id	sid	tid	token	lemma	pos
ejpam-5353	1	1	european	european	PROPN
ejpam-5353	1	2	journal	journal	PROPN
ejpam-5353	1	3	of	of	ADP
ejpam-5353	1	4	pure	pure	ADJ
ejpam-5353	1	5	and	and	CCONJ
ejpam-5353	1	6	applied	apply	VERB
ejpam-5353	1	7	mathematics	mathematic	NOUN
ejpam-5353	1	8	vol	vol	NOUN
ejpam-5353	1	9	.	.	PROPN
ejpam-5353	2	1	17	17	NUM
ejpam-5353	2	2	,	,	PUNCT
ejpam-5353	2	3	no	no	INTJ
ejpam-5353	2	4	.	.	NOUN
ejpam-5353	2	5	4	4	NUM
ejpam-5353	2	6	,	,	PUNCT
ejpam-5353	2	7	2024	2024	NUM
ejpam-5353	2	8	,	,	PUNCT
ejpam-5353	2	9	3492	3492	NUM
ejpam-5353	2	10	-	-	SYM
ejpam-5353	2	11	3516	3516	NUM
ejpam-5353	2	12	issn	issn	PROPN
ejpam-5353	2	13	1307	1307	NUM
ejpam-5353	2	14	-	-	SYM
ejpam-5353	2	15	5543	5543	NUM
ejpam-5353	2	16	–	–	PUNCT
ejpam-5353	3	1	ejpam.com	ejpam.com	X
ejpam-5353	3	2	published	publish	VERB
ejpam-5353	3	3	by	by	ADP
ejpam-5353	3	4	new	new	PROPN
ejpam-5353	3	5	york	york	PROPN
ejpam-5353	3	6	business	business	PROPN
ejpam-5353	3	7	global	global	ADJ
ejpam-5353	3	8	orthogonal	orthogonal	ADJ
ejpam-5353	3	9	decompositions	decomposition	NOUN
ejpam-5353	3	10	of	of	ADP
ejpam-5353	3	11	regular	regular	ADJ
ejpam-5353	3	12	graphs	graph	NOUN
ejpam-5353	3	13	and	and	CCONJ
ejpam-5353	3	14	designing	design	VERB
ejpam-5353	3	15	tree	tree	NOUN
ejpam-5353	3	16	-	-	PUNCT
ejpam-5353	3	17	hamming	ham	VERB
ejpam-5353	3	18	codes	code	NOUN
ejpam-5353	3	19	hanan	hanan	PROPN
ejpam-5353	3	20	shabana1,∗	shabana1,∗	PROPN
ejpam-5353	3	21	,	,	PUNCT
ejpam-5353	3	22	ramadan	ramadan	PROPN
ejpam-5353	3	23	el	el	PROPN
ejpam-5353	3	24	-	-	PROPN
ejpam-5353	3	25	shanawany1	shanawany1	PROPN
ejpam-5353	3	26	,	,	PUNCT
ejpam-5353	3	27	sahar	sahar	PROPN
ejpam-5353	3	28	halawa2	halawa2	NOUN
ejpam-5353	3	29	1	1	NUM
ejpam-5353	3	30	department	department	PROPN
ejpam-5353	3	31	of	of	ADP
ejpam-5353	3	32	physics	physics	PROPN
ejpam-5353	3	33	and	and	CCONJ
ejpam-5353	3	34	engineering	engineering	NOUN
ejpam-5353	3	35	mathematics	mathematic	NOUN
ejpam-5353	3	36	,	,	PUNCT
ejpam-5353	3	37	faculty	faculty	NOUN
ejpam-5353	3	38	of	of	ADP
ejpam-5353	3	39	electronic	electronic	ADJ
ejpam-5353	3	40	engineering	engineering	NOUN
ejpam-5353	3	41	,	,	PUNCT
ejpam-5353	3	42	menoufia	menoufia	PROPN
ejpam-5353	3	43	university	university	PROPN
ejpam-5353	3	44	,	,	PUNCT
ejpam-5353	3	45	egypt	egypt	PROPN
ejpam-5353	3	46	.	.	PROPN
ejpam-5353	4	1	2	2	NUM
ejpam-5353	4	2	department	department	NOUN
ejpam-5353	4	3	of	of	ADP
ejpam-5353	4	4	mathematics	mathematic	NOUN
ejpam-5353	4	5	,	,	PUNCT
ejpam-5353	4	6	faculty	faculty	NOUN
ejpam-5353	4	7	of	of	ADP
ejpam-5353	4	8	education	education	NOUN
ejpam-5353	4	9	,	,	PUNCT
ejpam-5353	4	10	ain	ain	PROPN
ejpam-5353	4	11	shams	shams	PROPN
ejpam-5353	4	12	university	university	PROPN
ejpam-5353	4	13	,	,	PUNCT
ejpam-5353	4	14	egypt	egypt	PROPN
ejpam-5353	4	15	.	.	PUNCT
ejpam-5353	5	1	abstract	abstract	PROPN
ejpam-5353	5	2	.	.	PUNCT
ejpam-5353	6	1	the	the	DET
ejpam-5353	6	2	paper	paper	NOUN
ejpam-5353	6	3	introduces	introduce	VERB
ejpam-5353	6	4	the	the	DET
ejpam-5353	6	5	concept	concept	NOUN
ejpam-5353	6	6	of	of	ADP
ejpam-5353	6	7	graph	graph	NOUN
ejpam-5353	6	8	decomposition	decomposition	NOUN
ejpam-5353	6	9	.	.	PUNCT
ejpam-5353	7	1	that	that	PRON
ejpam-5353	7	2	is	be	AUX
ejpam-5353	7	3	orthogonal	orthogonal	ADJ
ejpam-5353	7	4	decompositions	decomposition	NOUN
ejpam-5353	7	5	.	.	PUNCT
ejpam-5353	8	1	orthogonal	orthogonal	ADJ
ejpam-5353	8	2	decompositions	decomposition	NOUN
ejpam-5353	8	3	of	of	ADP
ejpam-5353	8	4	a	a	DET
ejpam-5353	8	5	graph	graph	NOUN
ejpam-5353	8	6	h	h	NOUN
ejpam-5353	8	7	are	be	AUX
ejpam-5353	8	8	a	a	DET
ejpam-5353	8	9	partitioning	partitioning	ADJ
ejpam-5353	8	10	h	h	NOUN
ejpam-5353	8	11	into	into	ADP
ejpam-5353	8	12	subgraphs	subgraph	NOUN
ejpam-5353	8	13	of	of	ADP
ejpam-5353	8	14	h	h	NOUN
ejpam-5353	8	15	such	such	ADJ
ejpam-5353	8	16	that	that	SCONJ
ejpam-5353	8	17	any	any	DET
ejpam-5353	8	18	two	two	NUM
ejpam-5353	8	19	subgraphs	subgraph	NOUN
ejpam-5353	8	20	intersect	intersect	ADJ
ejpam-5353	8	21	in	in	ADP
ejpam-5353	8	22	at	at	ADP
ejpam-5353	8	23	most	most	ADV
ejpam-5353	8	24	one	one	NUM
ejpam-5353	8	25	edge	edge	NOUN
ejpam-5353	8	26	.	.	PUNCT
ejpam-5353	9	1	these	these	DET
ejpam-5353	9	2	decompositions	decomposition	NOUN
ejpam-5353	9	3	are	be	AUX
ejpam-5353	9	4	called	call	VERB
ejpam-5353	9	5	g−orthogonal	g−orthogonal	ADJ
ejpam-5353	9	6	decompositions	decomposition	NOUN
ejpam-5353	9	7	of	of	ADP
ejpam-5353	9	8	h	h	NOUN
ejpam-5353	9	9	if	if	SCONJ
ejpam-5353	9	10	and	and	CCONJ
ejpam-5353	9	11	only	only	ADV
ejpam-5353	9	12	if	if	SCONJ
ejpam-5353	9	13	every	every	DET
ejpam-5353	9	14	subgraph	subgraph	NOUN
ejpam-5353	9	15	in	in	ADP
ejpam-5353	9	16	such	such	ADJ
ejpam-5353	9	17	decompositions	decomposition	NOUN
ejpam-5353	9	18	is	be	AUX
ejpam-5353	9	19	isomorphic	isomorphic	ADJ
ejpam-5353	9	20	to	to	ADP
ejpam-5353	9	21	the	the	DET
ejpam-5353	9	22	graph	graph	NOUN
ejpam-5353	10	1	g.	g.	NOUN
ejpam-5353	10	2	such	such	ADJ
ejpam-5353	10	3	decomposition	decomposition	NOUN
ejpam-5353	10	4	appears	appear	VERB
ejpam-5353	10	5	in	in	ADP
ejpam-5353	10	6	a	a	DET
ejpam-5353	10	7	lot	lot	NOUN
ejpam-5353	10	8	of	of	ADP
ejpam-5353	10	9	applications	application	NOUN
ejpam-5353	10	10	;	;	PUNCT
ejpam-5353	10	11	statistics	statistic	NOUN
ejpam-5353	10	12	,	,	PUNCT
ejpam-5353	10	13	information	information	NOUN
ejpam-5353	10	14	theory	theory	NOUN
ejpam-5353	10	15	,	,	PUNCT
ejpam-5353	10	16	in	in	ADP
ejpam-5353	10	17	the	the	DET
ejpam-5353	10	18	theory	theory	NOUN
ejpam-5353	10	19	of	of	ADP
ejpam-5353	10	20	experimental	experimental	ADJ
ejpam-5353	10	21	design	design	NOUN
ejpam-5353	10	22	,	,	PUNCT
ejpam-5353	10	23	and	and	CCONJ
ejpam-5353	10	24	many	many	ADJ
ejpam-5353	10	25	others	other	NOUN
ejpam-5353	10	26	.	.	PUNCT
ejpam-5353	11	1	an	an	DET
ejpam-5353	11	2	approach	approach	NOUN
ejpam-5353	11	3	of	of	ADP
ejpam-5353	11	4	constructing	construct	VERB
ejpam-5353	11	5	orthogonal	orthogonal	ADJ
ejpam-5353	11	6	decompositions	decomposition	NOUN
ejpam-5353	11	7	of	of	ADP
ejpam-5353	11	8	regular	regular	ADJ
ejpam-5353	11	9	graphs	graph	NOUN
ejpam-5353	11	10	is	be	AUX
ejpam-5353	11	11	introduced	introduce	VERB
ejpam-5353	11	12	here	here	ADV
ejpam-5353	11	13	.	.	PUNCT
ejpam-5353	12	1	application	application	NOUN
ejpam-5353	12	2	to	to	ADP
ejpam-5353	12	3	this	this	DET
ejpam-5353	12	4	approach	approach	NOUN
ejpam-5353	12	5	for	for	ADP
ejpam-5353	12	6	constructing	construct	VERB
ejpam-5353	12	7	tree	tree	NOUN
ejpam-5353	12	8	–	–	PUNCT
ejpam-5353	12	9	orthogonal	orthogonal	ADJ
ejpam-5353	12	10	decompositions	decomposition	NOUN
ejpam-5353	12	11	of	of	ADP
ejpam-5353	12	12	complete	complete	ADJ
ejpam-5353	12	13	bipartite	bipartite	NOUN
ejpam-5353	12	14	graphs	graph	NOUN
ejpam-5353	12	15	is	be	AUX
ejpam-5353	12	16	considered	consider	VERB
ejpam-5353	12	17	.	.	PUNCT
ejpam-5353	13	1	further	far	ADV
ejpam-5353	13	2	,	,	PUNCT
ejpam-5353	13	3	the	the	DET
ejpam-5353	13	4	use	use	NOUN
ejpam-5353	13	5	of	of	ADP
ejpam-5353	13	6	orthogonal	orthogonal	ADJ
ejpam-5353	13	7	decompositions	decomposition	NOUN
ejpam-5353	13	8	for	for	ADP
ejpam-5353	13	9	designing	design	VERB
ejpam-5353	13	10	tree	tree	NOUN
ejpam-5353	13	11	hamming	hamming	NOUN
ejpam-5353	13	12	codes	code	NOUN
ejpam-5353	13	13	is	be	AUX
ejpam-5353	13	14	also	also	ADV
ejpam-5353	13	15	discussed	discuss	VERB
ejpam-5353	13	16	along	along	ADP
ejpam-5353	13	17	with	with	ADP
ejpam-5353	13	18	examples	example	NOUN
ejpam-5353	13	19	.	.	PUNCT
ejpam-5353	14	1	the	the	DET
ejpam-5353	14	2	study	study	NOUN
ejpam-5353	14	3	shows	show	VERB
ejpam-5353	14	4	that	that	SCONJ
ejpam-5353	14	5	such	such	ADJ
ejpam-5353	14	6	codes	code	NOUN
ejpam-5353	14	7	have	have	VERB
ejpam-5353	14	8	efficient	efficient	ADJ
ejpam-5353	14	9	properties	property	NOUN
ejpam-5353	14	10	when	when	SCONJ
ejpam-5353	14	11	used	use	VERB
ejpam-5353	14	12	to	to	PART
ejpam-5353	14	13	detect	detect	VERB
ejpam-5353	14	14	and	and	CCONJ
ejpam-5353	14	15	correct	correct	VERB
ejpam-5353	14	16	the	the	DET
ejpam-5353	14	17	errors	error	NOUN
ejpam-5353	14	18	that	that	PRON
ejpam-5353	14	19	may	may	AUX
ejpam-5353	14	20	occur	occur	VERB
ejpam-5353	14	21	during	during	ADP
ejpam-5353	14	22	the	the	DET
ejpam-5353	14	23	transmission	transmission	NOUN
ejpam-5353	14	24	of	of	ADP
ejpam-5353	14	25	data	datum	NOUN
ejpam-5353	14	26	through	through	ADP
ejpam-5353	14	27	a	a	DET
ejpam-5353	14	28	network	network	NOUN
ejpam-5353	14	29	.	.	PUNCT
ejpam-5353	15	1	furthermore	furthermore	ADV
ejpam-5353	15	2	,	,	PUNCT
ejpam-5353	15	3	we	we	PRON
ejpam-5353	15	4	present	present	VERB
ejpam-5353	15	5	a	a	DET
ejpam-5353	15	6	method	method	NOUN
ejpam-5353	15	7	for	for	ADP
ejpam-5353	15	8	the	the	DET
ejpam-5353	15	9	recursive	recursive	ADJ
ejpam-5353	15	10	construction	construction	NOUN
ejpam-5353	15	11	of	of	ADP
ejpam-5353	15	12	orthogonal	orthogonal	ADJ
ejpam-5353	15	13	decompositions	decomposition	NOUN
ejpam-5353	15	14	.	.	PUNCT
ejpam-5353	16	1	2020	2020	NUM
ejpam-5353	16	2	mathematics	mathematic	NOUN
ejpam-5353	16	3	subject	subject	NOUN
ejpam-5353	16	4	classifications	classification	NOUN
ejpam-5353	16	5	:	:	PUNCT
ejpam-5353	16	6	05b30	05b30	NUM
ejpam-5353	16	7	,	,	PUNCT
ejpam-5353	16	8	0570	0570	NUM
ejpam-5353	16	9	,	,	PUNCT
ejpam-5353	16	10	94a60	94a60	NUM
ejpam-5353	16	11	,	,	PUNCT
ejpam-5353	16	12	94a62	94a62	NUM
ejpam-5353	16	13	key	key	ADJ
ejpam-5353	16	14	words	word	NOUN
ejpam-5353	16	15	and	and	CCONJ
ejpam-5353	16	16	phrases	phrase	NOUN
ejpam-5353	16	17	:	:	PUNCT
ejpam-5353	16	18	graph	graph	NOUN
ejpam-5353	16	19	decomposition	decomposition	NOUN
ejpam-5353	16	20	;	;	PUNCT
ejpam-5353	16	21	orthogonal	orthogonal	ADJ
ejpam-5353	16	22	cover	cover	NOUN
ejpam-5353	16	23	;	;	PUNCT
ejpam-5353	16	24	bipartite	bipartite	NOUN
ejpam-5353	16	25	graph	graph	NOUN
ejpam-5353	16	26	;	;	PUNCT
ejpam-5353	16	27	hamming	ham	VERB
ejpam-5353	16	28	codes	code	NOUN
ejpam-5353	16	29	1	1	NUM
ejpam-5353	16	30	.	.	PUNCT
ejpam-5353	17	1	introduction	introduction	NOUN
ejpam-5353	17	2	all	all	DET
ejpam-5353	17	3	graphs	graph	NOUN
ejpam-5353	17	4	being	be	AUX
ejpam-5353	17	5	discussed	discuss	VERB
ejpam-5353	17	6	here	here	ADV
ejpam-5353	17	7	are	be	AUX
ejpam-5353	17	8	undirected	undirected	ADJ
ejpam-5353	17	9	,	,	PUNCT
ejpam-5353	17	10	finite	finite	ADJ
ejpam-5353	17	11	,	,	PUNCT
ejpam-5353	17	12	and	and	CCONJ
ejpam-5353	17	13	do	do	AUX
ejpam-5353	17	14	not	not	PART
ejpam-5353	17	15	have	have	VERB
ejpam-5353	17	16	loops	loop	NOUN
ejpam-5353	17	17	or	or	CCONJ
ejpam-5353	17	18	multiple	multiple	ADJ
ejpam-5353	17	19	edges	edge	NOUN
ejpam-5353	17	20	.	.	PUNCT
ejpam-5353	18	1	for	for	ADP
ejpam-5353	18	2	standard	standard	ADJ
ejpam-5353	18	3	graph	graph	NOUN
ejpam-5353	18	4	-	-	PUNCT
ejpam-5353	18	5	theoretic	theoretic	NOUN
ejpam-5353	18	6	terminology	terminology	NOUN
ejpam-5353	18	7	,	,	PUNCT
ejpam-5353	18	8	we	we	PRON
ejpam-5353	18	9	refer	refer	VERB
ejpam-5353	18	10	to	to	ADP
ejpam-5353	18	11	[	[	X
ejpam-5353	18	12	1	1	NUM
ejpam-5353	18	13	]	]	PUNCT
ejpam-5353	18	14	.	.	PUNCT
ejpam-5353	19	1	a	a	DET
ejpam-5353	19	2	decomposition	decomposition	NOUN
ejpam-5353	19	3	of	of	ADP
ejpam-5353	19	4	a	a	DET
ejpam-5353	19	5	graph	graph	NOUN
ejpam-5353	19	6	h	h	NOUN
ejpam-5353	19	7	is	be	AUX
ejpam-5353	19	8	a	a	DET
ejpam-5353	19	9	set	set	NOUN
ejpam-5353	19	10	of	of	ADP
ejpam-5353	19	11	edge	edge	NOUN
ejpam-5353	19	12	-	-	PUNCT
ejpam-5353	19	13	disjoint	disjoint	NOUN
ejpam-5353	19	14	subgraphs	subgraphs	NOUN
ejpam-5353	19	15	of	of	ADP
ejpam-5353	19	16	h	h	NOUN
ejpam-5353	19	17	whose	whose	DET
ejpam-5353	19	18	union	union	NOUN
ejpam-5353	19	19	gives	give	VERB
ejpam-5353	19	20	the	the	DET
ejpam-5353	19	21	graph	graph	NOUN
ejpam-5353	19	22	h.	h.	PROPN
ejpam-5353	19	23	thus	thus	ADV
ejpam-5353	19	24	,	,	PUNCT
ejpam-5353	19	25	we	we	PRON
ejpam-5353	19	26	say	say	VERB
ejpam-5353	19	27	that	that	SCONJ
ejpam-5353	19	28	the	the	DET
ejpam-5353	19	29	set	set	NOUN
ejpam-5353	19	30	g	g	PROPN
ejpam-5353	19	31	=	=	SYM
ejpam-5353	19	32	{	{	PUNCT
ejpam-5353	19	33	g1	g1	PROPN
ejpam-5353	19	34	,	,	PUNCT
ejpam-5353	19	35	g2	g2	PROPN
ejpam-5353	19	36	,	,	PUNCT
ejpam-5353	19	37	·	·	PUNCT
ejpam-5353	19	38	·	·	PUNCT
ejpam-5353	19	39	·	·	PUNCT
ejpam-5353	19	40	,	,	PUNCT
ejpam-5353	19	41	gk	gk	PROPN
ejpam-5353	19	42	}	}	PUNCT
ejpam-5353	19	43	of	of	ADP
ejpam-5353	19	44	k	k	PROPN
ejpam-5353	19	45	subgraphs	subgraph	NOUN
ejpam-5353	19	46	of	of	ADP
ejpam-5353	19	47	h	h	NOUN
ejpam-5353	19	48	decompose	decompose	NOUN
ejpam-5353	19	49	h	h	NOUN
ejpam-5353	19	50	if	if	SCONJ
ejpam-5353	20	1	and	and	CCONJ
ejpam-5353	20	2	only	only	ADV
ejpam-5353	20	3	if	if	SCONJ
ejpam-5353	20	4	k⋃	k⋃	X
ejpam-5353	20	5	i=1	i=1	PROPN
ejpam-5353	21	1	gi	gi	PROPN
ejpam-5353	22	1	=	=	ADJ
ejpam-5353	23	1	h	h	PROPN
ejpam-5353	24	1	(	(	PUNCT
ejpam-5353	24	2	ignoring	ignore	VERB
ejpam-5353	24	3	isolated	isolated	ADJ
ejpam-5353	24	4	vertices	vertex	NOUN
ejpam-5353	24	5	)	)	PUNCT
ejpam-5353	24	6	&	&	CCONJ
ejpam-5353	24	7	k⋂	k⋂	PROPN
ejpam-5353	25	1	i=1	i=1	PROPN
ejpam-5353	25	2	gi	gi	X
ejpam-5353	25	3	=	=	PUNCT
ejpam-5353	25	4	ϕ(empty	ϕ(empty	NOUN
ejpam-5353	25	5	graph	graph	NOUN
ejpam-5353	25	6	)	)	PUNCT
ejpam-5353	25	7	.	.	PUNCT
ejpam-5353	26	1	if	if	SCONJ
ejpam-5353	26	2	gi	gi	NOUN
ejpam-5353	26	3	≊	≊	VERB
ejpam-5353	26	4	g	g	NOUN
ejpam-5353	26	5	for	for	ADP
ejpam-5353	26	6	each	each	DET
ejpam-5353	26	7	i	i	PRON
ejpam-5353	26	8	∈	∈	PROPN
ejpam-5353	26	9	{	{	PUNCT
ejpam-5353	26	10	1	1	NUM
ejpam-5353	26	11	,	,	PUNCT
ejpam-5353	26	12	2	2	NUM
ejpam-5353	26	13	,	,	PUNCT
ejpam-5353	26	14	·	·	PUNCT
ejpam-5353	26	15	·	·	PUNCT
ejpam-5353	26	16	·	·	PUNCT
ejpam-5353	27	1	k	k	X
ejpam-5353	27	2	}	}	PUNCT
ejpam-5353	27	3	,	,	PUNCT
ejpam-5353	27	4	then	then	ADV
ejpam-5353	27	5	g	g	PROPN
ejpam-5353	27	6	is	be	AUX
ejpam-5353	27	7	called	call	VERB
ejpam-5353	27	8	a	a	DET
ejpam-5353	27	9	decomposition	decomposition	NOUN
ejpam-5353	27	10	of	of	ADP
ejpam-5353	27	11	h	h	NOUN
ejpam-5353	27	12	by	by	ADP
ejpam-5353	27	13	g.	g.	PROPN
ejpam-5353	27	14	throughout	throughout	ADP
ejpam-5353	27	15	the	the	DET
ejpam-5353	27	16	paper	paper	NOUN
ejpam-5353	27	17	we	we	PRON
ejpam-5353	27	18	use	use	VERB
ejpam-5353	27	19	∗corresponding	∗corresponde	VERB
ejpam-5353	27	20	author	author	NOUN
ejpam-5353	27	21	.	.	PUNCT
ejpam-5353	28	1	doi	doi	NOUN
ejpam-5353	28	2	:	:	PUNCT
ejpam-5353	28	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5353	https://doi.org/10.29020/nybg.ejpam.v17i4.5353	PROPN
ejpam-5353	28	4	email	email	NOUN
ejpam-5353	28	5	addresses	address	VERB
ejpam-5353	28	6	:	:	PUNCT
ejpam-5353	28	7	hananshabana22@gmail.com	hananshabana22@gmail.com	X
ejpam-5353	28	8	(	(	PUNCT
ejpam-5353	28	9	h.	h.	PROPN
ejpam-5353	28	10	shabana	shabana	PROPN
ejpam-5353	28	11	)	)	PUNCT
ejpam-5353	28	12	,	,	PUNCT
ejpam-5353	28	13	ramadan.elshanawany380@gmail.com	ramadan.elshanawany380@gmail.com	X
ejpam-5353	28	14	(	(	PUNCT
ejpam-5353	28	15	r.	r.	PROPN
ejpam-5353	28	16	el	el	PROPN
ejpam-5353	28	17	-	-	PROPN
ejpam-5353	28	18	shanawany	shanawany	NOUN
ejpam-5353	28	19	)	)	PUNCT
ejpam-5353	28	20	,	,	PUNCT
ejpam-5353	28	21	saharreda@edu.asu.edu.eg	saharreda@edu.asu.edu.eg	PROPN
ejpam-5353	28	22	(	(	PUNCT
ejpam-5353	28	23	s.	s.	PROPN
ejpam-5353	28	24	halawa	halawa	PROPN
ejpam-5353	28	25	)	)	PUNCT
ejpam-5353	28	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5353	28	27	3492	3492	NUM
ejpam-5353	28	28	copyright	copyright	NOUN
ejpam-5353	28	29	:	:	PUNCT
ejpam-5353	28	30	©	©	PROPN
ejpam-5353	28	31	2024	2024	NUM
ejpam-5353	28	32	the	the	DET
ejpam-5353	28	33	author(s	author(s	NOUN
ejpam-5353	28	34	)	)	PUNCT
ejpam-5353	28	35	.	.	PUNCT
ejpam-5353	29	1	(	(	PUNCT
ejpam-5353	29	2	cc	cc	NOUN
ejpam-5353	29	3	by	by	ADP
ejpam-5353	29	4	-	-	PUNCT
ejpam-5353	29	5	nc	nc	PROPN
ejpam-5353	29	6	4.0	4.0	NUM
ejpam-5353	29	7	)	)	PUNCT
ejpam-5353	29	8	h.	h.	PROPN
ejpam-5353	29	9	shabana	shabana	PROPN
ejpam-5353	29	10	,	,	PUNCT
ejpam-5353	29	11	r.	r.	PROPN
ejpam-5353	29	12	el	el	PROPN
ejpam-5353	29	13	-	-	PROPN
ejpam-5353	29	14	shanawany	shanawany	NOUN
ejpam-5353	29	15	,	,	PUNCT
ejpam-5353	29	16	s.	s.	PROPN
ejpam-5353	29	17	halawa	halawa	PROPN
ejpam-5353	29	18	/	/	PUNCT
ejpam-5353	29	19	eur	eur	PROPN
ejpam-5353	29	20	.	.	PUNCT
ejpam-5353	30	1	j.	j.	PROPN
ejpam-5353	30	2	pure	pure	PROPN
ejpam-5353	30	3	appl	appl	PROPN
ejpam-5353	30	4	.	.	PROPN
ejpam-5353	30	5	math	math	PROPN
ejpam-5353	30	6	,	,	PUNCT
ejpam-5353	30	7	17	17	NUM
ejpam-5353	30	8	(	(	PUNCT
ejpam-5353	30	9	4	4	NUM
ejpam-5353	30	10	)	)	PUNCT
ejpam-5353	30	11	(	(	PUNCT
ejpam-5353	30	12	2024	2024	NUM
ejpam-5353	30	13	)	)	PUNCT
ejpam-5353	30	14	,	,	PUNCT
ejpam-5353	30	15	3492	3492	NUM
ejpam-5353	30	16	-	-	SYM
ejpam-5353	30	17	3516	3516	NUM
ejpam-5353	30	18	3493	3493	NUM
ejpam-5353	30	19	v	v	NOUN
ejpam-5353	30	20	(	(	PUNCT
ejpam-5353	30	21	x	x	NOUN
ejpam-5353	30	22	)	)	PUNCT
ejpam-5353	30	23	,	,	PUNCT
ejpam-5353	30	24	e(x	e(x	NUM
ejpam-5353	30	25	)	)	PUNCT
ejpam-5353	30	26	for	for	ADP
ejpam-5353	30	27	the	the	DET
ejpam-5353	30	28	vertex	vertex	NOUN
ejpam-5353	30	29	set	set	NOUN
ejpam-5353	30	30	and	and	CCONJ
ejpam-5353	30	31	edge	edge	NOUN
ejpam-5353	30	32	set	set	NOUN
ejpam-5353	30	33	of	of	ADP
ejpam-5353	30	34	the	the	DET
ejpam-5353	30	35	graph	graph	NOUN
ejpam-5353	30	36	x	x	PUNCT
ejpam-5353	30	37	respectively	respectively	ADV
ejpam-5353	30	38	,	,	PUNCT
ejpam-5353	30	39	pk	pk	NOUN
ejpam-5353	30	40	for	for	ADP
ejpam-5353	30	41	a	a	DET
ejpam-5353	30	42	path	path	NOUN
ejpam-5353	30	43	of	of	ADP
ejpam-5353	30	44	k	k	PROPN
ejpam-5353	30	45	vertices	vertex	NOUN
ejpam-5353	30	46	,	,	PUNCT
ejpam-5353	30	47	mg	mg	ADV
ejpam-5353	30	48	for	for	ADP
ejpam-5353	30	49	m	m	PROPN
ejpam-5353	30	50	disjoint	disjoint	NOUN
ejpam-5353	30	51	copies	copy	NOUN
ejpam-5353	30	52	of	of	ADP
ejpam-5353	30	53	g	g	NOUN
ejpam-5353	30	54	,	,	PUNCT
ejpam-5353	30	55	and	and	CCONJ
ejpam-5353	30	56	g∪h	g∪h	NOUN
ejpam-5353	30	57	for	for	ADP
ejpam-5353	30	58	disjoint	disjoint	NOUN
ejpam-5353	30	59	union	union	NOUN
ejpam-5353	30	60	of	of	ADP
ejpam-5353	30	61	graphs	graph	NOUN
ejpam-5353	30	62	g	g	PROPN
ejpam-5353	30	63	and	and	CCONJ
ejpam-5353	30	64	h.	h.	PROPN
ejpam-5353	30	65	let	let	VERB
ejpam-5353	30	66	g1	g1	PROPN
ejpam-5353	30	67	=	=	PRON
ejpam-5353	30	68	{	{	PUNCT
ejpam-5353	30	69	g1	g1	PROPN
ejpam-5353	30	70	,	,	PUNCT
ejpam-5353	30	71	g2	g2	PROPN
ejpam-5353	30	72	,	,	PUNCT
ejpam-5353	30	73	·	·	PUNCT
ejpam-5353	30	74	·	·	PUNCT
ejpam-5353	30	75	·	·	PUNCT
ejpam-5353	30	76	,	,	PUNCT
ejpam-5353	30	77	gk	gk	PROPN
ejpam-5353	30	78	}	}	PUNCT
ejpam-5353	30	79	and	and	CCONJ
ejpam-5353	30	80	g2	g2	PROPN
ejpam-5353	30	81	=	=	PUNCT
ejpam-5353	30	82	{	{	PUNCT
ejpam-5353	30	83	f1	f1	NOUN
ejpam-5353	30	84	,	,	PUNCT
ejpam-5353	30	85	f2	f2	PROPN
ejpam-5353	30	86	,	,	PUNCT
ejpam-5353	30	87	·	·	PUNCT
ejpam-5353	30	88	·	·	PUNCT
ejpam-5353	30	89	·	·	PUNCT
ejpam-5353	30	90	,	,	PUNCT
ejpam-5353	30	91	fk	fk	INTJ
ejpam-5353	30	92	}	}	PUNCT
ejpam-5353	30	93	be	be	AUX
ejpam-5353	30	94	two	two	NUM
ejpam-5353	30	95	distinct	distinct	ADJ
ejpam-5353	30	96	edge	edge	NOUN
ejpam-5353	30	97	decompositions	decomposition	NOUN
ejpam-5353	30	98	of	of	ADP
ejpam-5353	30	99	h	h	NOUN
ejpam-5353	30	100	by	by	ADP
ejpam-5353	30	101	g	g	PROPN
ejpam-5353	30	102	such	such	ADJ
ejpam-5353	30	103	that	that	PRON
ejpam-5353	30	104	for	for	ADP
ejpam-5353	30	105	each	each	DET
ejpam-5353	30	106	i	i	PRON
ejpam-5353	30	107	∈	∈	PROPN
ejpam-5353	30	108	{	{	PUNCT
ejpam-5353	30	109	1	1	NUM
ejpam-5353	30	110	,	,	PUNCT
ejpam-5353	30	111	2	2	NUM
ejpam-5353	30	112	,	,	PUNCT
ejpam-5353	30	113	·	·	PUNCT
ejpam-5353	30	114	·	·	PUNCT
ejpam-5353	30	115	·	·	PUNCT
ejpam-5353	31	1	k	k	X
ejpam-5353	31	2	}	}	PUNCT
ejpam-5353	31	3	,	,	PUNCT
ejpam-5353	31	4	gi	gi	INTJ
ejpam-5353	31	5	≊	≊	NOUN
ejpam-5353	31	6	g	g	NOUN
ejpam-5353	31	7	≊	≊	NOUN
ejpam-5353	31	8	fi	fi	NOUN
ejpam-5353	31	9	.	.	PUNCT
ejpam-5353	32	1	such	such	ADJ
ejpam-5353	32	2	two	two	NUM
ejpam-5353	32	3	decompositions	decomposition	NOUN
ejpam-5353	32	4	are	be	AUX
ejpam-5353	32	5	called	call	VERB
ejpam-5353	32	6	orthogonal	orthogonal	ADJ
ejpam-5353	32	7	decompositions	decomposition	NOUN
ejpam-5353	32	8	if	if	SCONJ
ejpam-5353	32	9	|e(gi	|e(gi	PROPN
ejpam-5353	32	10	)	)	PUNCT
ejpam-5353	32	11	∩	∩	NOUN
ejpam-5353	32	12	e(fj)|	e(fj)|	VERB
ejpam-5353	32	13	=	=	SYM
ejpam-5353	32	14	1	1	NUM
ejpam-5353	32	15	for	for	ADP
ejpam-5353	32	16	all	all	DET
ejpam-5353	32	17	i	i	PROPN
ejpam-5353	32	18	,	,	PUNCT
ejpam-5353	32	19	j	j	PROPN
ejpam-5353	32	20	∈	∈	PROPN
ejpam-5353	32	21	{	{	PUNCT
ejpam-5353	32	22	1	1	NUM
ejpam-5353	32	23	,	,	PUNCT
ejpam-5353	32	24	2	2	NUM
ejpam-5353	32	25	,	,	PUNCT
ejpam-5353	32	26	·	·	PUNCT
ejpam-5353	32	27	·	·	PUNCT
ejpam-5353	32	28	·	·	PUNCT
ejpam-5353	33	1	k	k	X
ejpam-5353	33	2	}	}	PUNCT
ejpam-5353	33	3	.	.	PUNCT
ejpam-5353	34	1	whence	whence	NOUN
ejpam-5353	34	2	,	,	PUNCT
ejpam-5353	34	3	the	the	DET
ejpam-5353	34	4	collection	collection	NOUN
ejpam-5353	34	5	{	{	PUNCT
ejpam-5353	34	6	g1	g1	PROPN
ejpam-5353	34	7	∪	∪	ADP
ejpam-5353	34	8	g2	g2	PROPN
ejpam-5353	34	9	}	}	PUNCT
ejpam-5353	34	10	is	be	AUX
ejpam-5353	34	11	equivalent	equivalent	ADJ
ejpam-5353	34	12	to	to	ADP
ejpam-5353	34	13	an	an	DET
ejpam-5353	34	14	orthogonal	orthogonal	ADJ
ejpam-5353	34	15	double	double	ADJ
ejpam-5353	34	16	cover	cover	NOUN
ejpam-5353	34	17	(	(	PUNCT
ejpam-5353	34	18	odc	odc	PROPN
ejpam-5353	34	19	)	)	PUNCT
ejpam-5353	34	20	of	of	ADP
ejpam-5353	34	21	h	h	PROPN
ejpam-5353	34	22	by	by	ADP
ejpam-5353	34	23	g.	g.	PROPN
ejpam-5353	34	24	an	an	DET
ejpam-5353	34	25	odc	odc	PROPN
ejpam-5353	34	26	of	of	ADP
ejpam-5353	34	27	h	h	NOUN
ejpam-5353	34	28	by	by	ADP
ejpam-5353	34	29	g	g	PROPN
ejpam-5353	34	30	is	be	AUX
ejpam-5353	34	31	a	a	DET
ejpam-5353	34	32	collection	collection	NOUN
ejpam-5353	35	1	f	f	NOUN
ejpam-5353	35	2	=	=	PRON
ejpam-5353	35	3	{	{	PUNCT
ejpam-5353	35	4	ϕ	ϕ	PROPN
ejpam-5353	35	5	(	(	PUNCT
ejpam-5353	35	6	x	x	NOUN
ejpam-5353	35	7	)	)	PUNCT
ejpam-5353	35	8	:	:	PUNCT
ejpam-5353	35	9	x	x	X
ejpam-5353	35	10	∈	∈	NOUN
ejpam-5353	35	11	v	v	ADP
ejpam-5353	35	12	(	(	PUNCT
ejpam-5353	35	13	h	h	NOUN
ejpam-5353	35	14	)	)	PUNCT
ejpam-5353	35	15	}	}	PUNCT
ejpam-5353	35	16	of	of	ADP
ejpam-5353	35	17	subgraphs	subgraph	NOUN
ejpam-5353	35	18	of	of	ADP
ejpam-5353	35	19	h	h	NOUN
ejpam-5353	35	20	all	all	PRON
ejpam-5353	35	21	isomorphic	isomorphic	ADJ
ejpam-5353	35	22	to	to	ADP
ejpam-5353	35	23	the	the	DET
ejpam-5353	35	24	graph	graph	NOUN
ejpam-5353	35	25	g	g	NOUN
ejpam-5353	35	26	,	,	PUNCT
ejpam-5353	35	27	such	such	ADJ
ejpam-5353	35	28	that	that	SCONJ
ejpam-5353	35	29	every	every	DET
ejpam-5353	35	30	edge	edge	NOUN
ejpam-5353	35	31	of	of	ADP
ejpam-5353	35	32	h	h	NOUN
ejpam-5353	35	33	belongs	belong	VERB
ejpam-5353	35	34	to	to	ADP
ejpam-5353	35	35	exactly	exactly	ADV
ejpam-5353	35	36	two	two	NUM
ejpam-5353	35	37	elements	element	NOUN
ejpam-5353	35	38	from	from	ADP
ejpam-5353	35	39	f	f	PROPN
ejpam-5353	35	40	and	and	CCONJ
ejpam-5353	35	41	any	any	DET
ejpam-5353	35	42	two	two	NUM
ejpam-5353	35	43	elements	element	NOUN
ejpam-5353	35	44	ϕ	ϕ	X
ejpam-5353	35	45	(	(	PUNCT
ejpam-5353	35	46	x1	x1	PROPN
ejpam-5353	35	47	)	)	PUNCT
ejpam-5353	35	48	and	and	CCONJ
ejpam-5353	35	49	ϕ	ϕ	X
ejpam-5353	35	50	(	(	PUNCT
ejpam-5353	35	51	x2	x2	PROPN
ejpam-5353	35	52	)	)	PUNCT
ejpam-5353	35	53	from	from	ADP
ejpam-5353	35	54	f	f	PROPN
ejpam-5353	35	55	have	have	VERB
ejpam-5353	35	56	a	a	DET
ejpam-5353	35	57	common	common	ADJ
ejpam-5353	35	58	edge	edge	NOUN
ejpam-5353	35	59	if	if	SCONJ
ejpam-5353	35	60	and	and	CCONJ
ejpam-5353	35	61	only	only	ADV
ejpam-5353	35	62	if	if	SCONJ
ejpam-5353	35	63	the	the	DET
ejpam-5353	35	64	edge	edge	NOUN
ejpam-5353	35	65	(	(	PUNCT
ejpam-5353	35	66	x1	x1	PROPN
ejpam-5353	35	67	,	,	PUNCT
ejpam-5353	35	68	x2	x2	PROPN
ejpam-5353	35	69	)	)	PUNCT
ejpam-5353	35	70	∈	∈	PROPN
ejpam-5353	35	71	e(h	e(h	PROPN
ejpam-5353	35	72	)	)	PUNCT
ejpam-5353	35	73	.	.	PUNCT
ejpam-5353	36	1	not	not	PART
ejpam-5353	36	2	all	all	DET
ejpam-5353	36	3	graphs	graph	NOUN
ejpam-5353	36	4	h	h	NOUN
ejpam-5353	36	5	have	have	VERB
ejpam-5353	36	6	an	an	DET
ejpam-5353	36	7	odc	odc	NOUN
ejpam-5353	36	8	.	.	PUNCT
ejpam-5353	37	1	the	the	DET
ejpam-5353	37	2	necessary	necessary	ADJ
ejpam-5353	37	3	condition	condition	NOUN
ejpam-5353	37	4	to	to	PART
ejpam-5353	37	5	find	find	VERB
ejpam-5353	37	6	an	an	DET
ejpam-5353	37	7	odc	odc	NOUN
ejpam-5353	37	8	of	of	ADP
ejpam-5353	37	9	h	h	NOUN
ejpam-5353	37	10	is	be	AUX
ejpam-5353	37	11	that	that	SCONJ
ejpam-5353	37	12	the	the	DET
ejpam-5353	37	13	graph	graph	NOUN
ejpam-5353	37	14	h	h	NOUN
ejpam-5353	37	15	is	be	AUX
ejpam-5353	37	16	regular	regular	ADJ
ejpam-5353	37	17	.	.	PUNCT
ejpam-5353	38	1	for	for	ADP
ejpam-5353	38	2	the	the	DET
ejpam-5353	38	3	complete	complete	ADJ
ejpam-5353	38	4	graph	graph	NOUN
ejpam-5353	38	5	kn	kn	PROPN
ejpam-5353	38	6	,	,	PUNCT
ejpam-5353	38	7	odc	odc	PROPN
ejpam-5353	38	8	is	be	AUX
ejpam-5353	38	9	extensively	extensively	ADV
ejpam-5353	38	10	studied	study	VERB
ejpam-5353	38	11	,	,	PUNCT
ejpam-5353	38	12	we	we	PRON
ejpam-5353	38	13	refer	refer	VERB
ejpam-5353	38	14	the	the	DET
ejpam-5353	38	15	reader	reader	NOUN
ejpam-5353	38	16	to	to	ADP
ejpam-5353	38	17	a	a	DET
ejpam-5353	38	18	survey	survey	NOUN
ejpam-5353	38	19	[	[	X
ejpam-5353	38	20	14	14	NUM
ejpam-5353	38	21	]	]	PUNCT
ejpam-5353	38	22	.	.	PUNCT
ejpam-5353	39	1	odc	odc	PROPN
ejpam-5353	39	2	of	of	ADP
ejpam-5353	39	3	cayley	cayley	ADJ
ejpam-5353	39	4	graphs	graph	NOUN
ejpam-5353	39	5	was	be	AUX
ejpam-5353	39	6	studied	study	VERB
ejpam-5353	39	7	in	in	ADP
ejpam-5353	39	8	[	[	X
ejpam-5353	39	9	6	6	NUM
ejpam-5353	39	10	,	,	PUNCT
ejpam-5353	39	11	7	7	NUM
ejpam-5353	39	12	,	,	PUNCT
ejpam-5353	39	13	10	10	NUM
ejpam-5353	39	14	]	]	PUNCT
ejpam-5353	39	15	.	.	PUNCT
ejpam-5353	40	1	an	an	DET
ejpam-5353	40	2	odc	odc	PROPN
ejpam-5353	40	3	f	f	NOUN
ejpam-5353	40	4	of	of	ADP
ejpam-5353	40	5	h	h	PROPN
ejpam-5353	40	6	is	be	AUX
ejpam-5353	40	7	cyclic	cyclic	ADJ
ejpam-5353	40	8	(	(	PUNCT
ejpam-5353	40	9	codc	codc	NOUN
ejpam-5353	40	10	)	)	PUNCT
ejpam-5353	40	11	if	if	SCONJ
ejpam-5353	40	12	the	the	DET
ejpam-5353	40	13	cyclic	cyclic	ADJ
ejpam-5353	40	14	group	group	NOUN
ejpam-5353	40	15	of	of	ADP
ejpam-5353	40	16	order	order	NOUN
ejpam-5353	40	17	|v	|v	PROPN
ejpam-5353	40	18	(	(	PUNCT
ejpam-5353	40	19	h)|	h)|	PROPN
ejpam-5353	40	20	is	be	AUX
ejpam-5353	40	21	a	a	DET
ejpam-5353	40	22	subgroup	subgroup	NOUN
ejpam-5353	40	23	of	of	ADP
ejpam-5353	40	24	the	the	DET
ejpam-5353	40	25	automorphism	automorphism	NOUN
ejpam-5353	40	26	group	group	NOUN
ejpam-5353	40	27	of	of	ADP
ejpam-5353	40	28	h	h	PROPN
ejpam-5353	40	29	(	(	PUNCT
ejpam-5353	40	30	the	the	DET
ejpam-5353	40	31	group	group	NOUN
ejpam-5353	40	32	of	of	ADP
ejpam-5353	40	33	automorphism	automorphism	NOUN
ejpam-5353	40	34	of	of	ADP
ejpam-5353	40	35	the	the	DET
ejpam-5353	40	36	graph	graph	NOUN
ejpam-5353	40	37	h	h	NOUN
ejpam-5353	40	38	which	which	PRON
ejpam-5353	40	39	preserves	preserve	VERB
ejpam-5353	40	40	the	the	DET
ejpam-5353	40	41	covering	covering	NOUN
ejpam-5353	40	42	)	)	PUNCT
ejpam-5353	41	1	[	[	X
ejpam-5353	41	2	16	16	NUM
ejpam-5353	41	3	]	]	PUNCT
ejpam-5353	41	4	.	.	PUNCT
ejpam-5353	42	1	sampathkumar	sampathkumar	PROPN
ejpam-5353	42	2	et	et	PROPN
ejpam-5353	42	3	al	al	PROPN
ejpam-5353	42	4	.	.	PUNCT
ejpam-5353	43	1	[	[	X
ejpam-5353	43	2	20	20	NUM
ejpam-5353	43	3	]	]	PUNCT
ejpam-5353	43	4	investigated	investigate	VERB
ejpam-5353	43	5	codcs	codc	NOUN
ejpam-5353	43	6	of	of	ADP
ejpam-5353	43	7	circulant	circulant	ADJ
ejpam-5353	43	8	graphs	graph	NOUN
ejpam-5353	43	9	by	by	ADP
ejpam-5353	43	10	4	4	NUM
ejpam-5353	43	11	-	-	PUNCT
ejpam-5353	43	12	regular	regular	ADJ
ejpam-5353	43	13	circulant	circulant	ADJ
ejpam-5353	43	14	graphs	graph	NOUN
ejpam-5353	43	15	.	.	PUNCT
ejpam-5353	44	1	in	in	ADP
ejpam-5353	44	2	[	[	X
ejpam-5353	44	3	11	11	NUM
ejpam-5353	44	4	]	]	PUNCT
ejpam-5353	44	5	,	,	PUNCT
ejpam-5353	44	6	the	the	DET
ejpam-5353	44	7	authors	author	NOUN
ejpam-5353	44	8	attacked	attack	VERB
ejpam-5353	44	9	the	the	DET
ejpam-5353	44	10	problem	problem	NOUN
ejpam-5353	44	11	of	of	ADP
ejpam-5353	44	12	the	the	DET
ejpam-5353	44	13	existence	existence	NOUN
ejpam-5353	44	14	of	of	ADP
ejpam-5353	44	15	odcs	odc	NOUN
ejpam-5353	44	16	of	of	ADP
ejpam-5353	44	17	2	2	NUM
ejpam-5353	44	18	-	-	PUNCT
ejpam-5353	44	19	regular	regular	ADJ
ejpam-5353	44	20	graphs	graph	NOUN
ejpam-5353	44	21	and	and	CCONJ
ejpam-5353	44	22	3	3	NUM
ejpam-5353	44	23	-	-	PUNCT
ejpam-5353	44	24	regular	regular	ADJ
ejpam-5353	44	25	graphs	graph	NOUN
ejpam-5353	44	26	.	.	PUNCT
ejpam-5353	45	1	sampathkumar	sampathkumar	PROPN
ejpam-5353	45	2	et	et	PROPN
ejpam-5353	45	3	al	al	PROPN
ejpam-5353	45	4	.	.	PUNCT
ejpam-5353	46	1	[	[	X
ejpam-5353	46	2	21	21	NUM
ejpam-5353	46	3	]	]	PUNCT
ejpam-5353	46	4	presented	present	VERB
ejpam-5353	46	5	σ−labeling	σ−labele	VERB
ejpam-5353	46	6	,	,	PUNCT
ejpam-5353	46	7	as	as	ADP
ejpam-5353	46	8	a	a	DET
ejpam-5353	46	9	special	special	ADJ
ejpam-5353	46	10	category	category	NOUN
ejpam-5353	46	11	of	of	ADP
ejpam-5353	46	12	orthogonal	orthogonal	ADJ
ejpam-5353	46	13	labeling	labeling	NOUN
ejpam-5353	46	14	.	.	PUNCT
ejpam-5353	47	1	using	use	VERB
ejpam-5353	47	2	σ−labeling	σ−labele	VERB
ejpam-5353	47	3	,	,	PUNCT
ejpam-5353	47	4	they	they	PRON
ejpam-5353	47	5	constructed	construct	VERB
ejpam-5353	47	6	codcs	codc	NOUN
ejpam-5353	47	7	of	of	ADP
ejpam-5353	47	8	circulant	circulant	ADJ
ejpam-5353	47	9	graphs	graph	NOUN
ejpam-5353	47	10	by	by	ADP
ejpam-5353	47	11	some	some	DET
ejpam-5353	47	12	caterpillars	caterpillar	NOUN
ejpam-5353	47	13	of	of	ADP
ejpam-5353	47	14	diameters	diameter	NOUN
ejpam-5353	47	15	4	4	NUM
ejpam-5353	47	16	.	.	PUNCT
ejpam-5353	47	17	higazy	higazy	PROPN
ejpam-5353	47	18	et	et	PROPN
ejpam-5353	47	19	al	al	PROPN
ejpam-5353	47	20	.	.	PUNCT
ejpam-5353	48	1	[	[	X
ejpam-5353	48	2	22	22	NUM
ejpam-5353	48	3	]	]	PUNCT
ejpam-5353	48	4	gave	give	VERB
ejpam-5353	48	5	a	a	DET
ejpam-5353	48	6	complete	complete	ADJ
ejpam-5353	48	7	classification	classification	NOUN
ejpam-5353	48	8	for	for	ADP
ejpam-5353	48	9	circulant	circulant	ADJ
ejpam-5353	48	10	graphs	graph	NOUN
ejpam-5353	48	11	of	of	ADP
ejpam-5353	48	12	degree	degree	NOUN
ejpam-5353	48	13	five	five	NUM
ejpam-5353	48	14	which	which	PRON
ejpam-5353	48	15	lead	lead	VERB
ejpam-5353	48	16	to	to	ADP
ejpam-5353	48	17	an	an	DET
ejpam-5353	48	18	odc	odc	NOUN
ejpam-5353	48	19	by	by	ADP
ejpam-5353	48	20	some	some	DET
ejpam-5353	48	21	graphs	graph	NOUN
ejpam-5353	48	22	.	.	PUNCT
ejpam-5353	49	1	the	the	DET
ejpam-5353	49	2	present	present	ADJ
ejpam-5353	49	3	paper	paper	NOUN
ejpam-5353	49	4	is	be	AUX
ejpam-5353	49	5	interested	interested	ADJ
ejpam-5353	49	6	in	in	ADP
ejpam-5353	49	7	studying	study	VERB
ejpam-5353	49	8	odc	odc	PROPN
ejpam-5353	49	9	for	for	ADP
ejpam-5353	49	10	balanced	balanced	ADJ
ejpam-5353	49	11	complete	complete	ADJ
ejpam-5353	49	12	bipartite	bipartite	PROPN
ejpam-5353	49	13	graph	graph	NOUN
ejpam-5353	49	14	kn	kn	PROPN
ejpam-5353	49	15	,	,	PUNCT
ejpam-5353	49	16	n.	n.	PROPN
ejpam-5353	49	17	given	give	VERB
ejpam-5353	49	18	a	a	DET
ejpam-5353	49	19	positive	positive	ADJ
ejpam-5353	49	20	integer	integer	NOUN
ejpam-5353	49	21	n	n	CCONJ
ejpam-5353	49	22	,	,	PUNCT
ejpam-5353	49	23	the	the	DET
ejpam-5353	49	24	balanced	balanced	ADJ
ejpam-5353	49	25	bipartite	bipartite	PROPN
ejpam-5353	49	26	graph	graph	PROPN
ejpam-5353	49	27	kn	kn	PROPN
ejpam-5353	49	28	,	,	PUNCT
ejpam-5353	49	29	n	n	PRON
ejpam-5353	49	30	is	be	AUX
ejpam-5353	49	31	a	a	DET
ejpam-5353	49	32	bipartite	bipartite	ADJ
ejpam-5353	49	33	graph	graph	NOUN
ejpam-5353	49	34	with	with	ADP
ejpam-5353	49	35	a	a	DET
ejpam-5353	49	36	2n−element	2n−element	NUM
ejpam-5353	49	37	vertex	vertex	NOUN
ejpam-5353	49	38	set	set	VERB
ejpam-5353	49	39	v	v	NOUN
ejpam-5353	49	40	.	.	PUNCT
ejpam-5353	50	1	this	this	PRON
ejpam-5353	50	2	set	set	VERB
ejpam-5353	50	3	v	v	NOUN
ejpam-5353	50	4	is	be	AUX
ejpam-5353	50	5	divided	divide	VERB
ejpam-5353	50	6	into	into	ADP
ejpam-5353	50	7	two	two	NUM
ejpam-5353	50	8	partite	partite	ADJ
ejpam-5353	50	9	sets	set	NOUN
ejpam-5353	50	10	of	of	ADP
ejpam-5353	50	11	vertices	vertex	NOUN
ejpam-5353	50	12	,	,	PUNCT
ejpam-5353	50	13	each	each	DET
ejpam-5353	50	14	containing	contain	VERB
ejpam-5353	50	15	n	n	PRON
ejpam-5353	50	16	elements	element	NOUN
ejpam-5353	50	17	.	.	PUNCT
ejpam-5353	51	1	the	the	DET
ejpam-5353	51	2	vertices	vertex	NOUN
ejpam-5353	51	3	of	of	ADP
ejpam-5353	51	4	kn	kn	PROPN
ejpam-5353	51	5	,	,	PUNCT
ejpam-5353	51	6	n	n	PRON
ejpam-5353	51	7	are	be	AUX
ejpam-5353	51	8	labeled	label	VERB
ejpam-5353	51	9	by	by	ADP
ejpam-5353	51	10	the	the	DET
ejpam-5353	51	11	elements	element	NOUN
ejpam-5353	51	12	of	of	ADP
ejpam-5353	51	13	zn	zn	NUM
ejpam-5353	51	14	×	×	PROPN
ejpam-5353	51	15	{	{	PUNCT
ejpam-5353	51	16	0	0	NUM
ejpam-5353	51	17	,	,	PUNCT
ejpam-5353	51	18	1	1	NUM
ejpam-5353	51	19	}	}	PUNCT
ejpam-5353	51	20	where	where	SCONJ
ejpam-5353	51	21	zn	zn	X
ejpam-5353	51	22	=	=	SYM
ejpam-5353	51	23	{	{	PUNCT
ejpam-5353	51	24	0	0	NUM
ejpam-5353	51	25	,	,	PUNCT
ejpam-5353	51	26	1	1	NUM
ejpam-5353	51	27	,	,	PUNCT
ejpam-5353	51	28	2	2	NUM
ejpam-5353	51	29	,	,	PUNCT
ejpam-5353	51	30	·	·	PUNCT
ejpam-5353	51	31	·	·	PUNCT
ejpam-5353	51	32	·	·	PUNCT
ejpam-5353	51	33	,	,	PUNCT
ejpam-5353	51	34	n	n	CCONJ
ejpam-5353	51	35	−	−	PROPN
ejpam-5353	51	36	1	1	NUM
ejpam-5353	51	37	}	}	PUNCT
ejpam-5353	51	38	represents	represent	VERB
ejpam-5353	51	39	all	all	DET
ejpam-5353	51	40	residue	residue	NOUN
ejpam-5353	51	41	classes	class	NOUN
ejpam-5353	51	42	modulo	modulo	VERB
ejpam-5353	51	43	n.	n.	VERB
ejpam-5353	51	44	the	the	DET
ejpam-5353	51	45	edge	edge	NOUN
ejpam-5353	51	46	set	set	NOUN
ejpam-5353	51	47	of	of	ADP
ejpam-5353	51	48	kn	kn	PROPN
ejpam-5353	51	49	,	,	PUNCT
ejpam-5353	51	50	n	n	PRON
ejpam-5353	51	51	is	be	AUX
ejpam-5353	51	52	defined	define	VERB
ejpam-5353	51	53	as	as	ADP
ejpam-5353	51	54	pairs	pair	NOUN
ejpam-5353	51	55	e(kn	e(kn	NUM
ejpam-5353	51	56	,	,	PUNCT
ejpam-5353	51	57	n	n	CCONJ
ejpam-5353	51	58	)	)	PUNCT
ejpam-5353	51	59	=	=	PRON
ejpam-5353	51	60	{	{	PUNCT
ejpam-5353	51	61	(	(	PUNCT
ejpam-5353	51	62	(	(	PUNCT
ejpam-5353	51	63	u	u	NOUN
ejpam-5353	51	64	,	,	PUNCT
ejpam-5353	51	65	0	0	NUM
ejpam-5353	51	66	)	)	PUNCT
ejpam-5353	51	67	,	,	PUNCT
ejpam-5353	51	68	(	(	PUNCT
ejpam-5353	51	69	v	v	NOUN
ejpam-5353	51	70	,	,	PUNCT
ejpam-5353	51	71	1	1	NUM
ejpam-5353	51	72	)	)	PUNCT
ejpam-5353	51	73	)	)	PUNCT
ejpam-5353	51	74	;	;	PUNCT
ejpam-5353	51	75	u	u	NOUN
ejpam-5353	51	76	,	,	PUNCT
ejpam-5353	51	77	v	v	PROPN
ejpam-5353	51	78	∈	∈	PROPN
ejpam-5353	51	79	zn	zn	NUM
ejpam-5353	51	80	}	}	PUNCT
ejpam-5353	51	81	.	.	PUNCT
ejpam-5353	52	1	for	for	ADP
ejpam-5353	52	2	simplicity	simplicity	NOUN
ejpam-5353	52	3	and	and	CCONJ
ejpam-5353	52	4	if	if	SCONJ
ejpam-5353	52	5	there	there	PRON
ejpam-5353	52	6	is	be	VERB
ejpam-5353	52	7	no	no	DET
ejpam-5353	52	8	danger	danger	NOUN
ejpam-5353	52	9	of	of	ADP
ejpam-5353	52	10	ambiguity	ambiguity	NOUN
ejpam-5353	52	11	,	,	PUNCT
ejpam-5353	52	12	we	we	PRON
ejpam-5353	52	13	use	use	VERB
ejpam-5353	52	14	vr	vr	NOUN
ejpam-5353	52	15	for	for	ADP
ejpam-5353	52	16	the	the	DET
ejpam-5353	52	17	vertex	vertex	NOUN
ejpam-5353	52	18	(	(	PUNCT
ejpam-5353	52	19	v	v	NOUN
ejpam-5353	52	20	,	,	PUNCT
ejpam-5353	52	21	r	r	NOUN
ejpam-5353	52	22	)	)	PUNCT
ejpam-5353	52	23	∈	∈	NOUN
ejpam-5353	52	24	zn×{0	zn×{0	NOUN
ejpam-5353	52	25	,	,	PUNCT
ejpam-5353	52	26	1	1	NUM
ejpam-5353	52	27	}	}	PUNCT
ejpam-5353	52	28	,	,	PUNCT
ejpam-5353	52	29	and	and	CCONJ
ejpam-5353	52	30	(	(	PUNCT
ejpam-5353	52	31	u0	u0	ADJ
ejpam-5353	52	32	,	,	PUNCT
ejpam-5353	52	33	v1	v1	NOUN
ejpam-5353	52	34	)	)	PUNCT
ejpam-5353	52	35	for	for	ADP
ejpam-5353	52	36	the	the	DET
ejpam-5353	52	37	edge	edge	NOUN
ejpam-5353	52	38	(	(	PUNCT
ejpam-5353	52	39	(	(	PUNCT
ejpam-5353	52	40	u	u	NOUN
ejpam-5353	52	41	,	,	PUNCT
ejpam-5353	52	42	0	0	NUM
ejpam-5353	52	43	)	)	PUNCT
ejpam-5353	52	44	,	,	PUNCT
ejpam-5353	52	45	(	(	PUNCT
ejpam-5353	52	46	v	v	NOUN
ejpam-5353	52	47	,	,	PUNCT
ejpam-5353	52	48	1	1	NUM
ejpam-5353	52	49	)	)	PUNCT
ejpam-5353	52	50	)	)	PUNCT
ejpam-5353	52	51	.	.	PUNCT
ejpam-5353	53	1	we	we	PRON
ejpam-5353	53	2	aim	aim	VERB
ejpam-5353	53	3	to	to	PART
ejpam-5353	53	4	construct	construct	VERB
ejpam-5353	53	5	an	an	DET
ejpam-5353	53	6	odc	odc	NOUN
ejpam-5353	53	7	of	of	ADP
ejpam-5353	53	8	kn	kn	PROPN
ejpam-5353	53	9	,	,	PUNCT
ejpam-5353	53	10	n	n	CCONJ
ejpam-5353	53	11	by	by	ADP
ejpam-5353	53	12	g	g	NOUN
ejpam-5353	53	13	where	where	SCONJ
ejpam-5353	53	14	g	g	PROPN
ejpam-5353	53	15	is	be	AUX
ejpam-5353	53	16	isomorphic	isomorphic	ADJ
ejpam-5353	53	17	to	to	ADP
ejpam-5353	53	18	certain	certain	ADJ
ejpam-5353	53	19	trees	tree	NOUN
ejpam-5353	53	20	with	with	ADP
ejpam-5353	53	21	n	n	NOUN
ejpam-5353	53	22	edges	edge	NOUN
ejpam-5353	53	23	.	.	PUNCT
ejpam-5353	54	1	in	in	ADP
ejpam-5353	54	2	the	the	DET
ejpam-5353	54	3	next	next	ADJ
ejpam-5353	54	4	section	section	NOUN
ejpam-5353	54	5	,	,	PUNCT
ejpam-5353	54	6	we	we	PRON
ejpam-5353	54	7	introduce	introduce	VERB
ejpam-5353	54	8	the	the	DET
ejpam-5353	54	9	fundamentals	fundamental	NOUN
ejpam-5353	54	10	of	of	ADP
ejpam-5353	54	11	our	our	PRON
ejpam-5353	54	12	approach	approach	NOUN
ejpam-5353	54	13	for	for	ADP
ejpam-5353	54	14	constructing	construct	VERB
ejpam-5353	54	15	an	an	DET
ejpam-5353	54	16	odc	odc	NOUN
ejpam-5353	54	17	of	of	ADP
ejpam-5353	54	18	kn	kn	PROPN
ejpam-5353	54	19	,	,	PUNCT
ejpam-5353	54	20	n.	n.	PROPN
ejpam-5353	54	21	we	we	PRON
ejpam-5353	54	22	call	call	VERB
ejpam-5353	54	23	this	this	DET
ejpam-5353	54	24	approach	approach	NOUN
ejpam-5353	54	25	a	a	DET
ejpam-5353	54	26	base	base	NOUN
ejpam-5353	54	27	-	-	PUNCT
ejpam-5353	54	28	generated	generate	VERB
ejpam-5353	54	29	approach	approach	NOUN
ejpam-5353	54	30	(	(	PUNCT
ejpam-5353	54	31	bga	bga	NOUN
ejpam-5353	54	32	)	)	PUNCT
ejpam-5353	54	33	.	.	PUNCT
ejpam-5353	55	1	section	section	NOUN
ejpam-5353	55	2	3	3	NUM
ejpam-5353	55	3	,	,	PUNCT
ejpam-5353	55	4	shows	show	VERB
ejpam-5353	55	5	the	the	DET
ejpam-5353	55	6	construction	construction	NOUN
ejpam-5353	55	7	of	of	ADP
ejpam-5353	55	8	odcs	odc	NOUN
ejpam-5353	55	9	of	of	ADP
ejpam-5353	55	10	kn	kn	PROPN
ejpam-5353	55	11	,	,	PUNCT
ejpam-5353	55	12	n	n	CCONJ
ejpam-5353	55	13	by	by	ADP
ejpam-5353	55	14	certain	certain	ADJ
ejpam-5353	55	15	trees	tree	NOUN
ejpam-5353	55	16	based	base	VERB
ejpam-5353	55	17	on	on	ADP
ejpam-5353	55	18	bga	bga	PROPN
ejpam-5353	55	19	introduced	introduce	VERB
ejpam-5353	55	20	in	in	ADP
ejpam-5353	55	21	section	section	NOUN
ejpam-5353	55	22	2	2	NUM
ejpam-5353	55	23	.	.	PUNCT
ejpam-5353	56	1	an	an	DET
ejpam-5353	56	2	application	application	NOUN
ejpam-5353	56	3	of	of	ADP
ejpam-5353	56	4	bga	bga	NOUN
ejpam-5353	56	5	in	in	ADP
ejpam-5353	56	6	designing	design	VERB
ejpam-5353	56	7	graph	graph	NOUN
ejpam-5353	56	8	error	error	NOUN
ejpam-5353	56	9	detecting	detecting	NOUN
ejpam-5353	56	10	and	and	CCONJ
ejpam-5353	56	11	correcting	correct	VERB
ejpam-5353	56	12	codes	code	NOUN
ejpam-5353	56	13	is	be	AUX
ejpam-5353	56	14	presented	present	VERB
ejpam-5353	56	15	in	in	ADP
ejpam-5353	56	16	section	section	NOUN
ejpam-5353	56	17	4	4	NUM
ejpam-5353	56	18	.	.	PUNCT
ejpam-5353	56	19	section	section	NOUN
ejpam-5353	56	20	5	5	NUM
ejpam-5353	56	21	introduces	introduce	VERB
ejpam-5353	56	22	a	a	DET
ejpam-5353	56	23	recursive	recursive	ADJ
ejpam-5353	56	24	construction	construction	NOUN
ejpam-5353	56	25	of	of	ADP
ejpam-5353	56	26	odc	odc	PROPN
ejpam-5353	56	27	of	of	ADP
ejpam-5353	56	28	higher	high	ADJ
ejpam-5353	56	29	order	order	NOUN
ejpam-5353	56	30	balanced	balanced	ADJ
ejpam-5353	56	31	complete	complete	ADJ
ejpam-5353	56	32	bipartite	bipartite	NOUN
ejpam-5353	56	33	graph	graph	NOUN
ejpam-5353	56	34	by	by	ADP
ejpam-5353	56	35	disjoint	disjoint	NOUN
ejpam-5353	56	36	trees	tree	NOUN
ejpam-5353	56	37	.	.	PUNCT
ejpam-5353	57	1	the	the	DET
ejpam-5353	57	2	conclusion	conclusion	NOUN
ejpam-5353	57	3	of	of	ADP
ejpam-5353	57	4	the	the	DET
ejpam-5353	57	5	paper	paper	NOUN
ejpam-5353	57	6	and	and	CCONJ
ejpam-5353	57	7	future	future	ADJ
ejpam-5353	57	8	work	work	NOUN
ejpam-5353	57	9	are	be	AUX
ejpam-5353	57	10	presented	present	VERB
ejpam-5353	57	11	in	in	ADP
ejpam-5353	57	12	section	section	NOUN
ejpam-5353	57	13	6	6	NUM
ejpam-5353	57	14	.	.	NOUN
ejpam-5353	57	15	2	2	NUM
ejpam-5353	57	16	.	.	X
ejpam-5353	57	17	fundamentals	fundamental	NOUN
ejpam-5353	57	18	of	of	ADP
ejpam-5353	57	19	base	base	NOUN
ejpam-5353	57	20	-	-	PUNCT
ejpam-5353	57	21	generated	generate	VERB
ejpam-5353	57	22	approach	approach	NOUN
ejpam-5353	57	23	to	to	PART
ejpam-5353	57	24	construct	construct	VERB
ejpam-5353	57	25	an	an	DET
ejpam-5353	57	26	odc	odc	NOUN
ejpam-5353	57	27	of	of	ADP
ejpam-5353	57	28	kn	kn	PROPN
ejpam-5353	57	29	,	,	PUNCT
ejpam-5353	57	30	n	n	CCONJ
ejpam-5353	57	31	we	we	PRON
ejpam-5353	57	32	have	have	VERB
ejpam-5353	57	33	to	to	PART
ejpam-5353	57	34	find	find	VERB
ejpam-5353	57	35	two	two	NUM
ejpam-5353	57	36	orthogonal	orthogonal	ADJ
ejpam-5353	57	37	decompositions	decomposition	NOUN
ejpam-5353	57	38	of	of	ADP
ejpam-5353	57	39	kn	kn	PROPN
ejpam-5353	57	40	,	,	PUNCT
ejpam-5353	57	41	n.	n.	NOUN
ejpam-5353	57	42	in	in	ADP
ejpam-5353	57	43	base	base	NOUN
ejpam-5353	57	44	-	-	PUNCT
ejpam-5353	57	45	generated	generate	VERB
ejpam-5353	57	46	approach	approach	NOUN
ejpam-5353	57	47	(	(	PUNCT
ejpam-5353	57	48	bga	bga	NOUN
ejpam-5353	57	49	)	)	PUNCT
ejpam-5353	57	50	we	we	PRON
ejpam-5353	57	51	first	first	ADV
ejpam-5353	57	52	seek	seek	VERB
ejpam-5353	57	53	to	to	PART
ejpam-5353	57	54	find	find	VERB
ejpam-5353	57	55	the	the	DET
ejpam-5353	57	56	base	base	NOUN
ejpam-5353	57	57	for	for	ADP
ejpam-5353	57	58	each	each	DET
ejpam-5353	57	59	decomposition	decomposition	NOUN
ejpam-5353	57	60	.	.	PUNCT
ejpam-5353	58	1	h.	h.	PROPN
ejpam-5353	58	2	shabana	shabana	PROPN
ejpam-5353	58	3	,	,	PUNCT
ejpam-5353	58	4	r.	r.	PROPN
ejpam-5353	58	5	el	el	PROPN
ejpam-5353	58	6	-	-	PROPN
ejpam-5353	58	7	shanawany	shanawany	NOUN
ejpam-5353	58	8	,	,	PUNCT
ejpam-5353	58	9	s.	s.	PROPN
ejpam-5353	58	10	halawa	halawa	PROPN
ejpam-5353	58	11	/	/	PUNCT
ejpam-5353	58	12	eur	eur	PROPN
ejpam-5353	58	13	.	.	PUNCT
ejpam-5353	59	1	j.	j.	PROPN
ejpam-5353	59	2	pure	pure	PROPN
ejpam-5353	59	3	appl	appl	PROPN
ejpam-5353	59	4	.	.	PROPN
ejpam-5353	59	5	math	math	PROPN
ejpam-5353	59	6	,	,	PUNCT
ejpam-5353	59	7	17	17	NUM
ejpam-5353	59	8	(	(	PUNCT
ejpam-5353	59	9	4	4	NUM
ejpam-5353	59	10	)	)	PUNCT
ejpam-5353	59	11	(	(	PUNCT
ejpam-5353	59	12	2024	2024	NUM
ejpam-5353	59	13	)	)	PUNCT
ejpam-5353	59	14	,	,	PUNCT
ejpam-5353	59	15	3492	3492	NUM
ejpam-5353	59	16	-	-	SYM
ejpam-5353	59	17	3516	3516	NUM
ejpam-5353	59	18	3494	3494	NUM
ejpam-5353	59	19	then	then	ADV
ejpam-5353	59	20	odc	odc	PROPN
ejpam-5353	59	21	is	be	AUX
ejpam-5353	59	22	generated	generate	VERB
ejpam-5353	59	23	from	from	ADP
ejpam-5353	59	24	such	such	ADJ
ejpam-5353	59	25	two	two	NUM
ejpam-5353	59	26	bases	basis	NOUN
ejpam-5353	59	27	.	.	PUNCT
ejpam-5353	60	1	let	let	VERB
ejpam-5353	60	2	us	we	PRON
ejpam-5353	60	3	introduce	introduce	VERB
ejpam-5353	60	4	the	the	DET
ejpam-5353	60	5	principals	principal	NOUN
ejpam-5353	60	6	of	of	ADP
ejpam-5353	60	7	this	this	DET
ejpam-5353	60	8	approach	approach	NOUN
ejpam-5353	60	9	.	.	PUNCT
ejpam-5353	61	1	assume	assume	VERB
ejpam-5353	61	2	e	e	X
ejpam-5353	61	3	=	=	SYM
ejpam-5353	61	4	(	(	PUNCT
ejpam-5353	61	5	a0	a0	PROPN
ejpam-5353	61	6	,	,	PUNCT
ejpam-5353	61	7	b1	b1	PROPN
ejpam-5353	61	8	)	)	PUNCT
ejpam-5353	61	9	be	be	VERB
ejpam-5353	61	10	an	an	DET
ejpam-5353	61	11	edge	edge	NOUN
ejpam-5353	61	12	belonging	belong	VERB
ejpam-5353	61	13	to	to	ADP
ejpam-5353	61	14	e(kn	e(kn	NUM
ejpam-5353	61	15	,	,	PUNCT
ejpam-5353	61	16	n).the	n).the	DET
ejpam-5353	61	17	length	length	NOUN
ejpam-5353	61	18	of	of	ADP
ejpam-5353	61	19	the	the	DET
ejpam-5353	61	20	edge	edge	NOUN
ejpam-5353	61	21	e	e	NOUN
ejpam-5353	61	22	is	be	AUX
ejpam-5353	61	23	defined	define	VERB
ejpam-5353	61	24	by	by	ADP
ejpam-5353	61	25	d(e	d(e	NOUN
ejpam-5353	61	26	)	)	PUNCT
ejpam-5353	62	1	=	=	SYM
ejpam-5353	62	2	b−	b−	PROPN
ejpam-5353	62	3	a	a	NOUN
ejpam-5353	62	4	,	,	PUNCT
ejpam-5353	62	5	where	where	SCONJ
ejpam-5353	62	6	addition	addition	NOUN
ejpam-5353	62	7	and	and	CCONJ
ejpam-5353	62	8	subtraction	subtraction	NOUN
ejpam-5353	62	9	are	be	AUX
ejpam-5353	62	10	calculated	calculate	VERB
ejpam-5353	62	11	modulo	modulo	PROPN
ejpam-5353	62	12	n.	n.	NOUN
ejpam-5353	62	13	definition	definition	NOUN
ejpam-5353	62	14	1	1	X
ejpam-5353	62	15	.	.	PUNCT
ejpam-5353	63	1	let	let	VERB
ejpam-5353	63	2	g	g	NOUN
ejpam-5353	63	3	to	to	PART
ejpam-5353	63	4	be	be	AUX
ejpam-5353	63	5	a	a	DET
ejpam-5353	63	6	subgraph	subgraph	NOUN
ejpam-5353	63	7	of	of	ADP
ejpam-5353	63	8	kn	kn	PROPN
ejpam-5353	63	9	,	,	PUNCT
ejpam-5353	63	10	n	n	CCONJ
ejpam-5353	63	11	,	,	PUNCT
ejpam-5353	63	12	and	and	CCONJ
ejpam-5353	63	13	s	s	PROPN
ejpam-5353	63	14	∈	∈	PROPN
ejpam-5353	63	15	zn	zn	X
ejpam-5353	63	16	.	.	PUNCT
ejpam-5353	64	1	then	then	ADV
ejpam-5353	64	2	the	the	DET
ejpam-5353	64	3	graph	graph	NOUN
ejpam-5353	64	4	g+s	g+s	VERB
ejpam-5353	64	5	(	(	PUNCT
ejpam-5353	64	6	or	or	CCONJ
ejpam-5353	64	7	gs	gs	INTJ
ejpam-5353	64	8	)	)	PUNCT
ejpam-5353	64	9	with	with	ADP
ejpam-5353	64	10	e(g+	e(g+	NUM
ejpam-5353	64	11	s	s	PART
ejpam-5353	64	12	)	)	PUNCT
ejpam-5353	64	13	=	=	SYM
ejpam-5353	64	14	{	{	PUNCT
ejpam-5353	64	15	(	(	PUNCT
ejpam-5353	64	16	(	(	PUNCT
ejpam-5353	64	17	a+	a+	X
ejpam-5353	64	18	s)0	s)0	NOUN
ejpam-5353	64	19	,	,	PUNCT
ejpam-5353	64	20	(	(	PUNCT
ejpam-5353	64	21	b+	b+	X
ejpam-5353	64	22	s)1	s)1	PROPN
ejpam-5353	64	23	)	)	PUNCT
ejpam-5353	64	24	;	;	PUNCT
ejpam-5353	64	25	(	(	PUNCT
ejpam-5353	64	26	a0	a0	NOUN
ejpam-5353	64	27	,	,	PUNCT
ejpam-5353	64	28	b1	b1	NOUN
ejpam-5353	64	29	)	)	PUNCT
ejpam-5353	64	30	∈	∈	PROPN
ejpam-5353	64	31	e(g	e(g	PROPN
ejpam-5353	64	32	)	)	PUNCT
ejpam-5353	64	33	}	}	PUNCT
ejpam-5353	64	34	is	be	AUX
ejpam-5353	64	35	called	call	VERB
ejpam-5353	64	36	stranslation	stranslation	NOUN
ejpam-5353	64	37	of	of	ADP
ejpam-5353	64	38	g.	g.	PROPN
ejpam-5353	64	39	definition	definition	NOUN
ejpam-5353	64	40	2	2	NUM
ejpam-5353	64	41	.	.	PUNCT
ejpam-5353	64	42	a	a	DET
ejpam-5353	64	43	subgraph	subgraph	NOUN
ejpam-5353	64	44	g	g	PROPN
ejpam-5353	64	45	of	of	ADP
ejpam-5353	64	46	kn	kn	PROPN
ejpam-5353	64	47	,	,	PUNCT
ejpam-5353	64	48	n	n	PROPN
ejpam-5353	64	49	is	be	AUX
ejpam-5353	64	50	called	call	VERB
ejpam-5353	64	51	a	a	DET
ejpam-5353	64	52	base	base	NOUN
ejpam-5353	64	53	of	of	ADP
ejpam-5353	64	54	an	an	DET
ejpam-5353	64	55	edge	edge	NOUN
ejpam-5353	64	56	decomposition	decomposition	NOUN
ejpam-5353	64	57	of	of	ADP
ejpam-5353	64	58	kn	kn	PROPN
ejpam-5353	64	59	,	,	PUNCT
ejpam-5353	64	60	n	n	CCONJ
ejpam-5353	64	61	by	by	ADP
ejpam-5353	64	62	g	g	PROPN
ejpam-5353	64	63	if	if	SCONJ
ejpam-5353	65	1	and	and	CCONJ
ejpam-5353	65	2	only	only	ADV
ejpam-5353	65	3	if	if	SCONJ
ejpam-5353	65	4	n−1⋃	n−1⋃	ADJ
ejpam-5353	65	5	s=0	s=0	X
ejpam-5353	65	6	{	{	PUNCT
ejpam-5353	65	7	e	e	X
ejpam-5353	65	8	(	(	PUNCT
ejpam-5353	65	9	g+	g+	NOUN
ejpam-5353	65	10	s	s	PART
ejpam-5353	65	11	)	)	PUNCT
ejpam-5353	65	12	}	}	PUNCT
ejpam-5353	65	13	=	=	SYM
ejpam-5353	65	14	e	e	X
ejpam-5353	65	15	(	(	PUNCT
ejpam-5353	65	16	kn	kn	PROPN
ejpam-5353	65	17	,	,	PUNCT
ejpam-5353	65	18	n	n	CCONJ
ejpam-5353	65	19	)	)	PUNCT
ejpam-5353	65	20	.	.	PUNCT
ejpam-5353	66	1	the	the	DET
ejpam-5353	66	2	next	next	ADJ
ejpam-5353	66	3	theorem	theorem	NOUN
ejpam-5353	66	4	proves	prove	VERB
ejpam-5353	66	5	the	the	DET
ejpam-5353	66	6	validity	validity	NOUN
ejpam-5353	66	7	of	of	ADP
ejpam-5353	66	8	the	the	DET
ejpam-5353	66	9	method	method	NOUN
ejpam-5353	66	10	by	by	ADP
ejpam-5353	66	11	which	which	PRON
ejpam-5353	66	12	we	we	PRON
ejpam-5353	66	13	build	build	VERB
ejpam-5353	66	14	a	a	DET
ejpam-5353	66	15	base	base	NOUN
ejpam-5353	66	16	.	.	PUNCT
ejpam-5353	67	1	theorem	theorem	NOUN
ejpam-5353	67	2	1	1	NUM
ejpam-5353	67	3	.	.	PUNCT
ejpam-5353	68	1	let	let	VERB
ejpam-5353	68	2	g	g	PRON
ejpam-5353	68	3	be	be	AUX
ejpam-5353	68	4	a	a	DET
ejpam-5353	68	5	subgraph	subgraph	NOUN
ejpam-5353	68	6	of	of	ADP
ejpam-5353	68	7	kn	kn	PROPN
ejpam-5353	68	8	,	,	PUNCT
ejpam-5353	68	9	n	n	PRON
ejpam-5353	68	10	such	such	ADJ
ejpam-5353	68	11	that	that	SCONJ
ejpam-5353	68	12	|e(g)|	|e(g)|	PROPN
ejpam-5353	68	13	=	=	SYM
ejpam-5353	68	14	n.	n.	NOUN
ejpam-5353	69	1	then	then	ADV
ejpam-5353	69	2	g	g	PROPN
ejpam-5353	69	3	is	be	AUX
ejpam-5353	69	4	a	a	DET
ejpam-5353	69	5	base	base	NOUN
ejpam-5353	69	6	of	of	ADP
ejpam-5353	69	7	an	an	DET
ejpam-5353	69	8	edge	edge	NOUN
ejpam-5353	69	9	decomposition	decomposition	NOUN
ejpam-5353	69	10	of	of	ADP
ejpam-5353	69	11	kn	kn	PROPN
ejpam-5353	69	12	,	,	PUNCT
ejpam-5353	69	13	n	n	CCONJ
ejpam-5353	69	14	by	by	ADP
ejpam-5353	69	15	g	g	PROPN
ejpam-5353	69	16	if	if	SCONJ
ejpam-5353	69	17	all	all	DET
ejpam-5353	69	18	the	the	DET
ejpam-5353	69	19	edges	edge	NOUN
ejpam-5353	69	20	of	of	ADP
ejpam-5353	69	21	g	g	NOUN
ejpam-5353	69	22	are	be	AUX
ejpam-5353	69	23	mutually	mutually	ADV
ejpam-5353	69	24	different	different	ADJ
ejpam-5353	69	25	in	in	ADP
ejpam-5353	69	26	lengths	length	NOUN
ejpam-5353	69	27	,	,	PUNCT
ejpam-5353	69	28	i.e.{d(e	i.e.{d(e	PROPN
ejpam-5353	69	29	)	)	PUNCT
ejpam-5353	69	30	;	;	PUNCT
ejpam-5353	69	31	e	e	PROPN
ejpam-5353	69	32	∈	∈	PROPN
ejpam-5353	69	33	e(g	e(g	PROPN
ejpam-5353	69	34	)	)	PUNCT
ejpam-5353	69	35	}	}	PUNCT
ejpam-5353	70	1	=	=	SYM
ejpam-5353	70	2	zn	zn	X
ejpam-5353	70	3	.	.	PUNCT
ejpam-5353	71	1	proof	proof	NOUN
ejpam-5353	71	2	.	.	PUNCT
ejpam-5353	72	1	let	let	VERB
ejpam-5353	72	2	x	x	PUNCT
ejpam-5353	72	3	=	=	PRON
ejpam-5353	72	4	{	{	PUNCT
ejpam-5353	72	5	(	(	PUNCT
ejpam-5353	72	6	ai	ai	PROPN
ejpam-5353	72	7	,	,	PUNCT
ejpam-5353	72	8	bi	bi	NOUN
ejpam-5353	72	9	)	)	PUNCT
ejpam-5353	72	10	;	;	PUNCT
ejpam-5353	72	11	i	i	PRON
ejpam-5353	72	12	∈	∈	PROPN
ejpam-5353	72	13	zn	zn	AUX
ejpam-5353	72	14	}	}	PUNCT
ejpam-5353	72	15	be	be	VERB
ejpam-5353	72	16	the	the	DET
ejpam-5353	72	17	set	set	NOUN
ejpam-5353	72	18	of	of	ADP
ejpam-5353	72	19	all	all	DET
ejpam-5353	72	20	edges	edge	NOUN
ejpam-5353	72	21	of	of	ADP
ejpam-5353	72	22	g	g	NOUN
ejpam-5353	72	23	,	,	PUNCT
ejpam-5353	72	24	such	such	ADJ
ejpam-5353	72	25	that	that	SCONJ
ejpam-5353	72	26	the	the	DET
ejpam-5353	72	27	edge	edge	NOUN
ejpam-5353	72	28	ei	ei	X
ejpam-5353	72	29	=	=	PUNCT
ejpam-5353	72	30	(	(	PUNCT
ejpam-5353	72	31	ai	ai	PROPN
ejpam-5353	72	32	,	,	PUNCT
ejpam-5353	72	33	bi	bi	NOUN
ejpam-5353	72	34	)	)	PUNCT
ejpam-5353	72	35	.	.	PUNCT
ejpam-5353	73	1	since	since	SCONJ
ejpam-5353	73	2	all	all	DET
ejpam-5353	73	3	the	the	DET
ejpam-5353	73	4	edges	edge	NOUN
ejpam-5353	73	5	of	of	ADP
ejpam-5353	73	6	g	g	NOUN
ejpam-5353	73	7	are	be	AUX
ejpam-5353	73	8	mutually	mutually	ADV
ejpam-5353	73	9	different	different	ADJ
ejpam-5353	73	10	in	in	ADP
ejpam-5353	73	11	lengths	length	NOUN
ejpam-5353	73	12	,	,	PUNCT
ejpam-5353	73	13	then	then	ADV
ejpam-5353	73	14	the	the	DET
ejpam-5353	73	15	set	set	NOUN
ejpam-5353	73	16	x	x	X
ejpam-5353	73	17	satisfies	satisfie	NOUN
ejpam-5353	73	18	{	{	PUNCT
ejpam-5353	73	19	bi	bi	NOUN
ejpam-5353	73	20	−	−	PROPN
ejpam-5353	73	21	ai	ai	VERB
ejpam-5353	73	22	;	;	PUNCT
ejpam-5353	73	23	i	i	PRON
ejpam-5353	73	24	∈	∈	PROPN
ejpam-5353	73	25	zn	zn	PROPN
ejpam-5353	73	26	}	}	PUNCT
ejpam-5353	73	27	=	=	SYM
ejpam-5353	74	1	zn	zn	AUX
ejpam-5353	74	2	.	.	PUNCT
ejpam-5353	74	3	let	let	VERB
ejpam-5353	74	4	di	di	NOUN
ejpam-5353	74	5	=	=	NOUN
ejpam-5353	74	6	bi	bi	NOUN
ejpam-5353	74	7	−	−	PROPN
ejpam-5353	74	8	ai	ai	VERB
ejpam-5353	74	9	that	that	PRON
ejpam-5353	74	10	is	be	AUX
ejpam-5353	74	11	a	a	DET
ejpam-5353	74	12	unique	unique	ADJ
ejpam-5353	74	13	for	for	ADP
ejpam-5353	74	14	every	every	DET
ejpam-5353	74	15	edge	edge	NOUN
ejpam-5353	74	16	(	(	PUNCT
ejpam-5353	74	17	ai	ai	NOUN
ejpam-5353	74	18	,	,	PUNCT
ejpam-5353	74	19	bi	bi	ADJ
ejpam-5353	74	20	)	)	PUNCT
ejpam-5353	74	21	∈	∈	PROPN
ejpam-5353	74	22	e(g	e(g	PROPN
ejpam-5353	74	23	)	)	PUNCT
ejpam-5353	74	24	;	;	PUNCT
ejpam-5353	74	25	i	i	PRON
ejpam-5353	74	26	∈	∈	PROPN
ejpam-5353	75	1	zn	zn	X
ejpam-5353	75	2	.	.	PUNCT
ejpam-5353	76	1	for	for	ADP
ejpam-5353	76	2	any	any	DET
ejpam-5353	76	3	s	s	NOUN
ejpam-5353	76	4	,	,	PUNCT
ejpam-5353	76	5	t	t	PROPN
ejpam-5353	76	6	∈	∈	PROPN
ejpam-5353	76	7	zn	zn	PROPN
ejpam-5353	76	8	and	and	CCONJ
ejpam-5353	76	9	s	s	PROPN
ejpam-5353	76	10	̸=	̸=	PROPN
ejpam-5353	76	11	t	t	PROPN
ejpam-5353	76	12	,	,	PUNCT
ejpam-5353	76	13	let	let	VERB
ejpam-5353	76	14	(	(	PUNCT
ejpam-5353	76	15	ai	ai	VERB
ejpam-5353	76	16	+	+	PROPN
ejpam-5353	76	17	s	s	PROPN
ejpam-5353	76	18	,	,	PUNCT
ejpam-5353	76	19	bi	bi	NOUN
ejpam-5353	76	20	+	+	PROPN
ejpam-5353	76	21	s	s	X
ejpam-5353	76	22	)	)	PUNCT
ejpam-5353	76	23	∈	∈	PROPN
ejpam-5353	76	24	e(gs	e(gs	PROPN
ejpam-5353	76	25	)	)	PUNCT
ejpam-5353	76	26	and	and	CCONJ
ejpam-5353	76	27	(	(	PUNCT
ejpam-5353	76	28	ai	ai	PROPN
ejpam-5353	76	29	+	+	PROPN
ejpam-5353	76	30	t	t	PROPN
ejpam-5353	76	31	,	,	PUNCT
ejpam-5353	76	32	bi	bi	PROPN
ejpam-5353	76	33	+	+	PROPN
ejpam-5353	76	34	t	t	PROPN
ejpam-5353	76	35	)	)	PUNCT
ejpam-5353	76	36	∈	∈	PROPN
ejpam-5353	76	37	e(gt	e(gt	PROPN
ejpam-5353	76	38	)	)	PUNCT
ejpam-5353	76	39	.	.	PUNCT
ejpam-5353	77	1	assume	assume	VERB
ejpam-5353	77	2	that	that	SCONJ
ejpam-5353	77	3	|e(gs	|e(gs	PROPN
ejpam-5353	77	4	)	)	PUNCT
ejpam-5353	77	5	∩	∩	NOUN
ejpam-5353	77	6	e(gt)|	e(gt)|	NOUN
ejpam-5353	77	7	=	=	NOUN
ejpam-5353	77	8	̸	̸	NUM
ejpam-5353	77	9	0	0	NUM
ejpam-5353	77	10	,	,	PUNCT
ejpam-5353	77	11	that	that	PRON
ejpam-5353	77	12	is	be	AUX
ejpam-5353	77	13	there	there	PRON
ejpam-5353	77	14	is	be	VERB
ejpam-5353	77	15	at	at	ADV
ejpam-5353	77	16	least	least	ADJ
ejpam-5353	77	17	one	one	NUM
ejpam-5353	77	18	edge	edge	NOUN
ejpam-5353	77	19	(	(	PUNCT
ejpam-5353	77	20	ai	ai	NOUN
ejpam-5353	77	21	,	,	PUNCT
ejpam-5353	77	22	bi	bi	ADJ
ejpam-5353	77	23	)	)	PUNCT
ejpam-5353	77	24	∈	∈	PROPN
ejpam-5353	77	25	|e(gs	|e(gs	PROPN
ejpam-5353	77	26	)	)	PUNCT
ejpam-5353	77	27	∩	∩	PROPN
ejpam-5353	77	28	e(gt)|	e(gt)|	ADJ
ejpam-5353	77	29	.	.	PUNCT
ejpam-5353	78	1	from	from	ADP
ejpam-5353	78	2	the	the	DET
ejpam-5353	78	3	definition	definition	NOUN
ejpam-5353	78	4	of	of	ADP
ejpam-5353	78	5	stranslation	stranslation	NOUN
ejpam-5353	78	6	of	of	ADP
ejpam-5353	78	7	g	g	NOUN
ejpam-5353	78	8	,	,	PUNCT
ejpam-5353	78	9	we	we	PRON
ejpam-5353	78	10	know	know	VERB
ejpam-5353	78	11	that	that	PRON
ejpam-5353	78	12	(	(	PUNCT
ejpam-5353	78	13	ai	ai	VERB
ejpam-5353	78	14	+	+	CCONJ
ejpam-5353	78	15	s−	s−	PROPN
ejpam-5353	78	16	s	s	PART
ejpam-5353	78	17	,	,	PUNCT
ejpam-5353	78	18	bi	bi	NOUN
ejpam-5353	78	19	+	+	CCONJ
ejpam-5353	78	20	s−	s−	PROPN
ejpam-5353	78	21	s	s	PART
ejpam-5353	78	22	)	)	PUNCT
ejpam-5353	78	23	=	=	SYM
ejpam-5353	78	24	(	(	PUNCT
ejpam-5353	78	25	ai	ai	PROPN
ejpam-5353	78	26	,	,	PUNCT
ejpam-5353	78	27	bi	bi	NOUN
ejpam-5353	78	28	)	)	PUNCT
ejpam-5353	78	29	.	.	PUNCT
ejpam-5353	79	1	also	also	ADV
ejpam-5353	79	2	(	(	PUNCT
ejpam-5353	79	3	ai	ai	VERB
ejpam-5353	79	4	+	+	CCONJ
ejpam-5353	79	5	t−	t−	PROPN
ejpam-5353	79	6	t	t	PROPN
ejpam-5353	79	7	,	,	PUNCT
ejpam-5353	79	8	bi	bi	NOUN
ejpam-5353	79	9	+	+	CCONJ
ejpam-5353	79	10	t−	t−	PROPN
ejpam-5353	79	11	t	t	PROPN
ejpam-5353	79	12	)	)	PUNCT
ejpam-5353	79	13	=	=	PRON
ejpam-5353	79	14	(	(	PUNCT
ejpam-5353	79	15	ai	ai	PROPN
ejpam-5353	79	16	,	,	PUNCT
ejpam-5353	79	17	bi	bi	NOUN
ejpam-5353	79	18	)	)	PUNCT
ejpam-5353	79	19	.	.	PUNCT
ejpam-5353	80	1	since	since	SCONJ
ejpam-5353	80	2	bi	bi	NOUN
ejpam-5353	80	3	−	−	PROPN
ejpam-5353	80	4	ai	ai	PROPN
ejpam-5353	80	5	=	=	NOUN
ejpam-5353	80	6	di	di	NOUN
ejpam-5353	80	7	is	be	AUX
ejpam-5353	80	8	unique	unique	ADJ
ejpam-5353	80	9	for	for	ADP
ejpam-5353	80	10	every	every	DET
ejpam-5353	80	11	edge	edge	NOUN
ejpam-5353	80	12	(	(	PUNCT
ejpam-5353	80	13	ai	ai	NOUN
ejpam-5353	80	14	,	,	PUNCT
ejpam-5353	80	15	bi	bi	ADJ
ejpam-5353	80	16	)	)	PUNCT
ejpam-5353	80	17	∈	∈	PROPN
ejpam-5353	80	18	e(g	e(g	PROPN
ejpam-5353	80	19	)	)	PUNCT
ejpam-5353	80	20	,	,	PUNCT
ejpam-5353	80	21	then	then	ADV
ejpam-5353	80	22	we	we	PRON
ejpam-5353	80	23	have	have	VERB
ejpam-5353	80	24	a	a	DET
ejpam-5353	80	25	contradiction	contradiction	NOUN
ejpam-5353	80	26	.	.	PUNCT
ejpam-5353	81	1	therefore	therefore	ADV
ejpam-5353	81	2	,	,	PUNCT
ejpam-5353	81	3	|e(gs	|e(gs	PROPN
ejpam-5353	81	4	)	)	PUNCT
ejpam-5353	81	5	∩	∩	PROPN
ejpam-5353	81	6	e(gt)|	e(gt)|	ADJ
ejpam-5353	81	7	=	=	SYM
ejpam-5353	81	8	0	0	NUM
ejpam-5353	81	9	for	for	ADP
ejpam-5353	81	10	any	any	DET
ejpam-5353	81	11	s	s	NOUN
ejpam-5353	81	12	,	,	PUNCT
ejpam-5353	81	13	t	t	PROPN
ejpam-5353	81	14	∈	∈	PROPN
ejpam-5353	81	15	zn	zn	PROPN
ejpam-5353	81	16	and	and	CCONJ
ejpam-5353	81	17	s	s	PROPN
ejpam-5353	81	18	̸=	̸=	PROPN
ejpam-5353	81	19	t.	t.	NOUN
ejpam-5353	81	20	moreover	moreover	ADV
ejpam-5353	81	21	,	,	PUNCT
ejpam-5353	81	22	n−1⋃	n−1⋃	NOUN
ejpam-5353	81	23	i=0	i=0	PROPN
ejpam-5353	81	24	{	{	PUNCT
ejpam-5353	81	25	e	e	NOUN
ejpam-5353	81	26	(	(	PUNCT
ejpam-5353	81	27	gi	gi	NOUN
ejpam-5353	81	28	)	)	PUNCT
ejpam-5353	81	29	}	}	PUNCT
ejpam-5353	81	30	=	=	SYM
ejpam-5353	81	31	e	e	X
ejpam-5353	81	32	(	(	PUNCT
ejpam-5353	81	33	kn	kn	PROPN
ejpam-5353	81	34	,	,	PUNCT
ejpam-5353	81	35	n	n	CCONJ
ejpam-5353	81	36	)	)	PUNCT
ejpam-5353	81	37	,	,	PUNCT
ejpam-5353	81	38	thus	thus	ADV
ejpam-5353	81	39	g	g	PROPN
ejpam-5353	81	40	is	be	AUX
ejpam-5353	81	41	a	a	DET
ejpam-5353	81	42	base	base	NOUN
ejpam-5353	81	43	of	of	ADP
ejpam-5353	81	44	an	an	DET
ejpam-5353	81	45	edge	edge	NOUN
ejpam-5353	81	46	decomposition	decomposition	NOUN
ejpam-5353	81	47	of	of	ADP
ejpam-5353	81	48	kn	kn	PROPN
ejpam-5353	81	49	,	,	PUNCT
ejpam-5353	81	50	n	n	CCONJ
ejpam-5353	81	51	by	by	ADP
ejpam-5353	81	52	g.	g.	PROPN
ejpam-5353	81	53	2.1	2.1	NUM
ejpam-5353	81	54	.	.	PUNCT
ejpam-5353	82	1	construction	construction	NOUN
ejpam-5353	82	2	of	of	ADP
ejpam-5353	82	3	an	an	DET
ejpam-5353	82	4	odc	odc	NOUN
ejpam-5353	82	5	of	of	ADP
ejpam-5353	82	6	kn	kn	PROPN
ejpam-5353	82	7	,	,	PUNCT
ejpam-5353	82	8	n	n	CCONJ
ejpam-5353	82	9	using	use	VERB
ejpam-5353	82	10	two	two	NUM
ejpam-5353	82	11	orthogonal	orthogonal	ADJ
ejpam-5353	82	12	bases	basis	NOUN
ejpam-5353	82	13	let	let	VERB
ejpam-5353	82	14	g1	g1	PROPN
ejpam-5353	82	15	and	and	CCONJ
ejpam-5353	82	16	g2	g2	PROPN
ejpam-5353	82	17	be	be	VERB
ejpam-5353	82	18	two	two	NUM
ejpam-5353	82	19	bases	basis	NOUN
ejpam-5353	82	20	of	of	ADP
ejpam-5353	82	21	two	two	NUM
ejpam-5353	82	22	decompositions	decomposition	NOUN
ejpam-5353	82	23	of	of	ADP
ejpam-5353	82	24	kn	kn	PROPN
ejpam-5353	82	25	,	,	PUNCT
ejpam-5353	82	26	n.	n.	VERB
ejpam-5353	82	27	such	such	ADJ
ejpam-5353	82	28	two	two	NUM
ejpam-5353	82	29	bases	basis	NOUN
ejpam-5353	82	30	are	be	AUX
ejpam-5353	82	31	orthogonal	orthogonal	ADJ
ejpam-5353	82	32	if	if	SCONJ
ejpam-5353	82	33	|e(g1	|e(g1	NOUN
ejpam-5353	82	34	)	)	PUNCT
ejpam-5353	82	35	∩	∩	NOUN
ejpam-5353	82	36	e(g2)|	e(g2)|	PROPN
ejpam-5353	82	37	=	=	PROPN
ejpam-5353	83	1	1	1	X
ejpam-5353	83	2	.	.	PUNCT
ejpam-5353	84	1	if	if	SCONJ
ejpam-5353	84	2	two	two	NUM
ejpam-5353	84	3	bases	basis	NOUN
ejpam-5353	84	4	g1	g1	NOUN
ejpam-5353	84	5	and	and	CCONJ
ejpam-5353	84	6	g2	g2	PROPN
ejpam-5353	84	7	are	be	AUX
ejpam-5353	84	8	orthogonal	orthogonal	ADJ
ejpam-5353	84	9	,	,	PUNCT
ejpam-5353	84	10	then	then	ADV
ejpam-5353	84	11	the	the	DET
ejpam-5353	84	12	collection	collection	NOUN
ejpam-5353	84	13	g	g	PROPN
ejpam-5353	84	14	=	=	PRON
ejpam-5353	84	15	{	{	PUNCT
ejpam-5353	84	16	gi	gi	X
ejpam-5353	84	17	a	a	PRON
ejpam-5353	84	18	:	:	PUNCT
ejpam-5353	84	19	a	a	DET
ejpam-5353	84	20	∈	∈	PROPN
ejpam-5353	84	21	zn	zn	X
ejpam-5353	84	22	,	,	PUNCT
ejpam-5353	84	23	i	i	PRON
ejpam-5353	84	24	∈	∈	PROPN
ejpam-5353	84	25	{	{	PUNCT
ejpam-5353	84	26	1	1	NUM
ejpam-5353	84	27	,	,	PUNCT
ejpam-5353	84	28	2	2	NUM
ejpam-5353	84	29	}	}	PUNCT
ejpam-5353	84	30	}	}	PUNCT
ejpam-5353	84	31	with	with	ADP
ejpam-5353	84	32	gi	gi	NUM
ejpam-5353	84	33	a	a	PRON
ejpam-5353	85	1	=	=	X
ejpam-5353	85	2	(	(	PUNCT
ejpam-5353	85	3	gi	gi	X
ejpam-5353	85	4	+	+	CCONJ
ejpam-5353	85	5	a	a	X
ejpam-5353	85	6	)	)	PUNCT
ejpam-5353	85	7	is	be	AUX
ejpam-5353	85	8	equivalent	equivalent	ADJ
ejpam-5353	85	9	to	to	ADP
ejpam-5353	85	10	an	an	DET
ejpam-5353	85	11	odc	odc	NOUN
ejpam-5353	85	12	of	of	ADP
ejpam-5353	85	13	kn	kn	PROPN
ejpam-5353	85	14	,	,	PUNCT
ejpam-5353	85	15	n.	n.	PROPN
ejpam-5353	85	16	moreover	moreover	ADV
ejpam-5353	85	17	,	,	PUNCT
ejpam-5353	85	18	g	g	PROPN
ejpam-5353	85	19	represents	represent	VERB
ejpam-5353	85	20	an	an	DET
ejpam-5353	85	21	odc	odc	NOUN
ejpam-5353	85	22	of	of	ADP
ejpam-5353	85	23	kn	kn	PROPN
ejpam-5353	85	24	,	,	PUNCT
ejpam-5353	85	25	n	n	CCONJ
ejpam-5353	85	26	by	by	ADP
ejpam-5353	85	27	g	g	PROPN
ejpam-5353	85	28	if	if	SCONJ
ejpam-5353	85	29	g1	g1	NOUN
ejpam-5353	85	30	≊	≊	VERB
ejpam-5353	85	31	g	g	NOUN
ejpam-5353	85	32	≊	≊	NOUN
ejpam-5353	85	33	g2	g2	PROPN
ejpam-5353	85	34	.	.	PUNCT
ejpam-5353	86	1	definition	definition	NOUN
ejpam-5353	86	2	3	3	X
ejpam-5353	86	3	.	.	PUNCT
ejpam-5353	87	1	let	let	VERB
ejpam-5353	87	2	g	g	NOUN
ejpam-5353	87	3	to	to	PART
ejpam-5353	87	4	be	be	AUX
ejpam-5353	87	5	be	be	AUX
ejpam-5353	87	6	a	a	DET
ejpam-5353	87	7	subgraph	subgraph	NOUN
ejpam-5353	87	8	of	of	ADP
ejpam-5353	87	9	kn	kn	PROPN
ejpam-5353	87	10	,	,	PUNCT
ejpam-5353	87	11	n	n	CCONJ
ejpam-5353	87	12	,	,	PUNCT
ejpam-5353	87	13	the	the	DET
ejpam-5353	87	14	subgraph	subgraph	NOUN
ejpam-5353	87	15	g	g	PROPN
ejpam-5353	87	16	′	′	NUM
ejpam-5353	87	17	of	of	ADP
ejpam-5353	87	18	kn	kn	PROPN
ejpam-5353	87	19	,	,	PUNCT
ejpam-5353	87	20	n	n	PROPN
ejpam-5353	87	21	with	with	ADP
ejpam-5353	87	22	e(g	e(g	PROPN
ejpam-5353	87	23	′	′	NUM
ejpam-5353	87	24	)	)	PUNCT
ejpam-5353	88	1	=	=	PRON
ejpam-5353	88	2	{	{	PUNCT
ejpam-5353	88	3	{	{	PUNCT
ejpam-5353	88	4	a0	a0	NOUN
ejpam-5353	88	5	,	,	PUNCT
ejpam-5353	88	6	b1	b1	PROPN
ejpam-5353	88	7	}	}	PUNCT
ejpam-5353	88	8	:	:	PUNCT
ejpam-5353	88	9	{	{	PUNCT
ejpam-5353	88	10	b0	b0	NOUN
ejpam-5353	88	11	,	,	PUNCT
ejpam-5353	88	12	a1	a1	NOUN
ejpam-5353	88	13	}	}	PUNCT
ejpam-5353	88	14	∈	∈	PROPN
ejpam-5353	88	15	e(g	e(g	PROPN
ejpam-5353	88	16	)	)	PUNCT
ejpam-5353	88	17	}	}	PUNCT
ejpam-5353	88	18	is	be	AUX
ejpam-5353	88	19	called	call	VERB
ejpam-5353	88	20	the	the	DET
ejpam-5353	88	21	symmetric	symmetric	ADJ
ejpam-5353	88	22	graph	graph	NOUN
ejpam-5353	88	23	of	of	ADP
ejpam-5353	88	24	g.	g.	PROPN
ejpam-5353	88	25	remark	remark	PROPN
ejpam-5353	88	26	1	1	NUM
ejpam-5353	88	27	.	.	PUNCT
ejpam-5353	89	1	the	the	DET
ejpam-5353	89	2	graph	graph	NOUN
ejpam-5353	89	3	g	g	ADP
ejpam-5353	89	4	′	′	NUM
ejpam-5353	89	5	is	be	AUX
ejpam-5353	89	6	a	a	DET
ejpam-5353	89	7	base	base	NOUN
ejpam-5353	89	8	of	of	ADP
ejpam-5353	89	9	a	a	DET
ejpam-5353	89	10	decomposition	decomposition	NOUN
ejpam-5353	89	11	of	of	ADP
ejpam-5353	89	12	kn	kn	PROPN
ejpam-5353	89	13	,	,	PUNCT
ejpam-5353	89	14	n	n	CCONJ
ejpam-5353	89	15	by	by	ADP
ejpam-5353	89	16	g	g	PROPN
ejpam-5353	89	17	if	if	SCONJ
ejpam-5353	90	1	and	and	CCONJ
ejpam-5353	90	2	only	only	ADV
ejpam-5353	90	3	if	if	SCONJ
ejpam-5353	90	4	g	g	PROPN
ejpam-5353	90	5	is	be	AUX
ejpam-5353	90	6	also	also	ADV
ejpam-5353	90	7	a	a	DET
ejpam-5353	90	8	base	base	NOUN
ejpam-5353	90	9	of	of	ADP
ejpam-5353	90	10	a	a	DET
ejpam-5353	90	11	decomposition	decomposition	NOUN
ejpam-5353	90	12	of	of	ADP
ejpam-5353	90	13	kn	kn	PROPN
ejpam-5353	90	14	,	,	PUNCT
ejpam-5353	90	15	n	n	CCONJ
ejpam-5353	90	16	by	by	ADP
ejpam-5353	90	17	g.	g.	PROPN
ejpam-5353	90	18	in	in	ADP
ejpam-5353	90	19	the	the	DET
ejpam-5353	90	20	next	next	ADJ
ejpam-5353	90	21	section	section	NOUN
ejpam-5353	90	22	,	,	PUNCT
ejpam-5353	90	23	we	we	PRON
ejpam-5353	90	24	use	use	VERB
ejpam-5353	90	25	an	an	DET
ejpam-5353	90	26	algebraic	algebraic	ADJ
ejpam-5353	90	27	representation	representation	NOUN
ejpam-5353	90	28	for	for	ADP
ejpam-5353	90	29	a	a	DET
ejpam-5353	90	30	base	base	NOUN
ejpam-5353	90	31	g	g	NOUN
ejpam-5353	90	32	of	of	ADP
ejpam-5353	90	33	a	a	DET
ejpam-5353	90	34	decomposition	decomposition	NOUN
ejpam-5353	90	35	of	of	ADP
ejpam-5353	90	36	kn	kn	PROPN
ejpam-5353	90	37	,	,	PUNCT
ejpam-5353	90	38	n.	n.	PROPN
ejpam-5353	90	39	h.	h.	PROPN
ejpam-5353	90	40	shabana	shabana	PROPN
ejpam-5353	90	41	,	,	PUNCT
ejpam-5353	90	42	r.	r.	PROPN
ejpam-5353	90	43	el	el	PROPN
ejpam-5353	90	44	-	-	PROPN
ejpam-5353	90	45	shanawany	shanawany	NOUN
ejpam-5353	90	46	,	,	PUNCT
ejpam-5353	90	47	s.	s.	PROPN
ejpam-5353	90	48	halawa	halawa	PROPN
ejpam-5353	90	49	/	/	PUNCT
ejpam-5353	90	50	eur	eur	PROPN
ejpam-5353	90	51	.	.	PUNCT
ejpam-5353	91	1	j.	j.	PROPN
ejpam-5353	91	2	pure	pure	PROPN
ejpam-5353	91	3	appl	appl	PROPN
ejpam-5353	91	4	.	.	PROPN
ejpam-5353	91	5	math	math	PROPN
ejpam-5353	91	6	,	,	PUNCT
ejpam-5353	91	7	17	17	NUM
ejpam-5353	91	8	(	(	PUNCT
ejpam-5353	91	9	4	4	NUM
ejpam-5353	91	10	)	)	PUNCT
ejpam-5353	91	11	(	(	PUNCT
ejpam-5353	91	12	2024	2024	NUM
ejpam-5353	91	13	)	)	PUNCT
ejpam-5353	91	14	,	,	PUNCT
ejpam-5353	91	15	3492	3492	NUM
ejpam-5353	91	16	-	-	SYM
ejpam-5353	91	17	3516	3516	NUM
ejpam-5353	91	18	3495	3495	NUM
ejpam-5353	91	19	2.2	2.2	NUM
ejpam-5353	91	20	.	.	PUNCT
ejpam-5353	92	1	bases	basis	NOUN
ejpam-5353	92	2	representation	representation	VERB
ejpam-5353	92	3	the	the	DET
ejpam-5353	92	4	representation	representation	NOUN
ejpam-5353	92	5	of	of	ADP
ejpam-5353	92	6	the	the	DET
ejpam-5353	92	7	base	base	NOUN
ejpam-5353	92	8	g	g	NOUN
ejpam-5353	92	9	is	be	AUX
ejpam-5353	92	10	given	give	VERB
ejpam-5353	92	11	by	by	ADP
ejpam-5353	92	12	the	the	DET
ejpam-5353	92	13	ordered	order	VERB
ejpam-5353	92	14	n	n	CCONJ
ejpam-5353	92	15	-	-	PUNCT
ejpam-5353	92	16	tuple	tuple	ADJ
ejpam-5353	92	17	v(g	v(g	PROPN
ejpam-5353	92	18	)	)	PUNCT
ejpam-5353	92	19	=	=	SYM
ejpam-5353	92	20	(	(	PUNCT
ejpam-5353	92	21	v0	v0	PROPN
ejpam-5353	92	22	,	,	PUNCT
ejpam-5353	92	23	v1	v1	NOUN
ejpam-5353	92	24	,	,	PUNCT
ejpam-5353	92	25	·	·	PUNCT
ejpam-5353	92	26	·	·	PUNCT
ejpam-5353	92	27	·	·	PUNCT
ejpam-5353	92	28	,	,	PUNCT
ejpam-5353	92	29	vn−1	vn−1	ADJ
ejpam-5353	92	30	)	)	PUNCT
ejpam-5353	92	31	∈	∈	PROPN
ejpam-5353	92	32	zn	zn	PROPN
ejpam-5353	92	33	×	×	PROPN
ejpam-5353	92	34	zn	zn	PROPN
ejpam-5353	92	35	×	×	PROPN
ejpam-5353	92	36	·	·	PUNCT
ejpam-5353	92	37	·	·	PUNCT
ejpam-5353	92	38	·	·	PUNCT
ejpam-5353	93	1	×	×	NOUN
ejpam-5353	93	2	zn︸	zn︸	PROPN
ejpam-5353	93	3	︷︷	︷︷	PROPN
ejpam-5353	93	4	︸	︸	ADP
ejpam-5353	93	5	n	n	NUM
ejpam-5353	93	6	times	time	NOUN
ejpam-5353	93	7	such	such	ADJ
ejpam-5353	93	8	that	that	SCONJ
ejpam-5353	93	9	vi	vi	PROPN
ejpam-5353	93	10	∈	∈	PROPN
ejpam-5353	93	11	zn	zn	X
ejpam-5353	93	12	for	for	ADP
ejpam-5353	93	13	all	all	PRON
ejpam-5353	93	14	i	i	PRON
ejpam-5353	93	15	∈	∈	PROPN
ejpam-5353	93	16	{	{	PUNCT
ejpam-5353	93	17	0	0	NUM
ejpam-5353	93	18	,	,	PUNCT
ejpam-5353	93	19	1	1	NUM
ejpam-5353	93	20	,	,	PUNCT
ejpam-5353	93	21	2	2	NUM
ejpam-5353	93	22	,	,	PUNCT
ejpam-5353	93	23	·	·	PUNCT
ejpam-5353	93	24	·	·	PUNCT
ejpam-5353	93	25	·	·	PUNCT
ejpam-5353	93	26	,	,	PUNCT
ejpam-5353	93	27	n−	n−	NOUN
ejpam-5353	93	28	1	1	NUM
ejpam-5353	93	29	}	}	PUNCT
ejpam-5353	93	30	and	and	CCONJ
ejpam-5353	93	31	(	(	PUNCT
ejpam-5353	93	32	vi)0	vi)0	PROPN
ejpam-5353	93	33	is	be	AUX
ejpam-5353	93	34	the	the	DET
ejpam-5353	93	35	unique	unique	ADJ
ejpam-5353	93	36	vertex	vertex	NOUN
ejpam-5353	93	37	(	(	PUNCT
ejpam-5353	93	38	(	(	PUNCT
ejpam-5353	93	39	vi	vi	NOUN
ejpam-5353	93	40	,	,	PUNCT
ejpam-5353	93	41	0	0	NUM
ejpam-5353	93	42	)	)	PUNCT
ejpam-5353	93	43	∈	∈	NOUN
ejpam-5353	93	44	zn×{0	zn×{0	NUM
ejpam-5353	93	45	}	}	PUNCT
ejpam-5353	93	46	)	)	PUNCT
ejpam-5353	93	47	that	that	PRON
ejpam-5353	93	48	belongs	belong	VERB
ejpam-5353	93	49	to	to	ADP
ejpam-5353	93	50	the	the	DET
ejpam-5353	93	51	unique	unique	ADJ
ejpam-5353	93	52	edge	edge	NOUN
ejpam-5353	93	53	of	of	ADP
ejpam-5353	93	54	length	length	NOUN
ejpam-5353	93	55	i	i	PRON
ejpam-5353	93	56	in	in	ADP
ejpam-5353	93	57	g.	g.	PROPN
ejpam-5353	93	58	the	the	DET
ejpam-5353	93	59	edge	edge	NOUN
ejpam-5353	93	60	set	set	NOUN
ejpam-5353	93	61	of	of	ADP
ejpam-5353	93	62	g	g	PROPN
ejpam-5353	93	63	is	be	AUX
ejpam-5353	93	64	e(g	e(g	PROPN
ejpam-5353	93	65	)	)	PUNCT
ejpam-5353	93	66	=	=	PRON
ejpam-5353	93	67	{	{	PUNCT
ejpam-5353	93	68	(	(	PUNCT
ejpam-5353	93	69	(	(	PUNCT
ejpam-5353	93	70	vi)0	vi)0	PROPN
ejpam-5353	93	71	,	,	PUNCT
ejpam-5353	93	72	(	(	PUNCT
ejpam-5353	93	73	vi	vi	NOUN
ejpam-5353	93	74	+	+	CCONJ
ejpam-5353	93	75	i)1	i)1	NOUN
ejpam-5353	93	76	)	)	PUNCT
ejpam-5353	93	77	;	;	PUNCT
ejpam-5353	93	78	0	0	NUM
ejpam-5353	93	79	≤	≤	NUM
ejpam-5353	94	1	i	i	PRON
ejpam-5353	94	2	≤	≤	ADJ
ejpam-5353	94	3	n−	n−	NOUN
ejpam-5353	94	4	1	1	NUM
ejpam-5353	94	5	}	}	PUNCT
ejpam-5353	94	6	.	.	PUNCT
ejpam-5353	95	1	for	for	ADP
ejpam-5353	95	2	instance	instance	NOUN
ejpam-5353	95	3	,	,	PUNCT
ejpam-5353	95	4	the	the	DET
ejpam-5353	95	5	base	base	NOUN
ejpam-5353	95	6	in	in	ADP
ejpam-5353	95	7	figure	figure	NOUN
ejpam-5353	95	8	1	1	NUM
ejpam-5353	95	9	is	be	AUX
ejpam-5353	95	10	represented	represent	VERB
ejpam-5353	95	11	by	by	ADP
ejpam-5353	95	12	the	the	DET
ejpam-5353	95	13	vector	vector	NOUN
ejpam-5353	95	14	v(p4	v(p4	X
ejpam-5353	95	15	)	)	PUNCT
ejpam-5353	95	16	=	=	SYM
ejpam-5353	95	17	(	(	PUNCT
ejpam-5353	95	18	0	0	NUM
ejpam-5353	95	19	,	,	PUNCT
ejpam-5353	95	20	1	1	NUM
ejpam-5353	95	21	,	,	PUNCT
ejpam-5353	95	22	1	1	NUM
ejpam-5353	95	23	)	)	PUNCT
ejpam-5353	95	24	,	,	PUNCT
ejpam-5353	95	25	(	(	PUNCT
ejpam-5353	95	26	e.g.	e.g.	ADV
ejpam-5353	95	27	(	(	PUNCT
ejpam-5353	95	28	10,01	10,01	NUM
ejpam-5353	95	29	)	)	PUNCT
ejpam-5353	95	30	is	be	AUX
ejpam-5353	95	31	the	the	DET
ejpam-5353	95	32	unique	unique	ADJ
ejpam-5353	95	33	edge	edge	NOUN
ejpam-5353	95	34	of	of	ADP
ejpam-5353	95	35	length	length	NOUN
ejpam-5353	95	36	2	2	NUM
ejpam-5353	95	37	,	,	PUNCT
ejpam-5353	95	38	thus	thus	ADV
ejpam-5353	95	39	v2	v2	VERB
ejpam-5353	95	40	=	=	SYM
ejpam-5353	95	41	1	1	NUM
ejpam-5353	95	42	)	)	PUNCT
ejpam-5353	95	43	.	.	PUNCT
ejpam-5353	96	1	if	if	SCONJ
ejpam-5353	96	2	g	g	PROPN
ejpam-5353	96	3	is	be	AUX
ejpam-5353	96	4	a	a	DET
ejpam-5353	96	5	base	base	NOUN
ejpam-5353	96	6	,	,	PUNCT
ejpam-5353	96	7	we	we	PRON
ejpam-5353	96	8	will	will	AUX
ejpam-5353	96	9	call	call	VERB
ejpam-5353	96	10	also	also	ADV
ejpam-5353	96	11	v(g	v(g	ADJ
ejpam-5353	96	12	)	)	PUNCT
ejpam-5353	96	13	a	a	DET
ejpam-5353	96	14	base	base	NOUN
ejpam-5353	96	15	.	.	PUNCT
ejpam-5353	97	1	figure	figure	NOUN
ejpam-5353	97	2	1	1	NUM
ejpam-5353	97	3	:	:	PUNCT
ejpam-5353	97	4	the	the	DET
ejpam-5353	97	5	base	base	NOUN
ejpam-5353	97	6	p4	p4	NOUN
ejpam-5353	97	7	in	in	ADP
ejpam-5353	97	8	k3,3	k3,3	PROPN
ejpam-5353	97	9	with	with	ADP
ejpam-5353	97	10	the	the	DET
ejpam-5353	97	11	length	length	NOUN
ejpam-5353	97	12	of	of	ADP
ejpam-5353	97	13	each	each	DET
ejpam-5353	97	14	edge	edge	NOUN
ejpam-5353	97	15	,	,	PUNCT
ejpam-5353	97	16	where	where	SCONJ
ejpam-5353	97	17	v(p4	v(p4	VERB
ejpam-5353	97	18	)	)	PUNCT
ejpam-5353	97	19	=	=	SYM
ejpam-5353	97	20	(	(	PUNCT
ejpam-5353	97	21	0	0	NUM
ejpam-5353	97	22	,	,	PUNCT
ejpam-5353	97	23	1	1	NUM
ejpam-5353	97	24	,	,	PUNCT
ejpam-5353	97	25	1	1	NUM
ejpam-5353	97	26	)	)	PUNCT
ejpam-5353	97	27	.	.	PUNCT
ejpam-5353	98	1	definition	definition	NOUN
ejpam-5353	98	2	4	4	NUM
ejpam-5353	98	3	.	.	PUNCT
ejpam-5353	98	4	let	let	VERB
ejpam-5353	98	5	v(g1	v(g1	NOUN
ejpam-5353	98	6	)	)	PUNCT
ejpam-5353	98	7	and	and	CCONJ
ejpam-5353	98	8	v(g2	v(g2	X
ejpam-5353	98	9	)	)	PUNCT
ejpam-5353	98	10	be	be	VERB
ejpam-5353	98	11	two	two	NUM
ejpam-5353	98	12	different	different	ADJ
ejpam-5353	98	13	bases	basis	NOUN
ejpam-5353	98	14	in	in	ADP
ejpam-5353	98	15	kn	kn	PROPN
ejpam-5353	98	16	,	,	PUNCT
ejpam-5353	98	17	n.	n.	PROPN
ejpam-5353	98	18	then	then	ADV
ejpam-5353	98	19	,	,	PUNCT
ejpam-5353	98	20	g1	g1	PROPN
ejpam-5353	98	21	and	and	CCONJ
ejpam-5353	98	22	g2	g2	PROPN
ejpam-5353	98	23	are	be	AUX
ejpam-5353	98	24	orthogonal	orthogonal	ADJ
ejpam-5353	98	25	if	if	SCONJ
ejpam-5353	98	26	and	and	CCONJ
ejpam-5353	98	27	only	only	ADV
ejpam-5353	98	28	if	if	SCONJ
ejpam-5353	98	29	{	{	PUNCT
ejpam-5353	98	30	vi(g1)−	vi(g1)−	NOUN
ejpam-5353	98	31	vi(g2	vi(g2	NOUN
ejpam-5353	98	32	)	)	PUNCT
ejpam-5353	98	33	:	:	PUNCT
ejpam-5353	99	1	i	i	PROPN
ejpam-5353	99	2	∈	∈	PROPN
ejpam-5353	99	3	zn	zn	PROPN
ejpam-5353	99	4	}	}	PUNCT
ejpam-5353	99	5	=	=	ADJ
ejpam-5353	99	6	zn	zn	X
ejpam-5353	99	7	.	.	PUNCT
ejpam-5353	99	8	theorem	theorem	NOUN
ejpam-5353	99	9	2	2	NUM
ejpam-5353	99	10	.	.	PUNCT
ejpam-5353	100	1	if	if	SCONJ
ejpam-5353	100	2	g1	g1	PROPN
ejpam-5353	100	3	0	0	PUNCT
ejpam-5353	100	4	and	and	CCONJ
ejpam-5353	100	5	g2	g2	PROPN
ejpam-5353	100	6	0	0	NUM
ejpam-5353	100	7	are	be	AUX
ejpam-5353	100	8	the	the	DET
ejpam-5353	100	9	orthogonal	orthogonal	ADJ
ejpam-5353	100	10	bases	basis	NOUN
ejpam-5353	100	11	in	in	ADP
ejpam-5353	100	12	kn	kn	PROPN
ejpam-5353	100	13	,	,	PUNCT
ejpam-5353	100	14	n	n	CCONJ
ejpam-5353	100	15	,	,	PUNCT
ejpam-5353	100	16	then	then	ADV
ejpam-5353	100	17	the	the	DET
ejpam-5353	100	18	collections	collection	NOUN
ejpam-5353	100	19	g1={g1	g1={g1	VERB
ejpam-5353	100	20	0+x	0+x	NUM
ejpam-5353	100	21	:	:	PUNCT
ejpam-5353	100	22	x	x	X
ejpam-5353	100	23	∈	∈	PROPN
ejpam-5353	100	24	zn	zn	PROPN
ejpam-5353	100	25	}	}	PUNCT
ejpam-5353	100	26	and	and	CCONJ
ejpam-5353	100	27	g2={g2	g2={g2	PROPN
ejpam-5353	100	28	0+y	0+y	NUM
ejpam-5353	100	29	:	:	PUNCT
ejpam-5353	100	30	y	y	PROPN
ejpam-5353	100	31	∈	∈	PROPN
ejpam-5353	100	32	zn	zn	PROPN
ejpam-5353	100	33	}	}	PUNCT
ejpam-5353	100	34	with	with	ADP
ejpam-5353	100	35	(	(	PUNCT
ejpam-5353	100	36	gi	gi	INTJ
ejpam-5353	100	37	0+x	0+x	NUM
ejpam-5353	100	38	=	=	PUNCT
ejpam-5353	100	39	(	(	PUNCT
ejpam-5353	100	40	gi	gi	NOUN
ejpam-5353	100	41	0	0	NUM
ejpam-5353	100	42	+	+	NUM
ejpam-5353	100	43	x	x	X
ejpam-5353	100	44	)	)	PUNCT
ejpam-5353	100	45	)	)	PUNCT
ejpam-5353	100	46	and	and	CCONJ
ejpam-5353	100	47	(	(	PUNCT
ejpam-5353	100	48	gi	gi	INTJ
ejpam-5353	100	49	0+y	0+y	NUM
ejpam-5353	100	50	=	=	SYM
ejpam-5353	100	51	(	(	PUNCT
ejpam-5353	100	52	gi	gi	NOUN
ejpam-5353	100	53	0	0	NUM
ejpam-5353	101	1	+	+	NUM
ejpam-5353	101	2	y	y	NOUN
ejpam-5353	101	3	)	)	PUNCT
ejpam-5353	101	4	)	)	PUNCT
ejpam-5353	102	1	for	for	ADP
ejpam-5353	102	2	i	i	PRON
ejpam-5353	102	3	∈	∈	PROPN
ejpam-5353	102	4	{	{	PUNCT
ejpam-5353	102	5	1	1	NUM
ejpam-5353	102	6	,	,	PUNCT
ejpam-5353	102	7	2	2	NUM
ejpam-5353	102	8	}	}	PUNCT
ejpam-5353	102	9	represent	represent	VERB
ejpam-5353	102	10	an	an	DET
ejpam-5353	102	11	odc	odc	NOUN
ejpam-5353	102	12	of	of	ADP
ejpam-5353	102	13	kn	kn	PROPN
ejpam-5353	102	14	,	,	PUNCT
ejpam-5353	102	15	n.	n.	NOUN
ejpam-5353	102	16	proof	proof	NOUN
ejpam-5353	102	17	.	.	PUNCT
ejpam-5353	103	1	since	since	SCONJ
ejpam-5353	103	2	g1	g1	PROPN
ejpam-5353	103	3	0	0	PROPN
ejpam-5353	103	4	and	and	CCONJ
ejpam-5353	103	5	g2	g2	PROPN
ejpam-5353	103	6	0	0	NUM
ejpam-5353	103	7	are	be	AUX
ejpam-5353	103	8	bases	basis	NOUN
ejpam-5353	103	9	then	then	ADV
ejpam-5353	103	10	each	each	DET
ejpam-5353	103	11	collection	collection	NOUN
ejpam-5353	103	12	from	from	ADP
ejpam-5353	103	13	the	the	DET
ejpam-5353	103	14	collections	collection	NOUN
ejpam-5353	103	15	g1={g1	g1={g1	PROPN
ejpam-5353	103	16	0+x	0+x	NUM
ejpam-5353	103	17	:	:	PUNCT
ejpam-5353	104	1	x	x	X
ejpam-5353	104	2	∈	∈	PROPN
ejpam-5353	104	3	zn	zn	PROPN
ejpam-5353	104	4	}	}	PUNCT
ejpam-5353	104	5	and	and	CCONJ
ejpam-5353	104	6	g2={g2	g2={g2	PROPN
ejpam-5353	104	7	0+y	0+y	NUM
ejpam-5353	104	8	:	:	PUNCT
ejpam-5353	104	9	y	y	PROPN
ejpam-5353	104	10	∈	∈	PROPN
ejpam-5353	104	11	zn	zn	PROPN
ejpam-5353	104	12	}	}	PUNCT
ejpam-5353	104	13	forms	form	VERB
ejpam-5353	104	14	an	an	DET
ejpam-5353	104	15	edge	edge	NOUN
ejpam-5353	104	16	decomposition	decomposition	NOUN
ejpam-5353	104	17	of	of	ADP
ejpam-5353	104	18	kn	kn	PROPN
ejpam-5353	104	19	,	,	PUNCT
ejpam-5353	104	20	n.	n.	PROPN
ejpam-5353	104	21	assume	assume	VERB
ejpam-5353	104	22	that	that	SCONJ
ejpam-5353	104	23	the	the	DET
ejpam-5353	104	24	edge	edge	NOUN
ejpam-5353	104	25	{	{	PUNCT
ejpam-5353	104	26	a0	a0	NOUN
ejpam-5353	104	27	,	,	PUNCT
ejpam-5353	104	28	b1	b1	PROPN
ejpam-5353	104	29	}	}	PUNCT
ejpam-5353	104	30	∈	∈	PROPN
ejpam-5353	104	31	e(kn	e(kn	NUM
ejpam-5353	104	32	,	,	PUNCT
ejpam-5353	104	33	n	n	CCONJ
ejpam-5353	104	34	)	)	PUNCT
ejpam-5353	104	35	.	.	PUNCT
ejpam-5353	105	1	then	then	ADV
ejpam-5353	105	2	there	there	PRON
ejpam-5353	105	3	are	be	VERB
ejpam-5353	105	4	exactly	exactly	ADV
ejpam-5353	105	5	two	two	NUM
ejpam-5353	105	6	graphs	graph	NOUN
ejpam-5353	105	7	g1	g1	NOUN
ejpam-5353	105	8	x	x	PUNCT
ejpam-5353	105	9	and	and	CCONJ
ejpam-5353	105	10	g2	g2	PROPN
ejpam-5353	105	11	y	y	PROPN
ejpam-5353	105	12	from	from	ADP
ejpam-5353	105	13	the	the	DET
ejpam-5353	105	14	collections	collection	NOUN
ejpam-5353	105	15	g1	g1	PROPN
ejpam-5353	105	16	and	and	CCONJ
ejpam-5353	105	17	g2	g2	PROPN
ejpam-5353	105	18	such	such	ADJ
ejpam-5353	105	19	that	that	SCONJ
ejpam-5353	105	20	{	{	PUNCT
ejpam-5353	105	21	a0	a0	NOUN
ejpam-5353	105	22	,	,	PUNCT
ejpam-5353	105	23	b1	b1	NOUN
ejpam-5353	105	24	}	}	PUNCT
ejpam-5353	105	25	∈	∈	PROPN
ejpam-5353	105	26	e(g1	e(g1	NOUN
ejpam-5353	105	27	x	x	X
ejpam-5353	105	28	)	)	PUNCT
ejpam-5353	105	29	and	and	CCONJ
ejpam-5353	105	30	{	{	PUNCT
ejpam-5353	105	31	a0	a0	NOUN
ejpam-5353	105	32	,	,	PUNCT
ejpam-5353	105	33	b1	b1	PROPN
ejpam-5353	105	34	}	}	PUNCT
ejpam-5353	105	35	∈	∈	PROPN
ejpam-5353	105	36	e(g2	e(g2	X
ejpam-5353	105	37	y	y	PROPN
ejpam-5353	105	38	)	)	PUNCT
ejpam-5353	105	39	.	.	PUNCT
ejpam-5353	106	1	moreover	moreover	ADV
ejpam-5353	106	2	,	,	PUNCT
ejpam-5353	106	3	for	for	ADP
ejpam-5353	106	4	any	any	DET
ejpam-5353	106	5	x	x	NOUN
ejpam-5353	106	6	,	,	PUNCT
ejpam-5353	106	7	y	y	PROPN
ejpam-5353	106	8	∈	∈	PROPN
ejpam-5353	106	9	zn	zn	PROPN
ejpam-5353	106	10	and	and	CCONJ
ejpam-5353	106	11	s	s	PROPN
ejpam-5353	106	12	,	,	PUNCT
ejpam-5353	106	13	t	t	PROPN
ejpam-5353	106	14	∈	∈	PROPN
ejpam-5353	106	15	{	{	PUNCT
ejpam-5353	106	16	1	1	NUM
ejpam-5353	106	17	,	,	PUNCT
ejpam-5353	106	18	2	2	NUM
ejpam-5353	106	19	}	}	PUNCT
ejpam-5353	106	20	,	,	PUNCT
ejpam-5353	106	21	∣∣e(gs	∣∣e(gs	NOUN
ejpam-5353	106	22	0+x	0+x	NUM
ejpam-5353	106	23	)	)	PUNCT
ejpam-5353	106	24	∩	∩	PROPN
ejpam-5353	106	25	e(gt	e(gt	NOUN
ejpam-5353	106	26	0+y	0+y	NOUN
ejpam-5353	106	27	)	)	PUNCT
ejpam-5353	106	28	∣∣	∣∣	X
ejpam-5353	107	1	=	=	SYM
ejpam-5353	107	2	0	0	PUNCT
ejpam-5353	107	3	whenever	whenever	SCONJ
ejpam-5353	107	4	s	s	VERB
ejpam-5353	107	5	=	=	NOUN
ejpam-5353	107	6	t.	t.	NOUN
ejpam-5353	107	7	besides	besides	SCONJ
ejpam-5353	107	8	that	that	PRON
ejpam-5353	107	9	,	,	PUNCT
ejpam-5353	107	10	there	there	PRON
ejpam-5353	107	11	is	be	VERB
ejpam-5353	107	12	a	a	DET
ejpam-5353	107	13	unique	unique	ADJ
ejpam-5353	107	14	vi	vi	NOUN
ejpam-5353	107	15	satisfies	satisfie	NOUN
ejpam-5353	107	16	vi(g	vi(g	ADP
ejpam-5353	107	17	1	1	NUM
ejpam-5353	107	18	0	0	NUM
ejpam-5353	107	19	)	)	PUNCT
ejpam-5353	107	20	−	−	NOUN
ejpam-5353	107	21	vi(g	vi(g	NOUN
ejpam-5353	107	22	2	2	NUM
ejpam-5353	107	23	0	0	NUM
ejpam-5353	107	24	)	)	PUNCT
ejpam-5353	107	25	=	=	SYM
ejpam-5353	108	1	b	b	X
ejpam-5353	108	2	−	−	PROPN
ejpam-5353	108	3	a	a	PRON
ejpam-5353	108	4	and	and	CCONJ
ejpam-5353	108	5	vi(g	vi(g	NUM
ejpam-5353	108	6	1	1	NUM
ejpam-5353	108	7	0	0	NUM
ejpam-5353	108	8	)	)	PUNCT
ejpam-5353	109	1	+	+	CCONJ
ejpam-5353	109	2	a	a	DET
ejpam-5353	109	3	=	=	PUNCT
ejpam-5353	109	4	vi(g	vi(g	ADJ
ejpam-5353	109	5	2	2	NUM
ejpam-5353	109	6	0	0	NUM
ejpam-5353	109	7	)	)	PUNCT
ejpam-5353	109	8	+	+	CCONJ
ejpam-5353	109	9	b.	b.	PROPN
ejpam-5353	109	10	thus	thus	ADV
ejpam-5353	109	11	,	,	PUNCT
ejpam-5353	109	12	there	there	PRON
ejpam-5353	109	13	is	be	VERB
ejpam-5353	109	14	exactly	exactly	ADV
ejpam-5353	109	15	one	one	NUM
ejpam-5353	109	16	edge	edge	NOUN
ejpam-5353	109	17	l	l	NOUN
ejpam-5353	109	18	=	=	SYM
ejpam-5353	109	19	{	{	PUNCT
ejpam-5353	109	20	(	(	PUNCT
ejpam-5353	109	21	vi(g0	vi(g0	NOUN
ejpam-5353	109	22	)	)	PUNCT
ejpam-5353	110	1	+	+	CCONJ
ejpam-5353	110	2	a)0	a)0	PROPN
ejpam-5353	110	3	,	,	PUNCT
ejpam-5353	110	4	(	(	PUNCT
ejpam-5353	110	5	vi(g0	vi(g0	NOUN
ejpam-5353	110	6	)	)	PUNCT
ejpam-5353	110	7	+	+	CCONJ
ejpam-5353	110	8	a+	a+	PUNCT
ejpam-5353	110	9	vi)1	vi)1	NOUN
ejpam-5353	110	10	}	}	PUNCT
ejpam-5353	110	11	∈	∈	NOUN
ejpam-5353	110	12	e(g1	e(g1	NOUN
ejpam-5353	110	13	0+x	0+x	NUM
ejpam-5353	110	14	)	)	PUNCT
ejpam-5353	110	15	and	and	CCONJ
ejpam-5353	110	16	l	l	NOUN
ejpam-5353	111	1	=	=	PUNCT
ejpam-5353	111	2	{	{	PUNCT
ejpam-5353	111	3	(	(	PUNCT
ejpam-5353	111	4	vi(g1	vi(g1	VERB
ejpam-5353	111	5	)	)	PUNCT
ejpam-5353	112	1	+	+	CCONJ
ejpam-5353	112	2	b)0	b)0	NOUN
ejpam-5353	112	3	,	,	PUNCT
ejpam-5353	112	4	(	(	PUNCT
ejpam-5353	112	5	vi(g1	vi(g1	VERB
ejpam-5353	112	6	)	)	PUNCT
ejpam-5353	113	1	+	+	NUM
ejpam-5353	113	2	b+	b+	NOUN
ejpam-5353	113	3	vi)1	vi)1	NOUN
ejpam-5353	113	4	}	}	PUNCT
ejpam-5353	113	5	∈	∈	PROPN
ejpam-5353	113	6	e(g2	e(g2	X
ejpam-5353	113	7	0+y	0+y	NUM
ejpam-5353	113	8	)	)	PUNCT
ejpam-5353	113	9	.	.	PUNCT
ejpam-5353	114	1	thus	thus	ADV
ejpam-5353	114	2	,	,	PUNCT
ejpam-5353	114	3	∣∣e(gs	∣∣e(gs	NOUN
ejpam-5353	114	4	0+x	0+x	NUM
ejpam-5353	114	5	)	)	PUNCT
ejpam-5353	114	6	∩	∩	PROPN
ejpam-5353	114	7	e(gt	e(gt	NOUN
ejpam-5353	114	8	0+y	0+y	NUM
ejpam-5353	114	9	)	)	PUNCT
ejpam-5353	114	10	∣∣	∣∣	NOUN
ejpam-5353	115	1	=	=	SYM
ejpam-5353	115	2	1	1	NUM
ejpam-5353	115	3	whenever	whenever	SCONJ
ejpam-5353	115	4	s	s	VERB
ejpam-5353	115	5	̸=	̸=	PROPN
ejpam-5353	115	6	t.	t.	PROPN
ejpam-5353	115	7	hereafter	hereafter	ADV
ejpam-5353	115	8	,	,	PUNCT
ejpam-5353	115	9	we	we	PRON
ejpam-5353	115	10	show	show	VERB
ejpam-5353	115	11	a	a	DET
ejpam-5353	115	12	method	method	NOUN
ejpam-5353	115	13	by	by	ADP
ejpam-5353	115	14	which	which	PRON
ejpam-5353	115	15	we	we	PRON
ejpam-5353	115	16	can	can	AUX
ejpam-5353	115	17	construct	construct	VERB
ejpam-5353	115	18	an	an	DET
ejpam-5353	115	19	odc	odc	NOUN
ejpam-5353	115	20	of	of	ADP
ejpam-5353	115	21	kn	kn	PROPN
ejpam-5353	115	22	,	,	PUNCT
ejpam-5353	115	23	n	n	CCONJ
ejpam-5353	115	24	using	use	VERB
ejpam-5353	115	25	only	only	ADV
ejpam-5353	115	26	one	one	NUM
ejpam-5353	115	27	base	base	NOUN
ejpam-5353	115	28	instead	instead	ADV
ejpam-5353	115	29	of	of	ADP
ejpam-5353	115	30	two	two	NUM
ejpam-5353	115	31	bases	basis	NOUN
ejpam-5353	115	32	.	.	PUNCT
ejpam-5353	116	1	definition	definition	NOUN
ejpam-5353	116	2	5	5	NUM
ejpam-5353	116	3	.	.	PUNCT
ejpam-5353	117	1	a	a	DET
ejpam-5353	117	2	base	base	NOUN
ejpam-5353	117	3	g	g	NOUN
ejpam-5353	117	4	is	be	AUX
ejpam-5353	117	5	called	call	VERB
ejpam-5353	117	6	a	a	DET
ejpam-5353	117	7	symmetric	symmetric	ADJ
ejpam-5353	117	8	base	base	NOUN
ejpam-5353	117	9	with	with	ADP
ejpam-5353	117	10	respect	respect	NOUN
ejpam-5353	117	11	to	to	ADP
ejpam-5353	117	12	zn	zn	PROPN
ejpam-5353	117	13	if	if	SCONJ
ejpam-5353	117	14	v(g	v(g	PROPN
ejpam-5353	117	15	)	)	PUNCT
ejpam-5353	117	16	and	and	CCONJ
ejpam-5353	117	17	v(g	v(g	PROPN
ejpam-5353	117	18	′	′	NUM
ejpam-5353	117	19	)	)	PUNCT
ejpam-5353	117	20	are	be	AUX
ejpam-5353	117	21	orthogonal	orthogonal	ADJ
ejpam-5353	117	22	.	.	PUNCT
ejpam-5353	118	1	the	the	DET
ejpam-5353	118	2	following	follow	VERB
ejpam-5353	118	3	theorem	theorem	ADJ
ejpam-5353	118	4	introduces	introduce	VERB
ejpam-5353	118	5	the	the	DET
ejpam-5353	118	6	condition	condition	NOUN
ejpam-5353	118	7	for	for	ADP
ejpam-5353	118	8	a	a	DET
ejpam-5353	118	9	symmetric	symmetric	ADJ
ejpam-5353	118	10	base	base	NOUN
ejpam-5353	118	11	.	.	PUNCT
ejpam-5353	119	1	h.	h.	PROPN
ejpam-5353	119	2	shabana	shabana	PROPN
ejpam-5353	119	3	,	,	PUNCT
ejpam-5353	119	4	r.	r.	PROPN
ejpam-5353	119	5	el	el	PROPN
ejpam-5353	119	6	-	-	PROPN
ejpam-5353	119	7	shanawany	shanawany	NOUN
ejpam-5353	119	8	,	,	PUNCT
ejpam-5353	119	9	s.	s.	PROPN
ejpam-5353	119	10	halawa	halawa	PROPN
ejpam-5353	119	11	/	/	PUNCT
ejpam-5353	119	12	eur	eur	PROPN
ejpam-5353	119	13	.	.	PUNCT
ejpam-5353	120	1	j.	j.	PROPN
ejpam-5353	120	2	pure	pure	PROPN
ejpam-5353	120	3	appl	appl	PROPN
ejpam-5353	120	4	.	.	PROPN
ejpam-5353	120	5	math	math	PROPN
ejpam-5353	120	6	,	,	PUNCT
ejpam-5353	120	7	17	17	NUM
ejpam-5353	120	8	(	(	PUNCT
ejpam-5353	120	9	4	4	NUM
ejpam-5353	120	10	)	)	PUNCT
ejpam-5353	120	11	(	(	PUNCT
ejpam-5353	120	12	2024	2024	NUM
ejpam-5353	120	13	)	)	PUNCT
ejpam-5353	120	14	,	,	PUNCT
ejpam-5353	120	15	3492	3492	NUM
ejpam-5353	120	16	-	-	SYM
ejpam-5353	120	17	3516	3516	NUM
ejpam-5353	120	18	3496	3496	NUM
ejpam-5353	120	19	theorem	theorem	VERB
ejpam-5353	120	20	3	3	NUM
ejpam-5353	120	21	.	.	PUNCT
ejpam-5353	121	1	a	a	DET
ejpam-5353	121	2	base	base	NOUN
ejpam-5353	121	3	g	g	NOUN
ejpam-5353	121	4	in	in	ADP
ejpam-5353	121	5	kn	kn	PROPN
ejpam-5353	121	6	,	,	PUNCT
ejpam-5353	121	7	n	n	PRON
ejpam-5353	121	8	represented	represent	VERB
ejpam-5353	121	9	by	by	ADP
ejpam-5353	121	10	the	the	DET
ejpam-5353	121	11	vector	vector	NOUN
ejpam-5353	121	12	v(g	v(g	PROPN
ejpam-5353	121	13	)	)	PUNCT
ejpam-5353	121	14	=	=	SYM
ejpam-5353	121	15	(	(	PUNCT
ejpam-5353	121	16	v0	v0	PROPN
ejpam-5353	121	17	,	,	PUNCT
ejpam-5353	121	18	v1	v1	NOUN
ejpam-5353	121	19	,	,	PUNCT
ejpam-5353	121	20	·	·	PUNCT
ejpam-5353	121	21	·	·	PUNCT
ejpam-5353	121	22	·	·	PUNCT
ejpam-5353	121	23	,	,	PUNCT
ejpam-5353	121	24	vn−1	vn−1	PROPN
ejpam-5353	121	25	)	)	PUNCT
ejpam-5353	121	26	is	be	AUX
ejpam-5353	121	27	called	call	VERB
ejpam-5353	121	28	a	a	DET
ejpam-5353	121	29	symmetric	symmetric	ADJ
ejpam-5353	121	30	base	base	NOUN
ejpam-5353	121	31	if	if	SCONJ
ejpam-5353	121	32	it	it	PRON
ejpam-5353	121	33	satisfies	satisfy	VERB
ejpam-5353	121	34	{	{	PUNCT
ejpam-5353	121	35	vi	vi	NOUN
ejpam-5353	121	36	−	−	NOUN
ejpam-5353	121	37	v−i	v−i	NOUN
ejpam-5353	122	1	+	+	CCONJ
ejpam-5353	122	2	i	i	NOUN
ejpam-5353	122	3	}	}	PUNCT
ejpam-5353	122	4	=	=	PUNCT
ejpam-5353	122	5	zn	zn	X
ejpam-5353	122	6	for	for	ADP
ejpam-5353	122	7	all	all	PRON
ejpam-5353	122	8	i	i	PRON
ejpam-5353	122	9	∈	∈	PROPN
ejpam-5353	122	10	zn	zn	X
ejpam-5353	122	11	.	.	PUNCT
ejpam-5353	123	1	proof	proof	NOUN
ejpam-5353	123	2	.	.	PUNCT
ejpam-5353	124	1	since	since	SCONJ
ejpam-5353	124	2	g	g	PROPN
ejpam-5353	124	3	is	be	AUX
ejpam-5353	124	4	a	a	DET
ejpam-5353	124	5	base	base	NOUN
ejpam-5353	124	6	in	in	ADP
ejpam-5353	124	7	kn	kn	PROPN
ejpam-5353	124	8	,	,	PUNCT
ejpam-5353	124	9	n.the	n.the	DET
ejpam-5353	124	10	graph	graph	NOUN
ejpam-5353	124	11	g	g	NOUN
ejpam-5353	124	12	′	′	NUM
ejpam-5353	124	13	is	be	AUX
ejpam-5353	124	14	also	also	ADV
ejpam-5353	124	15	a	a	DET
ejpam-5353	124	16	base	base	NOUN
ejpam-5353	124	17	in	in	ADP
ejpam-5353	124	18	kn	kn	PROPN
ejpam-5353	124	19	,	,	PUNCT
ejpam-5353	124	20	n	n	PRON
ejpam-5353	124	21	represented	represent	VERB
ejpam-5353	124	22	by	by	ADP
ejpam-5353	124	23	v(g	v(g	PROPN
ejpam-5353	124	24	′	′	NUM
ejpam-5353	124	25	)	)	PUNCT
ejpam-5353	124	26	.	.	PUNCT
ejpam-5353	125	1	let	let	VERB
ejpam-5353	125	2	the	the	DET
ejpam-5353	125	3	edge	edge	NOUN
ejpam-5353	125	4	e	e	NOUN
ejpam-5353	125	5	=	=	X
ejpam-5353	125	6	{	{	PUNCT
ejpam-5353	125	7	vi(g	vi(g	NOUN
ejpam-5353	125	8	′	′	NUM
ejpam-5353	125	9	)	)	PUNCT
ejpam-5353	125	10	,	,	PUNCT
ejpam-5353	125	11	vi(g	vi(g	NOUN
ejpam-5353	125	12	′	′	NUM
ejpam-5353	125	13	)	)	PUNCT
ejpam-5353	126	1	+	+	CCONJ
ejpam-5353	126	2	i	i	PRON
ejpam-5353	126	3	}	}	PUNCT
ejpam-5353	126	4	∈	∈	PROPN
ejpam-5353	126	5	e	e	X
ejpam-5353	126	6	(	(	PUNCT
ejpam-5353	126	7	g	g	PROPN
ejpam-5353	126	8	′	′	NUM
ejpam-5353	126	9	)	)	PUNCT
ejpam-5353	126	10	such	such	ADJ
ejpam-5353	126	11	that	that	SCONJ
ejpam-5353	126	12	the	the	DET
ejpam-5353	126	13	length	length	NOUN
ejpam-5353	126	14	of	of	ADP
ejpam-5353	126	15	e	e	NOUN
ejpam-5353	126	16	equals	equal	VERB
ejpam-5353	126	17	i.	i.	NOUN
ejpam-5353	126	18	following	follow	VERB
ejpam-5353	126	19	the	the	DET
ejpam-5353	126	20	definition	definition	NOUN
ejpam-5353	126	21	of	of	ADP
ejpam-5353	126	22	a	a	DET
ejpam-5353	126	23	symmetric	symmetric	ADJ
ejpam-5353	126	24	graph	graph	NOUN
ejpam-5353	126	25	,	,	PUNCT
ejpam-5353	126	26	the	the	DET
ejpam-5353	126	27	edge	edge	NOUN
ejpam-5353	126	28	{	{	PUNCT
ejpam-5353	126	29	vi(g	vi(g	NUM
ejpam-5353	126	30	′	′	NUM
ejpam-5353	126	31	)	)	PUNCT
ejpam-5353	127	1	+	+	CCONJ
ejpam-5353	127	2	i	i	PROPN
ejpam-5353	127	3	,	,	PUNCT
ejpam-5353	127	4	vi(g	vi(g	NOUN
ejpam-5353	127	5	′	′	NUM
ejpam-5353	127	6	)	)	PUNCT
ejpam-5353	127	7	}	}	PUNCT
ejpam-5353	127	8	of	of	ADP
ejpam-5353	127	9	length	length	NOUN
ejpam-5353	127	10	−i	−i	PROPN
ejpam-5353	127	11	will	will	AUX
ejpam-5353	127	12	belong	belong	VERB
ejpam-5353	127	13	to	to	ADP
ejpam-5353	127	14	e	e	PROPN
ejpam-5353	127	15	(	(	PUNCT
ejpam-5353	127	16	g	g	NOUN
ejpam-5353	127	17	)	)	PUNCT
ejpam-5353	127	18	.	.	PUNCT
ejpam-5353	128	1	whence	whence	NOUN
ejpam-5353	128	2	,	,	PUNCT
ejpam-5353	128	3	v−i(g	v−i(g	PROPN
ejpam-5353	128	4	)	)	PUNCT
ejpam-5353	129	1	=	=	PUNCT
ejpam-5353	129	2	vi(g	vi(g	NUM
ejpam-5353	129	3	′	′	NUM
ejpam-5353	129	4	)	)	PUNCT
ejpam-5353	130	1	+	+	CCONJ
ejpam-5353	130	2	i	i	PROPN
ejpam-5353	130	3	,	,	PUNCT
ejpam-5353	130	4	which	which	PRON
ejpam-5353	130	5	means	mean	VERB
ejpam-5353	130	6	that	that	PRON
ejpam-5353	130	7	vi(g	vi(g	NUM
ejpam-5353	130	8	′	′	NUM
ejpam-5353	130	9	)	)	PUNCT
ejpam-5353	131	1	=	=	PUNCT
ejpam-5353	131	2	v−i(g)−	v−i(g)−	NUM
ejpam-5353	131	3	i.	i.	NOUN
ejpam-5353	131	4	following	follow	VERB
ejpam-5353	131	5	definition	definition	NOUN
ejpam-5353	131	6	4	4	NUM
ejpam-5353	131	7	,	,	PUNCT
ejpam-5353	131	8	v(g	v(g	ADJ
ejpam-5353	131	9	)	)	PUNCT
ejpam-5353	131	10	and	and	CCONJ
ejpam-5353	131	11	v(g	v(g	PROPN
ejpam-5353	131	12	′	′	NUM
ejpam-5353	131	13	)	)	PUNCT
ejpam-5353	131	14	are	be	AUX
ejpam-5353	131	15	orthogonal	orthogonal	ADJ
ejpam-5353	131	16	if	if	SCONJ
ejpam-5353	131	17	{	{	PUNCT
ejpam-5353	131	18	vi(g)−	vi(g)−	NOUN
ejpam-5353	131	19	vi(g	vi(g	NOUN
ejpam-5353	131	20	′	′	NUM
ejpam-5353	131	21	)	)	PUNCT
ejpam-5353	131	22	;	;	PUNCT
ejpam-5353	131	23	i	i	PRON
ejpam-5353	131	24	∈	∈	PROPN
ejpam-5353	131	25	zn	zn	X
ejpam-5353	131	26	}	}	PUNCT
ejpam-5353	131	27	=	=	SYM
ejpam-5353	132	1	zn	zn	X
ejpam-5353	132	2	.	.	PUNCT
ejpam-5353	133	1	then	then	ADV
ejpam-5353	133	2	the	the	DET
ejpam-5353	133	3	necessary	necessary	ADJ
ejpam-5353	133	4	and	and	CCONJ
ejpam-5353	133	5	sufficient	sufficient	ADJ
ejpam-5353	133	6	condition	condition	NOUN
ejpam-5353	133	7	for	for	ADP
ejpam-5353	133	8	the	the	DET
ejpam-5353	133	9	orthogonality	orthogonality	NOUN
ejpam-5353	133	10	of	of	ADP
ejpam-5353	133	11	the	the	DET
ejpam-5353	133	12	bases	basis	NOUN
ejpam-5353	133	13	g	g	NOUN
ejpam-5353	133	14	and	and	CCONJ
ejpam-5353	133	15	g′	g′	NOUN
ejpam-5353	133	16	is	be	AUX
ejpam-5353	133	17	{	{	PUNCT
ejpam-5353	133	18	vi(g)−	vi(g)−	NOUN
ejpam-5353	133	19	v−i(g	v−i(g	NOUN
ejpam-5353	133	20	)	)	PUNCT
ejpam-5353	134	1	+	+	CCONJ
ejpam-5353	134	2	i	i	PRON
ejpam-5353	134	3	;	;	PUNCT
ejpam-5353	134	4	i	i	PROPN
ejpam-5353	134	5	∈	∈	PROPN
ejpam-5353	134	6	zn	zn	PROPN
ejpam-5353	134	7	}	}	PUNCT
ejpam-5353	134	8	=	=	SYM
ejpam-5353	134	9	zn	zn	X
ejpam-5353	134	10	.	.	PUNCT
ejpam-5353	135	1	since	since	SCONJ
ejpam-5353	135	2	g	g	PROPN
ejpam-5353	135	3	′	′	NUM
ejpam-5353	135	4	is	be	AUX
ejpam-5353	135	5	the	the	DET
ejpam-5353	135	6	symmetric	symmetric	ADJ
ejpam-5353	135	7	graph	graph	NOUN
ejpam-5353	135	8	of	of	ADP
ejpam-5353	135	9	g	g	NOUN
ejpam-5353	135	10	,	,	PUNCT
ejpam-5353	135	11	then	then	ADV
ejpam-5353	135	12	the	the	DET
ejpam-5353	135	13	base	base	NOUN
ejpam-5353	135	14	g	g	PROPN
ejpam-5353	135	15	is	be	AUX
ejpam-5353	135	16	a	a	DET
ejpam-5353	135	17	symmetric	symmetric	ADJ
ejpam-5353	135	18	base	base	NOUN
ejpam-5353	135	19	with	with	ADP
ejpam-5353	135	20	respect	respect	NOUN
ejpam-5353	135	21	to	to	ADP
ejpam-5353	135	22	zn	zn	PROPN
ejpam-5353	135	23	if	if	SCONJ
ejpam-5353	135	24	and	and	CCONJ
ejpam-5353	135	25	only	only	ADV
ejpam-5353	135	26	if	if	SCONJ
ejpam-5353	135	27	{	{	PUNCT
ejpam-5353	135	28	vi(g)−	vi(g)−	NOUN
ejpam-5353	135	29	v−i(g	v−i(g	VERB
ejpam-5353	135	30	)	)	PUNCT
ejpam-5353	136	1	+	+	CCONJ
ejpam-5353	136	2	i	i	PRON
ejpam-5353	136	3	;	;	PUNCT
ejpam-5353	136	4	i	i	PROPN
ejpam-5353	136	5	∈	∈	PROPN
ejpam-5353	136	6	zn	zn	PROPN
ejpam-5353	136	7	}	}	PUNCT
ejpam-5353	136	8	=	=	ADJ
ejpam-5353	136	9	zn	zn	X
ejpam-5353	136	10	.	.	PUNCT
ejpam-5353	136	11	theorem	theorem	VERB
ejpam-5353	136	12	3	3	NUM
ejpam-5353	136	13	yields	yield	NOUN
ejpam-5353	136	14	the	the	DET
ejpam-5353	136	15	next	next	ADJ
ejpam-5353	136	16	theorem	theorem	PROPN
ejpam-5353	136	17	.	.	PUNCT
ejpam-5353	136	18	theorem	theorem	NOUN
ejpam-5353	136	19	4	4	NUM
ejpam-5353	136	20	.	.	PUNCT
ejpam-5353	137	1	there	there	PRON
ejpam-5353	137	2	is	be	VERB
ejpam-5353	137	3	an	an	DET
ejpam-5353	137	4	odc	odc	NOUN
ejpam-5353	137	5	of	of	ADP
ejpam-5353	137	6	kn	kn	PROPN
ejpam-5353	137	7	,	,	PUNCT
ejpam-5353	137	8	n	n	CCONJ
ejpam-5353	137	9	by	by	ADP
ejpam-5353	137	10	g	g	PROPN
ejpam-5353	137	11	if	if	SCONJ
ejpam-5353	137	12	there	there	PRON
ejpam-5353	137	13	exists	exist	VERB
ejpam-5353	137	14	a	a	DET
ejpam-5353	137	15	symmetric	symmetric	ADJ
ejpam-5353	137	16	base	base	NOUN
ejpam-5353	137	17	that	that	PRON
ejpam-5353	137	18	is	be	AUX
ejpam-5353	137	19	isomorphic	isomorphic	ADJ
ejpam-5353	137	20	to	to	ADP
ejpam-5353	137	21	the	the	DET
ejpam-5353	137	22	graph	graph	NOUN
ejpam-5353	137	23	g.	g.	NOUN
ejpam-5353	137	24	in	in	ADP
ejpam-5353	137	25	the	the	DET
ejpam-5353	137	26	next	next	ADJ
ejpam-5353	137	27	section	section	NOUN
ejpam-5353	137	28	we	we	PRON
ejpam-5353	137	29	use	use	VERB
ejpam-5353	137	30	the	the	DET
ejpam-5353	137	31	symmetric	symmetric	ADJ
ejpam-5353	137	32	base	base	NOUN
ejpam-5353	137	33	in	in	ADP
ejpam-5353	137	34	constructing	construct	VERB
ejpam-5353	137	35	an	an	DET
ejpam-5353	137	36	odc	odc	NOUN
ejpam-5353	137	37	of	of	ADP
ejpam-5353	137	38	kn	kn	PROPN
ejpam-5353	137	39	,	,	PUNCT
ejpam-5353	137	40	n	n	CCONJ
ejpam-5353	137	41	by	by	ADP
ejpam-5353	137	42	different	different	ADJ
ejpam-5353	137	43	classes	class	NOUN
ejpam-5353	137	44	of	of	ADP
ejpam-5353	137	45	graphs	graph	NOUN
ejpam-5353	137	46	.	.	PUNCT
ejpam-5353	138	1	definition	definition	NOUN
ejpam-5353	138	2	6	6	NUM
ejpam-5353	138	3	.	.	PUNCT
ejpam-5353	139	1	let	let	VERB
ejpam-5353	139	2	r	r	NOUN
ejpam-5353	139	3	≥	≥	NUM
ejpam-5353	139	4	1	1	NUM
ejpam-5353	139	5	,	,	PUNCT
ejpam-5353	139	6	and	and	CCONJ
ejpam-5353	139	7	n1	n1	NOUN
ejpam-5353	139	8	,	,	PUNCT
ejpam-5353	139	9	n2	n2	NOUN
ejpam-5353	139	10	,	,	PUNCT
ejpam-5353	139	11	n3	n3	NOUN
ejpam-5353	139	12	,	,	PUNCT
ejpam-5353	139	13	·	·	PUNCT
ejpam-5353	139	14	·	·	PUNCT
ejpam-5353	139	15	·	·	PUNCT
ejpam-5353	139	16	,	,	PUNCT
ejpam-5353	139	17	nr	nr	PRON
ejpam-5353	139	18	be	be	VERB
ejpam-5353	139	19	positive	positive	ADJ
ejpam-5353	139	20	integers	integer	NOUN
ejpam-5353	139	21	such	such	ADJ
ejpam-5353	139	22	that	that	SCONJ
ejpam-5353	139	23	ni	ni	PROPN
ejpam-5353	139	24	≥	≥	PROPN
ejpam-5353	139	25	0	0	NUM
ejpam-5353	139	26	for	for	ADP
ejpam-5353	139	27	i	i	PRON
ejpam-5353	139	28	∈	∈	PROPN
ejpam-5353	139	29	{	{	PUNCT
ejpam-5353	139	30	1	1	NUM
ejpam-5353	139	31	,	,	PUNCT
ejpam-5353	139	32	3	3	NUM
ejpam-5353	139	33	,	,	PUNCT
ejpam-5353	139	34	·	·	PUNCT
ejpam-5353	139	35	·	·	PUNCT
ejpam-5353	139	36	·	·	PUNCT
ejpam-5353	139	37	,	,	PUNCT
ejpam-5353	139	38	r}.the	r}.the	DET
ejpam-5353	139	39	caterpillar	caterpillar	ADJ
ejpam-5353	139	40	tree	tree	NOUN
ejpam-5353	139	41	cr(n1	cr(n1	NOUN
ejpam-5353	139	42	,	,	PUNCT
ejpam-5353	139	43	n2	n2	NOUN
ejpam-5353	139	44	,	,	PUNCT
ejpam-5353	139	45	n3	n3	NOUN
ejpam-5353	139	46	,	,	PUNCT
ejpam-5353	139	47	·	·	PUNCT
ejpam-5353	139	48	·	·	PUNCT
ejpam-5353	139	49	·	·	PUNCT
ejpam-5353	139	50	,	,	PUNCT
ejpam-5353	139	51	nr	nr	CCONJ
ejpam-5353	139	52	)	)	PUNCT
ejpam-5353	139	53	is	be	AUX
ejpam-5353	139	54	the	the	DET
ejpam-5353	139	55	tree	tree	NOUN
ejpam-5353	139	56	obtained	obtain	VERB
ejpam-5353	139	57	from	from	ADP
ejpam-5353	139	58	the	the	DET
ejpam-5353	139	59	path	path	NOUN
ejpam-5353	140	1	pr	pr	NOUN
ejpam-5353	140	2	=	=	PUNCT
ejpam-5353	140	3	x1x2x3	x1x2x3	PROPN
ejpam-5353	140	4	·	·	PUNCT
ejpam-5353	140	5	·	·	PUNCT
ejpam-5353	140	6	·	·	PUNCT
ejpam-5353	140	7	xr	xr	PROPN
ejpam-5353	140	8	by	by	ADP
ejpam-5353	140	9	joining	join	VERB
ejpam-5353	140	10	vertex	vertex	NOUN
ejpam-5353	140	11	xi	xi	PROPN
ejpam-5353	140	12	to	to	ADP
ejpam-5353	140	13	ni	ni	PROPN
ejpam-5353	140	14	new	new	ADJ
ejpam-5353	140	15	vertices	vertex	NOUN
ejpam-5353	140	16	,	,	PUNCT
ejpam-5353	140	17	i	i	PRON
ejpam-5353	140	18	∈	∈	PROPN
ejpam-5353	140	19	{	{	PUNCT
ejpam-5353	140	20	1	1	NUM
ejpam-5353	140	21	,	,	PUNCT
ejpam-5353	140	22	2	2	NUM
ejpam-5353	140	23	,	,	PUNCT
ejpam-5353	140	24	·	·	PUNCT
ejpam-5353	140	25	·	·	PUNCT
ejpam-5353	140	26	·	·	PUNCT
ejpam-5353	140	27	,	,	PUNCT
ejpam-5353	140	28	r	r	NOUN
ejpam-5353	140	29	}	}	PUNCT
ejpam-5353	140	30	.	.	PUNCT
ejpam-5353	141	1	definition	definition	NOUN
ejpam-5353	141	2	7	7	NUM
ejpam-5353	141	3	.	.	PUNCT
ejpam-5353	142	1	let	let	VERB
ejpam-5353	142	2	δ	δ	PROPN
ejpam-5353	142	3	,	,	PUNCT
ejpam-5353	142	4	α	α	PROPN
ejpam-5353	142	5	be	be	VERB
ejpam-5353	142	6	positive	positive	ADJ
ejpam-5353	142	7	integers	integer	NOUN
ejpam-5353	142	8	and	and	CCONJ
ejpam-5353	142	9	the	the	DET
ejpam-5353	142	10	parameter	parameter	PROPN
ejpam-5353	142	11	xδ	xδ	PROPN
ejpam-5353	142	12	,	,	PUNCT
ejpam-5353	142	13	≥	≥	NOUN
ejpam-5353	142	14	0	0	NUM
ejpam-5353	142	15	.	.	PUNCT
ejpam-5353	143	1	the	the	DET
ejpam-5353	143	2	rooted	rooted	ADJ
ejpam-5353	143	3	tree	tree	NOUN
ejpam-5353	143	4	τα(x1	τα(x1	PROPN
ejpam-5353	143	5	,	,	PUNCT
ejpam-5353	143	6	x2	x2	PROPN
ejpam-5353	143	7	,	,	PUNCT
ejpam-5353	143	8	x3	x3	ADJ
ejpam-5353	143	9	,	,	PUNCT
ejpam-5353	143	10	·	·	PUNCT
ejpam-5353	143	11	·	·	PUNCT
ejpam-5353	143	12	·	·	PUNCT
ejpam-5353	143	13	,	,	PUNCT
ejpam-5353	143	14	xδ	xδ	PROPN
ejpam-5353	143	15	)	)	PUNCT
ejpam-5353	143	16	is	be	AUX
ejpam-5353	143	17	the	the	DET
ejpam-5353	143	18	tree	tree	NOUN
ejpam-5353	143	19	with	with	ADP
ejpam-5353	143	20	a	a	DET
ejpam-5353	143	21	root	root	NOUN
ejpam-5353	143	22	α	α	NOUN
ejpam-5353	143	23	(	(	PUNCT
ejpam-5353	143	24	α	α	PROPN
ejpam-5353	143	25	∈	∈	PROPN
ejpam-5353	143	26	v	v	NOUN
ejpam-5353	143	27	(	(	PUNCT
ejpam-5353	143	28	kn	kn	PROPN
ejpam-5353	143	29	,	,	PUNCT
ejpam-5353	143	30	n	n	CCONJ
ejpam-5353	143	31	)	)	PUNCT
ejpam-5353	143	32	)	)	PUNCT
ejpam-5353	143	33	and	and	CCONJ
ejpam-5353	143	34	for	for	ADP
ejpam-5353	143	35	all	all	PRON
ejpam-5353	143	36	i	i	PRON
ejpam-5353	143	37	∈	∈	PROPN
ejpam-5353	143	38	{	{	PUNCT
ejpam-5353	143	39	1	1	NUM
ejpam-5353	143	40	,	,	PUNCT
ejpam-5353	143	41	2	2	NUM
ejpam-5353	143	42	,	,	PUNCT
ejpam-5353	143	43	·	·	PUNCT
ejpam-5353	143	44	·	·	PUNCT
ejpam-5353	143	45	·	·	PUNCT
ejpam-5353	143	46	,	,	PUNCT
ejpam-5353	143	47	δ	δ	PROPN
ejpam-5353	143	48	}	}	PUNCT
ejpam-5353	143	49	,	,	PUNCT
ejpam-5353	143	50	xi	xi	X
ejpam-5353	143	51	is	be	AUX
ejpam-5353	143	52	the	the	DET
ejpam-5353	143	53	number	number	NOUN
ejpam-5353	143	54	of	of	ADP
ejpam-5353	143	55	leaves	leave	NOUN
ejpam-5353	143	56	of	of	ADP
ejpam-5353	143	57	level	level	NOUN
ejpam-5353	143	58	i.	i.	NOUN
ejpam-5353	143	59	figure	figure	NOUN
ejpam-5353	143	60	2	2	NUM
ejpam-5353	143	61	:	:	PUNCT
ejpam-5353	143	62	tree	tree	NOUN
ejpam-5353	143	63	τ00(1	τ00(1	NOUN
ejpam-5353	143	64	,	,	PUNCT
ejpam-5353	143	65	3	3	X
ejpam-5353	143	66	)	)	PUNCT
ejpam-5353	143	67	as	as	ADP
ejpam-5353	143	68	a	a	DET
ejpam-5353	143	69	subgraph	subgraph	NOUN
ejpam-5353	143	70	of	of	ADP
ejpam-5353	143	71	k4,4	k4,4	PROPN
ejpam-5353	143	72	.	.	PUNCT
ejpam-5353	144	1	for	for	ADP
ejpam-5353	144	2	example	example	NOUN
ejpam-5353	144	3	,	,	PUNCT
ejpam-5353	144	4	the	the	DET
ejpam-5353	144	5	graph	graph	NOUN
ejpam-5353	144	6	in	in	ADP
ejpam-5353	144	7	figure	figure	NOUN
ejpam-5353	144	8	2	2	NUM
ejpam-5353	144	9	,	,	PUNCT
ejpam-5353	144	10	represents	represent	VERB
ejpam-5353	144	11	a	a	DET
ejpam-5353	144	12	tree	tree	NOUN
ejpam-5353	144	13	τα(x1	τα(x1	NOUN
ejpam-5353	144	14	,	,	PUNCT
ejpam-5353	144	15	x2	x2	NUM
ejpam-5353	144	16	)	)	PUNCT
ejpam-5353	144	17	≊	≊	VERB
ejpam-5353	144	18	τ00(1	τ00(1	ADJ
ejpam-5353	144	19	,	,	PUNCT
ejpam-5353	144	20	3	3	NUM
ejpam-5353	144	21	)	)	PUNCT
ejpam-5353	144	22	as	as	ADP
ejpam-5353	144	23	a	a	DET
ejpam-5353	144	24	subgraph	subgraph	NOUN
ejpam-5353	144	25	of	of	ADP
ejpam-5353	144	26	k4,4	k4,4	PROPN
ejpam-5353	144	27	.	.	PUNCT
ejpam-5353	145	1	such	such	ADJ
ejpam-5353	145	2	tree	tree	NOUN
ejpam-5353	145	3	τ00(1	τ00(1	NOUN
ejpam-5353	145	4	,	,	PUNCT
ejpam-5353	145	5	3	3	X
ejpam-5353	145	6	)	)	PUNCT
ejpam-5353	145	7	is	be	AUX
ejpam-5353	145	8	a	a	DET
ejpam-5353	145	9	rooted	rooted	ADJ
ejpam-5353	145	10	tree	tree	NOUN
ejpam-5353	145	11	with	with	ADP
ejpam-5353	145	12	a	a	DET
ejpam-5353	145	13	root	root	NOUN
ejpam-5353	145	14	α	α	NOUN
ejpam-5353	145	15	=	=	SYM
ejpam-5353	145	16	00	00	PROPN
ejpam-5353	145	17	,	,	PUNCT
ejpam-5353	145	18	x1	x1	PROPN
ejpam-5353	145	19	=	=	SYM
ejpam-5353	145	20	1	1	NUM
ejpam-5353	145	21	(	(	PUNCT
ejpam-5353	145	22	one	one	NUM
ejpam-5353	145	23	leaf	leaf	NOUN
ejpam-5353	145	24	in	in	ADP
ejpam-5353	145	25	level	level	NOUN
ejpam-5353	145	26	1	1	NUM
ejpam-5353	145	27	)	)	PUNCT
ejpam-5353	145	28	,	,	PUNCT
ejpam-5353	145	29	while	while	SCONJ
ejpam-5353	145	30	x2	x2	PROPN
ejpam-5353	145	31	=	=	SYM
ejpam-5353	145	32	3	3	NUM
ejpam-5353	145	33	(	(	PUNCT
ejpam-5353	145	34	3	3	NUM
ejpam-5353	145	35	leaves	leave	NOUN
ejpam-5353	145	36	with	with	ADP
ejpam-5353	145	37	level	level	NOUN
ejpam-5353	145	38	2	2	NUM
ejpam-5353	145	39	)	)	PUNCT
ejpam-5353	145	40	.	.	PUNCT
ejpam-5353	146	1	remark	remark	NOUN
ejpam-5353	146	2	2	2	NUM
ejpam-5353	146	3	.	.	PUNCT
ejpam-5353	147	1	a	a	DET
ejpam-5353	147	2	path	path	NOUN
ejpam-5353	147	3	pr	pr	NOUN
ejpam-5353	147	4	is	be	AUX
ejpam-5353	147	5	caterpillar	caterpillar	ADJ
ejpam-5353	147	6	tree	tree	NOUN
ejpam-5353	147	7	cr(0	cr(0	NOUN
ejpam-5353	147	8	,	,	PUNCT
ejpam-5353	147	9	0	0	NUM
ejpam-5353	147	10	,	,	PUNCT
ejpam-5353	147	11	0	0	NUM
ejpam-5353	147	12	,	,	PUNCT
ejpam-5353	147	13	·	·	PUNCT
ejpam-5353	147	14	·	·	PUNCT
ejpam-5353	147	15	·	·	PUNCT
ejpam-5353	147	16	,	,	PUNCT
ejpam-5353	147	17	0←−−−−−−−→	0←−−−−−−−→	NUM
ejpam-5353	147	18	r	r	NOUN
ejpam-5353	147	19	)	)	PUNCT
ejpam-5353	147	20	h.	h.	PROPN
ejpam-5353	147	21	shabana	shabana	PROPN
ejpam-5353	147	22	,	,	PUNCT
ejpam-5353	147	23	r.	r.	PROPN
ejpam-5353	147	24	el	el	PROPN
ejpam-5353	147	25	-	-	PROPN
ejpam-5353	147	26	shanawany	shanawany	NOUN
ejpam-5353	147	27	,	,	PUNCT
ejpam-5353	147	28	s.	s.	PROPN
ejpam-5353	147	29	halawa	halawa	PROPN
ejpam-5353	147	30	/	/	PUNCT
ejpam-5353	147	31	eur	eur	PROPN
ejpam-5353	147	32	.	.	PUNCT
ejpam-5353	148	1	j.	j.	PROPN
ejpam-5353	148	2	pure	pure	PROPN
ejpam-5353	148	3	appl	appl	PROPN
ejpam-5353	148	4	.	.	PROPN
ejpam-5353	148	5	math	math	PROPN
ejpam-5353	148	6	,	,	PUNCT
ejpam-5353	148	7	17	17	NUM
ejpam-5353	148	8	(	(	PUNCT
ejpam-5353	148	9	4	4	NUM
ejpam-5353	148	10	)	)	PUNCT
ejpam-5353	148	11	(	(	PUNCT
ejpam-5353	148	12	2024	2024	NUM
ejpam-5353	148	13	)	)	PUNCT
ejpam-5353	148	14	,	,	PUNCT
ejpam-5353	148	15	3492	3492	NUM
ejpam-5353	148	16	-	-	SYM
ejpam-5353	148	17	3516	3516	NUM
ejpam-5353	148	18	3497	3497	NUM
ejpam-5353	148	19	3	3	NUM
ejpam-5353	148	20	.	.	PUNCT
ejpam-5353	149	1	designing	design	VERB
ejpam-5353	149	2	orthogonal	orthogonal	ADJ
ejpam-5353	149	3	decompositions	decomposition	NOUN
ejpam-5353	149	4	of	of	ADP
ejpam-5353	149	5	kn	kn	PROPN
ejpam-5353	149	6	,	,	PUNCT
ejpam-5353	149	7	n	n	CCONJ
ejpam-5353	149	8	by	by	ADP
ejpam-5353	149	9	certain	certain	ADJ
ejpam-5353	149	10	trees	tree	NOUN
ejpam-5353	149	11	in	in	ADP
ejpam-5353	149	12	this	this	DET
ejpam-5353	149	13	section	section	NOUN
ejpam-5353	149	14	,	,	PUNCT
ejpam-5353	149	15	we	we	PRON
ejpam-5353	149	16	claim	claim	VERB
ejpam-5353	149	17	to	to	PART
ejpam-5353	149	18	construct	construct	VERB
ejpam-5353	149	19	odc	odc	PROPN
ejpam-5353	149	20	of	of	ADP
ejpam-5353	149	21	kn	kn	PROPN
ejpam-5353	149	22	,	,	PUNCT
ejpam-5353	149	23	n	n	CCONJ
ejpam-5353	149	24	by	by	ADP
ejpam-5353	149	25	certain	certain	ADJ
ejpam-5353	149	26	trees	tree	NOUN
ejpam-5353	149	27	based	base	VERB
ejpam-5353	149	28	on	on	ADP
ejpam-5353	149	29	bga	bga	PROPN
ejpam-5353	149	30	approach	approach	NOUN
ejpam-5353	149	31	introduced	introduce	VERB
ejpam-5353	149	32	in	in	ADP
ejpam-5353	149	33	section	section	NOUN
ejpam-5353	149	34	2	2	NUM
ejpam-5353	149	35	.	.	SYM
ejpam-5353	149	36	3.1	3.1	NUM
ejpam-5353	149	37	.	.	PUNCT
ejpam-5353	149	38	orthogonal	orthogonal	ADJ
ejpam-5353	149	39	decompositions	decomposition	NOUN
ejpam-5353	149	40	of	of	ADP
ejpam-5353	149	41	kn	kn	PROPN
ejpam-5353	149	42	,	,	PUNCT
ejpam-5353	149	43	n	n	CCONJ
ejpam-5353	149	44	by	by	ADP
ejpam-5353	149	45	rooted	rooted	ADJ
ejpam-5353	149	46	trees	tree	NOUN
ejpam-5353	149	47	theorem	theorem	VERB
ejpam-5353	149	48	5	5	NUM
ejpam-5353	149	49	.	.	PUNCT
ejpam-5353	150	1	let	let	VERB
ejpam-5353	150	2	n	n	PRON
ejpam-5353	150	3	≥	≥	X
ejpam-5353	150	4	3	3	NUM
ejpam-5353	150	5	be	be	AUX
ejpam-5353	150	6	a	a	DET
ejpam-5353	150	7	positive	positive	ADJ
ejpam-5353	150	8	integer	integer	NOUN
ejpam-5353	150	9	and	and	CCONJ
ejpam-5353	150	10	x1	x1	PROPN
ejpam-5353	150	11	∈	∈	PROPN
ejpam-5353	150	12	{	{	PUNCT
ejpam-5353	150	13	1	1	NUM
ejpam-5353	150	14	,	,	PUNCT
ejpam-5353	150	15	2	2	NUM
ejpam-5353	150	16	}	}	PUNCT
ejpam-5353	150	17	,	,	PUNCT
ejpam-5353	150	18	then	then	ADV
ejpam-5353	150	19	there	there	PRON
ejpam-5353	150	20	is	be	VERB
ejpam-5353	150	21	a	a	DET
ejpam-5353	150	22	symmetric	symmetric	ADJ
ejpam-5353	150	23	base	base	NOUN
ejpam-5353	150	24	of	of	ADP
ejpam-5353	150	25	an	an	DET
ejpam-5353	150	26	odc	odc	NOUN
ejpam-5353	150	27	of	of	ADP
ejpam-5353	150	28	kn	kn	PROPN
ejpam-5353	150	29	,	,	PUNCT
ejpam-5353	150	30	n	n	CCONJ
ejpam-5353	150	31	by	by	ADP
ejpam-5353	150	32	g	g	PROPN
ejpam-5353	150	33	≊	≊	NOUN
ejpam-5353	150	34	τ01(x1	τ01(x1	NUM
ejpam-5353	150	35	,	,	PUNCT
ejpam-5353	150	36	⌊	⌊	PROPN
ejpam-5353	150	37	n−1	n−1	PROPN
ejpam-5353	150	38	2	2	NUM
ejpam-5353	150	39	⌋	⌋	NOUN
ejpam-5353	150	40	)	)	PUNCT
ejpam-5353	150	41	.	.	PUNCT
ejpam-5353	151	1	proof	proof	NOUN
ejpam-5353	151	2	.	.	PUNCT
ejpam-5353	152	1	case	case	NOUN
ejpam-5353	152	2	1	1	X
ejpam-5353	152	3	.	.	PUNCT
ejpam-5353	153	1	let	let	VERB
ejpam-5353	153	2	x1	x1	NOUN
ejpam-5353	154	1	=	=	SYM
ejpam-5353	154	2	1	1	NUM
ejpam-5353	154	3	,	,	PUNCT
ejpam-5353	154	4	m	m	VERB
ejpam-5353	154	5	∈	∈	NOUN
ejpam-5353	154	6	z+	z+	NUM
ejpam-5353	154	7	and	and	CCONJ
ejpam-5353	154	8	n	n	NOUN
ejpam-5353	154	9	=	=	ADJ
ejpam-5353	154	10	2m+1	2m+1	PROPN
ejpam-5353	154	11	.	.	PUNCT
ejpam-5353	155	1	then	then	ADV
ejpam-5353	155	2	the	the	DET
ejpam-5353	155	3	vector	vector	NOUN
ejpam-5353	155	4	v(g	v(g	PROPN
ejpam-5353	155	5	)	)	PUNCT
ejpam-5353	155	6	of	of	ADP
ejpam-5353	155	7	the	the	DET
ejpam-5353	155	8	base	base	NOUN
ejpam-5353	155	9	g	g	NOUN
ejpam-5353	155	10	,	,	PUNCT
ejpam-5353	155	11	is	be	AUX
ejpam-5353	155	12	defined	define	VERB
ejpam-5353	155	13	as	as	ADP
ejpam-5353	155	14	vi(g	vi(g	NOUN
ejpam-5353	155	15	)	)	PUNCT
ejpam-5353	156	1	=	=	PRON
ejpam-5353	156	2	{	{	PUNCT
ejpam-5353	156	3	i	i	PRON
ejpam-5353	156	4	if	if	SCONJ
ejpam-5353	156	5	0	0	NUM
ejpam-5353	156	6	≤	≤	NUM
ejpam-5353	157	1	i	i	PRON
ejpam-5353	158	1	≤	≤	NOUN
ejpam-5353	158	2	m	m	VERB
ejpam-5353	158	3	−i	−i	ADJ
ejpam-5353	158	4	if	if	SCONJ
ejpam-5353	158	5	m+	m+	NUM
ejpam-5353	158	6	1	1	NUM
ejpam-5353	158	7	≤	≤	NUM
ejpam-5353	159	1	i	i	X
ejpam-5353	159	2	≤	≤	ADV
ejpam-5353	159	3	2	2	NUM
ejpam-5353	159	4	m	m	VERB
ejpam-5353	159	5	therefore	therefore	ADV
ejpam-5353	159	6	,	,	PUNCT
ejpam-5353	159	7	v−i(g	v−i(g	PROPN
ejpam-5353	159	8	)	)	PUNCT
ejpam-5353	160	1	=	=	PRON
ejpam-5353	160	2	{	{	PUNCT
ejpam-5353	160	3	i	i	PRON
ejpam-5353	160	4	if	if	SCONJ
ejpam-5353	160	5	0	0	NUM
ejpam-5353	160	6	≤	≤	NUM
ejpam-5353	161	1	i	i	PRON
ejpam-5353	162	1	≤	≤	NOUN
ejpam-5353	162	2	m	m	VERB
ejpam-5353	162	3	−i	−i	ADJ
ejpam-5353	162	4	if	if	SCONJ
ejpam-5353	162	5	m+	m+	NUM
ejpam-5353	162	6	1	1	NUM
ejpam-5353	162	7	≤	≤	NUM
ejpam-5353	163	1	i	i	X
ejpam-5353	163	2	≤	≤	ADJ
ejpam-5353	163	3	2	2	NUM
ejpam-5353	163	4	m	m	NOUN
ejpam-5353	163	5	for	for	ADP
ejpam-5353	163	6	all	all	PRON
ejpam-5353	163	7	i	i	PRON
ejpam-5353	163	8	∈	∈	PROPN
ejpam-5353	163	9	z2m+1	z2m+1	PROPN
ejpam-5353	163	10	,	,	PUNCT
ejpam-5353	163	11	vi−v−i+	vi−v−i+	PROPN
ejpam-5353	163	12	i	i	NOUN
ejpam-5353	163	13	=	=	PUNCT
ejpam-5353	163	14	i.	i.	NOUN
ejpam-5353	163	15	by	by	ADP
ejpam-5353	163	16	theorem	theorem	NOUN
ejpam-5353	163	17	3	3	NUM
ejpam-5353	163	18	,	,	PUNCT
ejpam-5353	163	19	g	g	PROPN
ejpam-5353	163	20	is	be	AUX
ejpam-5353	163	21	a	a	DET
ejpam-5353	163	22	symmetric	symmetric	ADJ
ejpam-5353	163	23	base	base	NOUN
ejpam-5353	163	24	.	.	PUNCT
ejpam-5353	164	1	by	by	ADP
ejpam-5353	164	2	definition	definition	NOUN
ejpam-5353	164	3	of	of	ADP
ejpam-5353	164	4	v(g	v(g	PROPN
ejpam-5353	164	5	)	)	PUNCT
ejpam-5353	164	6	,	,	PUNCT
ejpam-5353	164	7	the	the	DET
ejpam-5353	164	8	graph	graph	NOUN
ejpam-5353	164	9	g	g	NOUN
ejpam-5353	164	10	≊	≊	NOUN
ejpam-5353	164	11	τ01(1,m	τ01(1,m	PROPN
ejpam-5353	164	12	)	)	PUNCT
ejpam-5353	164	13	.	.	PUNCT
ejpam-5353	165	1	e(g	e(g	NOUN
ejpam-5353	165	2	)	)	PUNCT
ejpam-5353	166	1	=	=	PRON
ejpam-5353	166	2	{	{	PUNCT
ejpam-5353	166	3	(	(	PUNCT
ejpam-5353	166	4	00	00	NUM
ejpam-5353	166	5	,	,	PUNCT
ejpam-5353	166	6	01	01	NUM
ejpam-5353	166	7	)	)	PUNCT
ejpam-5353	166	8	}	}	PUNCT
ejpam-5353	166	9	∪	∪	X
ejpam-5353	166	10	{	{	PUNCT
ejpam-5353	166	11	(	(	PUNCT
ejpam-5353	166	12	i0	i0	PROPN
ejpam-5353	166	13	,	,	PUNCT
ejpam-5353	166	14	01	01	NUM
ejpam-5353	166	15	)	)	PUNCT
ejpam-5353	166	16	:	:	PUNCT
ejpam-5353	166	17	1	1	NUM
ejpam-5353	166	18	≤	≤	NUM
ejpam-5353	166	19	i	i	X
ejpam-5353	166	20	≤	≤	NOUN
ejpam-5353	166	21	m	m	VERB
ejpam-5353	166	22	}	}	PUNCT
ejpam-5353	166	23	∪	∪	X
ejpam-5353	166	24	{	{	PUNCT
ejpam-5353	166	25	(	(	PUNCT
ejpam-5353	166	26	i0	i0	PROPN
ejpam-5353	166	27	,	,	PUNCT
ejpam-5353	166	28	(	(	PUNCT
ejpam-5353	166	29	2i)1	2i)1	NUM
ejpam-5353	166	30	:	:	SYM
ejpam-5353	166	31	1	1	NUM
ejpam-5353	166	32	≤	≤	NUM
ejpam-5353	166	33	i	i	X
ejpam-5353	166	34	≤	≤	NUM
ejpam-5353	166	35	m	m	VERB
ejpam-5353	166	36	)	)	PUNCT
ejpam-5353	166	37	}	}	PUNCT
ejpam-5353	166	38	case	case	NOUN
ejpam-5353	166	39	2	2	X
ejpam-5353	166	40	.	.	PUNCT
ejpam-5353	167	1	let	let	VERB
ejpam-5353	167	2	x1	x1	NOUN
ejpam-5353	167	3	=	=	SYM
ejpam-5353	167	4	2	2	NUM
ejpam-5353	167	5	,	,	PUNCT
ejpam-5353	167	6	m	m	VERB
ejpam-5353	167	7	∈	∈	NOUN
ejpam-5353	167	8	z+	z+	NUM
ejpam-5353	167	9	and	and	CCONJ
ejpam-5353	167	10	n	n	CCONJ
ejpam-5353	167	11	=	=	SYM
ejpam-5353	167	12	2	2	NUM
ejpam-5353	167	13	m	m	NOUN
ejpam-5353	167	14	,	,	PUNCT
ejpam-5353	167	15	then	then	ADV
ejpam-5353	167	16	the	the	DET
ejpam-5353	167	17	vector	vector	NOUN
ejpam-5353	167	18	v(g	v(g	PROPN
ejpam-5353	167	19	)	)	PUNCT
ejpam-5353	167	20	of	of	ADP
ejpam-5353	167	21	the	the	DET
ejpam-5353	167	22	base	base	NOUN
ejpam-5353	167	23	g	g	NOUN
ejpam-5353	167	24	is	be	AUX
ejpam-5353	167	25	defined	define	VERB
ejpam-5353	167	26	as	as	ADP
ejpam-5353	167	27	:	:	PUNCT
ejpam-5353	167	28	vi(g	vi(g	NUM
ejpam-5353	167	29	)	)	PUNCT
ejpam-5353	168	1	=	=	SYM
ejpam-5353	168	2	v−i(g	v−i(g	X
ejpam-5353	168	3	)	)	PUNCT
ejpam-5353	169	1	=	=	PRON
ejpam-5353	169	2	{	{	PUNCT
ejpam-5353	169	3	i	i	PRON
ejpam-5353	169	4	if	if	SCONJ
ejpam-5353	169	5	0	0	NUM
ejpam-5353	169	6	≤	≤	NUM
ejpam-5353	170	1	i	i	PRON
ejpam-5353	171	1	≤	≤	NOUN
ejpam-5353	171	2	m	m	VERB
ejpam-5353	171	3	−i	−i	ADJ
ejpam-5353	171	4	if	if	SCONJ
ejpam-5353	171	5	m+	m+	NUM
ejpam-5353	171	6	1	1	NUM
ejpam-5353	171	7	≤	≤	NUM
ejpam-5353	172	1	i	i	PRON
ejpam-5353	172	2	≤	≤	NOUN
ejpam-5353	173	1	2m−	2m−	NUM
ejpam-5353	173	2	1	1	NUM
ejpam-5353	173	3	for	for	ADP
ejpam-5353	173	4	i	i	PROPN
ejpam-5353	173	5	∈	∈	PROPN
ejpam-5353	173	6	z2	z2	PROPN
ejpam-5353	173	7	m	m	PROPN
ejpam-5353	173	8	,	,	PUNCT
ejpam-5353	173	9	vi	vi	NOUN
ejpam-5353	173	10	−	−	NOUN
ejpam-5353	173	11	v−i	v−i	NOUN
ejpam-5353	174	1	+	+	CCONJ
ejpam-5353	174	2	i	i	PRON
ejpam-5353	174	3	=	=	PUNCT
ejpam-5353	174	4	i.	i.	NOUN
ejpam-5353	174	5	by	by	ADP
ejpam-5353	174	6	theorem	theorem	NOUN
ejpam-5353	174	7	3	3	NUM
ejpam-5353	174	8	,	,	PUNCT
ejpam-5353	174	9	g	g	PROPN
ejpam-5353	174	10	is	be	AUX
ejpam-5353	174	11	a	a	DET
ejpam-5353	174	12	symmetric	symmetric	ADJ
ejpam-5353	174	13	base	base	NOUN
ejpam-5353	174	14	.	.	PUNCT
ejpam-5353	175	1	by	by	ADP
ejpam-5353	175	2	definition	definition	NOUN
ejpam-5353	175	3	of	of	ADP
ejpam-5353	175	4	v(g	v(g	PROPN
ejpam-5353	175	5	)	)	PUNCT
ejpam-5353	175	6	,	,	PUNCT
ejpam-5353	175	7	for	for	ADP
ejpam-5353	175	8	any	any	DET
ejpam-5353	175	9	i	i	PROPN
ejpam-5353	175	10	∈	∈	PROPN
ejpam-5353	175	11	z2	z2	PROPN
ejpam-5353	175	12	m	m	PROPN
ejpam-5353	175	13	,	,	PUNCT
ejpam-5353	175	14	the	the	DET
ejpam-5353	175	15	graph	graph	NOUN
ejpam-5353	175	16	g	g	PROPN
ejpam-5353	175	17	≊	≊	NOUN
ejpam-5353	175	18	τ01(2,m−	τ01(2,m−	PROPN
ejpam-5353	175	19	1	1	NUM
ejpam-5353	175	20	)	)	PUNCT
ejpam-5353	175	21	.	.	PUNCT
ejpam-5353	176	1	e(g	e(g	NOUN
ejpam-5353	176	2	)	)	PUNCT
ejpam-5353	177	1	=	=	PRON
ejpam-5353	177	2	{	{	PUNCT
ejpam-5353	177	3	(	(	PUNCT
ejpam-5353	177	4	00	00	NUM
ejpam-5353	177	5	,	,	PUNCT
ejpam-5353	177	6	01	01	NUM
ejpam-5353	177	7	)	)	PUNCT
ejpam-5353	177	8	}	}	PUNCT
ejpam-5353	177	9	∪	∪	X
ejpam-5353	177	10	{	{	PUNCT
ejpam-5353	177	11	(	(	PUNCT
ejpam-5353	177	12	i0	i0	PROPN
ejpam-5353	177	13	,	,	PUNCT
ejpam-5353	177	14	01	01	NUM
ejpam-5353	177	15	)	)	PUNCT
ejpam-5353	177	16	:	:	PUNCT
ejpam-5353	177	17	1	1	NUM
ejpam-5353	177	18	≤	≤	NUM
ejpam-5353	177	19	i	i	X
ejpam-5353	177	20	≤	≤	NOUN
ejpam-5353	177	21	m	m	VERB
ejpam-5353	177	22	}	}	PUNCT
ejpam-5353	177	23	∪	∪	X
ejpam-5353	177	24	{	{	PUNCT
ejpam-5353	177	25	(	(	PUNCT
ejpam-5353	177	26	i0	i0	PROPN
ejpam-5353	177	27	,	,	PUNCT
ejpam-5353	177	28	(	(	PUNCT
ejpam-5353	177	29	2i)1	2i)1	NUM
ejpam-5353	177	30	:	:	SYM
ejpam-5353	177	31	1	1	NUM
ejpam-5353	177	32	≤	≤	NUM
ejpam-5353	178	1	i	i	PRON
ejpam-5353	178	2	≤	≤	ADJ
ejpam-5353	178	3	m−	m−	PROPN
ejpam-5353	178	4	1	1	NUM
ejpam-5353	178	5	)	)	PUNCT
ejpam-5353	178	6	}	}	PUNCT
ejpam-5353	178	7	example	example	NOUN
ejpam-5353	179	1	1	1	X
ejpam-5353	179	2	.	.	PUNCT
ejpam-5353	179	3	there	there	PRON
ejpam-5353	179	4	is	be	VERB
ejpam-5353	179	5	an	an	DET
ejpam-5353	179	6	odc	odc	NOUN
ejpam-5353	179	7	of	of	ADP
ejpam-5353	179	8	k5,5	k5,5	PROPN
ejpam-5353	179	9	by	by	ADP
ejpam-5353	179	10	τ01(1	τ01(1	PROPN
ejpam-5353	179	11	,	,	PUNCT
ejpam-5353	179	12	2	2	NUM
ejpam-5353	179	13	)	)	PUNCT
ejpam-5353	179	14	,	,	PUNCT
ejpam-5353	179	15	since	since	SCONJ
ejpam-5353	179	16	v(g	v(g	NUM
ejpam-5353	179	17	)	)	PUNCT
ejpam-5353	179	18	=	=	SYM
ejpam-5353	179	19	(	(	PUNCT
ejpam-5353	179	20	0	0	NUM
ejpam-5353	179	21	,	,	PUNCT
ejpam-5353	179	22	1	1	NUM
ejpam-5353	179	23	,	,	PUNCT
ejpam-5353	179	24	2	2	NUM
ejpam-5353	179	25	,	,	PUNCT
ejpam-5353	179	26	2	2	NUM
ejpam-5353	179	27	,	,	PUNCT
ejpam-5353	179	28	1	1	NUM
ejpam-5353	179	29	)	)	PUNCT
ejpam-5353	179	30	is	be	AUX
ejpam-5353	179	31	a	a	DET
ejpam-5353	179	32	symmetric	symmetric	ADJ
ejpam-5353	179	33	base	base	NOUN
ejpam-5353	179	34	,	,	PUNCT
ejpam-5353	179	35	see	see	VERB
ejpam-5353	179	36	figure	figure	NOUN
ejpam-5353	179	37	3	3	NUM
ejpam-5353	179	38	.	.	PUNCT
ejpam-5353	180	1	h.	h.	PROPN
ejpam-5353	180	2	shabana	shabana	PROPN
ejpam-5353	180	3	,	,	PUNCT
ejpam-5353	180	4	r.	r.	PROPN
ejpam-5353	180	5	el	el	PROPN
ejpam-5353	180	6	-	-	PROPN
ejpam-5353	180	7	shanawany	shanawany	NOUN
ejpam-5353	180	8	,	,	PUNCT
ejpam-5353	180	9	s.	s.	PROPN
ejpam-5353	180	10	halawa	halawa	PROPN
ejpam-5353	180	11	/	/	PUNCT
ejpam-5353	180	12	eur	eur	PROPN
ejpam-5353	180	13	.	.	PUNCT
ejpam-5353	181	1	j.	j.	PROPN
ejpam-5353	181	2	pure	pure	PROPN
ejpam-5353	181	3	appl	appl	PROPN
ejpam-5353	181	4	.	.	PROPN
ejpam-5353	181	5	math	math	PROPN
ejpam-5353	181	6	,	,	PUNCT
ejpam-5353	181	7	17	17	NUM
ejpam-5353	181	8	(	(	PUNCT
ejpam-5353	181	9	4	4	NUM
ejpam-5353	181	10	)	)	PUNCT
ejpam-5353	181	11	(	(	PUNCT
ejpam-5353	181	12	2024	2024	NUM
ejpam-5353	181	13	)	)	PUNCT
ejpam-5353	181	14	,	,	PUNCT
ejpam-5353	181	15	3492	3492	NUM
ejpam-5353	181	16	-	-	SYM
ejpam-5353	181	17	3516	3516	NUM
ejpam-5353	181	18	3498	3498	NUM
ejpam-5353	181	19	figure	figure	NOUN
ejpam-5353	181	20	3	3	NUM
ejpam-5353	181	21	:	:	PUNCT
ejpam-5353	181	22	symmetric	symmetric	ADJ
ejpam-5353	181	23	base	base	NOUN
ejpam-5353	181	24	of	of	ADP
ejpam-5353	181	25	an	an	DET
ejpam-5353	181	26	odc	odc	NOUN
ejpam-5353	181	27	of	of	ADP
ejpam-5353	181	28	k5,5	k5,5	PROPN
ejpam-5353	181	29	by	by	ADP
ejpam-5353	181	30	τ01(1	τ01(1	PROPN
ejpam-5353	181	31	,	,	PUNCT
ejpam-5353	181	32	2	2	NUM
ejpam-5353	181	33	)	)	PUNCT
ejpam-5353	181	34	.	.	PUNCT
ejpam-5353	182	1	theorem	theorem	VERB
ejpam-5353	182	2	6	6	NUM
ejpam-5353	182	3	.	.	PUNCT
ejpam-5353	183	1	let	let	VERB
ejpam-5353	183	2	n	n	PRON
ejpam-5353	183	3	≥	≥	NUM
ejpam-5353	183	4	5	5	NUM
ejpam-5353	183	5	be	be	AUX
ejpam-5353	183	6	a	a	DET
ejpam-5353	183	7	positive	positive	ADJ
ejpam-5353	183	8	integer	integer	NOUN
ejpam-5353	183	9	,	,	PUNCT
ejpam-5353	183	10	then	then	ADV
ejpam-5353	183	11	there	there	PRON
ejpam-5353	183	12	is	be	VERB
ejpam-5353	183	13	an	an	DET
ejpam-5353	183	14	odc	odc	NOUN
ejpam-5353	183	15	of	of	ADP
ejpam-5353	183	16	kn	kn	PROPN
ejpam-5353	183	17	,	,	PUNCT
ejpam-5353	183	18	n	n	CCONJ
ejpam-5353	183	19	by	by	ADP
ejpam-5353	183	20	τ00(n−4	τ00(n−4	NOUN
ejpam-5353	183	21	,	,	PUNCT
ejpam-5353	183	22	2	2	X
ejpam-5353	183	23	)	)	PUNCT
ejpam-5353	183	24	proof	proof	NOUN
ejpam-5353	183	25	.	.	PUNCT
ejpam-5353	184	1	for	for	ADP
ejpam-5353	184	2	any	any	DET
ejpam-5353	184	3	positive	positive	ADJ
ejpam-5353	184	4	integer	integer	NOUN
ejpam-5353	184	5	n	n	PRON
ejpam-5353	184	6	≥	≥	NUM
ejpam-5353	184	7	5	5	NUM
ejpam-5353	184	8	,	,	PUNCT
ejpam-5353	184	9	the	the	DET
ejpam-5353	184	10	vectors	vector	NOUN
ejpam-5353	184	11	v(g	v(g	ADJ
ejpam-5353	184	12	)	)	PUNCT
ejpam-5353	184	13	and	and	CCONJ
ejpam-5353	184	14	u(f	u(f	NOUN
ejpam-5353	184	15	)	)	PUNCT
ejpam-5353	184	16	of	of	ADP
ejpam-5353	184	17	the	the	DET
ejpam-5353	184	18	bases	basis	NOUN
ejpam-5353	184	19	g	g	PROPN
ejpam-5353	184	20	and	and	CCONJ
ejpam-5353	184	21	f	f	PROPN
ejpam-5353	184	22	are	be	AUX
ejpam-5353	184	23	represented	represent	VERB
ejpam-5353	184	24	as	as	ADP
ejpam-5353	184	25	:	:	PUNCT
ejpam-5353	184	26	vi(g	vi(g	X
ejpam-5353	184	27	)	)	PUNCT
ejpam-5353	185	1	=	=	PUNCT
ejpam-5353	185	2			PUNCT
ejpam-5353	185	3	(	(	PUNCT
ejpam-5353	185	4	n−	n−	NOUN
ejpam-5353	185	5	2)i	2)i	NUM
ejpam-5353	185	6	if	if	SCONJ
ejpam-5353	185	7	i	i	PRON
ejpam-5353	185	8	=	=	NOUN
ejpam-5353	185	9	0	0	NUM
ejpam-5353	185	10	,	,	PUNCT
ejpam-5353	185	11	n−	n−	NOUN
ejpam-5353	185	12	2	2	NUM
ejpam-5353	185	13	−2i−	−2i−	SYM
ejpam-5353	185	14	1	1	NUM
ejpam-5353	185	15	if	if	SCONJ
ejpam-5353	185	16	i	i	PRON
ejpam-5353	185	17	=	=	NOUN
ejpam-5353	185	18	1	1	NUM
ejpam-5353	185	19	,	,	PUNCT
ejpam-5353	185	20	n−	n−	NOUN
ejpam-5353	185	21	1	1	NUM
ejpam-5353	185	22	−i	−i	NOUN
ejpam-5353	185	23	otherwise	otherwise	ADV
ejpam-5353	185	24	ui(f	ui(f	PUNCT
ejpam-5353	185	25	)	)	PUNCT
ejpam-5353	185	26	=	=	PUNCT
ejpam-5353	186	1			PUNCT
ejpam-5353	186	2	(	(	PUNCT
ejpam-5353	186	3	n−	n−	NOUN
ejpam-5353	186	4	1)i	1)i	NUM
ejpam-5353	186	5	if	if	SCONJ
ejpam-5353	186	6	i	i	PRON
ejpam-5353	186	7	=	=	NOUN
ejpam-5353	186	8	0	0	NUM
ejpam-5353	186	9	,	,	PUNCT
ejpam-5353	186	10	n−	n−	NOUN
ejpam-5353	186	11	2	2	NUM
ejpam-5353	186	12	−i−	−i−	ADP
ejpam-5353	186	13	1	1	NUM
ejpam-5353	186	14	if	if	SCONJ
ejpam-5353	186	15	i	i	PRON
ejpam-5353	186	16	=	=	NOUN
ejpam-5353	186	17	1	1	NUM
ejpam-5353	186	18	,	,	PUNCT
ejpam-5353	186	19	n−	n−	NOUN
ejpam-5353	186	20	1	1	NUM
ejpam-5353	186	21	0	0	NUM
ejpam-5353	186	22	otherwise	otherwise	ADV
ejpam-5353	186	23	from	from	ADP
ejpam-5353	186	24	the	the	DET
ejpam-5353	186	25	representation	representation	NOUN
ejpam-5353	186	26	of	of	ADP
ejpam-5353	186	27	v(g	v(g	PROPN
ejpam-5353	186	28	)	)	PUNCT
ejpam-5353	186	29	and	and	CCONJ
ejpam-5353	186	30	u(f	u(f	NOUN
ejpam-5353	186	31	)	)	PUNCT
ejpam-5353	186	32	,	,	PUNCT
ejpam-5353	186	33	vi(g)−ui(f	vi(g)−ui(f	NOUN
ejpam-5353	186	34	)	)	PUNCT
ejpam-5353	187	1	=	=	SYM
ejpam-5353	187	2	0	0	PUNCT
ejpam-5353	188	1	at	at	ADP
ejpam-5353	188	2	i	i	PROPN
ejpam-5353	188	3	=	=	NOUN
ejpam-5353	188	4	0	0	NUM
ejpam-5353	188	5	,	,	PUNCT
ejpam-5353	188	6	vi(g)−ui(f	vi(g)−ui(f	NUM
ejpam-5353	188	7	)	)	PUNCT
ejpam-5353	188	8	=	=	SYM
ejpam-5353	188	9	2	2	NUM
ejpam-5353	188	10	at	at	ADP
ejpam-5353	188	11	i	i	NOUN
ejpam-5353	188	12	=	=	PUNCT
ejpam-5353	188	13	n−	n−	NOUN
ejpam-5353	188	14	2	2	NUM
ejpam-5353	188	15	,	,	PUNCT
ejpam-5353	188	16	and	and	CCONJ
ejpam-5353	188	17	vi(g)−	vi(g)−	NOUN
ejpam-5353	188	18	ui(f	ui(f	PUNCT
ejpam-5353	188	19	)	)	PUNCT
ejpam-5353	189	1	=	=	SYM
ejpam-5353	189	2	−i	−i	ADV
ejpam-5353	189	3	otherwise	otherwise	ADV
ejpam-5353	189	4	.	.	PUNCT
ejpam-5353	190	1	consequently	consequently	ADV
ejpam-5353	190	2	,	,	PUNCT
ejpam-5353	190	3	{	{	PUNCT
ejpam-5353	190	4	vi(g)−	vi(g)−	NOUN
ejpam-5353	190	5	ui(f	ui(f	PUNCT
ejpam-5353	190	6	)	)	PUNCT
ejpam-5353	190	7	;	;	PUNCT
ejpam-5353	190	8	i	i	PRON
ejpam-5353	190	9	∈	∈	PROPN
ejpam-5353	190	10	zn	zn	PROPN
ejpam-5353	190	11	}	}	PUNCT
ejpam-5353	190	12	=	=	ADJ
ejpam-5353	190	13	zn	zn	X
ejpam-5353	190	14	.	.	PUNCT
ejpam-5353	191	1	by	by	ADP
ejpam-5353	191	2	theorem	theorem	NOUN
ejpam-5353	191	3	4	4	NUM
ejpam-5353	191	4	,	,	PUNCT
ejpam-5353	191	5	the	the	DET
ejpam-5353	191	6	two	two	NUM
ejpam-5353	191	7	bases	basis	NOUN
ejpam-5353	191	8	v(g	v(g	ADJ
ejpam-5353	191	9	)	)	PUNCT
ejpam-5353	191	10	and	and	CCONJ
ejpam-5353	191	11	u(f	u(f	NOUN
ejpam-5353	191	12	)	)	PUNCT
ejpam-5353	191	13	are	be	AUX
ejpam-5353	191	14	orthogonal	orthogonal	ADJ
ejpam-5353	191	15	.	.	PUNCT
ejpam-5353	192	1	moreover	moreover	ADV
ejpam-5353	192	2	,	,	PUNCT
ejpam-5353	192	3	the	the	DET
ejpam-5353	192	4	edges	edge	NOUN
ejpam-5353	192	5	set	set	VERB
ejpam-5353	192	6	e(g	e(g	PROPN
ejpam-5353	192	7	)	)	PUNCT
ejpam-5353	192	8	and	and	CCONJ
ejpam-5353	192	9	e(f	e(f	PROPN
ejpam-5353	192	10	)	)	PUNCT
ejpam-5353	192	11	of	of	ADP
ejpam-5353	192	12	the	the	DET
ejpam-5353	192	13	bases	basis	NOUN
ejpam-5353	192	14	g	g	PROPN
ejpam-5353	192	15	and	and	CCONJ
ejpam-5353	192	16	f	f	PROPN
ejpam-5353	192	17	respectively	respectively	ADV
ejpam-5353	192	18	can	can	AUX
ejpam-5353	192	19	be	be	AUX
ejpam-5353	192	20	represented	represent	VERB
ejpam-5353	192	21	by	by	ADP
ejpam-5353	192	22	:	:	PUNCT
ejpam-5353	192	23	e(g	e(g	PROPN
ejpam-5353	192	24	)	)	PUNCT
ejpam-5353	193	1	=	=	PRON
ejpam-5353	193	2	{	{	PUNCT
ejpam-5353	193	3	(	(	PUNCT
ejpam-5353	193	4	(	(	PUNCT
ejpam-5353	193	5	(	(	PUNCT
ejpam-5353	193	6	n−	n−	NOUN
ejpam-5353	193	7	2)i)0	2)i)0	NOUN
ejpam-5353	193	8	,	,	PUNCT
ejpam-5353	193	9	(	(	PUNCT
ejpam-5353	193	10	(	(	PUNCT
ejpam-5353	193	11	n−	n−	NOUN
ejpam-5353	193	12	1)i)1	1)i)1	NOUN
ejpam-5353	193	13	;	;	PUNCT
ejpam-5353	193	14	i	i	PROPN
ejpam-5353	193	15	=	=	SYM
ejpam-5353	193	16	0	0	NUM
ejpam-5353	193	17	,	,	PUNCT
ejpam-5353	193	18	n−	n−	NOUN
ejpam-5353	193	19	2	2	NUM
ejpam-5353	193	20	}	}	PUNCT
ejpam-5353	193	21	∪{((−2i−	∪{((−2i−	VERB
ejpam-5353	193	22	1)0	1)0	NUM
ejpam-5353	193	23	,	,	PUNCT
ejpam-5353	193	24	(	(	PUNCT
ejpam-5353	193	25	−i−	−i−	ADV
ejpam-5353	193	26	1)1	1)1	NUM
ejpam-5353	193	27	)	)	PUNCT
ejpam-5353	193	28	;	;	PUNCT
ejpam-5353	194	1	i	i	NOUN
ejpam-5353	194	2	=	=	NOUN
ejpam-5353	194	3	1	1	NUM
ejpam-5353	194	4	,	,	PUNCT
ejpam-5353	194	5	n−	n−	NOUN
ejpam-5353	194	6	1	1	NUM
ejpam-5353	194	7	}	}	PUNCT
ejpam-5353	194	8	∪{(−i0	∪{(−i0	PROPN
ejpam-5353	194	9	,	,	PUNCT
ejpam-5353	194	10	01	01	NUM
ejpam-5353	194	11	)	)	PUNCT
ejpam-5353	194	12	;	;	PUNCT
ejpam-5353	195	1	i	i	PROPN
ejpam-5353	195	2	∈	∈	PROPN
ejpam-5353	195	3	zn\	zn\	PROPN
ejpam-5353	195	4	{	{	PUNCT
ejpam-5353	195	5	0	0	NUM
ejpam-5353	195	6	,	,	PUNCT
ejpam-5353	195	7	1	1	NUM
ejpam-5353	195	8	,	,	PUNCT
ejpam-5353	195	9	n−	n−	NOUN
ejpam-5353	195	10	2	2	NUM
ejpam-5353	195	11	,	,	PUNCT
ejpam-5353	195	12	n−	n−	NOUN
ejpam-5353	195	13	1	1	NUM
ejpam-5353	195	14	}	}	PUNCT
ejpam-5353	195	15	}	}	PUNCT
ejpam-5353	195	16	and	and	CCONJ
ejpam-5353	195	17	e(f	e(f	PROPN
ejpam-5353	195	18	)	)	PUNCT
ejpam-5353	196	1	=	=	PRON
ejpam-5353	196	2	{	{	PUNCT
ejpam-5353	196	3	(	(	PUNCT
ejpam-5353	196	4	(	(	PUNCT
ejpam-5353	196	5	(	(	PUNCT
ejpam-5353	196	6	n−	n−	NOUN
ejpam-5353	196	7	1)i)0	1)i)0	NUM
ejpam-5353	196	8	,	,	PUNCT
ejpam-5353	196	9	01	01	NUM
ejpam-5353	196	10	)	)	PUNCT
ejpam-5353	196	11	;	;	PUNCT
ejpam-5353	197	1	i	i	NOUN
ejpam-5353	197	2	=	=	SYM
ejpam-5353	197	3	0	0	NUM
ejpam-5353	197	4	,	,	PUNCT
ejpam-5353	197	5	n−	n−	NOUN
ejpam-5353	197	6	2	2	NUM
ejpam-5353	197	7	}	}	PUNCT
ejpam-5353	197	8	∪{((−i−	∪{((−i−	ADV
ejpam-5353	197	9	1)0	1)0	PROPN
ejpam-5353	197	10	,	,	PUNCT
ejpam-5353	197	11	(	(	PUNCT
ejpam-5353	197	12	n−	n−	NOUN
ejpam-5353	197	13	1)1	1)1	NUM
ejpam-5353	197	14	)	)	PUNCT
ejpam-5353	197	15	;	;	PUNCT
ejpam-5353	197	16	i	i	NOUN
ejpam-5353	197	17	=	=	NOUN
ejpam-5353	197	18	1	1	NUM
ejpam-5353	197	19	,	,	PUNCT
ejpam-5353	197	20	n−	n−	NOUN
ejpam-5353	197	21	1	1	NUM
ejpam-5353	197	22	}	}	PUNCT
ejpam-5353	197	23	∪{(00	∪{(00	PROPN
ejpam-5353	197	24	,	,	PUNCT
ejpam-5353	197	25	i	i	PROPN
ejpam-5353	197	26	)	)	PUNCT
ejpam-5353	197	27	;	;	PUNCT
ejpam-5353	198	1	i	i	PROPN
ejpam-5353	198	2	∈	∈	PROPN
ejpam-5353	198	3	zn\	zn\	PROPN
ejpam-5353	198	4	{	{	PUNCT
ejpam-5353	198	5	0	0	NUM
ejpam-5353	198	6	,	,	PUNCT
ejpam-5353	198	7	1	1	NUM
ejpam-5353	198	8	,	,	PUNCT
ejpam-5353	198	9	n−	n−	NOUN
ejpam-5353	198	10	2	2	NUM
ejpam-5353	198	11	,	,	PUNCT
ejpam-5353	198	12	n−	n−	NOUN
ejpam-5353	198	13	1	1	NUM
ejpam-5353	198	14	}	}	PUNCT
ejpam-5353	198	15	}	}	PUNCT
ejpam-5353	198	16	therefore	therefore	ADV
ejpam-5353	198	17	,	,	PUNCT
ejpam-5353	198	18	g	g	PROPN
ejpam-5353	198	19	∼=	∼=	PROPN
ejpam-5353	198	20	f	f	NOUN
ejpam-5353	198	21	∼=	∼=	PROPN
ejpam-5353	198	22	τ00(n−	τ00(n−	NUM
ejpam-5353	198	23	4	4	NUM
ejpam-5353	198	24	,	,	PUNCT
ejpam-5353	198	25	2	2	NUM
ejpam-5353	198	26	)	)	PUNCT
ejpam-5353	198	27	.	.	PUNCT
ejpam-5353	199	1	h.	h.	PROPN
ejpam-5353	199	2	shabana	shabana	PROPN
ejpam-5353	199	3	,	,	PUNCT
ejpam-5353	199	4	r.	r.	PROPN
ejpam-5353	199	5	el	el	PROPN
ejpam-5353	199	6	-	-	PROPN
ejpam-5353	199	7	shanawany	shanawany	NOUN
ejpam-5353	199	8	,	,	PUNCT
ejpam-5353	199	9	s.	s.	PROPN
ejpam-5353	199	10	halawa	halawa	PROPN
ejpam-5353	199	11	/	/	PUNCT
ejpam-5353	199	12	eur	eur	PROPN
ejpam-5353	199	13	.	.	PUNCT
ejpam-5353	200	1	j.	j.	PROPN
ejpam-5353	200	2	pure	pure	PROPN
ejpam-5353	200	3	appl	appl	PROPN
ejpam-5353	200	4	.	.	PROPN
ejpam-5353	200	5	math	math	PROPN
ejpam-5353	200	6	,	,	PUNCT
ejpam-5353	200	7	17	17	NUM
ejpam-5353	200	8	(	(	PUNCT
ejpam-5353	200	9	4	4	NUM
ejpam-5353	200	10	)	)	PUNCT
ejpam-5353	200	11	(	(	PUNCT
ejpam-5353	200	12	2024	2024	NUM
ejpam-5353	200	13	)	)	PUNCT
ejpam-5353	200	14	,	,	PUNCT
ejpam-5353	200	15	3492	3492	NUM
ejpam-5353	200	16	-	-	SYM
ejpam-5353	200	17	3516	3516	NUM
ejpam-5353	200	18	3499	3499	NUM
ejpam-5353	200	19	theorem	theorem	NOUN
ejpam-5353	200	20	7	7	NUM
ejpam-5353	200	21	.	.	PUNCT
ejpam-5353	201	1	let	let	VERB
ejpam-5353	201	2	n	n	PRON
ejpam-5353	201	3	>	>	X
ejpam-5353	201	4	3	3	NUM
ejpam-5353	201	5	to	to	PART
ejpam-5353	201	6	be	be	AUX
ejpam-5353	201	7	an	an	DET
ejpam-5353	201	8	odd	odd	ADJ
ejpam-5353	201	9	integer	integer	NOUN
ejpam-5353	201	10	and	and	CCONJ
ejpam-5353	201	11	x1	x1	NUM
ejpam-5353	201	12	,	,	PUNCT
ejpam-5353	202	1	x2	x2	PROPN
ejpam-5353	202	2	and	and	CCONJ
ejpam-5353	202	3	γ	γ	PROPN
ejpam-5353	202	4	∈	∈	PROPN
ejpam-5353	202	5	zn	zn	X
ejpam-5353	202	6	.	.	PUNCT
ejpam-5353	203	1	then	then	ADV
ejpam-5353	203	2	there	there	PRON
ejpam-5353	203	3	is	be	VERB
ejpam-5353	203	4	a	a	DET
ejpam-5353	203	5	symmetric	symmetric	ADJ
ejpam-5353	203	6	base	base	NOUN
ejpam-5353	203	7	of	of	ADP
ejpam-5353	203	8	an	an	DET
ejpam-5353	203	9	odc	odc	NOUN
ejpam-5353	203	10	of	of	ADP
ejpam-5353	203	11	kn	kn	PROPN
ejpam-5353	203	12	,	,	PUNCT
ejpam-5353	203	13	n	n	CCONJ
ejpam-5353	203	14	by	by	ADP
ejpam-5353	203	15	g	g	PROPN
ejpam-5353	203	16	≊	≊	X
ejpam-5353	203	17	τ00(x1	τ00(x1	PROPN
ejpam-5353	203	18	,	,	PUNCT
ejpam-5353	203	19	x2	x2	PROPN
ejpam-5353	203	20	)	)	PUNCT
ejpam-5353	203	21	∪	∪	ADP
ejpam-5353	203	22	γk2	γk2	PROPN
ejpam-5353	203	23	.	.	PUNCT
ejpam-5353	204	1	proof	proof	NOUN
ejpam-5353	204	2	.	.	PUNCT
ejpam-5353	205	1	case	case	NOUN
ejpam-5353	205	2	1	1	X
ejpam-5353	205	3	.	.	PUNCT
ejpam-5353	206	1	let	let	VERB
ejpam-5353	206	2	m	m	PRON
ejpam-5353	206	3	,	,	PUNCT
ejpam-5353	206	4	n	n	X
ejpam-5353	206	5	be	be	VERB
ejpam-5353	206	6	positive	positive	ADJ
ejpam-5353	206	7	integers	integer	NOUN
ejpam-5353	206	8	such	such	ADJ
ejpam-5353	206	9	that	that	SCONJ
ejpam-5353	206	10	n	n	NOUN
ejpam-5353	206	11	=	=	SYM
ejpam-5353	206	12	2	2	NUM
ejpam-5353	206	13	m	m	NOUN
ejpam-5353	206	14	+	+	NOUN
ejpam-5353	206	15	1	1	NUM
ejpam-5353	206	16	,	,	PUNCT
ejpam-5353	206	17	n	n	CCONJ
ejpam-5353	206	18	>	>	X
ejpam-5353	206	19	3	3	NUM
ejpam-5353	206	20	and	and	CCONJ
ejpam-5353	206	21	n	n	NUM
ejpam-5353	206	22	≇	≇	PROPN
ejpam-5353	206	23	0mod	0mod	PROPN
ejpam-5353	206	24	3	3	X
ejpam-5353	206	25	.	.	PUNCT
ejpam-5353	207	1	the	the	DET
ejpam-5353	207	2	vector	vector	NOUN
ejpam-5353	207	3	v(g	v(g	PROPN
ejpam-5353	207	4	)	)	PUNCT
ejpam-5353	207	5	of	of	ADP
ejpam-5353	207	6	the	the	DET
ejpam-5353	207	7	base	base	NOUN
ejpam-5353	207	8	g	g	NOUN
ejpam-5353	207	9	is	be	AUX
ejpam-5353	207	10	defined	define	VERB
ejpam-5353	207	11	as	as	ADP
ejpam-5353	207	12	:	:	PUNCT
ejpam-5353	207	13	vi(g	vi(g	NUM
ejpam-5353	207	14	)	)	PUNCT
ejpam-5353	208	1	=	=	PRON
ejpam-5353	208	2	{	{	PUNCT
ejpam-5353	208	3	2i	2i	NOUN
ejpam-5353	208	4	if	if	SCONJ
ejpam-5353	208	5	0	0	NUM
ejpam-5353	208	6	≤	≤	NUM
ejpam-5353	208	7	i	i	PRON
ejpam-5353	209	1	≤	≤	NUM
ejpam-5353	209	2	m	m	VERB
ejpam-5353	209	3	0	0	NUM
ejpam-5353	210	1	if	if	SCONJ
ejpam-5353	210	2	m+	m+	NUM
ejpam-5353	210	3	1	1	NUM
ejpam-5353	210	4	≤	≤	NUM
ejpam-5353	210	5	i	i	X
ejpam-5353	210	6	≤	≤	ADJ
ejpam-5353	210	7	2	2	NUM
ejpam-5353	210	8	m	m	VERB
ejpam-5353	210	9	hence	hence	ADV
ejpam-5353	210	10	,	,	PUNCT
ejpam-5353	210	11	v−i(g	v−i(g	PROPN
ejpam-5353	210	12	)	)	PUNCT
ejpam-5353	211	1	=	=	PRON
ejpam-5353	211	2	{	{	PUNCT
ejpam-5353	211	3	0	0	NUM
ejpam-5353	211	4	if	if	SCONJ
ejpam-5353	211	5	0	0	NUM
ejpam-5353	211	6	≤	≤	NUM
ejpam-5353	211	7	i	i	VERB
ejpam-5353	211	8	≤	≤	NOUN
ejpam-5353	211	9	m	m	VERB
ejpam-5353	211	10	−2i	−2i	NOUN
ejpam-5353	211	11	if	if	SCONJ
ejpam-5353	211	12	m+	m+	NUM
ejpam-5353	211	13	1	1	NUM
ejpam-5353	211	14	≤	≤	NUM
ejpam-5353	211	15	i	i	X
ejpam-5353	211	16	≤	≤	ADJ
ejpam-5353	211	17	2	2	NUM
ejpam-5353	211	18	m	m	NOUN
ejpam-5353	211	19	for	for	ADP
ejpam-5353	211	20	i	i	PROPN
ejpam-5353	211	21	∈	∈	PROPN
ejpam-5353	211	22	z2m+1	z2m+1	PROPN
ejpam-5353	211	23	,	,	PUNCT
ejpam-5353	211	24	vi	vi	NOUN
ejpam-5353	211	25	−	−	NOUN
ejpam-5353	211	26	v−i	v−i	NOUN
ejpam-5353	212	1	+	+	CCONJ
ejpam-5353	213	1	i	i	NOUN
ejpam-5353	213	2	=	=	NOUN
ejpam-5353	213	3	3i	3i	NOUN
ejpam-5353	213	4	,	,	PUNCT
ejpam-5353	213	5	since	since	SCONJ
ejpam-5353	213	6	gcd(3	gcd(3	NOUN
ejpam-5353	213	7	,	,	PUNCT
ejpam-5353	213	8	2	2	NUM
ejpam-5353	213	9	m	m	NOUN
ejpam-5353	213	10	+	+	NOUN
ejpam-5353	213	11	1	1	NUM
ejpam-5353	213	12	)	)	PUNCT
ejpam-5353	213	13	=	=	SYM
ejpam-5353	213	14	1	1	NUM
ejpam-5353	213	15	,	,	PUNCT
ejpam-5353	213	16	by	by	ADP
ejpam-5353	213	17	theorem	theorem	NOUN
ejpam-5353	213	18	3	3	NUM
ejpam-5353	213	19	,	,	PUNCT
ejpam-5353	213	20	g	g	PROPN
ejpam-5353	213	21	is	be	AUX
ejpam-5353	213	22	a	a	DET
ejpam-5353	213	23	symmetric	symmetric	ADJ
ejpam-5353	213	24	base	base	NOUN
ejpam-5353	213	25	.	.	PUNCT
ejpam-5353	214	1	by	by	ADP
ejpam-5353	214	2	definition	definition	NOUN
ejpam-5353	214	3	of	of	ADP
ejpam-5353	214	4	v(g	v(g	PROPN
ejpam-5353	214	5	)	)	PUNCT
ejpam-5353	214	6	,	,	PUNCT
ejpam-5353	214	7	the	the	DET
ejpam-5353	214	8	graph	graph	NOUN
ejpam-5353	214	9	g	g	PROPN
ejpam-5353	214	10	≊	≊	NOUN
ejpam-5353	214	11	τ00(⌈n+1	τ00(⌈n+1	NUM
ejpam-5353	214	12	3	3	NUM
ejpam-5353	214	13	⌉	⌉	NOUN
ejpam-5353	214	14	,	,	PUNCT
ejpam-5353	214	15	⌈	⌈	X
ejpam-5353	214	16	n−3	n−3	PROPN
ejpam-5353	214	17	6	6	NUM
ejpam-5353	214	18	⌉	⌉	NOUN
ejpam-5353	214	19	)	)	PUNCT
ejpam-5353	214	20	∪	∪	ADP
ejpam-5353	214	21	⌊	⌊	ADP
ejpam-5353	214	22	n−1	n−1	PROPN
ejpam-5353	214	23	3	3	NUM
ejpam-5353	214	24	⌋k2	⌋k2	NOUN
ejpam-5353	214	25	,	,	PUNCT
ejpam-5353	214	26	where	where	SCONJ
ejpam-5353	214	27	x1	x1	PROPN
ejpam-5353	215	1	=	=	PUNCT
ejpam-5353	215	2	⌈n+1	⌈n+1	ADJ
ejpam-5353	215	3	3	3	NUM
ejpam-5353	215	4	⌉	⌉	NOUN
ejpam-5353	215	5	,	,	PUNCT
ejpam-5353	215	6	x2	x2	NOUN
ejpam-5353	215	7	=	=	PUNCT
ejpam-5353	215	8	⌈	⌈	X
ejpam-5353	215	9	n−3	n−3	PROPN
ejpam-5353	215	10	6	6	NUM
ejpam-5353	215	11	⌉	⌉	NOUN
ejpam-5353	215	12	and	and	CCONJ
ejpam-5353	215	13	γ	γ	X
ejpam-5353	215	14	=	=	SYM
ejpam-5353	215	15	⌊n−1	⌊n−1	ADJ
ejpam-5353	215	16	3	3	NUM
ejpam-5353	215	17	⌋.	⌋.	NOUN
ejpam-5353	215	18	case	case	NOUN
ejpam-5353	215	19	2	2	NUM
ejpam-5353	215	20	.	.	X
ejpam-5353	216	1	for	for	ADP
ejpam-5353	216	2	an	an	DET
ejpam-5353	216	3	odd	odd	ADJ
ejpam-5353	216	4	integer	integer	NOUN
ejpam-5353	216	5	n	n	CCONJ
ejpam-5353	216	6	>	>	X
ejpam-5353	216	7	3	3	NUM
ejpam-5353	216	8	,	,	PUNCT
ejpam-5353	216	9	n	n	PRON
ejpam-5353	216	10	≡	≡	PROPN
ejpam-5353	216	11	0mod	0mod	PROPN
ejpam-5353	216	12	3	3	X
ejpam-5353	216	13	,	,	PUNCT
ejpam-5353	216	14	the	the	DET
ejpam-5353	216	15	vector	vector	NOUN
ejpam-5353	216	16	v(g	v(g	PROPN
ejpam-5353	216	17	)	)	PUNCT
ejpam-5353	216	18	of	of	ADP
ejpam-5353	216	19	the	the	DET
ejpam-5353	216	20	base	base	NOUN
ejpam-5353	216	21	g	g	NOUN
ejpam-5353	216	22	is	be	AUX
ejpam-5353	216	23	represented	represent	VERB
ejpam-5353	216	24	as	as	ADP
ejpam-5353	216	25	:	:	PUNCT
ejpam-5353	216	26	vi(g)=	vi(g)=	ADJ
ejpam-5353	216	27	{	{	PUNCT
ejpam-5353	216	28	2i	2i	NOUN
ejpam-5353	216	29	if	if	SCONJ
ejpam-5353	216	30	0	0	NUM
ejpam-5353	216	31	≤	≤	NUM
ejpam-5353	217	1	i	i	PRON
ejpam-5353	217	2	≤	≤	ADJ
ejpam-5353	218	1	n−1	n−1	PROPN
ejpam-5353	218	2	2	2	NUM
ejpam-5353	218	3	0	0	NUM
ejpam-5353	218	4	if	if	SCONJ
ejpam-5353	218	5	n+1	n+1	PROPN
ejpam-5353	218	6	2	2	NUM
ejpam-5353	218	7	≤	≤	NUM
ejpam-5353	218	8	i	i	PRON
ejpam-5353	218	9	≤	≤	ADJ
ejpam-5353	218	10	n−	n−	NOUN
ejpam-5353	218	11	1	1	NUM
ejpam-5353	218	12	hence	hence	ADV
ejpam-5353	218	13	,	,	PUNCT
ejpam-5353	218	14	v−i(g)=	v−i(g)=	ADJ
ejpam-5353	218	15	{	{	PUNCT
ejpam-5353	218	16	0	0	NUM
ejpam-5353	218	17	if	if	SCONJ
ejpam-5353	218	18	0	0	NUM
ejpam-5353	218	19	≤	≤	NUM
ejpam-5353	219	1	i	i	PRON
ejpam-5353	219	2	≤	≤	NUM
ejpam-5353	219	3	n−1	n−1	PROPN
ejpam-5353	219	4	2	2	NUM
ejpam-5353	219	5	−2i	−2i	PROPN
ejpam-5353	219	6	if	if	SCONJ
ejpam-5353	219	7	n+1	n+1	PROPN
ejpam-5353	219	8	2	2	NUM
ejpam-5353	219	9	≤	≤	NUM
ejpam-5353	220	1	i	i	PRON
ejpam-5353	220	2	≤	≤	ADJ
ejpam-5353	220	3	n−	n−	NOUN
ejpam-5353	220	4	1	1	NUM
ejpam-5353	220	5	for	for	ADP
ejpam-5353	220	6	i	i	PROPN
ejpam-5353	220	7	∈	∈	PROPN
ejpam-5353	220	8	zn	zn	PROPN
ejpam-5353	220	9	,	,	PUNCT
ejpam-5353	220	10	vi−v−i+i	vi−v−i+i	NOUN
ejpam-5353	220	11	=	=	PUNCT
ejpam-5353	220	12	3i	3i	NOUN
ejpam-5353	220	13	.	.	PUNCT
ejpam-5353	221	1	by	by	ADP
ejpam-5353	221	2	theorem	theorem	NOUN
ejpam-5353	221	3	3	3	NUM
ejpam-5353	221	4	,	,	PUNCT
ejpam-5353	221	5	g	g	PROPN
ejpam-5353	221	6	is	be	AUX
ejpam-5353	221	7	a	a	DET
ejpam-5353	221	8	symmetric	symmetric	ADJ
ejpam-5353	221	9	base	base	NOUN
ejpam-5353	221	10	.	.	PUNCT
ejpam-5353	222	1	by	by	ADP
ejpam-5353	222	2	the	the	DET
ejpam-5353	222	3	definition	definition	NOUN
ejpam-5353	222	4	of	of	ADP
ejpam-5353	222	5	v(g	v(g	PROPN
ejpam-5353	222	6	)	)	PUNCT
ejpam-5353	222	7	,	,	PUNCT
ejpam-5353	222	8	the	the	DET
ejpam-5353	222	9	graph	graph	NOUN
ejpam-5353	222	10	g	g	NOUN
ejpam-5353	222	11	≊	≊	NOUN
ejpam-5353	222	12	τ00(n3	τ00(n3	PROPN
ejpam-5353	222	13	,	,	PUNCT
ejpam-5353	222	14	⌊	⌊	VERB
ejpam-5353	222	15	n+1	n+1	NUM
ejpam-5353	222	16	5	5	NUM
ejpam-5353	222	17	⌋)∪	⌋)∪	ADJ
ejpam-5353	222	18	⌊	⌊	VERB
ejpam-5353	222	19	n−4	n−4	NUM
ejpam-5353	222	20	5	5	NUM
ejpam-5353	222	21	⌋k2	⌋k2	NOUN
ejpam-5353	222	22	,	,	PUNCT
ejpam-5353	222	23	where	where	SCONJ
ejpam-5353	222	24	x1	x1	PROPN
ejpam-5353	222	25	=	=	SYM
ejpam-5353	222	26	n	n	PRON
ejpam-5353	222	27	3	3	NUM
ejpam-5353	222	28	,	,	PUNCT
ejpam-5353	222	29	x2	x2	PROPN
ejpam-5353	222	30	=	=	PUNCT
ejpam-5353	222	31	⌊	⌊	VERB
ejpam-5353	222	32	n+1	n+1	NUM
ejpam-5353	222	33	5	5	NUM
ejpam-5353	222	34	⌋	⌋	NOUN
ejpam-5353	222	35	and	and	CCONJ
ejpam-5353	222	36	γ	γ	X
ejpam-5353	222	37	=	=	X
ejpam-5353	222	38	⌊n−4	⌊n−4	X
ejpam-5353	222	39	5	5	NUM
ejpam-5353	222	40	⌋.	⌋.	ADV
ejpam-5353	222	41	theorem	theorem	VERB
ejpam-5353	222	42	8	8	NUM
ejpam-5353	222	43	.	.	PUNCT
ejpam-5353	223	1	let	let	VERB
ejpam-5353	223	2	n	n	PRON
ejpam-5353	223	3	>	>	X
ejpam-5353	223	4	3,and	3,and	NUM
ejpam-5353	224	1	n	n	NUM
ejpam-5353	224	2	≇	≇	PROPN
ejpam-5353	224	3	0mod	0mod	PROPN
ejpam-5353	225	1	3	3	NUM
ejpam-5353	225	2	be	be	AUX
ejpam-5353	225	3	an	an	DET
ejpam-5353	225	4	even	even	ADV
ejpam-5353	225	5	integer	integer	NOUN
ejpam-5353	225	6	,	,	PUNCT
ejpam-5353	225	7	then	then	ADV
ejpam-5353	225	8	there	there	PRON
ejpam-5353	225	9	is	be	VERB
ejpam-5353	225	10	an	an	DET
ejpam-5353	225	11	odc	odc	NOUN
ejpam-5353	225	12	of	of	ADP
ejpam-5353	225	13	kn	kn	PROPN
ejpam-5353	225	14	,	,	PUNCT
ejpam-5353	225	15	n	n	CCONJ
ejpam-5353	225	16	by	by	ADP
ejpam-5353	225	17	g	g	PROPN
ejpam-5353	225	18	≊	≊	NOUN
ejpam-5353	225	19	τ00(⌈n+2	τ00(⌈n+2	NUM
ejpam-5353	225	20	3	3	NUM
ejpam-5353	225	21	⌉	⌉	NOUN
ejpam-5353	225	22	,	,	PUNCT
ejpam-5353	225	23	⌈	⌈	X
ejpam-5353	225	24	n−3	n−3	PROPN
ejpam-5353	225	25	6	6	NUM
ejpam-5353	225	26	⌉	⌉	NOUN
ejpam-5353	225	27	)	)	PUNCT
ejpam-5353	225	28	∪	∪	ADP
ejpam-5353	225	29	⌊	⌊	ADP
ejpam-5353	225	30	n−2	n−2	PROPN
ejpam-5353	225	31	3	3	NUM
ejpam-5353	225	32	⌋k2	⌋k2	NOUN
ejpam-5353	225	33	.	.	PUNCT
ejpam-5353	226	1	proof	proof	NOUN
ejpam-5353	226	2	.	.	PUNCT
ejpam-5353	227	1	for	for	ADP
ejpam-5353	227	2	any	any	DET
ejpam-5353	227	3	even	even	ADV
ejpam-5353	227	4	integer	integer	NOUN
ejpam-5353	227	5	n	n	NOUN
ejpam-5353	227	6	=	=	SYM
ejpam-5353	227	7	2	2	NUM
ejpam-5353	227	8	m	m	NOUN
ejpam-5353	227	9	,	,	PUNCT
ejpam-5353	227	10	m	m	VERB
ejpam-5353	227	11	∈	∈	NOUN
ejpam-5353	227	12	z+	z+	PRON
ejpam-5353	227	13	,	,	PUNCT
ejpam-5353	227	14	the	the	DET
ejpam-5353	227	15	vector	vector	NOUN
ejpam-5353	227	16	v(g	v(g	PROPN
ejpam-5353	227	17	)	)	PUNCT
ejpam-5353	227	18	of	of	ADP
ejpam-5353	227	19	the	the	DET
ejpam-5353	227	20	base	base	NOUN
ejpam-5353	227	21	g	g	NOUN
ejpam-5353	227	22	is	be	AUX
ejpam-5353	227	23	defined	define	VERB
ejpam-5353	227	24	as	as	ADP
ejpam-5353	227	25	:	:	PUNCT
ejpam-5353	227	26	vi(g	vi(g	X
ejpam-5353	227	27	)	)	PUNCT
ejpam-5353	227	28	=	=	PRON
ejpam-5353	227	29	{	{	PUNCT
ejpam-5353	227	30	2i	2i	NOUN
ejpam-5353	227	31	if	if	SCONJ
ejpam-5353	227	32	0	0	NUM
ejpam-5353	227	33	≤	≤	NUM
ejpam-5353	227	34	i	i	PRON
ejpam-5353	227	35	≤	≤	PROPN
ejpam-5353	227	36	⌈n−1	⌈n−1	PROPN
ejpam-5353	227	37	2	2	NUM
ejpam-5353	227	38	⌉	⌉	X
ejpam-5353	227	39	0	0	NUM
ejpam-5353	227	40	if	if	SCONJ
ejpam-5353	227	41	⌈n+1	⌈n+1	PROPN
ejpam-5353	227	42	2	2	NUM
ejpam-5353	227	43	⌉	⌉	NOUN
ejpam-5353	227	44	≤	≤	NUM
ejpam-5353	227	45	i	i	PRON
ejpam-5353	227	46	≤	≤	ADJ
ejpam-5353	227	47	n−	n−	NOUN
ejpam-5353	227	48	1	1	NUM
ejpam-5353	227	49	hence	hence	ADV
ejpam-5353	227	50	,	,	PUNCT
ejpam-5353	227	51	v−i(g	v−i(g	PROPN
ejpam-5353	227	52	)	)	PUNCT
ejpam-5353	228	1	=	=	PRON
ejpam-5353	228	2	{	{	PUNCT
ejpam-5353	228	3	0	0	NUM
ejpam-5353	228	4	if	if	SCONJ
ejpam-5353	228	5	0	0	NUM
ejpam-5353	228	6	≤	≤	NUM
ejpam-5353	228	7	i	i	PRON
ejpam-5353	228	8	≤	≤	PROPN
ejpam-5353	228	9	⌈n−1	⌈n−1	NOUN
ejpam-5353	228	10	2	2	NUM
ejpam-5353	228	11	⌉	⌉	X
ejpam-5353	228	12	−2i	−2i	PROPN
ejpam-5353	228	13	if	if	SCONJ
ejpam-5353	228	14	⌈n+1	⌈n+1	ADJ
ejpam-5353	228	15	2	2	NUM
ejpam-5353	228	16	⌉	⌉	NOUN
ejpam-5353	228	17	≤	≤	NUM
ejpam-5353	229	1	i	i	PRON
ejpam-5353	229	2	≤	≤	ADJ
ejpam-5353	229	3	n−	n−	NOUN
ejpam-5353	229	4	1	1	NUM
ejpam-5353	229	5	for	for	ADP
ejpam-5353	229	6	i	i	PROPN
ejpam-5353	229	7	∈	∈	PROPN
ejpam-5353	229	8	z2	z2	PROPN
ejpam-5353	229	9	m	m	PROPN
ejpam-5353	229	10	,	,	PUNCT
ejpam-5353	229	11	vi−	vi−	NOUN
ejpam-5353	229	12	v−i	v−i	NOUN
ejpam-5353	230	1	+	+	CCONJ
ejpam-5353	230	2	i	i	NOUN
ejpam-5353	230	3	=	=	NOUN
ejpam-5353	230	4	3i	3i	NOUN
ejpam-5353	230	5	.	.	PUNCT
ejpam-5353	231	1	since	since	SCONJ
ejpam-5353	231	2	gcd(3	gcd(3	NOUN
ejpam-5353	231	3	,	,	PUNCT
ejpam-5353	231	4	2	2	NUM
ejpam-5353	231	5	m	m	NOUN
ejpam-5353	231	6	)	)	PUNCT
ejpam-5353	231	7	=	=	SYM
ejpam-5353	231	8	1	1	NUM
ejpam-5353	231	9	,	,	PUNCT
ejpam-5353	231	10	by	by	ADP
ejpam-5353	231	11	theorem	theorem	NOUN
ejpam-5353	231	12	3	3	NUM
ejpam-5353	231	13	,	,	PUNCT
ejpam-5353	231	14	g	g	PROPN
ejpam-5353	231	15	is	be	AUX
ejpam-5353	231	16	a	a	DET
ejpam-5353	231	17	symmetric	symmetric	ADJ
ejpam-5353	231	18	base	base	NOUN
ejpam-5353	231	19	.	.	PUNCT
ejpam-5353	232	1	moreover	moreover	ADV
ejpam-5353	232	2	,	,	PUNCT
ejpam-5353	232	3	the	the	DET
ejpam-5353	232	4	edges	edge	NOUN
ejpam-5353	232	5	set	set	VERB
ejpam-5353	232	6	e(g	e(g	PROPN
ejpam-5353	232	7	)	)	PUNCT
ejpam-5353	232	8	of	of	ADP
ejpam-5353	232	9	the	the	DET
ejpam-5353	232	10	basis	basis	NOUN
ejpam-5353	232	11	g	g	NOUN
ejpam-5353	232	12	can	can	AUX
ejpam-5353	232	13	be	be	AUX
ejpam-5353	232	14	represented	represent	VERB
ejpam-5353	232	15	by	by	ADP
ejpam-5353	232	16	:	:	PUNCT
ejpam-5353	232	17	e(g)=	e(g)=	X
ejpam-5353	232	18	{	{	PUNCT
ejpam-5353	232	19	(	(	PUNCT
ejpam-5353	232	20	(	(	PUNCT
ejpam-5353	232	21	2i)0	2i)0	NUM
ejpam-5353	232	22	,	,	PUNCT
ejpam-5353	232	23	(	(	PUNCT
ejpam-5353	232	24	3i)1	3i)1	NUM
ejpam-5353	232	25	)	)	PUNCT
ejpam-5353	232	26	:	:	PUNCT
ejpam-5353	232	27	0	0	NUM
ejpam-5353	232	28	≤	≤	NUM
ejpam-5353	233	1	i	i	PRON
ejpam-5353	233	2	≤	≤	ADJ
ejpam-5353	233	3	⌈n−	⌈n−	SYM
ejpam-5353	233	4	1	1	NUM
ejpam-5353	233	5	2	2	NUM
ejpam-5353	233	6	⌉	⌉	ADP
ejpam-5353	233	7	}	}	PUNCT
ejpam-5353	233	8	∪	∪	X
ejpam-5353	233	9	{	{	PUNCT
ejpam-5353	233	10	(	(	PUNCT
ejpam-5353	233	11	00	00	NUM
ejpam-5353	233	12	,	,	PUNCT
ejpam-5353	233	13	i1	i1	PROPN
ejpam-5353	233	14	)	)	PUNCT
ejpam-5353	233	15	:	:	PUNCT
ejpam-5353	234	1	⌈	⌈	NUM
ejpam-5353	234	2	n+	n+	ADP
ejpam-5353	234	3	1	1	NUM
ejpam-5353	234	4	2	2	NUM
ejpam-5353	234	5	⌉	⌉	NOUN
ejpam-5353	234	6	≤	≤	NUM
ejpam-5353	234	7	i	i	PRON
ejpam-5353	234	8	≤	≤	ADJ
ejpam-5353	234	9	n−	n−	NOUN
ejpam-5353	234	10	1	1	NUM
ejpam-5353	234	11	}	}	PUNCT
ejpam-5353	234	12	.	.	PUNCT
ejpam-5353	235	1	by	by	ADP
ejpam-5353	235	2	the	the	DET
ejpam-5353	235	3	definition	definition	NOUN
ejpam-5353	235	4	of	of	ADP
ejpam-5353	235	5	v(g	v(g	PROPN
ejpam-5353	235	6	)	)	PUNCT
ejpam-5353	235	7	,	,	PUNCT
ejpam-5353	235	8	the	the	DET
ejpam-5353	235	9	graph	graph	NOUN
ejpam-5353	235	10	g	g	NOUN
ejpam-5353	235	11	≊	≊	NOUN
ejpam-5353	235	12	τ00(⌈n+2	τ00(⌈n+2	NUM
ejpam-5353	235	13	3	3	NUM
ejpam-5353	235	14	⌉	⌉	NOUN
ejpam-5353	235	15	,	,	PUNCT
ejpam-5353	235	16	⌈	⌈	X
ejpam-5353	235	17	n−3	n−3	PROPN
ejpam-5353	235	18	6	6	NUM
ejpam-5353	235	19	⌉	⌉	NOUN
ejpam-5353	235	20	)	)	PUNCT
ejpam-5353	235	21	∪	∪	ADP
ejpam-5353	235	22	⌊	⌊	ADP
ejpam-5353	235	23	n−2	n−2	PROPN
ejpam-5353	235	24	3	3	NUM
ejpam-5353	235	25	⌋k2	⌋k2	PROPN
ejpam-5353	235	26	.	.	PUNCT
ejpam-5353	236	1	h.	h.	PROPN
ejpam-5353	236	2	shabana	shabana	PROPN
ejpam-5353	236	3	,	,	PUNCT
ejpam-5353	236	4	r.	r.	PROPN
ejpam-5353	236	5	el	el	PROPN
ejpam-5353	236	6	-	-	PROPN
ejpam-5353	236	7	shanawany	shanawany	NOUN
ejpam-5353	236	8	,	,	PUNCT
ejpam-5353	236	9	s.	s.	PROPN
ejpam-5353	236	10	halawa	halawa	PROPN
ejpam-5353	236	11	/	/	PUNCT
ejpam-5353	236	12	eur	eur	PROPN
ejpam-5353	236	13	.	.	PUNCT
ejpam-5353	237	1	j.	j.	PROPN
ejpam-5353	237	2	pure	pure	PROPN
ejpam-5353	237	3	appl	appl	PROPN
ejpam-5353	237	4	.	.	PROPN
ejpam-5353	237	5	math	math	PROPN
ejpam-5353	237	6	,	,	PUNCT
ejpam-5353	237	7	17	17	NUM
ejpam-5353	237	8	(	(	PUNCT
ejpam-5353	237	9	4	4	NUM
ejpam-5353	237	10	)	)	PUNCT
ejpam-5353	237	11	(	(	PUNCT
ejpam-5353	237	12	2024	2024	NUM
ejpam-5353	237	13	)	)	PUNCT
ejpam-5353	237	14	,	,	PUNCT
ejpam-5353	237	15	3492	3492	NUM
ejpam-5353	237	16	-	-	SYM
ejpam-5353	237	17	3516	3516	NUM
ejpam-5353	237	18	3500	3500	NUM
ejpam-5353	237	19	theorem	theorem	NOUN
ejpam-5353	237	20	9	9	NUM
ejpam-5353	237	21	.	.	PUNCT
ejpam-5353	238	1	let	let	VERB
ejpam-5353	238	2	m	m	PRON
ejpam-5353	238	3	>	>	X
ejpam-5353	238	4	2	2	NUM
ejpam-5353	238	5	,	,	PUNCT
ejpam-5353	238	6	m	m	VERB
ejpam-5353	238	7	≇	≇	PROPN
ejpam-5353	238	8	0mod	0mod	PROPN
ejpam-5353	238	9	3	3	NUM
ejpam-5353	238	10	,	,	PUNCT
ejpam-5353	238	11	and	and	CCONJ
ejpam-5353	238	12	m+	m+	NUM
ejpam-5353	238	13	3	3	NUM
ejpam-5353	238	14	to	to	PART
ejpam-5353	238	15	be	be	AUX
ejpam-5353	238	16	an	an	DET
ejpam-5353	238	17	odd	odd	ADJ
ejpam-5353	238	18	integer	integer	NOUN
ejpam-5353	238	19	.	.	PUNCT
ejpam-5353	239	1	then	then	ADV
ejpam-5353	239	2	there	there	PRON
ejpam-5353	239	3	is	be	VERB
ejpam-5353	239	4	a	a	DET
ejpam-5353	239	5	symmetric	symmetric	ADJ
ejpam-5353	239	6	base	base	NOUN
ejpam-5353	239	7	of	of	ADP
ejpam-5353	239	8	an	an	DET
ejpam-5353	239	9	odc	odc	NOUN
ejpam-5353	239	10	of	of	ADP
ejpam-5353	239	11	km+3,m+3	km+3,m+3	PUNCT
ejpam-5353	239	12	by	by	ADP
ejpam-5353	239	13	g	g	PROPN
ejpam-5353	239	14	∼=	∼=	PROPN
ejpam-5353	239	15	τ01(1	τ01(1	NOUN
ejpam-5353	239	16	,	,	PUNCT
ejpam-5353	239	17	2	2	NUM
ejpam-5353	239	18	)	)	PUNCT
ejpam-5353	239	19	∪	∪	NOUN
ejpam-5353	239	20	(	(	PUNCT
ejpam-5353	239	21	n−	n−	NOUN
ejpam-5353	239	22	5)k2	5)k2	NOUN
ejpam-5353	239	23	.	.	PUNCT
ejpam-5353	240	1	proof	proof	NOUN
ejpam-5353	240	2	.	.	PUNCT
ejpam-5353	241	1	for	for	ADP
ejpam-5353	241	2	all	all	DET
ejpam-5353	241	3	odd	odd	ADJ
ejpam-5353	241	4	integer	integer	NOUN
ejpam-5353	241	5	n	n	CCONJ
ejpam-5353	241	6	>	>	X
ejpam-5353	241	7	5	5	NUM
ejpam-5353	241	8	,	,	PUNCT
ejpam-5353	241	9	n	n	NOUN
ejpam-5353	241	10	=	=	PUNCT
ejpam-5353	241	11	m+	m+	NUM
ejpam-5353	241	12	3	3	NUM
ejpam-5353	241	13	such	such	ADJ
ejpam-5353	241	14	that	that	SCONJ
ejpam-5353	241	15	m	m	VERB
ejpam-5353	241	16	>	>	X
ejpam-5353	241	17	2	2	NUM
ejpam-5353	241	18	,	,	PUNCT
ejpam-5353	241	19	m	m	VERB
ejpam-5353	241	20	≇	≇	PROPN
ejpam-5353	241	21	0mod	0mod	PROPN
ejpam-5353	241	22	3	3	NUM
ejpam-5353	241	23	,	,	PUNCT
ejpam-5353	241	24	the	the	DET
ejpam-5353	241	25	vector	vector	NOUN
ejpam-5353	241	26	v(g	v(g	PROPN
ejpam-5353	241	27	)	)	PUNCT
ejpam-5353	241	28	of	of	ADP
ejpam-5353	241	29	the	the	DET
ejpam-5353	241	30	symmetric	symmetric	ADJ
ejpam-5353	241	31	base	base	NOUN
ejpam-5353	241	32	g	g	PROPN
ejpam-5353	241	33	can	can	AUX
ejpam-5353	241	34	be	be	AUX
ejpam-5353	241	35	defined	define	VERB
ejpam-5353	241	36	as	as	ADP
ejpam-5353	241	37	:	:	PUNCT
ejpam-5353	241	38	vi(g	vi(g	NUM
ejpam-5353	241	39	)	)	PUNCT
ejpam-5353	242	1	=	=	SYM
ejpam-5353	243	1			PUNCT
ejpam-5353	243	2	0	0	PUNCT
ejpam-5353	244	1	if	if	SCONJ
ejpam-5353	244	2	i	i	PRON
ejpam-5353	244	3	=	=	SYM
ejpam-5353	244	4	0	0	NUM
ejpam-5353	244	5	n−	n−	NOUN
ejpam-5353	244	6	1	1	NUM
ejpam-5353	244	7	if	if	SCONJ
ejpam-5353	244	8	i	i	PRON
ejpam-5353	244	9	=	=	NOUN
ejpam-5353	244	10	1	1	NUM
ejpam-5353	244	11	3	3	NUM
ejpam-5353	244	12	if	if	SCONJ
ejpam-5353	244	13	i	i	PRON
ejpam-5353	244	14	=	=	VERB
ejpam-5353	244	15	n−	n−	NOUN
ejpam-5353	244	16	1	1	NUM
ejpam-5353	244	17	xj	xj	NOUN
ejpam-5353	244	18	−	−	PROPN
ejpam-5353	245	1	i	i	PRON
ejpam-5353	245	2	if	if	SCONJ
ejpam-5353	245	3	i	i	PRON
ejpam-5353	245	4	∈	∈	VERB
ejpam-5353	245	5	{	{	PUNCT
ejpam-5353	245	6	2	2	NUM
ejpam-5353	245	7	,	,	PUNCT
ejpam-5353	245	8	3	3	NUM
ejpam-5353	245	9	,	,	PUNCT
ejpam-5353	245	10	·	·	PUNCT
ejpam-5353	245	11	·	·	PUNCT
ejpam-5353	245	12	·	·	PUNCT
ejpam-5353	245	13	,	,	PUNCT
ejpam-5353	245	14	m+	m+	NOUN
ejpam-5353	245	15	1	1	NUM
ejpam-5353	245	16	}	}	PUNCT
ejpam-5353	245	17	,	,	PUNCT
ejpam-5353	245	18	j	j	PROPN
ejpam-5353	245	19	=	=	SYM
ejpam-5353	245	20	i−	i−	PROPN
ejpam-5353	245	21	2	2	NUM
ejpam-5353	245	22	,	,	PUNCT
ejpam-5353	245	23	where	where	SCONJ
ejpam-5353	245	24	xj	xj	PROPN
ejpam-5353	245	25	=	=	SYM
ejpam-5353	245	26	1−j	1−j	NUM
ejpam-5353	245	27	,	,	PUNCT
ejpam-5353	245	28	for	for	ADP
ejpam-5353	245	29	j	j	PROPN
ejpam-5353	245	30	∈	∈	PROPN
ejpam-5353	245	31	{	{	PUNCT
ejpam-5353	245	32	0	0	NUM
ejpam-5353	245	33	,	,	PUNCT
ejpam-5353	245	34	1	1	NUM
ejpam-5353	245	35	,	,	PUNCT
ejpam-5353	245	36	2	2	NUM
ejpam-5353	245	37	,	,	PUNCT
ejpam-5353	245	38	·	·	PUNCT
ejpam-5353	245	39	·	·	PUNCT
ejpam-5353	245	40	·	·	PUNCT
ejpam-5353	245	41	,	,	PUNCT
ejpam-5353	245	42	m−	m−	PROPN
ejpam-5353	245	43	1	1	NUM
ejpam-5353	245	44	}	}	PUNCT
ejpam-5353	245	45	.	.	PUNCT
ejpam-5353	246	1	from	from	ADP
ejpam-5353	246	2	the	the	DET
ejpam-5353	246	3	definition	definition	NOUN
ejpam-5353	246	4	of	of	ADP
ejpam-5353	246	5	v(g	v(g	PROPN
ejpam-5353	246	6	)	)	PUNCT
ejpam-5353	246	7	,	,	PUNCT
ejpam-5353	246	8	we	we	PRON
ejpam-5353	246	9	find	find	VERB
ejpam-5353	246	10	that	that	SCONJ
ejpam-5353	246	11	vi−v−i+i	vi−v−i+i	PROPN
ejpam-5353	246	12	=	=	PUNCT
ejpam-5353	246	13	0	0	NUM
ejpam-5353	246	14	,	,	PUNCT
ejpam-5353	246	15	for	for	ADP
ejpam-5353	246	16	i	i	PROPN
ejpam-5353	246	17	=	=	NOUN
ejpam-5353	246	18	0	0	NUM
ejpam-5353	246	19	,	,	PUNCT
ejpam-5353	246	20	for	for	ADP
ejpam-5353	246	21	i	i	PROPN
ejpam-5353	246	22	=	=	NOUN
ejpam-5353	246	23	1	1	NUM
ejpam-5353	246	24	,	,	PUNCT
ejpam-5353	246	25	vi−v−i+i	vi−v−i+i	NOUN
ejpam-5353	246	26	=	=	PUNCT
ejpam-5353	247	1	n−3	n−3	PROPN
ejpam-5353	247	2	,	,	PUNCT
ejpam-5353	247	3	for	for	ADP
ejpam-5353	247	4	i	i	PROPN
ejpam-5353	247	5	=	=	SYM
ejpam-5353	247	6	n−1	n−1	PROPN
ejpam-5353	247	7	,	,	PUNCT
ejpam-5353	247	8	vi−v−i+i	vi−v−i+i	NOUN
ejpam-5353	247	9	=	=	NOUN
ejpam-5353	247	10	3	3	NUM
ejpam-5353	247	11	,	,	PUNCT
ejpam-5353	247	12	and	and	CCONJ
ejpam-5353	247	13	for	for	ADP
ejpam-5353	247	14	i	i	PRON
ejpam-5353	247	15	=	=	SYM
ejpam-5353	247	16	j+2	j+2	PROPN
ejpam-5353	247	17	,	,	PUNCT
ejpam-5353	247	18	j	j	PROPN
ejpam-5353	247	19	∈	∈	PROPN
ejpam-5353	247	20	{	{	PUNCT
ejpam-5353	247	21	0	0	NUM
ejpam-5353	247	22	,	,	PUNCT
ejpam-5353	247	23	1	1	NUM
ejpam-5353	247	24	,	,	PUNCT
ejpam-5353	247	25	2	2	NUM
ejpam-5353	247	26	,	,	PUNCT
ejpam-5353	247	27	·	·	PUNCT
ejpam-5353	247	28	·	·	PUNCT
ejpam-5353	247	29	·	·	PUNCT
ejpam-5353	247	30	,	,	PUNCT
ejpam-5353	247	31	m−	m−	PROPN
ejpam-5353	247	32	1	1	NUM
ejpam-5353	247	33	}	}	PUNCT
ejpam-5353	247	34	,	,	PUNCT
ejpam-5353	247	35	vi−	vi−	PROPN
ejpam-5353	247	36	v−i+	v−i+	PROPN
ejpam-5353	247	37	i	i	PRON
ejpam-5353	247	38	=	=	SYM
ejpam-5353	247	39	xj	xj	PROPN
ejpam-5353	247	40	−xm−(j+1)−	−xm−(j+1)−	PROPN
ejpam-5353	247	41	i.	i.	PROPN
ejpam-5353	247	42	by	by	ADP
ejpam-5353	247	43	theorem	theorem	NOUN
ejpam-5353	247	44	3	3	NUM
ejpam-5353	247	45	,	,	PUNCT
ejpam-5353	247	46	the	the	DET
ejpam-5353	247	47	base	base	NOUN
ejpam-5353	247	48	v(g	v(g	NOUN
ejpam-5353	247	49	)	)	PUNCT
ejpam-5353	247	50	is	be	AUX
ejpam-5353	247	51	symmetric	symmetric	ADJ
ejpam-5353	247	52	.	.	PUNCT
ejpam-5353	248	1	moreover	moreover	ADV
ejpam-5353	248	2	,	,	PUNCT
ejpam-5353	248	3	the	the	DET
ejpam-5353	248	4	edges	edge	NOUN
ejpam-5353	248	5	set	set	VERB
ejpam-5353	248	6	e(g	e(g	PROPN
ejpam-5353	248	7	)	)	PUNCT
ejpam-5353	248	8	of	of	ADP
ejpam-5353	248	9	the	the	DET
ejpam-5353	248	10	base	base	NOUN
ejpam-5353	248	11	g	g	PROPN
ejpam-5353	248	12	can	can	AUX
ejpam-5353	248	13	be	be	AUX
ejpam-5353	248	14	represented	represent	VERB
ejpam-5353	248	15	by	by	ADP
ejpam-5353	248	16	:	:	PUNCT
ejpam-5353	248	17	e(g	e(g	PROPN
ejpam-5353	248	18	)	)	PUNCT
ejpam-5353	249	1	=	=	PRON
ejpam-5353	249	2	{	{	PUNCT
ejpam-5353	249	3	(	(	PUNCT
ejpam-5353	249	4	00	00	NUM
ejpam-5353	249	5	,	,	PUNCT
ejpam-5353	249	6	01	01	NUM
ejpam-5353	249	7	)	)	PUNCT
ejpam-5353	249	8	,	,	PUNCT
ejpam-5353	249	9	(	(	PUNCT
ejpam-5353	249	10	(	(	PUNCT
ejpam-5353	249	11	n−	n−	NOUN
ejpam-5353	249	12	1)0	1)0	NUM
ejpam-5353	249	13	,	,	PUNCT
ejpam-5353	249	14	01	01	NUM
ejpam-5353	249	15	)	)	PUNCT
ejpam-5353	249	16	,	,	PUNCT
ejpam-5353	249	17	(	(	PUNCT
ejpam-5353	249	18	30	30	NUM
ejpam-5353	249	19	,	,	PUNCT
ejpam-5353	249	20	21	21	NUM
ejpam-5353	249	21	)	)	PUNCT
ejpam-5353	249	22	}	}	PUNCT
ejpam-5353	249	23	∪	∪	VERB
ejpam-5353	249	24	{	{	PUNCT
ejpam-5353	249	25	(	(	PUNCT
ejpam-5353	249	26	(	(	PUNCT
ejpam-5353	249	27	xj	xj	PROPN
ejpam-5353	249	28	−	−	PROPN
ejpam-5353	249	29	i)0	i)0	PROPN
ejpam-5353	249	30	,	,	PUNCT
ejpam-5353	249	31	(	(	PUNCT
ejpam-5353	249	32	xj)1	xj)1	PROPN
ejpam-5353	249	33	)	)	PUNCT
ejpam-5353	249	34	}	}	PUNCT
ejpam-5353	249	35	for	for	ADP
ejpam-5353	249	36	all	all	PRON
ejpam-5353	249	37	i	i	PRON
ejpam-5353	249	38	=	=	PUNCT
ejpam-5353	249	39	j	j	PROPN
ejpam-5353	249	40	+	+	CCONJ
ejpam-5353	249	41	2	2	NUM
ejpam-5353	249	42	,	,	PUNCT
ejpam-5353	249	43	j	j	PROPN
ejpam-5353	249	44	∈	∈	PROPN
ejpam-5353	249	45	{	{	PUNCT
ejpam-5353	249	46	0	0	NUM
ejpam-5353	249	47	,	,	PUNCT
ejpam-5353	249	48	1	1	NUM
ejpam-5353	249	49	,	,	PUNCT
ejpam-5353	249	50	2	2	NUM
ejpam-5353	249	51	,	,	PUNCT
ejpam-5353	249	52	·	·	PUNCT
ejpam-5353	249	53	·	·	PUNCT
ejpam-5353	249	54	·	·	PUNCT
ejpam-5353	249	55	,	,	PUNCT
ejpam-5353	249	56	m−	m−	PROPN
ejpam-5353	249	57	1	1	NUM
ejpam-5353	249	58	}	}	PUNCT
ejpam-5353	249	59	.	.	PUNCT
ejpam-5353	250	1	then	then	ADV
ejpam-5353	250	2	the	the	DET
ejpam-5353	250	3	graph	graph	NOUN
ejpam-5353	250	4	g	g	ADP
ejpam-5353	250	5	∼=	∼=	PROPN
ejpam-5353	250	6	τ01(1	τ01(1	NOUN
ejpam-5353	250	7	,	,	PUNCT
ejpam-5353	250	8	2	2	NUM
ejpam-5353	250	9	)	)	PUNCT
ejpam-5353	250	10	∪	∪	NOUN
ejpam-5353	250	11	(	(	PUNCT
ejpam-5353	250	12	n−	n−	NOUN
ejpam-5353	250	13	5)k2	5)k2	NOUN
ejpam-5353	250	14	.	.	PUNCT
ejpam-5353	251	1	theorem	theorem	VERB
ejpam-5353	251	2	10	10	NUM
ejpam-5353	251	3	.	.	PUNCT
ejpam-5353	252	1	let	let	VERB
ejpam-5353	252	2	n	n	PRON
ejpam-5353	252	3	≥	≥	X
ejpam-5353	252	4	3	3	NUM
ejpam-5353	252	5	to	to	PART
ejpam-5353	252	6	be	be	AUX
ejpam-5353	252	7	a	a	DET
ejpam-5353	252	8	positive	positive	ADJ
ejpam-5353	252	9	integer	integer	NOUN
ejpam-5353	252	10	,	,	PUNCT
ejpam-5353	252	11	then	then	ADV
ejpam-5353	252	12	there	there	PRON
ejpam-5353	252	13	is	be	VERB
ejpam-5353	252	14	a	a	DET
ejpam-5353	252	15	symmetric	symmetric	ADJ
ejpam-5353	252	16	base	base	NOUN
ejpam-5353	252	17	of	of	ADP
ejpam-5353	252	18	an	an	DET
ejpam-5353	252	19	odc	odc	NOUN
ejpam-5353	252	20	of	of	ADP
ejpam-5353	252	21	kn	kn	PROPN
ejpam-5353	252	22	,	,	PUNCT
ejpam-5353	252	23	n	n	CCONJ
ejpam-5353	252	24	by	by	ADP
ejpam-5353	252	25	c4(0	c4(0	PROPN
ejpam-5353	252	26	,	,	PUNCT
ejpam-5353	252	27	0	0	NUM
ejpam-5353	252	28	,	,	PUNCT
ejpam-5353	252	29	0	0	NUM
ejpam-5353	252	30	,	,	PUNCT
ejpam-5353	252	31	0	0	NUM
ejpam-5353	252	32	)	)	PUNCT
ejpam-5353	252	33	∪	∪	ADP
ejpam-5353	252	34	τ	τ	X
ejpam-5353	252	35	(	(	PUNCT
ejpam-5353	252	36	n−1)1(n−	n−1)1(n−	PROPN
ejpam-5353	252	37	3	3	NUM
ejpam-5353	252	38	)	)	PUNCT
ejpam-5353	252	39	.	.	PUNCT
ejpam-5353	253	1	proof	proof	NOUN
ejpam-5353	253	2	.	.	PUNCT
ejpam-5353	254	1	for	for	ADP
ejpam-5353	254	2	a	a	DET
ejpam-5353	254	3	positive	positive	ADJ
ejpam-5353	254	4	integer	integer	NOUN
ejpam-5353	254	5	n	n	PRON
ejpam-5353	254	6	≥	≥	NOUN
ejpam-5353	254	7	3	3	NUM
ejpam-5353	254	8	,	,	PUNCT
ejpam-5353	254	9	the	the	DET
ejpam-5353	254	10	vector	vector	NOUN
ejpam-5353	254	11	v(g	v(g	PROPN
ejpam-5353	254	12	)	)	PUNCT
ejpam-5353	254	13	of	of	ADP
ejpam-5353	254	14	the	the	DET
ejpam-5353	254	15	base	base	NOUN
ejpam-5353	254	16	g	g	PROPN
ejpam-5353	254	17	can	can	AUX
ejpam-5353	254	18	be	be	AUX
ejpam-5353	254	19	written	write	VERB
ejpam-5353	254	20	as	as	ADP
ejpam-5353	254	21	:	:	PUNCT
ejpam-5353	254	22	vi(g	vi(g	X
ejpam-5353	254	23	)	)	PUNCT
ejpam-5353	255	1	=	=	PUNCT
ejpam-5353	255	2			PUNCT
ejpam-5353	255	3	0	0	PUNCT
ejpam-5353	255	4	if	if	SCONJ
ejpam-5353	255	5	i	i	PRON
ejpam-5353	255	6	=	=	SYM
ejpam-5353	255	7	0	0	NUM
ejpam-5353	256	1	n−	n−	NOUN
ejpam-5353	256	2	1	1	NUM
ejpam-5353	256	3	if	if	SCONJ
ejpam-5353	256	4	i	i	PRON
ejpam-5353	256	5	=	=	NOUN
ejpam-5353	256	6	1	1	NUM
ejpam-5353	256	7	,	,	PUNCT
ejpam-5353	256	8	n−	n−	NOUN
ejpam-5353	256	9	1	1	NUM
ejpam-5353	256	10	−i−	−i−	ADP
ejpam-5353	256	11	1	1	NUM
ejpam-5353	256	12	otherwise	otherwise	ADV
ejpam-5353	256	13	,	,	PUNCT
ejpam-5353	256	14	therefore	therefore	ADV
ejpam-5353	256	15	,	,	PUNCT
ejpam-5353	256	16	v−i(g	v−i(g	PROPN
ejpam-5353	256	17	)	)	PUNCT
ejpam-5353	256	18	=	=	PUNCT
ejpam-5353	257	1			PUNCT
ejpam-5353	257	2	0	0	PUNCT
ejpam-5353	257	3	if	if	SCONJ
ejpam-5353	257	4	i	i	PRON
ejpam-5353	257	5	=	=	SYM
ejpam-5353	257	6	0	0	NUM
ejpam-5353	258	1	n−	n−	NOUN
ejpam-5353	258	2	1	1	NUM
ejpam-5353	258	3	if	if	SCONJ
ejpam-5353	258	4	i	i	PRON
ejpam-5353	258	5	=	=	NOUN
ejpam-5353	258	6	1	1	NUM
ejpam-5353	258	7	,	,	PUNCT
ejpam-5353	258	8	n−	n−	NOUN
ejpam-5353	258	9	1	1	NUM
ejpam-5353	258	10	i−	i−	PROPN
ejpam-5353	258	11	1	1	NUM
ejpam-5353	258	12	otherwise	otherwise	ADV
ejpam-5353	258	13	,	,	PUNCT
ejpam-5353	258	14	for	for	ADP
ejpam-5353	258	15	i	i	PRON
ejpam-5353	258	16	∈	∈	PROPN
ejpam-5353	258	17	{	{	PUNCT
ejpam-5353	258	18	0	0	NUM
ejpam-5353	258	19	,	,	PUNCT
ejpam-5353	258	20	1	1	NUM
ejpam-5353	258	21	,	,	PUNCT
ejpam-5353	258	22	n−	n−	NOUN
ejpam-5353	258	23	1	1	NUM
ejpam-5353	258	24	}	}	PUNCT
ejpam-5353	258	25	,	,	PUNCT
ejpam-5353	258	26	vi−	vi−	NUM
ejpam-5353	258	27	v−i	v−i	NOUN
ejpam-5353	259	1	+	+	CCONJ
ejpam-5353	259	2	i	i	NOUN
ejpam-5353	259	3	=	=	SYM
ejpam-5353	259	4	i.	i.	NOUN
ejpam-5353	259	5	for	for	ADP
ejpam-5353	259	6	any	any	DET
ejpam-5353	259	7	i	i	PROPN
ejpam-5353	259	8	∈	∈	PROPN
ejpam-5353	259	9	zn\	zn\	PROPN
ejpam-5353	259	10	{	{	PUNCT
ejpam-5353	259	11	0	0	NUM
ejpam-5353	259	12	,	,	PUNCT
ejpam-5353	259	13	1	1	NUM
ejpam-5353	259	14	,	,	PUNCT
ejpam-5353	259	15	n−	n−	NOUN
ejpam-5353	259	16	1	1	NUM
ejpam-5353	259	17	}	}	PUNCT
ejpam-5353	259	18	,	,	PUNCT
ejpam-5353	259	19	vi−	vi−	NUM
ejpam-5353	259	20	v−i	v−i	NOUN
ejpam-5353	260	1	+	+	CCONJ
ejpam-5353	260	2	i	i	NOUN
ejpam-5353	260	3	=	=	SYM
ejpam-5353	260	4	−i	−i	ADJ
ejpam-5353	260	5	.	.	PUNCT
ejpam-5353	261	1	consequently	consequently	ADV
ejpam-5353	261	2	,	,	PUNCT
ejpam-5353	261	3	{	{	PUNCT
ejpam-5353	261	4	vi	vi	NOUN
ejpam-5353	261	5	−	−	NOUN
ejpam-5353	261	6	v−i	v−i	NOUN
ejpam-5353	262	1	+	+	CCONJ
ejpam-5353	262	2	i	i	PRON
ejpam-5353	262	3	;	;	PUNCT
ejpam-5353	262	4	i	i	PROPN
ejpam-5353	262	5	∈	∈	PROPN
ejpam-5353	262	6	zn	zn	PROPN
ejpam-5353	262	7	}	}	PUNCT
ejpam-5353	262	8	=	=	ADJ
ejpam-5353	262	9	zn	zn	X
ejpam-5353	262	10	.	.	PUNCT
ejpam-5353	263	1	by	by	ADP
ejpam-5353	263	2	theorem	theorem	NOUN
ejpam-5353	263	3	3	3	NUM
ejpam-5353	263	4	,	,	PUNCT
ejpam-5353	263	5	the	the	DET
ejpam-5353	263	6	base	base	NOUN
ejpam-5353	263	7	v(g	v(g	NOUN
ejpam-5353	263	8	)	)	PUNCT
ejpam-5353	263	9	is	be	AUX
ejpam-5353	263	10	symmetric	symmetric	ADJ
ejpam-5353	263	11	.	.	PUNCT
ejpam-5353	264	1	moreover	moreover	ADV
ejpam-5353	264	2	the	the	DET
ejpam-5353	264	3	edges	edge	NOUN
ejpam-5353	264	4	set	set	VERB
ejpam-5353	264	5	e(g	e(g	PROPN
ejpam-5353	264	6	)	)	PUNCT
ejpam-5353	264	7	of	of	ADP
ejpam-5353	264	8	the	the	DET
ejpam-5353	264	9	base	base	NOUN
ejpam-5353	264	10	g	g	PROPN
ejpam-5353	264	11	can	can	AUX
ejpam-5353	264	12	be	be	AUX
ejpam-5353	264	13	represented	represent	VERB
ejpam-5353	264	14	by	by	ADP
ejpam-5353	264	15	:	:	PUNCT
ejpam-5353	264	16	e(g	e(g	PROPN
ejpam-5353	264	17	)	)	PUNCT
ejpam-5353	265	1	=	=	PRON
ejpam-5353	265	2	{	{	PUNCT
ejpam-5353	265	3	(	(	PUNCT
ejpam-5353	265	4	00	00	NUM
ejpam-5353	265	5	,	,	PUNCT
ejpam-5353	265	6	01	01	NUM
ejpam-5353	265	7	)	)	PUNCT
ejpam-5353	265	8	,	,	PUNCT
ejpam-5353	265	9	(	(	PUNCT
ejpam-5353	265	10	01	01	NUM
ejpam-5353	265	11	,	,	PUNCT
ejpam-5353	265	12	(	(	PUNCT
ejpam-5353	265	13	n−	n−	NOUN
ejpam-5353	265	14	1)0	1)0	NUM
ejpam-5353	265	15	)	)	PUNCT
ejpam-5353	265	16	,	,	PUNCT
ejpam-5353	265	17	(	(	PUNCT
ejpam-5353	265	18	(	(	PUNCT
ejpam-5353	265	19	n−	n−	NOUN
ejpam-5353	265	20	1)0	1)0	NUM
ejpam-5353	265	21	,	,	PUNCT
ejpam-5353	265	22	(	(	PUNCT
ejpam-5353	265	23	n−	n−	NOUN
ejpam-5353	265	24	2)1	2)1	NUM
ejpam-5353	265	25	)	)	PUNCT
ejpam-5353	265	26	}	}	PUNCT
ejpam-5353	265	27	∪{(β0	∪{(β0	PROPN
ejpam-5353	265	28	,	,	PUNCT
ejpam-5353	265	29	(	(	PUNCT
ejpam-5353	265	30	n−	n−	NOUN
ejpam-5353	265	31	1)1	1)1	NUM
ejpam-5353	265	32	)	)	PUNCT
ejpam-5353	265	33	:	:	PUNCT
ejpam-5353	265	34	1	1	NUM
ejpam-5353	265	35	≤	≤	NUM
ejpam-5353	265	36	β	β	X
ejpam-5353	265	37	≤	≤	NUM
ejpam-5353	265	38	n−	n−	NOUN
ejpam-5353	265	39	3	3	NUM
ejpam-5353	265	40	}	}	PUNCT
ejpam-5353	265	41	.	.	PUNCT
ejpam-5353	266	1	then	then	ADV
ejpam-5353	266	2	the	the	DET
ejpam-5353	266	3	graph	graph	NOUN
ejpam-5353	266	4	g	g	ADP
ejpam-5353	266	5	∼=	∼=	PROPN
ejpam-5353	266	6	c4(0	c4(0	NOUN
ejpam-5353	266	7	,	,	PUNCT
ejpam-5353	266	8	0	0	NUM
ejpam-5353	266	9	,	,	PUNCT
ejpam-5353	266	10	0	0	NUM
ejpam-5353	266	11	,	,	PUNCT
ejpam-5353	266	12	0	0	NUM
ejpam-5353	266	13	)	)	PUNCT
ejpam-5353	266	14	∪	∪	ADP
ejpam-5353	266	15	τ	τ	X
ejpam-5353	266	16	(	(	PUNCT
ejpam-5353	266	17	n−1)1(n−	n−1)1(n−	PROPN
ejpam-5353	266	18	3	3	NUM
ejpam-5353	266	19	)	)	PUNCT
ejpam-5353	266	20	.	.	PUNCT
ejpam-5353	267	1	h.	h.	PROPN
ejpam-5353	267	2	shabana	shabana	PROPN
ejpam-5353	267	3	,	,	PUNCT
ejpam-5353	267	4	r.	r.	PROPN
ejpam-5353	267	5	el	el	PROPN
ejpam-5353	267	6	-	-	PROPN
ejpam-5353	267	7	shanawany	shanawany	NOUN
ejpam-5353	267	8	,	,	PUNCT
ejpam-5353	267	9	s.	s.	PROPN
ejpam-5353	267	10	halawa	halawa	PROPN
ejpam-5353	267	11	/	/	PUNCT
ejpam-5353	267	12	eur	eur	PROPN
ejpam-5353	267	13	.	.	PUNCT
ejpam-5353	268	1	j.	j.	PROPN
ejpam-5353	268	2	pure	pure	PROPN
ejpam-5353	268	3	appl	appl	PROPN
ejpam-5353	268	4	.	.	PROPN
ejpam-5353	268	5	math	math	PROPN
ejpam-5353	268	6	,	,	PUNCT
ejpam-5353	268	7	17	17	NUM
ejpam-5353	268	8	(	(	PUNCT
ejpam-5353	268	9	4	4	NUM
ejpam-5353	268	10	)	)	PUNCT
ejpam-5353	268	11	(	(	PUNCT
ejpam-5353	268	12	2024	2024	NUM
ejpam-5353	268	13	)	)	PUNCT
ejpam-5353	268	14	,	,	PUNCT
ejpam-5353	268	15	3492	3492	NUM
ejpam-5353	268	16	-	-	SYM
ejpam-5353	268	17	3516	3516	NUM
ejpam-5353	268	18	3501	3501	NUM
ejpam-5353	268	19	3.2	3.2	NUM
ejpam-5353	268	20	.	.	PUNCT
ejpam-5353	269	1	odcs	odcs	PROPN
ejpam-5353	269	2	of	of	ADP
ejpam-5353	269	3	kn	kn	PROPN
ejpam-5353	269	4	,	,	PUNCT
ejpam-5353	269	5	n	n	CCONJ
ejpam-5353	269	6	by	by	ADP
ejpam-5353	269	7	a	a	DET
ejpam-5353	269	8	combination	combination	NOUN
ejpam-5353	269	9	of	of	ADP
ejpam-5353	269	10	caterpillar	caterpillar	ADJ
ejpam-5353	269	11	trees	tree	NOUN
ejpam-5353	269	12	theorem	theorem	VERB
ejpam-5353	269	13	11	11	NUM
ejpam-5353	269	14	.	.	PUNCT
ejpam-5353	270	1	let	let	VERB
ejpam-5353	270	2	α	α	PRON
ejpam-5353	270	3	,	,	PUNCT
ejpam-5353	270	4	β	β	X
ejpam-5353	270	5	and	and	CCONJ
ejpam-5353	270	6	γ	γ	PROPN
ejpam-5353	270	7	be	be	AUX
ejpam-5353	270	8	elements	element	NOUN
ejpam-5353	270	9	of	of	ADP
ejpam-5353	270	10	zn	zn	PROPN
ejpam-5353	270	11	.	.	PUNCT
ejpam-5353	271	1	for	for	ADP
ejpam-5353	271	2	all	all	DET
ejpam-5353	271	3	positive	positive	ADJ
ejpam-5353	271	4	integers	integer	NOUN
ejpam-5353	271	5	n	n	PRON
ejpam-5353	271	6	≥	≥	NOUN
ejpam-5353	271	7	7	7	NUM
ejpam-5353	271	8	,	,	PUNCT
ejpam-5353	271	9	and	and	CCONJ
ejpam-5353	271	10	n	n	PRON
ejpam-5353	271	11	≇	≇	PROPN
ejpam-5353	271	12	0mod	0mod	PROPN
ejpam-5353	271	13	3	3	X
ejpam-5353	271	14	,	,	PUNCT
ejpam-5353	271	15	there	there	PRON
ejpam-5353	271	16	is	be	VERB
ejpam-5353	271	17	a	a	DET
ejpam-5353	271	18	symmetric	symmetric	ADJ
ejpam-5353	271	19	base	base	NOUN
ejpam-5353	271	20	of	of	ADP
ejpam-5353	271	21	an	an	DET
ejpam-5353	271	22	odc	odc	NOUN
ejpam-5353	271	23	of	of	ADP
ejpam-5353	271	24	kn	kn	PROPN
ejpam-5353	271	25	,	,	PUNCT
ejpam-5353	271	26	n	n	CCONJ
ejpam-5353	271	27	by	by	ADP
ejpam-5353	271	28	αc4(0	αc4(0	X
ejpam-5353	271	29	,	,	PUNCT
ejpam-5353	271	30	0	0	NUM
ejpam-5353	271	31	,	,	PUNCT
ejpam-5353	271	32	0	0	NUM
ejpam-5353	271	33	,	,	PUNCT
ejpam-5353	271	34	0)∪βc3(0	0)∪βc3(0	PROPN
ejpam-5353	271	35	,	,	PUNCT
ejpam-5353	271	36	0	0	NUM
ejpam-5353	271	37	,	,	PUNCT
ejpam-5353	271	38	0)∪	0)∪	NOUN
ejpam-5353	271	39	γc2(0	γc2(0	NOUN
ejpam-5353	271	40	,	,	PUNCT
ejpam-5353	271	41	0	0	NUM
ejpam-5353	271	42	)	)	PUNCT
ejpam-5353	271	43	.	.	PUNCT
ejpam-5353	272	1	proof	proof	NOUN
ejpam-5353	272	2	.	.	PUNCT
ejpam-5353	273	1	case	case	NOUN
ejpam-5353	273	2	1	1	NUM
ejpam-5353	273	3	.	.	X
ejpam-5353	274	1	for	for	ADP
ejpam-5353	274	2	an	an	DET
ejpam-5353	274	3	even	even	ADV
ejpam-5353	274	4	integer	integer	NOUN
ejpam-5353	274	5	n	n	CCONJ
ejpam-5353	274	6	,	,	PUNCT
ejpam-5353	274	7	let	let	VERB
ejpam-5353	274	8	α	α	NOUN
ejpam-5353	274	9	=	=	SYM
ejpam-5353	274	10	2	2	NUM
ejpam-5353	274	11	,	,	PUNCT
ejpam-5353	274	12	β	β	X
ejpam-5353	274	13	=	=	SYM
ejpam-5353	274	14	n−8	n−8	PROPN
ejpam-5353	274	15	2	2	NUM
ejpam-5353	274	16	,	,	PUNCT
ejpam-5353	274	17	and	and	CCONJ
ejpam-5353	274	18	γ	γ	X
ejpam-5353	274	19	=	=	SYM
ejpam-5353	274	20	2	2	NUM
ejpam-5353	274	21	.	.	PUNCT
ejpam-5353	275	1	the	the	DET
ejpam-5353	275	2	vector	vector	NOUN
ejpam-5353	275	3	v(g	v(g	PROPN
ejpam-5353	275	4	)	)	PUNCT
ejpam-5353	275	5	of	of	ADP
ejpam-5353	275	6	a	a	DET
ejpam-5353	275	7	base	base	NOUN
ejpam-5353	275	8	g	g	NOUN
ejpam-5353	275	9	can	can	AUX
ejpam-5353	275	10	be	be	AUX
ejpam-5353	275	11	defined	define	VERB
ejpam-5353	275	12	as	as	ADP
ejpam-5353	275	13	:	:	PUNCT
ejpam-5353	275	14	vi(g	vi(g	NUM
ejpam-5353	275	15	)	)	PUNCT
ejpam-5353	276	1	=	=	PRON
ejpam-5353	276	2	{	{	PUNCT
ejpam-5353	276	3	−2i−	−2i−	NOUN
ejpam-5353	276	4	1	1	NUM
ejpam-5353	276	5	if	if	SCONJ
ejpam-5353	276	6	i	i	PRON
ejpam-5353	276	7	=	=	NOUN
ejpam-5353	276	8	1	1	NUM
ejpam-5353	276	9	,	,	PUNCT
ejpam-5353	276	10	n−	n−	NOUN
ejpam-5353	276	11	1	1	NUM
ejpam-5353	276	12	−2i	−2i	NOUN
ejpam-5353	276	13	otherwise	otherwise	ADV
ejpam-5353	276	14	,	,	PUNCT
ejpam-5353	276	15	hence	hence	ADV
ejpam-5353	276	16	,	,	PUNCT
ejpam-5353	276	17	v−i(g	v−i(g	PROPN
ejpam-5353	276	18	)	)	PUNCT
ejpam-5353	277	1	=	=	PRON
ejpam-5353	277	2	{	{	PUNCT
ejpam-5353	277	3	2i−	2i−	NUM
ejpam-5353	277	4	1	1	NUM
ejpam-5353	277	5	if	if	SCONJ
ejpam-5353	277	6	i	i	PRON
ejpam-5353	277	7	=	=	NOUN
ejpam-5353	277	8	1	1	NUM
ejpam-5353	277	9	,	,	PUNCT
ejpam-5353	277	10	n−	n−	NOUN
ejpam-5353	277	11	1	1	NUM
ejpam-5353	277	12	2i	2i	NOUN
ejpam-5353	277	13	otherwise	otherwise	ADV
ejpam-5353	277	14	for	for	ADP
ejpam-5353	277	15	any	any	DET
ejpam-5353	277	16	i	i	PROPN
ejpam-5353	277	17	∈	∈	PROPN
ejpam-5353	277	18	zn	zn	PROPN
ejpam-5353	277	19	,	,	PUNCT
ejpam-5353	277	20	vi−	vi−	PROPN
ejpam-5353	277	21	v−i	v−i	PROPN
ejpam-5353	278	1	+	+	NUM
ejpam-5353	278	2	i	i	PROPN
ejpam-5353	278	3	=	=	SYM
ejpam-5353	278	4	−3i	−3i	PROPN
ejpam-5353	278	5	.	.	PUNCT
ejpam-5353	279	1	by	by	ADP
ejpam-5353	279	2	theorem	theorem	NOUN
ejpam-5353	279	3	3	3	NUM
ejpam-5353	279	4	,	,	PUNCT
ejpam-5353	279	5	the	the	DET
ejpam-5353	279	6	base	base	NOUN
ejpam-5353	279	7	v(g	v(g	NOUN
ejpam-5353	279	8	)	)	PUNCT
ejpam-5353	279	9	is	be	AUX
ejpam-5353	279	10	symmetric	symmetric	ADJ
ejpam-5353	279	11	.	.	PUNCT
ejpam-5353	280	1	moreover	moreover	ADV
ejpam-5353	280	2	,	,	PUNCT
ejpam-5353	280	3	the	the	DET
ejpam-5353	280	4	edges	edge	NOUN
ejpam-5353	280	5	set	set	VERB
ejpam-5353	280	6	e(g	e(g	PROPN
ejpam-5353	280	7	)	)	PUNCT
ejpam-5353	280	8	of	of	ADP
ejpam-5353	280	9	the	the	DET
ejpam-5353	280	10	base	base	NOUN
ejpam-5353	280	11	g	g	PROPN
ejpam-5353	280	12	can	can	AUX
ejpam-5353	280	13	be	be	AUX
ejpam-5353	280	14	represented	represent	VERB
ejpam-5353	280	15	by	by	ADP
ejpam-5353	280	16	:	:	PUNCT
ejpam-5353	280	17	e(g	e(g	PROPN
ejpam-5353	280	18	)	)	PUNCT
ejpam-5353	281	1	=	=	PUNCT
ejpam-5353	281	2	{	{	PUNCT
ejpam-5353	281	3	10	10	NUM
ejpam-5353	281	4	,	,	PUNCT
ejpam-5353	281	5	01	01	NUM
ejpam-5353	281	6	,	,	PUNCT
ejpam-5353	281	7	00	00	NUM
ejpam-5353	281	8	,	,	PUNCT
ejpam-5353	281	9	(	(	PUNCT
ejpam-5353	281	10	n2	n2	ADJ
ejpam-5353	281	11	)	)	PUNCT
ejpam-5353	281	12	1	1	NUM
ejpam-5353	281	13	,	,	PUNCT
ejpam-5353	281	14	10	10	NUM
ejpam-5353	281	15	}	}	PUNCT
ejpam-5353	281	16	∪	∪	X
ejpam-5353	281	17	{	{	PUNCT
ejpam-5353	281	18	(	(	PUNCT
ejpam-5353	281	19	n−	n−	PROPN
ejpam-5353	281	20	3)0	3)0	NUM
ejpam-5353	281	21	,	,	PUNCT
ejpam-5353	281	22	(	(	PUNCT
ejpam-5353	281	23	n−	n−	NOUN
ejpam-5353	281	24	2)1	2)1	NUM
ejpam-5353	281	25	,	,	PUNCT
ejpam-5353	281	26	(	(	PUNCT
ejpam-5353	281	27	n	n	ADV
ejpam-5353	281	28	2	2	NUM
ejpam-5353	281	29	)	)	PUNCT
ejpam-5353	281	30	0	0	NUM
ejpam-5353	281	31	,	,	PUNCT
ejpam-5353	281	32	(	(	PUNCT
ejpam-5353	281	33	⌊	⌊	VERB
ejpam-5353	281	34	n−3	n−3	PROPN
ejpam-5353	281	35	2	2	NUM
ejpam-5353	281	36	⌋)1	⌋)1	PROPN
ejpam-5353	281	37	}	}	PUNCT
ejpam-5353	281	38	∪{(2	∪{(2	PROPN
ejpam-5353	281	39	,	,	PUNCT
ejpam-5353	281	40	n+2	n+2	PRON
ejpam-5353	281	41	2	2	NUM
ejpam-5353	281	42	)	)	PUNCT
ejpam-5353	281	43	,	,	PUNCT
ejpam-5353	281	44	(	(	PUNCT
ejpam-5353	281	45	n−	n−	NOUN
ejpam-5353	281	46	2	2	NUM
ejpam-5353	281	47	,	,	PUNCT
ejpam-5353	281	48	n−2	n−2	PROPN
ejpam-5353	281	49	2	2	NUM
ejpam-5353	281	50	)	)	PUNCT
ejpam-5353	281	51	}	}	PUNCT
ejpam-5353	281	52	∪	∪	X
ejpam-5353	281	53	{	{	PUNCT
ejpam-5353	281	54	(	(	PUNCT
ejpam-5353	281	55	n+4	n+4	NUM
ejpam-5353	281	56	2	2	NUM
ejpam-5353	281	57	)	)	PUNCT
ejpam-5353	281	58	1	1	NUM
ejpam-5353	281	59	,	,	PUNCT
ejpam-5353	281	60	40	40	NUM
ejpam-5353	281	61	,	,	PUNCT
ejpam-5353	281	62	21	21	NUM
ejpam-5353	281	63	}	}	PUNCT
ejpam-5353	281	64	∪	∪	X
ejpam-5353	281	65	{	{	PUNCT
ejpam-5353	281	66	(	(	PUNCT
ejpam-5353	281	67	n+6	n+6	NOUN
ejpam-5353	281	68	2	2	NUM
ejpam-5353	281	69	)	)	PUNCT
ejpam-5353	281	70	1	1	NUM
ejpam-5353	281	71	,	,	PUNCT
ejpam-5353	281	72	60	60	NUM
ejpam-5353	281	73	,	,	PUNCT
ejpam-5353	281	74	31	31	NUM
ejpam-5353	281	75	}	}	PUNCT
ejpam-5353	281	76	∪{(n+8	∪{(n+8	PROPN
ejpam-5353	281	77	2	2	NUM
ejpam-5353	281	78	)	)	PUNCT
ejpam-5353	281	79	1	1	NUM
ejpam-5353	281	80	,	,	PUNCT
ejpam-5353	281	81	80	80	NUM
ejpam-5353	281	82	,	,	PUNCT
ejpam-5353	281	83	41}∪	41}∪	NOUN
ejpam-5353	281	84	,	,	PUNCT
ejpam-5353	281	85	...	...	PUNCT
ejpam-5353	281	86	,	,	PUNCT
ejpam-5353	281	87	∪{(n−	∪{(n−	PROPN
ejpam-5353	281	88	3)1	3)1	NUM
ejpam-5353	281	89	,	,	PUNCT
ejpam-5353	281	90	(	(	PUNCT
ejpam-5353	281	91	n−	n−	NOUN
ejpam-5353	281	92	6)0	6)0	NUM
ejpam-5353	281	93	,	,	PUNCT
ejpam-5353	281	94	(	(	PUNCT
ejpam-5353	281	95	n−6	n−6	PROPN
ejpam-5353	281	96	2	2	NUM
ejpam-5353	281	97	)	)	PUNCT
ejpam-5353	281	98	1	1	NUM
ejpam-5353	281	99	}	}	PUNCT
ejpam-5353	281	100	then	then	ADV
ejpam-5353	281	101	the	the	DET
ejpam-5353	281	102	graph	graph	NOUN
ejpam-5353	281	103	g	g	NOUN
ejpam-5353	281	104	≊	≊	NUM
ejpam-5353	281	105	2c4(0	2c4(0	NUM
ejpam-5353	281	106	,	,	PUNCT
ejpam-5353	281	107	0	0	NUM
ejpam-5353	281	108	,	,	PUNCT
ejpam-5353	281	109	0	0	NUM
ejpam-5353	281	110	,	,	PUNCT
ejpam-5353	281	111	0	0	NUM
ejpam-5353	281	112	)	)	PUNCT
ejpam-5353	281	113	∪	∪	NOUN
ejpam-5353	281	114	(	(	PUNCT
ejpam-5353	281	115	p−	p−	NOUN
ejpam-5353	281	116	8)c3(0	8)c3(0	NOUN
ejpam-5353	281	117	,	,	PUNCT
ejpam-5353	281	118	0	0	NUM
ejpam-5353	281	119	,	,	PUNCT
ejpam-5353	281	120	0	0	NUM
ejpam-5353	281	121	)	)	PUNCT
ejpam-5353	281	122	∪	∪	ADP
ejpam-5353	281	123	2c2(0	2c2(0	NUM
ejpam-5353	281	124	,	,	PUNCT
ejpam-5353	281	125	0	0	NUM
ejpam-5353	281	126	)	)	PUNCT
ejpam-5353	281	127	.	.	PUNCT
ejpam-5353	282	1	case	case	NOUN
ejpam-5353	282	2	2	2	NUM
ejpam-5353	282	3	.	.	X
ejpam-5353	283	1	for	for	ADP
ejpam-5353	283	2	an	an	DET
ejpam-5353	283	3	n	n	CCONJ
ejpam-5353	283	4	odd	odd	ADJ
ejpam-5353	283	5	integer	integer	NOUN
ejpam-5353	283	6	n	n	CCONJ
ejpam-5353	283	7	,	,	PUNCT
ejpam-5353	283	8	let	let	VERB
ejpam-5353	283	9	α	α	NOUN
ejpam-5353	283	10	=	=	SYM
ejpam-5353	283	11	1	1	NUM
ejpam-5353	283	12	,	,	PUNCT
ejpam-5353	283	13	β	β	X
ejpam-5353	283	14	=	=	SYM
ejpam-5353	283	15	1	1	NUM
ejpam-5353	283	16	,	,	PUNCT
ejpam-5353	283	17	and	and	CCONJ
ejpam-5353	283	18	γ	γ	X
ejpam-5353	283	19	=	=	SYM
ejpam-5353	283	20	n−	n−	PROPN
ejpam-5353	283	21	5	5	NUM
ejpam-5353	283	22	.	.	PUNCT
ejpam-5353	284	1	the	the	DET
ejpam-5353	284	2	vector	vector	NOUN
ejpam-5353	284	3	v(g	v(g	PROPN
ejpam-5353	284	4	)	)	PUNCT
ejpam-5353	284	5	of	of	ADP
ejpam-5353	284	6	a	a	DET
ejpam-5353	284	7	base	base	NOUN
ejpam-5353	284	8	g	g	NOUN
ejpam-5353	284	9	can	can	AUX
ejpam-5353	284	10	be	be	AUX
ejpam-5353	284	11	defined	define	VERB
ejpam-5353	284	12	as	as	ADP
ejpam-5353	284	13	:	:	PUNCT
ejpam-5353	284	14	vi(g	vi(g	NUM
ejpam-5353	284	15	)	)	PUNCT
ejpam-5353	285	1	=	=	PRON
ejpam-5353	285	2	{	{	PUNCT
ejpam-5353	285	3	−2i−	−2i−	NOUN
ejpam-5353	285	4	1	1	NUM
ejpam-5353	285	5	if	if	SCONJ
ejpam-5353	285	6	i	i	PRON
ejpam-5353	285	7	=	=	NOUN
ejpam-5353	285	8	1	1	NUM
ejpam-5353	285	9	,	,	PUNCT
ejpam-5353	285	10	n−	n−	NOUN
ejpam-5353	285	11	1	1	NUM
ejpam-5353	285	12	−2i	−2i	NOUN
ejpam-5353	285	13	otherwise	otherwise	ADV
ejpam-5353	285	14	hence	hence	ADV
ejpam-5353	285	15	,	,	PUNCT
ejpam-5353	285	16	v−i(g	v−i(g	PROPN
ejpam-5353	285	17	)	)	PUNCT
ejpam-5353	286	1	=	=	PRON
ejpam-5353	286	2	{	{	PUNCT
ejpam-5353	286	3	2i−	2i−	NUM
ejpam-5353	286	4	1	1	NUM
ejpam-5353	286	5	if	if	SCONJ
ejpam-5353	286	6	i	i	PRON
ejpam-5353	286	7	=	=	NOUN
ejpam-5353	286	8	1	1	NUM
ejpam-5353	286	9	,	,	PUNCT
ejpam-5353	286	10	n−	n−	NOUN
ejpam-5353	286	11	1	1	NUM
ejpam-5353	286	12	2i	2i	NOUN
ejpam-5353	286	13	otherwise	otherwise	ADV
ejpam-5353	286	14	for	for	ADP
ejpam-5353	286	15	any	any	DET
ejpam-5353	286	16	i	i	PROPN
ejpam-5353	286	17	∈	∈	PROPN
ejpam-5353	286	18	zn	zn	PROPN
ejpam-5353	286	19	,	,	PUNCT
ejpam-5353	286	20	vi−	vi−	PROPN
ejpam-5353	286	21	v−i	v−i	PROPN
ejpam-5353	287	1	+	+	NUM
ejpam-5353	287	2	i	i	PROPN
ejpam-5353	287	3	=	=	SYM
ejpam-5353	287	4	−3i	−3i	PROPN
ejpam-5353	287	5	.	.	PUNCT
ejpam-5353	288	1	by	by	ADP
ejpam-5353	288	2	theorem	theorem	NOUN
ejpam-5353	288	3	3	3	NUM
ejpam-5353	288	4	,	,	PUNCT
ejpam-5353	288	5	the	the	DET
ejpam-5353	288	6	base	base	NOUN
ejpam-5353	288	7	v(g	v(g	NOUN
ejpam-5353	288	8	)	)	PUNCT
ejpam-5353	288	9	is	be	AUX
ejpam-5353	288	10	symmetric	symmetric	ADJ
ejpam-5353	288	11	.	.	PUNCT
ejpam-5353	289	1	moreover	moreover	ADV
ejpam-5353	289	2	the	the	DET
ejpam-5353	289	3	edges	edge	NOUN
ejpam-5353	289	4	set	set	VERB
ejpam-5353	289	5	e(g	e(g	PROPN
ejpam-5353	289	6	)	)	PUNCT
ejpam-5353	289	7	of	of	ADP
ejpam-5353	289	8	the	the	DET
ejpam-5353	289	9	base	base	NOUN
ejpam-5353	289	10	g	g	PROPN
ejpam-5353	289	11	can	can	AUX
ejpam-5353	289	12	be	be	AUX
ejpam-5353	289	13	represented	represent	VERB
ejpam-5353	289	14	by	by	ADP
ejpam-5353	289	15	:	:	PUNCT
ejpam-5353	289	16	e(g	e(g	PROPN
ejpam-5353	289	17	)	)	PUNCT
ejpam-5353	290	1	=	=	PRON
ejpam-5353	290	2	{	{	PUNCT
ejpam-5353	290	3	(	(	PUNCT
ejpam-5353	290	4	−2i−	−2i−	NOUN
ejpam-5353	290	5	1)0	1)0	PROPN
ejpam-5353	290	6	,	,	PUNCT
ejpam-5353	290	7	(	(	PUNCT
ejpam-5353	290	8	−i−	−i−	X
ejpam-5353	290	9	1)1	1)1	NUM
ejpam-5353	290	10	;	;	PUNCT
ejpam-5353	290	11	i	i	PRON
ejpam-5353	290	12	∈	∈	PROPN
ejpam-5353	290	13	{	{	PUNCT
ejpam-5353	290	14	1	1	NUM
ejpam-5353	290	15	,	,	PUNCT
ejpam-5353	290	16	n−	n−	NOUN
ejpam-5353	290	17	1	1	NUM
ejpam-5353	290	18	}	}	PUNCT
ejpam-5353	290	19	}	}	PUNCT
ejpam-5353	290	20	∪	∪	X
ejpam-5353	290	21	{	{	PUNCT
ejpam-5353	290	22	(	(	PUNCT
ejpam-5353	290	23	−2i)0	−2i)0	NOUN
ejpam-5353	290	24	,	,	PUNCT
ejpam-5353	290	25	(	(	PUNCT
ejpam-5353	290	26	−i)1	−i)1	NOUN
ejpam-5353	290	27	;	;	PUNCT
ejpam-5353	290	28	i	i	PROPN
ejpam-5353	290	29	∈	∈	PROPN
ejpam-5353	290	30	zn	zn	PROPN
ejpam-5353	290	31	\	\	PROPN
ejpam-5353	290	32	{	{	PUNCT
ejpam-5353	290	33	1	1	NUM
ejpam-5353	290	34	,	,	PUNCT
ejpam-5353	290	35	n−	n−	NOUN
ejpam-5353	290	36	1	1	NUM
ejpam-5353	290	37	}	}	PUNCT
ejpam-5353	290	38	}	}	PUNCT
ejpam-5353	290	39	then	then	ADV
ejpam-5353	290	40	the	the	DET
ejpam-5353	290	41	graph	graph	NOUN
ejpam-5353	290	42	g	g	NOUN
ejpam-5353	290	43	≊	≊	PUNCT
ejpam-5353	290	44	c4(0	c4(0	NOUN
ejpam-5353	290	45	,	,	PUNCT
ejpam-5353	290	46	0	0	NUM
ejpam-5353	290	47	,	,	PUNCT
ejpam-5353	290	48	0	0	NUM
ejpam-5353	290	49	,	,	PUNCT
ejpam-5353	290	50	0	0	NUM
ejpam-5353	290	51	)	)	PUNCT
ejpam-5353	290	52	∪	∪	ADP
ejpam-5353	290	53	c3(0	c3(0	PROPN
ejpam-5353	290	54	,	,	PUNCT
ejpam-5353	290	55	0	0	NUM
ejpam-5353	290	56	,	,	PUNCT
ejpam-5353	290	57	0	0	NUM
ejpam-5353	290	58	)	)	PUNCT
ejpam-5353	290	59	∪	∪	NOUN
ejpam-5353	290	60	(	(	PUNCT
ejpam-5353	290	61	n−	n−	NOUN
ejpam-5353	290	62	5)c2(0	5)c2(0	NOUN
ejpam-5353	290	63	,	,	PUNCT
ejpam-5353	290	64	0	0	NUM
ejpam-5353	290	65	)	)	PUNCT
ejpam-5353	290	66	.	.	PUNCT
ejpam-5353	291	1	theorem	theorem	NOUN
ejpam-5353	291	2	12	12	NUM
ejpam-5353	291	3	.	.	PUNCT
ejpam-5353	292	1	let	let	VERB
ejpam-5353	292	2	p	p	PRON
ejpam-5353	292	3	≥	≥	PROPN
ejpam-5353	292	4	13	13	NUM
ejpam-5353	292	5	to	to	PART
ejpam-5353	292	6	be	be	AUX
ejpam-5353	292	7	a	a	DET
ejpam-5353	292	8	prime	prime	ADJ
ejpam-5353	292	9	integer	integer	NOUN
ejpam-5353	292	10	,	,	PUNCT
ejpam-5353	292	11	then	then	ADV
ejpam-5353	292	12	there	there	ADV
ejpam-5353	292	13	an	an	DET
ejpam-5353	292	14	odc	odc	NOUN
ejpam-5353	292	15	of	of	ADP
ejpam-5353	292	16	kp	kp	PROPN
ejpam-5353	292	17	,	,	PUNCT
ejpam-5353	292	18	p	p	NOUN
ejpam-5353	292	19	by	by	ADP
ejpam-5353	292	20	g	g	PROPN
ejpam-5353	292	21	=	=	SYM
ejpam-5353	292	22	c4(0	c4(0	PROPN
ejpam-5353	292	23	,	,	PUNCT
ejpam-5353	292	24	0	0	NUM
ejpam-5353	292	25	,	,	PUNCT
ejpam-5353	292	26	0	0	NUM
ejpam-5353	292	27	,	,	PUNCT
ejpam-5353	292	28	0	0	NUM
ejpam-5353	292	29	)	)	PUNCT
ejpam-5353	292	30	∪	∪	ADP
ejpam-5353	292	31	c3(0	c3(0	PROPN
ejpam-5353	292	32	,	,	PUNCT
ejpam-5353	292	33	0	0	NUM
ejpam-5353	292	34	,	,	PUNCT
ejpam-5353	292	35	0	0	NUM
ejpam-5353	292	36	)	)	PUNCT
ejpam-5353	292	37	∪	∪	NOUN
ejpam-5353	292	38	(	(	PUNCT
ejpam-5353	292	39	p−	p−	NOUN
ejpam-5353	292	40	5)c2(0	5)c2(0	NOUN
ejpam-5353	292	41	,	,	PUNCT
ejpam-5353	292	42	0	0	NUM
ejpam-5353	292	43	)	)	PUNCT
ejpam-5353	292	44	.	.	PUNCT
ejpam-5353	293	1	h.	h.	PROPN
ejpam-5353	293	2	shabana	shabana	PROPN
ejpam-5353	293	3	,	,	PUNCT
ejpam-5353	293	4	r.	r.	PROPN
ejpam-5353	293	5	el	el	PROPN
ejpam-5353	293	6	-	-	PROPN
ejpam-5353	293	7	shanawany	shanawany	NOUN
ejpam-5353	293	8	,	,	PUNCT
ejpam-5353	293	9	s.	s.	PROPN
ejpam-5353	293	10	halawa	halawa	PROPN
ejpam-5353	293	11	/	/	PUNCT
ejpam-5353	293	12	eur	eur	PROPN
ejpam-5353	293	13	.	.	PUNCT
ejpam-5353	294	1	j.	j.	PROPN
ejpam-5353	294	2	pure	pure	PROPN
ejpam-5353	294	3	appl	appl	PROPN
ejpam-5353	294	4	.	.	PROPN
ejpam-5353	294	5	math	math	PROPN
ejpam-5353	294	6	,	,	PUNCT
ejpam-5353	294	7	17	17	NUM
ejpam-5353	294	8	(	(	PUNCT
ejpam-5353	294	9	4	4	NUM
ejpam-5353	294	10	)	)	PUNCT
ejpam-5353	294	11	(	(	PUNCT
ejpam-5353	294	12	2024	2024	NUM
ejpam-5353	294	13	)	)	PUNCT
ejpam-5353	294	14	,	,	PUNCT
ejpam-5353	294	15	3492	3492	NUM
ejpam-5353	294	16	-	-	SYM
ejpam-5353	294	17	3516	3516	NUM
ejpam-5353	294	18	3502	3502	NUM
ejpam-5353	294	19	proof	proof	NOUN
ejpam-5353	294	20	.	.	PUNCT
ejpam-5353	295	1	for	for	ADP
ejpam-5353	295	2	any	any	DET
ejpam-5353	295	3	prime	prime	ADJ
ejpam-5353	295	4	integer	integer	NOUN
ejpam-5353	295	5	p	p	PROPN
ejpam-5353	295	6	≥	≥	NUM
ejpam-5353	295	7	13	13	NUM
ejpam-5353	295	8	,	,	PUNCT
ejpam-5353	295	9	the	the	DET
ejpam-5353	295	10	vectors	vector	NOUN
ejpam-5353	295	11	v(g	v(g	ADJ
ejpam-5353	295	12	)	)	PUNCT
ejpam-5353	295	13	and	and	CCONJ
ejpam-5353	295	14	u(f	u(f	NOUN
ejpam-5353	295	15	)	)	PUNCT
ejpam-5353	295	16	of	of	ADP
ejpam-5353	295	17	the	the	DET
ejpam-5353	295	18	bases	basis	NOUN
ejpam-5353	295	19	g	g	PROPN
ejpam-5353	295	20	and	and	CCONJ
ejpam-5353	295	21	f	f	PROPN
ejpam-5353	295	22	are	be	AUX
ejpam-5353	295	23	:	:	PUNCT
ejpam-5353	295	24	vi(g	vi(g	X
ejpam-5353	295	25	)	)	PUNCT
ejpam-5353	296	1	=	=	PUNCT
ejpam-5353	296	2			PROPN
ejpam-5353	296	3	(	(	PUNCT
ejpam-5353	296	4	p−5	p−5	PROPN
ejpam-5353	296	5	2	2	NUM
ejpam-5353	296	6	)	)	PUNCT
ejpam-5353	296	7	i	i	PRON
ejpam-5353	296	8	if	if	SCONJ
ejpam-5353	296	9	i	i	PRON
ejpam-5353	296	10	=	=	NOUN
ejpam-5353	296	11	0	0	NUM
ejpam-5353	296	12	,	,	PUNCT
ejpam-5353	296	13	1	1	NUM
ejpam-5353	296	14	(	(	PUNCT
ejpam-5353	296	15	p−3	p−3	NOUN
ejpam-5353	296	16	2	2	NUM
ejpam-5353	296	17	)	)	PUNCT
ejpam-5353	296	18	i	i	PRON
ejpam-5353	296	19	if	if	SCONJ
ejpam-5353	296	20	2	2	NUM
ejpam-5353	296	21	≤	≤	NUM
ejpam-5353	296	22	i	i	NOUN
ejpam-5353	296	23	≤	≤	NOUN
ejpam-5353	296	24	p−	p−	NOUN
ejpam-5353	296	25	3	3	NUM
ejpam-5353	296	26	(	(	PUNCT
ejpam-5353	296	27	p−5	p−5	PROPN
ejpam-5353	296	28	2	2	NUM
ejpam-5353	296	29	)	)	PUNCT
ejpam-5353	296	30	i−	i−	ADV
ejpam-5353	296	31	2	2	NUM
ejpam-5353	296	32	if	if	SCONJ
ejpam-5353	296	33	i	i	PRON
ejpam-5353	296	34	=	=	NOUN
ejpam-5353	296	35	p−	p−	NOUN
ejpam-5353	296	36	2	2	NUM
ejpam-5353	296	37	,	,	PUNCT
ejpam-5353	296	38	p−	p−	NOUN
ejpam-5353	296	39	1	1	NUM
ejpam-5353	296	40	,	,	PUNCT
ejpam-5353	296	41	and	and	CCONJ
ejpam-5353	296	42	ui(f	ui(f	PUNCT
ejpam-5353	296	43	)	)	PUNCT
ejpam-5353	297	1	=	=	PUNCT
ejpam-5353	297	2			NOUN
ejpam-5353	297	3	(	(	PUNCT
ejpam-5353	297	4	⌈p−2	⌈p−2	X
ejpam-5353	297	5	2	2	NUM
ejpam-5353	297	6	⌉)i	⌉)i	NOUN
ejpam-5353	297	7	if	if	SCONJ
ejpam-5353	297	8	i	i	PRON
ejpam-5353	297	9	=	=	NOUN
ejpam-5353	297	10	0	0	NUM
ejpam-5353	297	11	,	,	PUNCT
ejpam-5353	297	12	1	1	NUM
ejpam-5353	297	13	(	(	PUNCT
ejpam-5353	297	14	⌈p2⌉)i	⌈p2⌉)i	VERB
ejpam-5353	297	15	if	if	SCONJ
ejpam-5353	297	16	2	2	NUM
ejpam-5353	297	17	≤	≤	NUM
ejpam-5353	297	18	i	i	NOUN
ejpam-5353	297	19	≤	≤	NOUN
ejpam-5353	297	20	p−	p−	NOUN
ejpam-5353	297	21	3	3	NUM
ejpam-5353	297	22	⌈p−2	⌈p−2	NOUN
ejpam-5353	297	23	2	2	NUM
ejpam-5353	297	24	⌉)i−	⌉)i−	PROPN
ejpam-5353	297	25	2	2	NUM
ejpam-5353	297	26	if	if	SCONJ
ejpam-5353	297	27	i	i	PRON
ejpam-5353	297	28	=	=	NOUN
ejpam-5353	297	29	p−	p−	NOUN
ejpam-5353	297	30	2	2	NUM
ejpam-5353	297	31	,	,	PUNCT
ejpam-5353	297	32	p−	p−	NOUN
ejpam-5353	297	33	1	1	NUM
ejpam-5353	297	34	,	,	PUNCT
ejpam-5353	297	35	hence	hence	ADV
ejpam-5353	297	36	,	,	PUNCT
ejpam-5353	297	37	vi(g)−ui(f	vi(g)−ui(f	NUM
ejpam-5353	297	38	)	)	PUNCT
ejpam-5353	297	39	=	=	SYM
ejpam-5353	298	1	(	(	PUNCT
ejpam-5353	298	2	p−5	p−5	PROPN
ejpam-5353	298	3	2	2	NUM
ejpam-5353	298	4	)	)	PUNCT
ejpam-5353	298	5	i−	i−	PROPN
ejpam-5353	298	6	(	(	PUNCT
ejpam-5353	298	7	⌈p−2	⌈p−2	PROPN
ejpam-5353	298	8	2	2	NUM
ejpam-5353	298	9	⌉	⌉	NOUN
ejpam-5353	298	10	)	)	PUNCT
ejpam-5353	299	1	i	i	PRON
ejpam-5353	299	2	if	if	SCONJ
ejpam-5353	299	3	i	i	PRON
ejpam-5353	299	4	∈	∈	VERB
ejpam-5353	299	5	{	{	PUNCT
ejpam-5353	299	6	0	0	NUM
ejpam-5353	299	7	,	,	PUNCT
ejpam-5353	299	8	1	1	NUM
ejpam-5353	299	9	}	}	PUNCT
ejpam-5353	299	10	,	,	PUNCT
ejpam-5353	299	11	vi(g)−ui(f	vi(g)−ui(f	NOUN
ejpam-5353	299	12	)	)	PUNCT
ejpam-5353	299	13	=	=	PUNCT
ejpam-5353	299	14	(	(	PUNCT
ejpam-5353	299	15	p−3	p−3	NOUN
ejpam-5353	299	16	2	2	NUM
ejpam-5353	299	17	)	)	PUNCT
ejpam-5353	299	18	i−	i−	PROPN
ejpam-5353	299	19	(	(	PUNCT
ejpam-5353	299	20	⌈p2⌉	⌈p2⌉	PROPN
ejpam-5353	299	21	)	)	PUNCT
ejpam-5353	299	22	i	i	PRON
ejpam-5353	299	23	if	if	SCONJ
ejpam-5353	299	24	i	i	PRON
ejpam-5353	299	25	∈	∈	VERB
ejpam-5353	299	26	{	{	PUNCT
ejpam-5353	299	27	2	2	NUM
ejpam-5353	299	28	,	,	PUNCT
ejpam-5353	299	29	3	3	NUM
ejpam-5353	299	30	,	,	PUNCT
ejpam-5353	299	31	·	·	PUNCT
ejpam-5353	299	32	·	·	PUNCT
ejpam-5353	299	33	·	·	PUNCT
ejpam-5353	299	34	,	,	PUNCT
ejpam-5353	299	35	p−	p−	NOUN
ejpam-5353	299	36	3	3	NUM
ejpam-5353	299	37	}	}	PUNCT
ejpam-5353	299	38	,	,	PUNCT
ejpam-5353	299	39	and	and	CCONJ
ejpam-5353	299	40	vi(g	vi(g	NOUN
ejpam-5353	299	41	)	)	PUNCT
ejpam-5353	299	42	−	−	NOUN
ejpam-5353	299	43	ui(f	ui(f	PUNCT
ejpam-5353	299	44	)	)	PUNCT
ejpam-5353	299	45	=	=	SYM
ejpam-5353	299	46	(	(	PUNCT
ejpam-5353	299	47	p−5	p−5	PROPN
ejpam-5353	299	48	2	2	NUM
ejpam-5353	299	49	)	)	PUNCT
ejpam-5353	299	50	i	i	PRON
ejpam-5353	299	51	−	−	VERB
ejpam-5353	299	52	⌈p−2	⌈p−2	NOUN
ejpam-5353	299	53	2	2	NUM
ejpam-5353	299	54	⌉)i	⌉)i	NOUN
ejpam-5353	299	55	if	if	SCONJ
ejpam-5353	299	56	i	i	PRON
ejpam-5353	299	57	∈	∈	PROPN
ejpam-5353	299	58	{	{	PUNCT
ejpam-5353	299	59	p−	p−	NOUN
ejpam-5353	299	60	2	2	NUM
ejpam-5353	299	61	,	,	PUNCT
ejpam-5353	299	62	p−	p−	NOUN
ejpam-5353	299	63	1	1	NUM
ejpam-5353	299	64	}	}	PUNCT
ejpam-5353	299	65	.	.	PUNCT
ejpam-5353	300	1	by	by	ADP
ejpam-5353	300	2	theorem	theorem	NOUN
ejpam-5353	300	3	4	4	NUM
ejpam-5353	300	4	,	,	PUNCT
ejpam-5353	300	5	then	then	ADV
ejpam-5353	300	6	the	the	DET
ejpam-5353	300	7	two	two	NUM
ejpam-5353	300	8	bases	basis	NOUN
ejpam-5353	300	9	v(g	v(g	ADJ
ejpam-5353	300	10	)	)	PUNCT
ejpam-5353	300	11	and	and	CCONJ
ejpam-5353	300	12	u(f	u(f	NOUN
ejpam-5353	300	13	)	)	PUNCT
ejpam-5353	300	14	are	be	AUX
ejpam-5353	300	15	orthogonal	orthogonal	ADJ
ejpam-5353	300	16	.	.	PUNCT
ejpam-5353	301	1	moreover	moreover	ADV
ejpam-5353	301	2	,	,	PUNCT
ejpam-5353	301	3	the	the	DET
ejpam-5353	301	4	edges	edge	NOUN
ejpam-5353	301	5	set	set	VERB
ejpam-5353	301	6	e(g	e(g	PROPN
ejpam-5353	301	7	)	)	PUNCT
ejpam-5353	301	8	and	and	CCONJ
ejpam-5353	301	9	e(f	e(f	PROPN
ejpam-5353	301	10	)	)	PUNCT
ejpam-5353	301	11	of	of	ADP
ejpam-5353	301	12	the	the	DET
ejpam-5353	301	13	bases	basis	NOUN
ejpam-5353	301	14	g	g	PROPN
ejpam-5353	301	15	and	and	CCONJ
ejpam-5353	301	16	f	f	PROPN
ejpam-5353	301	17	respectively	respectively	ADV
ejpam-5353	301	18	can	can	AUX
ejpam-5353	301	19	be	be	AUX
ejpam-5353	301	20	represented	represent	VERB
ejpam-5353	301	21	by	by	ADP
ejpam-5353	301	22	:	:	PUNCT
ejpam-5353	301	23	e(g	e(g	PROPN
ejpam-5353	301	24	)	)	PUNCT
ejpam-5353	302	1	=	=	PRON
ejpam-5353	302	2	{	{	PUNCT
ejpam-5353	302	3	(	(	PUNCT
ejpam-5353	302	4	(	(	PUNCT
ejpam-5353	302	5	(	(	PUNCT
ejpam-5353	302	6	p−5	p−5	PROPN
ejpam-5353	302	7	2	2	NUM
ejpam-5353	302	8	)	)	PUNCT
ejpam-5353	302	9	i	i	PROPN
ejpam-5353	302	10	)	)	PUNCT
ejpam-5353	302	11	0	0	NUM
ejpam-5353	302	12	,	,	PUNCT
ejpam-5353	302	13	(	(	PUNCT
ejpam-5353	302	14	(	(	PUNCT
ejpam-5353	302	15	p−3	p−3	NOUN
ejpam-5353	302	16	2	2	NUM
ejpam-5353	302	17	)	)	PUNCT
ejpam-5353	302	18	i	i	NOUN
ejpam-5353	302	19	)	)	PUNCT
ejpam-5353	302	20	1	1	NUM
ejpam-5353	302	21	)	)	PUNCT
ejpam-5353	302	22	;	;	PUNCT
ejpam-5353	302	23	i	i	PRON
ejpam-5353	302	24	∈	∈	PROPN
ejpam-5353	302	25	{	{	PUNCT
ejpam-5353	302	26	0	0	NUM
ejpam-5353	302	27	,	,	PUNCT
ejpam-5353	302	28	1	1	NUM
ejpam-5353	302	29	}	}	PUNCT
ejpam-5353	302	30	}	}	PUNCT
ejpam-5353	302	31	∪	∪	X
ejpam-5353	302	32	{	{	PUNCT
ejpam-5353	302	33	(	(	PUNCT
ejpam-5353	302	34	(	(	PUNCT
ejpam-5353	302	35	(	(	PUNCT
ejpam-5353	302	36	p−3	p−3	NOUN
ejpam-5353	302	37	2	2	NUM
ejpam-5353	302	38	)	)	PUNCT
ejpam-5353	302	39	i	i	PRON
ejpam-5353	302	40	)	)	PUNCT
ejpam-5353	302	41	0	0	NUM
ejpam-5353	302	42	,	,	PUNCT
ejpam-5353	302	43	(	(	PUNCT
ejpam-5353	302	44	(	(	PUNCT
ejpam-5353	302	45	p−1	p−1	PROPN
ejpam-5353	302	46	2	2	NUM
ejpam-5353	302	47	)	)	PUNCT
ejpam-5353	302	48	i	i	NOUN
ejpam-5353	302	49	)	)	PUNCT
ejpam-5353	302	50	1	1	NUM
ejpam-5353	302	51	)	)	PUNCT
ejpam-5353	302	52	;	;	PUNCT
ejpam-5353	302	53	i	i	PRON
ejpam-5353	302	54	∈	∈	PROPN
ejpam-5353	302	55	{	{	PUNCT
ejpam-5353	302	56	2	2	NUM
ejpam-5353	302	57	,	,	PUNCT
ejpam-5353	302	58	3	3	NUM
ejpam-5353	302	59	,	,	PUNCT
ejpam-5353	302	60	·	·	PUNCT
ejpam-5353	302	61	·	·	PUNCT
ejpam-5353	302	62	·	·	PUNCT
ejpam-5353	302	63	,	,	PUNCT
ejpam-5353	302	64	p−	p−	NOUN
ejpam-5353	302	65	3	3	NUM
ejpam-5353	302	66	}	}	PUNCT
ejpam-5353	302	67	}	}	PUNCT
ejpam-5353	302	68	∪	∪	X
ejpam-5353	302	69	{	{	PUNCT
ejpam-5353	302	70	(	(	PUNCT
ejpam-5353	302	71	(	(	PUNCT
ejpam-5353	302	72	(	(	PUNCT
ejpam-5353	302	73	p−5	p−5	PROPN
ejpam-5353	302	74	2	2	NUM
ejpam-5353	302	75	)	)	PUNCT
ejpam-5353	302	76	i−	i−	PROPN
ejpam-5353	302	77	2	2	NUM
ejpam-5353	302	78	)	)	PUNCT
ejpam-5353	302	79	0	0	NUM
ejpam-5353	302	80	,	,	PUNCT
ejpam-5353	302	81	(	(	PUNCT
ejpam-5353	302	82	(	(	PUNCT
ejpam-5353	302	83	p−3	p−3	NOUN
ejpam-5353	302	84	2	2	NUM
ejpam-5353	302	85	)	)	PUNCT
ejpam-5353	302	86	i−	i−	PROPN
ejpam-5353	302	87	2	2	NUM
ejpam-5353	302	88	)	)	PUNCT
ejpam-5353	302	89	1	1	NUM
ejpam-5353	302	90	)	)	PUNCT
ejpam-5353	302	91	;	;	PUNCT
ejpam-5353	302	92	i	i	PRON
ejpam-5353	302	93	∈	∈	PROPN
ejpam-5353	302	94	{	{	PUNCT
ejpam-5353	302	95	p−	p−	NOUN
ejpam-5353	302	96	2	2	NUM
ejpam-5353	302	97	,	,	PUNCT
ejpam-5353	302	98	p−	p−	NOUN
ejpam-5353	302	99	1	1	NUM
ejpam-5353	302	100	}	}	PUNCT
ejpam-5353	302	101	}	}	PUNCT
ejpam-5353	302	102	.	.	PUNCT
ejpam-5353	303	1	and	and	CCONJ
ejpam-5353	303	2	e(f	e(f	PROPN
ejpam-5353	303	3	)	)	PUNCT
ejpam-5353	304	1	=	=	PRON
ejpam-5353	304	2	{	{	PUNCT
ejpam-5353	304	3	(	(	PUNCT
ejpam-5353	304	4	(	(	PUNCT
ejpam-5353	304	5	⌈p−3	⌈p−3	NOUN
ejpam-5353	304	6	2	2	NUM
ejpam-5353	304	7	⌉i	⌉i	PROPN
ejpam-5353	304	8	)	)	PUNCT
ejpam-5353	304	9	0	0	NUM
ejpam-5353	304	10	,	,	PUNCT
ejpam-5353	304	11	(	(	PUNCT
ejpam-5353	304	12	⌈p−1	⌈p−1	X
ejpam-5353	304	13	2	2	NUM
ejpam-5353	304	14	⌉i	⌉i	VERB
ejpam-5353	304	15	)	)	PUNCT
ejpam-5353	304	16	1	1	NUM
ejpam-5353	304	17	)	)	PUNCT
ejpam-5353	304	18	;	;	PUNCT
ejpam-5353	304	19	i	i	PRON
ejpam-5353	304	20	∈	∈	PROPN
ejpam-5353	304	21	{	{	PUNCT
ejpam-5353	304	22	0	0	NUM
ejpam-5353	304	23	,	,	PUNCT
ejpam-5353	304	24	1	1	NUM
ejpam-5353	304	25	}	}	PUNCT
ejpam-5353	304	26	}	}	PUNCT
ejpam-5353	304	27	∪	∪	X
ejpam-5353	304	28	{	{	PUNCT
ejpam-5353	304	29	(	(	PUNCT
ejpam-5353	304	30	(	(	PUNCT
ejpam-5353	304	31	⌈p−5	⌈p−5	NOUN
ejpam-5353	304	32	2	2	NUM
ejpam-5353	304	33	⌉i	⌉i	PROPN
ejpam-5353	304	34	)	)	PUNCT
ejpam-5353	304	35	0	0	NUM
ejpam-5353	304	36	,	,	PUNCT
ejpam-5353	304	37	(	(	PUNCT
ejpam-5353	304	38	⌈p−3	⌈p−3	NOUN
ejpam-5353	304	39	2	2	NUM
ejpam-5353	304	40	⌉i	⌉i	PROPN
ejpam-5353	304	41	)	)	PUNCT
ejpam-5353	304	42	1	1	NUM
ejpam-5353	304	43	)	)	PUNCT
ejpam-5353	304	44	;	;	PUNCT
ejpam-5353	304	45	i	i	PRON
ejpam-5353	304	46	∈	∈	PROPN
ejpam-5353	304	47	{	{	PUNCT
ejpam-5353	304	48	2	2	NUM
ejpam-5353	304	49	,	,	PUNCT
ejpam-5353	304	50	3	3	NUM
ejpam-5353	304	51	,	,	PUNCT
ejpam-5353	304	52	·	·	PUNCT
ejpam-5353	304	53	·	·	PUNCT
ejpam-5353	304	54	·	·	PUNCT
ejpam-5353	304	55	,	,	PUNCT
ejpam-5353	304	56	p−	p−	NOUN
ejpam-5353	304	57	3	3	NUM
ejpam-5353	304	58	}	}	PUNCT
ejpam-5353	304	59	}	}	PUNCT
ejpam-5353	304	60	∪	∪	X
ejpam-5353	304	61	{	{	PUNCT
ejpam-5353	304	62	(	(	PUNCT
ejpam-5353	304	63	(	(	PUNCT
ejpam-5353	304	64	(	(	PUNCT
ejpam-5353	304	65	⌈p−3	⌈p−3	NOUN
ejpam-5353	304	66	2	2	NUM
ejpam-5353	304	67	⌉i	⌉i	PROPN
ejpam-5353	304	68	)	)	PUNCT
ejpam-5353	304	69	−	−	ADP
ejpam-5353	304	70	2	2	NUM
ejpam-5353	304	71	)	)	PUNCT
ejpam-5353	304	72	0	0	NUM
ejpam-5353	304	73	,	,	PUNCT
ejpam-5353	304	74	(	(	PUNCT
ejpam-5353	304	75	(	(	PUNCT
ejpam-5353	304	76	⌈p−1	⌈p−1	X
ejpam-5353	304	77	2	2	NUM
ejpam-5353	304	78	⌉i	⌉i	ADJ
ejpam-5353	304	79	)	)	PUNCT
ejpam-5353	304	80	−	−	ADP
ejpam-5353	304	81	2	2	NUM
ejpam-5353	304	82	)	)	PUNCT
ejpam-5353	304	83	1	1	NUM
ejpam-5353	304	84	)	)	PUNCT
ejpam-5353	304	85	;	;	PUNCT
ejpam-5353	304	86	i	i	PRON
ejpam-5353	304	87	∈	∈	PROPN
ejpam-5353	304	88	{	{	PUNCT
ejpam-5353	304	89	p−	p−	NOUN
ejpam-5353	304	90	2	2	NUM
ejpam-5353	304	91	,	,	PUNCT
ejpam-5353	304	92	p−	p−	NOUN
ejpam-5353	304	93	1	1	NUM
ejpam-5353	304	94	}	}	PUNCT
ejpam-5353	304	95	}	}	PUNCT
ejpam-5353	304	96	.	.	PUNCT
ejpam-5353	305	1	hence	hence	ADV
ejpam-5353	305	2	g	g	PROPN
ejpam-5353	305	3	≊	≊	PUNCT
ejpam-5353	306	1	f	f	NOUN
ejpam-5353	306	2	≊	≊	NOUN
ejpam-5353	306	3	c4(0	c4(0	PROPN
ejpam-5353	306	4	,	,	PUNCT
ejpam-5353	306	5	0	0	NUM
ejpam-5353	306	6	,	,	PUNCT
ejpam-5353	306	7	0	0	NUM
ejpam-5353	306	8	,	,	PUNCT
ejpam-5353	306	9	0	0	NUM
ejpam-5353	306	10	)	)	PUNCT
ejpam-5353	306	11	∪	∪	ADP
ejpam-5353	306	12	c3(0	c3(0	PROPN
ejpam-5353	306	13	,	,	PUNCT
ejpam-5353	306	14	0	0	NUM
ejpam-5353	306	15	,	,	PUNCT
ejpam-5353	306	16	0	0	NUM
ejpam-5353	306	17	)	)	PUNCT
ejpam-5353	306	18	∪	∪	NOUN
ejpam-5353	306	19	(	(	PUNCT
ejpam-5353	306	20	p−	p−	NOUN
ejpam-5353	306	21	5)c2(0	5)c2(0	NOUN
ejpam-5353	306	22	,	,	PUNCT
ejpam-5353	306	23	0	0	NUM
ejpam-5353	306	24	)	)	PUNCT
ejpam-5353	306	25	.	.	PUNCT
ejpam-5353	307	1	theorem	theorem	VERB
ejpam-5353	307	2	13	13	NUM
ejpam-5353	307	3	.	.	PUNCT
ejpam-5353	308	1	let	let	VERB
ejpam-5353	308	2	n	n	PRON
ejpam-5353	308	3	≥	≥	X
ejpam-5353	308	4	8	8	NUM
ejpam-5353	308	5	to	to	PART
ejpam-5353	308	6	be	be	AUX
ejpam-5353	308	7	a	a	DET
ejpam-5353	308	8	positive	positive	ADJ
ejpam-5353	308	9	integer	integer	NOUN
ejpam-5353	308	10	,	,	PUNCT
ejpam-5353	308	11	then	then	ADV
ejpam-5353	308	12	there	there	PRON
ejpam-5353	308	13	is	be	VERB
ejpam-5353	308	14	an	an	DET
ejpam-5353	308	15	odc	odc	NOUN
ejpam-5353	308	16	of	of	ADP
ejpam-5353	308	17	kn	kn	PROPN
ejpam-5353	308	18	,	,	PUNCT
ejpam-5353	308	19	n	n	CCONJ
ejpam-5353	308	20	by	by	ADP
ejpam-5353	308	21	c5(0	c5(0	PROPN
ejpam-5353	308	22	,	,	PUNCT
ejpam-5353	308	23	0	0	NUM
ejpam-5353	308	24	,	,	PUNCT
ejpam-5353	308	25	(	(	PUNCT
ejpam-5353	308	26	n−	n−	NOUN
ejpam-5353	308	27	4	4	NUM
ejpam-5353	308	28	)	)	PUNCT
ejpam-5353	308	29	,	,	PUNCT
ejpam-5353	308	30	0	0	NUM
ejpam-5353	308	31	,	,	PUNCT
ejpam-5353	308	32	0	0	NUM
ejpam-5353	308	33	)	)	PUNCT
ejpam-5353	308	34	.	.	PUNCT
ejpam-5353	309	1	proof	proof	NOUN
ejpam-5353	309	2	.	.	PUNCT
ejpam-5353	310	1	for	for	ADP
ejpam-5353	310	2	all	all	DET
ejpam-5353	310	3	positive	positive	ADJ
ejpam-5353	310	4	integers	integer	NOUN
ejpam-5353	310	5	n	n	PRON
ejpam-5353	310	6	≥	≥	NOUN
ejpam-5353	310	7	8	8	NUM
ejpam-5353	310	8	,	,	PUNCT
ejpam-5353	310	9	the	the	DET
ejpam-5353	310	10	vectors	vector	NOUN
ejpam-5353	310	11	v(g	v(g	ADJ
ejpam-5353	310	12	)	)	PUNCT
ejpam-5353	310	13	and	and	CCONJ
ejpam-5353	310	14	v(f	v(f	PROPN
ejpam-5353	310	15	)	)	PUNCT
ejpam-5353	310	16	of	of	ADP
ejpam-5353	310	17	the	the	DET
ejpam-5353	310	18	bases	basis	NOUN
ejpam-5353	310	19	g	g	PROPN
ejpam-5353	310	20	and	and	CCONJ
ejpam-5353	310	21	h.	h.	PROPN
ejpam-5353	310	22	shabana	shabana	PROPN
ejpam-5353	310	23	,	,	PUNCT
ejpam-5353	311	1	r.	r.	PROPN
ejpam-5353	311	2	el	el	PROPN
ejpam-5353	311	3	-	-	PROPN
ejpam-5353	311	4	shanawany	shanawany	NOUN
ejpam-5353	311	5	,	,	PUNCT
ejpam-5353	311	6	s.	s.	PROPN
ejpam-5353	311	7	halawa	halawa	PROPN
ejpam-5353	311	8	/	/	PUNCT
ejpam-5353	311	9	eur	eur	PROPN
ejpam-5353	311	10	.	.	PUNCT
ejpam-5353	312	1	j.	j.	PROPN
ejpam-5353	312	2	pure	pure	PROPN
ejpam-5353	312	3	appl	appl	PROPN
ejpam-5353	312	4	.	.	PROPN
ejpam-5353	312	5	math	math	PROPN
ejpam-5353	312	6	,	,	PUNCT
ejpam-5353	312	7	17	17	NUM
ejpam-5353	312	8	(	(	PUNCT
ejpam-5353	312	9	4	4	NUM
ejpam-5353	312	10	)	)	PUNCT
ejpam-5353	312	11	(	(	PUNCT
ejpam-5353	312	12	2024	2024	NUM
ejpam-5353	312	13	)	)	PUNCT
ejpam-5353	312	14	,	,	PUNCT
ejpam-5353	312	15	3492	3492	NUM
ejpam-5353	312	16	-	-	SYM
ejpam-5353	312	17	3516	3516	NUM
ejpam-5353	312	18	3503	3503	NUM
ejpam-5353	312	19	f	f	NOUN
ejpam-5353	312	20	are	be	AUX
ejpam-5353	312	21	defined	define	VERB
ejpam-5353	312	22	as	as	ADP
ejpam-5353	312	23	:	:	PUNCT
ejpam-5353	312	24	vi(g	vi(g	NUM
ejpam-5353	312	25	)	)	PUNCT
ejpam-5353	313	1	=	=	PUNCT
ejpam-5353	313	2			PUNCT
ejpam-5353	313	3	−3i	−3i	PROPN
ejpam-5353	313	4	if	if	SCONJ
ejpam-5353	313	5	i	i	PRON
ejpam-5353	313	6	=	=	NOUN
ejpam-5353	313	7	0	0	NUM
ejpam-5353	313	8	,	,	PUNCT
ejpam-5353	313	9	1	1	NUM
ejpam-5353	313	10	−i	−i	NOUN
ejpam-5353	313	11	if	if	SCONJ
ejpam-5353	313	12	2	2	NUM
ejpam-5353	313	13	≤	≤	NUM
ejpam-5353	313	14	i	i	NOUN
ejpam-5353	313	15	≤	≤	ADJ
ejpam-5353	313	16	n−	n−	NOUN
ejpam-5353	313	17	3	3	NUM
ejpam-5353	313	18	−2−	−2−	NOUN
ejpam-5353	313	19	3i	3i	NOUN
ejpam-5353	313	20	if	if	SCONJ
ejpam-5353	313	21	i	i	PRON
ejpam-5353	313	22	=	=	VERB
ejpam-5353	313	23	n−	n−	NOUN
ejpam-5353	313	24	2	2	NUM
ejpam-5353	313	25	,	,	PUNCT
ejpam-5353	313	26	n−	n−	NOUN
ejpam-5353	313	27	1	1	NUM
ejpam-5353	313	28	and	and	CCONJ
ejpam-5353	313	29	vi(f	vi(f	NOUN
ejpam-5353	313	30	)	)	PUNCT
ejpam-5353	313	31	=	=	PUNCT
ejpam-5353	314	1			PUNCT
ejpam-5353	314	2	−2i	−2i	PROPN
ejpam-5353	314	3	if	if	SCONJ
ejpam-5353	314	4	i	i	PRON
ejpam-5353	314	5	=	=	NOUN
ejpam-5353	314	6	0	0	NUM
ejpam-5353	314	7	,	,	PUNCT
ejpam-5353	314	8	1	1	NUM
ejpam-5353	314	9	0	0	NUM
ejpam-5353	314	10	if	if	SCONJ
ejpam-5353	314	11	2	2	NUM
ejpam-5353	314	12	≤	≤	NUM
ejpam-5353	314	13	i	i	NOUN
ejpam-5353	314	14	≤	≤	ADJ
ejpam-5353	314	15	n−	n−	NOUN
ejpam-5353	314	16	3	3	NUM
ejpam-5353	314	17	−2i−	−2i−	SYM
ejpam-5353	314	18	2	2	NUM
ejpam-5353	314	19	if	if	SCONJ
ejpam-5353	314	20	i	i	PRON
ejpam-5353	314	21	=	=	VERB
ejpam-5353	314	22	n−	n−	NOUN
ejpam-5353	314	23	2	2	NUM
ejpam-5353	314	24	,	,	PUNCT
ejpam-5353	314	25	n−	n−	NOUN
ejpam-5353	314	26	1	1	NUM
ejpam-5353	314	27	since	since	SCONJ
ejpam-5353	314	28	{	{	PUNCT
ejpam-5353	314	29	vi(g)−	vi(g)−	NOUN
ejpam-5353	314	30	vi(f	vi(f	NOUN
ejpam-5353	314	31	)	)	PUNCT
ejpam-5353	314	32	;	;	PUNCT
ejpam-5353	314	33	i	i	PRON
ejpam-5353	314	34	∈	∈	PROPN
ejpam-5353	314	35	zn	zn	PROPN
ejpam-5353	314	36	}	}	PUNCT
ejpam-5353	314	37	=	=	SYM
ejpam-5353	314	38	zn	zn	PROPN
ejpam-5353	314	39	,	,	PUNCT
ejpam-5353	314	40	following	follow	VERB
ejpam-5353	314	41	theorem	theorem	VERB
ejpam-5353	314	42	4	4	NUM
ejpam-5353	314	43	,	,	PUNCT
ejpam-5353	314	44	the	the	DET
ejpam-5353	314	45	bases	basis	NOUN
ejpam-5353	314	46	g	g	PROPN
ejpam-5353	314	47	and	and	CCONJ
ejpam-5353	314	48	f	f	PROPN
ejpam-5353	314	49	are	be	AUX
ejpam-5353	314	50	orthogonal	orthogonal	ADJ
ejpam-5353	314	51	.	.	PUNCT
ejpam-5353	315	1	from	from	ADP
ejpam-5353	315	2	the	the	DET
ejpam-5353	315	3	above	above	ADJ
ejpam-5353	315	4	definitions	definition	NOUN
ejpam-5353	315	5	of	of	ADP
ejpam-5353	315	6	vi(g	vi(g	NOUN
ejpam-5353	315	7	)	)	PUNCT
ejpam-5353	315	8	and	and	CCONJ
ejpam-5353	315	9	vi(f	vi(f	NOUN
ejpam-5353	315	10	)	)	PUNCT
ejpam-5353	315	11	with	with	ADP
ejpam-5353	315	12	the	the	DET
ejpam-5353	315	13	two	two	NUM
ejpam-5353	315	14	relations	relation	NOUN
ejpam-5353	315	15	e(g	e(g	PROPN
ejpam-5353	315	16	)	)	PUNCT
ejpam-5353	315	17	=	=	PRON
ejpam-5353	315	18	{	{	PUNCT
ejpam-5353	315	19	(	(	PUNCT
ejpam-5353	315	20	vi(g))0	vi(g))0	NOUN
ejpam-5353	315	21	,	,	PUNCT
ejpam-5353	315	22	(	(	PUNCT
ejpam-5353	315	23	vi(g	vi(g	NOUN
ejpam-5353	315	24	)	)	PUNCT
ejpam-5353	315	25	+	+	CCONJ
ejpam-5353	315	26	i)i	i)i	NOUN
ejpam-5353	315	27	}	}	PUNCT
ejpam-5353	315	28	and	and	CCONJ
ejpam-5353	315	29	e(f	e(f	PROPN
ejpam-5353	315	30	)	)	PUNCT
ejpam-5353	315	31	=	=	PRON
ejpam-5353	315	32	{	{	PUNCT
ejpam-5353	315	33	(	(	PUNCT
ejpam-5353	315	34	vi(f	vi(f	NOUN
ejpam-5353	315	35	)	)	PUNCT
ejpam-5353	315	36	)	)	PUNCT
ejpam-5353	315	37	0	0	NUM
ejpam-5353	315	38	,	,	PUNCT
ejpam-5353	315	39	(	(	PUNCT
ejpam-5353	315	40	vi(f	vi(f	X
ejpam-5353	315	41	)	)	PUNCT
ejpam-5353	315	42	+	+	CCONJ
ejpam-5353	315	43	i)i	i)i	NOUN
ejpam-5353	315	44	}	}	PUNCT
ejpam-5353	315	45	for	for	ADP
ejpam-5353	315	46	all	all	PRON
ejpam-5353	315	47	i	i	PRON
ejpam-5353	315	48	∈	∈	PROPN
ejpam-5353	315	49	zn	zn	PROPN
ejpam-5353	315	50	,	,	PUNCT
ejpam-5353	315	51	then	then	ADV
ejpam-5353	315	52	g	g	PROPN
ejpam-5353	315	53	≊	≊	NOUN
ejpam-5353	315	54	c5(0	c5(0	PROPN
ejpam-5353	315	55	,	,	PUNCT
ejpam-5353	315	56	0	0	NUM
ejpam-5353	315	57	,	,	PUNCT
ejpam-5353	315	58	(	(	PUNCT
ejpam-5353	315	59	n−	n−	NOUN
ejpam-5353	315	60	4	4	NUM
ejpam-5353	315	61	)	)	PUNCT
ejpam-5353	315	62	,	,	PUNCT
ejpam-5353	315	63	0	0	NUM
ejpam-5353	315	64	,	,	PUNCT
ejpam-5353	315	65	0	0	NUM
ejpam-5353	315	66	)	)	PUNCT
ejpam-5353	315	67	≊	≊	PRON
ejpam-5353	316	1	f	f	PROPN
ejpam-5353	316	2	.	.	PUNCT
ejpam-5353	317	1	theorem	theorem	PROPN
ejpam-5353	317	2	14	14	NUM
ejpam-5353	317	3	.	.	PUNCT
ejpam-5353	318	1	let	let	VERB
ejpam-5353	318	2	n	n	PART
ejpam-5353	318	3	to	to	PART
ejpam-5353	318	4	be	be	AUX
ejpam-5353	318	5	a	a	DET
ejpam-5353	318	6	positive	positive	ADJ
ejpam-5353	318	7	integer	integer	NOUN
ejpam-5353	318	8	such	such	ADJ
ejpam-5353	318	9	that	that	SCONJ
ejpam-5353	318	10	n	n	NUM
ejpam-5353	318	11	≥	≥	NOUN
ejpam-5353	318	12	5	5	NUM
ejpam-5353	318	13	,	,	PUNCT
ejpam-5353	318	14	then	then	ADV
ejpam-5353	318	15	there	there	PRON
ejpam-5353	318	16	is	be	VERB
ejpam-5353	318	17	a	a	DET
ejpam-5353	318	18	symmetric	symmetric	ADJ
ejpam-5353	318	19	base	base	NOUN
ejpam-5353	318	20	of	of	ADP
ejpam-5353	318	21	an	an	DET
ejpam-5353	318	22	odc	odc	NOUN
ejpam-5353	318	23	of	of	ADP
ejpam-5353	318	24	kn	kn	PROPN
ejpam-5353	318	25	,	,	PUNCT
ejpam-5353	318	26	n	n	CCONJ
ejpam-5353	318	27	by	by	ADP
ejpam-5353	318	28	g	g	PROPN
ejpam-5353	318	29	=	=	SYM
ejpam-5353	318	30	c3(1	c3(1	PROPN
ejpam-5353	318	31	,	,	PUNCT
ejpam-5353	318	32	0	0	NUM
ejpam-5353	318	33	,	,	PUNCT
ejpam-5353	318	34	n−	n−	NOUN
ejpam-5353	318	35	3	3	NUM
ejpam-5353	318	36	)	)	PUNCT
ejpam-5353	318	37	.	.	PUNCT
ejpam-5353	319	1	proof	proof	NOUN
ejpam-5353	319	2	.	.	PUNCT
ejpam-5353	320	1	for	for	ADP
ejpam-5353	320	2	n	n	X
ejpam-5353	320	3	≥	≥	NUM
ejpam-5353	320	4	5	5	NUM
ejpam-5353	320	5	,	,	PUNCT
ejpam-5353	320	6	the	the	DET
ejpam-5353	320	7	vector	vector	NOUN
ejpam-5353	320	8	v(g	v(g	PROPN
ejpam-5353	320	9	)	)	PUNCT
ejpam-5353	320	10	of	of	ADP
ejpam-5353	320	11	the	the	DET
ejpam-5353	320	12	base	base	NOUN
ejpam-5353	320	13	g	g	PROPN
ejpam-5353	320	14	can	can	AUX
ejpam-5353	320	15	be	be	AUX
ejpam-5353	320	16	defined	define	VERB
ejpam-5353	320	17	by	by	ADP
ejpam-5353	320	18	:	:	PUNCT
ejpam-5353	320	19	vi(g	vi(g	NUM
ejpam-5353	320	20	)	)	PUNCT
ejpam-5353	321	1	=	=	SYM
ejpam-5353	321	2	v−i(g	v−i(g	X
ejpam-5353	321	3	)	)	PUNCT
ejpam-5353	322	1	=	=	PRON
ejpam-5353	322	2	{	{	PUNCT
ejpam-5353	322	3	n−	n−	NOUN
ejpam-5353	322	4	1	1	NUM
ejpam-5353	323	1	if	if	SCONJ
ejpam-5353	323	2	i	i	PRON
ejpam-5353	323	3	=	=	NOUN
ejpam-5353	323	4	1	1	NUM
ejpam-5353	323	5	,	,	PUNCT
ejpam-5353	323	6	n−	n−	NOUN
ejpam-5353	323	7	1	1	NUM
ejpam-5353	323	8	1	1	NUM
ejpam-5353	323	9	otherwise	otherwise	ADV
ejpam-5353	323	10	for	for	ADP
ejpam-5353	323	11	any	any	DET
ejpam-5353	323	12	i	i	PROPN
ejpam-5353	323	13	∈	∈	PROPN
ejpam-5353	323	14	zn	zn	PROPN
ejpam-5353	323	15	,	,	PUNCT
ejpam-5353	323	16	vi−	vi−	NUM
ejpam-5353	323	17	v−i+i	v−i+i	PUNCT
ejpam-5353	323	18	=	=	SYM
ejpam-5353	323	19	i.	i.	NOUN
ejpam-5353	323	20	by	by	ADP
ejpam-5353	323	21	theorem	theorem	NOUN
ejpam-5353	323	22	3	3	NUM
ejpam-5353	323	23	,	,	PUNCT
ejpam-5353	323	24	the	the	DET
ejpam-5353	323	25	base	base	NOUN
ejpam-5353	323	26	v(g	v(g	NOUN
ejpam-5353	323	27	)	)	PUNCT
ejpam-5353	323	28	is	be	AUX
ejpam-5353	323	29	a	a	DET
ejpam-5353	323	30	symmetric	symmetric	NOUN
ejpam-5353	323	31	.	.	PUNCT
ejpam-5353	324	1	moreover	moreover	ADV
ejpam-5353	324	2	,	,	PUNCT
ejpam-5353	324	3	the	the	DET
ejpam-5353	324	4	edges	edge	NOUN
ejpam-5353	324	5	set	set	VERB
ejpam-5353	324	6	e(g	e(g	PROPN
ejpam-5353	324	7	)	)	PUNCT
ejpam-5353	324	8	of	of	ADP
ejpam-5353	324	9	the	the	DET
ejpam-5353	324	10	base	base	NOUN
ejpam-5353	324	11	g	g	PROPN
ejpam-5353	324	12	can	can	AUX
ejpam-5353	324	13	be	be	AUX
ejpam-5353	324	14	represented	represent	VERB
ejpam-5353	324	15	by	by	ADP
ejpam-5353	324	16	:	:	PUNCT
ejpam-5353	324	17	e(g	e(g	PROPN
ejpam-5353	324	18	)	)	PUNCT
ejpam-5353	325	1	=	=	PRON
ejpam-5353	325	2	{	{	PUNCT
ejpam-5353	325	3	01	01	NUM
ejpam-5353	325	4	,	,	PUNCT
ejpam-5353	325	5	(	(	PUNCT
ejpam-5353	325	6	n−	n−	NOUN
ejpam-5353	325	7	1)0	1)0	NUM
ejpam-5353	325	8	,	,	PUNCT
ejpam-5353	325	9	(	(	PUNCT
ejpam-5353	325	10	n−	n−	NOUN
ejpam-5353	325	11	2)1	2)1	NUM
ejpam-5353	325	12	}	}	PUNCT
ejpam-5353	325	13	∪10	∪10	NOUN
ejpam-5353	325	14	{	{	PUNCT
ejpam-5353	325	15	(	(	PUNCT
ejpam-5353	325	16	10	10	NUM
ejpam-5353	325	17	,	,	PUNCT
ejpam-5353	325	18	β1	β1	PROPN
ejpam-5353	325	19	)	)	PUNCT
ejpam-5353	325	20	:	:	PUNCT
ejpam-5353	325	21	β	β	X
ejpam-5353	325	22	∈	∈	PROPN
ejpam-5353	325	23	{	{	PUNCT
ejpam-5353	325	24	1	1	NUM
ejpam-5353	325	25	,	,	PUNCT
ejpam-5353	325	26	3	3	NUM
ejpam-5353	325	27	,	,	PUNCT
ejpam-5353	325	28	·	·	PUNCT
ejpam-5353	325	29	·	·	PUNCT
ejpam-5353	325	30	·	·	PUNCT
ejpam-5353	325	31	,	,	PUNCT
ejpam-5353	325	32	n−	n−	NOUN
ejpam-5353	325	33	1	1	NUM
ejpam-5353	325	34	}	}	PUNCT
ejpam-5353	325	35	}	}	PUNCT
ejpam-5353	325	36	thus	thus	ADV
ejpam-5353	325	37	,	,	PUNCT
ejpam-5353	325	38	the	the	DET
ejpam-5353	325	39	graph	graph	NOUN
ejpam-5353	325	40	g	g	ADP
ejpam-5353	325	41	∼=	∼=	PROPN
ejpam-5353	325	42	c3(1	c3(1	NOUN
ejpam-5353	325	43	,	,	PUNCT
ejpam-5353	325	44	0	0	NUM
ejpam-5353	325	45	,	,	PUNCT
ejpam-5353	325	46	n−	n−	NOUN
ejpam-5353	325	47	3	3	NUM
ejpam-5353	325	48	)	)	PUNCT
ejpam-5353	325	49	.	.	PUNCT
ejpam-5353	326	1	theorem	theorem	NOUN
ejpam-5353	326	2	15	15	NUM
ejpam-5353	326	3	.	.	PUNCT
ejpam-5353	327	1	let	let	VERB
ejpam-5353	327	2	p	p	PRON
ejpam-5353	327	3	≥	≥	NOUN
ejpam-5353	327	4	5	5	NUM
ejpam-5353	327	5	to	to	PART
ejpam-5353	327	6	be	be	AUX
ejpam-5353	327	7	prime	prime	ADJ
ejpam-5353	327	8	integer	integer	NOUN
ejpam-5353	327	9	,	,	PUNCT
ejpam-5353	327	10	then	then	ADV
ejpam-5353	327	11	there	there	PRON
ejpam-5353	327	12	is	be	VERB
ejpam-5353	327	13	a	a	DET
ejpam-5353	327	14	symmetric	symmetric	ADJ
ejpam-5353	327	15	base	base	NOUN
ejpam-5353	327	16	of	of	ADP
ejpam-5353	327	17	an	an	DET
ejpam-5353	327	18	odc	odc	NOUN
ejpam-5353	327	19	of	of	ADP
ejpam-5353	327	20	kp	kp	PROPN
ejpam-5353	327	21	,	,	PUNCT
ejpam-5353	327	22	p	p	NOUN
ejpam-5353	327	23	by	by	ADP
ejpam-5353	327	24	c5(0	c5(0	PROPN
ejpam-5353	327	25	,	,	PUNCT
ejpam-5353	327	26	0	0	NUM
ejpam-5353	327	27	,	,	PUNCT
ejpam-5353	327	28	0	0	NUM
ejpam-5353	327	29	,	,	PUNCT
ejpam-5353	327	30	0	0	NUM
ejpam-5353	327	31	,	,	PUNCT
ejpam-5353	327	32	0	0	NUM
ejpam-5353	327	33	)	)	PUNCT
ejpam-5353	327	34	∪	∪	NOUN
ejpam-5353	327	35	(	(	PUNCT
ejpam-5353	327	36	p−	p−	NOUN
ejpam-5353	327	37	4)c2(0	4)c2(0	NUM
ejpam-5353	327	38	,	,	PUNCT
ejpam-5353	327	39	0	0	NUM
ejpam-5353	327	40	)	)	PUNCT
ejpam-5353	327	41	.	.	PUNCT
ejpam-5353	328	1	proof	proof	NOUN
ejpam-5353	328	2	.	.	PUNCT
ejpam-5353	329	1	for	for	ADP
ejpam-5353	329	2	a	a	DET
ejpam-5353	329	3	prime	prime	ADJ
ejpam-5353	329	4	integer	integer	NOUN
ejpam-5353	329	5	p	p	PROPN
ejpam-5353	329	6	≥	≥	NUM
ejpam-5353	329	7	5	5	NUM
ejpam-5353	329	8	,	,	PUNCT
ejpam-5353	329	9	the	the	DET
ejpam-5353	329	10	vector	vector	NOUN
ejpam-5353	329	11	v(g	v(g	PROPN
ejpam-5353	329	12	)	)	PUNCT
ejpam-5353	329	13	of	of	ADP
ejpam-5353	329	14	the	the	DET
ejpam-5353	329	15	base	base	NOUN
ejpam-5353	329	16	g	g	NOUN
ejpam-5353	329	17	is	be	AUX
ejpam-5353	329	18	defined	define	VERB
ejpam-5353	329	19	as	as	ADP
ejpam-5353	329	20	:	:	PUNCT
ejpam-5353	329	21	vi(g	vi(g	NUM
ejpam-5353	329	22	)	)	PUNCT
ejpam-5353	330	1	=	=	PRON
ejpam-5353	330	2	{	{	PUNCT
ejpam-5353	330	3	i−	i−	PROPN
ejpam-5353	330	4	1	1	NUM
ejpam-5353	330	5	if	if	SCONJ
ejpam-5353	330	6	i	i	PRON
ejpam-5353	330	7	=	=	NOUN
ejpam-5353	330	8	1	1	NUM
ejpam-5353	330	9	,	,	PUNCT
ejpam-5353	330	10	p−	p−	NOUN
ejpam-5353	330	11	1	1	NUM
ejpam-5353	330	12	3	3	NUM
ejpam-5353	330	13	+	+	CCONJ
ejpam-5353	330	14	i	i	PRON
ejpam-5353	330	15	otherwise	otherwise	ADV
ejpam-5353	330	16	hence	hence	ADV
ejpam-5353	330	17	,	,	PUNCT
ejpam-5353	330	18	v−i(g	v−i(g	PROPN
ejpam-5353	330	19	)	)	PUNCT
ejpam-5353	331	1	=	=	PRON
ejpam-5353	331	2	{	{	PUNCT
ejpam-5353	331	3	−i−	−i−	ADV
ejpam-5353	331	4	1	1	NUM
ejpam-5353	331	5	if	if	SCONJ
ejpam-5353	331	6	i	i	PRON
ejpam-5353	331	7	=	=	NOUN
ejpam-5353	331	8	1	1	NUM
ejpam-5353	331	9	,	,	PUNCT
ejpam-5353	331	10	p−	p−	NOUN
ejpam-5353	331	11	1	1	NUM
ejpam-5353	331	12	3−	3−	NUM
ejpam-5353	331	13	i	i	PRON
ejpam-5353	331	14	otherwise	otherwise	ADV
ejpam-5353	331	15	for	for	ADP
ejpam-5353	331	16	any	any	DET
ejpam-5353	331	17	i	i	PROPN
ejpam-5353	331	18	∈	∈	PROPN
ejpam-5353	331	19	zp	zp	PROPN
ejpam-5353	331	20	,	,	PUNCT
ejpam-5353	331	21	vi−v−i+	vi−v−i+	PROPN
ejpam-5353	332	1	i	i	NOUN
ejpam-5353	332	2	=	=	NOUN
ejpam-5353	332	3	3i	3i	NOUN
ejpam-5353	332	4	,	,	PUNCT
ejpam-5353	332	5	since	since	SCONJ
ejpam-5353	332	6	gcd(3	gcd(3	NOUN
ejpam-5353	332	7	,	,	PUNCT
ejpam-5353	332	8	p	p	X
ejpam-5353	332	9	)	)	PUNCT
ejpam-5353	332	10	=	=	SYM
ejpam-5353	332	11	1	1	NUM
ejpam-5353	332	12	,	,	PUNCT
ejpam-5353	332	13	by	by	ADP
ejpam-5353	332	14	theorem	theorem	NOUN
ejpam-5353	332	15	3	3	NUM
ejpam-5353	332	16	,	,	PUNCT
ejpam-5353	332	17	g	g	PROPN
ejpam-5353	332	18	is	be	AUX
ejpam-5353	332	19	a	a	DET
ejpam-5353	332	20	symmetric	symmetric	ADJ
ejpam-5353	332	21	base	base	NOUN
ejpam-5353	332	22	.	.	PUNCT
ejpam-5353	333	1	by	by	ADP
ejpam-5353	333	2	the	the	DET
ejpam-5353	333	3	definition	definition	NOUN
ejpam-5353	333	4	of	of	ADP
ejpam-5353	333	5	v(g	v(g	PROPN
ejpam-5353	333	6	)	)	PUNCT
ejpam-5353	333	7	,	,	PUNCT
ejpam-5353	333	8	the	the	DET
ejpam-5353	333	9	base	base	NOUN
ejpam-5353	333	10	g	g	NOUN
ejpam-5353	333	11	∼=	∼=	PROPN
ejpam-5353	333	12	c5(0	c5(0	NOUN
ejpam-5353	333	13	,	,	PUNCT
ejpam-5353	333	14	0	0	NUM
ejpam-5353	333	15	,	,	PUNCT
ejpam-5353	333	16	0	0	NUM
ejpam-5353	333	17	,	,	PUNCT
ejpam-5353	333	18	0	0	NUM
ejpam-5353	333	19	,	,	PUNCT
ejpam-5353	333	20	0	0	NUM
ejpam-5353	333	21	)	)	PUNCT
ejpam-5353	333	22	∪	∪	NOUN
ejpam-5353	333	23	(	(	PUNCT
ejpam-5353	333	24	p−	p−	NOUN
ejpam-5353	333	25	4)c2(0	4)c2(0	NUM
ejpam-5353	333	26	,	,	PUNCT
ejpam-5353	333	27	0	0	NUM
ejpam-5353	333	28	)	)	PUNCT
ejpam-5353	333	29	.	.	PUNCT
ejpam-5353	334	1	h.	h.	PROPN
ejpam-5353	334	2	shabana	shabana	PROPN
ejpam-5353	334	3	,	,	PUNCT
ejpam-5353	334	4	r.	r.	PROPN
ejpam-5353	334	5	el	el	PROPN
ejpam-5353	334	6	-	-	PROPN
ejpam-5353	334	7	shanawany	shanawany	NOUN
ejpam-5353	334	8	,	,	PUNCT
ejpam-5353	334	9	s.	s.	PROPN
ejpam-5353	334	10	halawa	halawa	PROPN
ejpam-5353	334	11	/	/	PUNCT
ejpam-5353	334	12	eur	eur	PROPN
ejpam-5353	334	13	.	.	PUNCT
ejpam-5353	335	1	j.	j.	PROPN
ejpam-5353	335	2	pure	pure	PROPN
ejpam-5353	335	3	appl	appl	PROPN
ejpam-5353	335	4	.	.	PROPN
ejpam-5353	335	5	math	math	PROPN
ejpam-5353	335	6	,	,	PUNCT
ejpam-5353	335	7	17	17	NUM
ejpam-5353	335	8	(	(	PUNCT
ejpam-5353	335	9	4	4	NUM
ejpam-5353	335	10	)	)	PUNCT
ejpam-5353	335	11	(	(	PUNCT
ejpam-5353	335	12	2024	2024	NUM
ejpam-5353	335	13	)	)	PUNCT
ejpam-5353	335	14	,	,	PUNCT
ejpam-5353	335	15	3492	3492	NUM
ejpam-5353	335	16	-	-	SYM
ejpam-5353	335	17	3516	3516	NUM
ejpam-5353	335	18	3504	3504	NUM
ejpam-5353	335	19	theorem	theorem	VERB
ejpam-5353	335	20	16	16	NUM
ejpam-5353	335	21	.	.	PUNCT
ejpam-5353	336	1	let	let	VERB
ejpam-5353	336	2	p	p	PRON
ejpam-5353	336	3	≥	≥	NOUN
ejpam-5353	336	4	5	5	NUM
ejpam-5353	336	5	to	to	PART
ejpam-5353	336	6	be	be	AUX
ejpam-5353	336	7	prime	prime	ADJ
ejpam-5353	336	8	integer	integer	NOUN
ejpam-5353	336	9	such	such	ADJ
ejpam-5353	336	10	that	that	SCONJ
ejpam-5353	336	11	p	p	NOUN
ejpam-5353	336	12	=	=	SYM
ejpam-5353	336	13	5	5	NUM
ejpam-5353	336	14	+	+	NUM
ejpam-5353	336	15	6n	6n	NOUN
ejpam-5353	336	16	,	,	PUNCT
ejpam-5353	336	17	and	and	CCONJ
ejpam-5353	336	18	n	n	PRON
ejpam-5353	336	19	be	be	AUX
ejpam-5353	336	20	a	a	DET
ejpam-5353	336	21	non	non	ADJ
ejpam-5353	336	22	negative	negative	ADJ
ejpam-5353	336	23	integer	integer	NOUN
ejpam-5353	336	24	,	,	PUNCT
ejpam-5353	336	25	such	such	ADJ
ejpam-5353	336	26	that	that	SCONJ
ejpam-5353	336	27	n	n	PRON
ejpam-5353	336	28	̸=	̸=	PROPN
ejpam-5353	336	29	0mod	0mod	PROPN
ejpam-5353	336	30	5	5	NUM
ejpam-5353	336	31	,	,	PUNCT
ejpam-5353	336	32	then	then	ADV
ejpam-5353	336	33	there	there	PRON
ejpam-5353	336	34	is	be	VERB
ejpam-5353	336	35	a	a	DET
ejpam-5353	336	36	symmetric	symmetric	ADJ
ejpam-5353	336	37	base	base	NOUN
ejpam-5353	336	38	of	of	ADP
ejpam-5353	336	39	an	an	DET
ejpam-5353	336	40	odc	odc	NOUN
ejpam-5353	336	41	of	of	ADP
ejpam-5353	336	42	kp	kp	PROPN
ejpam-5353	336	43	,	,	PUNCT
ejpam-5353	336	44	p	p	NOUN
ejpam-5353	336	45	by	by	ADP
ejpam-5353	336	46	c3(0	c3(0	PROPN
ejpam-5353	336	47	,	,	PUNCT
ejpam-5353	336	48	0	0	NUM
ejpam-5353	336	49	,	,	PUNCT
ejpam-5353	336	50	0	0	NUM
ejpam-5353	336	51	)	)	PUNCT
ejpam-5353	336	52	∪	∪	ADP
ejpam-5353	336	53	cp−1(0	cp−1(0	PRON
ejpam-5353	336	54	,	,	PUNCT
ejpam-5353	336	55	0	0	NUM
ejpam-5353	336	56	,	,	PUNCT
ejpam-5353	336	57	·	·	PUNCT
ejpam-5353	336	58	·	·	PUNCT
ejpam-5353	336	59	·	·	PUNCT
ejpam-5353	336	60	,	,	PUNCT
ejpam-5353	336	61	0︸	0︸	PUNCT
ejpam-5353	337	1	︷︷	︷︷	PROPN
ejpam-5353	337	2	︸	︸	X
ejpam-5353	337	3	p−1	p−1	PROPN
ejpam-5353	337	4	times	time	NOUN
ejpam-5353	337	5	)	)	PUNCT
ejpam-5353	337	6	.	.	PUNCT
ejpam-5353	338	1	proof	proof	NOUN
ejpam-5353	338	2	.	.	PUNCT
ejpam-5353	339	1	for	for	ADP
ejpam-5353	339	2	all	all	DET
ejpam-5353	339	3	prime	prime	ADJ
ejpam-5353	339	4	integers	integer	NOUN
ejpam-5353	339	5	p	p	NOUN
ejpam-5353	339	6	≥	≥	NUM
ejpam-5353	339	7	5	5	NUM
ejpam-5353	339	8	,	,	PUNCT
ejpam-5353	339	9	p	p	NOUN
ejpam-5353	339	10	=	=	SYM
ejpam-5353	339	11	5	5	NUM
ejpam-5353	339	12	+	+	NUM
ejpam-5353	339	13	6n	6n	NOUN
ejpam-5353	339	14	,	,	PUNCT
ejpam-5353	339	15	and	and	CCONJ
ejpam-5353	339	16	a	a	DET
ejpam-5353	339	17	non	non	X
ejpam-5353	339	18	negative	negative	ADJ
ejpam-5353	339	19	integer	integer	NOUN
ejpam-5353	339	20	n	n	CCONJ
ejpam-5353	339	21	̸=	̸=	PROPN
ejpam-5353	339	22	0mod	0mod	PROPN
ejpam-5353	339	23	5.the	5.the	DET
ejpam-5353	339	24	vector	vector	NOUN
ejpam-5353	339	25	v(g	v(g	PROPN
ejpam-5353	339	26	)	)	PUNCT
ejpam-5353	339	27	of	of	ADP
ejpam-5353	339	28	the	the	DET
ejpam-5353	339	29	base	base	NOUN
ejpam-5353	339	30	g	g	PROPN
ejpam-5353	339	31	can	can	AUX
ejpam-5353	339	32	be	be	AUX
ejpam-5353	339	33	defined	define	VERB
ejpam-5353	339	34	as	as	ADP
ejpam-5353	339	35	:	:	PUNCT
ejpam-5353	339	36	vi(g	vi(g	NUM
ejpam-5353	339	37	)	)	PUNCT
ejpam-5353	340	1	=	=	PRON
ejpam-5353	340	2	{	{	PUNCT
ejpam-5353	340	3	0	0	NUM
ejpam-5353	340	4	if	if	SCONJ
ejpam-5353	340	5	i	i	PRON
ejpam-5353	340	6	=	=	SYM
ejpam-5353	340	7	0	0	NUM
ejpam-5353	340	8	i2	i2	PROPN
ejpam-5353	340	9	+	+	X
ejpam-5353	340	10	i+	i+	NUM
ejpam-5353	340	11	1	1	NUM
ejpam-5353	340	12	otherwise	otherwise	ADV
ejpam-5353	340	13	,	,	PUNCT
ejpam-5353	340	14	hence	hence	ADV
ejpam-5353	340	15	,	,	PUNCT
ejpam-5353	340	16	v−i(g	v−i(g	PROPN
ejpam-5353	340	17	)	)	PUNCT
ejpam-5353	341	1	=	=	PRON
ejpam-5353	342	1	{	{	PUNCT
ejpam-5353	342	2	0	0	NUM
ejpam-5353	342	3	if	if	SCONJ
ejpam-5353	342	4	i	i	PRON
ejpam-5353	342	5	=	=	SYM
ejpam-5353	342	6	0	0	NUM
ejpam-5353	342	7	i2	i2	PROPN
ejpam-5353	342	8	−	−	PROPN
ejpam-5353	342	9	i+	i+	NUM
ejpam-5353	342	10	1	1	NUM
ejpam-5353	342	11	otherwise	otherwise	ADV
ejpam-5353	342	12	from	from	ADP
ejpam-5353	342	13	the	the	DET
ejpam-5353	342	14	definition	definition	NOUN
ejpam-5353	342	15	of	of	ADP
ejpam-5353	342	16	vi(g	vi(g	NOUN
ejpam-5353	342	17	)	)	PUNCT
ejpam-5353	342	18	and	and	CCONJ
ejpam-5353	342	19	v−i(g	v−i(g	NOUN
ejpam-5353	342	20	)	)	PUNCT
ejpam-5353	342	21	,	,	PUNCT
ejpam-5353	342	22	{	{	PUNCT
ejpam-5353	342	23	vi	vi	NOUN
ejpam-5353	342	24	−	−	NOUN
ejpam-5353	342	25	v−i	v−i	NOUN
ejpam-5353	343	1	+	+	CCONJ
ejpam-5353	343	2	i	i	PRON
ejpam-5353	343	3	;	;	PUNCT
ejpam-5353	343	4	i	i	PROPN
ejpam-5353	343	5	∈	∈	PROPN
ejpam-5353	343	6	zp	zp	X
ejpam-5353	343	7	}	}	PUNCT
ejpam-5353	343	8	=	=	PROPN
ejpam-5353	343	9	zp	zp	X
ejpam-5353	343	10	.	.	PUNCT
ejpam-5353	343	11	by	by	ADP
ejpam-5353	343	12	theorem	theorem	NOUN
ejpam-5353	343	13	3	3	NUM
ejpam-5353	343	14	,	,	PUNCT
ejpam-5353	343	15	the	the	DET
ejpam-5353	343	16	base	base	NOUN
ejpam-5353	343	17	v(g	v(g	NOUN
ejpam-5353	343	18	)	)	PUNCT
ejpam-5353	343	19	is	be	AUX
ejpam-5353	343	20	symmetric	symmetric	ADJ
ejpam-5353	343	21	.	.	PUNCT
ejpam-5353	344	1	moreover	moreover	ADV
ejpam-5353	344	2	,	,	PUNCT
ejpam-5353	344	3	the	the	DET
ejpam-5353	344	4	edges	edge	NOUN
ejpam-5353	344	5	set	set	VERB
ejpam-5353	344	6	e(g	e(g	PROPN
ejpam-5353	344	7	)	)	PUNCT
ejpam-5353	344	8	of	of	ADP
ejpam-5353	344	9	the	the	DET
ejpam-5353	344	10	base	base	NOUN
ejpam-5353	344	11	g	g	PROPN
ejpam-5353	344	12	can	can	AUX
ejpam-5353	344	13	be	be	AUX
ejpam-5353	344	14	represented	represent	VERB
ejpam-5353	344	15	by	by	ADP
ejpam-5353	344	16	:	:	PUNCT
ejpam-5353	344	17	e(g	e(g	PROPN
ejpam-5353	344	18	)	)	PUNCT
ejpam-5353	345	1	=	=	PRON
ejpam-5353	345	2	{	{	PUNCT
ejpam-5353	345	3	(	(	PUNCT
ejpam-5353	345	4	00	00	NUM
ejpam-5353	345	5	,	,	PUNCT
ejpam-5353	345	6	01	01	NUM
ejpam-5353	345	7	)	)	PUNCT
ejpam-5353	345	8	,	,	PUNCT
ejpam-5353	345	9	(	(	PUNCT
ejpam-5353	345	10	10	10	NUM
ejpam-5353	345	11	,	,	PUNCT
ejpam-5353	345	12	01	01	NUM
ejpam-5353	345	13	)	)	PUNCT
ejpam-5353	345	14	}	}	PUNCT
ejpam-5353	345	15	∪	∪	VERB
ejpam-5353	345	16	{	{	PUNCT
ejpam-5353	345	17	(	(	PUNCT
ejpam-5353	345	18	(	(	PUNCT
ejpam-5353	345	19	i2	i2	PROPN
ejpam-5353	345	20	+	+	CCONJ
ejpam-5353	345	21	i+	i+	NUM
ejpam-5353	345	22	1)0	1)0	NOUN
ejpam-5353	345	23	,	,	PUNCT
ejpam-5353	345	24	(	(	PUNCT
ejpam-5353	345	25	(	(	PUNCT
ejpam-5353	345	26	i+	i+	X
ejpam-5353	345	27	1)2	1)2	NUM
ejpam-5353	345	28	)	)	PUNCT
ejpam-5353	345	29	1	1	NUM
ejpam-5353	345	30	)	)	PUNCT
ejpam-5353	345	31	;	;	PUNCT
ejpam-5353	345	32	1	1	NUM
ejpam-5353	345	33	≤	≤	NUM
ejpam-5353	345	34	i	i	X
ejpam-5353	345	35	≤	≤	ADJ
ejpam-5353	345	36	p−	p−	NOUN
ejpam-5353	345	37	2	2	NUM
ejpam-5353	345	38	}	}	PUNCT
ejpam-5353	345	39	thus	thus	ADV
ejpam-5353	345	40	the	the	DET
ejpam-5353	345	41	graph	graph	NOUN
ejpam-5353	345	42	g	g	ADP
ejpam-5353	345	43	∼=	∼=	PROPN
ejpam-5353	345	44	c3(0	c3(0	PROPN
ejpam-5353	345	45	,	,	PUNCT
ejpam-5353	345	46	0	0	NUM
ejpam-5353	345	47	,	,	PUNCT
ejpam-5353	345	48	0	0	NUM
ejpam-5353	345	49	)	)	PUNCT
ejpam-5353	345	50	∪	∪	ADP
ejpam-5353	345	51	cp−1(0	cp−1(0	PRON
ejpam-5353	345	52	,	,	PUNCT
ejpam-5353	345	53	0	0	NUM
ejpam-5353	345	54	,	,	PUNCT
ejpam-5353	345	55	·	·	PUNCT
ejpam-5353	345	56	·	·	PUNCT
ejpam-5353	345	57	·	·	PUNCT
ejpam-5353	345	58	,	,	PUNCT
ejpam-5353	345	59	0︸	0︸	PUNCT
ejpam-5353	345	60	︷︷	︷︷	PROPN
ejpam-5353	345	61	︸	︸	X
ejpam-5353	345	62	p−1	p−1	PROPN
ejpam-5353	345	63	times	time	NOUN
ejpam-5353	345	64	)	)	PUNCT
ejpam-5353	345	65	.	.	PUNCT
ejpam-5353	346	1	theorem	theorem	NOUN
ejpam-5353	346	2	17	17	NUM
ejpam-5353	346	3	.	.	PUNCT
ejpam-5353	347	1	let	let	VERB
ejpam-5353	347	2	m	m	PRON
ejpam-5353	347	3	≥	≥	NOUN
ejpam-5353	347	4	2	2	NUM
ejpam-5353	347	5	,	,	PUNCT
ejpam-5353	347	6	then	then	ADV
ejpam-5353	347	7	there	there	PRON
ejpam-5353	347	8	is	be	VERB
ejpam-5353	347	9	a	a	DET
ejpam-5353	347	10	symmetric	symmetric	ADJ
ejpam-5353	347	11	base	base	NOUN
ejpam-5353	347	12	of	of	ADP
ejpam-5353	347	13	an	an	DET
ejpam-5353	347	14	odc	odc	NOUN
ejpam-5353	347	15	of	of	ADP
ejpam-5353	347	16	km+3,m+3	km+3,m+3	PUNCT
ejpam-5353	347	17	by	by	ADP
ejpam-5353	347	18	g	g	NOUN
ejpam-5353	347	19	∼=	∼=	PROPN
ejpam-5353	347	20	c4(0	c4(0	NOUN
ejpam-5353	347	21	,	,	PUNCT
ejpam-5353	347	22	0	0	NUM
ejpam-5353	347	23	,	,	PUNCT
ejpam-5353	347	24	1,m−	1,m−	NUM
ejpam-5353	347	25	1	1	NUM
ejpam-5353	347	26	)	)	PUNCT
ejpam-5353	347	27	.	.	PUNCT
ejpam-5353	348	1	proof	proof	NOUN
ejpam-5353	348	2	.	.	PUNCT
ejpam-5353	349	1	for	for	ADP
ejpam-5353	349	2	a	a	DET
ejpam-5353	349	3	positive	positive	ADJ
ejpam-5353	349	4	integer	integer	NOUN
ejpam-5353	349	5	m	m	VERB
ejpam-5353	349	6	≥	≥	NOUN
ejpam-5353	349	7	2,the	2,the	NUM
ejpam-5353	349	8	vector	vector	NOUN
ejpam-5353	349	9	v(g	v(g	PROPN
ejpam-5353	349	10	)	)	PUNCT
ejpam-5353	349	11	of	of	ADP
ejpam-5353	349	12	the	the	DET
ejpam-5353	349	13	base	base	NOUN
ejpam-5353	349	14	g	g	PROPN
ejpam-5353	349	15	in	in	ADP
ejpam-5353	349	16	km+3,m+3	km+3,m+3	PRON
ejpam-5353	349	17	can	can	AUX
ejpam-5353	349	18	be	be	AUX
ejpam-5353	349	19	defined	define	VERB
ejpam-5353	349	20	as	as	ADP
ejpam-5353	349	21	:	:	PUNCT
ejpam-5353	349	22	vi(g	vi(g	NUM
ejpam-5353	349	23	)	)	PUNCT
ejpam-5353	349	24	=	=	PUNCT
ejpam-5353	350	1			PUNCT
ejpam-5353	350	2	0	0	PUNCT
ejpam-5353	350	3	if	if	SCONJ
ejpam-5353	350	4	i	i	PRON
ejpam-5353	350	5	=	=	NOUN
ejpam-5353	350	6	0	0	NUM
ejpam-5353	350	7	,	,	PUNCT
ejpam-5353	350	8	1	1	NUM
ejpam-5353	350	9	2	2	NUM
ejpam-5353	350	10	if	if	SCONJ
ejpam-5353	350	11	i	i	PRON
ejpam-5353	350	12	=	=	PUNCT
ejpam-5353	350	13	m+	m+	NUM
ejpam-5353	350	14	2	2	NUM
ejpam-5353	350	15	xj	xj	PROPN
ejpam-5353	350	16	if	if	SCONJ
ejpam-5353	350	17	i	i	PRON
ejpam-5353	350	18	∈	∈	PROPN
ejpam-5353	350	19	{	{	PUNCT
ejpam-5353	350	20	2	2	NUM
ejpam-5353	350	21	,	,	PUNCT
ejpam-5353	350	22	3	3	NUM
ejpam-5353	350	23	,	,	PUNCT
ejpam-5353	350	24	·	·	PUNCT
ejpam-5353	350	25	·	·	PUNCT
ejpam-5353	350	26	·	·	PUNCT
ejpam-5353	350	27	,	,	PUNCT
ejpam-5353	350	28	m+	m+	NOUN
ejpam-5353	350	29	1	1	NUM
ejpam-5353	350	30	}	}	PUNCT
ejpam-5353	350	31	,	,	PUNCT
ejpam-5353	350	32	j	j	PROPN
ejpam-5353	350	33	=	=	SYM
ejpam-5353	350	34	i−	i−	PROPN
ejpam-5353	350	35	2	2	NUM
ejpam-5353	350	36	,	,	PUNCT
ejpam-5353	350	37	where	where	SCONJ
ejpam-5353	350	38	xj	xj	PROPN
ejpam-5353	350	39	=	=	PROPN
ejpam-5353	350	40	1−	1−	NUM
ejpam-5353	350	41	j	j	PROPN
ejpam-5353	350	42	,	,	PUNCT
ejpam-5353	350	43	for	for	ADP
ejpam-5353	350	44	j	j	PROPN
ejpam-5353	350	45	∈	∈	PROPN
ejpam-5353	350	46	{	{	PUNCT
ejpam-5353	350	47	0	0	NUM
ejpam-5353	350	48	,	,	PUNCT
ejpam-5353	350	49	1	1	NUM
ejpam-5353	350	50	,	,	PUNCT
ejpam-5353	350	51	2	2	NUM
ejpam-5353	350	52	,	,	PUNCT
ejpam-5353	350	53	·	·	PUNCT
ejpam-5353	350	54	·	·	PUNCT
ejpam-5353	350	55	·	·	PUNCT
ejpam-5353	350	56	,	,	PUNCT
ejpam-5353	350	57	m−	m−	PROPN
ejpam-5353	350	58	1	1	NUM
ejpam-5353	350	59	}	}	PUNCT
ejpam-5353	350	60	.	.	PUNCT
ejpam-5353	351	1	moreover	moreover	ADV
ejpam-5353	351	2	,	,	PUNCT
ejpam-5353	351	3	vi	vi	ADJ
ejpam-5353	351	4	−	−	NOUN
ejpam-5353	352	1	v−i	v−i	NOUN
ejpam-5353	353	1	+	+	CCONJ
ejpam-5353	353	2	i	i	PRON
ejpam-5353	353	3	=	=	PUNCT
ejpam-5353	354	1			PUNCT
ejpam-5353	354	2	0	0	PUNCT
ejpam-5353	354	3	if	if	SCONJ
ejpam-5353	354	4	i	i	PRON
ejpam-5353	354	5	=	=	NOUN
ejpam-5353	354	6	0	0	PUNCT
ejpam-5353	355	1	−	−	PROPN
ejpam-5353	355	2	i	i	PRON
ejpam-5353	355	3	if	if	SCONJ
ejpam-5353	355	4	i	i	PRON
ejpam-5353	355	5	∈	∈	PROPN
ejpam-5353	355	6	{	{	PUNCT
ejpam-5353	355	7	1,m+	1,m+	NUM
ejpam-5353	355	8	2	2	NUM
ejpam-5353	355	9	}	}	PUNCT
ejpam-5353	355	10	xj	xj	NOUN
ejpam-5353	355	11	−	−	PROPN
ejpam-5353	355	12	xm−(j+1	xm−(j+1	PROPN
ejpam-5353	355	13	)	)	PUNCT
ejpam-5353	356	1	+	+	CCONJ
ejpam-5353	356	2	i	i	PRON
ejpam-5353	357	1	if	if	SCONJ
ejpam-5353	357	2	i	i	PRON
ejpam-5353	357	3	=	=	SYM
ejpam-5353	357	4	j	j	PROPN
ejpam-5353	357	5	+	+	PROPN
ejpam-5353	357	6	2	2	NUM
ejpam-5353	357	7	;	;	PUNCT
ejpam-5353	357	8	j	j	PROPN
ejpam-5353	357	9	∈	∈	PROPN
ejpam-5353	357	10	{	{	PUNCT
ejpam-5353	357	11	0	0	NUM
ejpam-5353	357	12	,	,	PUNCT
ejpam-5353	357	13	1	1	NUM
ejpam-5353	357	14	,	,	PUNCT
ejpam-5353	357	15	2	2	NUM
ejpam-5353	357	16	,	,	PUNCT
ejpam-5353	357	17	·	·	PUNCT
ejpam-5353	357	18	·	·	PUNCT
ejpam-5353	357	19	·	·	PUNCT
ejpam-5353	357	20	,	,	PUNCT
ejpam-5353	357	21	m−	m−	PROPN
ejpam-5353	357	22	1	1	NUM
ejpam-5353	357	23	}	}	PUNCT
ejpam-5353	357	24	.	.	PUNCT
ejpam-5353	358	1	hence	hence	ADV
ejpam-5353	358	2	,	,	PUNCT
ejpam-5353	358	3	{	{	PUNCT
ejpam-5353	358	4	vi	vi	NOUN
ejpam-5353	358	5	−	−	NOUN
ejpam-5353	358	6	v−i	v−i	NOUN
ejpam-5353	358	7	+	+	CCONJ
ejpam-5353	358	8	i	i	PRON
ejpam-5353	358	9	;	;	PUNCT
ejpam-5353	358	10	i	i	PRON
ejpam-5353	358	11	∈	∈	VERB
ejpam-5353	358	12	zm+3	zm+3	NUM
ejpam-5353	358	13	}	}	PUNCT
ejpam-5353	358	14	=	=	SYM
ejpam-5353	358	15	zm+3	zm+3	X
ejpam-5353	358	16	.	.	PUNCT
ejpam-5353	358	17	by	by	ADP
ejpam-5353	358	18	theorem	theorem	NOUN
ejpam-5353	358	19	3	3	NUM
ejpam-5353	358	20	,	,	PUNCT
ejpam-5353	358	21	the	the	DET
ejpam-5353	358	22	base	base	NOUN
ejpam-5353	358	23	v(g	v(g	NOUN
ejpam-5353	358	24	)	)	PUNCT
ejpam-5353	358	25	is	be	AUX
ejpam-5353	358	26	symmetric	symmetric	ADJ
ejpam-5353	358	27	.	.	PUNCT
ejpam-5353	359	1	moreover	moreover	ADV
ejpam-5353	359	2	,	,	PUNCT
ejpam-5353	359	3	the	the	DET
ejpam-5353	359	4	edges	edge	NOUN
ejpam-5353	359	5	set	set	VERB
ejpam-5353	359	6	e(g	e(g	PROPN
ejpam-5353	359	7	)	)	PUNCT
ejpam-5353	359	8	of	of	ADP
ejpam-5353	359	9	the	the	DET
ejpam-5353	359	10	base	base	NOUN
ejpam-5353	359	11	g	g	PROPN
ejpam-5353	359	12	can	can	AUX
ejpam-5353	359	13	be	be	AUX
ejpam-5353	359	14	represented	represent	VERB
ejpam-5353	359	15	by	by	ADP
ejpam-5353	359	16	:	:	PUNCT
ejpam-5353	359	17	h.	h.	PROPN
ejpam-5353	359	18	shabana	shabana	PROPN
ejpam-5353	359	19	,	,	PUNCT
ejpam-5353	359	20	r.	r.	PROPN
ejpam-5353	359	21	el	el	PROPN
ejpam-5353	359	22	-	-	PROPN
ejpam-5353	359	23	shanawany	shanawany	NOUN
ejpam-5353	359	24	,	,	PUNCT
ejpam-5353	359	25	s.	s.	PROPN
ejpam-5353	359	26	halawa	halawa	PROPN
ejpam-5353	359	27	/	/	PUNCT
ejpam-5353	359	28	eur	eur	PROPN
ejpam-5353	359	29	.	.	PUNCT
ejpam-5353	360	1	j.	j.	PROPN
ejpam-5353	360	2	pure	pure	PROPN
ejpam-5353	360	3	appl	appl	PROPN
ejpam-5353	360	4	.	.	PROPN
ejpam-5353	360	5	math	math	PROPN
ejpam-5353	360	6	,	,	PUNCT
ejpam-5353	360	7	17	17	NUM
ejpam-5353	360	8	(	(	PUNCT
ejpam-5353	360	9	4	4	NUM
ejpam-5353	360	10	)	)	PUNCT
ejpam-5353	360	11	(	(	PUNCT
ejpam-5353	360	12	2024	2024	NUM
ejpam-5353	360	13	)	)	PUNCT
ejpam-5353	360	14	,	,	PUNCT
ejpam-5353	360	15	3492	3492	NUM
ejpam-5353	360	16	-	-	SYM
ejpam-5353	360	17	3516	3516	NUM
ejpam-5353	360	18	3505	3505	NUM
ejpam-5353	360	19	e(g	e(g	NOUN
ejpam-5353	360	20	)	)	PUNCT
ejpam-5353	361	1	=	=	PRON
ejpam-5353	361	2	{	{	PUNCT
ejpam-5353	361	3	(	(	PUNCT
ejpam-5353	361	4	00	00	NUM
ejpam-5353	361	5	,	,	PUNCT
ejpam-5353	361	6	01	01	NUM
ejpam-5353	361	7	)	)	PUNCT
ejpam-5353	361	8	,	,	PUNCT
ejpam-5353	361	9	(	(	PUNCT
ejpam-5353	361	10	10	10	NUM
ejpam-5353	361	11	,	,	PUNCT
ejpam-5353	361	12	31	31	NUM
ejpam-5353	361	13	)	)	PUNCT
ejpam-5353	361	14	}	}	PUNCT
ejpam-5353	361	15	∪	∪	X
ejpam-5353	361	16	(	(	PUNCT
ejpam-5353	361	17	20	20	NUM
ejpam-5353	361	18	,	,	PUNCT
ejpam-5353	361	19	11	11	NUM
ejpam-5353	361	20	)	)	PUNCT
ejpam-5353	361	21	,	,	PUNCT
ejpam-5353	361	22	(	(	PUNCT
ejpam-5353	361	23	11	11	NUM
ejpam-5353	361	24	,	,	PUNCT
ejpam-5353	361	25	00	00	NUM
ejpam-5353	361	26	)	)	PUNCT
ejpam-5353	361	27	,	,	PUNCT
ejpam-5353	361	28	(	(	PUNCT
ejpam-5353	361	29	00	00	NUM
ejpam-5353	361	30	,	,	PUNCT
ejpam-5353	361	31	31	31	NUM
ejpam-5353	361	32	)	)	PUNCT
ejpam-5353	361	33	}	}	PUNCT
ejpam-5353	361	34	∪{((31	∪{((31	NOUN
ejpam-5353	361	35	,	,	PUNCT
ejpam-5353	361	36	(	(	PUNCT
ejpam-5353	361	37	3−	3−	NUM
ejpam-5353	361	38	i)0	i)0	NOUN
ejpam-5353	361	39	)	)	PUNCT
ejpam-5353	361	40	:	:	PUNCT
ejpam-5353	361	41	4	4	NUM
ejpam-5353	361	42	≤	≤	NUM
ejpam-5353	361	43	i	i	PRON
ejpam-5353	361	44	≤	≤	NUM
ejpam-5353	361	45	m+	m+	NUM
ejpam-5353	361	46	1	1	NUM
ejpam-5353	361	47	}	}	PUNCT
ejpam-5353	361	48	that	that	PRON
ejpam-5353	361	49	yields	yield	VERB
ejpam-5353	361	50	g	g	PROPN
ejpam-5353	361	51	∼=	∼=	PROPN
ejpam-5353	361	52	c4(0	c4(0	NOUN
ejpam-5353	361	53	,	,	PUNCT
ejpam-5353	361	54	0	0	NUM
ejpam-5353	361	55	,	,	PUNCT
ejpam-5353	361	56	1,m−	1,m−	NUM
ejpam-5353	361	57	1	1	NUM
ejpam-5353	361	58	)	)	PUNCT
ejpam-5353	361	59	.	.	PUNCT
ejpam-5353	362	1	theorem	theorem	NOUN
ejpam-5353	362	2	18	18	NUM
ejpam-5353	362	3	.	.	PUNCT
ejpam-5353	363	1	let	let	VERB
ejpam-5353	363	2	p	p	PRON
ejpam-5353	363	3	to	to	PART
ejpam-5353	363	4	be	be	AUX
ejpam-5353	363	5	a	a	DET
ejpam-5353	363	6	prime	prime	ADJ
ejpam-5353	363	7	integer	integer	NOUN
ejpam-5353	363	8	s.t	s.t	PROPN
ejpam-5353	363	9	p	p	PROPN
ejpam-5353	363	10	≥	≥	NUM
ejpam-5353	363	11	13	13	NUM
ejpam-5353	363	12	,	,	PUNCT
ejpam-5353	363	13	and	and	CCONJ
ejpam-5353	363	14	m	m	PROPN
ejpam-5353	363	15	=	=	VERB
ejpam-5353	363	16	n−	n−	NOUN
ejpam-5353	363	17	3	3	NUM
ejpam-5353	363	18	.	.	PUNCT
ejpam-5353	364	1	then	then	ADV
ejpam-5353	364	2	there	there	PRON
ejpam-5353	364	3	is	be	VERB
ejpam-5353	364	4	an	an	DET
ejpam-5353	364	5	odc	odc	NOUN
ejpam-5353	364	6	of	of	ADP
ejpam-5353	364	7	kp	kp	PROPN
ejpam-5353	364	8	,	,	PUNCT
ejpam-5353	364	9	p	p	NOUN
ejpam-5353	364	10	by	by	ADP
ejpam-5353	364	11	c4(0	c4(0	PROPN
ejpam-5353	364	12	,	,	PUNCT
ejpam-5353	364	13	0	0	NUM
ejpam-5353	364	14	,	,	PUNCT
ejpam-5353	364	15	0	0	NUM
ejpam-5353	364	16	,	,	PUNCT
ejpam-5353	364	17	0	0	NUM
ejpam-5353	364	18	)	)	PUNCT
ejpam-5353	364	19	∪	∪	ADP
ejpam-5353	364	20	2c3(0	2c3(0	NUM
ejpam-5353	364	21	,	,	PUNCT
ejpam-5353	364	22	0	0	NUM
ejpam-5353	364	23	,	,	PUNCT
ejpam-5353	364	24	0	0	NUM
ejpam-5353	364	25	)	)	PUNCT
ejpam-5353	364	26	∪	∪	NOUN
ejpam-5353	364	27	(	(	PUNCT
ejpam-5353	364	28	p−	p−	NOUN
ejpam-5353	364	29	7)c2(0	7)c2(0	NOUN
ejpam-5353	364	30	,	,	PUNCT
ejpam-5353	364	31	0	0	NUM
ejpam-5353	364	32	,	,	PUNCT
ejpam-5353	364	33	)	)	PUNCT
ejpam-5353	364	34	.	.	PUNCT
ejpam-5353	365	1	proof	proof	NOUN
ejpam-5353	365	2	.	.	PUNCT
ejpam-5353	366	1	for	for	ADP
ejpam-5353	366	2	a	a	DET
ejpam-5353	366	3	prime	prime	ADJ
ejpam-5353	366	4	integer	integer	NOUN
ejpam-5353	366	5	p	p	PROPN
ejpam-5353	366	6	≥	≥	NUM
ejpam-5353	366	7	13	13	NUM
ejpam-5353	366	8	,	,	PUNCT
ejpam-5353	366	9	the	the	DET
ejpam-5353	366	10	vectors	vector	NOUN
ejpam-5353	366	11	v(g	v(g	ADJ
ejpam-5353	366	12	)	)	PUNCT
ejpam-5353	366	13	and	and	CCONJ
ejpam-5353	366	14	u(f	u(f	NOUN
ejpam-5353	366	15	)	)	PUNCT
ejpam-5353	366	16	of	of	ADP
ejpam-5353	366	17	the	the	DET
ejpam-5353	366	18	bases	basis	NOUN
ejpam-5353	366	19	g	g	PROPN
ejpam-5353	366	20	and	and	CCONJ
ejpam-5353	366	21	f	f	PROPN
ejpam-5353	366	22	are	be	AUX
ejpam-5353	366	23	defined	define	VERB
ejpam-5353	366	24	as	as	ADP
ejpam-5353	366	25	:	:	PUNCT
ejpam-5353	366	26	vi(g	vi(g	X
ejpam-5353	366	27	)	)	PUNCT
ejpam-5353	367	1	=	=	PUNCT
ejpam-5353	368	1			PUNCT
ejpam-5353	368	2	i	i	PRON
ejpam-5353	368	3	if	if	SCONJ
ejpam-5353	368	4	i	i	PRON
ejpam-5353	368	5	=	=	NOUN
ejpam-5353	368	6	0	0	NUM
ejpam-5353	368	7	,	,	PUNCT
ejpam-5353	368	8	p−	p−	NOUN
ejpam-5353	368	9	1	1	NUM
ejpam-5353	368	10	3	3	NUM
ejpam-5353	368	11	if	if	SCONJ
ejpam-5353	368	12	i	i	PRON
ejpam-5353	368	13	=	=	SYM
ejpam-5353	368	14	1	1	NUM
ejpam-5353	368	15	xj	xj	NOUN
ejpam-5353	368	16	+	+	NOUN
ejpam-5353	368	17	3i	3i	NOUN
ejpam-5353	368	18	if	if	SCONJ
ejpam-5353	368	19	i	i	PRON
ejpam-5353	368	20	=	=	SYM
ejpam-5353	368	21	j	j	PROPN
ejpam-5353	368	22	+	+	CCONJ
ejpam-5353	368	23	2	2	NUM
ejpam-5353	368	24	,	,	PUNCT
ejpam-5353	368	25	j	j	PROPN
ejpam-5353	368	26	∈	∈	PROPN
ejpam-5353	368	27	{	{	PUNCT
ejpam-5353	368	28	0	0	NUM
ejpam-5353	368	29	,	,	PUNCT
ejpam-5353	368	30	1	1	NUM
ejpam-5353	368	31	,	,	PUNCT
ejpam-5353	368	32	2	2	NUM
ejpam-5353	368	33	,	,	PUNCT
ejpam-5353	368	34	·	·	PUNCT
ejpam-5353	368	35	·	·	PUNCT
ejpam-5353	368	36	·	·	PUNCT
ejpam-5353	368	37	,	,	PUNCT
ejpam-5353	368	38	m−	m−	PROPN
ejpam-5353	368	39	1	1	NUM
ejpam-5353	368	40	}	}	PUNCT
ejpam-5353	368	41	,	,	PUNCT
ejpam-5353	368	42	and	and	CCONJ
ejpam-5353	368	43	ui(f	ui(f	PUNCT
ejpam-5353	368	44	)	)	PUNCT
ejpam-5353	368	45	=	=	PUNCT
ejpam-5353	369	1			PUNCT
ejpam-5353	369	2	0	0	PUNCT
ejpam-5353	370	1	if	if	SCONJ
ejpam-5353	370	2	i	i	PRON
ejpam-5353	370	3	=	=	VERB
ejpam-5353	370	4	0	0	PUNCT
ejpam-5353	371	1	(	(	PUNCT
ejpam-5353	371	2	n−	n−	NOUN
ejpam-5353	371	3	2	2	NUM
ejpam-5353	371	4	)	)	PUNCT
ejpam-5353	371	5	if	if	SCONJ
ejpam-5353	371	6	i	i	PRON
ejpam-5353	371	7	=	=	NOUN
ejpam-5353	371	8	1	1	NUM
ejpam-5353	371	9	2−	2−	NUM
ejpam-5353	371	10	2i	2i	NOUN
ejpam-5353	371	11	if	if	SCONJ
ejpam-5353	371	12	i	i	PRON
ejpam-5353	371	13	=	=	NOUN
ejpam-5353	372	1	p−	p−	NOUN
ejpam-5353	372	2	1	1	NUM
ejpam-5353	372	3	xj	xj	NOUN
ejpam-5353	372	4	−	−	PROPN
ejpam-5353	372	5	2i	2i	NOUN
ejpam-5353	372	6	if	if	SCONJ
ejpam-5353	372	7	i	i	PRON
ejpam-5353	372	8	=	=	SYM
ejpam-5353	372	9	j	j	PROPN
ejpam-5353	373	1	+	+	CCONJ
ejpam-5353	373	2	2	2	NUM
ejpam-5353	373	3	,	,	PUNCT
ejpam-5353	373	4	j	j	PROPN
ejpam-5353	373	5	∈	∈	PROPN
ejpam-5353	373	6	{	{	PUNCT
ejpam-5353	373	7	0	0	NUM
ejpam-5353	373	8	,	,	PUNCT
ejpam-5353	373	9	1	1	NUM
ejpam-5353	373	10	,	,	PUNCT
ejpam-5353	373	11	2	2	NUM
ejpam-5353	373	12	,	,	PUNCT
ejpam-5353	373	13	·	·	PUNCT
ejpam-5353	373	14	·	·	PUNCT
ejpam-5353	373	15	·	·	PUNCT
ejpam-5353	373	16	,	,	PUNCT
ejpam-5353	373	17	m−	m−	PROPN
ejpam-5353	373	18	1	1	NUM
ejpam-5353	373	19	}	}	PUNCT
ejpam-5353	373	20	,	,	PUNCT
ejpam-5353	373	21	for	for	ADP
ejpam-5353	373	22	all	all	DET
ejpam-5353	373	23	i	i	PRON
ejpam-5353	373	24	∈	∈	PROPN
ejpam-5353	373	25	zp	zp	PROPN
ejpam-5353	373	26	,	,	PUNCT
ejpam-5353	373	27	vi(g	vi(g	NOUN
ejpam-5353	373	28	)	)	PUNCT
ejpam-5353	373	29	−	−	NOUN
ejpam-5353	373	30	ui(f	ui(f	PUNCT
ejpam-5353	373	31	)	)	PUNCT
ejpam-5353	374	1	=	=	SYM
ejpam-5353	374	2	5i	5i	NUM
ejpam-5353	374	3	.	.	PUNCT
ejpam-5353	375	1	by	by	ADP
ejpam-5353	375	2	theorem	theorem	NOUN
ejpam-5353	375	3	4	4	NUM
ejpam-5353	375	4	,	,	PUNCT
ejpam-5353	375	5	then	then	ADV
ejpam-5353	375	6	the	the	DET
ejpam-5353	375	7	two	two	NUM
ejpam-5353	375	8	bases	basis	NOUN
ejpam-5353	375	9	v(g	v(g	ADJ
ejpam-5353	375	10	)	)	PUNCT
ejpam-5353	375	11	and	and	CCONJ
ejpam-5353	375	12	u(f	u(f	NOUN
ejpam-5353	375	13	)	)	PUNCT
ejpam-5353	375	14	are	be	AUX
ejpam-5353	375	15	orthogonal	orthogonal	ADJ
ejpam-5353	375	16	.	.	PUNCT
ejpam-5353	376	1	moreover	moreover	ADV
ejpam-5353	376	2	the	the	DET
ejpam-5353	376	3	edges	edge	NOUN
ejpam-5353	376	4	set	set	VERB
ejpam-5353	376	5	e(g	e(g	PROPN
ejpam-5353	376	6	)	)	PUNCT
ejpam-5353	376	7	and	and	CCONJ
ejpam-5353	376	8	e(f	e(f	PROPN
ejpam-5353	376	9	)	)	PUNCT
ejpam-5353	376	10	of	of	ADP
ejpam-5353	376	11	the	the	DET
ejpam-5353	376	12	bases	basis	NOUN
ejpam-5353	376	13	g	g	PROPN
ejpam-5353	376	14	and	and	CCONJ
ejpam-5353	376	15	f	f	PROPN
ejpam-5353	376	16	respectively	respectively	ADV
ejpam-5353	376	17	can	can	AUX
ejpam-5353	376	18	be	be	AUX
ejpam-5353	376	19	represented	represent	VERB
ejpam-5353	376	20	by	by	ADP
ejpam-5353	376	21	:	:	PUNCT
ejpam-5353	376	22	e(g	e(g	PROPN
ejpam-5353	376	23	)	)	PUNCT
ejpam-5353	377	1	=	=	PRON
ejpam-5353	377	2	{	{	PUNCT
ejpam-5353	377	3	(	(	PUNCT
ejpam-5353	377	4	00	00	NUM
ejpam-5353	377	5	,	,	PUNCT
ejpam-5353	377	6	01	01	NUM
ejpam-5353	377	7	)	)	PUNCT
ejpam-5353	377	8	,	,	PUNCT
ejpam-5353	377	9	(	(	PUNCT
ejpam-5353	377	10	(	(	PUNCT
ejpam-5353	377	11	p−	p−	NOUN
ejpam-5353	377	12	1)0	1)0	NUM
ejpam-5353	377	13	,	,	PUNCT
ejpam-5353	377	14	(	(	PUNCT
ejpam-5353	377	15	p−	p−	NOUN
ejpam-5353	377	16	2)1	2)1	NUM
ejpam-5353	377	17	)	)	PUNCT
ejpam-5353	377	18	,	,	PUNCT
ejpam-5353	377	19	(	(	PUNCT
ejpam-5353	377	20	30	30	NUM
ejpam-5353	377	21	,	,	PUNCT
ejpam-5353	377	22	41	41	NUM
ejpam-5353	377	23	)	)	PUNCT
ejpam-5353	377	24	}	}	PUNCT
ejpam-5353	377	25	∪	∪	VERB
ejpam-5353	377	26	{	{	PUNCT
ejpam-5353	377	27	(	(	PUNCT
ejpam-5353	377	28	(	(	PUNCT
ejpam-5353	377	29	xj	xj	X
ejpam-5353	377	30	+	+	NUM
ejpam-5353	377	31	3i)0	3i)0	NUM
ejpam-5353	377	32	,	,	PUNCT
ejpam-5353	377	33	(	(	PUNCT
ejpam-5353	377	34	xj	xj	X
ejpam-5353	377	35	+	+	NUM
ejpam-5353	377	36	4i)1	4i)1	NUM
ejpam-5353	377	37	)	)	PUNCT
ejpam-5353	377	38	;	;	PUNCT
ejpam-5353	378	1	i	i	PRON
ejpam-5353	378	2	=	=	PUNCT
ejpam-5353	378	3	j	j	PROPN
ejpam-5353	378	4	+	+	CCONJ
ejpam-5353	378	5	2	2	NUM
ejpam-5353	378	6	,	,	PUNCT
ejpam-5353	378	7	j	j	PROPN
ejpam-5353	378	8	∈	∈	PROPN
ejpam-5353	378	9	{	{	PUNCT
ejpam-5353	378	10	0	0	NUM
ejpam-5353	378	11	,	,	PUNCT
ejpam-5353	378	12	1	1	NUM
ejpam-5353	378	13	,	,	PUNCT
ejpam-5353	378	14	2	2	NUM
ejpam-5353	378	15	,	,	PUNCT
ejpam-5353	378	16	·	·	PUNCT
ejpam-5353	378	17	·	·	PUNCT
ejpam-5353	378	18	·	·	PUNCT
ejpam-5353	378	19	,	,	PUNCT
ejpam-5353	378	20	m−	m−	PROPN
ejpam-5353	378	21	1	1	NUM
ejpam-5353	378	22	}	}	PUNCT
ejpam-5353	378	23	}	}	PUNCT
ejpam-5353	378	24	and	and	CCONJ
ejpam-5353	378	25	e(f	e(f	PROPN
ejpam-5353	378	26	)	)	PUNCT
ejpam-5353	379	1	=	=	PRON
ejpam-5353	379	2	{	{	PUNCT
ejpam-5353	379	3	(	(	PUNCT
ejpam-5353	379	4	00	00	NUM
ejpam-5353	379	5	,	,	PUNCT
ejpam-5353	379	6	01	01	NUM
ejpam-5353	379	7	)	)	PUNCT
ejpam-5353	379	8	,	,	PUNCT
ejpam-5353	379	9	(	(	PUNCT
ejpam-5353	379	10	(	(	PUNCT
ejpam-5353	379	11	p−	p−	NOUN
ejpam-5353	379	12	2)0	2)0	NUM
ejpam-5353	379	13	,	,	PUNCT
ejpam-5353	379	14	(	(	PUNCT
ejpam-5353	379	15	p−	p−	NOUN
ejpam-5353	379	16	1)1	1)1	NUM
ejpam-5353	379	17	)	)	PUNCT
ejpam-5353	379	18	,	,	PUNCT
ejpam-5353	379	19	(	(	PUNCT
ejpam-5353	379	20	40	40	NUM
ejpam-5353	379	21	,	,	PUNCT
ejpam-5353	379	22	31	31	NUM
ejpam-5353	379	23	)	)	PUNCT
ejpam-5353	379	24	}	}	PUNCT
ejpam-5353	379	25	∪	∪	VERB
ejpam-5353	379	26	{	{	PUNCT
ejpam-5353	379	27	(	(	PUNCT
ejpam-5353	379	28	(	(	PUNCT
ejpam-5353	379	29	xj	xj	PROPN
ejpam-5353	379	30	−	−	PROPN
ejpam-5353	379	31	2i)0	2i)0	NUM
ejpam-5353	379	32	,	,	PUNCT
ejpam-5353	379	33	(	(	PUNCT
ejpam-5353	379	34	xj	xj	PROPN
ejpam-5353	379	35	−	−	PROPN
ejpam-5353	379	36	i	i	PROPN
ejpam-5353	379	37	)	)	PUNCT
ejpam-5353	379	38	)	)	PUNCT
ejpam-5353	379	39	;	;	PUNCT
ejpam-5353	380	1	i	i	PRON
ejpam-5353	380	2	=	=	PUNCT
ejpam-5353	380	3	j	j	PROPN
ejpam-5353	380	4	+	+	CCONJ
ejpam-5353	380	5	2	2	NUM
ejpam-5353	380	6	,	,	PUNCT
ejpam-5353	380	7	j	j	PROPN
ejpam-5353	380	8	∈	∈	PROPN
ejpam-5353	380	9	{	{	PUNCT
ejpam-5353	380	10	0	0	NUM
ejpam-5353	380	11	,	,	PUNCT
ejpam-5353	380	12	1	1	NUM
ejpam-5353	380	13	,	,	PUNCT
ejpam-5353	380	14	2	2	NUM
ejpam-5353	380	15	,	,	PUNCT
ejpam-5353	380	16	·	·	PUNCT
ejpam-5353	380	17	·	·	PUNCT
ejpam-5353	380	18	·	·	PUNCT
ejpam-5353	380	19	,	,	PUNCT
ejpam-5353	380	20	m−	m−	PROPN
ejpam-5353	380	21	1	1	NUM
ejpam-5353	380	22	}	}	PUNCT
ejpam-5353	380	23	}	}	PUNCT
ejpam-5353	380	24	which	which	PRON
ejpam-5353	380	25	yields	yield	VERB
ejpam-5353	380	26	g	g	ADP
ejpam-5353	380	27	∼=	∼=	PROPN
ejpam-5353	380	28	f	f	NOUN
ejpam-5353	380	29	∼=	∼=	PROPN
ejpam-5353	380	30	c4(0	c4(0	NOUN
ejpam-5353	380	31	,	,	PUNCT
ejpam-5353	380	32	0	0	NUM
ejpam-5353	380	33	,	,	PUNCT
ejpam-5353	380	34	0	0	NUM
ejpam-5353	380	35	,	,	PUNCT
ejpam-5353	380	36	0	0	NUM
ejpam-5353	380	37	)	)	PUNCT
ejpam-5353	380	38	∪	∪	ADP
ejpam-5353	380	39	2c3(0	2c3(0	NUM
ejpam-5353	380	40	,	,	PUNCT
ejpam-5353	380	41	0	0	NUM
ejpam-5353	380	42	,	,	PUNCT
ejpam-5353	380	43	0	0	NUM
ejpam-5353	380	44	)	)	PUNCT
ejpam-5353	380	45	∪	∪	NOUN
ejpam-5353	380	46	(	(	PUNCT
ejpam-5353	380	47	p−	p−	NOUN
ejpam-5353	380	48	7)c2(0	7)c2(0	NOUN
ejpam-5353	380	49	,	,	PUNCT
ejpam-5353	380	50	0	0	NUM
ejpam-5353	380	51	,	,	PUNCT
ejpam-5353	380	52	)	)	PUNCT
ejpam-5353	380	53	.	.	PUNCT
ejpam-5353	381	1	theorem	theorem	NOUN
ejpam-5353	381	2	19	19	NUM
ejpam-5353	381	3	.	.	PUNCT
ejpam-5353	382	1	let	let	VERB
ejpam-5353	382	2	p	p	PRON
ejpam-5353	382	3	≥	≥	NOUN
ejpam-5353	382	4	7	7	NUM
ejpam-5353	382	5	to	to	PART
ejpam-5353	382	6	be	be	AUX
ejpam-5353	382	7	a	a	DET
ejpam-5353	382	8	prime	prime	ADJ
ejpam-5353	382	9	integer	integer	NOUN
ejpam-5353	382	10	,	,	PUNCT
ejpam-5353	382	11	then	then	ADV
ejpam-5353	382	12	there	there	PRON
ejpam-5353	382	13	is	be	VERB
ejpam-5353	382	14	an	an	DET
ejpam-5353	382	15	odc	odc	NOUN
ejpam-5353	382	16	of	of	ADP
ejpam-5353	382	17	kn	kn	PROPN
ejpam-5353	382	18	,	,	PUNCT
ejpam-5353	382	19	n	n	CCONJ
ejpam-5353	382	20	by	by	ADP
ejpam-5353	382	21	2c3(0	2c3(0	NUM
ejpam-5353	382	22	,	,	PUNCT
ejpam-5353	382	23	0	0	NUM
ejpam-5353	382	24	,	,	PUNCT
ejpam-5353	382	25	0	0	NUM
ejpam-5353	382	26	)	)	PUNCT
ejpam-5353	382	27	∪	∪	NOUN
ejpam-5353	382	28	(	(	PUNCT
ejpam-5353	382	29	p−	p−	NOUN
ejpam-5353	382	30	4)c2(0	4)c2(0	NUM
ejpam-5353	382	31	,	,	PUNCT
ejpam-5353	382	32	0	0	NUM
ejpam-5353	382	33	)	)	PUNCT
ejpam-5353	382	34	.	.	PUNCT
ejpam-5353	383	1	proof	proof	NOUN
ejpam-5353	383	2	.	.	PUNCT
ejpam-5353	384	1	for	for	ADP
ejpam-5353	384	2	any	any	DET
ejpam-5353	384	3	prime	prime	ADJ
ejpam-5353	384	4	integer	integer	NOUN
ejpam-5353	384	5	p	p	PROPN
ejpam-5353	384	6	≥	≥	NUM
ejpam-5353	384	7	7	7	NUM
ejpam-5353	384	8	,	,	PUNCT
ejpam-5353	384	9	α1	α1	PROPN
ejpam-5353	384	10	=	=	SYM
ejpam-5353	384	11	⌊3p−7	⌊3p−7	X
ejpam-5353	384	12	10	10	NUM
ejpam-5353	384	13	⌋	⌋	ADJ
ejpam-5353	384	14	,	,	PUNCT
ejpam-5353	384	15	α2	α2	PROPN
ejpam-5353	384	16	=	=	SYM
ejpam-5353	384	17	⌊2p3	⌊2p3	PROPN
ejpam-5353	384	18	⌋	⌋	NOUN
ejpam-5353	384	19	−	−	NOUN
ejpam-5353	385	1	1	1	NUM
ejpam-5353	385	2	,	,	PUNCT
ejpam-5353	385	3	the	the	DET
ejpam-5353	385	4	vectors	vector	NOUN
ejpam-5353	385	5	v(g	v(g	ADJ
ejpam-5353	385	6	)	)	PUNCT
ejpam-5353	385	7	,	,	PUNCT
ejpam-5353	385	8	v(m	v(m	NOUN
ejpam-5353	385	9	)	)	PUNCT
ejpam-5353	385	10	and	and	CCONJ
ejpam-5353	385	11	v(f	v(f	PROPN
ejpam-5353	385	12	)	)	PUNCT
ejpam-5353	385	13	of	of	ADP
ejpam-5353	385	14	the	the	DET
ejpam-5353	385	15	starters	starter	NOUN
ejpam-5353	385	16	g	g	PROPN
ejpam-5353	385	17	,	,	PUNCT
ejpam-5353	385	18	m	m	VERB
ejpam-5353	385	19	and	and	CCONJ
ejpam-5353	385	20	f	f	PROPN
ejpam-5353	385	21	are	be	AUX
ejpam-5353	385	22	defined	define	VERB
ejpam-5353	385	23	as	as	ADP
ejpam-5353	385	24	:	:	PUNCT
ejpam-5353	385	25	case	case	NOUN
ejpam-5353	385	26	1	1	X
ejpam-5353	385	27	.	.	PUNCT
ejpam-5353	386	1	let	let	VERB
ejpam-5353	386	2	p	p	PRON
ejpam-5353	386	3	be	be	AUX
ejpam-5353	386	4	a	a	DET
ejpam-5353	386	5	prime	prime	ADJ
ejpam-5353	386	6	integer	integer	NOUN
ejpam-5353	386	7	such	such	ADJ
ejpam-5353	386	8	that	that	SCONJ
ejpam-5353	386	9	p	p	PROPN
ejpam-5353	386	10	≡	≡	PROPN
ejpam-5353	386	11	1mod	1mod	PROPN
ejpam-5353	386	12	6	6	NUM
ejpam-5353	386	13	and	and	CCONJ
ejpam-5353	386	14	α1be	α1be	NUM
ejpam-5353	386	15	a	a	DET
ejpam-5353	386	16	positive	positive	ADJ
ejpam-5353	386	17	integer	integer	NOUN
ejpam-5353	386	18	α1	α1	PROPN
ejpam-5353	386	19	=	=	SYM
ejpam-5353	386	20	⌊3p−7	⌊3p−7	VERB
ejpam-5353	386	21	10	10	NUM
ejpam-5353	386	22	⌋.	⌋.	NOUN
ejpam-5353	386	23	the	the	DET
ejpam-5353	386	24	vectors	vector	NOUN
ejpam-5353	386	25	v(g	v(g	ADJ
ejpam-5353	386	26	)	)	PUNCT
ejpam-5353	386	27	,	,	PUNCT
ejpam-5353	386	28	u(m	u(m	PROPN
ejpam-5353	386	29	)	)	PUNCT
ejpam-5353	386	30	of	of	ADP
ejpam-5353	386	31	the	the	DET
ejpam-5353	386	32	bases	basis	NOUN
ejpam-5353	386	33	g	g	PROPN
ejpam-5353	386	34	and	and	CCONJ
ejpam-5353	386	35	m	m	PROPN
ejpam-5353	386	36	are	be	AUX
ejpam-5353	386	37	defined	define	VERB
ejpam-5353	386	38	as	as	ADP
ejpam-5353	386	39	:	:	PUNCT
ejpam-5353	386	40	h.	h.	PROPN
ejpam-5353	386	41	shabana	shabana	PROPN
ejpam-5353	386	42	,	,	PUNCT
ejpam-5353	386	43	r.	r.	PROPN
ejpam-5353	386	44	el	el	PROPN
ejpam-5353	386	45	-	-	PROPN
ejpam-5353	386	46	shanawany	shanawany	NOUN
ejpam-5353	386	47	,	,	PUNCT
ejpam-5353	386	48	s.	s.	PROPN
ejpam-5353	386	49	halawa	halawa	PROPN
ejpam-5353	386	50	/	/	PUNCT
ejpam-5353	386	51	eur	eur	PROPN
ejpam-5353	386	52	.	.	PUNCT
ejpam-5353	387	1	j.	j.	PROPN
ejpam-5353	387	2	pure	pure	PROPN
ejpam-5353	387	3	appl	appl	PROPN
ejpam-5353	387	4	.	.	PROPN
ejpam-5353	387	5	math	math	PROPN
ejpam-5353	387	6	,	,	PUNCT
ejpam-5353	387	7	17	17	NUM
ejpam-5353	387	8	(	(	PUNCT
ejpam-5353	387	9	4	4	NUM
ejpam-5353	387	10	)	)	PUNCT
ejpam-5353	387	11	(	(	PUNCT
ejpam-5353	387	12	2024	2024	NUM
ejpam-5353	387	13	)	)	PUNCT
ejpam-5353	387	14	,	,	PUNCT
ejpam-5353	387	15	3492	3492	NUM
ejpam-5353	387	16	-	-	SYM
ejpam-5353	387	17	3516	3516	NUM
ejpam-5353	387	18	3506	3506	NUM
ejpam-5353	387	19	vi(g	vi(g	NOUN
ejpam-5353	387	20	)	)	PUNCT
ejpam-5353	387	21	=	=	PUNCT
ejpam-5353	388	1			PUNCT
ejpam-5353	388	2	0	0	PUNCT
ejpam-5353	388	3	if	if	SCONJ
ejpam-5353	388	4	i	i	PRON
ejpam-5353	388	5	=	=	NOUN
ejpam-5353	388	6	0	0	NUM
ejpam-5353	388	7	,	,	PUNCT
ejpam-5353	388	8	p−	p−	NOUN
ejpam-5353	388	9	2	2	NUM
ejpam-5353	388	10	p−	p−	NOUN
ejpam-5353	388	11	1	1	NUM
ejpam-5353	388	12	if	if	SCONJ
ejpam-5353	388	13	i	i	PRON
ejpam-5353	388	14	=	=	NOUN
ejpam-5353	388	15	1	1	NUM
ejpam-5353	388	16	,	,	PUNCT
ejpam-5353	388	17	p−	p−	NOUN
ejpam-5353	388	18	1	1	NUM
ejpam-5353	388	19	i	i	PRON
ejpam-5353	388	20	otherwise	otherwise	ADV
ejpam-5353	388	21	and	and	CCONJ
ejpam-5353	388	22	ui(m	ui(m	NUM
ejpam-5353	388	23	)	)	PUNCT
ejpam-5353	388	24	=	=	PUNCT
ejpam-5353	388	25			PUNCT
ejpam-5353	388	26	α1i	α1i	NOUN
ejpam-5353	388	27	if	if	SCONJ
ejpam-5353	388	28	i	i	PRON
ejpam-5353	388	29	=	=	NOUN
ejpam-5353	388	30	0	0	NUM
ejpam-5353	388	31	,	,	PUNCT
ejpam-5353	388	32	p−	p−	NOUN
ejpam-5353	388	33	2	2	NUM
ejpam-5353	388	34	α1i−	α1i−	NOUN
ejpam-5353	388	35	1	1	NUM
ejpam-5353	388	36	if	if	SCONJ
ejpam-5353	388	37	i	i	PRON
ejpam-5353	388	38	=	=	NOUN
ejpam-5353	388	39	1	1	NUM
ejpam-5353	388	40	,	,	PUNCT
ejpam-5353	388	41	p−	p−	NOUN
ejpam-5353	388	42	1	1	NUM
ejpam-5353	388	43	(	(	PUNCT
ejpam-5353	388	44	α1	α1	PROPN
ejpam-5353	388	45	+	+	CCONJ
ejpam-5353	388	46	1)i	1)i	NUM
ejpam-5353	388	47	otherwise	otherwise	ADV
ejpam-5353	388	48	therefore	therefore	ADV
ejpam-5353	388	49	,	,	PUNCT
ejpam-5353	388	50	vi(g)−ui(m	vi(g)−ui(m	PROPN
ejpam-5353	388	51	)	)	PUNCT
ejpam-5353	388	52	=	=	PUNCT
ejpam-5353	388	53	−α1i	−α1i	PROPN
ejpam-5353	388	54	for	for	ADP
ejpam-5353	388	55	any	any	DET
ejpam-5353	388	56	i	i	PROPN
ejpam-5353	388	57	∈	∈	PROPN
ejpam-5353	388	58	zp	zp	VERB
ejpam-5353	388	59	.	.	PUNCT
ejpam-5353	388	60	consequently	consequently	ADV
ejpam-5353	388	61	,	,	PUNCT
ejpam-5353	388	62	{	{	PUNCT
ejpam-5353	388	63	vi(g)−ui(m	vi(g)−ui(m	NOUN
ejpam-5353	388	64	)	)	PUNCT
ejpam-5353	388	65	}	}	PUNCT
ejpam-5353	389	1	=	=	SYM
ejpam-5353	389	2	zp	zp	X
ejpam-5353	389	3	.	.	PUNCT
ejpam-5353	389	4	by	by	ADP
ejpam-5353	389	5	theorem	theorem	NOUN
ejpam-5353	389	6	4	4	NUM
ejpam-5353	389	7	,	,	PUNCT
ejpam-5353	389	8	then	then	ADV
ejpam-5353	389	9	the	the	DET
ejpam-5353	389	10	two	two	NUM
ejpam-5353	389	11	bases	basis	NOUN
ejpam-5353	389	12	v(g	v(g	ADJ
ejpam-5353	389	13	)	)	PUNCT
ejpam-5353	389	14	and	and	CCONJ
ejpam-5353	389	15	u(m	u(m	NOUN
ejpam-5353	389	16	)	)	PUNCT
ejpam-5353	389	17	are	be	AUX
ejpam-5353	389	18	orthogonal	orthogonal	ADJ
ejpam-5353	389	19	.	.	PUNCT
ejpam-5353	390	1	moreover	moreover	ADV
ejpam-5353	390	2	,	,	PUNCT
ejpam-5353	390	3	the	the	DET
ejpam-5353	390	4	edges	edge	NOUN
ejpam-5353	390	5	set	set	VERB
ejpam-5353	390	6	e(g	e(g	PROPN
ejpam-5353	390	7	)	)	PUNCT
ejpam-5353	390	8	and	and	CCONJ
ejpam-5353	390	9	e(m	e(m	NOUN
ejpam-5353	390	10	)	)	PUNCT
ejpam-5353	390	11	of	of	ADP
ejpam-5353	390	12	the	the	DET
ejpam-5353	390	13	bases	basis	NOUN
ejpam-5353	390	14	g	g	NOUN
ejpam-5353	390	15	and	and	CCONJ
ejpam-5353	390	16	m	m	VERB
ejpam-5353	390	17	respectively	respectively	ADV
ejpam-5353	390	18	,	,	PUNCT
ejpam-5353	390	19	can	can	AUX
ejpam-5353	390	20	be	be	AUX
ejpam-5353	390	21	represented	represent	VERB
ejpam-5353	390	22	by	by	ADP
ejpam-5353	390	23	:	:	PUNCT
ejpam-5353	390	24	e(g	e(g	PROPN
ejpam-5353	390	25	)	)	PUNCT
ejpam-5353	391	1	=	=	PRON
ejpam-5353	391	2	{	{	PUNCT
ejpam-5353	391	3	(	(	PUNCT
ejpam-5353	391	4	00	00	NUM
ejpam-5353	391	5	,	,	PUNCT
ejpam-5353	391	6	01	01	NUM
ejpam-5353	391	7	)	)	PUNCT
ejpam-5353	391	8	,	,	PUNCT
ejpam-5353	391	9	(	(	PUNCT
ejpam-5353	391	10	00,−21	00,−21	ADJ
ejpam-5353	391	11	)	)	PUNCT
ejpam-5353	391	12	}	}	PUNCT
ejpam-5353	391	13	∪{((p−	∪{((p−	VERB
ejpam-5353	391	14	1)0	1)0	PROPN
ejpam-5353	391	15	,	,	PUNCT
ejpam-5353	391	16	(	(	PUNCT
ejpam-5353	391	17	i−	i−	PROPN
ejpam-5353	391	18	1)1	1)1	NUM
ejpam-5353	391	19	)	)	PUNCT
ejpam-5353	391	20	;	;	PUNCT
ejpam-5353	392	1	i	i	NOUN
ejpam-5353	392	2	=	=	NOUN
ejpam-5353	392	3	1	1	NUM
ejpam-5353	392	4	,	,	PUNCT
ejpam-5353	392	5	p−	p−	NOUN
ejpam-5353	392	6	1	1	NUM
ejpam-5353	392	7	}	}	PUNCT
ejpam-5353	392	8	∪{(i0	∪{(i0	PROPN
ejpam-5353	392	9	,	,	PUNCT
ejpam-5353	392	10	2i1	2i1	NUM
ejpam-5353	392	11	)	)	PUNCT
ejpam-5353	392	12	;	;	PUNCT
ejpam-5353	393	1	i	i	PROPN
ejpam-5353	393	2	∈	∈	PROPN
ejpam-5353	393	3	zn\	zn\	PROPN
ejpam-5353	393	4	{	{	PUNCT
ejpam-5353	393	5	0	0	NUM
ejpam-5353	393	6	,	,	PUNCT
ejpam-5353	393	7	1	1	NUM
ejpam-5353	393	8	,	,	PUNCT
ejpam-5353	393	9	p−	p−	NOUN
ejpam-5353	393	10	2	2	NUM
ejpam-5353	393	11	,	,	PUNCT
ejpam-5353	393	12	p−	p−	NOUN
ejpam-5353	393	13	1	1	NUM
ejpam-5353	393	14	}	}	PUNCT
ejpam-5353	393	15	}	}	PUNCT
ejpam-5353	393	16	e(m	e(m	PROPN
ejpam-5353	393	17	)	)	PUNCT
ejpam-5353	393	18	=	=	PRON
ejpam-5353	393	19	{	{	PUNCT
ejpam-5353	393	20	(	(	PUNCT
ejpam-5353	393	21	(	(	PUNCT
ejpam-5353	393	22	α1i)0	α1i)0	X
ejpam-5353	393	23	,	,	PUNCT
ejpam-5353	393	24	(	(	PUNCT
ejpam-5353	393	25	(	(	PUNCT
ejpam-5353	393	26	α1	α1	PROPN
ejpam-5353	393	27	+	+	CCONJ
ejpam-5353	393	28	1)i)1	1)i)1	NOUN
ejpam-5353	393	29	)	)	PUNCT
ejpam-5353	393	30	;	;	PUNCT
ejpam-5353	393	31	i	i	NOUN
ejpam-5353	393	32	=	=	NOUN
ejpam-5353	393	33	0	0	NUM
ejpam-5353	393	34	,	,	PUNCT
ejpam-5353	393	35	p−	p−	NOUN
ejpam-5353	393	36	2	2	NUM
ejpam-5353	393	37	}	}	PUNCT
ejpam-5353	393	38	∪{((α1i−	∪{((α1i−	NOUN
ejpam-5353	393	39	1)0	1)0	NUM
ejpam-5353	393	40	,	,	PUNCT
ejpam-5353	393	41	(	(	PUNCT
ejpam-5353	393	42	(	(	PUNCT
ejpam-5353	393	43	(	(	PUNCT
ejpam-5353	393	44	α1	α1	X
ejpam-5353	393	45	+	+	CCONJ
ejpam-5353	393	46	1)i)−	1)i)−	NUM
ejpam-5353	393	47	1)1	1)1	NUM
ejpam-5353	393	48	)	)	PUNCT
ejpam-5353	393	49	;	;	PUNCT
ejpam-5353	393	50	i	i	NOUN
ejpam-5353	393	51	=	=	NOUN
ejpam-5353	393	52	1	1	NUM
ejpam-5353	393	53	,	,	PUNCT
ejpam-5353	393	54	p−	p−	NOUN
ejpam-5353	393	55	1	1	NUM
ejpam-5353	393	56	}	}	PUNCT
ejpam-5353	393	57	∪{(((α1	∪{(((α1	NOUN
ejpam-5353	393	58	+	+	CCONJ
ejpam-5353	393	59	1)i)0	1)i)0	NUM
ejpam-5353	393	60	,	,	PUNCT
ejpam-5353	393	61	(	(	PUNCT
ejpam-5353	393	62	(	(	PUNCT
ejpam-5353	393	63	α1	α1	PROPN
ejpam-5353	393	64	+	+	CCONJ
ejpam-5353	393	65	2)i)1	2)i)1	NOUN
ejpam-5353	393	66	)	)	PUNCT
ejpam-5353	393	67	;	;	PUNCT
ejpam-5353	394	1	i	i	PROPN
ejpam-5353	394	2	∈	∈	PROPN
ejpam-5353	394	3	zn\	zn\	PROPN
ejpam-5353	394	4	{	{	PUNCT
ejpam-5353	394	5	0	0	NUM
ejpam-5353	394	6	,	,	PUNCT
ejpam-5353	394	7	1	1	NUM
ejpam-5353	394	8	,	,	PUNCT
ejpam-5353	394	9	p−	p−	NOUN
ejpam-5353	394	10	2	2	NUM
ejpam-5353	394	11	,	,	PUNCT
ejpam-5353	394	12	p−	p−	NOUN
ejpam-5353	394	13	1	1	NUM
ejpam-5353	394	14	}	}	PUNCT
ejpam-5353	394	15	}	}	PUNCT
ejpam-5353	394	16	and	and	CCONJ
ejpam-5353	394	17	hence	hence	ADV
ejpam-5353	394	18	g	g	NOUN
ejpam-5353	394	19	∼=	∼=	PROPN
ejpam-5353	394	20	m	m	VERB
ejpam-5353	394	21	∼=	∼=	NOUN
ejpam-5353	394	22	2c3(0	2c3(0	NUM
ejpam-5353	394	23	,	,	PUNCT
ejpam-5353	394	24	0	0	NUM
ejpam-5353	394	25	,	,	PUNCT
ejpam-5353	394	26	0	0	NUM
ejpam-5353	394	27	)	)	PUNCT
ejpam-5353	394	28	∪	∪	NOUN
ejpam-5353	394	29	(	(	PUNCT
ejpam-5353	394	30	p−	p−	NOUN
ejpam-5353	394	31	4)c2(0	4)c2(0	NUM
ejpam-5353	394	32	,	,	PUNCT
ejpam-5353	394	33	0	0	NUM
ejpam-5353	394	34	)	)	PUNCT
ejpam-5353	394	35	.	.	PUNCT
ejpam-5353	395	1	case	case	NOUN
ejpam-5353	395	2	2	2	X
ejpam-5353	395	3	.	.	PUNCT
ejpam-5353	396	1	let	let	VERB
ejpam-5353	396	2	p	p	PRON
ejpam-5353	396	3	to	to	PART
ejpam-5353	396	4	be	be	AUX
ejpam-5353	396	5	a	a	DET
ejpam-5353	396	6	prime	prime	ADJ
ejpam-5353	396	7	integer	integer	NOUN
ejpam-5353	396	8	such	such	ADJ
ejpam-5353	396	9	that	that	SCONJ
ejpam-5353	396	10	p	p	PROPN
ejpam-5353	396	11	≡	≡	PROPN
ejpam-5353	396	12	5mod	5mod	PRON
ejpam-5353	396	13	6	6	NUM
ejpam-5353	396	14	and	and	CCONJ
ejpam-5353	396	15	α2	α2	ADJ
ejpam-5353	396	16	be	be	AUX
ejpam-5353	396	17	a	a	DET
ejpam-5353	396	18	positive	positive	ADJ
ejpam-5353	396	19	integer	integer	NOUN
ejpam-5353	396	20	α2	α2	NOUN
ejpam-5353	396	21	=	=	SYM
ejpam-5353	396	22	⌊2p3	⌊2p3	PROPN
ejpam-5353	396	23	⌋	⌋	NOUN
ejpam-5353	396	24	−	−	NOUN
ejpam-5353	397	1	1	1	X
ejpam-5353	397	2	.	.	PUNCT
ejpam-5353	398	1	the	the	DET
ejpam-5353	398	2	vectors	vector	NOUN
ejpam-5353	398	3	v(g	v(g	ADJ
ejpam-5353	398	4	)	)	PUNCT
ejpam-5353	398	5	,	,	PUNCT
ejpam-5353	399	1	h(f	h(f	PROPN
ejpam-5353	399	2	)	)	PUNCT
ejpam-5353	399	3	of	of	ADP
ejpam-5353	399	4	the	the	DET
ejpam-5353	399	5	bases	basis	NOUN
ejpam-5353	399	6	g	g	PROPN
ejpam-5353	399	7	and	and	CCONJ
ejpam-5353	399	8	f	f	PROPN
ejpam-5353	399	9	are	be	AUX
ejpam-5353	399	10	defined	define	VERB
ejpam-5353	399	11	as	as	ADP
ejpam-5353	399	12	:	:	PUNCT
ejpam-5353	399	13	vi(g	vi(g	NUM
ejpam-5353	399	14	)	)	PUNCT
ejpam-5353	399	15	=	=	PUNCT
ejpam-5353	400	1			PUNCT
ejpam-5353	400	2	0	0	PUNCT
ejpam-5353	400	3	if	if	SCONJ
ejpam-5353	400	4	i	i	PRON
ejpam-5353	400	5	=	=	NOUN
ejpam-5353	400	6	0	0	NUM
ejpam-5353	400	7	,	,	PUNCT
ejpam-5353	400	8	p−	p−	NOUN
ejpam-5353	400	9	2	2	NUM
ejpam-5353	400	10	p−	p−	NOUN
ejpam-5353	400	11	1	1	NUM
ejpam-5353	400	12	if	if	SCONJ
ejpam-5353	400	13	i	i	PRON
ejpam-5353	400	14	=	=	NOUN
ejpam-5353	400	15	1	1	NUM
ejpam-5353	400	16	,	,	PUNCT
ejpam-5353	400	17	p−	p−	NOUN
ejpam-5353	400	18	1	1	NUM
ejpam-5353	400	19	i	i	PRON
ejpam-5353	400	20	otherwise	otherwise	ADV
ejpam-5353	400	21	and	and	CCONJ
ejpam-5353	400	22	hi(f	hi(f	ADV
ejpam-5353	400	23	)	)	PUNCT
ejpam-5353	400	24	=	=	PUNCT
ejpam-5353	401	1			PUNCT
ejpam-5353	401	2	α2i	α2i	NUM
ejpam-5353	401	3	if	if	SCONJ
ejpam-5353	401	4	i	i	PRON
ejpam-5353	401	5	=	=	NOUN
ejpam-5353	401	6	0	0	NUM
ejpam-5353	401	7	,	,	PUNCT
ejpam-5353	401	8	p−	p−	NOUN
ejpam-5353	401	9	2	2	NUM
ejpam-5353	401	10	α2i−	α2i−	PROPN
ejpam-5353	401	11	1	1	NUM
ejpam-5353	401	12	if	if	SCONJ
ejpam-5353	401	13	i	i	PRON
ejpam-5353	401	14	=	=	NOUN
ejpam-5353	401	15	1	1	NUM
ejpam-5353	401	16	,	,	PUNCT
ejpam-5353	401	17	p−	p−	NOUN
ejpam-5353	401	18	1	1	NUM
ejpam-5353	401	19	(	(	PUNCT
ejpam-5353	401	20	α2	α2	ADJ
ejpam-5353	401	21	+	+	CCONJ
ejpam-5353	401	22	1)i	1)i	NUM
ejpam-5353	401	23	otherwise	otherwise	ADV
ejpam-5353	401	24	therefore	therefore	ADV
ejpam-5353	401	25	,	,	PUNCT
ejpam-5353	401	26	vi(g)−hi(f	vi(g)−hi(f	NOUN
ejpam-5353	401	27	)	)	PUNCT
ejpam-5353	401	28	=	=	PUNCT
ejpam-5353	402	1	−α2i	−α2i	NUM
ejpam-5353	402	2	for	for	ADP
ejpam-5353	402	3	any	any	DET
ejpam-5353	402	4	i	i	PROPN
ejpam-5353	402	5	∈	∈	PROPN
ejpam-5353	402	6	zp	zp	VERB
ejpam-5353	402	7	.	.	PUNCT
ejpam-5353	402	8	consequently	consequently	ADV
ejpam-5353	402	9	,	,	PUNCT
ejpam-5353	402	10	{	{	PUNCT
ejpam-5353	402	11	vi(g)−hi(f	vi(g)−hi(f	NOUN
ejpam-5353	402	12	)	)	PUNCT
ejpam-5353	402	13	}	}	PUNCT
ejpam-5353	403	1	=	=	SYM
ejpam-5353	403	2	zp	zp	X
ejpam-5353	403	3	.	.	PUNCT
ejpam-5353	403	4	by	by	ADP
ejpam-5353	403	5	theorem	theorem	NOUN
ejpam-5353	403	6	4	4	NUM
ejpam-5353	403	7	,	,	PUNCT
ejpam-5353	403	8	then	then	ADV
ejpam-5353	403	9	the	the	DET
ejpam-5353	403	10	two	two	NUM
ejpam-5353	403	11	bases	basis	NOUN
ejpam-5353	403	12	v(g	v(g	ADJ
ejpam-5353	403	13	)	)	PUNCT
ejpam-5353	403	14	and	and	CCONJ
ejpam-5353	403	15	h(f	h(f	PROPN
ejpam-5353	403	16	)	)	PUNCT
ejpam-5353	403	17	are	be	AUX
ejpam-5353	403	18	orthogonal	orthogonal	ADJ
ejpam-5353	403	19	.	.	PUNCT
ejpam-5353	404	1	moreover	moreover	ADV
ejpam-5353	404	2	,	,	PUNCT
ejpam-5353	404	3	the	the	DET
ejpam-5353	404	4	edges	edge	NOUN
ejpam-5353	404	5	set	set	VERB
ejpam-5353	404	6	e(f	e(f	PROPN
ejpam-5353	404	7	)	)	PUNCT
ejpam-5353	404	8	of	of	ADP
ejpam-5353	404	9	the	the	DET
ejpam-5353	404	10	basis	basis	NOUN
ejpam-5353	404	11	f	f	NOUN
ejpam-5353	404	12	can	can	AUX
ejpam-5353	404	13	be	be	AUX
ejpam-5353	404	14	represented	represent	VERB
ejpam-5353	404	15	by	by	ADP
ejpam-5353	404	16	:	:	PUNCT
ejpam-5353	404	17	e(f	e(f	PROPN
ejpam-5353	404	18	)	)	PUNCT
ejpam-5353	405	1	=	=	PRON
ejpam-5353	405	2	{	{	PUNCT
ejpam-5353	405	3	(	(	PUNCT
ejpam-5353	405	4	(	(	PUNCT
ejpam-5353	405	5	α2i)0	α2i)0	PROPN
ejpam-5353	405	6	,	,	PUNCT
ejpam-5353	405	7	(	(	PUNCT
ejpam-5353	405	8	(	(	PUNCT
ejpam-5353	405	9	α2	α2	ADJ
ejpam-5353	405	10	+	+	CCONJ
ejpam-5353	405	11	1)i)1	1)i)1	NOUN
ejpam-5353	405	12	)	)	PUNCT
ejpam-5353	405	13	;	;	PUNCT
ejpam-5353	406	1	i	i	NOUN
ejpam-5353	406	2	=	=	NOUN
ejpam-5353	406	3	0	0	NUM
ejpam-5353	406	4	,	,	PUNCT
ejpam-5353	406	5	p−	p−	NOUN
ejpam-5353	406	6	2	2	NUM
ejpam-5353	406	7	}	}	PUNCT
ejpam-5353	406	8	∪{((α2i−	∪{((α2i−	VERB
ejpam-5353	406	9	1)0	1)0	NUM
ejpam-5353	406	10	,	,	PUNCT
ejpam-5353	406	11	(	(	PUNCT
ejpam-5353	406	12	(	(	PUNCT
ejpam-5353	406	13	(	(	PUNCT
ejpam-5353	406	14	α2	α2	ADJ
ejpam-5353	406	15	+	+	CCONJ
ejpam-5353	406	16	1)i)−	1)i)−	NUM
ejpam-5353	406	17	1)1	1)1	NUM
ejpam-5353	406	18	)	)	PUNCT
ejpam-5353	406	19	;	;	PUNCT
ejpam-5353	407	1	i	i	NOUN
ejpam-5353	407	2	=	=	NOUN
ejpam-5353	407	3	1	1	NUM
ejpam-5353	407	4	,	,	PUNCT
ejpam-5353	407	5	p−	p−	NOUN
ejpam-5353	407	6	1	1	NUM
ejpam-5353	407	7	}	}	PUNCT
ejpam-5353	407	8	∪{(((α2	∪{(((α2	PUNCT
ejpam-5353	407	9	+	+	NUM
ejpam-5353	407	10	1)i)0	1)i)0	NUM
ejpam-5353	407	11	,	,	PUNCT
ejpam-5353	407	12	(	(	PUNCT
ejpam-5353	407	13	(	(	PUNCT
ejpam-5353	407	14	α2	α2	ADJ
ejpam-5353	407	15	+	+	CCONJ
ejpam-5353	407	16	2)i)1	2)i)1	NOUN
ejpam-5353	407	17	)	)	PUNCT
ejpam-5353	407	18	;	;	PUNCT
ejpam-5353	407	19	i	i	PROPN
ejpam-5353	407	20	∈	∈	PROPN
ejpam-5353	407	21	zn\	zn\	PROPN
ejpam-5353	407	22	{	{	PUNCT
ejpam-5353	407	23	0	0	NUM
ejpam-5353	407	24	,	,	PUNCT
ejpam-5353	407	25	1	1	NUM
ejpam-5353	407	26	,	,	PUNCT
ejpam-5353	407	27	p−	p−	NOUN
ejpam-5353	407	28	2	2	NUM
ejpam-5353	407	29	,	,	PUNCT
ejpam-5353	407	30	p−	p−	NOUN
ejpam-5353	407	31	1	1	NUM
ejpam-5353	407	32	}	}	PUNCT
ejpam-5353	407	33	}	}	PUNCT
ejpam-5353	407	34	and	and	CCONJ
ejpam-5353	407	35	hence	hence	ADV
ejpam-5353	407	36	f	f	PROPN
ejpam-5353	407	37	∼=	∼=	PROPN
ejpam-5353	407	38	2c3(0	2c3(0	NUM
ejpam-5353	407	39	,	,	PUNCT
ejpam-5353	407	40	0	0	NUM
ejpam-5353	407	41	,	,	PUNCT
ejpam-5353	407	42	0	0	NUM
ejpam-5353	407	43	)	)	PUNCT
ejpam-5353	407	44	∪	∪	NOUN
ejpam-5353	407	45	(	(	PUNCT
ejpam-5353	407	46	p−	p−	NOUN
ejpam-5353	407	47	4)c2(0	4)c2(0	NUM
ejpam-5353	407	48	,	,	PUNCT
ejpam-5353	407	49	0	0	NUM
ejpam-5353	407	50	)	)	PUNCT
ejpam-5353	407	51	.	.	PUNCT
ejpam-5353	408	1	h.	h.	PROPN
ejpam-5353	408	2	shabana	shabana	PROPN
ejpam-5353	408	3	,	,	PUNCT
ejpam-5353	408	4	r.	r.	PROPN
ejpam-5353	408	5	el	el	PROPN
ejpam-5353	408	6	-	-	PROPN
ejpam-5353	408	7	shanawany	shanawany	NOUN
ejpam-5353	408	8	,	,	PUNCT
ejpam-5353	408	9	s.	s.	PROPN
ejpam-5353	408	10	halawa	halawa	PROPN
ejpam-5353	408	11	/	/	PUNCT
ejpam-5353	408	12	eur	eur	PROPN
ejpam-5353	408	13	.	.	PUNCT
ejpam-5353	409	1	j.	j.	PROPN
ejpam-5353	409	2	pure	pure	PROPN
ejpam-5353	409	3	appl	appl	PROPN
ejpam-5353	409	4	.	.	PROPN
ejpam-5353	409	5	math	math	PROPN
ejpam-5353	409	6	,	,	PUNCT
ejpam-5353	409	7	17	17	NUM
ejpam-5353	409	8	(	(	PUNCT
ejpam-5353	409	9	4	4	NUM
ejpam-5353	409	10	)	)	PUNCT
ejpam-5353	409	11	(	(	PUNCT
ejpam-5353	409	12	2024	2024	NUM
ejpam-5353	409	13	)	)	PUNCT
ejpam-5353	409	14	,	,	PUNCT
ejpam-5353	409	15	3492	3492	NUM
ejpam-5353	409	16	-	-	SYM
ejpam-5353	409	17	3516	3516	NUM
ejpam-5353	409	18	3507	3507	NUM
ejpam-5353	409	19	theorem	theorem	VERB
ejpam-5353	409	20	20	20	NUM
ejpam-5353	409	21	.	.	PUNCT
ejpam-5353	410	1	let	let	VERB
ejpam-5353	410	2	p	p	PRON
ejpam-5353	410	3	>	>	X
ejpam-5353	410	4	7	7	NUM
ejpam-5353	410	5	to	to	PART
ejpam-5353	410	6	be	be	AUX
ejpam-5353	410	7	a	a	DET
ejpam-5353	410	8	prime	prime	ADJ
ejpam-5353	410	9	integer	integer	NOUN
ejpam-5353	410	10	,	,	PUNCT
ejpam-5353	410	11	then	then	ADV
ejpam-5353	410	12	there	there	PRON
ejpam-5353	410	13	is	be	VERB
ejpam-5353	410	14	an	an	DET
ejpam-5353	410	15	odc	odc	NOUN
ejpam-5353	410	16	of	of	ADP
ejpam-5353	410	17	kn	kn	PROPN
ejpam-5353	410	18	,	,	PUNCT
ejpam-5353	410	19	n	n	CCONJ
ejpam-5353	410	20	by	by	ADP
ejpam-5353	410	21	c3(1	c3(1	NOUN
ejpam-5353	410	22	,	,	PUNCT
ejpam-5353	410	23	p−	p−	NOUN
ejpam-5353	410	24	4	4	NUM
ejpam-5353	410	25	,	,	PUNCT
ejpam-5353	410	26	1	1	NUM
ejpam-5353	410	27	)	)	PUNCT
ejpam-5353	410	28	∪	∪	NOUN
ejpam-5353	410	29	(	(	PUNCT
ejpam-5353	410	30	p−	p−	NOUN
ejpam-5353	410	31	5)c2(0	5)c2(0	NOUN
ejpam-5353	410	32	,	,	PUNCT
ejpam-5353	410	33	0	0	NUM
ejpam-5353	410	34	)	)	PUNCT
ejpam-5353	410	35	.	.	PUNCT
ejpam-5353	411	1	proof	proof	NOUN
ejpam-5353	411	2	.	.	PUNCT
ejpam-5353	412	1	case	case	NOUN
ejpam-5353	412	2	1	1	NUM
ejpam-5353	412	3	.	.	X
ejpam-5353	413	1	for	for	ADP
ejpam-5353	413	2	any	any	DET
ejpam-5353	413	3	prime	prime	ADJ
ejpam-5353	413	4	integer	integer	NOUN
ejpam-5353	413	5	p	p	PROPN
ejpam-5353	413	6	>	>	X
ejpam-5353	413	7	7	7	NUM
ejpam-5353	414	1	such	such	ADJ
ejpam-5353	414	2	that	that	SCONJ
ejpam-5353	414	3	p	p	PROPN
ejpam-5353	414	4	≡	≡	PROPN
ejpam-5353	415	1	5mod	5mod	PRON
ejpam-5353	415	2	6	6	NUM
ejpam-5353	415	3	and	and	CCONJ
ejpam-5353	415	4	a	a	DET
ejpam-5353	415	5	positive	positive	ADJ
ejpam-5353	415	6	integer	integer	NOUN
ejpam-5353	415	7	α1	α1	PROPN
ejpam-5353	415	8	=	=	SYM
ejpam-5353	415	9	⌊p3⌋	⌊p3⌋	PROPN
ejpam-5353	415	10	,	,	PUNCT
ejpam-5353	415	11	the	the	DET
ejpam-5353	415	12	vectors	vector	NOUN
ejpam-5353	415	13	v(g	v(g	ADJ
ejpam-5353	415	14	)	)	PUNCT
ejpam-5353	415	15	and	and	CCONJ
ejpam-5353	415	16	u(m	u(m	NOUN
ejpam-5353	415	17	)	)	PUNCT
ejpam-5353	415	18	of	of	ADP
ejpam-5353	415	19	the	the	DET
ejpam-5353	415	20	bases	basis	NOUN
ejpam-5353	415	21	g	g	PROPN
ejpam-5353	415	22	and	and	CCONJ
ejpam-5353	415	23	m	m	PROPN
ejpam-5353	415	24	are	be	AUX
ejpam-5353	415	25	defined	define	VERB
ejpam-5353	415	26	as	as	ADP
ejpam-5353	415	27	:	:	PUNCT
ejpam-5353	415	28	vi(g	vi(g	NUM
ejpam-5353	415	29	)	)	PUNCT
ejpam-5353	415	30	=	=	PUNCT
ejpam-5353	416	1			PUNCT
ejpam-5353	416	2	0	0	PUNCT
ejpam-5353	416	3	if	if	SCONJ
ejpam-5353	416	4	i	i	PRON
ejpam-5353	416	5	=	=	NOUN
ejpam-5353	416	6	0	0	NUM
ejpam-5353	416	7	,	,	PUNCT
ejpam-5353	416	8	p−	p−	NOUN
ejpam-5353	416	9	2	2	NUM
ejpam-5353	416	10	p−	p−	NOUN
ejpam-5353	416	11	1	1	NUM
ejpam-5353	416	12	if	if	SCONJ
ejpam-5353	416	13	i	i	PRON
ejpam-5353	416	14	=	=	NOUN
ejpam-5353	416	15	1	1	NUM
ejpam-5353	416	16	,	,	PUNCT
ejpam-5353	416	17	p−	p−	NOUN
ejpam-5353	416	18	1	1	NUM
ejpam-5353	416	19	i	i	PRON
ejpam-5353	416	20	otherwise	otherwise	ADV
ejpam-5353	416	21	and	and	CCONJ
ejpam-5353	416	22	ui(m	ui(m	NUM
ejpam-5353	416	23	)	)	PUNCT
ejpam-5353	416	24	=	=	PUNCT
ejpam-5353	416	25			PUNCT
ejpam-5353	416	26	α1i	α1i	NOUN
ejpam-5353	416	27	if	if	SCONJ
ejpam-5353	416	28	i	i	PRON
ejpam-5353	416	29	=	=	NOUN
ejpam-5353	416	30	0	0	NUM
ejpam-5353	416	31	,	,	PUNCT
ejpam-5353	416	32	p−	p−	NOUN
ejpam-5353	416	33	2	2	NUM
ejpam-5353	416	34	α1i−	α1i−	NOUN
ejpam-5353	416	35	1	1	NUM
ejpam-5353	416	36	if	if	SCONJ
ejpam-5353	416	37	i	i	PRON
ejpam-5353	416	38	=	=	NOUN
ejpam-5353	416	39	1	1	NUM
ejpam-5353	416	40	,	,	PUNCT
ejpam-5353	416	41	p−	p−	NOUN
ejpam-5353	416	42	1	1	NUM
ejpam-5353	416	43	(	(	PUNCT
ejpam-5353	416	44	α1	α1	PROPN
ejpam-5353	416	45	+	+	CCONJ
ejpam-5353	416	46	1)i	1)i	NOUN
ejpam-5353	416	47	otherwise	otherwise	ADV
ejpam-5353	416	48	,	,	PUNCT
ejpam-5353	416	49	therefore	therefore	ADV
ejpam-5353	416	50	,	,	PUNCT
ejpam-5353	416	51	vi(g)−	vi(g)−	NOUN
ejpam-5353	416	52	ui(m	ui(m	NOUN
ejpam-5353	416	53	)	)	PUNCT
ejpam-5353	416	54	=	=	SYM
ejpam-5353	416	55	−α1i	−α1i	PROPN
ejpam-5353	416	56	for	for	ADP
ejpam-5353	416	57	every	every	DET
ejpam-5353	416	58	i	i	PROPN
ejpam-5353	416	59	∈	∈	PROPN
ejpam-5353	416	60	zp	zp	VERB
ejpam-5353	416	61	.	.	PUNCT
ejpam-5353	416	62	consequently	consequently	ADV
ejpam-5353	416	63	,	,	PUNCT
ejpam-5353	416	64	{	{	PUNCT
ejpam-5353	416	65	vi(g)−	vi(g)−	NOUN
ejpam-5353	416	66	ui(m	ui(m	NOUN
ejpam-5353	416	67	)	)	PUNCT
ejpam-5353	416	68	}	}	PUNCT
ejpam-5353	416	69	=	=	SYM
ejpam-5353	416	70	zp	zp	X
ejpam-5353	416	71	.	.	PUNCT
ejpam-5353	416	72	by	by	ADP
ejpam-5353	416	73	theorem	theorem	NOUN
ejpam-5353	416	74	4	4	NUM
ejpam-5353	416	75	,	,	PUNCT
ejpam-5353	416	76	then	then	ADV
ejpam-5353	416	77	the	the	DET
ejpam-5353	416	78	two	two	NUM
ejpam-5353	416	79	bases	basis	NOUN
ejpam-5353	416	80	v(g	v(g	ADJ
ejpam-5353	416	81	)	)	PUNCT
ejpam-5353	416	82	and	and	CCONJ
ejpam-5353	416	83	u(m	u(m	NOUN
ejpam-5353	416	84	)	)	PUNCT
ejpam-5353	416	85	are	be	AUX
ejpam-5353	416	86	orthogonal	orthogonal	ADJ
ejpam-5353	416	87	.	.	PUNCT
ejpam-5353	417	1	moreover	moreover	ADV
ejpam-5353	417	2	,	,	PUNCT
ejpam-5353	417	3	the	the	DET
ejpam-5353	417	4	edges	edge	NOUN
ejpam-5353	417	5	set	set	VERB
ejpam-5353	417	6	e(g	e(g	PROPN
ejpam-5353	417	7	)	)	PUNCT
ejpam-5353	417	8	and	and	CCONJ
ejpam-5353	417	9	e(m	e(m	NOUN
ejpam-5353	417	10	)	)	PUNCT
ejpam-5353	417	11	of	of	ADP
ejpam-5353	417	12	the	the	DET
ejpam-5353	417	13	bases	basis	NOUN
ejpam-5353	417	14	g	g	NOUN
ejpam-5353	417	15	and	and	CCONJ
ejpam-5353	417	16	m	m	VERB
ejpam-5353	417	17	respectively	respectively	ADV
ejpam-5353	417	18	,	,	PUNCT
ejpam-5353	417	19	can	can	AUX
ejpam-5353	417	20	be	be	AUX
ejpam-5353	417	21	represented	represent	VERB
ejpam-5353	417	22	by	by	ADP
ejpam-5353	417	23	:	:	PUNCT
ejpam-5353	417	24	e(g	e(g	PROPN
ejpam-5353	417	25	)	)	PUNCT
ejpam-5353	418	1	=	=	PRON
ejpam-5353	418	2	{	{	PUNCT
ejpam-5353	418	3	(	(	PUNCT
ejpam-5353	418	4	(	(	PUNCT
ejpam-5353	418	5	p−	p−	NOUN
ejpam-5353	418	6	1)0	1)0	NUM
ejpam-5353	418	7	,	,	PUNCT
ejpam-5353	418	8	(	(	PUNCT
ejpam-5353	418	9	i−	i−	PROPN
ejpam-5353	418	10	1)1	1)1	NUM
ejpam-5353	418	11	)	)	PUNCT
ejpam-5353	418	12	;	;	PUNCT
ejpam-5353	419	1	i	i	NOUN
ejpam-5353	419	2	=	=	NOUN
ejpam-5353	419	3	1	1	NUM
ejpam-5353	419	4	,	,	PUNCT
ejpam-5353	419	5	p−	p−	NOUN
ejpam-5353	419	6	1	1	NUM
ejpam-5353	419	7	}	}	PUNCT
ejpam-5353	419	8	∪{(00	∪{(00	ADJ
ejpam-5353	419	9	,	,	PUNCT
ejpam-5353	419	10	01	01	NUM
ejpam-5353	419	11	)	)	PUNCT
ejpam-5353	419	12	,	,	PUNCT
ejpam-5353	419	13	(	(	PUNCT
ejpam-5353	419	14	00,−21	00,−21	ADJ
ejpam-5353	419	15	)	)	PUNCT
ejpam-5353	419	16	}	}	PUNCT
ejpam-5353	419	17	∪{(i0	∪{(i0	PROPN
ejpam-5353	419	18	,	,	PUNCT
ejpam-5353	419	19	2i1	2i1	NUM
ejpam-5353	419	20	)	)	PUNCT
ejpam-5353	419	21	;	;	PUNCT
ejpam-5353	420	1	i	i	PROPN
ejpam-5353	420	2	∈	∈	PROPN
ejpam-5353	420	3	zn\	zn\	PROPN
ejpam-5353	420	4	{	{	PUNCT
ejpam-5353	420	5	0	0	NUM
ejpam-5353	420	6	,	,	PUNCT
ejpam-5353	420	7	1	1	NUM
ejpam-5353	420	8	,	,	PUNCT
ejpam-5353	420	9	p−	p−	NOUN
ejpam-5353	420	10	2	2	NUM
ejpam-5353	420	11	,	,	PUNCT
ejpam-5353	420	12	p−	p−	NOUN
ejpam-5353	420	13	1	1	NUM
ejpam-5353	420	14	}	}	PUNCT
ejpam-5353	420	15	}	}	PUNCT
ejpam-5353	420	16	and	and	CCONJ
ejpam-5353	420	17	e(m	e(m	NOUN
ejpam-5353	420	18	)	)	PUNCT
ejpam-5353	420	19	=	=	PRON
ejpam-5353	420	20	{	{	PUNCT
ejpam-5353	420	21	(	(	PUNCT
ejpam-5353	420	22	(	(	PUNCT
ejpam-5353	420	23	α1i)0	α1i)0	X
ejpam-5353	420	24	,	,	PUNCT
ejpam-5353	420	25	(	(	PUNCT
ejpam-5353	420	26	(	(	PUNCT
ejpam-5353	420	27	α1	α1	PROPN
ejpam-5353	420	28	+	+	CCONJ
ejpam-5353	420	29	1)i)1	1)i)1	NOUN
ejpam-5353	420	30	)	)	PUNCT
ejpam-5353	420	31	;	;	PUNCT
ejpam-5353	420	32	i	i	NOUN
ejpam-5353	420	33	=	=	NOUN
ejpam-5353	420	34	0	0	NUM
ejpam-5353	420	35	,	,	PUNCT
ejpam-5353	420	36	p−	p−	NOUN
ejpam-5353	420	37	2	2	NUM
ejpam-5353	420	38	}	}	PUNCT
ejpam-5353	420	39	∪{((α1i−	∪{((α1i−	NOUN
ejpam-5353	420	40	1)0	1)0	NUM
ejpam-5353	420	41	,	,	PUNCT
ejpam-5353	420	42	(	(	PUNCT
ejpam-5353	420	43	(	(	PUNCT
ejpam-5353	420	44	(	(	PUNCT
ejpam-5353	420	45	α1	α1	X
ejpam-5353	420	46	+	+	CCONJ
ejpam-5353	420	47	1)i)−	1)i)−	NUM
ejpam-5353	420	48	1)1	1)1	NUM
ejpam-5353	420	49	)	)	PUNCT
ejpam-5353	420	50	;	;	PUNCT
ejpam-5353	420	51	i	i	NOUN
ejpam-5353	420	52	=	=	NOUN
ejpam-5353	420	53	1	1	NUM
ejpam-5353	420	54	,	,	PUNCT
ejpam-5353	420	55	p−	p−	NOUN
ejpam-5353	420	56	1	1	NUM
ejpam-5353	420	57	}	}	PUNCT
ejpam-5353	420	58	∪{(((α1	∪{(((α1	NOUN
ejpam-5353	420	59	+	+	CCONJ
ejpam-5353	420	60	1)i)0	1)i)0	NUM
ejpam-5353	420	61	,	,	PUNCT
ejpam-5353	420	62	(	(	PUNCT
ejpam-5353	420	63	(	(	PUNCT
ejpam-5353	420	64	α1	α1	PROPN
ejpam-5353	420	65	+	+	CCONJ
ejpam-5353	420	66	2)i)1	2)i)1	NOUN
ejpam-5353	420	67	)	)	PUNCT
ejpam-5353	420	68	;	;	PUNCT
ejpam-5353	420	69	i	i	PROPN
ejpam-5353	420	70	∈	∈	PROPN
ejpam-5353	420	71	zn\	zn\	PROPN
ejpam-5353	420	72	{	{	PUNCT
ejpam-5353	420	73	0	0	NUM
ejpam-5353	420	74	,	,	PUNCT
ejpam-5353	420	75	1	1	NUM
ejpam-5353	420	76	,	,	PUNCT
ejpam-5353	420	77	p−	p−	NOUN
ejpam-5353	420	78	2	2	NUM
ejpam-5353	420	79	,	,	PUNCT
ejpam-5353	420	80	p−	p−	NOUN
ejpam-5353	420	81	1	1	NUM
ejpam-5353	420	82	}	}	PUNCT
ejpam-5353	420	83	}	}	PUNCT
ejpam-5353	420	84	and	and	CCONJ
ejpam-5353	420	85	hence	hence	ADV
ejpam-5353	420	86	g	g	NOUN
ejpam-5353	420	87	∼=	∼=	PROPN
ejpam-5353	420	88	m	m	VERB
ejpam-5353	420	89	∼=	∼=	NOUN
ejpam-5353	420	90	c3(1	c3(1	NOUN
ejpam-5353	420	91	,	,	PUNCT
ejpam-5353	420	92	p−	p−	NOUN
ejpam-5353	420	93	4	4	NUM
ejpam-5353	420	94	,	,	PUNCT
ejpam-5353	420	95	1	1	NUM
ejpam-5353	420	96	)	)	PUNCT
ejpam-5353	420	97	∪	∪	NOUN
ejpam-5353	420	98	(	(	PUNCT
ejpam-5353	420	99	p−	p−	NOUN
ejpam-5353	420	100	5)c2(0	5)c2(0	NOUN
ejpam-5353	420	101	,	,	PUNCT
ejpam-5353	420	102	0	0	NUM
ejpam-5353	420	103	)	)	PUNCT
ejpam-5353	420	104	.	.	PUNCT
ejpam-5353	421	1	case	case	NOUN
ejpam-5353	421	2	2	2	NUM
ejpam-5353	421	3	.	.	X
ejpam-5353	421	4	for	for	ADP
ejpam-5353	421	5	any	any	DET
ejpam-5353	421	6	prime	prime	ADJ
ejpam-5353	421	7	integer	integer	NOUN
ejpam-5353	421	8	p	p	PROPN
ejpam-5353	421	9	>	>	X
ejpam-5353	421	10	7	7	NUM
ejpam-5353	421	11	such	such	ADJ
ejpam-5353	421	12	that	that	SCONJ
ejpam-5353	421	13	p	p	PROPN
ejpam-5353	421	14	≡	≡	PROPN
ejpam-5353	422	1	1mod	1mod	PROPN
ejpam-5353	422	2	6	6	NUM
ejpam-5353	422	3	and	and	CCONJ
ejpam-5353	422	4	a	a	DET
ejpam-5353	422	5	positive	positive	ADJ
ejpam-5353	422	6	integer	integer	NOUN
ejpam-5353	422	7	α2	α2	NOUN
ejpam-5353	422	8	=	=	SYM
ejpam-5353	423	1	⌊3p−1	⌊3p−1	ADP
ejpam-5353	423	2	5	5	NUM
ejpam-5353	423	3	⌋	⌋	NOUN
ejpam-5353	423	4	,	,	PUNCT
ejpam-5353	423	5	the	the	DET
ejpam-5353	423	6	vectors	vector	NOUN
ejpam-5353	423	7	v(g	v(g	ADJ
ejpam-5353	423	8	)	)	PUNCT
ejpam-5353	423	9	and	and	CCONJ
ejpam-5353	423	10	h(f	h(f	PROPN
ejpam-5353	423	11	)	)	PUNCT
ejpam-5353	423	12	of	of	ADP
ejpam-5353	423	13	the	the	DET
ejpam-5353	423	14	bases	basis	NOUN
ejpam-5353	423	15	g	g	PROPN
ejpam-5353	423	16	and	and	CCONJ
ejpam-5353	423	17	f	f	PROPN
ejpam-5353	423	18	are	be	AUX
ejpam-5353	423	19	defined	define	VERB
ejpam-5353	423	20	as	as	ADP
ejpam-5353	423	21	:	:	PUNCT
ejpam-5353	423	22	vi(g	vi(g	NUM
ejpam-5353	423	23	)	)	PUNCT
ejpam-5353	423	24	=	=	PUNCT
ejpam-5353	424	1			PUNCT
ejpam-5353	424	2	0	0	PUNCT
ejpam-5353	424	3	if	if	SCONJ
ejpam-5353	424	4	i	i	PRON
ejpam-5353	424	5	=	=	NOUN
ejpam-5353	424	6	0	0	NUM
ejpam-5353	424	7	,	,	PUNCT
ejpam-5353	424	8	p−	p−	NOUN
ejpam-5353	424	9	2	2	NUM
ejpam-5353	424	10	p−	p−	NOUN
ejpam-5353	424	11	1	1	NUM
ejpam-5353	424	12	if	if	SCONJ
ejpam-5353	424	13	i	i	PRON
ejpam-5353	424	14	=	=	NOUN
ejpam-5353	424	15	1	1	NUM
ejpam-5353	424	16	,	,	PUNCT
ejpam-5353	424	17	p−	p−	NOUN
ejpam-5353	424	18	1	1	NUM
ejpam-5353	424	19	i	i	PRON
ejpam-5353	424	20	otherwise	otherwise	ADV
ejpam-5353	424	21	and	and	CCONJ
ejpam-5353	424	22	hi(f	hi(f	ADV
ejpam-5353	424	23	)	)	PUNCT
ejpam-5353	424	24	=	=	PUNCT
ejpam-5353	425	1			PUNCT
ejpam-5353	425	2	α2i	α2i	NUM
ejpam-5353	425	3	if	if	SCONJ
ejpam-5353	425	4	i	i	PRON
ejpam-5353	425	5	=	=	NOUN
ejpam-5353	425	6	0	0	NUM
ejpam-5353	425	7	,	,	PUNCT
ejpam-5353	425	8	p−	p−	NOUN
ejpam-5353	425	9	2	2	NUM
ejpam-5353	425	10	α2i−	α2i−	PROPN
ejpam-5353	425	11	1	1	NUM
ejpam-5353	425	12	if	if	SCONJ
ejpam-5353	425	13	i	i	PRON
ejpam-5353	425	14	=	=	NOUN
ejpam-5353	425	15	1	1	NUM
ejpam-5353	425	16	,	,	PUNCT
ejpam-5353	425	17	p−	p−	NOUN
ejpam-5353	425	18	1	1	NUM
ejpam-5353	425	19	(	(	PUNCT
ejpam-5353	425	20	α2	α2	ADJ
ejpam-5353	425	21	+	+	CCONJ
ejpam-5353	425	22	1)i	1)i	NUM
ejpam-5353	425	23	otherwise	otherwise	ADV
ejpam-5353	425	24	therefore	therefore	ADV
ejpam-5353	425	25	,	,	PUNCT
ejpam-5353	425	26	vi(g)−hi(f	vi(g)−hi(f	NOUN
ejpam-5353	425	27	)	)	PUNCT
ejpam-5353	425	28	=	=	PUNCT
ejpam-5353	426	1	−α2i	−α2i	NUM
ejpam-5353	426	2	for	for	ADP
ejpam-5353	426	3	every	every	DET
ejpam-5353	426	4	i	i	PROPN
ejpam-5353	426	5	∈	∈	PROPN
ejpam-5353	426	6	zp	zp	VERB
ejpam-5353	426	7	.	.	PUNCT
ejpam-5353	426	8	consequently	consequently	ADV
ejpam-5353	426	9	,	,	PUNCT
ejpam-5353	426	10	{	{	PUNCT
ejpam-5353	426	11	vi(g)−hi(f	vi(g)−hi(f	NOUN
ejpam-5353	426	12	)	)	PUNCT
ejpam-5353	426	13	}	}	PUNCT
ejpam-5353	427	1	=	=	SYM
ejpam-5353	427	2	zp	zp	X
ejpam-5353	427	3	.	.	PUNCT
ejpam-5353	427	4	by	by	ADP
ejpam-5353	427	5	theorem	theorem	NOUN
ejpam-5353	427	6	4	4	NUM
ejpam-5353	427	7	,	,	PUNCT
ejpam-5353	427	8	then	then	ADV
ejpam-5353	427	9	the	the	DET
ejpam-5353	427	10	two	two	NUM
ejpam-5353	427	11	bases	basis	NOUN
ejpam-5353	427	12	v(g	v(g	ADJ
ejpam-5353	427	13	)	)	PUNCT
ejpam-5353	427	14	and	and	CCONJ
ejpam-5353	427	15	h(f	h(f	PROPN
ejpam-5353	427	16	)	)	PUNCT
ejpam-5353	427	17	are	be	AUX
ejpam-5353	427	18	orthogonal	orthogonal	ADJ
ejpam-5353	427	19	.	.	PUNCT
ejpam-5353	428	1	moreover	moreover	ADV
ejpam-5353	428	2	,	,	PUNCT
ejpam-5353	428	3	the	the	DET
ejpam-5353	428	4	edges	edge	NOUN
ejpam-5353	428	5	set	set	VERB
ejpam-5353	428	6	e(f	e(f	PROPN
ejpam-5353	428	7	)	)	PUNCT
ejpam-5353	428	8	of	of	ADP
ejpam-5353	428	9	the	the	DET
ejpam-5353	428	10	bases	basis	NOUN
ejpam-5353	428	11	f	f	X
ejpam-5353	428	12	can	can	AUX
ejpam-5353	428	13	be	be	AUX
ejpam-5353	428	14	represented	represent	VERB
ejpam-5353	428	15	by	by	ADP
ejpam-5353	428	16	:	:	PUNCT
ejpam-5353	428	17	h.	h.	PROPN
ejpam-5353	428	18	shabana	shabana	PROPN
ejpam-5353	428	19	,	,	PUNCT
ejpam-5353	428	20	r.	r.	PROPN
ejpam-5353	428	21	el	el	PROPN
ejpam-5353	428	22	-	-	PROPN
ejpam-5353	428	23	shanawany	shanawany	NOUN
ejpam-5353	428	24	,	,	PUNCT
ejpam-5353	428	25	s.	s.	PROPN
ejpam-5353	428	26	halawa	halawa	PROPN
ejpam-5353	428	27	/	/	PUNCT
ejpam-5353	428	28	eur	eur	PROPN
ejpam-5353	428	29	.	.	PUNCT
ejpam-5353	429	1	j.	j.	PROPN
ejpam-5353	429	2	pure	pure	PROPN
ejpam-5353	429	3	appl	appl	PROPN
ejpam-5353	429	4	.	.	PROPN
ejpam-5353	429	5	math	math	PROPN
ejpam-5353	429	6	,	,	PUNCT
ejpam-5353	429	7	17	17	NUM
ejpam-5353	429	8	(	(	PUNCT
ejpam-5353	429	9	4	4	NUM
ejpam-5353	429	10	)	)	PUNCT
ejpam-5353	429	11	(	(	PUNCT
ejpam-5353	429	12	2024	2024	NUM
ejpam-5353	429	13	)	)	PUNCT
ejpam-5353	429	14	,	,	PUNCT
ejpam-5353	429	15	3492	3492	NUM
ejpam-5353	429	16	-	-	SYM
ejpam-5353	429	17	3516	3516	NUM
ejpam-5353	429	18	3508	3508	NUM
ejpam-5353	429	19	e(f	e(f	PROPN
ejpam-5353	429	20	)	)	PUNCT
ejpam-5353	430	1	=	=	PRON
ejpam-5353	430	2	{	{	PUNCT
ejpam-5353	430	3	(	(	PUNCT
ejpam-5353	430	4	(	(	PUNCT
ejpam-5353	430	5	α2i)0	α2i)0	PROPN
ejpam-5353	430	6	,	,	PUNCT
ejpam-5353	430	7	(	(	PUNCT
ejpam-5353	430	8	(	(	PUNCT
ejpam-5353	430	9	α2	α2	ADJ
ejpam-5353	430	10	+	+	CCONJ
ejpam-5353	430	11	1)i)1	1)i)1	NOUN
ejpam-5353	430	12	)	)	PUNCT
ejpam-5353	430	13	;	;	PUNCT
ejpam-5353	431	1	i	i	NOUN
ejpam-5353	431	2	=	=	NOUN
ejpam-5353	431	3	0	0	NUM
ejpam-5353	431	4	,	,	PUNCT
ejpam-5353	431	5	p−	p−	NOUN
ejpam-5353	431	6	2	2	NUM
ejpam-5353	431	7	}	}	PUNCT
ejpam-5353	431	8	∪{((α2i−	∪{((α2i−	VERB
ejpam-5353	431	9	1)0	1)0	NUM
ejpam-5353	431	10	,	,	PUNCT
ejpam-5353	431	11	(	(	PUNCT
ejpam-5353	431	12	(	(	PUNCT
ejpam-5353	431	13	(	(	PUNCT
ejpam-5353	431	14	α2	α2	ADJ
ejpam-5353	431	15	+	+	CCONJ
ejpam-5353	431	16	1)i)−	1)i)−	NUM
ejpam-5353	431	17	1)1	1)1	NUM
ejpam-5353	431	18	)	)	PUNCT
ejpam-5353	431	19	;	;	PUNCT
ejpam-5353	432	1	i	i	NOUN
ejpam-5353	432	2	=	=	NOUN
ejpam-5353	432	3	1	1	NUM
ejpam-5353	432	4	,	,	PUNCT
ejpam-5353	432	5	p−	p−	NOUN
ejpam-5353	432	6	1	1	NUM
ejpam-5353	432	7	}	}	PUNCT
ejpam-5353	432	8	∪{(((α2	∪{(((α2	PUNCT
ejpam-5353	432	9	+	+	NUM
ejpam-5353	432	10	1)i)0	1)i)0	NUM
ejpam-5353	432	11	,	,	PUNCT
ejpam-5353	432	12	(	(	PUNCT
ejpam-5353	432	13	(	(	PUNCT
ejpam-5353	432	14	α2	α2	ADJ
ejpam-5353	432	15	+	+	CCONJ
ejpam-5353	432	16	2)i)1	2)i)1	NOUN
ejpam-5353	432	17	)	)	PUNCT
ejpam-5353	432	18	;	;	PUNCT
ejpam-5353	432	19	i	i	PROPN
ejpam-5353	432	20	∈	∈	PROPN
ejpam-5353	432	21	zn\	zn\	PROPN
ejpam-5353	432	22	{	{	PUNCT
ejpam-5353	432	23	0	0	NUM
ejpam-5353	432	24	,	,	PUNCT
ejpam-5353	432	25	1	1	NUM
ejpam-5353	432	26	,	,	PUNCT
ejpam-5353	432	27	p−	p−	NOUN
ejpam-5353	432	28	2	2	NUM
ejpam-5353	432	29	,	,	PUNCT
ejpam-5353	432	30	p−	p−	NOUN
ejpam-5353	432	31	1	1	NUM
ejpam-5353	432	32	}	}	PUNCT
ejpam-5353	432	33	}	}	PUNCT
ejpam-5353	432	34	.	.	PUNCT
ejpam-5353	433	1	and	and	CCONJ
ejpam-5353	433	2	hence	hence	ADV
ejpam-5353	433	3	f	f	PROPN
ejpam-5353	433	4	∼=	∼=	PROPN
ejpam-5353	433	5	c3(1	c3(1	NOUN
ejpam-5353	433	6	,	,	PUNCT
ejpam-5353	433	7	p−	p−	NOUN
ejpam-5353	433	8	4	4	NUM
ejpam-5353	433	9	,	,	PUNCT
ejpam-5353	433	10	1	1	NUM
ejpam-5353	433	11	)	)	PUNCT
ejpam-5353	433	12	∪	∪	NOUN
ejpam-5353	433	13	(	(	PUNCT
ejpam-5353	433	14	p−	p−	NOUN
ejpam-5353	433	15	5)c2(0	5)c2(0	NOUN
ejpam-5353	433	16	,	,	PUNCT
ejpam-5353	433	17	0	0	NUM
ejpam-5353	433	18	)	)	PUNCT
ejpam-5353	433	19	.	.	PUNCT
ejpam-5353	434	1	theorem	theorem	NOUN
ejpam-5353	434	2	21	21	NUM
ejpam-5353	434	3	.	.	PUNCT
ejpam-5353	435	1	let	let	VERB
ejpam-5353	435	2	p	p	PRON
ejpam-5353	435	3	>	>	X
ejpam-5353	435	4	7	7	NUM
ejpam-5353	435	5	to	to	PART
ejpam-5353	435	6	be	be	AUX
ejpam-5353	435	7	a	a	DET
ejpam-5353	435	8	prime	prime	ADJ
ejpam-5353	435	9	integer	integer	NOUN
ejpam-5353	435	10	,	,	PUNCT
ejpam-5353	435	11	then	then	ADV
ejpam-5353	435	12	there	there	PRON
ejpam-5353	435	13	is	be	VERB
ejpam-5353	435	14	an	an	DET
ejpam-5353	435	15	odc	odc	NOUN
ejpam-5353	435	16	of	of	ADP
ejpam-5353	435	17	kp	kp	PROPN
ejpam-5353	435	18	,	,	PUNCT
ejpam-5353	435	19	p	p	NOUN
ejpam-5353	435	20	by	by	ADP
ejpam-5353	435	21	c4(0	c4(0	PROPN
ejpam-5353	435	22	,	,	PUNCT
ejpam-5353	435	23	0	0	NUM
ejpam-5353	435	24	,	,	PUNCT
ejpam-5353	435	25	0	0	NUM
ejpam-5353	435	26	,	,	PUNCT
ejpam-5353	435	27	0	0	NUM
ejpam-5353	435	28	)	)	PUNCT
ejpam-5353	435	29	∪	∪	ADP
ejpam-5353	435	30	2c3(0	2c3(0	NUM
ejpam-5353	435	31	,	,	PUNCT
ejpam-5353	435	32	0	0	NUM
ejpam-5353	435	33	,	,	PUNCT
ejpam-5353	435	34	0	0	NUM
ejpam-5353	435	35	)	)	PUNCT
ejpam-5353	435	36	∪	∪	NOUN
ejpam-5353	435	37	(	(	PUNCT
ejpam-5353	435	38	p−	p−	NOUN
ejpam-5353	435	39	7)c2(0	7)c2(0	NOUN
ejpam-5353	435	40	,	,	PUNCT
ejpam-5353	435	41	0	0	NUM
ejpam-5353	435	42	)	)	PUNCT
ejpam-5353	435	43	.	.	PUNCT
ejpam-5353	436	1	proof	proof	NOUN
ejpam-5353	436	2	.	.	PUNCT
ejpam-5353	437	1	for	for	ADP
ejpam-5353	437	2	any	any	DET
ejpam-5353	437	3	prime	prime	ADJ
ejpam-5353	437	4	integer	integer	NOUN
ejpam-5353	437	5	p	p	PROPN
ejpam-5353	437	6	>	>	X
ejpam-5353	437	7	7	7	NUM
ejpam-5353	437	8	,	,	PUNCT
ejpam-5353	437	9	the	the	DET
ejpam-5353	437	10	vectors	vector	NOUN
ejpam-5353	437	11	v(g	v(g	ADJ
ejpam-5353	437	12	)	)	PUNCT
ejpam-5353	437	13	and	and	CCONJ
ejpam-5353	437	14	u(f	u(f	NOUN
ejpam-5353	437	15	)	)	PUNCT
ejpam-5353	437	16	of	of	ADP
ejpam-5353	437	17	the	the	DET
ejpam-5353	437	18	starters	starter	NOUN
ejpam-5353	437	19	g	g	PROPN
ejpam-5353	438	1	and	and	CCONJ
ejpam-5353	438	2	f	f	PROPN
ejpam-5353	438	3	are	be	AUX
ejpam-5353	438	4	defined	define	VERB
ejpam-5353	438	5	respectively	respectively	ADV
ejpam-5353	438	6	as	as	ADP
ejpam-5353	438	7	:	:	PUNCT
ejpam-5353	438	8	vi(g	vi(g	X
ejpam-5353	438	9	)	)	PUNCT
ejpam-5353	439	1	=	=	SYM
ejpam-5353	440	1			PUNCT
ejpam-5353	440	2	0	0	PUNCT
ejpam-5353	441	1	if	if	SCONJ
ejpam-5353	441	2	i	i	PRON
ejpam-5353	441	3	=	=	VERB
ejpam-5353	441	4	0	0	PUNCT
ejpam-5353	442	1	(	(	PUNCT
ejpam-5353	442	2	p−1	p−1	PROPN
ejpam-5353	442	3	2	2	NUM
ejpam-5353	442	4	)	)	PUNCT
ejpam-5353	442	5	i−	i−	PROPN
ejpam-5353	442	6	1	1	NUM
ejpam-5353	442	7	if	if	SCONJ
ejpam-5353	442	8	i	i	PRON
ejpam-5353	442	9	=	=	NOUN
ejpam-5353	442	10	1	1	NUM
ejpam-5353	442	11	,	,	PUNCT
ejpam-5353	442	12	p−	p−	NOUN
ejpam-5353	442	13	1	1	NUM
ejpam-5353	442	14	(	(	PUNCT
ejpam-5353	442	15	p−3	p−3	NOUN
ejpam-5353	442	16	2	2	NUM
ejpam-5353	442	17	)	)	PUNCT
ejpam-5353	442	18	i−	i−	PROPN
ejpam-5353	442	19	1	1	NUM
ejpam-5353	442	20	otherwise	otherwise	ADV
ejpam-5353	442	21	and	and	CCONJ
ejpam-5353	442	22	ui(f	ui(f	PUNCT
ejpam-5353	442	23	)	)	PUNCT
ejpam-5353	442	24	=	=	PUNCT
ejpam-5353	443	1			PUNCT
ejpam-5353	443	2	0	0	PUNCT
ejpam-5353	444	1	if	if	SCONJ
ejpam-5353	444	2	i	i	PRON
ejpam-5353	444	3	=	=	VERB
ejpam-5353	444	4	0	0	PUNCT
ejpam-5353	445	1	(	(	PUNCT
ejpam-5353	445	2	p+1	p+1	NOUN
ejpam-5353	445	3	2	2	NUM
ejpam-5353	445	4	)	)	PUNCT
ejpam-5353	445	5	i−	i−	PROPN
ejpam-5353	445	6	1	1	NUM
ejpam-5353	445	7	if	if	SCONJ
ejpam-5353	445	8	i	i	PRON
ejpam-5353	445	9	=	=	NOUN
ejpam-5353	445	10	1	1	NUM
ejpam-5353	445	11	,	,	PUNCT
ejpam-5353	445	12	p−	p−	NOUN
ejpam-5353	445	13	1	1	NUM
ejpam-5353	445	14	(	(	PUNCT
ejpam-5353	445	15	p−1	p−1	PROPN
ejpam-5353	445	16	2	2	NUM
ejpam-5353	445	17	)	)	PUNCT
ejpam-5353	445	18	i−	i−	PROPN
ejpam-5353	445	19	1	1	NUM
ejpam-5353	445	20	otherwise	otherwise	ADV
ejpam-5353	445	21	thus	thus	ADV
ejpam-5353	445	22	,	,	PUNCT
ejpam-5353	445	23	for	for	ADP
ejpam-5353	445	24	any	any	DET
ejpam-5353	445	25	i	i	PROPN
ejpam-5353	445	26	∈	∈	PROPN
ejpam-5353	445	27	zp	zp	NOUN
ejpam-5353	445	28	,	,	PUNCT
ejpam-5353	445	29	vi(g)−	vi(g)−	NOUN
ejpam-5353	445	30	ui(f	ui(f	PUNCT
ejpam-5353	445	31	)	)	PUNCT
ejpam-5353	446	1	=	=	SYM
ejpam-5353	446	2	−i	−i	NOUN
ejpam-5353	446	3	.	.	PUNCT
ejpam-5353	447	1	consequently	consequently	ADV
ejpam-5353	447	2	,	,	PUNCT
ejpam-5353	447	3	{	{	PUNCT
ejpam-5353	447	4	vi(g)−	vi(g)−	NOUN
ejpam-5353	447	5	ui(f	ui(f	PUNCT
ejpam-5353	447	6	)	)	PUNCT
ejpam-5353	447	7	;	;	PUNCT
ejpam-5353	447	8	i	i	PRON
ejpam-5353	447	9	∈	∈	PROPN
ejpam-5353	447	10	zp	zp	X
ejpam-5353	447	11	}	}	PUNCT
ejpam-5353	447	12	=	=	SYM
ejpam-5353	447	13	zp	zp	X
ejpam-5353	447	14	.	.	PUNCT
ejpam-5353	447	15	by	by	ADP
ejpam-5353	447	16	theorem	theorem	NOUN
ejpam-5353	447	17	4	4	NUM
ejpam-5353	447	18	,	,	PUNCT
ejpam-5353	447	19	then	then	ADV
ejpam-5353	447	20	the	the	DET
ejpam-5353	447	21	two	two	NUM
ejpam-5353	447	22	bases	basis	NOUN
ejpam-5353	447	23	v(g	v(g	ADJ
ejpam-5353	447	24	)	)	PUNCT
ejpam-5353	447	25	and	and	CCONJ
ejpam-5353	447	26	u(f	u(f	NOUN
ejpam-5353	447	27	)	)	PUNCT
ejpam-5353	447	28	are	be	AUX
ejpam-5353	447	29	orthogonal	orthogonal	ADJ
ejpam-5353	447	30	.	.	PUNCT
ejpam-5353	448	1	moreover	moreover	ADV
ejpam-5353	448	2	,	,	PUNCT
ejpam-5353	448	3	the	the	DET
ejpam-5353	448	4	edges	edge	NOUN
ejpam-5353	448	5	set	set	VERB
ejpam-5353	448	6	e(g	e(g	PROPN
ejpam-5353	448	7	)	)	PUNCT
ejpam-5353	448	8	and	and	CCONJ
ejpam-5353	448	9	e(f	e(f	PROPN
ejpam-5353	448	10	)	)	PUNCT
ejpam-5353	448	11	of	of	ADP
ejpam-5353	448	12	the	the	DET
ejpam-5353	448	13	bases	basis	NOUN
ejpam-5353	448	14	g	g	NOUN
ejpam-5353	448	15	and	and	CCONJ
ejpam-5353	448	16	f	f	PROPN
ejpam-5353	448	17	respectively	respectively	ADV
ejpam-5353	448	18	,	,	PUNCT
ejpam-5353	448	19	can	can	AUX
ejpam-5353	448	20	be	be	AUX
ejpam-5353	448	21	represented	represent	VERB
ejpam-5353	448	22	by	by	ADP
ejpam-5353	448	23	:	:	PUNCT
ejpam-5353	448	24	e(g	e(g	PROPN
ejpam-5353	448	25	)	)	PUNCT
ejpam-5353	449	1	=	=	PRON
ejpam-5353	449	2	{	{	PUNCT
ejpam-5353	449	3	(	(	PUNCT
ejpam-5353	449	4	(	(	PUNCT
ejpam-5353	449	5	(	(	PUNCT
ejpam-5353	449	6	p−1	p−1	PROPN
ejpam-5353	449	7	2	2	NUM
ejpam-5353	449	8	)	)	PUNCT
ejpam-5353	449	9	i−	i−	PROPN
ejpam-5353	449	10	1	1	NUM
ejpam-5353	449	11	)	)	PUNCT
ejpam-5353	449	12	0	0	NUM
ejpam-5353	449	13	,	,	PUNCT
ejpam-5353	449	14	(	(	PUNCT
ejpam-5353	449	15	(	(	PUNCT
ejpam-5353	449	16	p+1	p+1	NOUN
ejpam-5353	449	17	2	2	NUM
ejpam-5353	449	18	)	)	PUNCT
ejpam-5353	449	19	i−	i−	PROPN
ejpam-5353	449	20	1	1	NUM
ejpam-5353	449	21	)	)	PUNCT
ejpam-5353	449	22	)	)	PUNCT
ejpam-5353	449	23	1	1	NUM
ejpam-5353	449	24	)	)	PUNCT
ejpam-5353	449	25	;	;	PUNCT
ejpam-5353	449	26	i	i	PRON
ejpam-5353	449	27	∈	∈	PROPN
ejpam-5353	449	28	{	{	PUNCT
ejpam-5353	449	29	1	1	NUM
ejpam-5353	449	30	,	,	PUNCT
ejpam-5353	449	31	p−	p−	NOUN
ejpam-5353	449	32	1	1	NUM
ejpam-5353	449	33	}	}	PUNCT
ejpam-5353	449	34	}	}	PUNCT
ejpam-5353	449	35	∪{(00	∪{(00	ADJ
ejpam-5353	449	36	,	,	PUNCT
ejpam-5353	449	37	01	01	NUM
ejpam-5353	449	38	)	)	PUNCT
ejpam-5353	449	39	}	}	PUNCT
ejpam-5353	449	40	∪	∪	X
ejpam-5353	449	41	{	{	PUNCT
ejpam-5353	449	42	(	(	PUNCT
ejpam-5353	449	43	(	(	PUNCT
ejpam-5353	449	44	(	(	PUNCT
ejpam-5353	449	45	p−3	p−3	NOUN
ejpam-5353	449	46	2	2	NUM
ejpam-5353	449	47	)	)	PUNCT
ejpam-5353	449	48	i−	i−	PROPN
ejpam-5353	449	49	1	1	NUM
ejpam-5353	449	50	)	)	PUNCT
ejpam-5353	449	51	0	0	NUM
ejpam-5353	449	52	,	,	PUNCT
ejpam-5353	449	53	(	(	PUNCT
ejpam-5353	449	54	(	(	PUNCT
ejpam-5353	449	55	p−1	p−1	PROPN
ejpam-5353	449	56	2	2	NUM
ejpam-5353	449	57	)	)	PUNCT
ejpam-5353	449	58	i−	i−	PROPN
ejpam-5353	449	59	1	1	NUM
ejpam-5353	449	60	)	)	PUNCT
ejpam-5353	449	61	)	)	PUNCT
ejpam-5353	449	62	1	1	NUM
ejpam-5353	449	63	)	)	PUNCT
ejpam-5353	449	64	;	;	PUNCT
ejpam-5353	450	1	i	i	PROPN
ejpam-5353	450	2	∈	∈	PROPN
ejpam-5353	450	3	zp\	zp\	PROPN
ejpam-5353	450	4	{	{	PUNCT
ejpam-5353	450	5	0	0	NUM
ejpam-5353	450	6	,	,	PUNCT
ejpam-5353	450	7	1	1	NUM
ejpam-5353	450	8	,	,	PUNCT
ejpam-5353	450	9	p−	p−	NOUN
ejpam-5353	450	10	1	1	NUM
ejpam-5353	450	11	}	}	PUNCT
ejpam-5353	450	12	}	}	PUNCT
ejpam-5353	450	13	and	and	CCONJ
ejpam-5353	450	14	e(f	e(f	PROPN
ejpam-5353	450	15	)	)	PUNCT
ejpam-5353	451	1	=	=	PRON
ejpam-5353	451	2	{	{	PUNCT
ejpam-5353	451	3	(	(	PUNCT
ejpam-5353	451	4	(	(	PUNCT
ejpam-5353	451	5	(	(	PUNCT
ejpam-5353	451	6	p+1	p+1	NOUN
ejpam-5353	451	7	2	2	NUM
ejpam-5353	451	8	)	)	PUNCT
ejpam-5353	451	9	i−	i−	PROPN
ejpam-5353	451	10	1	1	NUM
ejpam-5353	451	11	)	)	PUNCT
ejpam-5353	451	12	0	0	NUM
ejpam-5353	451	13	,	,	PUNCT
ejpam-5353	451	14	(	(	PUNCT
ejpam-5353	451	15	(	(	PUNCT
ejpam-5353	451	16	p+3	p+3	NOUN
ejpam-5353	451	17	2	2	NUM
ejpam-5353	451	18	)	)	PUNCT
ejpam-5353	451	19	i−	i−	PROPN
ejpam-5353	451	20	1	1	NUM
ejpam-5353	451	21	)	)	PUNCT
ejpam-5353	451	22	)	)	PUNCT
ejpam-5353	451	23	1	1	NUM
ejpam-5353	451	24	)	)	PUNCT
ejpam-5353	451	25	;	;	PUNCT
ejpam-5353	451	26	i	i	PRON
ejpam-5353	451	27	∈	∈	PROPN
ejpam-5353	451	28	{	{	PUNCT
ejpam-5353	451	29	1	1	NUM
ejpam-5353	451	30	,	,	PUNCT
ejpam-5353	451	31	p−	p−	NOUN
ejpam-5353	451	32	1	1	NUM
ejpam-5353	451	33	}	}	PUNCT
ejpam-5353	451	34	}	}	PUNCT
ejpam-5353	451	35	∪{(00	∪{(00	ADJ
ejpam-5353	451	36	,	,	PUNCT
ejpam-5353	451	37	01	01	NUM
ejpam-5353	451	38	)	)	PUNCT
ejpam-5353	451	39	}	}	PUNCT
ejpam-5353	451	40	∪	∪	X
ejpam-5353	451	41	{	{	PUNCT
ejpam-5353	451	42	(	(	PUNCT
ejpam-5353	451	43	(	(	PUNCT
ejpam-5353	451	44	(	(	PUNCT
ejpam-5353	451	45	p−1	p−1	PROPN
ejpam-5353	451	46	2	2	NUM
ejpam-5353	451	47	)	)	PUNCT
ejpam-5353	451	48	i−	i−	PROPN
ejpam-5353	451	49	1	1	NUM
ejpam-5353	451	50	)	)	PUNCT
ejpam-5353	451	51	0	0	NUM
ejpam-5353	451	52	,	,	PUNCT
ejpam-5353	451	53	(	(	PUNCT
ejpam-5353	451	54	(	(	PUNCT
ejpam-5353	451	55	p+1	p+1	NOUN
ejpam-5353	451	56	2	2	NUM
ejpam-5353	451	57	)	)	PUNCT
ejpam-5353	451	58	i−	i−	PROPN
ejpam-5353	451	59	1	1	NUM
ejpam-5353	451	60	)	)	PUNCT
ejpam-5353	451	61	)	)	PUNCT
ejpam-5353	451	62	1	1	NUM
ejpam-5353	451	63	)	)	PUNCT
ejpam-5353	451	64	;	;	PUNCT
ejpam-5353	452	1	i	i	PROPN
ejpam-5353	452	2	∈	∈	PROPN
ejpam-5353	452	3	zp\	zp\	PROPN
ejpam-5353	452	4	{	{	PUNCT
ejpam-5353	452	5	0	0	NUM
ejpam-5353	452	6	,	,	PUNCT
ejpam-5353	452	7	1	1	NUM
ejpam-5353	452	8	,	,	PUNCT
ejpam-5353	452	9	p−	p−	NOUN
ejpam-5353	452	10	1	1	NUM
ejpam-5353	452	11	}	}	PUNCT
ejpam-5353	452	12	}	}	PUNCT
ejpam-5353	452	13	.	.	PUNCT
ejpam-5353	453	1	hence	hence	ADV
ejpam-5353	453	2	,	,	PUNCT
ejpam-5353	453	3	g	g	PROPN
ejpam-5353	453	4	∼=	∼=	PROPN
ejpam-5353	453	5	f	f	NOUN
ejpam-5353	453	6	∼=	∼=	PROPN
ejpam-5353	453	7	c4(0	c4(0	NOUN
ejpam-5353	453	8	,	,	PUNCT
ejpam-5353	453	9	0	0	NUM
ejpam-5353	453	10	,	,	PUNCT
ejpam-5353	453	11	0	0	NUM
ejpam-5353	453	12	,	,	PUNCT
ejpam-5353	453	13	0	0	NUM
ejpam-5353	453	14	)	)	PUNCT
ejpam-5353	453	15	∪	∪	ADP
ejpam-5353	453	16	2c3(0	2c3(0	NUM
ejpam-5353	453	17	,	,	PUNCT
ejpam-5353	453	18	0	0	NUM
ejpam-5353	453	19	,	,	PUNCT
ejpam-5353	453	20	0	0	NUM
ejpam-5353	453	21	)	)	PUNCT
ejpam-5353	453	22	∪	∪	NOUN
ejpam-5353	453	23	(	(	PUNCT
ejpam-5353	453	24	p−	p−	NOUN
ejpam-5353	453	25	7)c2(0	7)c2(0	NOUN
ejpam-5353	453	26	,	,	PUNCT
ejpam-5353	453	27	0	0	NUM
ejpam-5353	453	28	)	)	PUNCT
ejpam-5353	453	29	.	.	PUNCT
ejpam-5353	454	1	h.	h.	PROPN
ejpam-5353	454	2	shabana	shabana	PROPN
ejpam-5353	454	3	,	,	PUNCT
ejpam-5353	454	4	r.	r.	PROPN
ejpam-5353	454	5	el	el	PROPN
ejpam-5353	454	6	-	-	PROPN
ejpam-5353	454	7	shanawany	shanawany	NOUN
ejpam-5353	454	8	,	,	PUNCT
ejpam-5353	454	9	s.	s.	PROPN
ejpam-5353	454	10	halawa	halawa	PROPN
ejpam-5353	454	11	/	/	PUNCT
ejpam-5353	454	12	eur	eur	PROPN
ejpam-5353	454	13	.	.	PUNCT
ejpam-5353	455	1	j.	j.	PROPN
ejpam-5353	455	2	pure	pure	PROPN
ejpam-5353	455	3	appl	appl	PROPN
ejpam-5353	455	4	.	.	PROPN
ejpam-5353	455	5	math	math	PROPN
ejpam-5353	455	6	,	,	PUNCT
ejpam-5353	455	7	17	17	NUM
ejpam-5353	455	8	(	(	PUNCT
ejpam-5353	455	9	4	4	NUM
ejpam-5353	455	10	)	)	PUNCT
ejpam-5353	455	11	(	(	PUNCT
ejpam-5353	455	12	2024	2024	NUM
ejpam-5353	455	13	)	)	PUNCT
ejpam-5353	455	14	,	,	PUNCT
ejpam-5353	455	15	3492	3492	NUM
ejpam-5353	455	16	-	-	SYM
ejpam-5353	455	17	3516	3516	NUM
ejpam-5353	455	18	3509	3509	NUM
ejpam-5353	455	19	4	4	NUM
ejpam-5353	455	20	.	.	PUNCT
ejpam-5353	455	21	treebinary	treebinary	ADJ
ejpam-5353	455	22	error	error	NOUN
ejpam-5353	455	23	detecting	detecting	NOUN
ejpam-5353	455	24	and	and	CCONJ
ejpam-5353	455	25	correcting	correct	VERB
ejpam-5353	455	26	codes	code	NOUN
ejpam-5353	455	27	various	various	ADJ
ejpam-5353	455	28	combinatorial	combinatorial	ADJ
ejpam-5353	455	29	designs	design	NOUN
ejpam-5353	455	30	and	and	CCONJ
ejpam-5353	455	31	related	related	ADJ
ejpam-5353	455	32	structures	structure	NOUN
ejpam-5353	455	33	can	can	AUX
ejpam-5353	455	34	be	be	AUX
ejpam-5353	455	35	utilized	utilize	VERB
ejpam-5353	455	36	to	to	PART
ejpam-5353	455	37	create	create	VERB
ejpam-5353	455	38	codes	code	NOUN
ejpam-5353	455	39	using	use	VERB
ejpam-5353	455	40	the	the	DET
ejpam-5353	455	41	incidence	incidence	ADJ
ejpam-5353	455	42	matrix	matrix	NOUN
ejpam-5353	455	43	.	.	PUNCT
ejpam-5353	456	1	the	the	DET
ejpam-5353	456	2	interaction	interaction	NOUN
ejpam-5353	456	3	between	between	ADP
ejpam-5353	456	4	designs	design	NOUN
ejpam-5353	456	5	and	and	CCONJ
ejpam-5353	456	6	codes	code	NOUN
ejpam-5353	456	7	has	have	AUX
ejpam-5353	456	8	led	lead	VERB
ejpam-5353	456	9	to	to	ADP
ejpam-5353	456	10	many	many	ADJ
ejpam-5353	456	11	intriguing	intriguing	ADJ
ejpam-5353	456	12	and	and	CCONJ
ejpam-5353	456	13	valuable	valuable	ADJ
ejpam-5353	456	14	results	result	NOUN
ejpam-5353	456	15	[	[	X
ejpam-5353	456	16	12	12	NUM
ejpam-5353	456	17	]	]	PUNCT
ejpam-5353	456	18	as	as	ADP
ejpam-5353	456	19	a	a	DET
ejpam-5353	456	20	good	good	ADJ
ejpam-5353	456	21	survey	survey	NOUN
ejpam-5353	456	22	.	.	PUNCT
ejpam-5353	457	1	lately	lately	ADV
ejpam-5353	457	2	,	,	PUNCT
ejpam-5353	457	3	there	there	PRON
ejpam-5353	457	4	has	have	AUX
ejpam-5353	457	5	been	be	AUX
ejpam-5353	457	6	a	a	DET
ejpam-5353	457	7	heightened	heightened	ADJ
ejpam-5353	457	8	focus	focus	NOUN
ejpam-5353	457	9	on	on	ADP
ejpam-5353	457	10	codes	code	NOUN
ejpam-5353	457	11	derived	derive	VERB
ejpam-5353	457	12	from	from	ADP
ejpam-5353	457	13	graphs	graph	NOUN
ejpam-5353	457	14	.	.	PUNCT
ejpam-5353	458	1	the	the	DET
ejpam-5353	458	2	literature	literature	NOUN
ejpam-5353	458	3	extensively	extensively	ADV
ejpam-5353	458	4	delves	delve	VERB
ejpam-5353	458	5	into	into	ADP
ejpam-5353	458	6	the	the	DET
ejpam-5353	458	7	relationship	relationship	NOUN
ejpam-5353	458	8	between	between	ADP
ejpam-5353	458	9	codes	code	NOUN
ejpam-5353	458	10	and	and	CCONJ
ejpam-5353	458	11	graphs	graph	NOUN
ejpam-5353	458	12	from	from	ADP
ejpam-5353	458	13	multiple	multiple	ADJ
ejpam-5353	458	14	perspectives	perspective	NOUN
ejpam-5353	458	15	.	.	PUNCT
ejpam-5353	459	1	the	the	DET
ejpam-5353	459	2	primary	primary	ADJ
ejpam-5353	459	3	aim	aim	NOUN
ejpam-5353	459	4	of	of	ADP
ejpam-5353	459	5	these	these	DET
ejpam-5353	459	6	studies	study	NOUN
ejpam-5353	459	7	is	be	AUX
ejpam-5353	459	8	to	to	PART
ejpam-5353	459	9	select	select	VERB
ejpam-5353	459	10	a	a	DET
ejpam-5353	459	11	specific	specific	ADJ
ejpam-5353	459	12	class	class	NOUN
ejpam-5353	459	13	of	of	ADP
ejpam-5353	459	14	graphs	graph	NOUN
ejpam-5353	459	15	and	and	CCONJ
ejpam-5353	459	16	form	form	NOUN
ejpam-5353	459	17	codes	code	NOUN
ejpam-5353	459	18	from	from	ADP
ejpam-5353	459	19	the	the	DET
ejpam-5353	459	20	graph	graph	NOUN
ejpam-5353	459	21	’s	’s	PART
ejpam-5353	459	22	adjacency	adjacency	NOUN
ejpam-5353	459	23	matrix	matrix	NOUN
ejpam-5353	459	24	.	.	PUNCT
ejpam-5353	460	1	the	the	DET
ejpam-5353	460	2	characteristics	characteristic	NOUN
ejpam-5353	460	3	of	of	ADP
ejpam-5353	460	4	the	the	DET
ejpam-5353	460	5	graph	graph	NOUN
ejpam-5353	460	6	can	can	AUX
ejpam-5353	460	7	give	give	VERB
ejpam-5353	460	8	rise	rise	NOUN
ejpam-5353	460	9	to	to	ADP
ejpam-5353	460	10	diverse	diverse	ADJ
ejpam-5353	460	11	types	type	NOUN
ejpam-5353	460	12	of	of	ADP
ejpam-5353	460	13	codes	code	NOUN
ejpam-5353	460	14	,	,	PUNCT
ejpam-5353	460	15	including	include	VERB
ejpam-5353	460	16	self	self	NOUN
ejpam-5353	460	17	-	-	PUNCT
ejpam-5353	460	18	dual	dual	ADJ
ejpam-5353	460	19	codes	code	NOUN
ejpam-5353	460	20	,	,	PUNCT
ejpam-5353	460	21	self	self	NOUN
ejpam-5353	460	22	-	-	PUNCT
ejpam-5353	460	23	orthogonal	orthogonal	ADJ
ejpam-5353	460	24	codes	code	NOUN
ejpam-5353	460	25	,	,	PUNCT
ejpam-5353	460	26	authentication	authentication	NOUN
ejpam-5353	460	27	codes	code	NOUN
ejpam-5353	460	28	,	,	PUNCT
ejpam-5353	460	29	etc	etc	X
ejpam-5353	460	30	.	.	X
ejpam-5353	460	31	further	further	ADJ
ejpam-5353	460	32	details	detail	NOUN
ejpam-5353	460	33	on	on	ADP
ejpam-5353	460	34	this	this	DET
ejpam-5353	460	35	subject	subject	NOUN
ejpam-5353	460	36	can	can	AUX
ejpam-5353	460	37	be	be	AUX
ejpam-5353	460	38	found	find	VERB
ejpam-5353	460	39	in	in	ADP
ejpam-5353	460	40	[	[	X
ejpam-5353	460	41	2	2	NUM
ejpam-5353	460	42	,	,	PUNCT
ejpam-5353	460	43	4	4	NUM
ejpam-5353	460	44	,	,	PUNCT
ejpam-5353	460	45	5	5	NUM
ejpam-5353	460	46	,	,	PUNCT
ejpam-5353	460	47	8	8	NUM
ejpam-5353	460	48	,	,	PUNCT
ejpam-5353	460	49	9	9	NUM
ejpam-5353	460	50	,	,	PUNCT
ejpam-5353	460	51	13	13	NUM
ejpam-5353	460	52	,	,	PUNCT
ejpam-5353	460	53	15	15	NUM
ejpam-5353	460	54	,	,	PUNCT
ejpam-5353	460	55	17–19	17–19	NUM
ejpam-5353	460	56	]	]	PUNCT
ejpam-5353	460	57	.	.	PUNCT
ejpam-5353	461	1	binary	binary	ADJ
ejpam-5353	461	2	codes	code	NOUN
ejpam-5353	461	3	can	can	AUX
ejpam-5353	461	4	be	be	AUX
ejpam-5353	461	5	produced	produce	VERB
ejpam-5353	461	6	from	from	ADP
ejpam-5353	461	7	various	various	ADJ
ejpam-5353	461	8	graphs	graph	NOUN
ejpam-5353	461	9	such	such	ADJ
ejpam-5353	461	10	as	as	ADP
ejpam-5353	461	11	paley	paley	ADJ
ejpam-5353	461	12	graphs	graph	NOUN
ejpam-5353	461	13	and	and	CCONJ
ejpam-5353	461	14	latin	latin	ADJ
ejpam-5353	461	15	square	square	ADJ
ejpam-5353	461	16	graphs	graph	NOUN
ejpam-5353	461	17	[	[	X
ejpam-5353	461	18	3	3	NUM
ejpam-5353	461	19	,	,	PUNCT
ejpam-5353	461	20	23	23	NUM
ejpam-5353	461	21	]	]	PUNCT
ejpam-5353	461	22	.	.	PUNCT
ejpam-5353	462	1	furthermore	furthermore	ADV
ejpam-5353	462	2	,	,	PUNCT
ejpam-5353	462	3	non	non	ADJ
ejpam-5353	462	4	-	-	ADJ
ejpam-5353	462	5	isomorphic	isomorphic	ADJ
ejpam-5353	462	6	codes	code	NOUN
ejpam-5353	462	7	have	have	AUX
ejpam-5353	462	8	been	be	AUX
ejpam-5353	462	9	generated	generate	VERB
ejpam-5353	462	10	from	from	ADP
ejpam-5353	462	11	non	non	ADJ
ejpam-5353	462	12	-	-	ADJ
ejpam-5353	462	13	isomorphic	isomorphic	ADJ
ejpam-5353	462	14	graphs	graph	NOUN
ejpam-5353	462	15	.	.	PUNCT
ejpam-5353	463	1	this	this	DET
ejpam-5353	463	2	section	section	NOUN
ejpam-5353	463	3	focuses	focus	VERB
ejpam-5353	463	4	on	on	ADP
ejpam-5353	463	5	binary	binary	ADJ
ejpam-5353	463	6	codes	code	NOUN
ejpam-5353	463	7	originating	originate	VERB
ejpam-5353	463	8	from	from	ADP
ejpam-5353	463	9	the	the	DET
ejpam-5353	463	10	row	row	NOUN
ejpam-5353	463	11	span	span	NOUN
ejpam-5353	463	12	of	of	ADP
ejpam-5353	463	13	the	the	DET
ejpam-5353	463	14	incidence	incidence	ADJ
ejpam-5353	463	15	matrices	matrix	NOUN
ejpam-5353	463	16	of	of	ADP
ejpam-5353	463	17	particular	particular	ADJ
ejpam-5353	463	18	graphs	graph	NOUN
ejpam-5353	463	19	that	that	PRON
ejpam-5353	463	20	appear	appear	VERB
ejpam-5353	463	21	as	as	ADP
ejpam-5353	463	22	induced	induced	ADJ
ejpam-5353	463	23	subgraphs	subgraph	NOUN
ejpam-5353	463	24	of	of	ADP
ejpam-5353	463	25	complete	complete	ADJ
ejpam-5353	463	26	bipartite	bipartite	NOUN
ejpam-5353	463	27	graphs	graph	NOUN
ejpam-5353	463	28	.	.	PUNCT
ejpam-5353	464	1	these	these	DET
ejpam-5353	464	2	codes	code	NOUN
ejpam-5353	464	3	are	be	AUX
ejpam-5353	464	4	termed	term	VERB
ejpam-5353	464	5	binary	binary	ADJ
ejpam-5353	464	6	graph	graph	NOUN
ejpam-5353	464	7	-	-	PUNCT
ejpam-5353	464	8	codes	code	NOUN
ejpam-5353	464	9	.	.	PUNCT
ejpam-5353	465	1	additionally	additionally	ADV
ejpam-5353	465	2	,	,	PUNCT
ejpam-5353	465	3	if	if	SCONJ
ejpam-5353	465	4	each	each	DET
ejpam-5353	465	5	codeword	codeword	NOUN
ejpam-5353	465	6	in	in	ADP
ejpam-5353	465	7	a	a	DET
ejpam-5353	465	8	graph	graph	NOUN
ejpam-5353	465	9	-	-	PUNCT
ejpam-5353	465	10	code	code	NOUN
ejpam-5353	465	11	corresponds	correspond	NOUN
ejpam-5353	465	12	to	to	ADP
ejpam-5353	465	13	a	a	DET
ejpam-5353	465	14	graph	graph	NOUN
ejpam-5353	465	15	that	that	PRON
ejpam-5353	465	16	is	be	AUX
ejpam-5353	465	17	isomorphic	isomorphic	ADJ
ejpam-5353	465	18	to	to	PART
ejpam-5353	465	19	graph	graph	VERB
ejpam-5353	465	20	g	g	PROPN
ejpam-5353	465	21	,	,	PUNCT
ejpam-5353	465	22	the	the	DET
ejpam-5353	465	23	code	code	NOUN
ejpam-5353	465	24	is	be	AUX
ejpam-5353	465	25	known	know	VERB
ejpam-5353	465	26	as	as	ADP
ejpam-5353	465	27	a	a	DET
ejpam-5353	465	28	binary	binary	ADJ
ejpam-5353	465	29	g−code	g−code	NOUN
ejpam-5353	465	30	.	.	PUNCT
ejpam-5353	466	1	by	by	ADP
ejpam-5353	466	2	utilizing	utilize	VERB
ejpam-5353	466	3	an	an	DET
ejpam-5353	466	4	odc	odc	NOUN
ejpam-5353	466	5	of	of	ADP
ejpam-5353	466	6	a	a	DET
ejpam-5353	466	7	complete	complete	ADJ
ejpam-5353	466	8	bipartite	bipartite	NOUN
ejpam-5353	466	9	graph	graph	NOUN
ejpam-5353	466	10	,	,	PUNCT
ejpam-5353	466	11	we	we	PRON
ejpam-5353	466	12	develop	develop	VERB
ejpam-5353	466	13	binary	binary	ADJ
ejpam-5353	466	14	codes	code	NOUN
ejpam-5353	466	15	that	that	PRON
ejpam-5353	466	16	ensure	ensure	VERB
ejpam-5353	466	17	the	the	DET
ejpam-5353	466	18	inner	inner	ADJ
ejpam-5353	466	19	product	product	NOUN
ejpam-5353	466	20	of	of	ADP
ejpam-5353	466	21	any	any	DET
ejpam-5353	466	22	two	two	NUM
ejpam-5353	466	23	codewords	codeword	NOUN
ejpam-5353	466	24	is	be	AUX
ejpam-5353	466	25	less	less	ADJ
ejpam-5353	466	26	than	than	ADP
ejpam-5353	466	27	or	or	CCONJ
ejpam-5353	466	28	equal	equal	ADJ
ejpam-5353	466	29	to	to	ADP
ejpam-5353	466	30	1	1	NUM
ejpam-5353	466	31	.	.	PUNCT
ejpam-5353	467	1	therefore	therefore	ADV
ejpam-5353	467	2	,	,	PUNCT
ejpam-5353	467	3	binary	binary	NOUN
ejpam-5353	467	4	g−codes	g−code	NOUN
ejpam-5353	467	5	are	be	AUX
ejpam-5353	467	6	viewed	view	VERB
ejpam-5353	467	7	as	as	ADP
ejpam-5353	467	8	a	a	DET
ejpam-5353	467	9	distinct	distinct	ADJ
ejpam-5353	467	10	subset	subset	NOUN
ejpam-5353	467	11	of	of	ADP
ejpam-5353	467	12	orthogonal	orthogonal	ADJ
ejpam-5353	467	13	codes	code	NOUN
ejpam-5353	467	14	.	.	PUNCT
ejpam-5353	468	1	the	the	DET
ejpam-5353	468	2	unique	unique	ADJ
ejpam-5353	468	3	properties	property	NOUN
ejpam-5353	468	4	of	of	ADP
ejpam-5353	468	5	an	an	DET
ejpam-5353	468	6	odc	odc	NOUN
ejpam-5353	468	7	of	of	ADP
ejpam-5353	468	8	a	a	DET
ejpam-5353	468	9	complete	complete	ADJ
ejpam-5353	468	10	bipartite	bipartite	NOUN
ejpam-5353	468	11	graph	graph	NOUN
ejpam-5353	468	12	suggest	suggest	VERB
ejpam-5353	468	13	that	that	SCONJ
ejpam-5353	468	14	binary	binary	ADJ
ejpam-5353	468	15	g−codes	g−code	NOUN
ejpam-5353	468	16	derived	derive	VERB
ejpam-5353	468	17	from	from	ADP
ejpam-5353	468	18	odcs	odc	NOUN
ejpam-5353	468	19	may	may	AUX
ejpam-5353	468	20	serve	serve	VERB
ejpam-5353	468	21	as	as	ADP
ejpam-5353	468	22	effective	effective	ADJ
ejpam-5353	468	23	error	error	NOUN
ejpam-5353	468	24	detection	detection	NOUN
ejpam-5353	468	25	and	and	CCONJ
ejpam-5353	468	26	correction	correction	NOUN
ejpam-5353	468	27	codes	code	NOUN
ejpam-5353	468	28	.	.	PUNCT
ejpam-5353	469	1	theorem	theorem	NOUN
ejpam-5353	469	2	22	22	NUM
ejpam-5353	469	3	.	.	PUNCT
ejpam-5353	470	1	let	let	VERB
ejpam-5353	470	2	there	there	PRON
ejpam-5353	470	3	is	be	VERB
ejpam-5353	470	4	an	an	DET
ejpam-5353	470	5	odc	odc	NOUN
ejpam-5353	470	6	of	of	ADP
ejpam-5353	470	7	kn	kn	PROPN
ejpam-5353	470	8	,	,	PUNCT
ejpam-5353	470	9	n	n	CCONJ
ejpam-5353	470	10	by	by	ADP
ejpam-5353	470	11	a	a	DET
ejpam-5353	470	12	tree	tree	NOUN
ejpam-5353	470	13	.	.	PUNCT
ejpam-5353	471	1	then	then	ADV
ejpam-5353	471	2	there	there	PRON
ejpam-5353	471	3	is	be	VERB
ejpam-5353	471	4	a	a	DET
ejpam-5353	471	5	treebinary	treebinary	ADJ
ejpam-5353	471	6	code	code	NOUN
ejpam-5353	471	7	of	of	ADP
ejpam-5353	471	8	length	length	NOUN
ejpam-5353	471	9	n2	n2	NOUN
ejpam-5353	471	10	.	.	PUNCT
ejpam-5353	472	1	proof	proof	NOUN
ejpam-5353	472	2	.	.	PUNCT
ejpam-5353	473	1	given	give	VERB
ejpam-5353	473	2	an	an	DET
ejpam-5353	473	3	odc	odc	NOUN
ejpam-5353	473	4	g	g	NOUN
ejpam-5353	473	5	=	=	PRON
ejpam-5353	473	6	{	{	PUNCT
ejpam-5353	473	7	gi	gi	X
ejpam-5353	473	8	a	a	PRON
ejpam-5353	473	9	:	:	PUNCT
ejpam-5353	473	10	a	a	DET
ejpam-5353	473	11	∈	∈	PROPN
ejpam-5353	473	12	zn	zn	X
ejpam-5353	473	13	,	,	PUNCT
ejpam-5353	473	14	i	i	PRON
ejpam-5353	473	15	∈	∈	PROPN
ejpam-5353	473	16	{	{	PUNCT
ejpam-5353	473	17	1	1	NUM
ejpam-5353	473	18	,	,	PUNCT
ejpam-5353	473	19	2	2	NUM
ejpam-5353	473	20	}	}	PUNCT
ejpam-5353	473	21	}	}	PUNCT
ejpam-5353	473	22	of	of	ADP
ejpam-5353	473	23	kn	kn	PROPN
ejpam-5353	473	24	,	,	PUNCT
ejpam-5353	473	25	n	n	CCONJ
ejpam-5353	473	26	by	by	ADP
ejpam-5353	473	27	a	a	DET
ejpam-5353	473	28	tree	tree	NOUN
ejpam-5353	473	29	g.	g.	NOUN
ejpam-5353	473	30	the	the	DET
ejpam-5353	473	31	incidence	incidence	NOUN
ejpam-5353	473	32	matrix	matrix	NOUN
ejpam-5353	473	33	l	l	NOUN
ejpam-5353	473	34	=	=	PUNCT
ejpam-5353	473	35	l	l	X
ejpam-5353	473	36	(	(	PUNCT
ejpam-5353	473	37	s	s	PROPN
ejpam-5353	473	38	,	,	PUNCT
ejpam-5353	473	39	t	t	PROPN
ejpam-5353	473	40	)	)	PUNCT
ejpam-5353	473	41	for	for	ADP
ejpam-5353	473	42	such	such	ADJ
ejpam-5353	473	43	odc	odc	PROPN
ejpam-5353	473	44	g	g	PROPN
ejpam-5353	473	45	=	=	PRON
ejpam-5353	473	46	{	{	PUNCT
ejpam-5353	473	47	gi	gi	X
ejpam-5353	473	48	a	a	NOUN
ejpam-5353	473	49	;	;	PUNCT
ejpam-5353	473	50	a	a	DET
ejpam-5353	473	51	∈	∈	PROPN
ejpam-5353	473	52	zn	zn	X
ejpam-5353	473	53	,	,	PUNCT
ejpam-5353	473	54	i	i	PRON
ejpam-5353	473	55	∈	∈	PROPN
ejpam-5353	473	56	{	{	PUNCT
ejpam-5353	473	57	1	1	NUM
ejpam-5353	473	58	,	,	PUNCT
ejpam-5353	473	59	2	2	NUM
ejpam-5353	473	60	}	}	PUNCT
ejpam-5353	473	61	}	}	PUNCT
ejpam-5353	473	62	is	be	AUX
ejpam-5353	473	63	a	a	DET
ejpam-5353	473	64	2n×	2n×	NUM
ejpam-5353	473	65	n2	n2	ADJ
ejpam-5353	473	66	binary	binary	ADJ
ejpam-5353	473	67	matrix	matrix	NOUN
ejpam-5353	473	68	showing	show	VERB
ejpam-5353	473	69	the	the	DET
ejpam-5353	473	70	relation	relation	NOUN
ejpam-5353	473	71	between	between	ADP
ejpam-5353	473	72	the	the	DET
ejpam-5353	473	73	edges	edge	NOUN
ejpam-5353	473	74	of	of	ADP
ejpam-5353	473	75	kn	kn	PROPN
ejpam-5353	473	76	,	,	PUNCT
ejpam-5353	473	77	n	n	PROPN
ejpam-5353	473	78	and	and	CCONJ
ejpam-5353	473	79	the	the	DET
ejpam-5353	473	80	the	the	DET
ejpam-5353	473	81	members	member	NOUN
ejpam-5353	473	82	of	of	ADP
ejpam-5353	473	83	g	g	NOUN
ejpam-5353	473	84	such	such	ADJ
ejpam-5353	473	85	that	that	SCONJ
ejpam-5353	473	86	every	every	DET
ejpam-5353	473	87	row	row	NOUN
ejpam-5353	473	88	in	in	ADP
ejpam-5353	473	89	l	l	NOUN
ejpam-5353	473	90	corresponds	correspond	VERB
ejpam-5353	473	91	to	to	ADP
ejpam-5353	473	92	a	a	DET
ejpam-5353	473	93	unique	unique	ADJ
ejpam-5353	473	94	graph	graph	NOUN
ejpam-5353	473	95	in	in	ADP
ejpam-5353	473	96	g	g	PROPN
ejpam-5353	473	97	and	and	CCONJ
ejpam-5353	473	98	every	every	DET
ejpam-5353	473	99	column	column	NOUN
ejpam-5353	473	100	in	in	ADP
ejpam-5353	473	101	l	l	NOUN
ejpam-5353	473	102	corresponds	correspond	VERB
ejpam-5353	473	103	to	to	ADP
ejpam-5353	473	104	a	a	DET
ejpam-5353	473	105	unique	unique	ADJ
ejpam-5353	473	106	edge	edge	NOUN
ejpam-5353	473	107	in	in	ADP
ejpam-5353	473	108	kn	kn	PROPN
ejpam-5353	473	109	,	,	PUNCT
ejpam-5353	473	110	n.	n.	PROPN
ejpam-5353	473	111	let	let	VERB
ejpam-5353	473	112	the	the	DET
ejpam-5353	473	113	edge	edge	NOUN
ejpam-5353	473	114	(	(	PUNCT
ejpam-5353	473	115	α0	α0	ADJ
ejpam-5353	473	116	,	,	PUNCT
ejpam-5353	473	117	β1	β1	PROPN
ejpam-5353	473	118	)	)	PUNCT
ejpam-5353	473	119	∈	∈	PROPN
ejpam-5353	473	120	e	e	X
ejpam-5353	473	121	(	(	PUNCT
ejpam-5353	473	122	kn	kn	PROPN
ejpam-5353	473	123	,	,	PUNCT
ejpam-5353	473	124	n	n	CCONJ
ejpam-5353	473	125	)	)	PUNCT
ejpam-5353	473	126	.	.	PUNCT
ejpam-5353	474	1	then	then	ADV
ejpam-5353	474	2	l	l	PROPN
ejpam-5353	474	3	has	have	VERB
ejpam-5353	474	4	a	a	DET
ejpam-5353	474	5	unique	unique	ADJ
ejpam-5353	474	6	column	column	NOUN
ejpam-5353	474	7	t	t	PROPN
ejpam-5353	474	8	corresponds	correspond	VERB
ejpam-5353	474	9	to	to	ADP
ejpam-5353	474	10	this	this	DET
ejpam-5353	474	11	edge	edge	NOUN
ejpam-5353	474	12	(	(	PUNCT
ejpam-5353	474	13	α0	α0	ADJ
ejpam-5353	474	14	,	,	PUNCT
ejpam-5353	474	15	β1	β1	PROPN
ejpam-5353	474	16	)	)	PUNCT
ejpam-5353	474	17	.	.	PUNCT
ejpam-5353	475	1	such	such	ADJ
ejpam-5353	475	2	column	column	NOUN
ejpam-5353	475	3	t	t	PROPN
ejpam-5353	475	4	is	be	AUX
ejpam-5353	475	5	defined	define	VERB
ejpam-5353	475	6	from	from	ADP
ejpam-5353	475	7	an	an	DET
ejpam-5353	475	8	injective	injective	ADJ
ejpam-5353	475	9	function	function	NOUN
ejpam-5353	475	10	c	c	NOUN
ejpam-5353	475	11	:	:	PUNCT
ejpam-5353	476	1	e	e	X
ejpam-5353	476	2	(	(	PUNCT
ejpam-5353	476	3	kn	kn	PROPN
ejpam-5353	476	4	,	,	PUNCT
ejpam-5353	476	5	n)→	n)→	PROPN
ejpam-5353	476	6	{	{	PUNCT
ejpam-5353	476	7	0	0	NUM
ejpam-5353	476	8	,	,	PUNCT
ejpam-5353	476	9	1	1	NUM
ejpam-5353	476	10	,	,	PUNCT
ejpam-5353	476	11	·	·	PUNCT
ejpam-5353	476	12	·	·	PUNCT
ejpam-5353	476	13	·	·	PUNCT
ejpam-5353	476	14	,	,	PUNCT
ejpam-5353	476	15	n2	n2	NOUN
ejpam-5353	476	16	−	−	PROPN
ejpam-5353	476	17	1	1	NUM
ejpam-5353	476	18	}	}	PUNCT
ejpam-5353	477	1	where	where	SCONJ
ejpam-5353	477	2	c	c	X
ejpam-5353	477	3	(	(	PUNCT
ejpam-5353	477	4	(	(	PUNCT
ejpam-5353	477	5	α0	α0	ADJ
ejpam-5353	477	6	,	,	PUNCT
ejpam-5353	477	7	β1	β1	PROPN
ejpam-5353	477	8	)	)	PUNCT
ejpam-5353	477	9	)	)	PUNCT
ejpam-5353	478	1	=	=	SYM
ejpam-5353	478	2	t	t	NOUN
ejpam-5353	478	3	=	=	PUNCT
ejpam-5353	478	4	nα	nα	PROPN
ejpam-5353	478	5	+	+	NOUN
ejpam-5353	478	6	β	β	X
ejpam-5353	478	7	;	;	PUNCT
ejpam-5353	478	8	α	α	X
ejpam-5353	478	9	,	,	PUNCT
ejpam-5353	478	10	β	β	X
ejpam-5353	478	11	∈	∈	PROPN
ejpam-5353	478	12	zn	zn	X
ejpam-5353	478	13	.	.	PUNCT
ejpam-5353	479	1	for	for	ADP
ejpam-5353	479	2	each	each	PRON
ejpam-5353	479	3	a	a	DET
ejpam-5353	479	4	graph	graph	NOUN
ejpam-5353	479	5	gi	gi	VERB
ejpam-5353	479	6	a	a	PRON
ejpam-5353	479	7	:	:	PUNCT
ejpam-5353	479	8	(	(	PUNCT
ejpam-5353	479	9	a	a	DET
ejpam-5353	479	10	∈	∈	PROPN
ejpam-5353	479	11	zn	zn	NUM
ejpam-5353	479	12	,	,	PUNCT
ejpam-5353	479	13	i	i	PRON
ejpam-5353	479	14	∈	∈	PROPN
ejpam-5353	479	15	{	{	PUNCT
ejpam-5353	479	16	1	1	NUM
ejpam-5353	479	17	,	,	PUNCT
ejpam-5353	479	18	2	2	NUM
ejpam-5353	479	19	}	}	PUNCT
ejpam-5353	479	20	)	)	PUNCT
ejpam-5353	479	21	,	,	PUNCT
ejpam-5353	479	22	a	a	DET
ejpam-5353	479	23	∈	∈	PROPN
ejpam-5353	479	24	zn	zn	NOUN
ejpam-5353	479	25	from	from	ADP
ejpam-5353	479	26	g	g	NOUN
ejpam-5353	479	27	,	,	PUNCT
ejpam-5353	479	28	there	there	PRON
ejpam-5353	479	29	is	be	VERB
ejpam-5353	479	30	exactly	exactly	ADV
ejpam-5353	479	31	one	one	NUM
ejpam-5353	479	32	row	row	NOUN
ejpam-5353	479	33	s	s	X
ejpam-5353	479	34	∈	∈	NOUN
ejpam-5353	479	35	{	{	PUNCT
ejpam-5353	479	36	0	0	NUM
ejpam-5353	479	37	,	,	PUNCT
ejpam-5353	479	38	1	1	NUM
ejpam-5353	479	39	,	,	PUNCT
ejpam-5353	479	40	·	·	PUNCT
ejpam-5353	479	41	·	·	PUNCT
ejpam-5353	479	42	·	·	PUNCT
ejpam-5353	479	43	,	,	PUNCT
ejpam-5353	480	1	2n−	2n−	PROPN
ejpam-5353	480	2	1	1	NUM
ejpam-5353	480	3	}	}	PUNCT
ejpam-5353	480	4	in	in	ADP
ejpam-5353	480	5	l	l	NOUN
ejpam-5353	480	6	corresponds	correspond	NOUN
ejpam-5353	480	7	to	to	PART
ejpam-5353	480	8	gi	gi	VERB
ejpam-5353	480	9	a	a	PRON
ejpam-5353	480	10	according	accord	VERB
ejpam-5353	480	11	the	the	DET
ejpam-5353	480	12	injective	injective	ADJ
ejpam-5353	480	13	function	function	NOUN
ejpam-5353	480	14	rg	rg	NOUN
ejpam-5353	480	15	:	:	PUNCT
ejpam-5353	480	16	zn	zn	PROPN
ejpam-5353	480	17	×	×	PROPN
ejpam-5353	480	18	{	{	PUNCT
ejpam-5353	480	19	1	1	NUM
ejpam-5353	480	20	,	,	PUNCT
ejpam-5353	480	21	2	2	NUM
ejpam-5353	480	22	}	}	PUNCT
ejpam-5353	480	23	→	→	SYM
ejpam-5353	480	24	{	{	PUNCT
ejpam-5353	480	25	0	0	NUM
ejpam-5353	480	26	,	,	PUNCT
ejpam-5353	480	27	1	1	NUM
ejpam-5353	480	28	,	,	PUNCT
ejpam-5353	480	29	·	·	PUNCT
ejpam-5353	480	30	·	·	PUNCT
ejpam-5353	480	31	·	·	PUNCT
ejpam-5353	480	32	,	,	PUNCT
ejpam-5353	480	33	2n−	2n−	PROPN
ejpam-5353	480	34	1	1	NUM
ejpam-5353	480	35	}	}	PUNCT
ejpam-5353	480	36	where	where	SCONJ
ejpam-5353	480	37	rg	rg	PROPN
ejpam-5353	480	38	(	(	PUNCT
ejpam-5353	480	39	a	a	PROPN
ejpam-5353	480	40	,	,	PUNCT
ejpam-5353	480	41	i	i	NOUN
ejpam-5353	480	42	)	)	PUNCT
ejpam-5353	480	43	=	=	PUNCT
ejpam-5353	480	44	s	s	PART
ejpam-5353	480	45	=	=	PUNCT
ejpam-5353	480	46	{	{	PUNCT
ejpam-5353	480	47	a	a	X
ejpam-5353	480	48	if	if	SCONJ
ejpam-5353	480	49	i	i	PRON
ejpam-5353	480	50	=	=	SYM
ejpam-5353	480	51	1	1	X
ejpam-5353	480	52	a+	a+	SYM
ejpam-5353	480	53	n	n	NOUN
ejpam-5353	480	54	if	if	SCONJ
ejpam-5353	480	55	i	i	PRON
ejpam-5353	480	56	=	=	NOUN
ejpam-5353	480	57	2	2	X
ejpam-5353	480	58	.	.	PUNCT
ejpam-5353	480	59	then	then	ADV
ejpam-5353	480	60	,	,	PUNCT
ejpam-5353	480	61	the	the	DET
ejpam-5353	480	62	incidence	incidence	NOUN
ejpam-5353	480	63	matrix	matrix	NOUN
ejpam-5353	480	64	l	l	NOUN
ejpam-5353	480	65	=	=	PUNCT
ejpam-5353	480	66	l	l	X
ejpam-5353	480	67	(	(	PUNCT
ejpam-5353	480	68	s	s	PROPN
ejpam-5353	480	69	,	,	PUNCT
ejpam-5353	480	70	t	t	PROPN
ejpam-5353	480	71	)	)	PUNCT
ejpam-5353	480	72	of	of	ADP
ejpam-5353	480	73	an	an	DET
ejpam-5353	480	74	odc	odc	PROPN
ejpam-5353	480	75	g	g	NOUN
ejpam-5353	480	76	is	be	AUX
ejpam-5353	480	77	defined	define	VERB
ejpam-5353	480	78	as	as	ADP
ejpam-5353	480	79	l	l	NOUN
ejpam-5353	480	80	(	(	PUNCT
ejpam-5353	480	81	s	s	PROPN
ejpam-5353	480	82	,	,	PUNCT
ejpam-5353	480	83	t	t	PROPN
ejpam-5353	480	84	)	)	PUNCT
ejpam-5353	480	85	=	=	PRON
ejpam-5353	480	86	{	{	PUNCT
ejpam-5353	480	87	1	1	NUM
ejpam-5353	481	1	if	if	SCONJ
ejpam-5353	481	2	(	(	PUNCT
ejpam-5353	481	3	α0	α0	ADJ
ejpam-5353	481	4	,	,	PUNCT
ejpam-5353	481	5	β1	β1	PROPN
ejpam-5353	481	6	)	)	PUNCT
ejpam-5353	481	7	∈	∈	PROPN
ejpam-5353	481	8	e	e	X
ejpam-5353	481	9	(	(	PUNCT
ejpam-5353	481	10	gi	gi	INTJ
ejpam-5353	481	11	a	a	PRON
ejpam-5353	481	12	)	)	PUNCT
ejpam-5353	481	13	0	0	PUNCT
ejpam-5353	482	1	if	if	SCONJ
ejpam-5353	482	2	(	(	PUNCT
ejpam-5353	482	3	α0	α0	ADJ
ejpam-5353	482	4	,	,	PUNCT
ejpam-5353	482	5	β1	β1	PROPN
ejpam-5353	482	6	)	)	PUNCT
ejpam-5353	482	7	/∈	/∈	PUNCT
ejpam-5353	483	1	e	e	NOUN
ejpam-5353	483	2	(	(	PUNCT
ejpam-5353	483	3	gi	gi	INTJ
ejpam-5353	483	4	a	a	PRON
ejpam-5353	483	5	)	)	PUNCT
ejpam-5353	483	6	h.	h.	PROPN
ejpam-5353	483	7	shabana	shabana	PROPN
ejpam-5353	483	8	,	,	PUNCT
ejpam-5353	483	9	r.	r.	PROPN
ejpam-5353	483	10	el	el	PROPN
ejpam-5353	483	11	-	-	PROPN
ejpam-5353	483	12	shanawany	shanawany	NOUN
ejpam-5353	483	13	,	,	PUNCT
ejpam-5353	483	14	s.	s.	PROPN
ejpam-5353	483	15	halawa	halawa	PROPN
ejpam-5353	483	16	/	/	PUNCT
ejpam-5353	483	17	eur	eur	PROPN
ejpam-5353	483	18	.	.	PUNCT
ejpam-5353	484	1	j.	j.	PROPN
ejpam-5353	484	2	pure	pure	PROPN
ejpam-5353	484	3	appl	appl	PROPN
ejpam-5353	484	4	.	.	PROPN
ejpam-5353	484	5	math	math	PROPN
ejpam-5353	484	6	,	,	PUNCT
ejpam-5353	484	7	17	17	NUM
ejpam-5353	484	8	(	(	PUNCT
ejpam-5353	484	9	4	4	NUM
ejpam-5353	484	10	)	)	PUNCT
ejpam-5353	484	11	(	(	PUNCT
ejpam-5353	484	12	2024	2024	NUM
ejpam-5353	484	13	)	)	PUNCT
ejpam-5353	484	14	,	,	PUNCT
ejpam-5353	484	15	3492	3492	NUM
ejpam-5353	484	16	-	-	SYM
ejpam-5353	484	17	3516	3516	NUM
ejpam-5353	484	18	3510	3510	NUM
ejpam-5353	484	19	the	the	DET
ejpam-5353	484	20	rows	row	NOUN
ejpam-5353	484	21	of	of	ADP
ejpam-5353	484	22	l	l	NOUN
ejpam-5353	484	23	can	can	AUX
ejpam-5353	484	24	form	form	VERB
ejpam-5353	484	25	a	a	DET
ejpam-5353	484	26	graph	graph	NOUN
ejpam-5353	484	27	binary	binary	PROPN
ejpam-5353	484	28	code	code	PROPN
ejpam-5353	484	29	.	.	PUNCT
ejpam-5353	485	1	this	this	DET
ejpam-5353	485	2	binary	binary	PROPN
ejpam-5353	485	3	code	code	PROPN
ejpam-5353	485	4	will	will	AUX
ejpam-5353	485	5	be	be	AUX
ejpam-5353	485	6	denoted	denote	VERB
ejpam-5353	485	7	as	as	ADP
ejpam-5353	485	8	cr	cr	X
ejpam-5353	485	9	.	.	PUNCT
ejpam-5353	486	1	the	the	DET
ejpam-5353	486	2	encoding	encoding	NOUN
ejpam-5353	486	3	process	process	NOUN
ejpam-5353	486	4	in	in	ADP
ejpam-5353	486	5	cr	cr	PROPN
ejpam-5353	486	6	is	be	AUX
ejpam-5353	486	7	manipulated	manipulate	VERB
ejpam-5353	486	8	in	in	ADP
ejpam-5353	486	9	two	two	NUM
ejpam-5353	486	10	consecutive	consecutive	ADJ
ejpam-5353	486	11	steps	step	NOUN
ejpam-5353	486	12	.	.	PUNCT
ejpam-5353	487	1	suppose	suppose	VERB
ejpam-5353	487	2	that	that	SCONJ
ejpam-5353	487	3	(	(	PUNCT
ejpam-5353	487	4	a	a	X
ejpam-5353	487	5	,	,	PUNCT
ejpam-5353	487	6	i	i	NOUN
ejpam-5353	487	7	)	)	PUNCT
ejpam-5353	487	8	∈	∈	PROPN
ejpam-5353	487	9	zn×{1	zn×{1	NOUN
ejpam-5353	487	10	,	,	PUNCT
ejpam-5353	487	11	2	2	NUM
ejpam-5353	487	12	}	}	PUNCT
ejpam-5353	487	13	is	be	AUX
ejpam-5353	487	14	a	a	DET
ejpam-5353	487	15	plain	plain	ADJ
ejpam-5353	487	16	text	text	NOUN
ejpam-5353	487	17	.	.	PUNCT
ejpam-5353	487	18	.	.	PUNCT
ejpam-5353	488	1	in	in	ADP
ejpam-5353	488	2	order	order	NOUN
ejpam-5353	488	3	to	to	PART
ejpam-5353	488	4	build	build	VERB
ejpam-5353	488	5	the	the	DET
ejpam-5353	488	6	cipher	cipher	ADJ
ejpam-5353	488	7	text	text	NOUN
ejpam-5353	488	8	for	for	ADP
ejpam-5353	488	9	(	(	PUNCT
ejpam-5353	488	10	a	a	PROPN
ejpam-5353	488	11	,	,	PUNCT
ejpam-5353	488	12	i	i	PROPN
ejpam-5353	488	13	)	)	PUNCT
ejpam-5353	488	14	,	,	PUNCT
ejpam-5353	488	15	firstly	firstly	ADV
ejpam-5353	488	16	,	,	PUNCT
ejpam-5353	488	17	we	we	PRON
ejpam-5353	488	18	calculate	calculate	VERB
ejpam-5353	488	19	s	s	VERB
ejpam-5353	488	20	=	=	X
ejpam-5353	488	21	rg	rg	X
ejpam-5353	488	22	(	(	PUNCT
ejpam-5353	488	23	a	a	PROPN
ejpam-5353	488	24	,	,	PUNCT
ejpam-5353	488	25	i	i	PROPN
ejpam-5353	488	26	)	)	PUNCT
ejpam-5353	488	27	.	.	PUNCT
ejpam-5353	489	1	using	use	VERB
ejpam-5353	489	2	the	the	DET
ejpam-5353	489	3	above	above	ADJ
ejpam-5353	489	4	definition	definition	NOUN
ejpam-5353	489	5	of	of	ADP
ejpam-5353	489	6	rg	rg	PROPN
ejpam-5353	489	7	.	.	PUNCT
ejpam-5353	490	1	secondly	secondly	ADV
ejpam-5353	490	2	,	,	PUNCT
ejpam-5353	490	3	the	the	DET
ejpam-5353	490	4	cipher	cipher	ADJ
ejpam-5353	490	5	text	text	NOUN
ejpam-5353	490	6	corresponds	correspond	VERB
ejpam-5353	490	7	to	to	ADP
ejpam-5353	490	8	the	the	DET
ejpam-5353	490	9	plain	plain	ADJ
ejpam-5353	490	10	text	text	NOUN
ejpam-5353	490	11	(	(	PUNCT
ejpam-5353	490	12	a	a	X
ejpam-5353	490	13	,	,	PUNCT
ejpam-5353	490	14	i	i	NOUN
ejpam-5353	490	15	)	)	PUNCT
ejpam-5353	490	16	is	be	AUX
ejpam-5353	490	17	the	the	DET
ejpam-5353	490	18	concatenation	concatenation	NOUN
ejpam-5353	490	19	of	of	ADP
ejpam-5353	490	20	bits	bit	NOUN
ejpam-5353	490	21	of	of	ADP
ejpam-5353	490	22	the	the	DET
ejpam-5353	490	23	row	row	NOUN
ejpam-5353	490	24	s	s	NOUN
ejpam-5353	490	25	in	in	ADP
ejpam-5353	490	26	the	the	DET
ejpam-5353	490	27	matrix	matrix	NOUN
ejpam-5353	490	28	lso	lso	NOUN
ejpam-5353	490	29	will	will	AUX
ejpam-5353	490	30	be	be	AUX
ejpam-5353	490	31	the	the	DET
ejpam-5353	490	32	codeword	codeword	NOUN
ejpam-5353	490	33	ls0ls1ls2···ls(n2−1	ls0ls1ls2···ls(n2−1	NOUN
ejpam-5353	490	34	)	)	PUNCT
ejpam-5353	490	35	is	be	AUX
ejpam-5353	490	36	the	the	DET
ejpam-5353	490	37	corresponding	corresponding	ADJ
ejpam-5353	490	38	cipher	cipher	ADJ
ejpam-5353	490	39	text	text	NOUN
ejpam-5353	490	40	(	(	PUNCT
ejpam-5353	490	41	of	of	ADP
ejpam-5353	490	42	length	length	NOUN
ejpam-5353	490	43	n2	n2	NOUN
ejpam-5353	490	44	)	)	PUNCT
ejpam-5353	490	45	to	to	ADP
ejpam-5353	490	46	the	the	DET
ejpam-5353	490	47	a	a	DET
ejpam-5353	490	48	plain	plain	ADJ
ejpam-5353	490	49	text	text	NOUN
ejpam-5353	490	50	(	(	PUNCT
ejpam-5353	490	51	a	a	PRON
ejpam-5353	490	52	,	,	PUNCT
ejpam-5353	490	53	i	i	PROPN
ejpam-5353	490	54	)	)	PUNCT
ejpam-5353	490	55	.	.	PUNCT
ejpam-5353	491	1	the	the	DET
ejpam-5353	491	2	definition	definition	NOUN
ejpam-5353	491	3	of	of	ADP
ejpam-5353	491	4	the	the	DET
ejpam-5353	491	5	matrix	matrix	NOUN
ejpam-5353	491	6	l	l	NOUN
ejpam-5353	491	7	=	=	PUNCT
ejpam-5353	491	8	l	l	X
ejpam-5353	491	9	(	(	PUNCT
ejpam-5353	491	10	s	s	PROPN
ejpam-5353	491	11	,	,	PUNCT
ejpam-5353	491	12	t	t	PROPN
ejpam-5353	491	13	)	)	PUNCT
ejpam-5353	491	14	implies	imply	VERB
ejpam-5353	491	15	that	that	SCONJ
ejpam-5353	491	16	every	every	DET
ejpam-5353	491	17	row	row	NOUN
ejpam-5353	491	18	in	in	ADP
ejpam-5353	491	19	l	l	NOUN
ejpam-5353	491	20	is	be	AUX
ejpam-5353	491	21	isomorphic	isomorphic	ADJ
ejpam-5353	491	22	to	to	ADP
ejpam-5353	491	23	the	the	DET
ejpam-5353	491	24	tree	tree	NOUN
ejpam-5353	492	1	g.	g.	NOUN
ejpam-5353	492	2	whence	whence	NOUN
ejpam-5353	493	1	every	every	DET
ejpam-5353	493	2	codeword	codeword	NOUN
ejpam-5353	493	3	in	in	ADP
ejpam-5353	493	4	cr	cr	PROPN
ejpam-5353	493	5	is	be	AUX
ejpam-5353	493	6	also	also	ADV
ejpam-5353	493	7	so	so	ADV
ejpam-5353	493	8	.	.	PUNCT
ejpam-5353	494	1	thus	thus	ADV
ejpam-5353	494	2	,	,	PUNCT
ejpam-5353	494	3	cr	cr	PROPN
ejpam-5353	494	4	is	be	AUX
ejpam-5353	494	5	a	a	DET
ejpam-5353	494	6	tree	tree	NOUN
ejpam-5353	494	7	binary	binary	PROPN
ejpam-5353	494	8	code	code	NOUN
ejpam-5353	494	9	induced	induce	VERB
ejpam-5353	494	10	from	from	ADP
ejpam-5353	494	11	an	an	DET
ejpam-5353	494	12	odc	odc	NOUN
ejpam-5353	494	13	of	of	ADP
ejpam-5353	494	14	kn	kn	PROPN
ejpam-5353	494	15	,	,	PUNCT
ejpam-5353	494	16	n	n	CCONJ
ejpam-5353	494	17	by	by	ADP
ejpam-5353	494	18	a	a	DET
ejpam-5353	494	19	tree	tree	NOUN
ejpam-5353	494	20	g.	g.	NOUN
ejpam-5353	494	21	the	the	DET
ejpam-5353	494	22	significance	significance	NOUN
ejpam-5353	494	23	of	of	ADP
ejpam-5353	494	24	the	the	DET
ejpam-5353	494	25	hamming	hamming	NOUN
ejpam-5353	494	26	distance	distance	NOUN
ejpam-5353	494	27	in	in	ADP
ejpam-5353	494	28	binary	binary	ADJ
ejpam-5353	494	29	codes	code	NOUN
ejpam-5353	494	30	lies	lie	VERB
ejpam-5353	494	31	in	in	ADP
ejpam-5353	494	32	its	its	PRON
ejpam-5353	494	33	ability	ability	NOUN
ejpam-5353	494	34	to	to	PART
ejpam-5353	494	35	determine	determine	VERB
ejpam-5353	494	36	error	error	NOUN
ejpam-5353	494	37	detection	detection	NOUN
ejpam-5353	494	38	and	and	CCONJ
ejpam-5353	494	39	correction	correction	NOUN
ejpam-5353	494	40	capabilities	capability	NOUN
ejpam-5353	494	41	within	within	ADP
ejpam-5353	494	42	the	the	DET
ejpam-5353	494	43	code	code	NOUN
ejpam-5353	494	44	.	.	PUNCT
ejpam-5353	495	1	consider	consider	VERB
ejpam-5353	495	2	a	a	DET
ejpam-5353	495	3	binary	binary	ADJ
ejpam-5353	495	4	code	code	NOUN
ejpam-5353	495	5	c	c	NOUN
ejpam-5353	495	6	,	,	PUNCT
ejpam-5353	495	7	where	where	SCONJ
ejpam-5353	495	8	each	each	DET
ejpam-5353	495	9	codeword	codeword	NOUN
ejpam-5353	495	10	has	have	VERB
ejpam-5353	495	11	a	a	DET
ejpam-5353	495	12	length	length	NOUN
ejpam-5353	495	13	of	of	ADP
ejpam-5353	495	14	h.	h.	PROPN
ejpam-5353	495	15	let	let	VERB
ejpam-5353	495	16	x	x	PUNCT
ejpam-5353	495	17	=	=	PUNCT
ejpam-5353	495	18	x1x2	x1x2	X
ejpam-5353	495	19	·	·	PUNCT
ejpam-5353	495	20	·	·	PUNCT
ejpam-5353	495	21	·	·	PUNCT
ejpam-5353	495	22	xh	xh	PROPN
ejpam-5353	495	23	and	and	CCONJ
ejpam-5353	495	24	y	y	PROPN
ejpam-5353	495	25	=	=	PROPN
ejpam-5353	495	26	y1y2	y1y2	PROPN
ejpam-5353	495	27	·	·	PUNCT
ejpam-5353	495	28	·	·	PUNCT
ejpam-5353	495	29	·	·	PUNCT
ejpam-5353	495	30	yh	yh	PRON
ejpam-5353	495	31	be	be	AUX
ejpam-5353	495	32	two	two	NUM
ejpam-5353	495	33	codewords	codeword	NOUN
ejpam-5353	495	34	from	from	ADP
ejpam-5353	495	35	c.the	c.the	DET
ejpam-5353	495	36	distance	distance	NOUN
ejpam-5353	496	1	d	d	NOUN
ejpam-5353	496	2	(	(	PUNCT
ejpam-5353	496	3	x	x	X
ejpam-5353	496	4	,	,	PUNCT
ejpam-5353	496	5	y	y	PROPN
ejpam-5353	496	6	)	)	PUNCT
ejpam-5353	496	7	between	between	ADP
ejpam-5353	496	8	x	x	SYM
ejpam-5353	496	9	and	and	CCONJ
ejpam-5353	496	10	y	y	PROPN
ejpam-5353	496	11	is	be	AUX
ejpam-5353	496	12	calculated	calculate	VERB
ejpam-5353	496	13	as	as	ADP
ejpam-5353	496	14	the	the	DET
ejpam-5353	496	15	count	count	NOUN
ejpam-5353	496	16	of	of	ADP
ejpam-5353	496	17	differing	differ	VERB
ejpam-5353	496	18	bits	bit	NOUN
ejpam-5353	496	19	between	between	ADP
ejpam-5353	496	20	x	x	PROPN
ejpam-5353	496	21	and	and	CCONJ
ejpam-5353	496	22	y.	y.	PROPN
ejpam-5353	496	23	hence	hence	ADV
ejpam-5353	496	24	,	,	PUNCT
ejpam-5353	496	25	d	d	X
ejpam-5353	496	26	(	(	PUNCT
ejpam-5353	496	27	x	x	X
ejpam-5353	496	28	,	,	PUNCT
ejpam-5353	496	29	y	y	PROPN
ejpam-5353	496	30	)	)	PUNCT
ejpam-5353	497	1	=	=	PUNCT
ejpam-5353	498	1	∑h	∑h	PROPN
ejpam-5353	498	2	i=1	i=1	PROPN
ejpam-5353	498	3	d	d	X
ejpam-5353	498	4	(	(	PUNCT
ejpam-5353	498	5	xi	xi	PROPN
ejpam-5353	498	6	,	,	PUNCT
ejpam-5353	498	7	yi	yi	PROPN
ejpam-5353	498	8	)	)	PUNCT
ejpam-5353	498	9	where	where	SCONJ
ejpam-5353	498	10	,	,	PUNCT
ejpam-5353	498	11	d	d	X
ejpam-5353	498	12	(	(	PUNCT
ejpam-5353	498	13	xi	xi	PROPN
ejpam-5353	498	14	,	,	PUNCT
ejpam-5353	498	15	yi	yi	NOUN
ejpam-5353	498	16	)	)	PUNCT
ejpam-5353	498	17	=	=	SYM
ejpam-5353	498	18	0	0	PUNCT
ejpam-5353	499	1	if	if	SCONJ
ejpam-5353	499	2	xi	xi	PROPN
ejpam-5353	499	3	=	=	PUNCT
ejpam-5353	499	4	yi	yi	PROPN
ejpam-5353	499	5	and	and	CCONJ
ejpam-5353	499	6	d	d	PROPN
ejpam-5353	499	7	(	(	PUNCT
ejpam-5353	499	8	xi	xi	PROPN
ejpam-5353	499	9	,	,	PUNCT
ejpam-5353	499	10	yi	yi	PROPN
ejpam-5353	499	11	)	)	PUNCT
ejpam-5353	499	12	=	=	SYM
ejpam-5353	499	13	1	1	NUM
ejpam-5353	499	14	if	if	SCONJ
ejpam-5353	499	15	xi	xi	NUM
ejpam-5353	499	16	̸=	̸=	PROPN
ejpam-5353	499	17	yi	yi	PROPN
ejpam-5353	499	18	.	.	PUNCT
ejpam-5353	500	1	the	the	DET
ejpam-5353	500	2	distance	distance	NOUN
ejpam-5353	500	3	d	d	X
ejpam-5353	500	4	(	(	PUNCT
ejpam-5353	500	5	x	x	X
ejpam-5353	500	6	,	,	PUNCT
ejpam-5353	500	7	y	y	PROPN
ejpam-5353	500	8	)	)	PUNCT
ejpam-5353	500	9	for	for	ADP
ejpam-5353	500	10	any	any	DET
ejpam-5353	500	11	codewords	codeword	NOUN
ejpam-5353	500	12	x	x	PUNCT
ejpam-5353	500	13	and	and	CCONJ
ejpam-5353	500	14	y	y	PROPN
ejpam-5353	500	15	in	in	ADP
ejpam-5353	500	16	the	the	DET
ejpam-5353	500	17	binary	binary	PROPN
ejpam-5353	500	18	code	code	PROPN
ejpam-5353	500	19	c	c	PROPN
ejpam-5353	500	20	follows	follow	VERB
ejpam-5353	500	21	specific	specific	ADJ
ejpam-5353	500	22	properties	property	NOUN
ejpam-5353	500	23	:	:	PUNCT
ejpam-5353	500	24	(	(	PUNCT
ejpam-5353	500	25	i	i	NOUN
ejpam-5353	500	26	)	)	PUNCT
ejpam-5353	501	1	d	d	PROPN
ejpam-5353	501	2	(	(	PUNCT
ejpam-5353	501	3	x	x	X
ejpam-5353	501	4	,	,	PUNCT
ejpam-5353	501	5	y	y	PROPN
ejpam-5353	501	6	)	)	PUNCT
ejpam-5353	501	7	≥	≥	PROPN
ejpam-5353	501	8	0	0	NUM
ejpam-5353	501	9	.	.	PUNCT
ejpam-5353	502	1	(	(	PUNCT
ejpam-5353	502	2	ii	ii	NOUN
ejpam-5353	502	3	)	)	PUNCT
ejpam-5353	502	4	d	d	NOUN
ejpam-5353	502	5	(	(	PUNCT
ejpam-5353	502	6	x	x	X
ejpam-5353	502	7	,	,	PUNCT
ejpam-5353	502	8	y	y	PROPN
ejpam-5353	502	9	)	)	PUNCT
ejpam-5353	503	1	=	=	PUNCT
ejpam-5353	503	2	0	0	PUNCT
ejpam-5353	504	1	if	if	SCONJ
ejpam-5353	504	2	and	and	CCONJ
ejpam-5353	504	3	only	only	ADV
ejpam-5353	504	4	if	if	SCONJ
ejpam-5353	504	5	x	x	X
ejpam-5353	504	6	=	=	SYM
ejpam-5353	504	7	y.	y.	NOUN
ejpam-5353	504	8	(	(	PUNCT
ejpam-5353	504	9	iii	iii	NOUN
ejpam-5353	504	10	)	)	PUNCT
ejpam-5353	504	11	d	d	NOUN
ejpam-5353	504	12	(	(	PUNCT
ejpam-5353	504	13	y	y	NOUN
ejpam-5353	504	14	,	,	PUNCT
ejpam-5353	504	15	x	x	NOUN
ejpam-5353	504	16	)	)	PUNCT
ejpam-5353	504	17	=	=	SYM
ejpam-5353	505	1	d	d	NOUN
ejpam-5353	505	2	(	(	PUNCT
ejpam-5353	505	3	x	x	X
ejpam-5353	505	4	,	,	PUNCT
ejpam-5353	505	5	y	y	PROPN
ejpam-5353	505	6	)	)	PUNCT
ejpam-5353	505	7	.	.	PUNCT
ejpam-5353	506	1	(	(	PUNCT
ejpam-5353	506	2	iv	iv	X
ejpam-5353	506	3	)	)	PUNCT
ejpam-5353	506	4	d	d	NOUN
ejpam-5353	506	5	(	(	PUNCT
ejpam-5353	506	6	x	x	X
ejpam-5353	506	7	,	,	PUNCT
ejpam-5353	506	8	z	z	NOUN
ejpam-5353	506	9	)	)	PUNCT
ejpam-5353	506	10	≤	≤	NUM
ejpam-5353	507	1	d	d	NOUN
ejpam-5353	507	2	(	(	PUNCT
ejpam-5353	507	3	x	x	X
ejpam-5353	507	4	,	,	PUNCT
ejpam-5353	507	5	y	y	PROPN
ejpam-5353	507	6	)	)	PUNCT
ejpam-5353	508	1	+	+	CCONJ
ejpam-5353	509	1	d	d	X
ejpam-5353	509	2	(	(	PUNCT
ejpam-5353	509	3	y	y	PROPN
ejpam-5353	509	4	,	,	PUNCT
ejpam-5353	509	5	z	z	NOUN
ejpam-5353	509	6	)	)	PUNCT
ejpam-5353	509	7	.	.	PUNCT
ejpam-5353	510	1	the	the	DET
ejpam-5353	510	2	minimum	minimum	ADJ
ejpam-5353	510	3	distance	distance	NOUN
ejpam-5353	510	4	d	d	NOUN
ejpam-5353	510	5	(	(	PUNCT
ejpam-5353	510	6	c	c	NOUN
ejpam-5353	510	7	)	)	PUNCT
ejpam-5353	510	8	of	of	ADP
ejpam-5353	510	9	a	a	DET
ejpam-5353	510	10	code	code	NOUN
ejpam-5353	510	11	c	c	NOUN
ejpam-5353	510	12	is	be	AUX
ejpam-5353	510	13	defined	define	VERB
ejpam-5353	510	14	as	as	ADP
ejpam-5353	510	15	d	d	PROPN
ejpam-5353	510	16	(	(	PUNCT
ejpam-5353	510	17	c	c	NOUN
ejpam-5353	510	18	)	)	PUNCT
ejpam-5353	511	1	=	=	SYM
ejpam-5353	511	2	min	min	NOUN
ejpam-5353	511	3	{	{	PUNCT
ejpam-5353	511	4	d	d	X
ejpam-5353	511	5	(	(	PUNCT
ejpam-5353	511	6	x	x	X
ejpam-5353	511	7	,	,	PUNCT
ejpam-5353	511	8	y	y	PROPN
ejpam-5353	511	9	)	)	PUNCT
ejpam-5353	511	10	;	;	PUNCT
ejpam-5353	511	11	x	x	X
ejpam-5353	511	12	,	,	PUNCT
ejpam-5353	511	13	y	y	PROPN
ejpam-5353	511	14	∈	∈	PROPN
ejpam-5353	511	15	c	c	PROPN
ejpam-5353	511	16	and	and	CCONJ
ejpam-5353	511	17	x	x	SYM
ejpam-5353	511	18	̸=	̸=	PROPN
ejpam-5353	511	19	y	y	PROPN
ejpam-5353	511	20	}	}	PUNCT
ejpam-5353	511	21	.	.	PUNCT
ejpam-5353	512	1	lemma	lemma	PROPN
ejpam-5353	512	2	1	1	X
ejpam-5353	512	3	.	.	PUNCT
ejpam-5353	513	1	let	let	VERB
ejpam-5353	513	2	cr	cr	NOUN
ejpam-5353	513	3	be	be	AUX
ejpam-5353	513	4	a	a	DET
ejpam-5353	513	5	tree	tree	NOUN
ejpam-5353	513	6	binary	binary	NOUN
ejpam-5353	513	7	codes	code	NOUN
ejpam-5353	513	8	constructed	construct	VERB
ejpam-5353	513	9	from	from	ADP
ejpam-5353	513	10	the	the	DET
ejpam-5353	513	11	rows	row	NOUN
ejpam-5353	513	12	of	of	ADP
ejpam-5353	513	13	the	the	DET
ejpam-5353	513	14	incidence	incidence	NOUN
ejpam-5353	513	15	matrix	matrix	NOUN
ejpam-5353	513	16	of	of	ADP
ejpam-5353	513	17	an	an	DET
ejpam-5353	513	18	odc	odc	NOUN
ejpam-5353	513	19	of	of	ADP
ejpam-5353	513	20	kn	kn	PROPN
ejpam-5353	513	21	,	,	PUNCT
ejpam-5353	513	22	n	n	CCONJ
ejpam-5353	513	23	by	by	ADP
ejpam-5353	513	24	a	a	DET
ejpam-5353	513	25	tree	tree	NOUN
ejpam-5353	513	26	.	.	PUNCT
ejpam-5353	514	1	then	then	ADV
ejpam-5353	514	2	the	the	DET
ejpam-5353	514	3	minimum	minimum	ADJ
ejpam-5353	514	4	distance	distance	NOUN
ejpam-5353	514	5	d	d	PROPN
ejpam-5353	514	6	(	(	PUNCT
ejpam-5353	514	7	cr	cr	NOUN
ejpam-5353	514	8	)	)	PUNCT
ejpam-5353	514	9	is	be	AUX
ejpam-5353	514	10	2n−	2n−	PROPN
ejpam-5353	514	11	2	2	NUM
ejpam-5353	514	12	.	.	PUNCT
ejpam-5353	515	1	proof	proof	NOUN
ejpam-5353	515	2	.	.	PUNCT
ejpam-5353	516	1	from	from	ADP
ejpam-5353	516	2	the	the	DET
ejpam-5353	516	3	relation	relation	NOUN
ejpam-5353	516	4	between	between	ADP
ejpam-5353	516	5	odc	odc	PROPN
ejpam-5353	516	6	and	and	CCONJ
ejpam-5353	516	7	the	the	DET
ejpam-5353	516	8	incidence	incidence	NOUN
ejpam-5353	516	9	matrix	matrix	NOUN
ejpam-5353	516	10	l	l	NOUN
ejpam-5353	516	11	,	,	PUNCT
ejpam-5353	516	12	there	there	PRON
ejpam-5353	516	13	exists	exist	VERB
ejpam-5353	516	14	n	n	PRON
ejpam-5353	516	15	1	1	NUM
ejpam-5353	516	16	’s	’s	NOUN
ejpam-5353	516	17	in	in	ADP
ejpam-5353	516	18	every	every	DET
ejpam-5353	516	19	row	row	NOUN
ejpam-5353	516	20	.	.	PUNCT
ejpam-5353	517	1	any	any	DET
ejpam-5353	517	2	two	two	NUM
ejpam-5353	517	3	rows	row	NOUN
ejpam-5353	517	4	have	have	VERB
ejpam-5353	517	5	at	at	ADP
ejpam-5353	517	6	most	most	ADJ
ejpam-5353	517	7	1	1	NUM
ejpam-5353	517	8	position	position	NOUN
ejpam-5353	517	9	of	of	ADP
ejpam-5353	517	10	1	1	NUM
ejpam-5353	517	11	’s	’s	PART
ejpam-5353	517	12	common	common	ADJ
ejpam-5353	517	13	.	.	PUNCT
ejpam-5353	518	1	then	then	ADV
ejpam-5353	518	2	the	the	DET
ejpam-5353	518	3	minimum	minimum	ADJ
ejpam-5353	518	4	distance	distance	NOUN
ejpam-5353	518	5	of	of	ADP
ejpam-5353	518	6	cr	cr	PROPN
ejpam-5353	518	7	is	be	AUX
ejpam-5353	518	8	2	2	NUM
ejpam-5353	518	9	(	(	PUNCT
ejpam-5353	518	10	n−	n−	NOUN
ejpam-5353	518	11	1	1	NUM
ejpam-5353	518	12	)	)	PUNCT
ejpam-5353	518	13	=	=	PUNCT
ejpam-5353	519	1	2n−	2n−	NUM
ejpam-5353	519	2	2	2	NUM
ejpam-5353	519	3	.	.	PUNCT
ejpam-5353	519	4	theorem	theorem	VERB
ejpam-5353	519	5	23	23	NUM
ejpam-5353	519	6	.	.	PUNCT
ejpam-5353	520	1	the	the	DET
ejpam-5353	520	2	binary	binary	PROPN
ejpam-5353	520	3	code	code	PROPN
ejpam-5353	520	4	cr	cr	PROPN
ejpam-5353	520	5	can	can	AUX
ejpam-5353	520	6	detect	detect	VERB
ejpam-5353	520	7	up	up	ADP
ejpam-5353	520	8	to	to	ADP
ejpam-5353	520	9	2n	2n	NUM
ejpam-5353	520	10	−	−	ADP
ejpam-5353	520	11	3	3	NUM
ejpam-5353	520	12	errors	error	NOUN
ejpam-5353	520	13	or	or	CCONJ
ejpam-5353	520	14	correct	correct	VERB
ejpam-5353	520	15	up	up	ADP
ejpam-5353	520	16	to⌊	to⌊	NUM
ejpam-5353	520	17	2n−3	2n−3	NUM
ejpam-5353	520	18	2	2	NUM
ejpam-5353	520	19	⌋	⌋	NOUN
ejpam-5353	520	20	errors	error	NOUN
ejpam-5353	520	21	.	.	PUNCT
ejpam-5353	521	1	proof	proof	NOUN
ejpam-5353	521	2	.	.	PUNCT
ejpam-5353	522	1	from	from	ADP
ejpam-5353	522	2	lemma	lemma	PROPN
ejpam-5353	522	3	1	1	NUM
ejpam-5353	522	4	,	,	PUNCT
ejpam-5353	522	5	the	the	DET
ejpam-5353	522	6	minimum	minimum	ADJ
ejpam-5353	522	7	distance	distance	NOUN
ejpam-5353	522	8	of	of	ADP
ejpam-5353	522	9	cr	cr	PROPN
ejpam-5353	522	10	is	be	AUX
ejpam-5353	522	11	2	2	NUM
ejpam-5353	522	12	(	(	PUNCT
ejpam-5353	522	13	n−	n−	NOUN
ejpam-5353	522	14	1	1	NUM
ejpam-5353	522	15	)	)	PUNCT
ejpam-5353	522	16	.	.	PUNCT
ejpam-5353	523	1	thus	thus	ADV
ejpam-5353	523	2	,	,	PUNCT
ejpam-5353	523	3	in	in	ADP
ejpam-5353	523	4	order	order	NOUN
ejpam-5353	523	5	to	to	PART
ejpam-5353	523	6	change	change	VERB
ejpam-5353	523	7	any	any	DET
ejpam-5353	523	8	codeword	codeword	NOUN
ejpam-5353	523	9	to	to	ADP
ejpam-5353	523	10	another	another	DET
ejpam-5353	523	11	codeword	codeword	NOUN
ejpam-5353	523	12	requires	require	VERB
ejpam-5353	523	13	at	at	ADP
ejpam-5353	523	14	least	least	ADJ
ejpam-5353	523	15	2n−	2n−	NUM
ejpam-5353	523	16	2	2	NUM
ejpam-5353	523	17	bit	bit	NOUN
ejpam-5353	523	18	changes	change	NOUN
ejpam-5353	523	19	.	.	PUNCT
ejpam-5353	524	1	whence	whence	NOUN
ejpam-5353	524	2	,	,	PUNCT
ejpam-5353	524	3	cr	cr	PROPN
ejpam-5353	524	4	can	can	AUX
ejpam-5353	524	5	detect	detect	VERB
ejpam-5353	524	6	up	up	ADP
ejpam-5353	524	7	to	to	ADP
ejpam-5353	524	8	2n−2−1	2n−2−1	NUM
ejpam-5353	524	9	=	=	SYM
ejpam-5353	524	10	2n−3	2n−3	NUM
ejpam-5353	524	11	errors	error	NOUN
ejpam-5353	524	12	,	,	PUNCT
ejpam-5353	524	13	since	since	SCONJ
ejpam-5353	524	14	any	any	DET
ejpam-5353	524	15	2n−3	2n−3	NUM
ejpam-5353	524	16	transmission	transmission	NOUN
ejpam-5353	524	17	errors	error	NOUN
ejpam-5353	524	18	can	can	AUX
ejpam-5353	524	19	not	not	PART
ejpam-5353	524	20	change	change	VERB
ejpam-5353	524	21	one	one	NUM
ejpam-5353	524	22	codeword	codeword	NOUN
ejpam-5353	524	23	to	to	ADP
ejpam-5353	524	24	another	another	PRON
ejpam-5353	524	25	.	.	PUNCT
ejpam-5353	525	1	hence	hence	ADV
ejpam-5353	525	2	,	,	PUNCT
ejpam-5353	525	3	in	in	ADP
ejpam-5353	525	4	order	order	NOUN
ejpam-5353	525	5	to	to	PART
ejpam-5353	525	6	have	have	AUX
ejpam-5353	525	7	a	a	DET
ejpam-5353	525	8	guarantee	guarantee	NOUN
ejpam-5353	525	9	the	the	DET
ejpam-5353	525	10	detection	detection	NOUN
ejpam-5353	525	11	of	of	ADP
ejpam-5353	525	12	up	up	ADP
ejpam-5353	525	13	to	to	ADP
ejpam-5353	525	14	k	k	PROPN
ejpam-5353	525	15	errors	error	NOUN
ejpam-5353	525	16	in	in	ADP
ejpam-5353	525	17	all	all	DET
ejpam-5353	525	18	cases	case	NOUN
ejpam-5353	525	19	,	,	PUNCT
ejpam-5353	525	20	the	the	DET
ejpam-5353	525	21	minimum	minimum	ADJ
ejpam-5353	525	22	distance	distance	NOUN
ejpam-5353	525	23	of	of	ADP
ejpam-5353	525	24	the	the	DET
ejpam-5353	525	25	code	code	PROPN
ejpam-5353	525	26	cr	cr	PROPN
ejpam-5353	525	27	,	,	PUNCT
ejpam-5353	525	28	d	d	PROPN
ejpam-5353	525	29	(	(	PUNCT
ejpam-5353	525	30	cr	cr	NOUN
ejpam-5353	525	31	)	)	PUNCT
ejpam-5353	525	32	=	=	PUNCT
ejpam-5353	526	1	k	k	PROPN
ejpam-5353	527	1	+	+	NOUN
ejpam-5353	527	2	1	1	X
ejpam-5353	527	3	.	.	PUNCT
ejpam-5353	527	4	the	the	DET
ejpam-5353	527	5	geometric	geometric	ADJ
ejpam-5353	527	6	concept	concept	NOUN
ejpam-5353	527	7	for	for	ADP
ejpam-5353	527	8	finding	find	VERB
ejpam-5353	527	9	d	d	X
ejpam-5353	527	10	(	(	PUNCT
ejpam-5353	527	11	cr	cr	NOUN
ejpam-5353	527	12	)	)	PUNCT
ejpam-5353	527	13	in	in	ADP
ejpam-5353	527	14	error	error	NOUN
ejpam-5353	527	15	detection	detection	NOUN
ejpam-5353	527	16	is	be	AUX
ejpam-5353	527	17	shown	show	VERB
ejpam-5353	527	18	in	in	ADP
ejpam-5353	527	19	figure	figure	NOUN
ejpam-5353	527	20	4	4	NUM
ejpam-5353	527	21	.	.	PUNCT
ejpam-5353	528	1	h.	h.	PROPN
ejpam-5353	528	2	shabana	shabana	PROPN
ejpam-5353	528	3	,	,	PUNCT
ejpam-5353	528	4	r.	r.	PROPN
ejpam-5353	528	5	el	el	PROPN
ejpam-5353	528	6	-	-	PROPN
ejpam-5353	528	7	shanawany	shanawany	NOUN
ejpam-5353	528	8	,	,	PUNCT
ejpam-5353	528	9	s.	s.	PROPN
ejpam-5353	528	10	halawa	halawa	PROPN
ejpam-5353	528	11	/	/	PUNCT
ejpam-5353	528	12	eur	eur	PROPN
ejpam-5353	528	13	.	.	PUNCT
ejpam-5353	529	1	j.	j.	PROPN
ejpam-5353	529	2	pure	pure	PROPN
ejpam-5353	529	3	appl	appl	PROPN
ejpam-5353	529	4	.	.	PROPN
ejpam-5353	529	5	math	math	PROPN
ejpam-5353	529	6	,	,	PUNCT
ejpam-5353	529	7	17	17	NUM
ejpam-5353	529	8	(	(	PUNCT
ejpam-5353	529	9	4	4	NUM
ejpam-5353	529	10	)	)	PUNCT
ejpam-5353	529	11	(	(	PUNCT
ejpam-5353	529	12	2024	2024	NUM
ejpam-5353	529	13	)	)	PUNCT
ejpam-5353	529	14	,	,	PUNCT
ejpam-5353	529	15	3492	3492	NUM
ejpam-5353	529	16	-	-	SYM
ejpam-5353	529	17	3516	3516	NUM
ejpam-5353	529	18	3511	3511	NUM
ejpam-5353	529	19	suppose	suppose	VERB
ejpam-5353	529	20	that	that	SCONJ
ejpam-5353	529	21	the	the	DET
ejpam-5353	529	22	codeword	codeword	NOUN
ejpam-5353	529	23	u	u	NOUN
ejpam-5353	529	24	was	be	AUX
ejpam-5353	529	25	sent	send	VERB
ejpam-5353	529	26	but	but	CCONJ
ejpam-5353	529	27	for	for	ADP
ejpam-5353	529	28	some	some	DET
ejpam-5353	529	29	reason	reason	NOUN
ejpam-5353	529	30	v	v	NOUN
ejpam-5353	529	31	was	be	AUX
ejpam-5353	529	32	received	receive	VERB
ejpam-5353	529	33	and	and	CCONJ
ejpam-5353	529	34	d	d	X
ejpam-5353	529	35	(	(	PUNCT
ejpam-5353	529	36	u	u	NOUN
ejpam-5353	529	37	,	,	PUNCT
ejpam-5353	529	38	v	v	NOUN
ejpam-5353	529	39	)	)	PUNCT
ejpam-5353	529	40	≤	≤	NOUN
ejpam-5353	529	41	2n−3	2n−3	NUM
ejpam-5353	529	42	2	2	NUM
ejpam-5353	529	43	,	,	PUNCT
ejpam-5353	529	44	that	that	PRON
ejpam-5353	529	45	is	be	AUX
ejpam-5353	529	46	less	less	ADJ
ejpam-5353	529	47	than	than	ADP
ejpam-5353	529	48	2n−3	2n−3	NUM
ejpam-5353	529	49	2	2	NUM
ejpam-5353	529	50	errors	error	NOUN
ejpam-5353	529	51	occurred	occur	VERB
ejpam-5353	529	52	.	.	PUNCT
ejpam-5353	530	1	subsequently	subsequently	ADV
ejpam-5353	530	2	,	,	PUNCT
ejpam-5353	530	3	the	the	DET
ejpam-5353	530	4	distance	distance	NOUN
ejpam-5353	530	5	between	between	ADP
ejpam-5353	530	6	v	v	NOUN
ejpam-5353	530	7	and	and	CCONJ
ejpam-5353	530	8	any	any	DET
ejpam-5353	530	9	codeword	codeword	NOUN
ejpam-5353	530	10	,	,	PUNCT
ejpam-5353	530	11	excluding	exclude	VERB
ejpam-5353	530	12	u	u	NOUN
ejpam-5353	530	13	,	,	PUNCT
ejpam-5353	530	14	exceeds	exceed	VERB
ejpam-5353	530	15	2n−3	2n−3	NUM
ejpam-5353	530	16	2	2	NUM
ejpam-5353	530	17	.	.	PUNCT
ejpam-5353	531	1	let	let	VERB
ejpam-5353	531	2	w	w	PROPN
ejpam-5353	531	3	∈	∈	PROPN
ejpam-5353	532	1	cr	cr	NOUN
ejpam-5353	532	2	then	then	ADV
ejpam-5353	532	3	d	d	X
ejpam-5353	532	4	(	(	PUNCT
ejpam-5353	532	5	u	u	NOUN
ejpam-5353	532	6	,	,	PUNCT
ejpam-5353	532	7	w	w	NOUN
ejpam-5353	532	8	)	)	PUNCT
ejpam-5353	532	9	≥	≥	NOUN
ejpam-5353	532	10	2n−	2n−	NUM
ejpam-5353	532	11	2	2	NUM
ejpam-5353	532	12	.	.	PUNCT
ejpam-5353	533	1	therefore	therefore	ADV
ejpam-5353	533	2	,	,	PUNCT
ejpam-5353	533	3	if	if	SCONJ
ejpam-5353	533	4	u	u	NOUN
ejpam-5353	533	5	is	be	AUX
ejpam-5353	533	6	the	the	DET
ejpam-5353	533	7	closest	close	ADJ
ejpam-5353	533	8	codeword	codeword	NOUN
ejpam-5353	533	9	to	to	ADP
ejpam-5353	533	10	v	v	NOUN
ejpam-5353	533	11	,	,	PUNCT
ejpam-5353	533	12	the	the	DET
ejpam-5353	533	13	amount	amount	NOUN
ejpam-5353	533	14	of	of	ADP
ejpam-5353	533	15	bit	bit	NOUN
ejpam-5353	533	16	changes	change	NOUN
ejpam-5353	533	17	needed	need	VERB
ejpam-5353	533	18	to	to	PART
ejpam-5353	533	19	switch	switch	VERB
ejpam-5353	533	20	from	from	ADP
ejpam-5353	533	21	u	u	NOUN
ejpam-5353	533	22	to	to	ADP
ejpam-5353	533	23	v	v	NOUN
ejpam-5353	533	24	(	(	PUNCT
ejpam-5353	533	25	the	the	DET
ejpam-5353	533	26	number	number	NOUN
ejpam-5353	533	27	of	of	ADP
ejpam-5353	533	28	errors	error	NOUN
ejpam-5353	533	29	in	in	ADP
ejpam-5353	533	30	the	the	DET
ejpam-5353	533	31	transmission	transmission	NOUN
ejpam-5353	533	32	channel	channel	NOUN
ejpam-5353	533	33	)	)	PUNCT
ejpam-5353	533	34	is	be	AUX
ejpam-5353	533	35	lower	low	ADJ
ejpam-5353	533	36	than	than	SCONJ
ejpam-5353	533	37	the	the	DET
ejpam-5353	533	38	number	number	NOUN
ejpam-5353	533	39	of	of	ADP
ejpam-5353	533	40	errors	error	NOUN
ejpam-5353	533	41	needed	need	VERB
ejpam-5353	533	42	to	to	PART
ejpam-5353	533	43	switch	switch	VERB
ejpam-5353	533	44	from	from	ADP
ejpam-5353	533	45	any	any	DET
ejpam-5353	533	46	other	other	ADJ
ejpam-5353	533	47	codeword	codeword	NOUN
ejpam-5353	533	48	to	to	ADP
ejpam-5353	533	49	v.	v.	ADP
ejpam-5353	533	50	the	the	DET
ejpam-5353	533	51	substitution	substitution	NOUN
ejpam-5353	533	52	of	of	ADP
ejpam-5353	533	53	v	v	NOUN
ejpam-5353	533	54	with	with	ADP
ejpam-5353	533	55	u	u	NOUN
ejpam-5353	533	56	enables	enable	VERB
ejpam-5353	533	57	cr	cr	NOUN
ejpam-5353	533	58	to	to	PART
ejpam-5353	533	59	rectify	rectify	VERB
ejpam-5353	533	60	up	up	ADP
ejpam-5353	533	61	to	to	ADP
ejpam-5353	533	62	2n	2n	NUM
ejpam-5353	533	63	errors	error	NOUN
ejpam-5353	533	64	.	.	PUNCT
ejpam-5353	534	1	therefore	therefore	ADV
ejpam-5353	534	2	,	,	PUNCT
ejpam-5353	534	3	to	to	PART
ejpam-5353	534	4	ensure	ensure	VERB
ejpam-5353	534	5	the	the	DET
ejpam-5353	534	6	correction	correction	NOUN
ejpam-5353	534	7	of	of	ADP
ejpam-5353	534	8	k	k	PROPN
ejpam-5353	534	9	errors	error	NOUN
ejpam-5353	534	10	in	in	ADP
ejpam-5353	534	11	all	all	DET
ejpam-5353	534	12	instances	instance	NOUN
ejpam-5353	534	13	,	,	PUNCT
ejpam-5353	534	14	the	the	DET
ejpam-5353	534	15	minimum	minimum	ADJ
ejpam-5353	534	16	distance	distance	NOUN
ejpam-5353	534	17	of	of	ADP
ejpam-5353	534	18	code	code	NOUN
ejpam-5353	534	19	cr	cr	PROPN
ejpam-5353	534	20	d	d	PROPN
ejpam-5353	534	21	(	(	PUNCT
ejpam-5353	534	22	cr	cr	X
ejpam-5353	534	23	)	)	PUNCT
ejpam-5353	534	24	=	=	PUNCT
ejpam-5353	535	1	2k+1.the	2k+1.the	DET
ejpam-5353	535	2	geometric	geometric	ADJ
ejpam-5353	535	3	principle	principle	NOUN
ejpam-5353	535	4	for	for	ADP
ejpam-5353	535	5	determining	determine	VERB
ejpam-5353	535	6	d	d	PROPN
ejpam-5353	535	7	(	(	PUNCT
ejpam-5353	535	8	cr	cr	NOUN
ejpam-5353	535	9	)	)	PUNCT
ejpam-5353	535	10	in	in	ADP
ejpam-5353	535	11	error	error	NOUN
ejpam-5353	535	12	correction	correction	NOUN
ejpam-5353	535	13	is	be	AUX
ejpam-5353	535	14	presented	present	VERB
ejpam-5353	535	15	in	in	ADP
ejpam-5353	535	16	figure	figure	NOUN
ejpam-5353	535	17	5	5	NUM
ejpam-5353	535	18	.	.	PUNCT
ejpam-5353	535	19	figure	figure	VERB
ejpam-5353	535	20	4	4	NUM
ejpam-5353	535	21	:	:	PUNCT
ejpam-5353	535	22	the	the	DET
ejpam-5353	535	23	geometric	geometric	ADJ
ejpam-5353	535	24	concept	concept	NOUN
ejpam-5353	535	25	for	for	ADP
ejpam-5353	535	26	finding	find	VERB
ejpam-5353	535	27	d	d	X
ejpam-5353	535	28	(	(	PUNCT
ejpam-5353	535	29	cr	cr	NOUN
ejpam-5353	535	30	)	)	PUNCT
ejpam-5353	535	31	in	in	ADP
ejpam-5353	535	32	error	error	NOUN
ejpam-5353	535	33	detection	detection	NOUN
ejpam-5353	535	34	.	.	PUNCT
ejpam-5353	536	1	figure	figure	NOUN
ejpam-5353	536	2	5	5	NUM
ejpam-5353	536	3	:	:	PUNCT
ejpam-5353	536	4	the	the	DET
ejpam-5353	536	5	geometric	geometric	ADJ
ejpam-5353	536	6	concept	concept	NOUN
ejpam-5353	536	7	for	for	ADP
ejpam-5353	536	8	finding	find	VERB
ejpam-5353	536	9	d	d	X
ejpam-5353	536	10	(	(	PUNCT
ejpam-5353	536	11	cr	cr	NOUN
ejpam-5353	536	12	)	)	PUNCT
ejpam-5353	536	13	in	in	ADP
ejpam-5353	536	14	error	error	NOUN
ejpam-5353	536	15	correction	correction	NOUN
ejpam-5353	536	16	.	.	PUNCT
ejpam-5353	537	1	h.	h.	PROPN
ejpam-5353	537	2	shabana	shabana	PROPN
ejpam-5353	537	3	,	,	PUNCT
ejpam-5353	537	4	r.	r.	PROPN
ejpam-5353	537	5	el	el	PROPN
ejpam-5353	537	6	-	-	PROPN
ejpam-5353	537	7	shanawany	shanawany	NOUN
ejpam-5353	537	8	,	,	PUNCT
ejpam-5353	537	9	s.	s.	PROPN
ejpam-5353	537	10	halawa	halawa	PROPN
ejpam-5353	537	11	/	/	PUNCT
ejpam-5353	537	12	eur	eur	PROPN
ejpam-5353	537	13	.	.	PUNCT
ejpam-5353	538	1	j.	j.	PROPN
ejpam-5353	538	2	pure	pure	PROPN
ejpam-5353	538	3	appl	appl	PROPN
ejpam-5353	538	4	.	.	PROPN
ejpam-5353	538	5	math	math	PROPN
ejpam-5353	538	6	,	,	PUNCT
ejpam-5353	538	7	17	17	NUM
ejpam-5353	538	8	(	(	PUNCT
ejpam-5353	538	9	4	4	NUM
ejpam-5353	538	10	)	)	PUNCT
ejpam-5353	538	11	(	(	PUNCT
ejpam-5353	538	12	2024	2024	NUM
ejpam-5353	538	13	)	)	PUNCT
ejpam-5353	538	14	,	,	PUNCT
ejpam-5353	538	15	3492	3492	NUM
ejpam-5353	538	16	-	-	SYM
ejpam-5353	538	17	3516	3516	NUM
ejpam-5353	538	18	3512	3512	NUM
ejpam-5353	538	19	example	example	NOUN
ejpam-5353	538	20	2	2	NUM
ejpam-5353	538	21	.	.	PUNCT
ejpam-5353	539	1	let	let	VERB
ejpam-5353	539	2	the	the	DET
ejpam-5353	539	3	vector	vector	NOUN
ejpam-5353	539	4	(	(	PUNCT
ejpam-5353	539	5	0	0	NUM
ejpam-5353	539	6	,	,	PUNCT
ejpam-5353	539	7	1	1	NUM
ejpam-5353	539	8	,	,	PUNCT
ejpam-5353	539	9	2	2	NUM
ejpam-5353	539	10	,	,	PUNCT
ejpam-5353	539	11	1	1	NUM
ejpam-5353	539	12	)	)	PUNCT
ejpam-5353	539	13	be	be	AUX
ejpam-5353	539	14	a	a	DET
ejpam-5353	539	15	symmetric	symmetric	ADJ
ejpam-5353	539	16	base	base	NOUN
ejpam-5353	539	17	for	for	ADP
ejpam-5353	539	18	an	an	DET
ejpam-5353	539	19	odc	odc	NOUN
ejpam-5353	539	20	of	of	ADP
ejpam-5353	539	21	k4,4	k4,4	PROPN
ejpam-5353	539	22	by	by	ADP
ejpam-5353	539	23	τ	τ	PROPN
ejpam-5353	539	24	01(2	01(2	PROPN
ejpam-5353	539	25	,	,	PUNCT
ejpam-5353	539	26	1	1	NUM
ejpam-5353	539	27	)	)	PUNCT
ejpam-5353	539	28	.	.	PUNCT
ejpam-5353	540	1	the	the	DET
ejpam-5353	540	2	two	two	NUM
ejpam-5353	540	3	orthogonal	orthogonal	ADJ
ejpam-5353	540	4	decompositions	decomposition	NOUN
ejpam-5353	540	5	generated	generate	VERB
ejpam-5353	540	6	from	from	ADP
ejpam-5353	540	7	the	the	DET
ejpam-5353	540	8	vector	vector	NOUN
ejpam-5353	540	9	(	(	PUNCT
ejpam-5353	540	10	0	0	NUM
ejpam-5353	540	11	,	,	PUNCT
ejpam-5353	540	12	1	1	NUM
ejpam-5353	540	13	,	,	PUNCT
ejpam-5353	540	14	2	2	NUM
ejpam-5353	540	15	,	,	PUNCT
ejpam-5353	540	16	1	1	NUM
ejpam-5353	540	17	)	)	PUNCT
ejpam-5353	540	18	are	be	AUX
ejpam-5353	540	19	shown	show	VERB
ejpam-5353	540	20	in	in	ADP
ejpam-5353	540	21	figure	figure	NOUN
ejpam-5353	540	22	6.the	6.the	DET
ejpam-5353	540	23	incidence	incidence	NOUN
ejpam-5353	540	24	matrix	matrix	NOUN
ejpam-5353	540	25	l	l	NOUN
ejpam-5353	540	26	=	=	PUNCT
ejpam-5353	540	27	l	l	X
ejpam-5353	540	28	(	(	PUNCT
ejpam-5353	540	29	s	s	PROPN
ejpam-5353	540	30	,	,	PUNCT
ejpam-5353	540	31	t	t	PROPN
ejpam-5353	540	32	)	)	PUNCT
ejpam-5353	540	33	for	for	ADP
ejpam-5353	540	34	such	such	ADJ
ejpam-5353	540	35	odc	odc	PROPN
ejpam-5353	540	36	is	be	AUX
ejpam-5353	540	37	a	a	DET
ejpam-5353	540	38	8×16	8×16	NUM
ejpam-5353	540	39	binary	binary	ADJ
ejpam-5353	540	40	matrix	matrix	NOUN
ejpam-5353	540	41	where	where	SCONJ
ejpam-5353	540	42	the	the	DET
ejpam-5353	540	43	rows	row	NOUN
ejpam-5353	540	44	correspond	correspond	VERB
ejpam-5353	540	45	to	to	ADP
ejpam-5353	540	46	elements	element	NOUN
ejpam-5353	540	47	of	of	ADP
ejpam-5353	540	48	odc	odc	PROPN
ejpam-5353	540	49	g	g	PROPN
ejpam-5353	540	50	=	=	PRON
ejpam-5353	540	51	{	{	PUNCT
ejpam-5353	540	52	gi	gi	NOUN
ejpam-5353	540	53	0+x	0+x	NUM
ejpam-5353	540	54	:	:	PUNCT
ejpam-5353	540	55	x	x	X
ejpam-5353	540	56	∈	∈	PROPN
ejpam-5353	540	57	z4	z4	X
ejpam-5353	540	58	,	,	PUNCT
ejpam-5353	540	59	i	i	PRON
ejpam-5353	540	60	∈	∈	PROPN
ejpam-5353	540	61	{	{	PUNCT
ejpam-5353	540	62	1	1	NUM
ejpam-5353	540	63	,	,	PUNCT
ejpam-5353	540	64	2	2	NUM
ejpam-5353	540	65	}	}	PUNCT
ejpam-5353	540	66	}	}	PUNCT
ejpam-5353	540	67	of	of	ADP
ejpam-5353	540	68	k4,4.the	k4,4.the	DET
ejpam-5353	540	69	following	follow	VERB
ejpam-5353	540	70	matrix	matrix	NOUN
ejpam-5353	540	71	is	be	AUX
ejpam-5353	540	72	the	the	DET
ejpam-5353	540	73	incidence	incidence	ADJ
ejpam-5353	540	74	matrix	matrix	NOUN
ejpam-5353	540	75	l	l	NOUN
ejpam-5353	540	76	(	(	PUNCT
ejpam-5353	540	77	s	s	PROPN
ejpam-5353	540	78	,	,	PUNCT
ejpam-5353	540	79	t	t	PROPN
ejpam-5353	540	80	)	)	PUNCT
ejpam-5353	540	81	for	for	ADP
ejpam-5353	540	82	the	the	DET
ejpam-5353	540	83	odc	odc	PROPN
ejpam-5353	540	84	(	(	PUNCT
ejpam-5353	540	85	described	describe	VERB
ejpam-5353	540	86	in	in	ADP
ejpam-5353	540	87	figure	figure	NOUN
ejpam-5353	540	88	6	6	NUM
ejpam-5353	540	89	)	)	PUNCT
ejpam-5353	540	90	of	of	ADP
ejpam-5353	540	91	k4,4	k4,4	PROPN
ejpam-5353	540	92	by	by	ADP
ejpam-5353	540	93	τ01(2	τ01(2	PROPN
ejpam-5353	540	94	,	,	PUNCT
ejpam-5353	540	95	1	1	NUM
ejpam-5353	540	96	)	)	PUNCT
ejpam-5353	540	97	.	.	PUNCT
ejpam-5353	541	1	from	from	ADP
ejpam-5353	541	2	the	the	DET
ejpam-5353	541	3	rows	row	NOUN
ejpam-5353	541	4	of	of	ADP
ejpam-5353	541	5	the	the	DET
ejpam-5353	541	6	matrix	matrix	NOUN
ejpam-5353	541	7	l	l	NOUN
ejpam-5353	541	8	(	(	PUNCT
ejpam-5353	541	9	s	s	PROPN
ejpam-5353	541	10	,	,	PUNCT
ejpam-5353	541	11	t	t	PROPN
ejpam-5353	541	12	)	)	PUNCT
ejpam-5353	541	13	we	we	PRON
ejpam-5353	541	14	construct	construct	VERB
ejpam-5353	541	15	the	the	DET
ejpam-5353	541	16	code	code	NOUN
ejpam-5353	541	17	cr	cr	ADP
ejpam-5353	541	18	such	such	ADJ
ejpam-5353	541	19	that	that	SCONJ
ejpam-5353	541	20	cr	cr	PROPN
ejpam-5353	541	21	has	have	VERB
ejpam-5353	541	22	8	8	NUM
ejpam-5353	541	23	codewords	codeword	NOUN
ejpam-5353	541	24	each	each	PRON
ejpam-5353	541	25	of	of	ADP
ejpam-5353	541	26	length	length	NOUN
ejpam-5353	541	27	16	16	NUM
ejpam-5353	541	28	.	.	PUNCT
ejpam-5353	542	1	figure	figure	VERB
ejpam-5353	542	2	6	6	NUM
ejpam-5353	542	3	:	:	PUNCT
ejpam-5353	542	4	an	an	DET
ejpam-5353	542	5	odc	odc	NOUN
ejpam-5353	542	6	of	of	ADP
ejpam-5353	542	7	k4,4	k4,4	PROPN
ejpam-5353	542	8	by	by	ADP
ejpam-5353	542	9	τ01(2	τ01(2	PROPN
ejpam-5353	542	10	,	,	PUNCT
ejpam-5353	542	11	1	1	NUM
ejpam-5353	542	12	)	)	PUNCT
ejpam-5353	542	13	where	where	SCONJ
ejpam-5353	542	14	the	the	DET
ejpam-5353	542	15	vector	vector	NOUN
ejpam-5353	542	16	(	(	PUNCT
ejpam-5353	542	17	0	0	NUM
ejpam-5353	542	18	,	,	PUNCT
ejpam-5353	542	19	1	1	NUM
ejpam-5353	542	20	,	,	PUNCT
ejpam-5353	542	21	2	2	NUM
ejpam-5353	542	22	,	,	PUNCT
ejpam-5353	542	23	1	1	NUM
ejpam-5353	542	24	)	)	PUNCT
ejpam-5353	542	25	is	be	AUX
ejpam-5353	542	26	the	the	DET
ejpam-5353	542	27	symmetric	symmetric	ADJ
ejpam-5353	542	28	base	base	NOUN
ejpam-5353	542	29	for	for	ADP
ejpam-5353	542	30	this	this	DET
ejpam-5353	542	31	odc	odc	PROPN
ejpam-5353	542	32	.	.	PUNCT
ejpam-5353	543	1			NOUN
ejpam-5353	543	2	1	1	NUM
ejpam-5353	543	3	0	0	NUM
ejpam-5353	543	4	0	0	NUM
ejpam-5353	543	5	0	0	NUM
ejpam-5353	543	6	1	1	NUM
ejpam-5353	543	7	0	0	NUM
ejpam-5353	543	8	1	1	NUM
ejpam-5353	543	9	0	0	NUM
ejpam-5353	543	10	1	1	NUM
ejpam-5353	543	11	0	0	NUM
ejpam-5353	543	12	0	0	NUM
ejpam-5353	543	13	0	0	NUM
ejpam-5353	543	14	0	0	NUM
ejpam-5353	543	15	0	0	NUM
ejpam-5353	543	16	0	0	NUM
ejpam-5353	543	17	0	0	NUM
ejpam-5353	543	18	0	0	NUM
ejpam-5353	543	19	0	0	NUM
ejpam-5353	543	20	0	0	NUM
ejpam-5353	543	21	0	0	NUM
ejpam-5353	543	22	0	0	NUM
ejpam-5353	543	23	1	1	NUM
ejpam-5353	543	24	0	0	NUM
ejpam-5353	543	25	0	0	NUM
ejpam-5353	543	26	0	0	NUM
ejpam-5353	543	27	1	1	NUM
ejpam-5353	543	28	0	0	NUM
ejpam-5353	543	29	1	1	NUM
ejpam-5353	543	30	0	0	NUM
ejpam-5353	543	31	1	1	NUM
ejpam-5353	543	32	0	0	NUM
ejpam-5353	543	33	0	0	NUM
ejpam-5353	543	34	0	0	NUM
ejpam-5353	543	35	0	0	NUM
ejpam-5353	543	36	1	1	NUM
ejpam-5353	543	37	0	0	NUM
ejpam-5353	543	38	0	0	NUM
ejpam-5353	543	39	0	0	NUM
ejpam-5353	543	40	0	0	NUM
ejpam-5353	543	41	0	0	NUM
ejpam-5353	543	42	0	0	NUM
ejpam-5353	543	43	0	0	NUM
ejpam-5353	543	44	1	1	NUM
ejpam-5353	543	45	0	0	NUM
ejpam-5353	543	46	1	1	NUM
ejpam-5353	543	47	0	0	NUM
ejpam-5353	543	48	1	1	NUM
ejpam-5353	543	49	0	0	NUM
ejpam-5353	543	50	0	0	NUM
ejpam-5353	543	51	1	1	NUM
ejpam-5353	543	52	0	0	NUM
ejpam-5353	543	53	1	1	NUM
ejpam-5353	543	54	0	0	NUM
ejpam-5353	543	55	0	0	NUM
ejpam-5353	543	56	0	0	NUM
ejpam-5353	543	57	1	1	NUM
ejpam-5353	543	58	0	0	NUM
ejpam-5353	543	59	0	0	NUM
ejpam-5353	543	60	0	0	NUM
ejpam-5353	543	61	0	0	NUM
ejpam-5353	543	62	0	0	NUM
ejpam-5353	543	63	0	0	NUM
ejpam-5353	543	64	0	0	NUM
ejpam-5353	543	65	1	1	NUM
ejpam-5353	543	66	1	1	NUM
ejpam-5353	543	67	1	1	NUM
ejpam-5353	543	68	1	1	NUM
ejpam-5353	543	69	0	0	NUM
ejpam-5353	543	70	0	0	NUM
ejpam-5353	543	71	0	0	NUM
ejpam-5353	543	72	0	0	NUM
ejpam-5353	543	73	0	0	NUM
ejpam-5353	543	74	0	0	NUM
ejpam-5353	543	75	1	1	NUM
ejpam-5353	543	76	0	0	NUM
ejpam-5353	543	77	0	0	NUM
ejpam-5353	543	78	0	0	NUM
ejpam-5353	543	79	0	0	NUM
ejpam-5353	543	80	0	0	NUM
ejpam-5353	543	81	0	0	NUM
ejpam-5353	543	82	0	0	NUM
ejpam-5353	543	83	0	0	NUM
ejpam-5353	543	84	0	0	NUM
ejpam-5353	543	85	0	0	NUM
ejpam-5353	543	86	0	0	NUM
ejpam-5353	543	87	1	1	NUM
ejpam-5353	543	88	1	1	NUM
ejpam-5353	543	89	1	1	NUM
ejpam-5353	543	90	0	0	NUM
ejpam-5353	543	91	0	0	NUM
ejpam-5353	543	92	0	0	NUM
ejpam-5353	543	93	0	0	NUM
ejpam-5353	543	94	0	0	NUM
ejpam-5353	543	95	0	0	NUM
ejpam-5353	543	96	1	1	NUM
ejpam-5353	543	97	0	0	NUM
ejpam-5353	543	98	0	0	NUM
ejpam-5353	543	99	0	0	NUM
ejpam-5353	543	100	0	0	NUM
ejpam-5353	543	101	1	1	NUM
ejpam-5353	543	102	0	0	NUM
ejpam-5353	543	103	0	0	NUM
ejpam-5353	543	104	0	0	NUM
ejpam-5353	543	105	0	0	NUM
ejpam-5353	543	106	1	1	NUM
ejpam-5353	543	107	0	0	NUM
ejpam-5353	543	108	1	1	NUM
ejpam-5353	543	109	1	1	NUM
ejpam-5353	543	110	0	0	NUM
ejpam-5353	543	111	0	0	NUM
ejpam-5353	543	112	0	0	NUM
ejpam-5353	543	113	0	0	NUM
ejpam-5353	543	114	0	0	NUM
ejpam-5353	543	115	0	0	NUM
ejpam-5353	543	116	0	0	NUM
ejpam-5353	543	117	0	0	NUM
ejpam-5353	543	118	1	1	NUM
ejpam-5353	543	119	0	0	NUM
ejpam-5353	543	120	0	0	NUM
ejpam-5353	543	121	0	0	NUM
ejpam-5353	543	122	0	0	NUM
ejpam-5353	543	123	0	0	NUM
ejpam-5353	543	124	0	0	NUM
ejpam-5353	543	125	0	0	NUM
ejpam-5353	543	126	1	1	NUM
ejpam-5353	543	127	1	1	NUM
ejpam-5353	543	128	0	0	NUM
ejpam-5353	543	129	1	1	NUM
ejpam-5353	543	130			NOUN
ejpam-5353	543	131	←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→	←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→	NOUN
ejpam-5353	543	132	the	the	DET
ejpam-5353	543	133	incidence	incidence	NOUN
ejpam-5353	543	134	matrix	matrix	NOUN
ejpam-5353	543	135	l(s	l(s	PROPN
ejpam-5353	543	136	,	,	PUNCT
ejpam-5353	543	137	t	t	PROPN
ejpam-5353	543	138	)	)	PUNCT
ejpam-5353	543	139	for	for	ADP
ejpam-5353	543	140	the	the	DET
ejpam-5353	543	141	odc	odc	PROPN
ejpam-5353	543	142	described	describe	VERB
ejpam-5353	543	143	in	in	ADP
ejpam-5353	543	144	figure	figure	NOUN
ejpam-5353	543	145	6	6	NUM
ejpam-5353	543	146	↓	↓	NOUN
ejpam-5353	543	147	cr	cr	PROPN
ejpam-5353	543	148	=	=	PUNCT
ejpam-5353	543	149			PROPN
ejpam-5353	543	150	1000101010000000	1000101010000000	NUM
ejpam-5353	543	151	,	,	PUNCT
ejpam-5353	543	152	0000010001010100	0000010001010100	NUM
ejpam-5353	543	153	,	,	PUNCT
ejpam-5353	543	154	001000000010100	001000000010100	NUM
ejpam-5353	543	155	,	,	PUNCT
ejpam-5353	543	156	01010010000000	01010010000000	NUM
ejpam-5353	543	157	,	,	PUNCT
ejpam-5353	543	158	1110000001000000	1110000001000000	NUM
ejpam-5353	543	159	,	,	PUNCT
ejpam-5353	543	160	0000011100000010	0000011100000010	NUM
ejpam-5353	543	161	,	,	PUNCT
ejpam-5353	543	162	0001000010110000	0001000010110000	NUM
ejpam-5353	543	163	,	,	PUNCT
ejpam-5353	543	164	0000100000001101	0000100000001101	NUM
ejpam-5353	544	1			NOUN
ejpam-5353	544	2	←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→	←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→	PROPN
ejpam-5353	544	3	the	the	DET
ejpam-5353	544	4	code	code	NOUN
ejpam-5353	544	5	cr	cr	PROPN
ejpam-5353	544	6	deduced	deduce	VERB
ejpam-5353	544	7	from	from	ADP
ejpam-5353	544	8	the	the	DET
ejpam-5353	544	9	rows	row	NOUN
ejpam-5353	544	10	of	of	ADP
ejpam-5353	544	11	the	the	DET
ejpam-5353	544	12	above	above	ADJ
ejpam-5353	544	13	incidence	incidence	NOUN
ejpam-5353	544	14	matrix	matrix	NOUN
ejpam-5353	544	15	l(s	l(s	PROPN
ejpam-5353	544	16	,	,	PUNCT
ejpam-5353	544	17	t	t	PROPN
ejpam-5353	544	18	)	)	PUNCT
ejpam-5353	544	19	h.	h.	PROPN
ejpam-5353	544	20	shabana	shabana	PROPN
ejpam-5353	544	21	,	,	PUNCT
ejpam-5353	544	22	r.	r.	PROPN
ejpam-5353	544	23	el	el	PROPN
ejpam-5353	544	24	-	-	PROPN
ejpam-5353	544	25	shanawany	shanawany	NOUN
ejpam-5353	544	26	,	,	PUNCT
ejpam-5353	544	27	s.	s.	PROPN
ejpam-5353	544	28	halawa	halawa	PROPN
ejpam-5353	544	29	/	/	PUNCT
ejpam-5353	544	30	eur	eur	PROPN
ejpam-5353	544	31	.	.	PUNCT
ejpam-5353	545	1	j.	j.	PROPN
ejpam-5353	545	2	pure	pure	PROPN
ejpam-5353	545	3	appl	appl	PROPN
ejpam-5353	545	4	.	.	PROPN
ejpam-5353	545	5	math	math	PROPN
ejpam-5353	545	6	,	,	PUNCT
ejpam-5353	545	7	17	17	NUM
ejpam-5353	545	8	(	(	PUNCT
ejpam-5353	545	9	4	4	NUM
ejpam-5353	545	10	)	)	PUNCT
ejpam-5353	545	11	(	(	PUNCT
ejpam-5353	545	12	2024	2024	NUM
ejpam-5353	545	13	)	)	PUNCT
ejpam-5353	545	14	,	,	PUNCT
ejpam-5353	545	15	3492	3492	NUM
ejpam-5353	545	16	-	-	SYM
ejpam-5353	545	17	3516	3516	NUM
ejpam-5353	545	18	3513	3513	NUM
ejpam-5353	545	19	5	5	NUM
ejpam-5353	545	20	.	.	PUNCT
ejpam-5353	545	21	recursive	recursive	ADJ
ejpam-5353	545	22	construction	construction	NOUN
ejpam-5353	545	23	of	of	ADP
ejpam-5353	545	24	an	an	DET
ejpam-5353	545	25	odc	odc	NOUN
ejpam-5353	545	26	by	by	ADP
ejpam-5353	545	27	disjoint	disjoint	NOUN
ejpam-5353	545	28	trees	tree	NOUN
ejpam-5353	545	29	hereafter	hereafter	ADV
ejpam-5353	546	1	,	,	PUNCT
ejpam-5353	546	2	we	we	PRON
ejpam-5353	546	3	will	will	AUX
ejpam-5353	546	4	show	show	VERB
ejpam-5353	546	5	how	how	SCONJ
ejpam-5353	546	6	to	to	PART
ejpam-5353	546	7	use	use	VERB
ejpam-5353	546	8	an	an	DET
ejpam-5353	546	9	odc	odc	NOUN
ejpam-5353	546	10	of	of	ADP
ejpam-5353	546	11	small	small	ADJ
ejpam-5353	546	12	complete	complete	ADJ
ejpam-5353	546	13	bipartite	bipartite	NOUN
ejpam-5353	546	14	graphs	graph	NOUN
ejpam-5353	546	15	to	to	PART
ejpam-5353	546	16	construct	construct	VERB
ejpam-5353	546	17	an	an	DET
ejpam-5353	546	18	odc	odc	NOUN
ejpam-5353	546	19	of	of	ADP
ejpam-5353	546	20	larger	large	ADJ
ejpam-5353	546	21	complete	complete	ADJ
ejpam-5353	546	22	bipartite	bipartite	NOUN
ejpam-5353	546	23	graphs	graph	NOUN
ejpam-5353	546	24	.	.	PUNCT
ejpam-5353	547	1	in	in	ADP
ejpam-5353	547	2	the	the	DET
ejpam-5353	547	3	following	following	NOUN
ejpam-5353	547	4	,	,	PUNCT
ejpam-5353	547	5	for	for	ADP
ejpam-5353	547	6	simplicity	simplicity	NOUN
ejpam-5353	547	7	,	,	PUNCT
ejpam-5353	547	8	if	if	SCONJ
ejpam-5353	547	9	(	(	PUNCT
ejpam-5353	547	10	x	x	NOUN
ejpam-5353	547	11	,	,	PUNCT
ejpam-5353	547	12	y	y	PROPN
ejpam-5353	547	13	)	)	PUNCT
ejpam-5353	547	14	∈	∈	PROPN
ejpam-5353	547	15	zm	zm	PROPN
ejpam-5353	547	16	×	×	PROPN
ejpam-5353	547	17	zn	zn	PROPN
ejpam-5353	547	18	,	,	PUNCT
ejpam-5353	547	19	we	we	PRON
ejpam-5353	547	20	use	use	VERB
ejpam-5353	547	21	xy	xy	PROPN
ejpam-5353	547	22	for	for	ADP
ejpam-5353	547	23	(	(	PUNCT
ejpam-5353	547	24	x	x	NOUN
ejpam-5353	547	25	,	,	PUNCT
ejpam-5353	547	26	y	y	PROPN
ejpam-5353	547	27	)	)	PUNCT
ejpam-5353	547	28	.	.	PUNCT
ejpam-5353	548	1	theorem	theorem	VERB
ejpam-5353	548	2	24	24	NUM
ejpam-5353	548	3	.	.	PUNCT
ejpam-5353	549	1	let	let	VERB
ejpam-5353	549	2	m	m	PROPN
ejpam-5353	549	3	≡	≡	PROPN
ejpam-5353	549	4	1mod	1mod	PROPN
ejpam-5353	549	5	6	6	NUM
ejpam-5353	549	6	or	or	CCONJ
ejpam-5353	549	7	m	m	PROPN
ejpam-5353	549	8	≡	≡	PROPN
ejpam-5353	549	9	5mod	5mod	DET
ejpam-5353	549	10	6	6	NUM
ejpam-5353	549	11	and	and	CCONJ
ejpam-5353	549	12	let	let	VERB
ejpam-5353	549	13	n	n	PRON
ejpam-5353	549	14	be	be	AUX
ejpam-5353	549	15	a	a	DET
ejpam-5353	549	16	positive	positive	ADJ
ejpam-5353	549	17	integer	integer	NOUN
ejpam-5353	549	18	.	.	PUNCT
ejpam-5353	550	1	if	if	SCONJ
ejpam-5353	550	2	v(g	v(g	NUM
ejpam-5353	550	3	)	)	PUNCT
ejpam-5353	550	4	=	=	SYM
ejpam-5353	550	5	(	(	PUNCT
ejpam-5353	550	6	v0	v0	PROPN
ejpam-5353	550	7	,	,	PUNCT
ejpam-5353	550	8	v1	v1	NOUN
ejpam-5353	550	9	,	,	PUNCT
ejpam-5353	550	10	·	·	PUNCT
ejpam-5353	550	11	·	·	PUNCT
ejpam-5353	550	12	·	·	PUNCT
ejpam-5353	550	13	,	,	PUNCT
ejpam-5353	550	14	vn−1	vn−1	PROPN
ejpam-5353	550	15	)	)	PUNCT
ejpam-5353	550	16	be	be	VERB
ejpam-5353	550	17	a	a	DET
ejpam-5353	550	18	symmetric	symmetric	ADJ
ejpam-5353	550	19	base	base	NOUN
ejpam-5353	550	20	for	for	ADP
ejpam-5353	550	21	an	an	DET
ejpam-5353	550	22	odc	odc	NOUN
ejpam-5353	550	23	of	of	ADP
ejpam-5353	550	24	kn	kn	PROPN
ejpam-5353	550	25	,	,	PUNCT
ejpam-5353	550	26	n	n	CCONJ
ejpam-5353	550	27	by	by	ADP
ejpam-5353	550	28	a	a	DET
ejpam-5353	550	29	certain	certain	ADJ
ejpam-5353	550	30	tree	tree	NOUN
ejpam-5353	550	31	g	g	NOUN
ejpam-5353	550	32	,	,	PUNCT
ejpam-5353	550	33	then	then	ADV
ejpam-5353	550	34	there	there	PRON
ejpam-5353	550	35	is	be	VERB
ejpam-5353	550	36	an	an	DET
ejpam-5353	550	37	odc	odc	NOUN
ejpam-5353	550	38	of	of	ADP
ejpam-5353	550	39	kmn	kmn	PROPN
ejpam-5353	550	40	,	,	PUNCT
ejpam-5353	550	41	mn	mn	PROPN
ejpam-5353	550	42	by	by	ADP
ejpam-5353	550	43	mg	mg	PROPN
ejpam-5353	550	44	with	with	ADP
ejpam-5353	550	45	respect	respect	NOUN
ejpam-5353	550	46	to	to	ADP
ejpam-5353	550	47	zn×zm	zn×zm	PROPN
ejpam-5353	550	48	,	,	PUNCT
ejpam-5353	550	49	(	(	PUNCT
ejpam-5353	550	50	the	the	DET
ejpam-5353	550	51	cartesian	cartesian	ADJ
ejpam-5353	550	52	product	product	NOUN
ejpam-5353	550	53	of	of	ADP
ejpam-5353	550	54	the	the	DET
ejpam-5353	550	55	groups	group	NOUN
ejpam-5353	550	56	zn	zn	PROPN
ejpam-5353	550	57	and	and	CCONJ
ejpam-5353	550	58	zm	zm	PROPN
ejpam-5353	550	59	)	)	PUNCT
ejpam-5353	550	60	.	.	PUNCT
ejpam-5353	551	1	proof	proof	NOUN
ejpam-5353	551	2	.	.	PUNCT
ejpam-5353	552	1	let	let	VERB
ejpam-5353	552	2	the	the	DET
ejpam-5353	552	3	vector	vector	NOUN
ejpam-5353	552	4	u(f	u(f	PROPN
ejpam-5353	552	5	)	)	PUNCT
ejpam-5353	553	1	=	=	SYM
ejpam-5353	553	2	(	(	PUNCT
ejpam-5353	553	3	u0	u0	ADJ
ejpam-5353	553	4	,	,	PUNCT
ejpam-5353	553	5	u1	u1	NOUN
ejpam-5353	553	6	,	,	PUNCT
ejpam-5353	553	7	·	·	PUNCT
ejpam-5353	553	8	·	·	PUNCT
ejpam-5353	553	9	·	·	PUNCT
ejpam-5353	553	10	,	,	PUNCT
ejpam-5353	553	11	um−1	um−1	NOUN
ejpam-5353	553	12	)	)	PUNCT
ejpam-5353	553	13	=	=	SYM
ejpam-5353	554	1	(	(	PUNCT
ejpam-5353	554	2	0	0	NUM
ejpam-5353	554	3	,	,	PUNCT
ejpam-5353	554	4	1	1	NUM
ejpam-5353	554	5	,	,	PUNCT
ejpam-5353	554	6	·	·	PUNCT
ejpam-5353	554	7	·	·	PUNCT
ejpam-5353	554	8	·	·	PUNCT
ejpam-5353	554	9	,	,	PUNCT
ejpam-5353	554	10	m	m	VERB
ejpam-5353	554	11	−	−	NOUN
ejpam-5353	554	12	1	1	NUM
ejpam-5353	554	13	)	)	PUNCT
ejpam-5353	554	14	represent	represent	VERB
ejpam-5353	554	15	a	a	DET
ejpam-5353	554	16	base	base	NOUN
ejpam-5353	554	17	in	in	ADP
ejpam-5353	554	18	km	km	PROPN
ejpam-5353	554	19	,	,	PUNCT
ejpam-5353	554	20	m	m	VERB
ejpam-5353	554	21	with	with	ADP
ejpam-5353	554	22	respect	respect	NOUN
ejpam-5353	554	23	to	to	ADP
ejpam-5353	554	24	zm	zm	PROPN
ejpam-5353	554	25	.	.	PUNCT
ejpam-5353	555	1	from	from	ADP
ejpam-5353	555	2	the	the	DET
ejpam-5353	555	3	definition	definition	NOUN
ejpam-5353	555	4	of	of	ADP
ejpam-5353	555	5	u(f	u(f	PROPN
ejpam-5353	555	6	)	)	PUNCT
ejpam-5353	555	7	,	,	PUNCT
ejpam-5353	555	8	we	we	PRON
ejpam-5353	555	9	can	can	AUX
ejpam-5353	555	10	conclude	conclude	VERB
ejpam-5353	555	11	that	that	SCONJ
ejpam-5353	555	12	{	{	PUNCT
ejpam-5353	555	13	ui	ui	NOUN
ejpam-5353	555	14	−	−	PROPN
ejpam-5353	555	15	u−i	u−i	PROPN
ejpam-5353	555	16	+	+	CCONJ
ejpam-5353	556	1	i	i	PRON
ejpam-5353	556	2	;	;	PUNCT
ejpam-5353	556	3	i	i	PROPN
ejpam-5353	556	4	∈	∈	PROPN
ejpam-5353	556	5	zm	zm	PROPN
ejpam-5353	556	6	}	}	PUNCT
ejpam-5353	556	7	=	=	SYM
ejpam-5353	556	8	zm	zm	PROPN
ejpam-5353	556	9	.	.	PUNCT
ejpam-5353	557	1	therefore	therefore	ADV
ejpam-5353	557	2	,	,	PUNCT
ejpam-5353	557	3	u(f	u(f	PROPN
ejpam-5353	557	4	)	)	PUNCT
ejpam-5353	557	5	is	be	AUX
ejpam-5353	557	6	a	a	DET
ejpam-5353	557	7	symmetric	symmetric	ADJ
ejpam-5353	557	8	base	base	NOUN
ejpam-5353	557	9	an	an	DET
ejpam-5353	557	10	odc	odc	NOUN
ejpam-5353	557	11	of	of	ADP
ejpam-5353	557	12	km	km	PROPN
ejpam-5353	557	13	,	,	PUNCT
ejpam-5353	557	14	m.	m.	NOUN
ejpam-5353	557	15	whence	whence	NOUN
ejpam-5353	557	16	,	,	PUNCT
ejpam-5353	557	17	m	m	VERB
ejpam-5353	557	18	≡	≡	PROPN
ejpam-5353	557	19	1mod	1mod	PROPN
ejpam-5353	557	20	6	6	NUM
ejpam-5353	557	21	or	or	CCONJ
ejpam-5353	557	22	m	m	PROPN
ejpam-5353	557	23	≡	≡	PROPN
ejpam-5353	558	1	5mod	5mod	PROPN
ejpam-5353	558	2	6	6	NUM
ejpam-5353	558	3	the	the	DET
ejpam-5353	558	4	base	base	NOUN
ejpam-5353	558	5	f	f	PROPN
ejpam-5353	558	6	is	be	AUX
ejpam-5353	558	7	isomorphic	isomorphic	ADJ
ejpam-5353	558	8	to	to	ADP
ejpam-5353	558	9	mk2	mk2	PROPN
ejpam-5353	558	10	.	.	PUNCT
ejpam-5353	559	1	since	since	SCONJ
ejpam-5353	559	2	the	the	DET
ejpam-5353	559	3	vector	vector	NOUN
ejpam-5353	559	4	v(g	v(g	PROPN
ejpam-5353	559	5	)	)	PUNCT
ejpam-5353	559	6	=	=	SYM
ejpam-5353	559	7	(	(	PUNCT
ejpam-5353	559	8	v0	v0	PROPN
ejpam-5353	559	9	,	,	PUNCT
ejpam-5353	559	10	v1	v1	NOUN
ejpam-5353	559	11	,	,	PUNCT
ejpam-5353	559	12	·	·	PUNCT
ejpam-5353	559	13	·	·	PUNCT
ejpam-5353	559	14	·	·	PUNCT
ejpam-5353	559	15	,	,	PUNCT
ejpam-5353	559	16	vn−1	vn−1	PROPN
ejpam-5353	559	17	)	)	PUNCT
ejpam-5353	559	18	is	be	AUX
ejpam-5353	559	19	a	a	DET
ejpam-5353	559	20	symmetric	symmetric	ADJ
ejpam-5353	559	21	base	base	NOUN
ejpam-5353	559	22	for	for	ADP
ejpam-5353	559	23	an	an	DET
ejpam-5353	559	24	odc	odc	NOUN
ejpam-5353	559	25	of	of	ADP
ejpam-5353	559	26	kn	kn	PROPN
ejpam-5353	559	27	,	,	PUNCT
ejpam-5353	559	28	n.	n.	PROPN
ejpam-5353	559	29	taking	take	VERB
ejpam-5353	559	30	the	the	DET
ejpam-5353	559	31	cartesian	cartesian	ADJ
ejpam-5353	559	32	product	product	NOUN
ejpam-5353	559	33	of	of	ADP
ejpam-5353	559	34	the	the	DET
ejpam-5353	559	35	two	two	NUM
ejpam-5353	559	36	vectors	vector	NOUN
ejpam-5353	559	37	v(g	v(g	ADJ
ejpam-5353	559	38	)	)	PUNCT
ejpam-5353	559	39	and	and	CCONJ
ejpam-5353	559	40	u(f	u(f	NOUN
ejpam-5353	559	41	)	)	PUNCT
ejpam-5353	559	42	implies	imply	VERB
ejpam-5353	559	43	that	that	SCONJ
ejpam-5353	559	44	v(g	v(g	ADJ
ejpam-5353	559	45	)	)	PUNCT
ejpam-5353	559	46	×	×	NOUN
ejpam-5353	559	47	u(f	u(f	NOUN
ejpam-5353	559	48	)	)	PUNCT
ejpam-5353	559	49	=	=	SYM
ejpam-5353	559	50	(	(	PUNCT
ejpam-5353	559	51	(	(	PUNCT
ejpam-5353	559	52	v0	v0	NOUN
ejpam-5353	559	53	,	,	PUNCT
ejpam-5353	559	54	u0	u0	ADJ
ejpam-5353	559	55	)	)	PUNCT
ejpam-5353	559	56	,	,	PUNCT
ejpam-5353	559	57	(	(	PUNCT
ejpam-5353	559	58	v0	v0	NOUN
ejpam-5353	559	59	,	,	PUNCT
ejpam-5353	559	60	u1	u1	NOUN
ejpam-5353	559	61	)	)	PUNCT
ejpam-5353	559	62	,	,	PUNCT
ejpam-5353	559	63	·	·	PUNCT
ejpam-5353	559	64	·	·	PUNCT
ejpam-5353	559	65	·	·	PUNCT
ejpam-5353	559	66	,	,	PUNCT
ejpam-5353	559	67	(	(	PUNCT
ejpam-5353	559	68	vi	vi	PROPN
ejpam-5353	559	69	,	,	PUNCT
ejpam-5353	559	70	uj	uj	NOUN
ejpam-5353	559	71	)	)	PUNCT
ejpam-5353	559	72	,	,	PUNCT
ejpam-5353	559	73	·	·	PUNCT
ejpam-5353	559	74	·	·	PUNCT
ejpam-5353	559	75	·	·	PUNCT
ejpam-5353	559	76	,	,	PUNCT
ejpam-5353	559	77	(	(	PUNCT
ejpam-5353	559	78	vn−1	vn−1	ADJ
ejpam-5353	559	79	,	,	PUNCT
ejpam-5353	559	80	um−1	um−1	PROPN
ejpam-5353	559	81	)	)	PUNCT
ejpam-5353	559	82	;	;	PUNCT
ejpam-5353	559	83	i	i	PRON
ejpam-5353	559	84	∈	∈	PROPN
ejpam-5353	559	85	zn	zn	PROPN
ejpam-5353	559	86	,	,	PUNCT
ejpam-5353	559	87	j	j	PROPN
ejpam-5353	559	88	∈	∈	PROPN
ejpam-5353	559	89	zm	zm	PROPN
ejpam-5353	559	90	)	)	PUNCT
ejpam-5353	559	91	is	be	AUX
ejpam-5353	559	92	also	also	ADV
ejpam-5353	559	93	a	a	DET
ejpam-5353	559	94	symmetric	symmetric	ADJ
ejpam-5353	559	95	base	base	NOUN
ejpam-5353	559	96	of	of	ADP
ejpam-5353	559	97	an	an	DET
ejpam-5353	559	98	odc	odc	PROPN
ejpam-5353	559	99	of	of	ADP
ejpam-5353	559	100	kmn	kmn	PROPN
ejpam-5353	559	101	,	,	PUNCT
ejpam-5353	559	102	mn	mn	PROPN
ejpam-5353	559	103	by	by	ADP
ejpam-5353	559	104	g×	g×	PROPN
ejpam-5353	559	105	f	f	PROPN
ejpam-5353	559	106	with	with	ADP
ejpam-5353	559	107	respect	respect	NOUN
ejpam-5353	559	108	to	to	ADP
ejpam-5353	559	109	zn	zn	PROPN
ejpam-5353	559	110	×	×	PROPN
ejpam-5353	559	111	zm	zm	PROPN
ejpam-5353	559	112	,	,	PUNCT
ejpam-5353	559	113	as	as	ADP
ejpam-5353	559	114	{	{	PUNCT
ejpam-5353	559	115	(	(	PUNCT
ejpam-5353	559	116	vi	vi	NOUN
ejpam-5353	559	117	,	,	PUNCT
ejpam-5353	559	118	uj)−	uj)−	NUM
ejpam-5353	559	119	(	(	PUNCT
ejpam-5353	559	120	v−i	v−i	PROPN
ejpam-5353	559	121	,	,	PUNCT
ejpam-5353	559	122	u−j	u−j	PROPN
ejpam-5353	559	123	)	)	PUNCT
ejpam-5353	560	1	+	+	CCONJ
ejpam-5353	560	2	(	(	PUNCT
ejpam-5353	560	3	i	i	PROPN
ejpam-5353	560	4	,	,	PUNCT
ejpam-5353	560	5	j	j	PROPN
ejpam-5353	560	6	)	)	PUNCT
ejpam-5353	560	7	;	;	PUNCT
ejpam-5353	560	8	i	i	PRON
ejpam-5353	560	9	∈	∈	PROPN
ejpam-5353	560	10	zn	zn	PROPN
ejpam-5353	560	11	,	,	PUNCT
ejpam-5353	560	12	j	j	PROPN
ejpam-5353	560	13	∈	∈	PROPN
ejpam-5353	560	14	zm	zm	PROPN
ejpam-5353	560	15	}	}	PUNCT
ejpam-5353	560	16	=	=	SYM
ejpam-5353	560	17	zn	zn	NUM
ejpam-5353	560	18	×	×	PROPN
ejpam-5353	560	19	zm	zm	PROPN
ejpam-5353	560	20	,	,	PUNCT
ejpam-5353	560	21	.	.	PUNCT
ejpam-5353	561	1	moreover	moreover	ADV
ejpam-5353	561	2	,	,	PUNCT
ejpam-5353	561	3	the	the	DET
ejpam-5353	561	4	edge	edge	NOUN
ejpam-5353	561	5	set	set	NOUN
ejpam-5353	561	6	of	of	ADP
ejpam-5353	561	7	the	the	DET
ejpam-5353	561	8	the	the	DET
ejpam-5353	561	9	base	base	NOUN
ejpam-5353	561	10	g×	g×	X
ejpam-5353	561	11	f	f	PROPN
ejpam-5353	561	12	is	be	AUX
ejpam-5353	561	13	e(g×	e(g×	ADJ
ejpam-5353	561	14	f	f	NOUN
ejpam-5353	561	15	)	)	PUNCT
ejpam-5353	562	1	=	=	PRON
ejpam-5353	562	2	{	{	PUNCT
ejpam-5353	562	3	(	(	PUNCT
ejpam-5353	562	4	vi	vi	NOUN
ejpam-5353	562	5	,	,	PUNCT
ejpam-5353	562	6	uj)0	uj)0	ADJ
ejpam-5353	562	7	,	,	PUNCT
ejpam-5353	562	8	+	+	PROPN
ejpam-5353	562	9	(	(	PUNCT
ejpam-5353	562	10	(	(	PUNCT
ejpam-5353	562	11	vi	vi	PROPN
ejpam-5353	562	12	,	,	PUNCT
ejpam-5353	562	13	uj	uj	NOUN
ejpam-5353	562	14	)	)	PUNCT
ejpam-5353	563	1	+	+	CCONJ
ejpam-5353	563	2	(	(	PUNCT
ejpam-5353	563	3	i	i	NOUN
ejpam-5353	563	4	,	,	PUNCT
ejpam-5353	563	5	j))1	j))1	PROPN
ejpam-5353	563	6	;	;	PUNCT
ejpam-5353	563	7	i	i	PROPN
ejpam-5353	563	8	∈	∈	PROPN
ejpam-5353	564	1	zn	zn	PROPN
ejpam-5353	564	2	,	,	PUNCT
ejpam-5353	564	3	j	j	PROPN
ejpam-5353	564	4	∈	∈	PROPN
ejpam-5353	564	5	zm	zm	PROPN
ejpam-5353	564	6	}	}	PUNCT
ejpam-5353	564	7	.	.	PUNCT
ejpam-5353	565	1	from	from	ADP
ejpam-5353	565	2	the	the	DET
ejpam-5353	565	3	vectors	vector	NOUN
ejpam-5353	565	4	u(f	u(f	NOUN
ejpam-5353	565	5	)	)	PUNCT
ejpam-5353	565	6	and	and	CCONJ
ejpam-5353	565	7	v(g	v(g	NOUN
ejpam-5353	565	8	)	)	PUNCT
ejpam-5353	565	9	the	the	DET
ejpam-5353	565	10	baseg×f	baseg×f	PROPN
ejpam-5353	565	11	is	be	AUX
ejpam-5353	565	12	isomorphic	isomorphic	ADJ
ejpam-5353	565	13	tomg	tomg	NOUN
ejpam-5353	565	14	wheneverm	wheneverm	NOUN
ejpam-5353	565	15	≡	≡	PROPN
ejpam-5353	565	16	1mod	1mod	PROPN
ejpam-5353	565	17	6	6	NUM
ejpam-5353	565	18	or	or	CCONJ
ejpam-5353	565	19	m	m	PROPN
ejpam-5353	565	20	≡	≡	PROPN
ejpam-5353	566	1	5mod	5mod	DET
ejpam-5353	566	2	6	6	NUM
ejpam-5353	566	3	and	and	CCONJ
ejpam-5353	566	4	n	n	PRON
ejpam-5353	566	5	be	be	AUX
ejpam-5353	566	6	a	a	DET
ejpam-5353	566	7	positive	positive	ADJ
ejpam-5353	566	8	integer	integer	NOUN
ejpam-5353	566	9	.	.	PUNCT
ejpam-5353	567	1	note	note	VERB
ejpam-5353	567	2	that	that	SCONJ
ejpam-5353	567	3	the	the	DET
ejpam-5353	567	4	the	the	DET
ejpam-5353	567	5	vertices	vertex	NOUN
ejpam-5353	567	6	of	of	ADP
ejpam-5353	567	7	kmn	kmn	PROPN
ejpam-5353	567	8	,	,	PUNCT
ejpam-5353	567	9	mn	mn	PROPN
ejpam-5353	567	10	are	be	AUX
ejpam-5353	567	11	labelled	label	VERB
ejpam-5353	567	12	by	by	ADP
ejpam-5353	567	13	the	the	DET
ejpam-5353	567	14	elements	element	NOUN
ejpam-5353	567	15	of	of	ADP
ejpam-5353	567	16	zn	zn	PROPN
ejpam-5353	567	17	×zm	×zm	PROPN
ejpam-5353	567	18	×{0	×{0	VERB
ejpam-5353	567	19	,	,	PUNCT
ejpam-5353	567	20	1}.for	1}.for	ADP
ejpam-5353	567	21	the	the	DET
ejpam-5353	567	22	vertex	vertex	NOUN
ejpam-5353	567	23	(	(	PUNCT
ejpam-5353	567	24	x	x	NOUN
ejpam-5353	567	25	,	,	PUNCT
ejpam-5353	567	26	y	y	PROPN
ejpam-5353	567	27	,	,	PUNCT
ejpam-5353	567	28	i	i	PROPN
ejpam-5353	567	29	)	)	PUNCT
ejpam-5353	567	30	we	we	PRON
ejpam-5353	567	31	write	write	VERB
ejpam-5353	567	32	(	(	PUNCT
ejpam-5353	567	33	xy)0	xy)0	NOUN
ejpam-5353	567	34	where	where	SCONJ
ejpam-5353	567	35	x	x	SYM
ejpam-5353	567	36	∈	∈	PROPN
ejpam-5353	567	37	zn	zn	PROPN
ejpam-5353	567	38	,	,	PUNCT
ejpam-5353	567	39	y	y	PROPN
ejpam-5353	567	40	∈	∈	PROPN
ejpam-5353	567	41	zn	zn	PROPN
ejpam-5353	567	42	,	,	PUNCT
ejpam-5353	567	43	i	i	PRON
ejpam-5353	567	44	∈	∈	PROPN
ejpam-5353	567	45	{	{	PUNCT
ejpam-5353	567	46	0	0	NUM
ejpam-5353	567	47	,	,	PUNCT
ejpam-5353	567	48	1	1	NUM
ejpam-5353	567	49	}	}	PUNCT
ejpam-5353	567	50	,	,	PUNCT
ejpam-5353	567	51	and	and	CCONJ
ejpam-5353	567	52	zn	zn	X
ejpam-5353	567	53	=	=	SYM
ejpam-5353	567	54	{	{	PUNCT
ejpam-5353	567	55	0	0	NUM
ejpam-5353	567	56	,	,	PUNCT
ejpam-5353	567	57	1	1	NUM
ejpam-5353	567	58	,	,	PUNCT
ejpam-5353	567	59	2	2	NUM
ejpam-5353	567	60	,	,	PUNCT
ejpam-5353	567	61	·	·	PUNCT
ejpam-5353	567	62	·	·	PUNCT
ejpam-5353	567	63	·	·	PUNCT
ejpam-5353	567	64	,	,	PUNCT
ejpam-5353	567	65	n−1	n−1	PROPN
ejpam-5353	567	66	}	}	PUNCT
ejpam-5353	567	67	is	be	AUX
ejpam-5353	567	68	the	the	DET
ejpam-5353	567	69	group	group	NOUN
ejpam-5353	567	70	of	of	ADP
ejpam-5353	567	71	all	all	DET
ejpam-5353	567	72	residual	residual	ADJ
ejpam-5353	567	73	classes	class	NOUN
ejpam-5353	567	74	modulo	modulo	VERB
ejpam-5353	567	75	n	n	SYM
ejpam-5353	567	76	,	,	PUNCT
ejpam-5353	567	77	zm	zm	PROPN
ejpam-5353	567	78	=	=	PROPN
ejpam-5353	567	79	{	{	PUNCT
ejpam-5353	567	80	0	0	NUM
ejpam-5353	567	81	,	,	PUNCT
ejpam-5353	567	82	1	1	NUM
ejpam-5353	567	83	,	,	PUNCT
ejpam-5353	567	84	2	2	NUM
ejpam-5353	567	85	,	,	PUNCT
ejpam-5353	567	86	·	·	PUNCT
ejpam-5353	567	87	·	·	PUNCT
ejpam-5353	567	88	·	·	PUNCT
ejpam-5353	567	89	,	,	PUNCT
ejpam-5353	567	90	m−	m−	PROPN
ejpam-5353	567	91	1	1	NUM
ejpam-5353	567	92	}	}	PUNCT
ejpam-5353	567	93	is	be	AUX
ejpam-5353	567	94	the	the	DET
ejpam-5353	567	95	group	group	NOUN
ejpam-5353	567	96	of	of	ADP
ejpam-5353	567	97	all	all	DET
ejpam-5353	567	98	residual	residual	ADJ
ejpam-5353	567	99	classes	class	NOUN
ejpam-5353	567	100	modulo	modulo	VERB
ejpam-5353	567	101	m.	m.	NOUN
ejpam-5353	567	102	example	example	NOUN
ejpam-5353	568	1	3	3	X
ejpam-5353	568	2	.	.	PUNCT
ejpam-5353	568	3	given	give	VERB
ejpam-5353	568	4	the	the	DET
ejpam-5353	568	5	vector	vector	NOUN
ejpam-5353	568	6	v(f	v(f	PROPN
ejpam-5353	568	7	)	)	PUNCT
ejpam-5353	569	1	=	=	PUNCT
ejpam-5353	569	2	(	(	PUNCT
ejpam-5353	569	3	0	0	NUM
ejpam-5353	569	4	,	,	PUNCT
ejpam-5353	569	5	1	1	NUM
ejpam-5353	569	6	,	,	PUNCT
ejpam-5353	569	7	2	2	NUM
ejpam-5353	569	8	,	,	PUNCT
ejpam-5353	569	9	3	3	NUM
ejpam-5353	569	10	,	,	PUNCT
ejpam-5353	569	11	4	4	NUM
ejpam-5353	569	12	)	)	PUNCT
ejpam-5353	569	13	as	as	ADP
ejpam-5353	569	14	a	a	DET
ejpam-5353	569	15	symmetric	symmetric	ADJ
ejpam-5353	569	16	base	base	NOUN
ejpam-5353	569	17	for	for	ADP
ejpam-5353	569	18	an	an	DET
ejpam-5353	569	19	odc	odc	NOUN
ejpam-5353	569	20	of	of	ADP
ejpam-5353	569	21	k5,5	k5,5	PROPN
ejpam-5353	569	22	by	by	ADP
ejpam-5353	569	23	5k2	5k2	NUM
ejpam-5353	569	24	.	.	PUNCT
ejpam-5353	570	1	if	if	SCONJ
ejpam-5353	570	2	there	there	PRON
ejpam-5353	570	3	is	be	VERB
ejpam-5353	570	4	an	an	DET
ejpam-5353	570	5	odc	odc	NOUN
ejpam-5353	570	6	of	of	ADP
ejpam-5353	570	7	k3,3	k3,3	PROPN
ejpam-5353	570	8	by	by	ADP
ejpam-5353	570	9	τ01(1	τ01(1	PROPN
ejpam-5353	570	10	,	,	PUNCT
ejpam-5353	570	11	1	1	NUM
ejpam-5353	570	12	)	)	PUNCT
ejpam-5353	570	13	where	where	SCONJ
ejpam-5353	570	14	the	the	DET
ejpam-5353	570	15	vector	vector	NOUN
ejpam-5353	570	16	v(g	v(g	PROPN
ejpam-5353	570	17	)	)	PUNCT
ejpam-5353	570	18	=	=	SYM
ejpam-5353	570	19	(	(	PUNCT
ejpam-5353	570	20	0	0	NUM
ejpam-5353	570	21	,	,	PUNCT
ejpam-5353	570	22	1	1	NUM
ejpam-5353	570	23	,	,	PUNCT
ejpam-5353	570	24	1	1	NUM
ejpam-5353	570	25	)	)	PUNCT
ejpam-5353	570	26	is	be	AUX
ejpam-5353	570	27	the	the	DET
ejpam-5353	570	28	symmetric	symmetric	ADJ
ejpam-5353	570	29	base	base	NOUN
ejpam-5353	570	30	for	for	ADP
ejpam-5353	570	31	this	this	DET
ejpam-5353	570	32	odc	odc	NOUN
ejpam-5353	570	33	then	then	ADV
ejpam-5353	570	34	we	we	PRON
ejpam-5353	570	35	have	have	VERB
ejpam-5353	570	36	a	a	DET
ejpam-5353	570	37	guarantee	guarantee	NOUN
ejpam-5353	570	38	that	that	SCONJ
ejpam-5353	570	39	there	there	PRON
ejpam-5353	570	40	is	be	VERB
ejpam-5353	570	41	an	an	DET
ejpam-5353	570	42	odc	odc	NOUN
ejpam-5353	570	43	of	of	ADP
ejpam-5353	570	44	k15,15	k15,15	PROPN
ejpam-5353	570	45	by	by	ADP
ejpam-5353	570	46	5τ01(1	5τ01(1	NUM
ejpam-5353	570	47	,	,	PUNCT
ejpam-5353	570	48	1	1	NUM
ejpam-5353	570	49	)	)	PUNCT
ejpam-5353	570	50	and	and	CCONJ
ejpam-5353	570	51	the	the	DET
ejpam-5353	570	52	v(g)×	v(g)×	NOUN
ejpam-5353	570	53	u(f	u(f	PROPN
ejpam-5353	570	54	)	)	PUNCT
ejpam-5353	570	55	=	=	SYM
ejpam-5353	570	56	(	(	PUNCT
ejpam-5353	570	57	00	00	NUM
ejpam-5353	570	58	,	,	PUNCT
ejpam-5353	570	59	01	01	NUM
ejpam-5353	570	60	,	,	PUNCT
ejpam-5353	570	61	02	02	NUM
ejpam-5353	570	62	,	,	PUNCT
ejpam-5353	570	63	03	03	NUM
ejpam-5353	570	64	,	,	PUNCT
ejpam-5353	570	65	04	04	NUM
ejpam-5353	570	66	,	,	PUNCT
ejpam-5353	570	67	10	10	NUM
ejpam-5353	570	68	,	,	PUNCT
ejpam-5353	570	69	11	11	NUM
ejpam-5353	570	70	,	,	PUNCT
ejpam-5353	570	71	12	12	NUM
ejpam-5353	570	72	,	,	PUNCT
ejpam-5353	570	73	13	13	NUM
ejpam-5353	570	74	,	,	PUNCT
ejpam-5353	570	75	14	14	NUM
ejpam-5353	570	76	,	,	PUNCT
ejpam-5353	570	77	10	10	NUM
ejpam-5353	570	78	,	,	PUNCT
ejpam-5353	570	79	11	11	NUM
ejpam-5353	570	80	,	,	PUNCT
ejpam-5353	570	81	12	12	NUM
ejpam-5353	570	82	,	,	PUNCT
ejpam-5353	570	83	13	13	NUM
ejpam-5353	570	84	,	,	PUNCT
ejpam-5353	570	85	14	14	NUM
ejpam-5353	570	86	)	)	PUNCT
ejpam-5353	570	87	the	the	DET
ejpam-5353	570	88	base	base	NOUN
ejpam-5353	570	89	g×	g×	X
ejpam-5353	570	90	f	f	PROPN
ejpam-5353	570	91	is	be	AUX
ejpam-5353	570	92	illustrated	illustrate	VERB
ejpam-5353	570	93	in	in	ADP
ejpam-5353	570	94	figure	figure	NOUN
ejpam-5353	570	95	7	7	NUM
ejpam-5353	570	96	references	reference	NOUN
ejpam-5353	570	97	3514	3514	NUM
ejpam-5353	570	98	figure	figure	NOUN
ejpam-5353	570	99	7	7	NUM
ejpam-5353	570	100	:	:	PUNCT
ejpam-5353	570	101	symmetric	symmetric	ADJ
ejpam-5353	570	102	base	base	NOUN
ejpam-5353	570	103	for	for	ADP
ejpam-5353	570	104	an	an	DET
ejpam-5353	570	105	odc	odc	NOUN
ejpam-5353	570	106	of	of	ADP
ejpam-5353	570	107	k15,15	k15,15	PROPN
ejpam-5353	570	108	by	by	ADP
ejpam-5353	570	109	5τ01(1	5τ01(1	NUM
ejpam-5353	570	110	,	,	PUNCT
ejpam-5353	570	111	1	1	NUM
ejpam-5353	570	112	)	)	PUNCT
ejpam-5353	570	113	.	.	PUNCT
ejpam-5353	571	1	6	6	X
ejpam-5353	571	2	.	.	X
ejpam-5353	571	3	concluding	conclude	VERB
ejpam-5353	571	4	remarks	remark	VERB
ejpam-5353	571	5	the	the	DET
ejpam-5353	571	6	paper	paper	NOUN
ejpam-5353	571	7	delves	delf	NOUN
ejpam-5353	571	8	into	into	ADP
ejpam-5353	571	9	the	the	DET
ejpam-5353	571	10	concept	concept	NOUN
ejpam-5353	571	11	of	of	ADP
ejpam-5353	571	12	graph	graph	NOUN
ejpam-5353	571	13	decomposition	decomposition	NOUN
ejpam-5353	571	14	,	,	PUNCT
ejpam-5353	571	15	particularly	particularly	ADV
ejpam-5353	571	16	focusing	focus	VERB
ejpam-5353	571	17	on	on	ADP
ejpam-5353	571	18	orthogonal	orthogonal	ADJ
ejpam-5353	571	19	decompositions	decomposition	NOUN
ejpam-5353	571	20	.	.	PUNCT
ejpam-5353	572	1	in	in	ADP
ejpam-5353	572	2	this	this	DET
ejpam-5353	572	3	context	context	NOUN
ejpam-5353	572	4	,	,	PUNCT
ejpam-5353	572	5	a	a	DET
ejpam-5353	572	6	graph	graph	NOUN
ejpam-5353	572	7	h	h	NOUN
ejpam-5353	572	8	is	be	AUX
ejpam-5353	572	9	divided	divide	VERB
ejpam-5353	572	10	into	into	ADP
ejpam-5353	572	11	subgraphs	subgraph	NOUN
ejpam-5353	572	12	in	in	ADP
ejpam-5353	572	13	such	such	DET
ejpam-5353	572	14	a	a	DET
ejpam-5353	572	15	way	way	NOUN
ejpam-5353	572	16	that	that	PRON
ejpam-5353	572	17	any	any	DET
ejpam-5353	572	18	two	two	NUM
ejpam-5353	572	19	subgraphs	subgraphs	NOUN
ejpam-5353	572	20	share	share	VERB
ejpam-5353	572	21	at	at	ADP
ejpam-5353	572	22	most	most	ADV
ejpam-5353	572	23	one	one	NUM
ejpam-5353	572	24	edge	edge	NOUN
ejpam-5353	572	25	.	.	PUNCT
ejpam-5353	573	1	these	these	DET
ejpam-5353	573	2	decompositions	decomposition	NOUN
ejpam-5353	573	3	are	be	AUX
ejpam-5353	573	4	referred	refer	VERB
ejpam-5353	573	5	to	to	ADP
ejpam-5353	573	6	as	as	ADP
ejpam-5353	573	7	g−orthogonal	g−orthogonal	ADJ
ejpam-5353	573	8	decompositions	decomposition	NOUN
ejpam-5353	573	9	if	if	SCONJ
ejpam-5353	573	10	each	each	DET
ejpam-5353	573	11	subgraph	subgraph	NOUN
ejpam-5353	573	12	is	be	AUX
ejpam-5353	573	13	isomorphic	isomorphic	ADJ
ejpam-5353	573	14	to	to	ADP
ejpam-5353	573	15	the	the	DET
ejpam-5353	573	16	graph	graph	NOUN
ejpam-5353	573	17	g.	g.	VERB
ejpam-5353	573	18	the	the	DET
ejpam-5353	573	19	applications	application	NOUN
ejpam-5353	573	20	of	of	ADP
ejpam-5353	573	21	such	such	ADJ
ejpam-5353	573	22	decompositions	decomposition	NOUN
ejpam-5353	573	23	are	be	AUX
ejpam-5353	573	24	widespread	widespread	ADJ
ejpam-5353	573	25	,	,	PUNCT
ejpam-5353	573	26	encompassing	encompass	VERB
ejpam-5353	573	27	fields	field	NOUN
ejpam-5353	573	28	like	like	ADP
ejpam-5353	573	29	statistics	statistic	NOUN
ejpam-5353	573	30	,	,	PUNCT
ejpam-5353	573	31	information	information	NOUN
ejpam-5353	573	32	theory	theory	NOUN
ejpam-5353	573	33	,	,	PUNCT
ejpam-5353	573	34	and	and	CCONJ
ejpam-5353	573	35	experimental	experimental	ADJ
ejpam-5353	573	36	design	design	NOUN
ejpam-5353	573	37	theory	theory	NOUN
ejpam-5353	573	38	.	.	PUNCT
ejpam-5353	574	1	the	the	DET
ejpam-5353	574	2	document	document	NOUN
ejpam-5353	574	3	also	also	ADV
ejpam-5353	574	4	introduces	introduce	VERB
ejpam-5353	574	5	an	an	DET
ejpam-5353	574	6	approach	approach	NOUN
ejpam-5353	574	7	for	for	ADP
ejpam-5353	574	8	constructing	construct	VERB
ejpam-5353	574	9	orthogonal	orthogonal	ADJ
ejpam-5353	574	10	decompositions	decomposition	NOUN
ejpam-5353	574	11	of	of	ADP
ejpam-5353	574	12	regular	regular	ADJ
ejpam-5353	574	13	graphs	graph	NOUN
ejpam-5353	574	14	and	and	CCONJ
ejpam-5353	574	15	discusses	discuss	VERB
ejpam-5353	574	16	its	its	PRON
ejpam-5353	574	17	utilization	utilization	NOUN
ejpam-5353	574	18	in	in	ADP
ejpam-5353	574	19	creating	create	VERB
ejpam-5353	574	20	tree	tree	NOUN
ejpam-5353	574	21	-	-	PUNCT
ejpam-5353	574	22	orthogonal	orthogonal	ADJ
ejpam-5353	574	23	decompositions	decomposition	NOUN
ejpam-5353	574	24	of	of	ADP
ejpam-5353	574	25	complete	complete	ADJ
ejpam-5353	574	26	bipartite	bipartite	NOUN
ejpam-5353	574	27	graphs	graph	NOUN
ejpam-5353	574	28	.	.	PUNCT
ejpam-5353	575	1	additionally	additionally	ADV
ejpam-5353	575	2	,	,	PUNCT
ejpam-5353	575	3	the	the	DET
ejpam-5353	575	4	use	use	NOUN
ejpam-5353	575	5	of	of	ADP
ejpam-5353	575	6	orthogonal	orthogonal	ADJ
ejpam-5353	575	7	decompositions	decomposition	NOUN
ejpam-5353	575	8	in	in	ADP
ejpam-5353	575	9	designing	design	VERB
ejpam-5353	575	10	hamming	ham	VERB
ejpam-5353	575	11	tree	tree	NOUN
ejpam-5353	575	12	-	-	PUNCT
ejpam-5353	575	13	codes	code	NOUN
ejpam-5353	575	14	is	be	AUX
ejpam-5353	575	15	explored	explore	VERB
ejpam-5353	575	16	,	,	PUNCT
ejpam-5353	575	17	supported	support	VERB
ejpam-5353	575	18	by	by	ADP
ejpam-5353	575	19	examples	example	NOUN
ejpam-5353	575	20	showcasing	showcase	VERB
ejpam-5353	575	21	their	their	PRON
ejpam-5353	575	22	effectiveness	effectiveness	NOUN
ejpam-5353	575	23	in	in	ADP
ejpam-5353	575	24	error	error	NOUN
ejpam-5353	575	25	detection	detection	NOUN
ejpam-5353	575	26	and	and	CCONJ
ejpam-5353	575	27	correction	correction	NOUN
ejpam-5353	575	28	during	during	ADP
ejpam-5353	575	29	data	datum	NOUN
ejpam-5353	575	30	transmission	transmission	NOUN
ejpam-5353	575	31	.	.	PUNCT
ejpam-5353	576	1	in	in	ADP
ejpam-5353	576	2	future	future	ADJ
ejpam-5353	576	3	wok	wok	NOUN
ejpam-5353	576	4	,	,	PUNCT
ejpam-5353	576	5	further	further	ADJ
ejpam-5353	576	6	investigations	investigation	NOUN
ejpam-5353	576	7	will	will	AUX
ejpam-5353	576	8	be	be	AUX
ejpam-5353	576	9	planed	plane	VERB
ejpam-5353	576	10	to	to	PART
ejpam-5353	576	11	manipulate	manipulate	VERB
ejpam-5353	576	12	our	our	PRON
ejpam-5353	576	13	approach	approach	NOUN
ejpam-5353	576	14	to	to	ADP
ejpam-5353	576	15	work	work	VERB
ejpam-5353	576	16	on	on	ADP
ejpam-5353	576	17	irregular	irregular	ADJ
ejpam-5353	576	18	graphs	graph	NOUN
ejpam-5353	576	19	.	.	PUNCT
ejpam-5353	577	1	declaration	declaration	NOUN
ejpam-5353	577	2	of	of	ADP
ejpam-5353	577	3	conflicting	conflicting	ADJ
ejpam-5353	577	4	interests	interest	NOUN
ejpam-5353	577	5	the	the	DET
ejpam-5353	577	6	authors	author	NOUN
ejpam-5353	577	7	declared	declare	VERB
ejpam-5353	577	8	no	no	DET
ejpam-5353	577	9	potential	potential	ADJ
ejpam-5353	577	10	conflicts	conflict	NOUN
ejpam-5353	577	11	of	of	ADP
ejpam-5353	577	12	interest	interest	NOUN
ejpam-5353	577	13	with	with	ADP
ejpam-5353	577	14	respect	respect	NOUN
ejpam-5353	577	15	to	to	ADP
ejpam-5353	577	16	the	the	DET
ejpam-5353	577	17	research	research	NOUN
ejpam-5353	577	18	,	,	PUNCT
ejpam-5353	577	19	authorship	authorship	NOUN
ejpam-5353	577	20	,	,	PUNCT
ejpam-5353	577	21	and/or	and/or	CCONJ
ejpam-5353	577	22	publication	publication	NOUN
ejpam-5353	577	23	of	of	ADP
ejpam-5353	577	24	this	this	DET
ejpam-5353	577	25	article	article	NOUN
ejpam-5353	577	26	.	.	PUNCT
ejpam-5353	578	1	acknowledgements	acknowledgement	NOUN
ejpam-5353	578	2	we	we	PRON
ejpam-5353	578	3	are	be	AUX
ejpam-5353	578	4	grateful	grateful	ADJ
ejpam-5353	578	5	to	to	ADP
ejpam-5353	578	6	the	the	DET
ejpam-5353	578	7	reviewers	reviewer	NOUN
ejpam-5353	578	8	for	for	ADP
ejpam-5353	578	9	a	a	DET
ejpam-5353	578	10	number	number	NOUN
ejpam-5353	578	11	of	of	ADP
ejpam-5353	578	12	valuable	valuable	ADJ
ejpam-5353	578	13	remarks	remark	NOUN
ejpam-5353	578	14	and	and	CCONJ
ejpam-5353	578	15	suggestions	suggestion	NOUN
ejpam-5353	578	16	.	.	PUNCT
ejpam-5353	579	1	references	reference	NOUN
ejpam-5353	579	2	[	[	X
ejpam-5353	579	3	1	1	NUM
ejpam-5353	579	4	]	]	PUNCT
ejpam-5353	579	5	r.	r.	PROPN
ejpam-5353	579	6	balakrishnan	balakrishnan	PROPN
ejpam-5353	579	7	and	and	CCONJ
ejpam-5353	579	8	k.	k.	PROPN
ejpam-5353	579	9	ranganathan	ranganathan	PROPN
ejpam-5353	579	10	.	.	PUNCT
ejpam-5353	580	1	a	a	DET
ejpam-5353	580	2	textbook	textbook	NOUN
ejpam-5353	580	3	of	of	ADP
ejpam-5353	580	4	graph	graph	NOUN
ejpam-5353	580	5	theory	theory	NOUN
ejpam-5353	580	6	.	.	PUNCT
ejpam-5353	581	1	springer	springer	NOUN
ejpam-5353	581	2	,	,	PUNCT
ejpam-5353	581	3	berlin	berlin	PROPN
ejpam-5353	581	4	,	,	PUNCT
ejpam-5353	581	5	2012	2012	NUM
ejpam-5353	581	6	.	.	PUNCT
ejpam-5353	582	1	[	[	X
ejpam-5353	582	2	2	2	X
ejpam-5353	582	3	]	]	PUNCT
ejpam-5353	582	4	o.	o.	NOUN
ejpam-5353	582	5	g.	g.	PROPN
ejpam-5353	582	6	el	el	PROPN
ejpam-5353	582	7	barbary	barbary	PROPN
ejpam-5353	582	8	and	and	CCONJ
ejpam-5353	582	9	radwan	radwan	PROPN
ejpam-5353	582	10	abu	abu	PROPN
ejpam-5353	582	11	gdairi	gdairi	PROPN
ejpam-5353	582	12	.	.	PUNCT
ejpam-5353	583	1	neutrosophic	neutrosophic	ADJ
ejpam-5353	583	2	logic	logic	NOUN
ejpam-5353	583	3	-	-	PUNCT
ejpam-5353	583	4	based	base	VERB
ejpam-5353	583	5	document	document	NOUN
ejpam-5353	583	6	summarization	summarization	NOUN
ejpam-5353	583	7	.	.	PUNCT
ejpam-5353	584	1	journal	journal	NOUN
ejpam-5353	584	2	of	of	ADP
ejpam-5353	584	3	mathematics	mathematic	NOUN
ejpam-5353	584	4	,	,	PUNCT
ejpam-5353	584	5	2021(11):article	2021(11):article	NUM
ejpam-5353	584	6	i	i	NOUN
ejpam-5353	584	7	d	d	NOUN
ejpam-5353	584	8	:	:	PUNCT
ejpam-5353	584	9	9938693	9938693	NUM
ejpam-5353	584	10	,	,	PUNCT
ejpam-5353	584	11	2021	2021	NUM
ejpam-5353	584	12	.	.	PUNCT
ejpam-5353	585	1	[	[	X
ejpam-5353	585	2	3	3	X
ejpam-5353	585	3	]	]	X
ejpam-5353	585	4	c.j	c.j	PROPN
ejpam-5353	585	5	.	.	PROPN
ejpam-5353	585	6	colbourn	colbourn	PROPN
ejpam-5353	585	7	and	and	CCONJ
ejpam-5353	585	8	j.	j.	PROPN
ejpam-5353	585	9	h.	h.	PROPN
ejpam-5353	585	10	dinitz	dinitz	PROPN
ejpam-5353	585	11	.	.	PUNCT
ejpam-5353	586	1	handbook	handbook	NOUN
ejpam-5353	586	2	of	of	ADP
ejpam-5353	586	3	combinatorial	combinatorial	ADJ
ejpam-5353	586	4	designs	design	NOUN
ejpam-5353	586	5	,	,	PUNCT
ejpam-5353	586	6	2nd	2nd	ADJ
ejpam-5353	586	7	ed	ed	NOUN
ejpam-5353	586	8	.	.	PUNCT
ejpam-5353	587	1	chapman	chapman	PROPN
ejpam-5353	587	2	and	and	CCONJ
ejpam-5353	587	3	hall	hall	PROPN
ejpam-5353	587	4	-	-	PUNCT
ejpam-5353	587	5	crc	crc	PROPN
ejpam-5353	587	6	,	,	PUNCT
ejpam-5353	587	7	berlin	berlin	PROPN
ejpam-5353	587	8	,	,	PUNCT
ejpam-5353	587	9	2007	2007	NUM
ejpam-5353	587	10	.	.	PUNCT
ejpam-5353	588	1	references	reference	NOUN
ejpam-5353	588	2	3515	3515	NUM
ejpam-5353	588	3	[	[	X
ejpam-5353	588	4	4	4	NUM
ejpam-5353	588	5	]	]	X
ejpam-5353	588	6	r.	r.	PROPN
ejpam-5353	588	7	abu	abu	PROPN
ejpam-5353	588	8	-	-	PUNCT
ejpam-5353	588	9	gdairi	gdairi	PROPN
ejpam-5353	588	10	,	,	PUNCT
ejpam-5353	588	11	a.	a.	PROPN
ejpam-5353	588	12	a.	a.	PROPN
ejpam-5353	588	13	el	el	PROPN
ejpam-5353	588	14	atik	atik	PROPN
ejpam-5353	588	15	,	,	PUNCT
ejpam-5353	588	16	m.	m.	PROPN
ejpam-5353	588	17	k.	k.	PROPN
ejpam-5353	589	1	el	el	PROPN
ejpam-5353	589	2	-	-	PROPN
ejpam-5353	589	3	bably	bably	PROPN
ejpam-5353	589	4	and	and	CCONJ
ejpam-5353	589	5	m.	m.	NOUN
ejpam-5353	589	6	a.	a.	PROPN
ejpam-5353	589	7	el	el	PROPN
ejpam-5353	589	8	-	-	PROPN
ejpam-5353	589	9	gayar	gayar	NOUN
ejpam-5353	589	10	.	.	PUNCT
ejpam-5353	590	1	topological	topological	ADJ
ejpam-5353	590	2	visualization	visualization	NOUN
ejpam-5353	590	3	and	and	CCONJ
ejpam-5353	590	4	graph	graph	VERB
ejpam-5353	590	5	analysis	analysis	NOUN
ejpam-5353	590	6	of	of	ADP
ejpam-5353	590	7	rough	rough	ADJ
ejpam-5353	590	8	sets	set	NOUN
ejpam-5353	590	9	via	via	ADP
ejpam-5353	590	10	neighborhoods	neighborhood	NOUN
ejpam-5353	590	11	:	:	PUNCT
ejpam-5353	590	12	a	a	DET
ejpam-5353	590	13	medical	medical	ADJ
ejpam-5353	590	14	application	application	NOUN
ejpam-5353	590	15	using	use	VERB
ejpam-5353	590	16	human	human	ADJ
ejpam-5353	590	17	heart	heart	NOUN
ejpam-5353	590	18	data	datum	NOUN
ejpam-5353	590	19	.	.	PUNCT
ejpam-5353	591	1	aims	aim	VERB
ejpam-5353	591	2	mathematics	mathematic	NOUN
ejpam-5353	591	3	.	.	PUNCT
ejpam-5353	591	4	,	,	PUNCT
ejpam-5353	591	5	8(11):26945–26967	8(11):26945–26967	NUM
ejpam-5353	591	6	,	,	PUNCT
ejpam-5353	591	7	2023	2023	NUM
ejpam-5353	591	8	.	.	PUNCT
ejpam-5353	592	1	[	[	X
ejpam-5353	592	2	5	5	X
ejpam-5353	592	3	]	]	PUNCT
ejpam-5353	592	4	h.	h.	PROPN
ejpam-5353	592	5	shabana	shabana	PROPN
ejpam-5353	592	6	,	,	PUNCT
ejpam-5353	592	7	r.	r.	PROPN
ejpam-5353	592	8	el	el	PROPN
ejpam-5353	592	9	-	-	PROPN
ejpam-5353	592	10	shanawany	shanawany	PROPN
ejpam-5353	592	11	and	and	CCONJ
ejpam-5353	592	12	s.	s.	PROPN
ejpam-5353	592	13	r.	r.	PROPN
ejpam-5353	592	14	halawa	halawa	PROPN
ejpam-5353	592	15	.	.	PUNCT
ejpam-5353	593	1	graph	graph	NOUN
ejpam-5353	593	2	design	design	NOUN
ejpam-5353	593	3	for	for	ADP
ejpam-5353	593	4	data	datum	NOUN
ejpam-5353	593	5	authentication	authentication	NOUN
ejpam-5353	593	6	over	over	ADP
ejpam-5353	593	7	insecure	insecure	ADJ
ejpam-5353	593	8	communication	communication	NOUN
ejpam-5353	593	9	channel	channel	NOUN
ejpam-5353	593	10	.	.	PUNCT
ejpam-5353	594	1	alexandria	alexandria	PROPN
ejpam-5353	594	2	engineering	engineering	PROPN
ejpam-5353	594	3	journal	journal	PROPN
ejpam-5353	594	4	,	,	PUNCT
ejpam-5353	594	5	75:649–662	75:649–662	NOUN
ejpam-5353	594	6	,	,	PUNCT
ejpam-5353	594	7	2023	2023	NUM
ejpam-5353	594	8	.	.	PUNCT
ejpam-5353	595	1	[	[	X
ejpam-5353	595	2	6	6	NUM
ejpam-5353	595	3	]	]	X
ejpam-5353	595	4	r	r	NOUN
ejpam-5353	595	5	scapellato	scapellato	PROPN
ejpam-5353	595	6	,	,	PUNCT
ejpam-5353	595	7	r.	r.	PROPN
ejpam-5353	595	8	el	el	PROPN
ejpam-5353	595	9	-	-	PROPN
ejpam-5353	595	10	shanawany	shanawany	NOUN
ejpam-5353	595	11	and	and	CCONJ
ejpam-5353	595	12	m.	m.	NOUN
ejpam-5353	595	13	higazy	higazy	NOUN
ejpam-5353	595	14	.	.	PUNCT
ejpam-5353	596	1	orthogonal	orthogonal	ADJ
ejpam-5353	596	2	double	double	ADJ
ejpam-5353	596	3	covers	cover	NOUN
ejpam-5353	596	4	of	of	ADP
ejpam-5353	596	5	cayley	cayley	ADJ
ejpam-5353	596	6	graphs	graph	NOUN
ejpam-5353	596	7	.	.	PUNCT
ejpam-5353	597	1	discrete	discrete	ADJ
ejpam-5353	597	2	appl	appl	PROPN
ejpam-5353	597	3	math	math	NOUN
ejpam-5353	597	4	.	.	PUNCT
ejpam-5353	597	5	,	,	PUNCT
ejpam-5353	597	6	157:3111–3118	157:3111–3118	NUM
ejpam-5353	597	7	,	,	PUNCT
ejpam-5353	597	8	2009	2009	NUM
ejpam-5353	597	9	.	.	PUNCT
ejpam-5353	598	1	[	[	X
ejpam-5353	598	2	7	7	X
ejpam-5353	598	3	]	]	X
ejpam-5353	598	4	s.	s.	PROPN
ejpam-5353	598	5	el	el	PROPN
ejpam-5353	598	6	-	-	PUNCT
ejpam-5353	598	7	serafi	serafi	PROPN
ejpam-5353	598	8	,	,	PUNCT
ejpam-5353	598	9	r.	r.	PROPN
ejpam-5353	598	10	el	el	PROPN
ejpam-5353	598	11	-	-	NOUN
ejpam-5353	598	12	shanawany	shanawany	NOUN
ejpam-5353	598	13	,	,	PUNCT
ejpam-5353	598	14	and	and	CCONJ
ejpam-5353	598	15	h.	h.	PROPN
ejpam-5353	598	16	shabana	shabana	PROPN
ejpam-5353	598	17	.	.	PUNCT
ejpam-5353	599	1	orthogonal	orthogonal	ADJ
ejpam-5353	599	2	double	double	ADJ
ejpam-5353	599	3	cover	cover	NOUN
ejpam-5353	599	4	of	of	ADP
ejpam-5353	599	5	complete	complete	ADJ
ejpam-5353	599	6	bipartite	bipartite	NOUN
ejpam-5353	599	7	graph	graph	NOUN
ejpam-5353	599	8	by	by	ADP
ejpam-5353	599	9	disjoint	disjoint	NOUN
ejpam-5353	599	10	union	union	NOUN
ejpam-5353	599	11	of	of	ADP
ejpam-5353	599	12	complete	complete	ADJ
ejpam-5353	599	13	bipartite	bipartite	NOUN
ejpam-5353	599	14	graphs	graph	NOUN
ejpam-5353	599	15	.	.	PUNCT
ejpam-5353	600	1	ain	ain	PROPN
ejpam-5353	600	2	shams	shams	PROPN
ejpam-5353	600	3	eng	eng	PROPN
ejpam-5353	600	4	.	.	PUNCT
ejpam-5353	601	1	j.	j.	PROPN
ejpam-5353	601	2	,	,	PUNCT
ejpam-5353	601	3	6:657–660	6:657–660	PROPN
ejpam-5353	601	4	,	,	PUNCT
ejpam-5353	601	5	2015	2015	NUM
ejpam-5353	601	6	.	.	PUNCT
ejpam-5353	602	1	[	[	X
ejpam-5353	602	2	8	8	NUM
ejpam-5353	602	3	]	]	X
ejpam-5353	602	4	w.	w.	NOUN
ejpam-5353	602	5	fish	fish	PROPN
ejpam-5353	602	6	,	,	PUNCT
ejpam-5353	602	7	r.	r.	PROPN
ejpam-5353	602	8	fray	fray	PROPN
ejpam-5353	602	9	and	and	CCONJ
ejpam-5353	602	10	e.	e.	PROPN
ejpam-5353	602	11	mwambene	mwambene	PROPN
ejpam-5353	602	12	.	.	PUNCT
ejpam-5353	603	1	binary	binary	ADJ
ejpam-5353	603	2	codes	code	NOUN
ejpam-5353	603	3	from	from	ADP
ejpam-5353	603	4	the	the	DET
ejpam-5353	603	5	complements	complement	NOUN
ejpam-5353	603	6	of	of	ADP
ejpam-5353	603	7	the	the	DET
ejpam-5353	603	8	triangular	triangular	NOUN
ejpam-5353	603	9	graphs	graph	NOUN
ejpam-5353	603	10	.	.	PUNCT
ejpam-5353	604	1	quaestiones	quaestione	NOUN
ejpam-5353	604	2	mathematicae	mathematicae	PROPN
ejpam-5353	604	3	,	,	PUNCT
ejpam-5353	604	4	33:399–408	33:399–408	NUM
ejpam-5353	604	5	,	,	PUNCT
ejpam-5353	604	6	2010	2010	NUM
ejpam-5353	604	7	.	.	PUNCT
ejpam-5353	605	1	[	[	X
ejpam-5353	605	2	9	9	NUM
ejpam-5353	605	3	]	]	PUNCT
ejpam-5353	605	4	m.	m.	NOUN
ejpam-5353	605	5	grassl	grassl	NOUN
ejpam-5353	605	6	and	and	CCONJ
ejpam-5353	605	7	m.	m.	NOUN
ejpam-5353	605	8	harada	harada	PROPN
ejpam-5353	605	9	.	.	PUNCT
ejpam-5353	606	1	new	new	ADJ
ejpam-5353	606	2	self	self	NOUN
ejpam-5353	606	3	-	-	PUNCT
ejpam-5353	606	4	dual	dual	ADJ
ejpam-5353	606	5	additive	additive	ADJ
ejpam-5353	606	6	f4	f4	NOUN
ejpam-5353	606	7	-	-	PUNCT
ejpam-5353	606	8	codes	code	NOUN
ejpam-5353	606	9	constructed	construct	VERB
ejpam-5353	606	10	from	from	ADP
ejpam-5353	606	11	circulant	circulant	ADJ
ejpam-5353	606	12	graphs	graph	NOUN
ejpam-5353	606	13	.	.	PUNCT
ejpam-5353	607	1	discrete	discrete	ADJ
ejpam-5353	607	2	math	math	NOUN
ejpam-5353	607	3	.	.	PUNCT
ejpam-5353	607	4	,	,	PUNCT
ejpam-5353	607	5	340:399–403	340:399–403	NUM
ejpam-5353	607	6	,	,	PUNCT
ejpam-5353	607	7	2017	2017	NUM
ejpam-5353	607	8	.	.	PUNCT
ejpam-5353	608	1	[	[	X
ejpam-5353	608	2	10	10	NUM
ejpam-5353	608	3	]	]	X
ejpam-5353	608	4	r.	r.	PROPN
ejpam-5353	608	5	el	el	PROPN
ejpam-5353	608	6	-	-	PROPN
ejpam-5353	608	7	shanawany	shanawany	NOUN
ejpam-5353	608	8	,	,	PUNCT
ejpam-5353	608	9	s.	s.	PROPN
ejpam-5353	608	10	a.	a.	PROPN
ejpam-5353	608	11	el	el	PROPN
ejpam-5353	608	12	-	-	PUNCT
ejpam-5353	608	13	sheikh	sheikh	PROPN
ejpam-5353	608	14	,	,	PUNCT
ejpam-5353	608	15	s.	s.	PROPN
ejpam-5353	608	16	r.	r.	PROPN
ejpam-5353	608	17	halawa	halawa	PROPN
ejpam-5353	608	18	and	and	CCONJ
ejpam-5353	608	19	h.	h.	PROPN
ejpam-5353	608	20	shabana	shabana	PROPN
ejpam-5353	608	21	.	.	PUNCT
ejpam-5353	609	1	graph	graph	NOUN
ejpam-5353	609	2	based	base	VERB
ejpam-5353	609	3	approach	approach	NOUN
ejpam-5353	609	4	for	for	ADP
ejpam-5353	609	5	error	error	NOUN
ejpam-5353	609	6	-	-	PUNCT
ejpam-5353	609	7	detecting	detect	VERB
ejpam-5353	609	8	and	and	CCONJ
ejpam-5353	609	9	correcting	correct	VERB
ejpam-5353	609	10	codes	code	NOUN
ejpam-5353	609	11	.	.	PUNCT
ejpam-5353	610	1	applied	apply	VERB
ejpam-5353	610	2	mathematics	mathematic	NOUN
ejpam-5353	610	3	and	and	CCONJ
ejpam-5353	610	4	information	information	NOUN
ejpam-5353	610	5	sciences	sciences	PROPN
ejpam-5353	610	6	,	,	PUNCT
ejpam-5353	610	7	16:995–1003	16:995–1003	NUM
ejpam-5353	610	8	,	,	PUNCT
ejpam-5353	610	9	2022	2022	NUM
ejpam-5353	610	10	.	.	PUNCT
ejpam-5353	611	1	[	[	X
ejpam-5353	611	2	11	11	NUM
ejpam-5353	611	3	]	]	PUNCT
ejpam-5353	611	4	s.	s.	PROPN
ejpam-5353	611	5	hartmann	hartmann	PROPN
ejpam-5353	611	6	and	and	CCONJ
ejpam-5353	611	7	u.	u.	PROPN
ejpam-5353	611	8	schumacher	schumacher	PROPN
ejpam-5353	611	9	.	.	PUNCT
ejpam-5353	612	1	orthogonal	orthogonal	ADJ
ejpam-5353	612	2	double	double	ADJ
ejpam-5353	612	3	covers	cover	NOUN
ejpam-5353	612	4	of	of	ADP
ejpam-5353	612	5	general	general	ADJ
ejpam-5353	612	6	graphs	graph	NOUN
ejpam-5353	612	7	.	.	PUNCT
ejpam-5353	613	1	graphs	graph	NOUN
ejpam-5353	613	2	combin.discrete	combin.discrete	PROPN
ejpam-5353	613	3	appl	appl	PROPN
ejpam-5353	613	4	.	.	PUNCT
ejpam-5353	614	1	math	math	PROPN
ejpam-5353	614	2	.	.	PUNCT
ejpam-5353	614	3	,	,	PUNCT
ejpam-5353	614	4	138:107–116	138:107–116	NUM
ejpam-5353	614	5	,	,	PUNCT
ejpam-5353	614	6	2004	2004	NUM
ejpam-5353	614	7	.	.	PUNCT
ejpam-5353	615	1	[	[	X
ejpam-5353	615	2	12	12	NUM
ejpam-5353	615	3	]	]	X
ejpam-5353	615	4	e.	e.	PROPN
ejpam-5353	615	5	f.	f.	PROPN
ejpam-5353	615	6	assmus	assmus	PROPN
ejpam-5353	615	7	.	.	PUNCT
ejpam-5353	616	1	jr	jr	PROPN
ejpam-5353	616	2	,	,	PUNCT
ejpam-5353	616	3	j.	j.	PROPN
ejpam-5353	616	4	d.	d.	PROPN
ejpam-5353	616	5	key	key	PROPN
ejpam-5353	616	6	.	.	PUNCT
ejpam-5353	617	1	designs	design	NOUN
ejpam-5353	617	2	and	and	CCONJ
ejpam-5353	617	3	codes	code	NOUN
ejpam-5353	617	4	:	:	PUNCT
ejpam-5353	617	5	an	an	DET
ejpam-5353	617	6	update	update	NOUN
ejpam-5353	617	7	.	.	PUNCT
ejpam-5353	618	1	des	des	PROPN
ejpam-5353	618	2	.	.	PROPN
ejpam-5353	618	3	codes	code	NOUN
ejpam-5353	618	4	cryptogr	cryptogr	NOUN
ejpam-5353	618	5	.	.	PUNCT
ejpam-5353	618	6	,	,	PUNCT
ejpam-5353	618	7	9:7–27	9:7–27	NUM
ejpam-5353	618	8	,	,	PUNCT
ejpam-5353	618	9	1996	1996	NUM
ejpam-5353	618	10	.	.	PUNCT
ejpam-5353	619	1	[	[	X
ejpam-5353	619	2	13	13	NUM
ejpam-5353	619	3	]	]	PUNCT
ejpam-5353	619	4	j.	j.	PROPN
ejpam-5353	619	5	d.	d.	PROPN
ejpam-5353	619	6	key	key	PROPN
ejpam-5353	619	7	and	and	CCONJ
ejpam-5353	619	8	b.	b.	PROPN
ejpam-5353	619	9	g.	g.	PROPN
ejpam-5353	619	10	rodrigues	rodrigues	PROPN
ejpam-5353	619	11	.	.	PUNCT
ejpam-5353	620	1	lcd	lcd	NOUN
ejpam-5353	620	2	codes	code	NOUN
ejpam-5353	620	3	from	from	ADP
ejpam-5353	620	4	adjacency	adjacency	NOUN
ejpam-5353	620	5	matrices	matrix	NOUN
ejpam-5353	620	6	of	of	ADP
ejpam-5353	620	7	graphs	graph	NOUN
ejpam-5353	620	8	.	.	PUNCT
ejpam-5353	621	1	appl	appl	PROPN
ejpam-5353	621	2	.	.	PUNCT
ejpam-5353	622	1	alg	alg	PROPN
ejpam-5353	622	2	.	.	PUNCT
ejpam-5353	623	1	eng	eng	PROPN
ejpam-5353	623	2	.	.	PROPN
ejpam-5353	623	3	comm	comm	NOUN
ejpam-5353	623	4	.	.	PUNCT
ejpam-5353	624	1	comp	comp	PROPN
ejpam-5353	624	2	.	.	PUNCT
ejpam-5353	624	3	,	,	PUNCT
ejpam-5353	624	4	29:227–244	29:227–244	PROPN
ejpam-5353	624	5	,	,	PUNCT
ejpam-5353	624	6	2018	2018	NUM
ejpam-5353	624	7	.	.	PUNCT
ejpam-5353	625	1	[	[	X
ejpam-5353	625	2	14	14	NUM
ejpam-5353	625	3	]	]	SYM
ejpam-5353	625	4	h.-d.o.f	h.-d.o.f	NOUN
ejpam-5353	625	5	.	.	PROPN
ejpam-5353	625	6	gronau	gronau	PROPN
ejpam-5353	625	7	,	,	PUNCT
ejpam-5353	625	8	s.	s.	PROPN
ejpam-5353	625	9	hartmann	hartmann	PROPN
ejpam-5353	625	10	,	,	PUNCT
ejpam-5353	625	11	m.	m.	NOUN
ejpam-5353	625	12	grüttmüller	grüttmüller	NOUN
ejpam-5353	625	13	,	,	PUNCT
ejpam-5353	625	14	u.	u.	PROPN
ejpam-5353	625	15	leck	leck	PROPN
ejpam-5353	625	16	and	and	CCONJ
ejpam-5353	625	17	v.	v.	ADP
ejpam-5353	625	18	leck	leck	PROPN
ejpam-5353	625	19	.	.	PUNCT
ejpam-5353	626	1	on	on	ADP
ejpam-5353	626	2	orthogonal	orthogonal	ADJ
ejpam-5353	626	3	double	double	ADJ
ejpam-5353	626	4	covers	cover	NOUN
ejpam-5353	626	5	of	of	ADP
ejpam-5353	626	6	graphs	graph	NOUN
ejpam-5353	626	7	.	.	PUNCT
ejpam-5353	627	1	codes	code	NOUN
ejpam-5353	627	2	cryptogr	cryptogr	NOUN
ejpam-5353	627	3	.	.	PUNCT
ejpam-5353	627	4	,	,	PUNCT
ejpam-5353	627	5	27:49–91	27:49–91	NUM
ejpam-5353	627	6	,	,	PUNCT
ejpam-5353	627	7	2002	2002	NUM
ejpam-5353	627	8	.	.	PUNCT
ejpam-5353	628	1	[	[	X
ejpam-5353	628	2	15	15	NUM
ejpam-5353	628	3	]	]	X
ejpam-5353	628	4	d.	d.	PROPN
ejpam-5353	628	5	leemans	leemans	PROPN
ejpam-5353	628	6	and	and	CCONJ
ejpam-5353	628	7	b.	b.	PROPN
ejpam-5353	628	8	g.	g.	PROPN
ejpam-5353	628	9	rodrigues	rodrigues	PROPN
ejpam-5353	628	10	.	.	PUNCT
ejpam-5353	629	1	binary	binary	ADJ
ejpam-5353	629	2	codes	code	NOUN
ejpam-5353	629	3	of	of	ADP
ejpam-5353	629	4	some	some	DET
ejpam-5353	629	5	strongly	strongly	ADV
ejpam-5353	629	6	regular	regular	ADJ
ejpam-5353	629	7	subgraphs	subgraph	NOUN
ejpam-5353	629	8	of	of	ADP
ejpam-5353	629	9	the	the	DET
ejpam-5353	629	10	mclaughlin	mclaughlin	PROPN
ejpam-5353	629	11	graph	graph	NOUN
ejpam-5353	629	12	.	.	PUNCT
ejpam-5353	630	1	des	des	PROPN
ejpam-5353	630	2	.	.	PROPN
ejpam-5353	630	3	codes	code	NOUN
ejpam-5353	630	4	cryptogr	cryptogr	NOUN
ejpam-5353	630	5	.	.	PUNCT
ejpam-5353	630	6	,	,	PUNCT
ejpam-5353	630	7	67:93–109	67:93–109	NUM
ejpam-5353	630	8	,	,	PUNCT
ejpam-5353	630	9	2013	2013	NUM
ejpam-5353	630	10	.	.	PUNCT
ejpam-5353	631	1	[	[	X
ejpam-5353	631	2	16	16	NUM
ejpam-5353	631	3	]	]	PUNCT
ejpam-5353	631	4	h.-d.o.f	h.-d.o.f	NOUN
ejpam-5353	631	5	.	.	PUNCT
ejpam-5353	631	6	gronau	gronau	PROPN
ejpam-5353	631	7	,	,	PUNCT
ejpam-5353	631	8	r.c	r.c	PROPN
ejpam-5353	631	9	.	.	PROPN
ejpam-5353	631	10	mullin	mullin	PROPN
ejpam-5353	631	11	and	and	CCONJ
ejpam-5353	631	12	a.	a.	PROPN
ejpam-5353	631	13	rosa	rosa	PROPN
ejpam-5353	631	14	.	.	PUNCT
ejpam-5353	632	1	on	on	ADP
ejpam-5353	632	2	orthogonal	orthogonal	ADJ
ejpam-5353	632	3	double	double	ADJ
ejpam-5353	632	4	covers	cover	NOUN
ejpam-5353	632	5	of	of	ADP
ejpam-5353	632	6	complete	complete	ADJ
ejpam-5353	632	7	graphs	graph	NOUN
ejpam-5353	632	8	by	by	ADP
ejpam-5353	632	9	trees	tree	NOUN
ejpam-5353	632	10	.	.	PUNCT
ejpam-5353	633	1	graphs	graph	NOUN
ejpam-5353	633	2	combin	combin	NOUN
ejpam-5353	633	3	.	.	PUNCT
ejpam-5353	633	4	,	,	PUNCT
ejpam-5353	633	5	13:251–262	13:251–262	NUM
ejpam-5353	633	6	,	,	PUNCT
ejpam-5353	633	7	1997	1997	NUM
ejpam-5353	633	8	.	.	PUNCT
ejpam-5353	634	1	[	[	X
ejpam-5353	634	2	17	17	NUM
ejpam-5353	634	3	]	]	X
ejpam-5353	634	4	w.	w.	PROPN
ejpam-5353	634	5	h.	h.	PROPN
ejpam-5353	634	6	haemers	haemers	PROPN
ejpam-5353	634	7	,	,	PUNCT
ejpam-5353	634	8	r.	r.	PROPN
ejpam-5353	634	9	peeters	peeter	NOUN
ejpam-5353	634	10	and	and	CCONJ
ejpam-5353	634	11	j.m	j.m	PROPN
ejpam-5353	634	12	.	.	PROPN
ejpam-5353	634	13	rijckevorsel	rijckevorsel	NOUN
ejpam-5353	634	14	.	.	PUNCT
ejpam-5353	635	1	binary	binary	ADJ
ejpam-5353	635	2	codes	code	NOUN
ejpam-5353	635	3	of	of	ADP
ejpam-5353	635	4	strongly	strongly	ADV
ejpam-5353	635	5	regular	regular	ADJ
ejpam-5353	635	6	graphs	graph	NOUN
ejpam-5353	635	7	.	.	PUNCT
ejpam-5353	636	1	des	des	PROPN
ejpam-5353	636	2	.	.	PROPN
ejpam-5353	636	3	codes	code	NOUN
ejpam-5353	636	4	cryptogr	cryptogr	NOUN
ejpam-5353	636	5	.	.	PUNCT
ejpam-5353	636	6	,	,	PUNCT
ejpam-5353	636	7	17:187–209	17:187–209	NUM
ejpam-5353	636	8	,	,	PUNCT
ejpam-5353	636	9	1999	1999	NUM
ejpam-5353	636	10	.	.	PUNCT
ejpam-5353	637	1	[	[	X
ejpam-5353	637	2	18	18	NUM
ejpam-5353	637	3	]	]	X
ejpam-5353	637	4	d.	d.	PROPN
ejpam-5353	637	5	crnkovic	crnkovic	PROPN
ejpam-5353	637	6	,	,	PUNCT
ejpam-5353	637	7	m.	m.	NOUN
ejpam-5353	637	8	maximovic	maximovic	PROPN
ejpam-5353	637	9	,	,	PUNCT
ejpam-5353	637	10	b.	b.	PROPN
ejpam-5353	637	11	rodrigues	rodrigues	PROPN
ejpam-5353	637	12	and	and	CCONJ
ejpam-5353	637	13	s.	s.	PROPN
ejpam-5353	637	14	rukavina	rukavina	PROPN
ejpam-5353	637	15	.	.	PUNCT
ejpam-5353	638	1	self	self	NOUN
ejpam-5353	638	2	-	-	PUNCT
ejpam-5353	638	3	orthogonal	orthogonal	ADJ
ejpam-5353	638	4	codes	code	NOUN
ejpam-5353	638	5	from	from	ADP
ejpam-5353	638	6	the	the	DET
ejpam-5353	638	7	strongly	strongly	ADV
ejpam-5353	638	8	regular	regular	ADJ
ejpam-5353	638	9	graphs	graph	NOUN
ejpam-5353	638	10	on	on	ADP
ejpam-5353	638	11	up	up	ADP
ejpam-5353	638	12	to	to	PART
ejpam-5353	638	13	40	40	NUM
ejpam-5353	638	14	vertices	vertex	NOUN
ejpam-5353	638	15	.	.	PUNCT
ejpam-5353	639	1	adv	adv	PROPN
ejpam-5353	639	2	.	.	PUNCT
ejpam-5353	639	3	math	math	PROPN
ejpam-5353	639	4	.	.	PUNCT
ejpam-5353	640	1	communications	communication	NOUN
ejpam-5353	640	2	,	,	PUNCT
ejpam-5353	640	3	10:555–582	10:555–582	NUM
ejpam-5353	640	4	,	,	PUNCT
ejpam-5353	640	5	2016	2016	NUM
ejpam-5353	640	6	.	.	PUNCT
ejpam-5353	641	1	references	reference	NOUN
ejpam-5353	641	2	3516	3516	NUM
ejpam-5353	641	3	[	[	X
ejpam-5353	641	4	19	19	NUM
ejpam-5353	641	5	]	]	X
ejpam-5353	641	6	d.	d.	PROPN
ejpam-5353	641	7	crnkovic	crnkovic	PROPN
ejpam-5353	641	8	,	,	PUNCT
ejpam-5353	641	9	b.	b.	PROPN
ejpam-5353	641	10	g.	g.	PROPN
ejpam-5353	641	11	rodrigues	rodrigues	PROPN
ejpam-5353	641	12	,	,	PUNCT
ejpam-5353	641	13	s.	s.	PROPN
ejpam-5353	641	14	rukavina	rukavina	PROPN
ejpam-5353	641	15	and	and	CCONJ
ejpam-5353	641	16	l.	l.	PROPN
ejpam-5353	641	17	simcic	simcic	PROPN
ejpam-5353	641	18	.	.	PUNCT
ejpam-5353	642	1	ternary	ternary	ADJ
ejpam-5353	642	2	codes	code	NOUN
ejpam-5353	642	3	from	from	ADP
ejpam-5353	642	4	the	the	DET
ejpam-5353	642	5	strongly	strongly	ADV
ejpam-5353	642	6	regular	regular	ADJ
ejpam-5353	642	7	(	(	PUNCT
ejpam-5353	642	8	45	45	NUM
ejpam-5353	642	9	,	,	PUNCT
ejpam-5353	642	10	12	12	NUM
ejpam-5353	642	11	,	,	PUNCT
ejpam-5353	642	12	3	3	NUM
ejpam-5353	642	13	,	,	PUNCT
ejpam-5353	642	14	3	3	X
ejpam-5353	642	15	)	)	PUNCT
ejpam-5353	642	16	graphs	graph	NOUN
ejpam-5353	642	17	and	and	CCONJ
ejpam-5353	642	18	orbit	orbit	NOUN
ejpam-5353	642	19	matrices	matrix	NOUN
ejpam-5353	642	20	of	of	ADP
ejpam-5353	642	21	2-(45	2-(45	NUM
ejpam-5353	642	22	,	,	PUNCT
ejpam-5353	642	23	12	12	NUM
ejpam-5353	642	24	,	,	PUNCT
ejpam-5353	642	25	3	3	X
ejpam-5353	642	26	)	)	PUNCT
ejpam-5353	642	27	designs	design	NOUN
ejpam-5353	642	28	.	.	PUNCT
ejpam-5353	643	1	discrete	discrete	ADJ
ejpam-5353	643	2	math	math	NOUN
ejpam-5353	643	3	.	.	PUNCT
ejpam-5353	643	4	,	,	PUNCT
ejpam-5353	643	5	312:3000–3010	312:3000–3010	PROPN
ejpam-5353	643	6	,	,	PUNCT
ejpam-5353	643	7	2012	2012	NUM
ejpam-5353	643	8	.	.	PUNCT
ejpam-5353	644	1	[	[	X
ejpam-5353	644	2	20	20	NUM
ejpam-5353	644	3	]	]	PUNCT
ejpam-5353	644	4	r.	r.	PROPN
ejpam-5353	644	5	sampathkumar	sampathkumar	PROPN
ejpam-5353	644	6	and	and	CCONJ
ejpam-5353	644	7	s.	s.	PROPN
ejpam-5353	644	8	srinivasan	srinivasan	PROPN
ejpam-5353	644	9	.	.	PUNCT
ejpam-5353	645	1	cyclic	cyclic	PROPN
ejpam-5353	645	2	orthogonal	orthogonal	ADJ
ejpam-5353	645	3	doubl	doubl	NOUN
ejpam-5353	645	4	covers	cover	NOUN
ejpam-5353	645	5	of	of	ADP
ejpam-5353	645	6	4	4	NUM
ejpam-5353	645	7	-	-	PUNCT
ejpam-5353	645	8	regular	regular	ADJ
ejpam-5353	645	9	circulant	circulant	ADJ
ejpam-5353	645	10	graphs	graph	NOUN
ejpam-5353	645	11	.	.	PUNCT
ejpam-5353	646	1	discrete	discrete	ADJ
ejpam-5353	646	2	mathematics	mathematic	NOUN
ejpam-5353	646	3	,	,	PUNCT
ejpam-5353	646	4	311:2417–2422	311:2417–2422	NUM
ejpam-5353	646	5	,	,	PUNCT
ejpam-5353	646	6	2011	2011	NUM
ejpam-5353	646	7	.	.	PUNCT
ejpam-5353	647	1	[	[	X
ejpam-5353	647	2	21	21	NUM
ejpam-5353	647	3	]	]	X
ejpam-5353	647	4	r.	r.	PROPN
ejpam-5353	647	5	sampathkumar	sampathkumar	PROPN
ejpam-5353	647	6	and	and	CCONJ
ejpam-5353	647	7	v.	v.	ADP
ejpam-5353	647	8	sriram	sriram	PROPN
ejpam-5353	647	9	.	.	PUNCT
ejpam-5353	648	1	orthogonal	orthogonal	PROPN
ejpam-5353	648	2	σ−labeling	σ−labele	VERB
ejpam-5353	648	3	of	of	ADP
ejpam-5353	648	4	graphs	graph	NOUN
ejpam-5353	648	5	.	.	PUNCT
ejpam-5353	649	1	akce	akce	PROPN
ejpam-5353	649	2	international	international	PROPN
ejpam-5353	649	3	journal	journal	NOUN
ejpam-5353	649	4	of	of	ADP
ejpam-5353	649	5	graphs	graph	NOUN
ejpam-5353	649	6	and	and	CCONJ
ejpam-5353	649	7	combinatorics	combinatoric	NOUN
ejpam-5353	649	8	,	,	PUNCT
ejpam-5353	649	9	5(1):57–60	5(1):57–60	NUM
ejpam-5353	649	10	,	,	PUNCT
ejpam-5353	649	11	2008	2008	NUM
ejpam-5353	649	12	.	.	PUNCT
ejpam-5353	650	1	[	[	X
ejpam-5353	650	2	22	22	NUM
ejpam-5353	650	3	]	]	PUNCT
ejpam-5353	650	4	m.	m.	NOUN
ejpam-5353	650	5	higazy	higazy	NOUN
ejpam-5353	650	6	,	,	PUNCT
ejpam-5353	650	7	r.	r.	PROPN
ejpam-5353	650	8	scapellato	scapellato	PROPN
ejpam-5353	650	9	and	and	CCONJ
ejpam-5353	650	10	y.	y.	PROPN
ejpam-5353	650	11	s.	s.	PROPN
ejpam-5353	650	12	hamed	hamed	PROPN
ejpam-5353	650	13	.	.	PUNCT
ejpam-5353	651	1	a	a	DET
ejpam-5353	651	2	complete	complete	ADJ
ejpam-5353	651	3	classification	classification	NOUN
ejpam-5353	651	4	of	of	ADP
ejpam-5353	651	5	5	5	NUM
ejpam-5353	651	6	-	-	PUNCT
ejpam-5353	651	7	regular	regular	ADJ
ejpam-5353	651	8	circulant	circulant	ADJ
ejpam-5353	651	9	graphs	graph	NOUN
ejpam-5353	651	10	that	that	PRON
ejpam-5353	651	11	allow	allow	VERB
ejpam-5353	651	12	cyclic	cyclic	ADJ
ejpam-5353	651	13	orthogonal	orthogonal	ADJ
ejpam-5353	651	14	double	double	ADJ
ejpam-5353	651	15	covers	cover	NOUN
ejpam-5353	651	16	.	.	PUNCT
ejpam-5353	652	1	journal	journal	NOUN
ejpam-5353	652	2	of	of	ADP
ejpam-5353	652	3	algebraic	algebraic	PROPN
ejpam-5353	652	4	combinatorics	combinatoric	NOUN
ejpam-5353	652	5	,	,	PUNCT
ejpam-5353	652	6	53:593–611	53:593–611	PROPN
ejpam-5353	652	7	,	,	PUNCT
ejpam-5353	652	8	2021	2021	NUM
ejpam-5353	652	9	.	.	PUNCT
ejpam-5353	653	1	[	[	X
ejpam-5353	653	2	23	23	X
ejpam-5353	653	3	]	]	X
ejpam-5353	653	4	v.	v.	PROPN
ejpam-5353	653	5	d.	d.	PROPN
ejpam-5353	653	6	tonchev	tonchev	PROPN
ejpam-5353	653	7	.	.	PUNCT
ejpam-5353	654	1	binary	binary	PROPN
ejpam-5353	654	2	codes	code	NOUN
ejpam-5353	654	3	derived	derive	VERB
ejpam-5353	654	4	from	from	ADP
ejpam-5353	654	5	the	the	DET
ejpam-5353	654	6	hoffman	hoffman	NOUN
ejpam-5353	654	7	-	-	PUNCT
ejpam-5353	654	8	singleton	singleton	PROPN
ejpam-5353	654	9	and	and	CCONJ
ejpam-5353	654	10	higman	higman	ADJ
ejpam-5353	654	11	-	-	PUNCT
ejpam-5353	654	12	sims	sim	NOUN
ejpam-5353	654	13	graphs	graph	NOUN
ejpam-5353	654	14	.	.	PUNCT
ejpam-5353	655	1	ieee	ieee	PROPN
ejpam-5353	655	2	trans	trans	PROPN
ejpam-5353	655	3	.	.	PUNCT
ejpam-5353	656	1	inform	inform	VERB
ejpam-5353	656	2	.	.	PUNCT
ejpam-5353	657	1	theory	theory	NOUN
ejpam-5353	657	2	.	.	PUNCT
ejpam-5353	657	3	,	,	PUNCT
ejpam-5353	657	4	43:1021–1025	43:1021–1025	NUM
ejpam-5353	657	5	,	,	PUNCT
ejpam-5353	657	6	1997	1997	NUM
ejpam-5353	657	7	.	.	PUNCT