejpam-2339	315	10	15	15	NUM
ejpam-2339	315	11	,	,	PUNCT
ejpam-2339	315	12	p	p	NOUN
ejpam-2339	315	13	=	=	NOUN
ejpam-2339	315	14	4	4	NUM
ejpam-2339	315	15	and	and	CCONJ
ejpam-2339	315	16	d	d	NOUN
ejpam-2339	315	17	=	=	SYM
ejpam-2339	315	18	17	17	NUM
ejpam-2339	315	19	.	.	PUNCT
ejpam-2339	316	1	then	then	ADV
ejpam-2339	316	2	2t1	2t1	NUM
ejpam-2339	317	1	=	=	SYM
ejpam-2339	317	2	215	215	NUM
ejpam-2339	317	3	=	=	SYM
ejpam-2339	317	4	32768	32768	NUM
ejpam-2339	317	5	>	>	X
ejpam-2339	317	6	29u1	29u1	NUM
ejpam-2339	317	7	=	=	SYM
ejpam-2339	317	8	18432	18432	NUM
ejpam-2339	317	9	.	.	PUNCT
ejpam-2339	318	1	in	in	ADP
ejpam-2339	318	2	that	that	DET
ejpam-2339	318	3	case	case	NOUN
ejpam-2339	318	4	group	group	NOUN
ejpam-2339	318	5	order	order	NOUN
ejpam-2339	318	6	would	would	AUX
ejpam-2339	318	7	be	be	AUX
ejpam-2339	318	8	|g|=	|g|=	VERB
ejpam-2339	318	9	22d+2u2	22d+2u2	NUM
ejpam-2339	318	10	1	1	NUM
ejpam-2339	318	11	=	=	SYM
ejpam-2339	318	12	236	236	NUM
ejpam-2339	318	13	·	·	SYM
ejpam-2339	318	14	362	362	NUM
ejpam-2339	318	15	.	.	PUNCT
ejpam-2339	319	1	5	5	NUM
ejpam-2339	319	2	.	.	PUNCT
ejpam-2339	319	3	dihedral	dihedral	ADJ
ejpam-2339	319	4	case	case	NOUN
ejpam-2339	319	5	this	this	DET
ejpam-2339	319	6	section	section	NOUN
ejpam-2339	319	7	covers	cover	VERB
ejpam-2339	319	8	types	type	NOUN
ejpam-2339	319	9	of	of	ADP
ejpam-2339	319	10	groups	group	NOUN
ejpam-2339	319	11	of	of	ADP
ejpam-2339	319	12	order	order	NOUN
ejpam-2339	319	13	4u2	4u2	NUM
ejpam-2339	319	14	which	which	PRON
ejpam-2339	319	15	also	also	ADV
ejpam-2339	319	16	contain	contain	VERB
ejpam-2339	319	17	a	a	DET
ejpam-2339	319	18	2	2	NUM
ejpam-2339	319	19	-	-	PUNCT
ejpam-2339	319	20	subgroup	subgroup	NOUN
ejpam-2339	319	21	of	of	ADP
ejpam-2339	319	22	dihedral	dihedral	ADJ
ejpam-2339	319	23	type	type	NOUN
ejpam-2339	319	24	.	.	PUNCT
ejpam-2339	320	1	this	this	PRON
ejpam-2339	320	2	means	mean	VERB
ejpam-2339	320	3	that	that	SCONJ
ejpam-2339	320	4	2	2	NUM
ejpam-2339	320	5	-	-	PUNCT
ejpam-2339	320	6	subgroup	subgroup	NOUN
ejpam-2339	320	7	has	have	VERB
ejpam-2339	320	8	a	a	DET
ejpam-2339	320	9	normal	normal	ADJ
ejpam-2339	320	10	cyclic	cyclic	ADJ
ejpam-2339	320	11	subgroup	subgroup	NOUN
ejpam-2339	320	12	,	,	PUNCT
ejpam-2339	320	13	while	while	SCONJ
ejpam-2339	320	14	outer	outer	ADJ
ejpam-2339	320	15	elements	element	NOUN
ejpam-2339	320	16	either	either	CCONJ
ejpam-2339	320	17	commute	commute	VERB
ejpam-2339	320	18	or	or	CCONJ
ejpam-2339	320	19	invert	invert	NOUN
ejpam-2339	320	20	generator	generator	NOUN
ejpam-2339	320	21	of	of	ADP
ejpam-2339	320	22	that	that	DET
ejpam-2339	320	23	normal	normal	ADJ
ejpam-2339	320	24	subgroup	subgroup	NOUN
ejpam-2339	320	25	.	.	PUNCT
ejpam-2339	321	1	theorem	theorem	VERB
ejpam-2339	321	2	7	7	NUM
ejpam-2339	321	3	.	.	PUNCT
ejpam-2339	322	1	let	let	VERB
ejpam-2339	322	2	g	g	NOUN
ejpam-2339	322	3	=	=	PUNCT
ejpam-2339	323	1	h	h	NOUN
ejpam-2339	323	2	×	×	PROPN
ejpam-2339	323	3	l	l	NOUN
ejpam-2339	323	4	be	be	VERB
ejpam-2339	323	5	a	a	DET
ejpam-2339	323	6	group	group	NOUN
ejpam-2339	323	7	of	of	ADP
ejpam-2339	323	8	order	order	NOUN
ejpam-2339	323	9	4u2	4u2	NUM
ejpam-2339	323	10	and	and	CCONJ
ejpam-2339	323	11	|l|	|l|	NOUN
ejpam-2339	323	12	=	=	NOUN
ejpam-2339	323	13	u2	u2	PROPN
ejpam-2339	323	14	1	1	NUM
ejpam-2339	323	15	.	.	PUNCT
ejpam-2339	324	1	let	let	VERB
ejpam-2339	324	2	h	h	NOUN
ejpam-2339	324	3	=	=	PUNCT
ejpam-2339	324	4	〈	〈	PROPN
ejpam-2339	324	5	x	x	SYM
ejpam-2339	324	6	,	,	PUNCT
ejpam-2339	324	7	y1	y1	PROPN
ejpam-2339	324	8	,	,	PUNCT
ejpam-2339	324	9	.	.	PUNCT
ejpam-2339	324	10	.	.	PUNCT
ejpam-2339	325	1	.	.	PUNCT
ejpam-2339	326	1	,	,	PUNCT
ejpam-2339	326	2	ys	ys	NOUN
ejpam-2339	326	3	〉	〉	NOUN
ejpam-2339	326	4	has	have	VERB
ejpam-2339	326	5	order	order	NOUN
ejpam-2339	326	6	22d+2	22d+2	NUM
ejpam-2339	326	7	and	and	CCONJ
ejpam-2339	326	8	o(x	o(x	PROPN
ejpam-2339	326	9	)	)	PUNCT
ejpam-2339	326	10	=	=	PUNCT
ejpam-2339	327	1	2	2	NUM
ejpam-2339	327	2	t	t	NOUN
ejpam-2339	327	3	where	where	SCONJ
ejpam-2339	327	4	x	x	PUNCT
ejpam-2339	327	5	yi	yi	PROPN
ejpam-2339	327	6	∈	∈	PROPN
ejpam-2339	327	7	{	{	PUNCT
ejpam-2339	327	8	x	x	NOUN
ejpam-2339	327	9	,	,	PUNCT
ejpam-2339	327	10	x−1	x−1	PROPN
ejpam-2339	327	11	}	}	PUNCT
ejpam-2339	327	12	.	.	PUNCT
ejpam-2339	328	1	if	if	SCONJ
ejpam-2339	328	2	ch(x	ch(x	NUM
ejpam-2339	328	3	)	)	PUNCT
ejpam-2339	329	1	′	′	NUM
ejpam-2339	330	1	∩	∩	PROPN
ejpam-2339	330	2	〈	〈	NOUN
ejpam-2339	330	3	x	x	X
ejpam-2339	330	4	〉	〉	NOUN
ejpam-2339	330	5	≤	≤	NUM
ejpam-2339	330	6	〈	〈	PROPN
ejpam-2339	330	7	x2t−p	x2t−p	PROPN
ejpam-2339	330	8	〉	〉	NOUN
ejpam-2339	330	9	and	and	CCONJ
ejpam-2339	330	10	o(x	o(x	PROPN
ejpam-2339	330	11	)	)	PUNCT
ejpam-2339	330	12	≥	≥	NOUN
ejpam-2339	330	13	2p+3u	2p+3u	NUM
ejpam-2339	330	14	,	,	PUNCT
ejpam-2339	330	15	then	then	ADV
ejpam-2339	330	16	g	g	PROPN
ejpam-2339	330	17	is	be	AUX
ejpam-2339	330	18	not	not	PART
ejpam-2339	330	19	a	a	DET
ejpam-2339	330	20	hadamard	hadamard	ADJ
ejpam-2339	330	21	group	group	NOUN
ejpam-2339	330	22	.	.	PUNCT
ejpam-2339	331	1	proof	proof	NOUN
ejpam-2339	331	2	.	.	PUNCT
ejpam-2339	332	1	we	we	PRON
ejpam-2339	332	2	will	will	AUX
ejpam-2339	332	3	use	use	VERB
ejpam-2339	332	4	the	the	DET
ejpam-2339	332	5	same	same	ADJ
ejpam-2339	332	6	approach	approach	NOUN
ejpam-2339	332	7	as	as	ADP
ejpam-2339	332	8	in	in	ADP
ejpam-2339	332	9	proof	proof	NOUN
ejpam-2339	332	10	of	of	ADP
ejpam-2339	332	11	theorem	theorem	NOUN
ejpam-2339	332	12	6	6	NUM
ejpam-2339	332	13	.	.	PUNCT
ejpam-2339	333	1	let	let	VERB
ejpam-2339	333	2	us	we	PRON
ejpam-2339	333	3	assume	assume	VERB
ejpam-2339	333	4	that	that	SCONJ
ejpam-2339	333	5	g	g	PROPN
ejpam-2339	333	6	posses	posse	VERB
ejpam-2339	333	7	a	a	DET
ejpam-2339	333	8	difference	difference	NOUN
ejpam-2339	333	9	set	set	VERB
ejpam-2339	333	10	d	d	NOUN
ejpam-2339	333	11	with	with	ADP
ejpam-2339	333	12	parameters	parameter	NOUN
ejpam-2339	333	13	(	(	PUNCT
ejpam-2339	333	14	4u2	4u2	NUM
ejpam-2339	333	15	,	,	PUNCT
ejpam-2339	333	16	2u2	2u2	NUM
ejpam-2339	334	1	−	−	PROPN
ejpam-2339	334	2	u	u	NOUN
ejpam-2339	334	3	,	,	PUNCT
ejpam-2339	334	4	u2	u2	PROPN
ejpam-2339	334	5	−	−	PROPN
ejpam-2339	334	6	u	u	NOUN
ejpam-2339	334	7	)	)	PUNCT
ejpam-2339	334	8	.	.	PUNCT
ejpam-2339	335	1	this	this	DET
ejpam-2339	335	2	time	time	NOUN
ejpam-2339	335	3	,	,	PUNCT
ejpam-2339	335	4	we	we	PRON
ejpam-2339	335	5	will	will	AUX
ejpam-2339	335	6	have	have	VERB
ejpam-2339	335	7	to	to	PART
ejpam-2339	335	8	develop	develop	VERB
ejpam-2339	335	9	a	a	DET
ejpam-2339	335	10	2	2	NUM
ejpam-2339	335	11	-	-	PUNCT
ejpam-2339	335	12	dimensional	dimensional	ADJ
ejpam-2339	335	13	representations	representation	NOUN
ejpam-2339	335	14	.	.	PUNCT
ejpam-2339	336	1	like	like	INTJ
ejpam-2339	336	2	before	before	ADP
ejpam-2339	336	3	u	u	NOUN
ejpam-2339	336	4	=	=	NOUN
ejpam-2339	336	5	2du1	2du1	NUM
ejpam-2339	336	6	.	.	PUNCT
ejpam-2339	337	1	since	since	SCONJ
ejpam-2339	337	2	[	[	X
ejpam-2339	337	3	h	h	X
ejpam-2339	337	4	:	:	PUNCT
ejpam-2339	337	5	ch(x	ch(x	X
ejpam-2339	337	6	)	)	PUNCT
ejpam-2339	337	7	]	]	PUNCT
ejpam-2339	337	8	=	=	SYM
ejpam-2339	337	9	2	2	NUM
ejpam-2339	337	10	,	,	PUNCT
ejpam-2339	337	11	every	every	DET
ejpam-2339	337	12	h	h	NOUN
ejpam-2339	337	13	∈	∈	NOUN
ejpam-2339	337	14	h	h	NOUN
ejpam-2339	337	15	can	can	AUX
ejpam-2339	337	16	be	be	AUX
ejpam-2339	337	17	written	write	VERB
ejpam-2339	337	18	as	as	ADP
ejpam-2339	337	19	h	h	NOUN
ejpam-2339	337	20	=	=	PROPN
ejpam-2339	337	21	c	c	PROPN
ejpam-2339	337	22	ym	ym	PROPN
ejpam-2339	337	23	,	,	PUNCT
ejpam-2339	337	24	where	where	SCONJ
ejpam-2339	337	25	c	c	PROPN
ejpam-2339	337	26	∈	∈	PROPN
ejpam-2339	337	27	ch(x	ch(x	NOUN
ejpam-2339	337	28	)	)	PUNCT
ejpam-2339	337	29	and	and	CCONJ
ejpam-2339	337	30	m	m	PROPN
ejpam-2339	337	31	∈	∈	NOUN
ejpam-2339	337	32	{	{	PUNCT
ejpam-2339	337	33	0,1	0,1	NOUN
ejpam-2339	337	34	}	}	PUNCT
ejpam-2339	337	35	.	.	PUNCT
ejpam-2339	338	1	so	so	ADV
ejpam-2339	338	2	,	,	PUNCT
ejpam-2339	338	3	every	every	DET
ejpam-2339	338	4	g	g	PROPN
ejpam-2339	338	5	∈	∈	PROPN
ejpam-2339	338	6	g	g	PROPN
ejpam-2339	338	7	can	can	AUX
ejpam-2339	338	8	be	be	AUX
ejpam-2339	338	9	written	write	VERB
ejpam-2339	338	10	as	as	ADP
ejpam-2339	338	11	g	g	NOUN
ejpam-2339	338	12	=	=	NOUN
ejpam-2339	338	13	x	x	X
ejpam-2339	338	14	ic1	ic1	VERB
ejpam-2339	338	15	yml	yml	NOUN
ejpam-2339	338	16	,	,	PUNCT
ejpam-2339	338	17	where	where	SCONJ
ejpam-2339	338	18	c1	c1	PROPN
ejpam-2339	338	19	∈	∈	PROPN
ejpam-2339	338	20	ch(x	ch(x	PUNCT
ejpam-2339	338	21	)	)	PUNCT
ejpam-2339	338	22	\	\	PUNCT
ejpam-2339	339	1	〈	〈	PROPN
ejpam-2339	339	2	x	x	X
ejpam-2339	339	3	〉	〉	NOUN
ejpam-2339	339	4	and	and	CCONJ
ejpam-2339	339	5	l	l	NOUN
ejpam-2339	339	6	∈	∈	PROPN
ejpam-2339	339	7	l.	l.	NOUN
ejpam-2339	339	8	then	then	ADV
ejpam-2339	339	9	,	,	PUNCT
ejpam-2339	339	10	for	for	ADP
ejpam-2339	339	11	every	every	DET
ejpam-2339	339	12	w=	w=	NOUN
ejpam-2339	339	13	1,2	1,2	NUM
ejpam-2339	339	14	,	,	PUNCT
ejpam-2339	339	15	.	.	PUNCT
ejpam-2339	339	16	.	.	PUNCT
ejpam-2339	339	17	.	.	PUNCT
ejpam-2339	340	1	,	,	PUNCT
ejpam-2339	340	2	2t−p	2t−p	INTJ
ejpam-2339	340	3	we	we	PRON
ejpam-2339	340	4	define	define	VERB
ejpam-2339	340	5	φw	φw	NOUN
ejpam-2339	340	6	:	:	PUNCT
ejpam-2339	340	7	g→	g→	NOUN
ejpam-2339	340	8	gl(2,c	gl(2,c	NOUN
ejpam-2339	340	9	)	)	PUNCT
ejpam-2339	340	10	by	by	ADP
ejpam-2339	340	11	φw(x	φw(x	X
ejpam-2339	340	12	ic1	ic1	VERB
ejpam-2339	340	13	yml	yml	NOUN
ejpam-2339	340	14	)	)	PUNCT
ejpam-2339	340	15	=	=	PUNCT
ejpam-2339	340	16	�	�	PROPN
ejpam-2339	340	17	ǫ2pwi	ǫ2pwi	PROPN
ejpam-2339	340	18	0	0	NUM
ejpam-2339	340	19	0	0	NUM
ejpam-2339	340	20	ǫ−2pwi	ǫ−2pwi	PROPN
ejpam-2339	340	21	�	�	NOUN
ejpam-2339	340	22	�	�	PROPN
ejpam-2339	340	23	0	0	NUM
ejpam-2339	340	24	1	1	NUM
ejpam-2339	340	25	1	1	NUM
ejpam-2339	340	26	0	0	NUM
ejpam-2339	340	27	�	�	PROPN
ejpam-2339	340	28	m	m	NOUN
ejpam-2339	340	29	.	.	PUNCT
ejpam-2339	341	1	because	because	SCONJ
ejpam-2339	341	2	of	of	ADP
ejpam-2339	341	3	ch(x	ch(x	X
ejpam-2339	341	4	)	)	PUNCT
ejpam-2339	341	5	′	′	NUM
ejpam-2339	341	6	∩	∩	PROPN
ejpam-2339	341	7	〈	〈	NOUN
ejpam-2339	341	8	x	x	X
ejpam-2339	341	9	〉	〉	NOUN
ejpam-2339	341	10	≤	≤	NUM
ejpam-2339	341	11	〈	〈	PROPN
ejpam-2339	341	12	x2t−p	x2t−p	PROPN
ejpam-2339	341	13	〉	〉	PROPN
ejpam-2339	341	14	,	,	PUNCT
ejpam-2339	341	15	map	map	VERB
ejpam-2339	341	16	φw	φw	NOUN
ejpam-2339	341	17	is	be	AUX
ejpam-2339	341	18	well	well	ADV
ejpam-2339	341	19	defined	define	VERB
ejpam-2339	341	20	2	2	NUM
ejpam-2339	341	21	-	-	PUNCT
ejpam-2339	341	22	dimensional	dimensional	ADJ
ejpam-2339	341	23	representation	representation	NOUN
ejpam-2339	341	24	.	.	PUNCT
ejpam-2339	342	1	difference	difference	NOUN
ejpam-2339	342	2	set	set	VERB
ejpam-2339	342	3	d	d	NOUN
ejpam-2339	342	4	,	,	PUNCT
ejpam-2339	342	5	after	after	SCONJ
ejpam-2339	342	6	been	be	AUX
ejpam-2339	342	7	taken	take	VERB
ejpam-2339	342	8	modulo	modulo	ADJ
ejpam-2339	342	9	〈	〈	PROPN
ejpam-2339	342	10	x	x	SYM
ejpam-2339	342	11	〉	〉	NOUN
ejpam-2339	342	12	,	,	PUNCT
ejpam-2339	342	13	becomes	become	VERB
ejpam-2339	342	14	d	d	NOUN
ejpam-2339	342	15	=	=	PUNCT
ejpam-2339	343	1	∑a	∑a	PROPN
ejpam-2339	343	2	i=1	i=1	PROPN
ejpam-2339	343	3	xni	xni	PROPN
ejpam-2339	344	1	+	+	PUNCT
ejpam-2339	345	1	∑r	∑r	PROPN
ejpam-2339	345	2	j=1	j=1	PROPN
ejpam-2339	345	3	�	�	PROPN
ejpam-2339	345	4	∑t	∑t	PROPN
ejpam-2339	345	5	j	j	PROPN
ejpam-2339	346	1	s=1	s=1	X
ejpam-2339	346	2	xm	xm	PROPN
ejpam-2339	346	3	js	js	PROPN
ejpam-2339	346	4	�	�	PROPN
ejpam-2339	346	5	g	g	PROPN
ejpam-2339	346	6	j	j	PROPN
ejpam-2339	346	7	.	.	PUNCT
ejpam-2339	347	1	this	this	DET
ejpam-2339	347	2	time	time	NOUN
ejpam-2339	347	3	,	,	PUNCT
ejpam-2339	347	4	we	we	PRON
ejpam-2339	347	5	need	need	VERB
ejpam-2339	347	6	to	to	PART
ejpam-2339	347	7	separate	separate	ADJ
ejpam-2339	347	8	indices	index	NOUN
ejpam-2339	347	9	.	.	PUNCT
ejpam-2339	348	1	let	let	VERB
ejpam-2339	348	2	’s	’s	NOUN
ejpam-2339	348	3	use	use	VERB
ejpam-2339	348	4	j1	j1	NOUN
ejpam-2339	348	5	if	if	SCONJ
ejpam-2339	348	6	x	x	PRON
ejpam-2339	348	7	g	g	NOUN
ejpam-2339	348	8	j1	j1	PROPN
ejpam-2339	348	9	=	=	PUNCT
ejpam-2339	348	10	x	x	X
ejpam-2339	348	11	,	,	PUNCT
ejpam-2339	348	12	and	and	CCONJ
ejpam-2339	348	13	j2	j2	PROPN
ejpam-2339	349	1	when	when	SCONJ
ejpam-2339	349	2	g	g	PROPN
ejpam-2339	349	3	j2	j2	PROPN
ejpam-2339	349	4	=	=	SYM
ejpam-2339	349	5	x−1	x−1	PROPN
ejpam-2339	349	6	.	.	PUNCT
ejpam-2339	350	1	thus	thus	ADV
ejpam-2339	350	2	,	,	PUNCT
ejpam-2339	350	3	from	from	ADP
ejpam-2339	350	4	φw(d)φw(d	φw(d)φw(d	X
ejpam-2339	350	5	(	(	PUNCT
ejpam-2339	350	6	−1	−1	NOUN
ejpam-2339	350	7	)	)	PUNCT
ejpam-2339	350	8	)	)	PUNCT
ejpam-2339	351	1	=	=	PUNCT
ejpam-2339	351	2	u2	u2	PROPN
ejpam-2339	351	3	i2	i2	PROPN
ejpam-2339	351	4	,	,	PUNCT
ejpam-2339	351	5	where	where	SCONJ
ejpam-2339	351	6	i2	i2	PROPN
ejpam-2339	351	7	is	be	AUX
ejpam-2339	351	8	a	a	DET
ejpam-2339	351	9	2×	2×	NUM
ejpam-2339	351	10	2	2	NUM
ejpam-2339	351	11	identity	identity	NOUN
ejpam-2339	351	12	matrix	matrix	NOUN
ejpam-2339	351	13	,	,	PUNCT
ejpam-2339	351	14	we	we	PRON
ejpam-2339	351	15	get	get	VERB
ejpam-2339	351	16	�	�	PROPN
ejpam-2339	351	17	�	�	PROPN
ejpam-2339	351	18	�	�	PROPN
ejpam-2339	351	19	�	�	PROPN
ejpam-2339	351	20	�	�	PROPN
ejpam-2339	351	21	�	�	PROPN
ejpam-2339	351	22	∑	∑	PUNCT
ejpam-2339	351	23	i	i	PRON
ejpam-2339	351	24	ǫ2pwn1	ǫ2pwn1	NUM
ejpam-2339	352	1	+	+	CCONJ
ejpam-2339	352	2	∑	∑	PROPN
ejpam-2339	352	3	j1	j1	PROPN
ejpam-2339	352	4	ǫ2pwm	ǫ2pwm	PROPN
ejpam-2339	352	5	j1	j1	PROPN
ejpam-2339	352	6	+	+	CCONJ
ejpam-2339	352	7	∑	∑	PROPN
ejpam-2339	352	8	j2	j2	PROPN
ejpam-2339	352	9	ǫ2pwm	ǫ2pwm	PROPN
ejpam-2339	352	10	j2	j2	PROPN
ejpam-2339	352	11	�	�	PROPN
ejpam-2339	352	12	�	�	PROPN
ejpam-2339	352	13	�	�	PROPN
ejpam-2339	352	14	�	�	PROPN
ejpam-2339	352	15	�	�	PROPN
ejpam-2339	352	16	�	�	PROPN
ejpam-2339	352	17	=	=	SYM
ejpam-2339	352	18	u	u	PROPN
ejpam-2339	352	19	where	where	SCONJ
ejpam-2339	352	20	w=	w=	NOUN
ejpam-2339	352	21	1,2	1,2	NUM
ejpam-2339	352	22	,	,	PUNCT
ejpam-2339	352	23	.	.	PUNCT
ejpam-2339	352	24	.	.	PUNCT
ejpam-2339	352	25	.	.	PUNCT
ejpam-2339	353	1	,	,	PUNCT
ejpam-2339	354	1	2t−p−1	2t−p−1	NUM
ejpam-2339	354	2	.	.	PUNCT
ejpam-2339	355	1	therefore	therefore	ADV
ejpam-2339	355	2	,	,	PUNCT
ejpam-2339	355	3	polynomial	polynomial	ADJ
ejpam-2339	355	4	∑	∑	PUNCT
ejpam-2339	355	5	i	i	PRON
ejpam-2339	355	6	ǫ	ǫ	PRON
ejpam-2339	355	7	2pn1	2pn1	NUM
ejpam-2339	355	8	+	+	ADJ
ejpam-2339	355	9	∑	∑	PROPN
ejpam-2339	355	10	j1	j1	PROPN
ejpam-2339	355	11	ǫ2pm	ǫ2pm	NUM
ejpam-2339	355	12	j1	j1	PROPN
ejpam-2339	355	13	+	+	CCONJ
ejpam-2339	355	14	∑	∑	PROPN
ejpam-2339	355	15	j2	j2	PROPN
ejpam-2339	355	16	ǫ2pm	ǫ2pm	PROPN
ejpam-2339	355	17	j2	j2	PROPN
ejpam-2339	355	18	is	be	AUX
ejpam-2339	355	19	a	a	DET
ejpam-2339	355	20	norm	norm	NOUN
ejpam-2339	355	21	invariant	invariant	ADJ
ejpam-2339	355	22	of	of	ADP
ejpam-2339	355	23	norm	norm	NOUN
ejpam-2339	356	1	u.	u.	ADV
ejpam-2339	356	2	now	now	ADV
ejpam-2339	356	3	,	,	PUNCT
ejpam-2339	356	4	proof	proof	NOUN
ejpam-2339	356	5	continues	continue	VERB
ejpam-2339	356	6	as	as	ADP
ejpam-2339	356	7	for	for	ADP
ejpam-2339	356	8	theorem	theorem	NOUN
ejpam-2339	356	9	6	6	NUM
ejpam-2339	356	10	.	.	PUNCT
ejpam-2339	356	11	references	reference	NOUN
ejpam-2339	356	12	457	457	NUM
ejpam-2339	356	13	6	6	NUM
ejpam-2339	356	14	.	.	PUNCT
ejpam-2339	356	15	one	one	NUM
ejpam-2339	356	16	infinite	infinite	ADJ
ejpam-2339	356	17	series	series	NOUN
ejpam-2339	356	18	of	of	ADP
ejpam-2339	356	19	groups	group	NOUN
ejpam-2339	356	20	for	for	ADP
ejpam-2339	356	21	dihedral	dihedral	ADJ
ejpam-2339	356	22	case	case	NOUN
ejpam-2339	356	23	this	this	DET
ejpam-2339	356	24	section	section	NOUN
ejpam-2339	356	25	offers	offer	VERB
ejpam-2339	356	26	one	one	NUM
ejpam-2339	356	27	construction	construction	NOUN
ejpam-2339	356	28	of	of	ADP
ejpam-2339	356	29	infinite	infinite	ADJ
ejpam-2339	356	30	series	series	NOUN
ejpam-2339	356	31	of	of	ADP
ejpam-2339	356	32	groups	group	NOUN
ejpam-2339	356	33	that	that	PRON
ejpam-2339	356	34	are	be	AUX
ejpam-2339	356	35	within	within	ADP
ejpam-2339	356	36	conditions	condition	NOUN
ejpam-2339	356	37	of	of	ADP
ejpam-2339	356	38	theorem	theorem	NOUN
ejpam-2339	356	39	7	7	NUM
ejpam-2339	356	40	.	.	X
ejpam-2339	357	1	we	we	PRON
ejpam-2339	357	2	start	start	VERB
ejpam-2339	357	3	by	by	ADP
ejpam-2339	357	4	taking	take	VERB
ejpam-2339	357	5	a	a	DET
ejpam-2339	357	6	group	group	NOUN
ejpam-2339	357	7	h	h	NOUN
ejpam-2339	357	8	=	=	PUNCT
ejpam-2339	357	9	〈	〈	PROPN
ejpam-2339	357	10	x	x	SYM
ejpam-2339	357	11	,	,	PUNCT
ejpam-2339	357	12	y1	y1	PROPN
ejpam-2339	357	13	,	,	PUNCT
ejpam-2339	357	14	y2	y2	NOUN
ejpam-2339	357	15	〉	〉	NOUN
ejpam-2339	357	16	,	,	PUNCT
ejpam-2339	357	17	where	where	SCONJ
ejpam-2339	357	18	o(x	o(x	ADJ
ejpam-2339	357	19	)	)	PUNCT
ejpam-2339	357	20	=	=	PUNCT
ejpam-2339	358	1	22t1	22t1	NUM
ejpam-2339	358	2	,	,	PUNCT
ejpam-2339	358	3	o(yi	o(yi	NUM
ejpam-2339	358	4	)	)	PUNCT
ejpam-2339	359	1	=	=	SYM
ejpam-2339	359	2	2si	2si	NOUN
ejpam-2339	359	3	and	and	CCONJ
ejpam-2339	359	4	x	x	ADJ
ejpam-2339	359	5	yi	yi	PROPN
ejpam-2339	359	6	=	=	SYM
ejpam-2339	359	7	x−1	x−1	PROPN
ejpam-2339	359	8	.	.	PUNCT
ejpam-2339	360	1	it	it	PRON
ejpam-2339	360	2	is	be	AUX
ejpam-2339	360	3	easy	easy	ADJ
ejpam-2339	360	4	to	to	PART
ejpam-2339	360	5	see	see	VERB
ejpam-2339	360	6	that	that	PRON
ejpam-2339	361	1	[	[	X
ejpam-2339	361	2	h	h	X
ejpam-2339	361	3	:	:	PUNCT
ejpam-2339	361	4	ch(x	ch(x	X
ejpam-2339	361	5	)	)	PUNCT
ejpam-2339	361	6	]	]	PUNCT
ejpam-2339	362	1	=	=	PUNCT
ejpam-2339	362	2	2	2	X
ejpam-2339	362	3	.	.	PUNCT
ejpam-2339	362	4	firstly	firstly	ADV
ejpam-2339	362	5	,	,	PUNCT
ejpam-2339	362	6	let	let	VERB
ejpam-2339	362	7	us	we	PRON
ejpam-2339	362	8	show	show	VERB
ejpam-2339	362	9	that	that	SCONJ
ejpam-2339	362	10	assumption	assumption	NOUN
ejpam-2339	363	1	[	[	X
ejpam-2339	363	2	y1	y1	X
ejpam-2339	363	3	,	,	PUNCT
ejpam-2339	363	4	y2	y2	NOUN
ejpam-2339	363	5	]	]	PUNCT
ejpam-2339	363	6	∈	∈	PROPN
ejpam-2339	363	7	〈	〈	PROPN
ejpam-2339	363	8	x	x	SYM
ejpam-2339	363	9	〉	〉	NOUN
ejpam-2339	363	10	forces	force	NOUN
ejpam-2339	363	11	that	that	PRON
ejpam-2339	363	12	〈	〈	VERB
ejpam-2339	363	13	y2	y2	NOUN
ejpam-2339	363	14	1	1	NUM
ejpam-2339	363	15	,	,	PUNCT
ejpam-2339	363	16	y2	y2	PROPN
ejpam-2339	363	17	2	2	NUM
ejpam-2339	363	18	〉	〉	NOUN
ejpam-2339	363	19	≤	≤	ADJ
ejpam-2339	363	20	z(h	z(h	NUM
ejpam-2339	363	21	)	)	PUNCT
ejpam-2339	363	22	.	.	PUNCT
ejpam-2339	364	1	from	from	ADP
ejpam-2339	364	2	assumption	assumption	NOUN
ejpam-2339	364	3	we	we	PRON
ejpam-2339	364	4	get	get	VERB
ejpam-2339	364	5	that	that	SCONJ
ejpam-2339	364	6	there	there	PRON
ejpam-2339	364	7	is	be	VERB
ejpam-2339	364	8	some	some	DET
ejpam-2339	364	9	α	α	NOUN
ejpam-2339	365	1	such	such	ADJ
ejpam-2339	365	2	that	that	SCONJ
ejpam-2339	365	3	[	[	X
ejpam-2339	365	4	y1	y1	X
ejpam-2339	365	5	,	,	PUNCT
ejpam-2339	365	6	y2	y2	NOUN
ejpam-2339	365	7	]	]	PUNCT
ejpam-2339	365	8	=	=	PUNCT
ejpam-2339	366	1	xα	xα	PROPN
ejpam-2339	366	2	.	.	PUNCT
ejpam-2339	367	1	then	then	ADV
ejpam-2339	367	2	y1	y1	INTJ
ejpam-2339	367	3	y2	y2	NOUN
ejpam-2339	367	4	=	=	PUNCT
ejpam-2339	368	1	y2	y2	INTJ
ejpam-2339	368	2	y1	y1	INTJ
ejpam-2339	368	3	xα	xα	PUNCT
ejpam-2339	369	1	and	and	CCONJ
ejpam-2339	369	2	y2	y2	PROPN
ejpam-2339	369	3	y1	y1	NOUN
ejpam-2339	369	4	=	=	PUNCT
ejpam-2339	369	5	y1	y1	NOUN
ejpam-2339	369	6	y2	y2	NOUN
ejpam-2339	369	7	x−α	x−α	NOUN
ejpam-2339	369	8	.	.	PUNCT
ejpam-2339	370	1	using	use	VERB
ejpam-2339	370	2	this	this	PRON
ejpam-2339	370	3	we	we	PRON
ejpam-2339	370	4	get	get	VERB
ejpam-2339	370	5	,	,	PUNCT
ejpam-2339	370	6	y2	y2	PROPN
ejpam-2339	370	7	2	2	NUM
ejpam-2339	370	8	y1	y1	NOUN
ejpam-2339	370	9	=	=	PUNCT
ejpam-2339	370	10	y2	y2	NOUN
ejpam-2339	370	11	y2	y2	NOUN
ejpam-2339	370	12	y1	y1	NOUN
ejpam-2339	371	1	=	=	PUNCT
ejpam-2339	371	2	y2	y2	NOUN
ejpam-2339	371	3	y1	y1	NOUN
ejpam-2339	371	4	y2	y2	NOUN
ejpam-2339	371	5	x−α	x−α	PUNCT
ejpam-2339	371	6	=	=	SYM
ejpam-2339	372	1	y1	y1	NOUN
ejpam-2339	372	2	y2	y2	NOUN
ejpam-2339	372	3	x−α	x−α	PROPN
ejpam-2339	372	4	y2	y2	INTJ
ejpam-2339	372	5	x−α	x−α	PUNCT
ejpam-2339	373	1	=	=	SYM
ejpam-2339	374	1	y1	y1	INTJ
ejpam-2339	375	1	y2	y2	INTJ
ejpam-2339	376	1	y2	y2	INTJ
ejpam-2339	376	2	xαx−α	xαx−α	PUNCT
ejpam-2339	377	1	=	=	SYM
ejpam-2339	377	2	y1	y1	NOUN
ejpam-2339	378	1	y2	y2	NOUN
ejpam-2339	378	2	2	2	NUM
ejpam-2339	378	3	.	.	PUNCT
ejpam-2339	379	1	it	it	PRON
ejpam-2339	379	2	is	be	AUX
ejpam-2339	379	3	clear	clear	ADJ
ejpam-2339	379	4	that	that	SCONJ
ejpam-2339	379	5	[	[	X
ejpam-2339	379	6	y2	y2	NOUN
ejpam-2339	379	7	2	2	NUM
ejpam-2339	379	8	,	,	PUNCT
ejpam-2339	379	9	y2	y2	NOUN
ejpam-2339	379	10	]	]	PUNCT
ejpam-2339	380	1	=	=	PUNCT
ejpam-2339	381	1	[	[	X
ejpam-2339	381	2	y	y	PROPN
ejpam-2339	381	3	2	2	NUM
ejpam-2339	381	4	2	2	NUM
ejpam-2339	381	5	,	,	PUNCT
ejpam-2339	381	6	x	x	X
ejpam-2339	381	7	]	]	X
ejpam-2339	381	8	=	=	SYM
ejpam-2339	381	9	1	1	NUM
ejpam-2339	381	10	,	,	PUNCT
ejpam-2339	381	11	therefore	therefore	ADV
ejpam-2339	381	12	y2	y2	PROPN
ejpam-2339	381	13	2	2	NUM
ejpam-2339	381	14	∈	∈	PROPN
ejpam-2339	381	15	z(h	z(h	NUM
ejpam-2339	381	16	)	)	PUNCT
ejpam-2339	381	17	.	.	PUNCT
ejpam-2339	382	1	due	due	ADP
ejpam-2339	382	2	to	to	ADP
ejpam-2339	382	3	symmetry	symmetry	NOUN
ejpam-2339	382	4	,	,	PUNCT
ejpam-2339	382	5	similar	similar	ADJ
ejpam-2339	382	6	works	work	NOUN
ejpam-2339	382	7	for	for	ADP
ejpam-2339	382	8	y2	y2	PROPN
ejpam-2339	382	9	1	1	NUM
ejpam-2339	382	10	.	.	PUNCT
ejpam-2339	383	1	thus	thus	ADV
ejpam-2339	383	2	,	,	PUNCT
ejpam-2339	383	3	〈	〈	ADJ
ejpam-2339	383	4	y2	y2	NOUN
ejpam-2339	383	5	1	1	NUM
ejpam-2339	383	6	,	,	PUNCT
ejpam-2339	383	7	y2	y2	PROPN
ejpam-2339	383	8	2	2	NUM
ejpam-2339	383	9	〉	〉	NOUN
ejpam-2339	383	10	≤	≤	ADJ
ejpam-2339	383	11	z(h	z(h	NUM
ejpam-2339	383	12	)	)	PUNCT
ejpam-2339	383	13	.	.	PUNCT
ejpam-2339	384	1	now	now	ADV
ejpam-2339	384	2	,	,	PUNCT
ejpam-2339	384	3	let	let	VERB
ejpam-2339	384	4	us	we	PRON
ejpam-2339	384	5	show	show	VERB
ejpam-2339	384	6	that	that	SCONJ
ejpam-2339	384	7	ch(x	ch(x	PUNCT
ejpam-2339	384	8	)	)	PUNCT
ejpam-2339	384	9	=	=	PUNCT
ejpam-2339	385	1	〈	〈	NOUN
ejpam-2339	385	2	x	x	SYM
ejpam-2339	385	3	,	,	PUNCT
ejpam-2339	385	4	y2	y2	PROPN
ejpam-2339	385	5	1	1	NUM
ejpam-2339	385	6	,	,	PUNCT
ejpam-2339	385	7	y2	y2	PROPN
ejpam-2339	385	8	2	2	NUM
ejpam-2339	385	9	,	,	PUNCT
ejpam-2339	385	10	y1	y1	NOUN
ejpam-2339	385	11	y2	y2	NOUN
ejpam-2339	385	12	〉	〉	NOUN
ejpam-2339	385	13	≤	≤	NUM
ejpam-2339	385	14	h	h	NOUN
ejpam-2339	385	15	is	be	AUX
ejpam-2339	385	16	abelian	abelian	ADJ
ejpam-2339	385	17	subgroup	subgroup	NOUN
ejpam-2339	385	18	of	of	ADP
ejpam-2339	385	19	index	index	NOUN
ejpam-2339	385	20	2	2	NUM
ejpam-2339	385	21	.	.	PUNCT
ejpam-2339	385	22	by	by	ADP
ejpam-2339	385	23	previous	previous	ADJ
ejpam-2339	385	24	argument	argument	NOUN
ejpam-2339	385	25	and	and	CCONJ
ejpam-2339	385	26	because	because	SCONJ
ejpam-2339	385	27	of	of	ADP
ejpam-2339	385	28	x	x	SYM
ejpam-2339	385	29	y1	y1	NOUN
ejpam-2339	385	30	y2	y2	NOUN
ejpam-2339	386	1	=	=	PUNCT
ejpam-2339	386	2	x	x	NOUN
ejpam-2339	386	3	,	,	PUNCT
ejpam-2339	386	4	it	it	PRON
ejpam-2339	386	5	is	be	AUX
ejpam-2339	386	6	clear	clear	ADJ
ejpam-2339	386	7	that	that	SCONJ
ejpam-2339	386	8	c1	c1	PROPN
ejpam-2339	386	9	:	:	PUNCT
ejpam-2339	386	10	=	=	PUNCT
ejpam-2339	386	11	〈	〈	PROPN
ejpam-2339	386	12	x	x	SYM
ejpam-2339	386	13	,	,	PUNCT
ejpam-2339	386	14	y2	y2	PROPN
ejpam-2339	386	15	1	1	NUM
ejpam-2339	386	16	,	,	PUNCT
ejpam-2339	386	17	y2	y2	PROPN
ejpam-2339	386	18	2	2	NUM
ejpam-2339	386	19	,	,	PUNCT
ejpam-2339	386	20	y1	y1	NOUN
ejpam-2339	386	21	y2	y2	NOUN
ejpam-2339	386	22	〉	〉	NOUN
ejpam-2339	386	23	≤	≤	NOUN
ejpam-2339	386	24	ch(x	ch(x	NOUN
ejpam-2339	386	25	)	)	PUNCT
ejpam-2339	386	26	.	.	PUNCT
ejpam-2339	387	1	we	we	PRON
ejpam-2339	387	2	obtain	obtain	VERB
ejpam-2339	387	3	|h|=	|h|=	NOUN
ejpam-2339	387	4	22t1+s1+s2	22t1+s1+s2	NUM
ejpam-2339	387	5	and	and	CCONJ
ejpam-2339	387	6	|c1|=	|c1|=	PROPN
ejpam-2339	387	7	22t1+s1+s2−2	22t1+s1+s2−2	PROPN
ejpam-2339	387	8	.	.	PUNCT
ejpam-2339	388	1	take	take	VERB
ejpam-2339	388	2	c2	c2	PROPN
ejpam-2339	388	3	=	=	PUNCT
ejpam-2339	388	4	〈	〈	PROPN
ejpam-2339	388	5	c1	c1	NOUN
ejpam-2339	388	6	,	,	PUNCT
ejpam-2339	388	7	y1	y1	NOUN
ejpam-2339	388	8	y2	y2	NOUN
ejpam-2339	388	9	〉	〉	NOUN
ejpam-2339	388	10	.	.	PUNCT
ejpam-2339	389	1	since	since	SCONJ
ejpam-2339	389	2	(	(	PUNCT
ejpam-2339	389	3	y1	y1	NOUN
ejpam-2339	389	4	y2	y2	PROPN
ejpam-2339	389	5	)	)	PUNCT
ejpam-2339	389	6	2	2	NUM
ejpam-2339	389	7	=	=	SYM
ejpam-2339	389	8	y2	y2	NOUN
ejpam-2339	389	9	1	1	NUM
ejpam-2339	389	10	y2	y2	NOUN
ejpam-2339	389	11	2	2	NUM
ejpam-2339	389	12	xα	xα	NOUN
ejpam-2339	389	13	∈	∈	PROPN
ejpam-2339	389	14	c1	c1	NOUN
ejpam-2339	389	15	,	,	PUNCT
ejpam-2339	389	16	we	we	PRON
ejpam-2339	389	17	conclude	conclude	VERB
ejpam-2339	389	18	that	that	SCONJ
ejpam-2339	389	19	[	[	X
ejpam-2339	389	20	c2	c2	PROPN
ejpam-2339	389	21	:	:	PUNCT
ejpam-2339	389	22	c1	c1	PROPN
ejpam-2339	389	23	]	]	PUNCT
ejpam-2339	389	24	=	=	SYM
ejpam-2339	389	25	2	2	NUM
ejpam-2339	389	26	,	,	PUNCT
ejpam-2339	389	27	thus	thus	ADV
ejpam-2339	389	28	[	[	X
ejpam-2339	389	29	h	h	NOUN
ejpam-2339	389	30	:	:	PUNCT
ejpam-2339	389	31	c2	c2	PROPN
ejpam-2339	389	32	]	]	PUNCT
ejpam-2339	389	33	=	=	SYM
ejpam-2339	389	34	2	2	X
ejpam-2339	389	35	.	.	X
ejpam-2339	389	36	hence	hence	ADV
ejpam-2339	389	37	c2	c2	PROPN
ejpam-2339	389	38	=	=	SYM
ejpam-2339	389	39	ch(x	ch(x	X
ejpam-2339	389	40	)	)	PUNCT
ejpam-2339	389	41	.	.	PUNCT
ejpam-2339	390	1	it	it	PRON
ejpam-2339	390	2	is	be	AUX
ejpam-2339	390	3	clear	clear	ADJ
ejpam-2339	390	4	that	that	SCONJ
ejpam-2339	390	5	ch(x	ch(x	X
ejpam-2339	390	6	)	)	PUNCT
ejpam-2339	390	7	is	be	AUX
ejpam-2339	390	8	abelian	abelian	ADJ
ejpam-2339	390	9	.	.	PUNCT
ejpam-2339	391	1	then	then	ADV
ejpam-2339	391	2	ch(x	ch(x	PUNCT
ejpam-2339	391	3	)	)	PUNCT
ejpam-2339	391	4	′	′	NUM
ejpam-2339	391	5	∩	∩	X
ejpam-2339	391	6	〈	〈	NOUN
ejpam-2339	391	7	x〉=	x〉=	NOUN
ejpam-2339	391	8	{	{	PUNCT
ejpam-2339	391	9	1	1	NUM
ejpam-2339	391	10	}	}	PUNCT
ejpam-2339	391	11	.	.	PUNCT
ejpam-2339	392	1	after	after	ADP
ejpam-2339	392	2	this	this	PRON
ejpam-2339	392	3	,	,	PUNCT
ejpam-2339	392	4	let	let	VERB
ejpam-2339	392	5	us	we	PRON
ejpam-2339	392	6	take	take	VERB
ejpam-2339	392	7	concrete	concrete	ADJ
ejpam-2339	392	8	numbers	number	NOUN
ejpam-2339	392	9	.	.	PUNCT
ejpam-2339	393	1	put	put	VERB
ejpam-2339	393	2	s1	s1	NOUN
ejpam-2339	393	3	=	=	SYM
ejpam-2339	393	4	s2	s2	NOUN
ejpam-2339	393	5	=	=	PUNCT
ejpam-2339	393	6	3	3	NUM
ejpam-2339	393	7	and	and	CCONJ
ejpam-2339	393	8	[	[	X
ejpam-2339	393	9	y1	y1	X
ejpam-2339	393	10	,	,	PUNCT
ejpam-2339	393	11	y2	y2	NOUN
ejpam-2339	393	12	]	]	PUNCT
ejpam-2339	394	1	=	=	PUNCT
ejpam-2339	394	2	x2t1−1	x2t1−1	PROPN
ejpam-2339	394	3	(	(	PUNCT
ejpam-2339	394	4	although	although	ADV
ejpam-2339	394	5	,	,	PUNCT
ejpam-2339	394	6	by	by	ADP
ejpam-2339	394	7	previously	previously	ADV
ejpam-2339	394	8	proven	prove	VERB
ejpam-2339	394	9	facts	fact	NOUN
ejpam-2339	394	10	,	,	PUNCT
ejpam-2339	394	11	it	it	PRON
ejpam-2339	394	12	is	be	AUX
ejpam-2339	394	13	sufficient	sufficient	ADJ
ejpam-2339	394	14	to	to	PART
ejpam-2339	394	15	assume	assume	VERB
ejpam-2339	394	16	[	[	X
ejpam-2339	394	17	y1	y1	INTJ
ejpam-2339	394	18	,	,	PUNCT
ejpam-2339	394	19	y2	y2	NOUN
ejpam-2339	394	20	]	]	PUNCT
ejpam-2339	394	21	∈	∈	PROPN
ejpam-2339	394	22	〈	〈	PROPN
ejpam-2339	394	23	x	x	X
ejpam-2339	394	24	〉	〉	NOUN
ejpam-2339	394	25	)	)	PUNCT
ejpam-2339	394	26	.	.	PUNCT
ejpam-2339	395	1	let	let	VERB
ejpam-2339	395	2	l1	l1	PROPN
ejpam-2339	395	3	be	be	AUX
ejpam-2339	395	4	a	a	DET
ejpam-2339	395	5	group	group	NOUN
ejpam-2339	395	6	of	of	ADP
ejpam-2339	395	7	order	order	NOUN
ejpam-2339	395	8	u2	u2	NOUN
ejpam-2339	395	9	1	1	NUM
ejpam-2339	395	10	and	and	CCONJ
ejpam-2339	395	11	g	g	NOUN
ejpam-2339	395	12	=	=	NOUN
ejpam-2339	395	13	h	h	NOUN
ejpam-2339	396	1	×	×	NOUN
ejpam-2339	396	2	l	l	NOUN
ejpam-2339	396	3	of	of	ADP
ejpam-2339	396	4	order	order	NOUN
ejpam-2339	396	5	4u2	4u2	PUNCT
ejpam-2339	397	1	=	=	PUNCT
ejpam-2339	398	1	22t1	22t1	NUM
ejpam-2339	398	2	+	+	NOUN
ejpam-2339	398	3	6u2	6u2	NUM
ejpam-2339	398	4	1	1	NUM
ejpam-2339	398	5	.	.	PUNCT
ejpam-2339	398	6	define	define	VERB
ejpam-2339	398	7	d	d	NOUN
ejpam-2339	398	8	=	=	PROPN
ejpam-2339	398	9	t1	t1	NOUN
ejpam-2339	398	10	+	+	NOUN
ejpam-2339	399	1	2	2	X
ejpam-2339	399	2	.	.	X
ejpam-2339	399	3	then	then	ADV
ejpam-2339	399	4	|h|	|h|	PROPN
ejpam-2339	399	5	=	=	SYM
ejpam-2339	399	6	22d+2	22d+2	PROPN
ejpam-2339	399	7	and	and	CCONJ
ejpam-2339	399	8	,	,	PUNCT
ejpam-2339	399	9	as	as	SCONJ
ejpam-2339	399	10	proved	prove	VERB
ejpam-2339	399	11	,	,	PUNCT
ejpam-2339	399	12	ch(x	ch(x	X
ejpam-2339	399	13	)	)	PUNCT
ejpam-2339	399	14	=	=	PUNCT
ejpam-2339	400	1	〈	〈	NOUN
ejpam-2339	400	2	x	x	SYM
ejpam-2339	400	3	,	,	PUNCT
ejpam-2339	400	4	y2	y2	PROPN
ejpam-2339	400	5	1	1	NUM
ejpam-2339	400	6	,	,	PUNCT
ejpam-2339	400	7	y2	y2	PROPN
ejpam-2339	400	8	2	2	NUM
ejpam-2339	400	9	,	,	PUNCT
ejpam-2339	400	10	y1	y1	NOUN
ejpam-2339	400	11	y2	y2	NOUN
ejpam-2339	400	12	〉	〉	NOUN
ejpam-2339	400	13	.	.	PUNCT
ejpam-2339	401	1	as	as	SCONJ
ejpam-2339	401	2	shown	show	VERB
ejpam-2339	401	3	,	,	PUNCT
ejpam-2339	401	4	ch(x	ch(x	NUM
ejpam-2339	401	5	)	)	PUNCT
ejpam-2339	401	6	′	′	NUM
ejpam-2339	401	7	∩	∩	PROPN
ejpam-2339	401	8	〈	〈	NOUN
ejpam-2339	401	9	x	x	X
ejpam-2339	401	10	〉	〉	NOUN
ejpam-2339	401	11	≤	≤	NUM
ejpam-2339	401	12	〈	〈	PROPN
ejpam-2339	401	13	x2t1−p	x2t1−p	PROPN
ejpam-2339	401	14	〉	〉	NOUN
ejpam-2339	401	15	for	for	ADP
ejpam-2339	401	16	any	any	DET
ejpam-2339	401	17	p.	p.	NOUN
ejpam-2339	401	18	if	if	SCONJ
ejpam-2339	401	19	o(x	o(x	PROPN
ejpam-2339	401	20	)	)	PUNCT
ejpam-2339	401	21	≥	≥	NOUN
ejpam-2339	401	22	2p+3u	2p+3u	NUM
ejpam-2339	401	23	then	then	ADV
ejpam-2339	401	24	we	we	PRON
ejpam-2339	401	25	would	would	AUX
ejpam-2339	401	26	be	be	AUX
ejpam-2339	401	27	within	within	ADP
ejpam-2339	401	28	conditions	condition	NOUN
ejpam-2339	401	29	of	of	ADP
ejpam-2339	401	30	theorem	theorem	NOUN
ejpam-2339	401	31	7	7	NUM
ejpam-2339	401	32	.	.	PUNCT
ejpam-2339	401	33	because	because	SCONJ
ejpam-2339	401	34	of	of	ADP
ejpam-2339	401	35	u	u	NOUN
ejpam-2339	401	36	=	=	PROPN
ejpam-2339	401	37	2t1	2t1	NUM
ejpam-2339	401	38	+	+	NOUN
ejpam-2339	401	39	2u1	2u1	NUM
ejpam-2339	401	40	,	,	PUNCT
ejpam-2339	401	41	we	we	PRON
ejpam-2339	401	42	need	need	VERB
ejpam-2339	401	43	o(x	o(x	PROPN
ejpam-2339	401	44	)	)	PUNCT
ejpam-2339	401	45	=	=	SYM
ejpam-2339	402	1	22t1	22t1	NUM
ejpam-2339	402	2	≥	≥	NUM
ejpam-2339	402	3	2p+3	2p+3	PROPN
ejpam-2339	402	4	·	·	PUNCT
ejpam-2339	402	5	2t1	2t1	NUM
ejpam-2339	402	6	+	+	NOUN
ejpam-2339	402	7	2u1	2u1	NUM
ejpam-2339	402	8	.	.	PUNCT
ejpam-2339	403	1	this	this	PRON
ejpam-2339	403	2	gives	give	VERB
ejpam-2339	403	3	us	we	PRON
ejpam-2339	403	4	a	a	DET
ejpam-2339	403	5	conditions	condition	NOUN
ejpam-2339	403	6	that	that	PRON
ejpam-2339	403	7	chosen	choose	VERB
ejpam-2339	403	8	group	group	NOUN
ejpam-2339	403	9	parameters	parameter	NOUN
ejpam-2339	403	10	should	should	AUX
ejpam-2339	403	11	fulfil	fulfil	VERB
ejpam-2339	403	12	:	:	PUNCT
ejpam-2339	403	13	2t1−p−5	2t1−p−5	NUM
ejpam-2339	403	14	≥	≥	NUM
ejpam-2339	403	15	u1	u1	VERB
ejpam-2339	403	16	≥	≥	PROPN
ejpam-2339	403	17	1	1	NUM
ejpam-2339	403	18	.	.	PUNCT
ejpam-2339	404	1	so	so	ADV
ejpam-2339	404	2	,	,	PUNCT
ejpam-2339	404	3	let	let	VERB
ejpam-2339	404	4	us	we	PRON
ejpam-2339	404	5	,	,	PUNCT
ejpam-2339	404	6	for	for	ADP
ejpam-2339	404	7	example	example	NOUN
ejpam-2339	404	8	choose	choose	X
ejpam-2339	404	9	u1	u1	NOUN
ejpam-2339	404	10	=	=	SYM
ejpam-2339	404	11	10	10	NUM
ejpam-2339	404	12	,	,	PUNCT
ejpam-2339	404	13	p	p	NOUN
ejpam-2339	404	14	=	=	NOUN
ejpam-2339	404	15	2	2	NUM
ejpam-2339	404	16	,	,	PUNCT
ejpam-2339	404	17	t1	t1	NOUN
ejpam-2339	404	18	=	=	NOUN
ejpam-2339	405	1	11	11	NUM
ejpam-2339	405	2	.	.	PUNCT
ejpam-2339	406	1	then	then	ADV
ejpam-2339	406	2	2t1−p−5	2t1−p−5	NUM
ejpam-2339	406	3	=	=	SYM
ejpam-2339	406	4	24	24	NUM
ejpam-2339	406	5	=	=	SYM
ejpam-2339	406	6	16≥	16≥	NUM
ejpam-2339	406	7	10=	10=	NUM
ejpam-2339	406	8	u1	u1	NOUN
ejpam-2339	406	9	.	.	PUNCT
ejpam-2339	407	1	then	then	ADV
ejpam-2339	407	2	o(x	o(x	PROPN
ejpam-2339	407	3	)	)	PUNCT
ejpam-2339	407	4	=	=	PUNCT
ejpam-2339	408	1	22t1	22t1	NUM
ejpam-2339	408	2	=	=	NUM
ejpam-2339	408	3	222	222	NUM
ejpam-2339	408	4	.	.	PUNCT
ejpam-2339	409	1	thus	thus	ADV
ejpam-2339	409	2	,	,	PUNCT
ejpam-2339	409	3	the	the	DET
ejpam-2339	409	4	group	group	NOUN
ejpam-2339	409	5	g	g	PROPN
ejpam-2339	409	6	=	=	PROPN
ejpam-2339	409	7	〈	〈	PROPN
ejpam-2339	409	8	x	x	PROPN
ejpam-2339	409	9	,	,	PUNCT
ejpam-2339	409	10	y1	y1	PROPN
ejpam-2339	409	11	,	,	PUNCT
ejpam-2339	409	12	y2	y2	PROPN
ejpam-2339	409	13	|	|	ADV
ejpam-2339	409	14	x	x	SYM
ejpam-2339	409	15	222	222	NUM
ejpam-2339	409	16	=	=	NUM
ejpam-2339	409	17	y8	y8	PROPN
ejpam-2339	409	18	1	1	NUM
ejpam-2339	409	19	=	=	SYM
ejpam-2339	409	20	y8	y8	PROPN
ejpam-2339	409	21	2	2	NUM
ejpam-2339	409	22	=	=	SYM
ejpam-2339	409	23	1	1	NUM
ejpam-2339	409	24	,	,	PUNCT
ejpam-2339	409	25	x	x	X
ejpam-2339	409	26	yi	yi	NOUN
ejpam-2339	409	27	=	=	SYM
ejpam-2339	409	28	x−1	x−1	PROPN
ejpam-2339	409	29	,	,	PUNCT
ejpam-2339	409	30	[	[	X
ejpam-2339	409	31	y1	y1	X
ejpam-2339	409	32	,	,	PUNCT
ejpam-2339	409	33	y2	y2	NOUN
ejpam-2339	409	34	]	]	PUNCT
ejpam-2339	409	35	=	=	SYM
ejpam-2339	409	36	x221	x221	NUM
ejpam-2339	409	37	〉	〉	NOUN
ejpam-2339	409	38	×	×	NOUN
ejpam-2339	409	39	l	l	NOUN
ejpam-2339	409	40	,	,	PUNCT
ejpam-2339	409	41	where	where	SCONJ
ejpam-2339	409	42	|l1|=	|l1|=	PROPN
ejpam-2339	409	43	u2	u2	NOUN
ejpam-2339	409	44	1	1	NUM
ejpam-2339	409	45	=	=	SYM
ejpam-2339	409	46	102	102	NUM
ejpam-2339	409	47	is	be	AUX
ejpam-2339	409	48	one	one	NUM
ejpam-2339	409	49	concrete	concrete	ADJ
ejpam-2339	409	50	example	example	NOUN
ejpam-2339	409	51	.	.	PUNCT
ejpam-2339	410	1	group	group	NOUN
ejpam-2339	410	2	order	order	NOUN
ejpam-2339	410	3	is	be	AUX
ejpam-2339	410	4	|g|=	|g|=	NOUN
ejpam-2339	410	5	228	228	NUM
ejpam-2339	410	6	·	·	SYM
ejpam-2339	410	7	102	102	NUM
ejpam-2339	410	8	.	.	PUNCT
ejpam-2339	411	1	references	reference	NOUN
ejpam-2339	411	2	[	[	X
ejpam-2339	411	3	1	1	X
ejpam-2339	411	4	]	]	PUNCT
ejpam-2339	411	5	t.	t.	PROPN
ejpam-2339	411	6	beth	beth	PROPN
ejpam-2339	411	7	,	,	PUNCT
ejpam-2339	411	8	d.	d.	PROPN
ejpam-2339	411	9	jungnickel	jungnickel	PROPN
ejpam-2339	411	10	and	and	CCONJ
ejpam-2339	411	11	h.	h.	PROPN
ejpam-2339	411	12	lenz	lenz	PROPN
ejpam-2339	411	13	.	.	PUNCT
ejpam-2339	412	1	design	design	PROPN
ejpam-2339	412	2	theory	theory	NOUN
ejpam-2339	412	3	,	,	PUNCT
ejpam-2339	412	4	bibliographisches	bibliographisches	PROPN
ejpam-2339	412	5	institut	institut	PROPN
ejpam-2339	412	6	,	,	PUNCT
ejpam-2339	412	7	manheimwien	manheimwien	PROPN
ejpam-2339	412	8	-	-	PUNCT
ejpam-2339	412	9	zürich	zürich	NOUN
ejpam-2339	412	10	,	,	PUNCT
ejpam-2339	412	11	1985	1985	NUM
ejpam-2339	412	12	.	.	PUNCT
ejpam-2339	413	1	[	[	X
ejpam-2339	413	2	2	2	NUM
ejpam-2339	413	3	]	]	X
ejpam-2339	413	4	d.	d.	PROPN
ejpam-2339	413	5	jungnickel	jungnickel	PROPN
ejpam-2339	413	6	,	,	PUNCT
ejpam-2339	413	7	a.	a.	PROPN
ejpam-2339	413	8	pott	pott	PROPN
ejpam-2339	413	9	and	and	CCONJ
ejpam-2339	413	10	k.w	k.w	PROPN
ejpam-2339	413	11	.	.	PROPN
ejpam-2339	413	12	smith	smith	PROPN
ejpam-2339	413	13	.	.	PUNCT
ejpam-2339	413	14	difference	difference	NOUN
ejpam-2339	413	15	sets	set	NOUN
ejpam-2339	413	16	,	,	PUNCT
ejpam-2339	413	17	in	in	ADP
ejpam-2339	413	18	c.	c.	PROPN
ejpam-2339	413	19	j.	j.	PROPN
ejpam-2339	413	20	colburn	colburn	PROPN
ejpam-2339	413	21	,	,	PUNCT
ejpam-2339	413	22	j.h	j.h	PROPN
ejpam-2339	413	23	.	.	PROPN
ejpam-2339	413	24	dinitz	dinitz	PROPN
ejpam-2339	413	25	,	,	PUNCT
ejpam-2339	413	26	editors	editor	NOUN
ejpam-2339	413	27	,	,	PUNCT
ejpam-2339	413	28	the	the	DET
ejpam-2339	413	29	handbook	handbook	NOUN
ejpam-2339	413	30	of	of	ADP
ejpam-2339	413	31	combinatorial	combinatorial	ADJ
ejpam-2339	413	32	designs	design	NOUN
ejpam-2339	413	33	,	,	PUNCT
ejpam-2339	413	34	second	second	ADJ
ejpam-2339	413	35	edition	edition	NOUN
ejpam-2339	413	36	,	,	PUNCT
ejpam-2339	413	37	419	419	NUM
ejpam-2339	413	38	-	-	SYM
ejpam-2339	413	39	435	435	NUM
ejpam-2339	413	40	.	.	PUNCT
ejpam-2339	414	1	crc	crc	PROPN
ejpam-2339	414	2	press	press	PROPN
ejpam-2339	414	3	,	,	PUNCT
ejpam-2339	414	4	2007	2007	NUM
ejpam-2339	414	5	.	.	PUNCT
ejpam-2339	415	1	[	[	X
ejpam-2339	415	2	3	3	X
ejpam-2339	415	3	]	]	PUNCT
ejpam-2339	415	4	j.	j.	PROPN
ejpam-2339	415	5	mandić	mandić	PROPN
ejpam-2339	415	6	,	,	PUNCT
ejpam-2339	415	7	m.	m.	NOUN
ejpam-2339	415	8	o.	o.	PROPN
ejpam-2339	415	9	pavčević	pavčević	PROPN
ejpam-2339	415	10	and	and	CCONJ
ejpam-2339	415	11	k.tabak	k.tabak	ADV
ejpam-2339	415	12	.	.	PUNCT
ejpam-2339	416	1	on	on	ADP
ejpam-2339	416	2	difference	difference	NOUN
ejpam-2339	416	3	sets	set	NOUN
ejpam-2339	416	4	in	in	ADP
ejpam-2339	416	5	high	high	ADJ
ejpam-2339	416	6	exponent	exponent	NOUN
ejpam-2339	416	7	2	2	NUM
ejpam-2339	416	8	-	-	PUNCT
ejpam-2339	416	9	groups	group	NOUN
ejpam-2339	416	10	,	,	PUNCT
ejpam-2339	416	11	journal	journal	NOUN
ejpam-2339	416	12	of	of	ADP
ejpam-2339	416	13	algebraic	algebraic	PROPN
ejpam-2339	416	14	combinatorics	combinatoric	NOUN
ejpam-2339	416	15	,	,	PUNCT
ejpam-2339	416	16	38	38	NUM
ejpam-2339	416	17	,	,	PUNCT
ejpam-2339	416	18	785	785	NUM
ejpam-2339	416	19	-	-	SYM
ejpam-2339	416	20	795	795	NUM
ejpam-2339	416	21	.	.	PUNCT
ejpam-2339	416	22	2013	2013	NUM
ejpam-2339	417	1	[	[	X
ejpam-2339	417	2	4	4	NUM
ejpam-2339	417	3	]	]	PUNCT
ejpam-2339	417	4	a.	a.	PROPN
ejpam-2339	417	5	pott	pott	PROPN
ejpam-2339	417	6	.	.	PUNCT
ejpam-2339	418	1	finite	finite	PROPN
ejpam-2339	418	2	geometry	geometry	NOUN
ejpam-2339	418	3	and	and	CCONJ
ejpam-2339	418	4	character	character	NOUN
ejpam-2339	418	5	theory	theory	NOUN
ejpam-2339	418	6	,	,	PUNCT
ejpam-2339	418	7	springer	springer	NOUN
ejpam-2339	418	8	-	-	PUNCT
ejpam-2339	418	9	verlag	verlag	PROPN
ejpam-2339	418	10	,	,	PUNCT
ejpam-2339	418	11	berlin	berlin	PROPN
ejpam-2339	418	12	-	-	PUNCT
ejpam-2339	418	13	heidelberg	heidelberg	PROPN
ejpam-2339	418	14	,	,	PUNCT
ejpam-2339	418	15	1995	1995	NUM
ejpam-2339	418	16	.	.	PUNCT
ejpam-2339	419	1	[	[	X
ejpam-2339	419	2	5	5	X
ejpam-2339	419	3	]	]	PUNCT
ejpam-2339	419	4	b.	b.	PROPN
ejpam-2339	419	5	schmidt	schmidt	PROPN
ejpam-2339	419	6	.	.	PUNCT
ejpam-2339	420	1	characters	character	NOUN
ejpam-2339	420	2	and	and	CCONJ
ejpam-2339	420	3	cyclotomic	cyclotomic	ADJ
ejpam-2339	420	4	fields	field	NOUN
ejpam-2339	420	5	in	in	ADP
ejpam-2339	420	6	finite	finite	ADJ
ejpam-2339	420	7	geometry	geometry	NOUN
ejpam-2339	420	8	,	,	PUNCT
ejpam-2339	420	9	springer	springer	NOUN
ejpam-2339	420	10	,	,	PUNCT
ejpam-2339	420	11	berlinheidelberg	berlinheidelberg	PROPN
ejpam-2339	420	12	,	,	PUNCT
ejpam-2339	420	13	2002	2002	NUM
ejpam-2339	420	14	.	.	PUNCT
ejpam-2339	421	1	[	[	X
ejpam-2339	421	2	6	6	NUM
ejpam-2339	421	3	]	]	PUNCT
ejpam-2339	421	4	r.	r.	PROPN
ejpam-2339	421	5	j.	j.	PROPN
ejpam-2339	421	6	turyn	turyn	PROPN
ejpam-2339	421	7	.	.	PUNCT
ejpam-2339	422	1	character	character	NOUN
ejpam-2339	422	2	sums	sum	NOUN
ejpam-2339	422	3	and	and	CCONJ
ejpam-2339	422	4	difference	difference	NOUN
ejpam-2339	422	5	sets	set	NOUN
ejpam-2339	422	6	,	,	PUNCT
ejpam-2339	422	7	pacific	pacific	PROPN
ejpam-2339	422	8	journal	journal	NOUN
ejpam-2339	422	9	of	of	ADP
ejpam-2339	422	10	mathematics	mathematic	NOUN
ejpam-2339	422	11	,	,	PUNCT
ejpam-2339	422	12	15	15	NUM
ejpam-2339	422	13	,	,	PUNCT
ejpam-2339	422	14	319346	319346	NUM
ejpam-2339	422	15	.	.	PUNCT
ejpam-2339	423	1	1965	1965	NUM
ejpam-2339	423	2	.	.	PUNCT