id	sid	tid	token	lemma	pos
ejpam-6729	1	1	european	european	PROPN
ejpam-6729	1	2	journal	journal	PROPN
ejpam-6729	1	3	of	of	ADP
ejpam-6729	1	4	pure	pure	ADJ
ejpam-6729	1	5	and	and	CCONJ
ejpam-6729	1	6	applied	applied	ADJ
ejpam-6729	1	7	mathematics	mathematic	NOUN
ejpam-6729	1	8	2025	2025	NUM
ejpam-6729	1	9	,	,	PUNCT
ejpam-6729	1	10	vol	vol	NOUN
ejpam-6729	1	11	.	.	PROPN
ejpam-6729	1	12	18	18	NUM
ejpam-6729	1	13	,	,	PUNCT
ejpam-6729	1	14	issue	issue	NOUN
ejpam-6729	1	15	4	4	NUM
ejpam-6729	1	16	,	,	PUNCT
ejpam-6729	1	17	article	article	NOUN
ejpam-6729	1	18	number	number	NOUN
ejpam-6729	1	19	6729	6729	NUM
ejpam-6729	1	20	issn	issn	PROPN
ejpam-6729	1	21	1307	1307	NUM
ejpam-6729	1	22	-	-	SYM
ejpam-6729	1	23	5543	5543	NUM
ejpam-6729	1	24	–	–	PUNCT
ejpam-6729	1	25	ejpam.com	ejpam.com	X
ejpam-6729	1	26	published	publish	VERB
ejpam-6729	1	27	by	by	ADP
ejpam-6729	1	28	new	new	PROPN
ejpam-6729	1	29	york	york	PROPN
ejpam-6729	1	30	business	business	PROPN
ejpam-6729	1	31	global	global	ADJ
ejpam-6729	1	32	property	property	NOUN
ejpam-6729	1	33	hypergraphs	hypergraph	NOUN
ejpam-6729	1	34	and	and	CCONJ
ejpam-6729	1	35	property	property	NOUN
ejpam-6729	1	36	superhypergraphs	superhypergraph	NOUN
ejpam-6729	1	37	for	for	ADP
ejpam-6729	1	38	data	datum	NOUN
ejpam-6729	1	39	analysis	analysis	NOUN
ejpam-6729	1	40	takaaki	takaaki	NOUN
ejpam-6729	1	41	fujita1,∗	fujita1,∗	PROPN
ejpam-6729	1	42	,	,	PUNCT
ejpam-6729	1	43	florentin	florentin	NOUN
ejpam-6729	1	44	smarandache2	smarandache2	PROPN
ejpam-6729	1	45	1	1	NUM
ejpam-6729	1	46	independent	independent	ADJ
ejpam-6729	1	47	researcher	researcher	NOUN
ejpam-6729	1	48	,	,	PUNCT
ejpam-6729	1	49	shinjuku	shinjuku	PROPN
ejpam-6729	1	50	,	,	PUNCT
ejpam-6729	1	51	shinjuku	shinjuku	PROPN
ejpam-6729	1	52	-	-	PUNCT
ejpam-6729	1	53	ku	ku	PROPN
ejpam-6729	1	54	,	,	PUNCT
ejpam-6729	1	55	tokyo	tokyo	PROPN
ejpam-6729	1	56	,	,	PUNCT
ejpam-6729	1	57	japan	japan	PROPN
ejpam-6729	1	58	2	2	NUM
ejpam-6729	1	59	university	university	NOUN
ejpam-6729	1	60	of	of	ADP
ejpam-6729	1	61	new	new	PROPN
ejpam-6729	1	62	mexico	mexico	PROPN
ejpam-6729	1	63	,	,	PUNCT
ejpam-6729	1	64	gallup	gallup	PROPN
ejpam-6729	1	65	campus	campus	PROPN
ejpam-6729	1	66	,	,	PUNCT
ejpam-6729	1	67	nm	nm	PROPN
ejpam-6729	1	68	87301	87301	NUM
ejpam-6729	1	69	,	,	PUNCT
ejpam-6729	1	70	usa	usa	PROPN
ejpam-6729	1	71	abstract	abstract	NOUN
ejpam-6729	1	72	.	.	PUNCT
ejpam-6729	2	1	graph	graph	NOUN
ejpam-6729	2	2	theory	theory	NOUN
ejpam-6729	2	3	provides	provide	VERB
ejpam-6729	2	4	a	a	DET
ejpam-6729	2	5	rigorous	rigorous	ADJ
ejpam-6729	2	6	mathematical	mathematical	ADJ
ejpam-6729	2	7	foundation	foundation	NOUN
ejpam-6729	2	8	for	for	ADP
ejpam-6729	2	9	modeling	model	VERB
ejpam-6729	2	10	relationships	relationship	NOUN
ejpam-6729	2	11	by	by	ADP
ejpam-6729	2	12	representing	represent	VERB
ejpam-6729	2	13	entities	entity	NOUN
ejpam-6729	2	14	as	as	ADP
ejpam-6729	2	15	vertices	vertex	NOUN
ejpam-6729	2	16	and	and	CCONJ
ejpam-6729	2	17	their	their	PRON
ejpam-6729	2	18	interactions	interaction	NOUN
ejpam-6729	2	19	as	as	ADP
ejpam-6729	2	20	edges	edge	NOUN
ejpam-6729	2	21	[	[	X
ejpam-6729	2	22	1	1	NUM
ejpam-6729	2	23	,	,	PUNCT
ejpam-6729	2	24	2	2	NUM
ejpam-6729	2	25	]	]	PUNCT
ejpam-6729	2	26	.	.	PUNCT
ejpam-6729	3	1	hypergraphs	hypergraphs	PROPN
ejpam-6729	3	2	generalize	generalize	VERB
ejpam-6729	3	3	this	this	DET
ejpam-6729	3	4	paradigm	paradigm	NOUN
ejpam-6729	3	5	by	by	ADP
ejpam-6729	3	6	allowing	allow	VERB
ejpam-6729	3	7	hyperedges	hyperedge	NOUN
ejpam-6729	3	8	to	to	PART
ejpam-6729	3	9	connect	connect	VERB
ejpam-6729	3	10	arbitrary	arbitrary	ADJ
ejpam-6729	3	11	subsets	subset	NOUN
ejpam-6729	3	12	of	of	ADP
ejpam-6729	3	13	vertices	vertex	NOUN
ejpam-6729	3	14	[	[	X
ejpam-6729	3	15	3	3	NUM
ejpam-6729	3	16	]	]	PUNCT
ejpam-6729	3	17	,	,	PUNCT
ejpam-6729	3	18	and	and	CCONJ
ejpam-6729	3	19	superhypergraphs	superhypergraph	NOUN
ejpam-6729	3	20	extend	extend	VERB
ejpam-6729	3	21	it	it	PRON
ejpam-6729	3	22	further	far	ADV
ejpam-6729	3	23	via	via	ADP
ejpam-6729	3	24	iterated	iterated	ADJ
ejpam-6729	3	25	powerset	powerset	NOUN
ejpam-6729	3	26	constructions	construction	NOUN
ejpam-6729	3	27	that	that	PRON
ejpam-6729	3	28	capture	capture	VERB
ejpam-6729	3	29	hierarchical	hierarchical	ADJ
ejpam-6729	3	30	,	,	PUNCT
ejpam-6729	3	31	multi	multi	ADJ
ejpam-6729	3	32	-	-	ADJ
ejpam-6729	3	33	layer	layer	ADJ
ejpam-6729	3	34	linkages	linkage	NOUN
ejpam-6729	3	35	among	among	ADP
ejpam-6729	3	36	edges	edge	NOUN
ejpam-6729	3	37	[	[	X
ejpam-6729	3	38	4	4	NUM
ejpam-6729	3	39	,	,	PUNCT
ejpam-6729	3	40	5	5	NUM
ejpam-6729	3	41	]	]	PUNCT
ejpam-6729	3	42	.	.	PUNCT
ejpam-6729	4	1	these	these	DET
ejpam-6729	4	2	enriched	enrich	VERB
ejpam-6729	4	3	models	model	NOUN
ejpam-6729	4	4	support	support	VERB
ejpam-6729	4	5	applications	application	NOUN
ejpam-6729	4	6	across	across	ADP
ejpam-6729	4	7	biology	biology	NOUN
ejpam-6729	4	8	,	,	PUNCT
ejpam-6729	4	9	social	social	ADJ
ejpam-6729	4	10	networks	network	NOUN
ejpam-6729	4	11	,	,	PUNCT
ejpam-6729	4	12	signal	signal	ADJ
ejpam-6729	4	13	processing	processing	NOUN
ejpam-6729	4	14	,	,	PUNCT
ejpam-6729	4	15	and	and	CCONJ
ejpam-6729	4	16	knowledge	knowledge	NOUN
ejpam-6729	4	17	representation	representation	NOUN
ejpam-6729	4	18	.	.	PUNCT
ejpam-6729	5	1	property	property	NOUN
ejpam-6729	5	2	graphs	graph	NOUN
ejpam-6729	5	3	are	be	AUX
ejpam-6729	5	4	directed	direct	VERB
ejpam-6729	5	5	multigraphs	multigraph	NOUN
ejpam-6729	5	6	in	in	ADP
ejpam-6729	5	7	which	which	DET
ejpam-6729	5	8	vertices	vertice	VERB
ejpam-6729	5	9	and	and	CCONJ
ejpam-6729	5	10	edges	edge	NOUN
ejpam-6729	5	11	carry	carry	VERB
ejpam-6729	5	12	key	key	ADJ
ejpam-6729	5	13	–	–	PUNCT
ejpam-6729	5	14	value	value	NOUN
ejpam-6729	5	15	properties	property	NOUN
ejpam-6729	5	16	and	and	CCONJ
ejpam-6729	5	17	edges	edge	NOUN
ejpam-6729	5	18	additionally	additionally	ADV
ejpam-6729	5	19	bear	bear	VERB
ejpam-6729	5	20	labels	label	NOUN
ejpam-6729	5	21	,	,	PUNCT
ejpam-6729	5	22	enabling	enable	VERB
ejpam-6729	5	23	schema	schema	NOUN
ejpam-6729	5	24	-	-	PUNCT
ejpam-6729	5	25	flexible	flexible	ADJ
ejpam-6729	5	26	modeling	modeling	NOUN
ejpam-6729	5	27	of	of	ADP
ejpam-6729	5	28	heterogeneous	heterogeneous	ADJ
ejpam-6729	5	29	,	,	PUNCT
ejpam-6729	5	30	real	real	ADJ
ejpam-6729	5	31	-	-	PUNCT
ejpam-6729	5	32	world	world	NOUN
ejpam-6729	5	33	data(cf.[6–8	data(cf.[6–8	PROPN
ejpam-6729	5	34	]	]	PUNCT
ejpam-6729	5	35	)	)	PUNCT
ejpam-6729	5	36	.	.	PUNCT
ejpam-6729	6	1	in	in	ADP
ejpam-6729	6	2	this	this	DET
ejpam-6729	6	3	paper	paper	NOUN
ejpam-6729	6	4	,	,	PUNCT
ejpam-6729	6	5	we	we	PRON
ejpam-6729	6	6	show	show	VERB
ejpam-6729	6	7	how	how	SCONJ
ejpam-6729	6	8	to	to	PART
ejpam-6729	6	9	elevate	elevate	VERB
ejpam-6729	6	10	property	property	NOUN
ejpam-6729	6	11	graphs	graph	NOUN
ejpam-6729	6	12	to	to	ADP
ejpam-6729	6	13	the	the	DET
ejpam-6729	6	14	settings	setting	NOUN
ejpam-6729	6	15	of	of	ADP
ejpam-6729	6	16	hypergraphs	hypergraph	NOUN
ejpam-6729	6	17	and	and	CCONJ
ejpam-6729	6	18	superhypergraphs	superhypergraph	NOUN
ejpam-6729	6	19	by	by	ADP
ejpam-6729	6	20	introducing	introduce	VERB
ejpam-6729	6	21	formal	formal	ADJ
ejpam-6729	6	22	definitions	definition	NOUN
ejpam-6729	6	23	for	for	ADP
ejpam-6729	6	24	property	property	NOUN
ejpam-6729	6	25	hypergraphs	hypergraph	NOUN
ejpam-6729	6	26	and	and	CCONJ
ejpam-6729	6	27	property	property	NOUN
ejpam-6729	6	28	superhypergraphs	superhypergraph	NOUN
ejpam-6729	6	29	and	and	CCONJ
ejpam-6729	6	30	presenting	present	VERB
ejpam-6729	6	31	preliminary	preliminary	ADJ
ejpam-6729	6	32	theoretical	theoretical	ADJ
ejpam-6729	6	33	results	result	NOUN
ejpam-6729	6	34	that	that	PRON
ejpam-6729	6	35	demonstrate	demonstrate	VERB
ejpam-6729	6	36	their	their	PRON
ejpam-6729	6	37	expressive	expressive	ADJ
ejpam-6729	6	38	power	power	NOUN
ejpam-6729	6	39	.	.	PUNCT
ejpam-6729	7	1	2020	2020	NUM
ejpam-6729	7	2	mathematics	mathematic	NOUN
ejpam-6729	7	3	subject	subject	NOUN
ejpam-6729	7	4	classifications	classification	NOUN
ejpam-6729	7	5	:	:	PUNCT
ejpam-6729	7	6	05c65	05c65	NUM
ejpam-6729	7	7	key	key	ADJ
ejpam-6729	7	8	words	word	NOUN
ejpam-6729	7	9	and	and	CCONJ
ejpam-6729	7	10	phrases	phrase	NOUN
ejpam-6729	7	11	:	:	PUNCT
ejpam-6729	7	12	property	property	NOUN
ejpam-6729	7	13	graphs	graph	NOUN
ejpam-6729	7	14	,	,	PUNCT
ejpam-6729	7	15	superhypergraphs	superhypergraph	NOUN
ejpam-6729	7	16	,	,	PUNCT
ejpam-6729	7	17	hypergraphs	hypergraph	NOUN
ejpam-6729	7	18	,	,	PUNCT
ejpam-6729	7	19	property	property	NOUN
ejpam-6729	7	20	superhypergraphs	superhypergraph	NOUN
ejpam-6729	7	21	,	,	PUNCT
ejpam-6729	7	22	property	property	NOUN
ejpam-6729	7	23	hypergraphs	hypergraph	NOUN
ejpam-6729	7	24	1	1	NUM
ejpam-6729	7	25	.	.	PUNCT
ejpam-6729	8	1	introduction	introduction	NOUN
ejpam-6729	8	2	classical	classical	ADJ
ejpam-6729	8	3	graphs	graph	NOUN
ejpam-6729	8	4	model	model	VERB
ejpam-6729	8	5	binary	binary	NOUN
ejpam-6729	8	6	relations	relation	NOUN
ejpam-6729	8	7	by	by	ADP
ejpam-6729	8	8	representing	represent	VERB
ejpam-6729	8	9	entities	entity	NOUN
ejpam-6729	8	10	as	as	ADP
ejpam-6729	8	11	vertices	vertex	NOUN
ejpam-6729	8	12	and	and	CCONJ
ejpam-6729	8	13	their	their	PRON
ejpam-6729	8	14	pairwise	pairwise	NOUN
ejpam-6729	8	15	connections	connection	NOUN
ejpam-6729	8	16	as	as	ADP
ejpam-6729	8	17	edges	edge	NOUN
ejpam-6729	8	18	[	[	X
ejpam-6729	8	19	1	1	NUM
ejpam-6729	8	20	,	,	PUNCT
ejpam-6729	8	21	9	9	NUM
ejpam-6729	8	22	]	]	PUNCT
ejpam-6729	8	23	.	.	PUNCT
ejpam-6729	9	1	hypergraphs	hypergraph	NOUN
ejpam-6729	9	2	extend	extend	VERB
ejpam-6729	9	3	this	this	DET
ejpam-6729	9	4	notion	notion	NOUN
ejpam-6729	9	5	by	by	ADP
ejpam-6729	9	6	allowing	allow	VERB
ejpam-6729	9	7	each	each	DET
ejpam-6729	9	8	hyperedge	hyperedge	NOUN
ejpam-6729	9	9	to	to	PART
ejpam-6729	9	10	join	join	VERB
ejpam-6729	9	11	any	any	DET
ejpam-6729	9	12	nonempty	nonempty	ADJ
ejpam-6729	9	13	collection	collection	NOUN
ejpam-6729	9	14	of	of	ADP
ejpam-6729	9	15	vertices	vertex	NOUN
ejpam-6729	9	16	,	,	PUNCT
ejpam-6729	9	17	thereby	thereby	ADV
ejpam-6729	9	18	capturing	capture	VERB
ejpam-6729	9	19	higher‑order	higher‑order	NOUN
ejpam-6729	9	20	interactions	interaction	NOUN
ejpam-6729	9	21	[	[	X
ejpam-6729	9	22	10–12	10–12	NUM
ejpam-6729	9	23	]	]	PUNCT
ejpam-6729	9	24	.	.	PUNCT
ejpam-6729	10	1	however	however	ADV
ejpam-6729	10	2	,	,	PUNCT
ejpam-6729	10	3	even	even	ADV
ejpam-6729	10	4	hypergraphs	hypergraph	NOUN
ejpam-6729	10	5	can	can	AUX
ejpam-6729	10	6	not	not	PART
ejpam-6729	10	7	naturally	naturally	ADV
ejpam-6729	10	8	express	express	VERB
ejpam-6729	10	9	nested	nested	ADJ
ejpam-6729	10	10	or	or	CCONJ
ejpam-6729	10	11	hierarchical	hierarchical	ADJ
ejpam-6729	10	12	groupings	grouping	NOUN
ejpam-6729	10	13	.	.	PUNCT
ejpam-6729	11	1	to	to	PART
ejpam-6729	11	2	remedy	remedy	VERB
ejpam-6729	11	3	this	this	PRON
ejpam-6729	11	4	,	,	PUNCT
ejpam-6729	11	5	superhypergraphs	superhypergraph	NOUN
ejpam-6729	11	6	were	be	AUX
ejpam-6729	11	7	introduced	introduce	VERB
ejpam-6729	11	8	:	:	PUNCT
ejpam-6729	11	9	by	by	ADP
ejpam-6729	11	10	iteratively	iteratively	ADV
ejpam-6729	11	11	applying	apply	VERB
ejpam-6729	11	12	the	the	DET
ejpam-6729	11	13	powerset	powerset	NOUN
ejpam-6729	11	14	operation	operation	NOUN
ejpam-6729	11	15	to	to	ADP
ejpam-6729	11	16	the	the	DET
ejpam-6729	11	17	vertex	vertex	NOUN
ejpam-6729	11	18	set	set	NOUN
ejpam-6729	11	19	,	,	PUNCT
ejpam-6729	11	20	one	one	PRON
ejpam-6729	11	21	obtains	obtain	VERB
ejpam-6729	11	22	multi‑layered	multi‑layered	ADJ
ejpam-6729	11	23	networks	network	NOUN
ejpam-6729	11	24	that	that	PRON
ejpam-6729	11	25	encode	encode	VERB
ejpam-6729	11	26	nested	nested	ADJ
ejpam-6729	11	27	relationships	relationship	NOUN
ejpam-6729	11	28	among	among	ADP
ejpam-6729	11	29	vertex	vertex	NOUN
ejpam-6729	11	30	clusters	cluster	NOUN
ejpam-6729	11	31	[	[	X
ejpam-6729	11	32	13–15	13–15	NUM
ejpam-6729	11	33	]	]	PUNCT
ejpam-6729	11	34	.	.	PUNCT
ejpam-6729	12	1	this	this	DET
ejpam-6729	12	2	construction	construction	NOUN
ejpam-6729	12	3	is	be	AUX
ejpam-6729	12	4	versatile	versatile	ADV
ejpam-6729	12	5	enough	enough	ADV
ejpam-6729	12	6	to	to	PART
ejpam-6729	12	7	subsume	subsume	VERB
ejpam-6729	12	8	a	a	DET
ejpam-6729	12	9	wide	wide	ADJ
ejpam-6729	12	10	range	range	NOUN
ejpam-6729	12	11	of	of	ADP
ejpam-6729	12	12	graph	graph	NOUN
ejpam-6729	12	13	models	model	NOUN
ejpam-6729	12	14	—	—	PUNCT
ejpam-6729	12	15	including	include	VERB
ejpam-6729	12	16	hypergraphs	hypergraph	NOUN
ejpam-6729	12	17	and	and	CCONJ
ejpam-6729	12	18	multihypergraphs	multihypergraph	NOUN
ejpam-6729	12	19	—	—	PUNCT
ejpam-6729	12	20	under	under	ADP
ejpam-6729	12	21	a	a	DET
ejpam-6729	12	22	single	single	ADJ
ejpam-6729	12	23	unifying	unifying	ADJ
ejpam-6729	12	24	framework	framework	NOUN
ejpam-6729	12	25	.	.	PUNCT
ejpam-6729	13	1	∗corresponding	∗corresponde	VERB
ejpam-6729	13	2	author	author	NOUN
ejpam-6729	13	3	.	.	PUNCT
ejpam-6729	14	1	doi	doi	NOUN
ejpam-6729	14	2	:	:	PUNCT
ejpam-6729	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6729	https://doi.org/10.29020/nybg.ejpam.v18i4.6729	ADJ
ejpam-6729	14	4	email	email	NOUN
ejpam-6729	14	5	addresses	address	VERB
ejpam-6729	14	6	:	:	PUNCT
ejpam-6729	14	7	takaaki.fujita060@gmail.com	takaaki.fujita060@gmail.com	X
ejpam-6729	14	8	(	(	PUNCT
ejpam-6729	14	9	t.	t.	PROPN
ejpam-6729	14	10	fujita	fujita	PROPN
ejpam-6729	14	11	)	)	PUNCT
ejpam-6729	14	12	,	,	PUNCT
ejpam-6729	14	13	smarand@unm.edu	smarand@unm.edu	PROPN
ejpam-6729	14	14	(	(	PUNCT
ejpam-6729	14	15	f.	f.	PROPN
ejpam-6729	14	16	smarandache	smarandache	PROPN
ejpam-6729	14	17	)	)	PUNCT
ejpam-6729	14	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6729	15	1	1	1	NUM
ejpam-6729	15	2	copyright	copyright	NOUN
ejpam-6729	15	3	:	:	PUNCT
ejpam-6729	15	4	©	©	PROPN
ejpam-6729	15	5	2025	2025	NUM
ejpam-6729	15	6	the	the	DET
ejpam-6729	15	7	author(s	author(s	NOUN
ejpam-6729	15	8	)	)	PUNCT
ejpam-6729	15	9	.	.	PUNCT
ejpam-6729	16	1	(	(	PUNCT
ejpam-6729	16	2	cc	cc	NOUN
ejpam-6729	16	3	by	by	ADP
ejpam-6729	16	4	-	-	PUNCT
ejpam-6729	16	5	nc	nc	PROPN
ejpam-6729	16	6	4.0	4.0	NUM
ejpam-6729	16	7	)	)	PUNCT
ejpam-6729	16	8	t.	t.	PROPN
ejpam-6729	16	9	fujita	fujita	PROPN
ejpam-6729	16	10	,	,	PUNCT
ejpam-6729	16	11	f.	f.	PROPN
ejpam-6729	16	12	smarandache	smarandache	PROPN
ejpam-6729	16	13	/	/	SYM
ejpam-6729	16	14	eur	eur	PROPN
ejpam-6729	16	15	.	.	PUNCT
ejpam-6729	17	1	j.	j.	PROPN
ejpam-6729	17	2	pure	pure	PROPN
ejpam-6729	17	3	appl	appl	PROPN
ejpam-6729	17	4	.	.	PROPN
ejpam-6729	17	5	math	math	PROPN
ejpam-6729	17	6	,	,	PUNCT
ejpam-6729	17	7	18	18	NUM
ejpam-6729	17	8	(	(	PUNCT
ejpam-6729	17	9	4	4	NUM
ejpam-6729	17	10	)	)	PUNCT
ejpam-6729	17	11	(	(	PUNCT
ejpam-6729	17	12	2025	2025	NUM
ejpam-6729	17	13	)	)	PUNCT
ejpam-6729	17	14	,	,	PUNCT
ejpam-6729	17	15	6729	6729	NUM
ejpam-6729	17	16	2	2	NUM
ejpam-6729	17	17	of	of	ADP
ejpam-6729	17	18	36	36	NUM
ejpam-6729	17	19	directed	direct	VERB
ejpam-6729	17	20	variants	variant	NOUN
ejpam-6729	17	21	of	of	ADP
ejpam-6729	17	22	these	these	DET
ejpam-6729	17	23	structures	structure	NOUN
ejpam-6729	17	24	—	—	PUNCT
ejpam-6729	17	25	such	such	ADJ
ejpam-6729	17	26	as	as	ADP
ejpam-6729	17	27	directed	direct	VERB
ejpam-6729	17	28	graphs	graph	NOUN
ejpam-6729	17	29	[	[	X
ejpam-6729	17	30	16	16	NUM
ejpam-6729	17	31	]	]	PUNCT
ejpam-6729	17	32	,	,	PUNCT
ejpam-6729	17	33	directed	direct	VERB
ejpam-6729	17	34	hypergraphs	hypergraph	NOUN
ejpam-6729	18	1	[	[	X
ejpam-6729	18	2	17–19	17–19	NUM
ejpam-6729	18	3	]	]	PUNCT
ejpam-6729	18	4	,	,	PUNCT
ejpam-6729	18	5	and	and	CCONJ
ejpam-6729	18	6	directed	direct	VERB
ejpam-6729	18	7	superhypergraphs[20]—are	superhypergraphs[20]—are	VERB
ejpam-6729	18	8	also	also	ADV
ejpam-6729	18	9	well	well	ADV
ejpam-6729	18	10	-	-	PUNCT
ejpam-6729	18	11	known	know	VERB
ejpam-6729	18	12	and	and	CCONJ
ejpam-6729	18	13	have	have	AUX
ejpam-6729	18	14	been	be	AUX
ejpam-6729	18	15	extensively	extensively	ADV
ejpam-6729	18	16	studied	study	VERB
ejpam-6729	18	17	in	in	ADP
ejpam-6729	18	18	numerous	numerous	ADJ
ejpam-6729	18	19	research	research	NOUN
ejpam-6729	18	20	papers	paper	NOUN
ejpam-6729	18	21	.	.	PUNCT
ejpam-6729	19	1	data	datum	NOUN
ejpam-6729	19	2	modeling	modeling	NOUN
ejpam-6729	19	3	is	be	AUX
ejpam-6729	19	4	the	the	DET
ejpam-6729	19	5	process	process	NOUN
ejpam-6729	19	6	of	of	ADP
ejpam-6729	19	7	defining	define	VERB
ejpam-6729	19	8	and	and	CCONJ
ejpam-6729	19	9	organizing	organize	VERB
ejpam-6729	19	10	data	datum	NOUN
ejpam-6729	19	11	structures	structure	NOUN
ejpam-6729	19	12	,	,	PUNCT
ejpam-6729	19	13	relationships	relationship	NOUN
ejpam-6729	19	14	,	,	PUNCT
ejpam-6729	19	15	and	and	CCONJ
ejpam-6729	19	16	constraints	constraint	NOUN
ejpam-6729	19	17	to	to	PART
ejpam-6729	19	18	support	support	VERB
ejpam-6729	19	19	storage	storage	NOUN
ejpam-6729	19	20	,	,	PUNCT
ejpam-6729	19	21	retrieval	retrieval	NOUN
ejpam-6729	19	22	,	,	PUNCT
ejpam-6729	19	23	and	and	CCONJ
ejpam-6729	19	24	analysis	analysis	NOUN
ejpam-6729	19	25	[	[	X
ejpam-6729	19	26	21–23	21–23	X
ejpam-6729	19	27	]	]	X
ejpam-6729	19	28	.	.	PUNCT
ejpam-6729	20	1	a	a	DET
ejpam-6729	20	2	property	property	NOUN
ejpam-6729	20	3	graph	graph	NOUN
ejpam-6729	20	4	is	be	AUX
ejpam-6729	20	5	a	a	DET
ejpam-6729	20	6	directed	direct	VERB
ejpam-6729	20	7	multigraph	multigraph	NOUN
ejpam-6729	20	8	in	in	ADP
ejpam-6729	20	9	which	which	PRON
ejpam-6729	20	10	both	both	DET
ejpam-6729	20	11	vertices	vertice	VERB
ejpam-6729	20	12	and	and	CCONJ
ejpam-6729	20	13	edges	edge	NOUN
ejpam-6729	20	14	carry	carry	VERB
ejpam-6729	20	15	arbitrary	arbitrary	ADJ
ejpam-6729	20	16	key	key	ADJ
ejpam-6729	20	17	–	–	PUNCT
ejpam-6729	20	18	value	value	NOUN
ejpam-6729	20	19	attributes	attribute	NOUN
ejpam-6729	20	20	,	,	PUNCT
ejpam-6729	20	21	and	and	CCONJ
ejpam-6729	20	22	each	each	DET
ejpam-6729	20	23	edge	edge	NOUN
ejpam-6729	20	24	is	be	AUX
ejpam-6729	20	25	labeled	label	VERB
ejpam-6729	20	26	.	.	PUNCT
ejpam-6729	21	1	this	this	DET
ejpam-6729	21	2	schema‑flexible	schema‑flexible	ADJ
ejpam-6729	21	3	model	model	NOUN
ejpam-6729	21	4	enables	enable	VERB
ejpam-6729	21	5	the	the	DET
ejpam-6729	21	6	representation	representation	NOUN
ejpam-6729	21	7	of	of	ADP
ejpam-6729	21	8	rich	rich	ADJ
ejpam-6729	21	9	relational	relational	ADJ
ejpam-6729	21	10	data	datum	NOUN
ejpam-6729	21	11	[	[	X
ejpam-6729	21	12	6–8	6–8	NOUN
ejpam-6729	21	13	]	]	X
ejpam-6729	21	14	.	.	PUNCT
ejpam-6729	22	1	although	although	SCONJ
ejpam-6729	22	2	research	research	NOUN
ejpam-6729	22	3	on	on	ADP
ejpam-6729	22	4	hypergraphs	hypergraph	NOUN
ejpam-6729	22	5	,	,	PUNCT
ejpam-6729	22	6	superhypergraphs	superhypergraph	NOUN
ejpam-6729	22	7	,	,	PUNCT
ejpam-6729	22	8	and	and	CCONJ
ejpam-6729	22	9	property	property	NOUN
ejpam-6729	22	10	graphs	graph	NOUN
ejpam-6729	22	11	is	be	AUX
ejpam-6729	22	12	well	well	ADV
ejpam-6729	22	13	established	establish	VERB
ejpam-6729	22	14	,	,	PUNCT
ejpam-6729	22	15	the	the	DET
ejpam-6729	22	16	specific	specific	ADJ
ejpam-6729	22	17	combinations	combination	NOUN
ejpam-6729	22	18	—	—	PUNCT
ejpam-6729	22	19	property	property	NOUN
ejpam-6729	22	20	hypergraphs	hypergraph	NOUN
ejpam-6729	22	21	and	and	CCONJ
ejpam-6729	22	22	property	property	NOUN
ejpam-6729	22	23	superhypergraphs	superhypergraph	NOUN
ejpam-6729	22	24	—	—	PUNCT
ejpam-6729	22	25	have	have	AUX
ejpam-6729	22	26	received	receive	VERB
ejpam-6729	22	27	little	little	ADJ
ejpam-6729	22	28	attention	attention	NOUN
ejpam-6729	22	29	.	.	PUNCT
ejpam-6729	23	1	in	in	ADP
ejpam-6729	23	2	this	this	DET
ejpam-6729	23	3	paper	paper	NOUN
ejpam-6729	23	4	,	,	PUNCT
ejpam-6729	23	5	we	we	PRON
ejpam-6729	23	6	fill	fill	VERB
ejpam-6729	23	7	this	this	DET
ejpam-6729	23	8	gap	gap	NOUN
ejpam-6729	23	9	by	by	ADP
ejpam-6729	23	10	providing	provide	VERB
ejpam-6729	23	11	formal	formal	ADJ
ejpam-6729	23	12	definitions	definition	NOUN
ejpam-6729	23	13	for	for	ADP
ejpam-6729	23	14	property	property	NOUN
ejpam-6729	23	15	hypergraphs	hypergraph	NOUN
ejpam-6729	23	16	and	and	CCONJ
ejpam-6729	23	17	property	property	NOUN
ejpam-6729	23	18	superhypergraphs	superhypergraph	NOUN
ejpam-6729	23	19	and	and	CCONJ
ejpam-6729	23	20	by	by	ADP
ejpam-6729	23	21	presenting	present	VERB
ejpam-6729	23	22	preliminary	preliminary	ADJ
ejpam-6729	23	23	theoretical	theoretical	ADJ
ejpam-6729	23	24	results	result	NOUN
ejpam-6729	23	25	that	that	PRON
ejpam-6729	23	26	demonstrate	demonstrate	VERB
ejpam-6729	23	27	their	their	PRON
ejpam-6729	23	28	expressive	expressive	ADJ
ejpam-6729	23	29	power	power	NOUN
ejpam-6729	23	30	.	.	PUNCT
ejpam-6729	24	1	the	the	DET
ejpam-6729	24	2	author	author	NOUN
ejpam-6729	24	3	believes	believe	VERB
ejpam-6729	24	4	that	that	SCONJ
ejpam-6729	24	5	one	one	NUM
ejpam-6729	24	6	of	of	ADP
ejpam-6729	24	7	the	the	DET
ejpam-6729	24	8	advantages	advantage	NOUN
ejpam-6729	24	9	of	of	ADP
ejpam-6729	24	10	these	these	DET
ejpam-6729	24	11	frameworks	framework	NOUN
ejpam-6729	24	12	is	be	AUX
ejpam-6729	24	13	that	that	SCONJ
ejpam-6729	24	14	property	property	NOUN
ejpam-6729	24	15	graphs	graph	NOUN
ejpam-6729	24	16	can	can	AUX
ejpam-6729	24	17	also	also	ADV
ejpam-6729	24	18	be	be	AUX
ejpam-6729	24	19	applied	apply	VERB
ejpam-6729	24	20	to	to	ADP
ejpam-6729	24	21	more	more	ADV
ejpam-6729	24	22	hierarchical	hierarchical	ADJ
ejpam-6729	24	23	concepts	concept	NOUN
ejpam-6729	24	24	.	.	PUNCT
ejpam-6729	25	1	this	this	DET
ejpam-6729	25	2	subsection	subsection	NOUN
ejpam-6729	25	3	explains	explain	VERB
ejpam-6729	25	4	the	the	DET
ejpam-6729	25	5	structure	structure	NOUN
ejpam-6729	25	6	of	of	ADP
ejpam-6729	25	7	the	the	DET
ejpam-6729	25	8	paper	paper	NOUN
ejpam-6729	25	9	.	.	PUNCT
ejpam-6729	26	1	section	section	NOUN
ejpam-6729	26	2	2	2	NUM
ejpam-6729	26	3	provides	provide	VERB
ejpam-6729	26	4	an	an	DET
ejpam-6729	26	5	overview	overview	NOUN
ejpam-6729	26	6	of	of	ADP
ejpam-6729	26	7	superhypergraphs	superhypergraph	NOUN
ejpam-6729	26	8	,	,	PUNCT
ejpam-6729	26	9	hypergraphs	hypergraph	NOUN
ejpam-6729	26	10	,	,	PUNCT
ejpam-6729	26	11	and	and	CCONJ
ejpam-6729	26	12	property	property	NOUN
ejpam-6729	26	13	graphs	graph	NOUN
ejpam-6729	26	14	.	.	PUNCT
ejpam-6729	27	1	section	section	NOUN
ejpam-6729	27	2	3	3	NUM
ejpam-6729	27	3	examines	examine	VERB
ejpam-6729	27	4	property	property	NOUN
ejpam-6729	27	5	hypergraphs	hypergraph	NOUN
ejpam-6729	27	6	,	,	PUNCT
ejpam-6729	27	7	discussing	discuss	VERB
ejpam-6729	27	8	their	their	PRON
ejpam-6729	27	9	applications	application	NOUN
ejpam-6729	27	10	and	and	CCONJ
ejpam-6729	27	11	key	key	ADJ
ejpam-6729	27	12	characteristics	characteristic	NOUN
ejpam-6729	27	13	.	.	PUNCT
ejpam-6729	28	1	section	section	NOUN
ejpam-6729	28	2	4	4	NUM
ejpam-6729	28	3	investigates	investigate	VERB
ejpam-6729	28	4	property	property	NOUN
ejpam-6729	28	5	superhypergraphs	superhypergraph	NOUN
ejpam-6729	28	6	,	,	PUNCT
ejpam-6729	28	7	presenting	present	VERB
ejpam-6729	28	8	applications	application	NOUN
ejpam-6729	28	9	and	and	CCONJ
ejpam-6729	28	10	structural	structural	ADJ
ejpam-6729	28	11	properties	property	NOUN
ejpam-6729	28	12	.	.	PUNCT
ejpam-6729	29	1	section	section	NOUN
ejpam-6729	29	2	5	5	NUM
ejpam-6729	29	3	offers	offer	VERB
ejpam-6729	29	4	concluding	conclude	VERB
ejpam-6729	29	5	remarks	remark	NOUN
ejpam-6729	29	6	and	and	CCONJ
ejpam-6729	29	7	outlines	outline	VERB
ejpam-6729	29	8	possible	possible	ADJ
ejpam-6729	29	9	directions	direction	NOUN
ejpam-6729	29	10	for	for	ADP
ejpam-6729	29	11	future	future	ADJ
ejpam-6729	29	12	research	research	NOUN
ejpam-6729	29	13	.	.	PUNCT
ejpam-6729	30	1	2	2	X
ejpam-6729	30	2	.	.	X
ejpam-6729	30	3	preliminaries	preliminary	NOUN
ejpam-6729	30	4	throughout	throughout	ADP
ejpam-6729	30	5	this	this	DET
ejpam-6729	30	6	paper	paper	NOUN
ejpam-6729	30	7	,	,	PUNCT
ejpam-6729	30	8	we	we	PRON
ejpam-6729	30	9	adopt	adopt	VERB
ejpam-6729	30	10	a	a	DET
ejpam-6729	30	11	consistent	consistent	ADJ
ejpam-6729	30	12	vocabulary	vocabulary	NOUN
ejpam-6729	30	13	and	and	CCONJ
ejpam-6729	30	14	notation	notation	NOUN
ejpam-6729	30	15	.	.	PUNCT
ejpam-6729	31	1	unless	unless	SCONJ
ejpam-6729	31	2	otherwise	otherwise	ADV
ejpam-6729	31	3	noted	note	VERB
ejpam-6729	31	4	,	,	PUNCT
ejpam-6729	31	5	all	all	DET
ejpam-6729	31	6	graphs	graph	NOUN
ejpam-6729	31	7	considered	consider	VERB
ejpam-6729	31	8	are	be	AUX
ejpam-6729	31	9	finite	finite	ADJ
ejpam-6729	31	10	.	.	PUNCT
ejpam-6729	32	1	for	for	ADP
ejpam-6729	32	2	further	further	ADJ
ejpam-6729	32	3	background	background	NOUN
ejpam-6729	32	4	on	on	ADP
ejpam-6729	32	5	less	less	ADV
ejpam-6729	32	6	familiar	familiar	ADJ
ejpam-6729	32	7	operations	operation	NOUN
ejpam-6729	32	8	or	or	CCONJ
ejpam-6729	32	9	concepts	concept	NOUN
ejpam-6729	32	10	,	,	PUNCT
ejpam-6729	32	11	the	the	DET
ejpam-6729	32	12	interested	interested	ADJ
ejpam-6729	32	13	reader	reader	NOUN
ejpam-6729	32	14	is	be	AUX
ejpam-6729	32	15	referred	refer	VERB
ejpam-6729	32	16	to	to	ADP
ejpam-6729	32	17	the	the	DET
ejpam-6729	32	18	cited	cite	VERB
ejpam-6729	32	19	literature	literature	NOUN
ejpam-6729	32	20	.	.	PUNCT
ejpam-6729	33	1	2.1	2.1	NUM
ejpam-6729	33	2	.	.	PUNCT
ejpam-6729	33	3	superhypergraphs	superhypergraph	VERB
ejpam-6729	33	4	a	a	DET
ejpam-6729	33	5	finite	finite	ADJ
ejpam-6729	33	6	hypergraph	hypergraph	NOUN
ejpam-6729	33	7	generalizes	generalize	VERB
ejpam-6729	33	8	the	the	DET
ejpam-6729	33	9	classical	classical	ADJ
ejpam-6729	33	10	graph	graph	NOUN
ejpam-6729	33	11	model	model	NOUN
ejpam-6729	33	12	by	by	ADP
ejpam-6729	33	13	permitting	permit	VERB
ejpam-6729	33	14	hyperedges	hyperedge	NOUN
ejpam-6729	33	15	that	that	PRON
ejpam-6729	33	16	connect	connect	VERB
ejpam-6729	33	17	any	any	DET
ejpam-6729	33	18	non‐empty	non‐empty	NOUN
ejpam-6729	33	19	subset	subset	NOUN
ejpam-6729	33	20	of	of	ADP
ejpam-6729	33	21	vertices	vertex	NOUN
ejpam-6729	33	22	[	[	X
ejpam-6729	33	23	10	10	NUM
ejpam-6729	33	24	,	,	PUNCT
ejpam-6729	33	25	24	24	NUM
ejpam-6729	33	26	,	,	PUNCT
ejpam-6729	33	27	25	25	NUM
ejpam-6729	33	28	]	]	PUNCT
ejpam-6729	33	29	.	.	PUNCT
ejpam-6729	34	1	building	build	VERB
ejpam-6729	34	2	on	on	ADP
ejpam-6729	34	3	this	this	DET
ejpam-6729	34	4	concept	concept	NOUN
ejpam-6729	34	5	,	,	PUNCT
ejpam-6729	34	6	a	a	DET
ejpam-6729	34	7	finite	finite	ADJ
ejpam-6729	34	8	superhypergraph	superhypergraph	NOUN
ejpam-6729	34	9	is	be	AUX
ejpam-6729	34	10	obtained	obtain	VERB
ejpam-6729	34	11	by	by	ADP
ejpam-6729	34	12	iteratively	iteratively	ADV
ejpam-6729	34	13	applying	apply	VERB
ejpam-6729	34	14	the	the	DET
ejpam-6729	34	15	powerset	powerset	NOUN
ejpam-6729	34	16	operator	operator	NOUN
ejpam-6729	34	17	,	,	PUNCT
ejpam-6729	34	18	thereby	thereby	ADV
ejpam-6729	34	19	creating	create	VERB
ejpam-6729	34	20	nested	nested	ADJ
ejpam-6729	34	21	hierarchies	hierarchy	NOUN
ejpam-6729	34	22	of	of	ADP
ejpam-6729	34	23	vertex	vertex	NOUN
ejpam-6729	34	24	and	and	CCONJ
ejpam-6729	34	25	edge	edge	NOUN
ejpam-6729	34	26	sets	set	NOUN
ejpam-6729	34	27	that	that	PRON
ejpam-6729	34	28	encode	encode	ADJ
ejpam-6729	34	29	multi‐layered	multi‐layere	VERB
ejpam-6729	34	30	relationships	relationship	NOUN
ejpam-6729	34	31	[	[	X
ejpam-6729	34	32	26	26	NUM
ejpam-6729	34	33	,	,	PUNCT
ejpam-6729	34	34	27	27	NUM
ejpam-6729	34	35	]	]	PUNCT
ejpam-6729	34	36	.	.	PUNCT
ejpam-6729	35	1	such	such	ADJ
ejpam-6729	35	2	structures	structure	NOUN
ejpam-6729	35	3	have	have	AUX
ejpam-6729	35	4	demonstrated	demonstrate	VERB
ejpam-6729	35	5	utility	utility	NOUN
ejpam-6729	35	6	in	in	ADP
ejpam-6729	35	7	areas	area	NOUN
ejpam-6729	35	8	ranging	range	VERB
ejpam-6729	35	9	from	from	ADP
ejpam-6729	35	10	molecular	molecular	ADJ
ejpam-6729	35	11	design	design	NOUN
ejpam-6729	35	12	and	and	CCONJ
ejpam-6729	35	13	complex‐network	complex‐network	NOUN
ejpam-6729	35	14	analysis	analysis	NOUN
ejpam-6729	35	15	to	to	ADP
ejpam-6729	35	16	advanced	advanced	ADJ
ejpam-6729	35	17	signal‐processing	signal‐processing	NOUN
ejpam-6729	35	18	pipelines	pipeline	NOUN
ejpam-6729	35	19	[	[	X
ejpam-6729	35	20	28–30	28–30	NOUN
ejpam-6729	35	21	]	]	PUNCT
ejpam-6729	35	22	.	.	PUNCT
ejpam-6729	36	1	unless	unless	SCONJ
ejpam-6729	36	2	stated	state	VERB
ejpam-6729	36	3	otherwise	otherwise	ADV
ejpam-6729	36	4	,	,	PUNCT
ejpam-6729	36	5	the	the	DET
ejpam-6729	36	6	integer	integer	NOUN
ejpam-6729	36	7	n	n	PROPN
ejpam-6729	36	8	in	in	ADP
ejpam-6729	36	9	pn	pn	PROPN
ejpam-6729	36	10	(	(	PUNCT
ejpam-6729	36	11	·	·	PUNCT
ejpam-6729	36	12	)	)	PUNCT
ejpam-6729	36	13	or	or	CCONJ
ejpam-6729	36	14	in	in	ADP
ejpam-6729	36	15	an	an	DET
ejpam-6729	36	16	n	n	PRON
ejpam-6729	36	17	-	-	PUNCT
ejpam-6729	36	18	superhypergraph	superhypergraph	NOUN
ejpam-6729	36	19	is	be	AUX
ejpam-6729	36	20	assumed	assume	VERB
ejpam-6729	36	21	to	to	PART
ejpam-6729	36	22	be	be	AUX
ejpam-6729	36	23	non‐negative	non‐negative	ADJ
ejpam-6729	36	24	.	.	PUNCT
ejpam-6729	37	1	definition	definition	NOUN
ejpam-6729	37	2	1	1	NUM
ejpam-6729	37	3	(	(	PUNCT
ejpam-6729	37	4	base	base	NOUN
ejpam-6729	37	5	set	set	NOUN
ejpam-6729	37	6	)	)	PUNCT
ejpam-6729	37	7	.	.	PUNCT
ejpam-6729	38	1	a	a	DET
ejpam-6729	38	2	base	base	NOUN
ejpam-6729	38	3	set	set	NOUN
ejpam-6729	38	4	s	s	VERB
ejpam-6729	38	5	is	be	AUX
ejpam-6729	38	6	the	the	DET
ejpam-6729	38	7	initial	initial	ADJ
ejpam-6729	38	8	universe	universe	NOUN
ejpam-6729	38	9	of	of	ADP
ejpam-6729	38	10	discourse	discourse	NOUN
ejpam-6729	38	11	:	:	PUNCT
ejpam-6729	38	12	s	s	X
ejpam-6729	38	13	=	=	PUNCT
ejpam-6729	38	14	{	{	PUNCT
ejpam-6729	38	15	x	x	X
ejpam-6729	38	16	|	|	ADV
ejpam-6729	38	17	x	x	PUNCT
ejpam-6729	38	18	belongs	belong	VERB
ejpam-6729	38	19	to	to	ADP
ejpam-6729	38	20	the	the	DET
ejpam-6729	38	21	context	context	NOUN
ejpam-6729	38	22	at	at	ADP
ejpam-6729	38	23	hand	hand	NOUN
ejpam-6729	38	24	}	}	PUNCT
ejpam-6729	38	25	.	.	PUNCT
ejpam-6729	39	1	every	every	DET
ejpam-6729	39	2	element	element	NOUN
ejpam-6729	39	3	that	that	PRON
ejpam-6729	39	4	appears	appear	VERB
ejpam-6729	39	5	in	in	ADP
ejpam-6729	39	6	p(s	p(s	NOUN
ejpam-6729	39	7	)	)	PUNCT
ejpam-6729	39	8	or	or	CCONJ
ejpam-6729	39	9	in	in	ADP
ejpam-6729	39	10	any	any	DET
ejpam-6729	39	11	iterated	iterated	ADJ
ejpam-6729	39	12	powerset	powerset	NOUN
ejpam-6729	39	13	pn(s	pn(s	NOUN
ejpam-6729	39	14	)	)	PUNCT
ejpam-6729	39	15	must	must	AUX
ejpam-6729	39	16	of	of	ADP
ejpam-6729	39	17	course	course	NOUN
ejpam-6729	39	18	lie	lie	VERB
ejpam-6729	39	19	in	in	ADP
ejpam-6729	39	20	s.	s.	PROPN
ejpam-6729	39	21	t.	t.	PROPN
ejpam-6729	39	22	fujita	fujita	PROPN
ejpam-6729	39	23	,	,	PUNCT
ejpam-6729	39	24	f.	f.	PROPN
ejpam-6729	39	25	smarandache	smarandache	PROPN
ejpam-6729	39	26	/	/	SYM
ejpam-6729	39	27	eur	eur	PROPN
ejpam-6729	39	28	.	.	PUNCT
ejpam-6729	40	1	j.	j.	PROPN
ejpam-6729	40	2	pure	pure	PROPN
ejpam-6729	40	3	appl	appl	PROPN
ejpam-6729	40	4	.	.	PROPN
ejpam-6729	40	5	math	math	PROPN
ejpam-6729	40	6	,	,	PUNCT
ejpam-6729	40	7	18	18	NUM
ejpam-6729	40	8	(	(	PUNCT
ejpam-6729	40	9	4	4	NUM
ejpam-6729	40	10	)	)	PUNCT
ejpam-6729	40	11	(	(	PUNCT
ejpam-6729	40	12	2025	2025	NUM
ejpam-6729	40	13	)	)	PUNCT
ejpam-6729	40	14	,	,	PUNCT
ejpam-6729	40	15	6729	6729	NUM
ejpam-6729	40	16	3	3	NUM
ejpam-6729	40	17	of	of	ADP
ejpam-6729	40	18	36	36	NUM
ejpam-6729	40	19	definition	definition	NOUN
ejpam-6729	40	20	2	2	NUM
ejpam-6729	40	21	(	(	PUNCT
ejpam-6729	40	22	powerset	powerset	NOUN
ejpam-6729	40	23	)	)	PUNCT
ejpam-6729	40	24	.	.	PUNCT
ejpam-6729	41	1	(	(	PUNCT
ejpam-6729	41	2	cf.[31	cf.[31	PROPN
ejpam-6729	41	3	,	,	PUNCT
ejpam-6729	41	4	32	32	NUM
ejpam-6729	41	5	]	]	PUNCT
ejpam-6729	41	6	)	)	PUNCT
ejpam-6729	41	7	for	for	ADP
ejpam-6729	41	8	a	a	DET
ejpam-6729	41	9	set	set	NOUN
ejpam-6729	41	10	s	s	PROPN
ejpam-6729	41	11	,	,	PUNCT
ejpam-6729	41	12	the	the	DET
ejpam-6729	41	13	powerset	powerset	NOUN
ejpam-6729	41	14	p(s	p(s	NOUN
ejpam-6729	41	15	)	)	PUNCT
ejpam-6729	41	16	is	be	AUX
ejpam-6729	41	17	the	the	DET
ejpam-6729	41	18	family	family	NOUN
ejpam-6729	41	19	of	of	ADP
ejpam-6729	41	20	all	all	DET
ejpam-6729	41	21	subsets	subset	NOUN
ejpam-6729	41	22	of	of	ADP
ejpam-6729	41	23	s	s	NOUN
ejpam-6729	41	24	:	:	PUNCT
ejpam-6729	41	25	p(s	p(s	NUM
ejpam-6729	41	26	)	)	PUNCT
ejpam-6729	42	1	=	=	PRON
ejpam-6729	42	2	{	{	PUNCT
ejpam-6729	42	3	a	a	DET
ejpam-6729	42	4	⊆	⊆	NUM
ejpam-6729	42	5	s	s	NOUN
ejpam-6729	42	6	}	}	PUNCT
ejpam-6729	42	7	.	.	PUNCT
ejpam-6729	43	1	this	this	DET
ejpam-6729	43	2	collection	collection	NOUN
ejpam-6729	43	3	includes	include	VERB
ejpam-6729	43	4	both	both	PRON
ejpam-6729	43	5	s	s	VERB
ejpam-6729	43	6	itself	itself	PRON
ejpam-6729	43	7	and	and	CCONJ
ejpam-6729	43	8	the	the	DET
ejpam-6729	43	9	empty	empty	ADJ
ejpam-6729	43	10	set	set	NOUN
ejpam-6729	43	11	∅.	∅.	PRON
ejpam-6729	43	12	definition	definition	NOUN
ejpam-6729	43	13	3	3	NUM
ejpam-6729	43	14	(	(	PUNCT
ejpam-6729	43	15	hypergraph	hypergraph	NOUN
ejpam-6729	43	16	)	)	PUNCT
ejpam-6729	43	17	.	.	PUNCT
ejpam-6729	44	1	[	[	X
ejpam-6729	44	2	3	3	NUM
ejpam-6729	44	3	,	,	PUNCT
ejpam-6729	44	4	33	33	NUM
ejpam-6729	44	5	]	]	PUNCT
ejpam-6729	44	6	a	a	DET
ejpam-6729	44	7	hypergraph	hypergraph	NOUN
ejpam-6729	44	8	is	be	AUX
ejpam-6729	44	9	an	an	DET
ejpam-6729	44	10	ordered	order	VERB
ejpam-6729	44	11	pair	pair	NOUN
ejpam-6729	44	12	h	h	NOUN
ejpam-6729	44	13	=	=	SYM
ejpam-6729	44	14	(	(	PUNCT
ejpam-6729	44	15	v	v	NOUN
ejpam-6729	44	16	,	,	PUNCT
ejpam-6729	44	17	e	e	NOUN
ejpam-6729	44	18	)	)	PUNCT
ejpam-6729	44	19	where	where	SCONJ
ejpam-6729	44	20	•	•	NUM
ejpam-6729	44	21	v	v	NOUN
ejpam-6729	44	22	is	be	AUX
ejpam-6729	44	23	a	a	DET
ejpam-6729	44	24	finite	finite	ADJ
ejpam-6729	44	25	vertex	vertex	NOUN
ejpam-6729	44	26	set	set	NOUN
ejpam-6729	44	27	,	,	PUNCT
ejpam-6729	44	28	and	and	CCONJ
ejpam-6729	44	29	•	•	NUM
ejpam-6729	44	30	e	e	NOUN
ejpam-6729	44	31	is	be	AUX
ejpam-6729	44	32	a	a	DET
ejpam-6729	44	33	finite	finite	ADJ
ejpam-6729	44	34	family	family	NOUN
ejpam-6729	44	35	of	of	ADP
ejpam-6729	44	36	non	non	ADJ
ejpam-6729	44	37	-	-	ADJ
ejpam-6729	44	38	empty	empty	ADJ
ejpam-6729	44	39	subsets	subset	NOUN
ejpam-6729	44	40	of	of	ADP
ejpam-6729	44	41	v	v	NOUN
ejpam-6729	44	42	;	;	PUNCT
ejpam-6729	44	43	the	the	DET
ejpam-6729	44	44	members	member	NOUN
ejpam-6729	44	45	of	of	ADP
ejpam-6729	44	46	e	e	PROPN
ejpam-6729	44	47	are	be	AUX
ejpam-6729	44	48	called	call	VERB
ejpam-6729	44	49	hyperedges	hyperedge	NOUN
ejpam-6729	44	50	.	.	PUNCT
ejpam-6729	45	1	hypergraphs	hypergraph	NOUN
ejpam-6729	45	2	naturally	naturally	ADV
ejpam-6729	45	3	represent	represent	VERB
ejpam-6729	45	4	interactions	interaction	NOUN
ejpam-6729	45	5	that	that	PRON
ejpam-6729	45	6	involve	involve	VERB
ejpam-6729	45	7	more	more	ADJ
ejpam-6729	45	8	than	than	ADP
ejpam-6729	45	9	two	two	NUM
ejpam-6729	45	10	participants	participant	NOUN
ejpam-6729	45	11	.	.	PUNCT
ejpam-6729	46	1	example	example	NOUN
ejpam-6729	46	2	1	1	NUM
ejpam-6729	46	3	(	(	PUNCT
ejpam-6729	46	4	hypergraph	hypergraph	VERB
ejpam-6729	46	5	model	model	NOUN
ejpam-6729	46	6	for	for	ADP
ejpam-6729	46	7	market	market	NOUN
ejpam-6729	46	8	-	-	PUNCT
ejpam-6729	46	9	basket	basket	NOUN
ejpam-6729	46	10	analysis	analysis	NOUN
ejpam-6729	46	11	)	)	PUNCT
ejpam-6729	46	12	.	.	PUNCT
ejpam-6729	47	1	market	market	NOUN
ejpam-6729	47	2	-	-	PUNCT
ejpam-6729	47	3	basket	basket	NOUN
ejpam-6729	47	4	analysis	analysis	NOUN
ejpam-6729	47	5	seeks	seek	VERB
ejpam-6729	47	6	to	to	PART
ejpam-6729	47	7	uncover	uncover	VERB
ejpam-6729	47	8	groups	group	NOUN
ejpam-6729	47	9	of	of	ADP
ejpam-6729	47	10	products	product	NOUN
ejpam-6729	47	11	that	that	PRON
ejpam-6729	47	12	are	be	AUX
ejpam-6729	47	13	purchased	purchase	VERB
ejpam-6729	47	14	together	together	ADV
ejpam-6729	47	15	.	.	PUNCT
ejpam-6729	48	1	a	a	DET
ejpam-6729	48	2	compact	compact	ADJ
ejpam-6729	48	3	way	way	NOUN
ejpam-6729	48	4	to	to	PART
ejpam-6729	48	5	represent	represent	VERB
ejpam-6729	48	6	the	the	DET
ejpam-6729	48	7	entire	entire	ADJ
ejpam-6729	48	8	transaction	transaction	NOUN
ejpam-6729	48	9	log	log	NOUN
ejpam-6729	48	10	is	be	AUX
ejpam-6729	48	11	to	to	PART
ejpam-6729	48	12	view	view	VERB
ejpam-6729	48	13	it	it	PRON
ejpam-6729	48	14	as	as	ADP
ejpam-6729	48	15	a	a	DET
ejpam-6729	48	16	hypergraph	hypergraph	NOUN
ejpam-6729	48	17	in	in	ADP
ejpam-6729	48	18	the	the	DET
ejpam-6729	48	19	sense	sense	NOUN
ejpam-6729	48	20	of	of	ADP
ejpam-6729	48	21	definition	definition	NOUN
ejpam-6729	48	22	3	3	NUM
ejpam-6729	48	23	.	.	PUNCT
ejpam-6729	48	24	vertex	vertex	PROPN
ejpam-6729	48	25	set	set	NOUN
ejpam-6729	48	26	.	.	PUNCT
ejpam-6729	49	1	let	let	VERB
ejpam-6729	49	2	v	v	VERB
ejpam-6729	49	3	=	=	NOUN
ejpam-6729	49	4	{	{	PUNCT
ejpam-6729	49	5	bread	bread	NOUN
ejpam-6729	49	6	,	,	PUNCT
ejpam-6729	49	7	butter	butter	NOUN
ejpam-6729	49	8	,	,	PUNCT
ejpam-6729	49	9	milk	milk	NOUN
ejpam-6729	49	10	,	,	PUNCT
ejpam-6729	49	11	eggs	egg	NOUN
ejpam-6729	49	12	,	,	PUNCT
ejpam-6729	49	13	coffee	coffee	NOUN
ejpam-6729	49	14	,	,	PUNCT
ejpam-6729	49	15	cheese	cheese	NOUN
ejpam-6729	49	16	}	}	PUNCT
ejpam-6729	49	17	be	be	AUX
ejpam-6729	49	18	the	the	DET
ejpam-6729	49	19	collection	collection	NOUN
ejpam-6729	49	20	of	of	ADP
ejpam-6729	49	21	six	six	NUM
ejpam-6729	49	22	distinct	distinct	ADJ
ejpam-6729	49	23	items	item	NOUN
ejpam-6729	49	24	sold	sell	VERB
ejpam-6729	49	25	in	in	ADP
ejpam-6729	49	26	a	a	DET
ejpam-6729	49	27	small	small	ADJ
ejpam-6729	49	28	grocery	grocery	NOUN
ejpam-6729	49	29	store	store	NOUN
ejpam-6729	49	30	.	.	PUNCT
ejpam-6729	50	1	observed	observe	VERB
ejpam-6729	50	2	transactions	transaction	NOUN
ejpam-6729	50	3	(	(	PUNCT
ejpam-6729	50	4	hyperedges	hyperedge	NOUN
ejpam-6729	50	5	)	)	PUNCT
ejpam-6729	50	6	.	.	PUNCT
ejpam-6729	51	1	during	during	ADP
ejpam-6729	51	2	one	one	NUM
ejpam-6729	51	3	afternoon	afternoon	NOUN
ejpam-6729	51	4	the	the	DET
ejpam-6729	51	5	cash	cash	NOUN
ejpam-6729	51	6	register	register	NOUN
ejpam-6729	51	7	records	record	VERB
ejpam-6729	51	8	four	four	NUM
ejpam-6729	51	9	baskets	basket	NOUN
ejpam-6729	51	10	:	:	PUNCT
ejpam-6729	51	11	t1	t1	NOUN
ejpam-6729	51	12	=	=	PUNCT
ejpam-6729	51	13	{	{	PUNCT
ejpam-6729	51	14	bread	bread	NOUN
ejpam-6729	51	15	,	,	PUNCT
ejpam-6729	51	16	butter	butter	NOUN
ejpam-6729	51	17	,	,	PUNCT
ejpam-6729	51	18	milk	milk	NOUN
ejpam-6729	51	19	}	}	PUNCT
ejpam-6729	51	20	,	,	PUNCT
ejpam-6729	51	21	t2	t2	NOUN
ejpam-6729	51	22	=	=	SYM
ejpam-6729	51	23	{	{	PUNCT
ejpam-6729	51	24	coffee	coffee	NOUN
ejpam-6729	51	25	,	,	PUNCT
ejpam-6729	51	26	milk	milk	NOUN
ejpam-6729	51	27	}	}	PUNCT
ejpam-6729	51	28	,	,	PUNCT
ejpam-6729	51	29	t3	t3	PROPN
ejpam-6729	51	30	=	=	PUNCT
ejpam-6729	51	31	{	{	PUNCT
ejpam-6729	51	32	bread	bread	NOUN
ejpam-6729	51	33	,	,	PUNCT
ejpam-6729	51	34	eggs	egg	NOUN
ejpam-6729	51	35	,	,	PUNCT
ejpam-6729	51	36	cheese	cheese	NOUN
ejpam-6729	51	37	}	}	PUNCT
ejpam-6729	51	38	,	,	PUNCT
ejpam-6729	52	1	t4	t4	PROPN
ejpam-6729	52	2	=	=	PROPN
ejpam-6729	52	3	{	{	PUNCT
ejpam-6729	52	4	butter	butter	NOUN
ejpam-6729	52	5	,	,	PUNCT
ejpam-6729	52	6	eggs	egg	NOUN
ejpam-6729	52	7	,	,	PUNCT
ejpam-6729	52	8	milk	milk	NOUN
ejpam-6729	52	9	}	}	PUNCT
ejpam-6729	52	10	.	.	PUNCT
ejpam-6729	53	1	each	each	DET
ejpam-6729	53	2	transaction	transaction	NOUN
ejpam-6729	53	3	is	be	AUX
ejpam-6729	53	4	a	a	DET
ejpam-6729	53	5	non	non	ADJ
ejpam-6729	53	6	-	-	ADJ
ejpam-6729	53	7	empty	empty	ADJ
ejpam-6729	53	8	subset	subset	NOUN
ejpam-6729	53	9	of	of	ADP
ejpam-6729	53	10	v	v	NOUN
ejpam-6729	53	11	and	and	CCONJ
ejpam-6729	53	12	is	be	AUX
ejpam-6729	53	13	therefore	therefore	ADV
ejpam-6729	53	14	admissible	admissible	ADJ
ejpam-6729	53	15	as	as	ADP
ejpam-6729	53	16	a	a	DET
ejpam-6729	53	17	hyperedge	hyperedge	NOUN
ejpam-6729	53	18	.	.	PUNCT
ejpam-6729	54	1	resulting	result	VERB
ejpam-6729	54	2	hypergraph	hypergraph	NOUN
ejpam-6729	54	3	.	.	PUNCT
ejpam-6729	55	1	define	define	NOUN
ejpam-6729	55	2	e	e	PROPN
ejpam-6729	55	3	=	=	PUNCT
ejpam-6729	55	4	{	{	PUNCT
ejpam-6729	55	5	t1	t1	NOUN
ejpam-6729	55	6	,	,	PUNCT
ejpam-6729	55	7	t2	t2	NOUN
ejpam-6729	55	8	,	,	PUNCT
ejpam-6729	55	9	t3	t3	PROPN
ejpam-6729	55	10	,	,	PUNCT
ejpam-6729	55	11	t4	t4	PROPN
ejpam-6729	55	12	}	}	PUNCT
ejpam-6729	55	13	.	.	PUNCT
ejpam-6729	56	1	the	the	DET
ejpam-6729	56	2	pair	pair	NOUN
ejpam-6729	56	3	h	h	NOUN
ejpam-6729	56	4	=	=	SYM
ejpam-6729	56	5	(	(	PUNCT
ejpam-6729	56	6	v	v	NOUN
ejpam-6729	56	7	,	,	PUNCT
ejpam-6729	56	8	e	e	NOUN
ejpam-6729	56	9	)	)	PUNCT
ejpam-6729	56	10	is	be	AUX
ejpam-6729	56	11	a	a	DET
ejpam-6729	56	12	hypergraph	hypergraph	NOUN
ejpam-6729	56	13	whose	whose	DET
ejpam-6729	56	14	hyperedges	hyperedge	NOUN
ejpam-6729	56	15	correspond	correspond	VERB
ejpam-6729	56	16	one	one	NUM
ejpam-6729	56	17	-	-	PUNCT
ejpam-6729	56	18	to	to	ADP
ejpam-6729	56	19	-	-	PUNCT
ejpam-6729	56	20	one	one	NUM
ejpam-6729	56	21	with	with	ADP
ejpam-6729	56	22	the	the	DET
ejpam-6729	56	23	observed	observe	VERB
ejpam-6729	56	24	baskets	basket	NOUN
ejpam-6729	56	25	.	.	PUNCT
ejpam-6729	57	1	mining	mining	NOUN
ejpam-6729	57	2	tasks	task	NOUN
ejpam-6729	57	3	enabled	enable	VERB
ejpam-6729	57	4	by	by	ADP
ejpam-6729	57	5	this	this	DET
ejpam-6729	57	6	representation	representation	NOUN
ejpam-6729	57	7	•	•	NOUN
ejpam-6729	57	8	support	support	NOUN
ejpam-6729	57	9	counting	counting	NOUN
ejpam-6729	57	10	:	:	PUNCT
ejpam-6729	57	11	the	the	DET
ejpam-6729	57	12	degree	degree	NOUN
ejpam-6729	57	13	of	of	ADP
ejpam-6729	57	14	a	a	DET
ejpam-6729	57	15	vertex	vertex	NOUN
ejpam-6729	57	16	equals	equal	VERB
ejpam-6729	57	17	the	the	DET
ejpam-6729	57	18	number	number	NOUN
ejpam-6729	57	19	of	of	ADP
ejpam-6729	57	20	baskets	basket	NOUN
ejpam-6729	57	21	that	that	PRON
ejpam-6729	57	22	contain	contain	VERB
ejpam-6729	57	23	the	the	DET
ejpam-6729	57	24	corresponding	corresponding	ADJ
ejpam-6729	57	25	item	item	NOUN
ejpam-6729	57	26	,	,	PUNCT
ejpam-6729	57	27	providing	provide	VERB
ejpam-6729	57	28	its	its	PRON
ejpam-6729	57	29	purchase	purchase	NOUN
ejpam-6729	57	30	frequency	frequency	NOUN
ejpam-6729	57	31	.	.	PUNCT
ejpam-6729	58	1	•	•	NUM
ejpam-6729	58	2	frequent	frequent	ADJ
ejpam-6729	58	3	-	-	PUNCT
ejpam-6729	58	4	itemset	itemset	VERB
ejpam-6729	58	5	discovery	discovery	NOUN
ejpam-6729	58	6	:	:	PUNCT
ejpam-6729	58	7	any	any	DET
ejpam-6729	58	8	subset	subset	NOUN
ejpam-6729	58	9	of	of	ADP
ejpam-6729	58	10	vertices	vertex	NOUN
ejpam-6729	58	11	that	that	PRON
ejpam-6729	58	12	appears	appear	VERB
ejpam-6729	58	13	together	together	ADV
ejpam-6729	58	14	in	in	ADP
ejpam-6729	58	15	a	a	DET
ejpam-6729	58	16	sufficient	sufficient	ADJ
ejpam-6729	58	17	number	number	NOUN
ejpam-6729	58	18	of	of	ADP
ejpam-6729	58	19	hyperedges	hyperedge	NOUN
ejpam-6729	58	20	constitutes	constitute	VERB
ejpam-6729	58	21	a	a	DET
ejpam-6729	58	22	frequent	frequent	ADJ
ejpam-6729	58	23	pattern	pattern	NOUN
ejpam-6729	58	24	.	.	PUNCT
ejpam-6729	59	1	t.	t.	PROPN
ejpam-6729	59	2	fujita	fujita	PROPN
ejpam-6729	59	3	,	,	PUNCT
ejpam-6729	59	4	f.	f.	PROPN
ejpam-6729	59	5	smarandache	smarandache	PROPN
ejpam-6729	59	6	/	/	SYM
ejpam-6729	59	7	eur	eur	PROPN
ejpam-6729	59	8	.	.	PUNCT
ejpam-6729	60	1	j.	j.	PROPN
ejpam-6729	60	2	pure	pure	PROPN
ejpam-6729	60	3	appl	appl	PROPN
ejpam-6729	60	4	.	.	PROPN
ejpam-6729	60	5	math	math	PROPN
ejpam-6729	60	6	,	,	PUNCT
ejpam-6729	60	7	18	18	NUM
ejpam-6729	60	8	(	(	PUNCT
ejpam-6729	60	9	4	4	NUM
ejpam-6729	60	10	)	)	PUNCT
ejpam-6729	60	11	(	(	PUNCT
ejpam-6729	60	12	2025	2025	NUM
ejpam-6729	60	13	)	)	PUNCT
ejpam-6729	60	14	,	,	PUNCT
ejpam-6729	60	15	6729	6729	NUM
ejpam-6729	60	16	4	4	NUM
ejpam-6729	60	17	of	of	ADP
ejpam-6729	60	18	36	36	NUM
ejpam-6729	60	19	•	•	NUM
ejpam-6729	60	20	hyperedge	hyperedge	NOUN
ejpam-6729	60	21	clustering	cluster	VERB
ejpam-6729	60	22	:	:	PUNCT
ejpam-6729	60	23	grouping	group	VERB
ejpam-6729	60	24	baskets	basket	NOUN
ejpam-6729	60	25	that	that	PRON
ejpam-6729	60	26	share	share	VERB
ejpam-6729	60	27	many	many	ADJ
ejpam-6729	60	28	items	item	NOUN
ejpam-6729	60	29	can	can	AUX
ejpam-6729	60	30	reveal	reveal	VERB
ejpam-6729	60	31	customer	customer	NOUN
ejpam-6729	60	32	segments	segment	NOUN
ejpam-6729	60	33	with	with	ADP
ejpam-6729	60	34	similar	similar	ADJ
ejpam-6729	60	35	buying	buying	NOUN
ejpam-6729	60	36	habits	habit	NOUN
ejpam-6729	60	37	.	.	PUNCT
ejpam-6729	61	1	•	•	NUM
ejpam-6729	61	2	edge	edge	NOUN
ejpam-6729	61	3	contraction	contraction	NOUN
ejpam-6729	61	4	for	for	ADP
ejpam-6729	61	5	category	category	NOUN
ejpam-6729	61	6	analysis	analysis	NOUN
ejpam-6729	61	7	:	:	PUNCT
ejpam-6729	61	8	by	by	ADP
ejpam-6729	61	9	merging	merge	VERB
ejpam-6729	61	10	vertices	vertex	NOUN
ejpam-6729	61	11	into	into	ADP
ejpam-6729	61	12	higher	high	ADJ
ejpam-6729	61	13	-	-	PUNCT
ejpam-6729	61	14	level	level	NOUN
ejpam-6729	61	15	product	product	NOUN
ejpam-6729	61	16	categories	category	NOUN
ejpam-6729	61	17	(	(	PUNCT
ejpam-6729	61	18	e.g.	e.g.	ADV
ejpam-6729	61	19	dairy	dairy	NOUN
ejpam-6729	61	20	,	,	PUNCT
ejpam-6729	61	21	bakery	bakery	NOUN
ejpam-6729	61	22	)	)	PUNCT
ejpam-6729	61	23	,	,	PUNCT
ejpam-6729	61	24	the	the	DET
ejpam-6729	61	25	same	same	ADJ
ejpam-6729	61	26	hypergraph	hypergraph	NOUN
ejpam-6729	61	27	can	can	AUX
ejpam-6729	61	28	be	be	AUX
ejpam-6729	61	29	coarsened	coarsen	VERB
ejpam-6729	61	30	without	without	ADP
ejpam-6729	61	31	revisiting	revisit	VERB
ejpam-6729	61	32	the	the	DET
ejpam-6729	61	33	raw	raw	ADJ
ejpam-6729	61	34	data	datum	NOUN
ejpam-6729	61	35	.	.	PUNCT
ejpam-6729	62	1	the	the	DET
ejpam-6729	62	2	hypergraph	hypergraph	NOUN
ejpam-6729	62	3	model	model	NOUN
ejpam-6729	62	4	thus	thus	ADV
ejpam-6729	62	5	captures	capture	VERB
ejpam-6729	62	6	all	all	DET
ejpam-6729	62	7	transactions	transaction	NOUN
ejpam-6729	62	8	simultaneously	simultaneously	ADV
ejpam-6729	62	9	while	while	SCONJ
ejpam-6729	62	10	retaining	retain	VERB
ejpam-6729	62	11	enough	enough	ADJ
ejpam-6729	62	12	structure	structure	NOUN
ejpam-6729	62	13	to	to	PART
ejpam-6729	62	14	support	support	VERB
ejpam-6729	62	15	the	the	DET
ejpam-6729	62	16	full	full	ADJ
ejpam-6729	62	17	spectrum	spectrum	NOUN
ejpam-6729	62	18	of	of	ADP
ejpam-6729	62	19	basket	basket	NOUN
ejpam-6729	62	20	-	-	PUNCT
ejpam-6729	62	21	mining	mining	NOUN
ejpam-6729	62	22	algorithms	algorithm	NOUN
ejpam-6729	62	23	,	,	PUNCT
ejpam-6729	62	24	from	from	ADP
ejpam-6729	62	25	simple	simple	ADJ
ejpam-6729	62	26	frequency	frequency	NOUN
ejpam-6729	62	27	counts	count	NOUN
ejpam-6729	62	28	to	to	ADP
ejpam-6729	62	29	sophisticated	sophisticated	ADJ
ejpam-6729	62	30	community	community	NOUN
ejpam-6729	62	31	detection	detection	NOUN
ejpam-6729	62	32	among	among	ADP
ejpam-6729	62	33	both	both	DET
ejpam-6729	62	34	items	item	NOUN
ejpam-6729	62	35	and	and	CCONJ
ejpam-6729	62	36	customers	customer	NOUN
ejpam-6729	62	37	.	.	PUNCT
ejpam-6729	63	1	definition	definition	NOUN
ejpam-6729	63	2	4	4	NUM
ejpam-6729	63	3	(	(	PUNCT
ejpam-6729	63	4	n	n	CCONJ
ejpam-6729	63	5	-	-	PUNCT
ejpam-6729	63	6	th	th	VERB
ejpam-6729	63	7	powerset	powerset	NOUN
ejpam-6729	63	8	)	)	PUNCT
ejpam-6729	63	9	.	.	PUNCT
ejpam-6729	64	1	[	[	X
ejpam-6729	64	2	34	34	NUM
ejpam-6729	64	3	,	,	PUNCT
ejpam-6729	64	4	35	35	NUM
ejpam-6729	64	5	]	]	PUNCT
ejpam-6729	64	6	let	let	VERB
ejpam-6729	64	7	x	x	PRON
ejpam-6729	64	8	be	be	AUX
ejpam-6729	64	9	a	a	DET
ejpam-6729	64	10	set	set	NOUN
ejpam-6729	64	11	.	.	PUNCT
ejpam-6729	65	1	the	the	DET
ejpam-6729	65	2	first	first	ADJ
ejpam-6729	65	3	powerset	powerset	NOUN
ejpam-6729	65	4	is	be	AUX
ejpam-6729	65	5	p1(x	p1(x	NOUN
ejpam-6729	65	6	)	)	PUNCT
ejpam-6729	65	7	=	=	SYM
ejpam-6729	65	8	p(x	p(x	PROPN
ejpam-6729	65	9	)	)	PUNCT
ejpam-6729	65	10	.	.	PUNCT
ejpam-6729	66	1	for	for	ADP
ejpam-6729	66	2	n	n	PRON
ejpam-6729	66	3	≥	≥	NUM
ejpam-6729	66	4	1	1	NUM
ejpam-6729	66	5	we	we	PRON
ejpam-6729	66	6	define	define	VERB
ejpam-6729	66	7	pn+1(x	pn+1(x	NOUN
ejpam-6729	66	8	)	)	PUNCT
ejpam-6729	67	1	=	=	SYM
ejpam-6729	67	2	p	p	NOUN
ejpam-6729	67	3	(	(	PUNCT
ejpam-6729	67	4	pn(x	pn(x	X
ejpam-6729	67	5	)	)	PUNCT
ejpam-6729	67	6	)	)	PUNCT
ejpam-6729	67	7	.	.	PUNCT
ejpam-6729	68	1	when	when	SCONJ
ejpam-6729	68	2	the	the	DET
ejpam-6729	68	3	empty	empty	ADJ
ejpam-6729	68	4	set	set	NOUN
ejpam-6729	68	5	is	be	AUX
ejpam-6729	68	6	excluded	exclude	VERB
ejpam-6729	68	7	one	one	NUM
ejpam-6729	68	8	writes	write	VERB
ejpam-6729	68	9	p∗	p∗	ADJ
ejpam-6729	68	10	n(x	n(x	X
ejpam-6729	68	11	)	)	PUNCT
ejpam-6729	68	12	=	=	NOUN
ejpam-6729	68	13	pn(x	pn(x	X
ejpam-6729	68	14	)	)	PUNCT
ejpam-6729	68	15	\	\	NOUN
ejpam-6729	68	16	{	{	PUNCT
ejpam-6729	68	17	∅	∅	NOUN
ejpam-6729	68	18	}	}	PUNCT
ejpam-6729	68	19	.	.	PUNCT
ejpam-6729	69	1	example	example	NOUN
ejpam-6729	69	2	2	2	NUM
ejpam-6729	69	3	(	(	PUNCT
ejpam-6729	69	4	n	n	CCONJ
ejpam-6729	69	5	-	-	PUNCT
ejpam-6729	69	6	th	th	VERB
ejpam-6729	69	7	powerset	powerset	NOUN
ejpam-6729	69	8	in	in	ADP
ejpam-6729	69	9	market	market	NOUN
ejpam-6729	69	10	-	-	PUNCT
ejpam-6729	69	11	basket	basket	NOUN
ejpam-6729	69	12	data	datum	NOUN
ejpam-6729	69	13	mining	mining	NOUN
ejpam-6729	69	14	)	)	PUNCT
ejpam-6729	69	15	.	.	PUNCT
ejpam-6729	70	1	suppose	suppose	VERB
ejpam-6729	70	2	a	a	DET
ejpam-6729	70	3	supermarket	supermarket	NOUN
ejpam-6729	70	4	tracks	track	VERB
ejpam-6729	70	5	customer	customer	NOUN
ejpam-6729	70	6	purchases	purchase	NOUN
ejpam-6729	70	7	over	over	ADP
ejpam-6729	70	8	a	a	DET
ejpam-6729	70	9	single	single	ADJ
ejpam-6729	70	10	week	week	NOUN
ejpam-6729	70	11	and	and	CCONJ
ejpam-6729	70	12	observes	observe	VERB
ejpam-6729	70	13	the	the	DET
ejpam-6729	70	14	following	follow	VERB
ejpam-6729	70	15	five	five	NUM
ejpam-6729	70	16	items	item	NOUN
ejpam-6729	70	17	:	:	PUNCT
ejpam-6729	70	18	x	x	SYM
ejpam-6729	70	19	=	=	NOUN
ejpam-6729	70	20	{	{	PUNCT
ejpam-6729	70	21	bread	bread	NOUN
ejpam-6729	70	22	,	,	PUNCT
ejpam-6729	70	23	milk	milk	NOUN
ejpam-6729	70	24	,	,	PUNCT
ejpam-6729	70	25	eggs	egg	NOUN
ejpam-6729	70	26	,	,	PUNCT
ejpam-6729	70	27	butter	butter	NOUN
ejpam-6729	70	28	,	,	PUNCT
ejpam-6729	70	29	coffee	coffee	NOUN
ejpam-6729	70	30	}	}	PUNCT
ejpam-6729	70	31	.	.	PUNCT
ejpam-6729	71	1	p1(x	p1(x	NOUN
ejpam-6729	71	2	)	)	PUNCT
ejpam-6729	71	3	=	=	SYM
ejpam-6729	71	4	p(x	p(x	NOUN
ejpam-6729	71	5	):	):	PUNCT
ejpam-6729	71	6	candidate	candidate	NOUN
ejpam-6729	71	7	itemsets	itemset	NOUN
ejpam-6729	71	8	.	.	PUNCT
ejpam-6729	72	1	every	every	DET
ejpam-6729	72	2	non	non	ADJ
ejpam-6729	72	3	-	-	ADJ
ejpam-6729	72	4	empty	empty	ADJ
ejpam-6729	72	5	subset	subset	NOUN
ejpam-6729	72	6	of	of	ADP
ejpam-6729	72	7	x	x	SYM
ejpam-6729	72	8	is	be	AUX
ejpam-6729	72	9	a	a	DET
ejpam-6729	72	10	candidate	candidate	NOUN
ejpam-6729	72	11	itemset	itemset	VERB
ejpam-6729	72	12	.	.	PUNCT
ejpam-6729	73	1	for	for	ADP
ejpam-6729	73	2	instance	instance	NOUN
ejpam-6729	73	3	,	,	PUNCT
ejpam-6729	73	4	{	{	PUNCT
ejpam-6729	73	5	bread	bread	NOUN
ejpam-6729	73	6	,	,	PUNCT
ejpam-6729	73	7	butter	butter	NOUN
ejpam-6729	73	8	}	}	PUNCT
ejpam-6729	73	9	or	or	CCONJ
ejpam-6729	73	10	{	{	PUNCT
ejpam-6729	73	11	milk	milk	NOUN
ejpam-6729	73	12	,	,	PUNCT
ejpam-6729	73	13	eggs	egg	NOUN
ejpam-6729	73	14	,	,	PUNCT
ejpam-6729	73	15	coffee	coffee	NOUN
ejpam-6729	73	16	}	}	PUNCT
ejpam-6729	73	17	.	.	PUNCT
ejpam-6729	74	1	standard	standard	ADJ
ejpam-6729	74	2	algorithms	algorithm	NOUN
ejpam-6729	74	3	such	such	ADJ
ejpam-6729	74	4	as	as	ADP
ejpam-6729	74	5	apriori	apriori	ADV
ejpam-6729	74	6	scan	scan	NOUN
ejpam-6729	74	7	the	the	DET
ejpam-6729	74	8	transaction	transaction	NOUN
ejpam-6729	74	9	log	log	VERB
ejpam-6729	74	10	to	to	PART
ejpam-6729	74	11	determine	determine	VERB
ejpam-6729	74	12	which	which	PRON
ejpam-6729	74	13	of	of	ADP
ejpam-6729	74	14	these	these	DET
ejpam-6729	74	15	subsets	subset	NOUN
ejpam-6729	74	16	occur	occur	VERB
ejpam-6729	74	17	frequently	frequently	ADV
ejpam-6729	74	18	.	.	PUNCT
ejpam-6729	75	1	p2(x	p2(x	X
ejpam-6729	75	2	)	)	PUNCT
ejpam-6729	75	3	=	=	SYM
ejpam-6729	76	1	p	p	X
ejpam-6729	76	2	(	(	PUNCT
ejpam-6729	76	3	p1(x	p1(x	NOUN
ejpam-6729	76	4	)	)	PUNCT
ejpam-6729	76	5	)	)	PUNCT
ejpam-6729	76	6	:	:	PUNCT
ejpam-6729	76	7	clusters	cluster	NOUN
ejpam-6729	76	8	of	of	ADP
ejpam-6729	76	9	itemsets	itemset	NOUN
ejpam-6729	76	10	.	.	PUNCT
ejpam-6729	77	1	the	the	DET
ejpam-6729	77	2	second	second	ADJ
ejpam-6729	77	3	powerset	powerset	NOUN
ejpam-6729	77	4	groups	group	NOUN
ejpam-6729	77	5	itemsets	itemset	VERB
ejpam-6729	77	6	into	into	ADP
ejpam-6729	77	7	itemset	itemset	ADJ
ejpam-6729	77	8	clusters	cluster	NOUN
ejpam-6729	77	9	.	.	PUNCT
ejpam-6729	78	1	an	an	DET
ejpam-6729	78	2	analyst	analyst	NOUN
ejpam-6729	78	3	may	may	AUX
ejpam-6729	78	4	,	,	PUNCT
ejpam-6729	78	5	for	for	ADP
ejpam-6729	78	6	example	example	NOUN
ejpam-6729	78	7	,	,	PUNCT
ejpam-6729	78	8	collect	collect	VERB
ejpam-6729	78	9	all	all	DET
ejpam-6729	78	10	frequent	frequent	ADJ
ejpam-6729	78	11	two	two	NUM
ejpam-6729	78	12	-	-	PUNCT
ejpam-6729	78	13	item	item	NOUN
ejpam-6729	78	14	combinations	combination	NOUN
ejpam-6729	78	15	that	that	PRON
ejpam-6729	78	16	involve	involve	VERB
ejpam-6729	78	17	coffee	coffee	NOUN
ejpam-6729	78	18	:	:	PUNCT
ejpam-6729	78	19	ccoffee	ccoffee	NOUN
ejpam-6729	78	20	=	=	SYM
ejpam-6729	78	21	{	{	PUNCT
ejpam-6729	78	22	{	{	PUNCT
ejpam-6729	78	23	coffee	coffee	NOUN
ejpam-6729	78	24	,	,	PUNCT
ejpam-6729	78	25	milk	milk	NOUN
ejpam-6729	78	26	}	}	PUNCT
ejpam-6729	78	27	,	,	PUNCT
ejpam-6729	78	28	{	{	PUNCT
ejpam-6729	78	29	coffee	coffee	NOUN
ejpam-6729	78	30	,	,	PUNCT
ejpam-6729	78	31	bread	bread	NOUN
ejpam-6729	78	32	}	}	PUNCT
ejpam-6729	78	33	,	,	PUNCT
ejpam-6729	78	34	{	{	PUNCT
ejpam-6729	78	35	coffee	coffee	NOUN
ejpam-6729	78	36	,	,	PUNCT
ejpam-6729	78	37	eggs	egg	NOUN
ejpam-6729	78	38	}	}	PUNCT
ejpam-6729	78	39	}	}	PUNCT
ejpam-6729	78	40	∈	∈	PROPN
ejpam-6729	78	41	p2(x	p2(x	NOUN
ejpam-6729	78	42	)	)	PUNCT
ejpam-6729	78	43	.	.	PUNCT
ejpam-6729	79	1	p3(x	p3(x	X
ejpam-6729	79	2	)	)	PUNCT
ejpam-6729	79	3	=	=	SYM
ejpam-6729	80	1	p	p	X
ejpam-6729	80	2	(	(	PUNCT
ejpam-6729	80	3	p2(x	p2(x	NOUN
ejpam-6729	80	4	)	)	PUNCT
ejpam-6729	80	5	)	)	PUNCT
ejpam-6729	80	6	:	:	PUNCT
ejpam-6729	81	1	meta	meta	ADJ
ejpam-6729	81	2	-	-	PUNCT
ejpam-6729	81	3	clusters	cluster	NOUN
ejpam-6729	81	4	.	.	PUNCT
ejpam-6729	82	1	the	the	DET
ejpam-6729	82	2	third	third	ADJ
ejpam-6729	82	3	powerset	powerset	NOUN
ejpam-6729	82	4	organises	organise	VERB
ejpam-6729	82	5	clusters	cluster	NOUN
ejpam-6729	82	6	of	of	ADP
ejpam-6729	82	7	itemsets	itemset	NOUN
ejpam-6729	82	8	into	into	ADP
ejpam-6729	82	9	meta	meta	ADJ
ejpam-6729	82	10	-	-	PUNCT
ejpam-6729	82	11	clusters	cluster	NOUN
ejpam-6729	82	12	.	.	PUNCT
ejpam-6729	83	1	one	one	PRON
ejpam-6729	83	2	might	might	AUX
ejpam-6729	83	3	place	place	VERB
ejpam-6729	83	4	all	all	PRON
ejpam-6729	83	5	itemset	itemset	VERB
ejpam-6729	83	6	clusters	cluster	NOUN
ejpam-6729	83	7	whose	whose	DET
ejpam-6729	83	8	underlying	underlying	ADJ
ejpam-6729	83	9	products	product	NOUN
ejpam-6729	83	10	form	form	VERB
ejpam-6729	83	11	a	a	DET
ejpam-6729	83	12	typical	typical	ADJ
ejpam-6729	83	13	breakfast	breakfast	NOUN
ejpam-6729	83	14	assortment	assortment	NOUN
ejpam-6729	83	15	into	into	ADP
ejpam-6729	83	16	a	a	DET
ejpam-6729	83	17	single	single	ADJ
ejpam-6729	83	18	meta	meta	ADJ
ejpam-6729	83	19	-	-	PUNCT
ejpam-6729	83	20	cluster	cluster	NOUN
ejpam-6729	83	21	:	:	PUNCT
ejpam-6729	83	22	mbreakfast	mbreakfast	NOUN
ejpam-6729	83	23	=	=	SYM
ejpam-6729	83	24	{	{	PUNCT
ejpam-6729	83	25	ccoffee	ccoffee	NOUN
ejpam-6729	83	26	,	,	PUNCT
ejpam-6729	83	27	cmilk	cmilk	NOUN
ejpam-6729	83	28	,	,	PUNCT
ejpam-6729	83	29	ceggs	ceggs	NOUN
ejpam-6729	83	30	}	}	PUNCT
ejpam-6729	83	31	∈	∈	PROPN
ejpam-6729	83	32	p3(x	p3(x	PROPN
ejpam-6729	83	33	)	)	PUNCT
ejpam-6729	83	34	.	.	PUNCT
ejpam-6729	84	1	interpretation	interpretation	NOUN
ejpam-6729	84	2	.	.	PUNCT
ejpam-6729	85	1	•	•	NUM
ejpam-6729	85	2	level	level	NOUN
ejpam-6729	85	3	1	1	NUM
ejpam-6729	85	4	(	(	PUNCT
ejpam-6729	85	5	p1(x	p1(x	NOUN
ejpam-6729	85	6	)	)	PUNCT
ejpam-6729	85	7	)	)	PUNCT
ejpam-6729	85	8	supports	support	VERB
ejpam-6729	85	9	traditional	traditional	ADJ
ejpam-6729	85	10	frequent	frequent	ADJ
ejpam-6729	85	11	-	-	PUNCT
ejpam-6729	85	12	itemset	itemset	NOUN
ejpam-6729	85	13	mining	mining	NOUN
ejpam-6729	85	14	.	.	PUNCT
ejpam-6729	86	1	•	•	NUM
ejpam-6729	86	2	level	level	NOUN
ejpam-6729	86	3	2	2	NUM
ejpam-6729	86	4	(	(	PUNCT
ejpam-6729	86	5	p2(x	p2(x	NOUN
ejpam-6729	86	6	)	)	PUNCT
ejpam-6729	86	7	)	)	PUNCT
ejpam-6729	86	8	enables	enable	VERB
ejpam-6729	86	9	discovery	discovery	NOUN
ejpam-6729	86	10	of	of	ADP
ejpam-6729	86	11	correlated	correlate	VERB
ejpam-6729	86	12	patterns	pattern	NOUN
ejpam-6729	86	13	,	,	PUNCT
ejpam-6729	86	14	such	such	ADJ
ejpam-6729	86	15	as	as	ADP
ejpam-6729	86	16	sets	set	NOUN
ejpam-6729	86	17	of	of	ADP
ejpam-6729	86	18	itemsets	itemset	NOUN
ejpam-6729	86	19	that	that	PRON
ejpam-6729	86	20	often	often	ADV
ejpam-6729	86	21	appear	appear	VERB
ejpam-6729	86	22	together	together	ADV
ejpam-6729	86	23	across	across	ADP
ejpam-6729	86	24	many	many	ADJ
ejpam-6729	86	25	market	market	NOUN
ejpam-6729	86	26	segments	segment	NOUN
ejpam-6729	86	27	.	.	PUNCT
ejpam-6729	87	1	•	•	NUM
ejpam-6729	87	2	level	level	NOUN
ejpam-6729	87	3	3	3	NUM
ejpam-6729	87	4	(	(	PUNCT
ejpam-6729	87	5	p3(x	p3(x	NOUN
ejpam-6729	87	6	)	)	PUNCT
ejpam-6729	87	7	)	)	PUNCT
ejpam-6729	87	8	facilitates	facilitate	VERB
ejpam-6729	87	9	higher	high	ADJ
ejpam-6729	87	10	-	-	PUNCT
ejpam-6729	87	11	order	order	NOUN
ejpam-6729	87	12	reasoning	reasoning	NOUN
ejpam-6729	87	13	,	,	PUNCT
ejpam-6729	87	14	e.g.	e.g.	ADV
ejpam-6729	87	15	comparing	compare	VERB
ejpam-6729	87	16	entire	entire	ADJ
ejpam-6729	87	17	pattern	pattern	NOUN
ejpam-6729	87	18	families	family	NOUN
ejpam-6729	87	19	between	between	ADP
ejpam-6729	87	20	different	different	ADJ
ejpam-6729	87	21	seasons	season	NOUN
ejpam-6729	87	22	or	or	CCONJ
ejpam-6729	87	23	geographical	geographical	ADJ
ejpam-6729	87	24	regions	region	NOUN
ejpam-6729	87	25	.	.	PUNCT
ejpam-6729	88	1	t.	t.	PROPN
ejpam-6729	88	2	fujita	fujita	PROPN
ejpam-6729	88	3	,	,	PUNCT
ejpam-6729	88	4	f.	f.	PROPN
ejpam-6729	88	5	smarandache	smarandache	PROPN
ejpam-6729	88	6	/	/	SYM
ejpam-6729	88	7	eur	eur	PROPN
ejpam-6729	88	8	.	.	PUNCT
ejpam-6729	89	1	j.	j.	PROPN
ejpam-6729	89	2	pure	pure	PROPN
ejpam-6729	89	3	appl	appl	PROPN
ejpam-6729	89	4	.	.	PROPN
ejpam-6729	89	5	math	math	PROPN
ejpam-6729	89	6	,	,	PUNCT
ejpam-6729	89	7	18	18	NUM
ejpam-6729	89	8	(	(	PUNCT
ejpam-6729	89	9	4	4	NUM
ejpam-6729	89	10	)	)	PUNCT
ejpam-6729	89	11	(	(	PUNCT
ejpam-6729	89	12	2025	2025	NUM
ejpam-6729	89	13	)	)	PUNCT
ejpam-6729	89	14	,	,	PUNCT
ejpam-6729	89	15	6729	6729	NUM
ejpam-6729	89	16	5	5	NUM
ejpam-6729	89	17	of	of	ADP
ejpam-6729	89	18	36	36	NUM
ejpam-6729	89	19	in	in	ADP
ejpam-6729	89	20	practical	practical	ADJ
ejpam-6729	89	21	pipelines	pipeline	NOUN
ejpam-6729	89	22	,	,	PUNCT
ejpam-6729	89	23	each	each	DET
ejpam-6729	89	24	higher	high	ADJ
ejpam-6729	89	25	powerset	powerset	NOUN
ejpam-6729	89	26	serves	serve	VERB
ejpam-6729	89	27	as	as	ADP
ejpam-6729	89	28	the	the	DET
ejpam-6729	89	29	search	search	NOUN
ejpam-6729	89	30	space	space	NOUN
ejpam-6729	89	31	for	for	ADP
ejpam-6729	89	32	progressively	progressively	ADV
ejpam-6729	89	33	more	more	ADJ
ejpam-6729	89	34	abstract	abstract	ADJ
ejpam-6729	89	35	data	data	NOUN
ejpam-6729	89	36	-	-	PUNCT
ejpam-6729	89	37	mining	mining	NOUN
ejpam-6729	89	38	tasks	task	NOUN
ejpam-6729	89	39	:	:	PUNCT
ejpam-6729	89	40	association	association	NOUN
ejpam-6729	89	41	-	-	PUNCT
ejpam-6729	89	42	rule	rule	NOUN
ejpam-6729	89	43	discovery	discovery	NOUN
ejpam-6729	89	44	at	at	ADP
ejpam-6729	89	45	level	level	NOUN
ejpam-6729	89	46	1	1	NUM
ejpam-6729	89	47	,	,	PUNCT
ejpam-6729	89	48	pattern	pattern	NOUN
ejpam-6729	89	49	clustering	cluster	VERB
ejpam-6729	89	50	at	at	ADP
ejpam-6729	89	51	level	level	NOUN
ejpam-6729	89	52	2	2	NUM
ejpam-6729	89	53	,	,	PUNCT
ejpam-6729	89	54	and	and	CCONJ
ejpam-6729	89	55	meta	meta	ADJ
ejpam-6729	89	56	-	-	PUNCT
ejpam-6729	89	57	pattern	pattern	NOUN
ejpam-6729	89	58	comparison	comparison	NOUN
ejpam-6729	89	59	or	or	CCONJ
ejpam-6729	89	60	visual	visual	ADJ
ejpam-6729	89	61	analytics	analytic	NOUN
ejpam-6729	89	62	at	at	ADP
ejpam-6729	89	63	level	level	NOUN
ejpam-6729	89	64	3	3	NUM
ejpam-6729	89	65	and	and	CCONJ
ejpam-6729	89	66	beyond	beyond	ADP
ejpam-6729	89	67	.	.	PUNCT
ejpam-6729	90	1	definition	definition	NOUN
ejpam-6729	90	2	5	5	NUM
ejpam-6729	90	3	(	(	PUNCT
ejpam-6729	90	4	n	n	CCONJ
ejpam-6729	90	5	-	-	PUNCT
ejpam-6729	90	6	superhypergraph	superhypergraph	NOUN
ejpam-6729	90	7	)	)	PUNCT
ejpam-6729	90	8	.	.	PUNCT
ejpam-6729	91	1	(	(	PUNCT
ejpam-6729	91	2	cf	cf	NOUN
ejpam-6729	91	3	.	.	PUNCT
ejpam-6729	92	1	[	[	X
ejpam-6729	92	2	13	13	NUM
ejpam-6729	92	3	]	]	PUNCT
ejpam-6729	92	4	)	)	PUNCT
ejpam-6729	92	5	fix	fix	VERB
ejpam-6729	92	6	a	a	DET
ejpam-6729	92	7	finite	finite	NOUN
ejpam-6729	92	8	,	,	PUNCT
ejpam-6729	92	9	nonempty	nonempty	ADJ
ejpam-6729	92	10	base	base	NOUN
ejpam-6729	92	11	set	set	VERB
ejpam-6729	92	12	v0	v0	NOUN
ejpam-6729	92	13	and	and	CCONJ
ejpam-6729	92	14	define	define	VERB
ejpam-6729	92	15	the	the	DET
ejpam-6729	92	16	iterated	iterated	ADJ
ejpam-6729	92	17	powerset	powerset	NOUN
ejpam-6729	92	18	by	by	ADP
ejpam-6729	92	19	p0(v0	p0(v0	VERB
ejpam-6729	92	20	)	)	PUNCT
ejpam-6729	92	21	:	:	PUNCT
ejpam-6729	92	22	=	=	SYM
ejpam-6729	92	23	v0	v0	PROPN
ejpam-6729	92	24	,	,	PUNCT
ejpam-6729	92	25	pk+1(v0	pk+1(v0	NUM
ejpam-6729	92	26	)	)	PUNCT
ejpam-6729	92	27	:	:	PUNCT
ejpam-6729	93	1	=	=	SYM
ejpam-6729	93	2	p	p	X
ejpam-6729	93	3	(	(	PUNCT
ejpam-6729	93	4	pk(v0	pk(v0	PROPN
ejpam-6729	93	5	)	)	PUNCT
ejpam-6729	93	6	)	)	PUNCT
ejpam-6729	94	1	(	(	PUNCT
ejpam-6729	94	2	k	k	PROPN
ejpam-6729	94	3	∈	∈	PROPN
ejpam-6729	94	4	n	n	CCONJ
ejpam-6729	94	5	)	)	PUNCT
ejpam-6729	94	6	.	.	PUNCT
ejpam-6729	95	1	for	for	ADP
ejpam-6729	95	2	an	an	DET
ejpam-6729	95	3	integer	integer	NOUN
ejpam-6729	95	4	n	n	PRON
ejpam-6729	95	5	≥	≥	NOUN
ejpam-6729	95	6	0	0	NUM
ejpam-6729	95	7	,	,	PUNCT
ejpam-6729	95	8	an	an	DET
ejpam-6729	95	9	n	n	NOUN
ejpam-6729	95	10	-	-	PUNCT
ejpam-6729	95	11	superhypergraph	superhypergraph	NOUN
ejpam-6729	95	12	on	on	ADP
ejpam-6729	95	13	v0	v0	NOUN
ejpam-6729	95	14	is	be	AUX
ejpam-6729	95	15	a	a	DET
ejpam-6729	95	16	pair	pair	NOUN
ejpam-6729	95	17	shg(n	shg(n	PROPN
ejpam-6729	95	18	)	)	PUNCT
ejpam-6729	95	19	=	=	SYM
ejpam-6729	95	20	(	(	PUNCT
ejpam-6729	95	21	v	v	NOUN
ejpam-6729	95	22	,	,	PUNCT
ejpam-6729	95	23	e	e	NOUN
ejpam-6729	95	24	)	)	PUNCT
ejpam-6729	95	25	such	such	ADJ
ejpam-6729	95	26	that	that	SCONJ
ejpam-6729	95	27	v	v	ADP
ejpam-6729	95	28	⊆	⊆	NUM
ejpam-6729	95	29	pn(v0	pn(v0	NOUN
ejpam-6729	95	30	)	)	PUNCT
ejpam-6729	95	31	and	and	CCONJ
ejpam-6729	95	32	e	e	X
ejpam-6729	95	33	⊆	⊆	NUM
ejpam-6729	95	34	p(v	p(v	NOUN
ejpam-6729	95	35	)	)	PUNCT
ejpam-6729	95	36	\	\	NOUN
ejpam-6729	95	37	{	{	PUNCT
ejpam-6729	95	38	∅	∅	NOUN
ejpam-6729	95	39	}	}	PUNCT
ejpam-6729	95	40	.	.	PUNCT
ejpam-6729	96	1	elements	element	NOUN
ejpam-6729	96	2	of	of	ADP
ejpam-6729	96	3	v	v	NOUN
ejpam-6729	96	4	are	be	AUX
ejpam-6729	96	5	called	call	VERB
ejpam-6729	96	6	n	n	CCONJ
ejpam-6729	96	7	-	-	PUNCT
ejpam-6729	96	8	supervertices	supervertice	NOUN
ejpam-6729	96	9	and	and	CCONJ
ejpam-6729	96	10	elements	element	NOUN
ejpam-6729	96	11	of	of	ADP
ejpam-6729	96	12	e	e	NOUN
ejpam-6729	96	13	are	be	AUX
ejpam-6729	96	14	n	n	PRON
ejpam-6729	96	15	-	-	PUNCT
ejpam-6729	96	16	superedges	superedge	NOUN
ejpam-6729	96	17	.	.	PUNCT
ejpam-6729	97	1	(	(	PUNCT
ejpam-6729	97	2	in	in	ADP
ejpam-6729	97	3	particular	particular	ADJ
ejpam-6729	97	4	,	,	PUNCT
ejpam-6729	97	5	each	each	DET
ejpam-6729	97	6	n	n	NOUN
ejpam-6729	97	7	-	-	PUNCT
ejpam-6729	97	8	superedge	superedge	NOUN
ejpam-6729	97	9	is	be	AUX
ejpam-6729	97	10	a	a	DET
ejpam-6729	97	11	nonempty	nonempty	ADJ
ejpam-6729	97	12	subset	subset	NOUN
ejpam-6729	97	13	of	of	ADP
ejpam-6729	97	14	v	v	NOUN
ejpam-6729	97	15	.	.	PUNCT
ejpam-6729	97	16	)	)	PUNCT
ejpam-6729	98	1	table	table	NOUN
ejpam-6729	98	2	1	1	NUM
ejpam-6729	98	3	provides	provide	VERB
ejpam-6729	98	4	a	a	DET
ejpam-6729	98	5	concise	concise	ADJ
ejpam-6729	98	6	overview	overview	NOUN
ejpam-6729	98	7	of	of	ADP
ejpam-6729	98	8	graphs	graph	NOUN
ejpam-6729	98	9	,	,	PUNCT
ejpam-6729	98	10	hypergraphs	hypergraph	NOUN
ejpam-6729	98	11	,	,	PUNCT
ejpam-6729	98	12	and	and	CCONJ
ejpam-6729	98	13	n	n	CCONJ
ejpam-6729	98	14	-	-	PUNCT
ejpam-6729	98	15	superhypergraphs	superhypergraph	NOUN
ejpam-6729	98	16	.	.	PUNCT
ejpam-6729	99	1	in	in	ADP
ejpam-6729	99	2	particular	particular	ADJ
ejpam-6729	99	3	,	,	PUNCT
ejpam-6729	99	4	superhypergraphs	superhypergraph	NOUN
ejpam-6729	99	5	are	be	AUX
ejpam-6729	99	6	expected	expect	VERB
ejpam-6729	99	7	to	to	PART
ejpam-6729	99	8	offer	offer	VERB
ejpam-6729	99	9	an	an	DET
ejpam-6729	99	10	intuitive	intuitive	ADJ
ejpam-6729	99	11	way	way	NOUN
ejpam-6729	99	12	to	to	PART
ejpam-6729	99	13	represent	represent	VERB
ejpam-6729	99	14	hierarchical	hierarchical	ADJ
ejpam-6729	99	15	network	network	NOUN
ejpam-6729	99	16	structures	structure	NOUN
ejpam-6729	99	17	that	that	PRON
ejpam-6729	99	18	commonly	commonly	ADV
ejpam-6729	99	19	arise	arise	VERB
ejpam-6729	99	20	in	in	ADP
ejpam-6729	99	21	real	real	ADJ
ejpam-6729	99	22	-	-	PUNCT
ejpam-6729	99	23	world	world	NOUN
ejpam-6729	99	24	systems	system	NOUN
ejpam-6729	99	25	.	.	PUNCT
ejpam-6729	100	1	table	table	NOUN
ejpam-6729	100	2	1	1	NUM
ejpam-6729	100	3	:	:	PUNCT
ejpam-6729	100	4	concise	concise	ADJ
ejpam-6729	100	5	overview	overview	NOUN
ejpam-6729	100	6	of	of	ADP
ejpam-6729	100	7	graph	graph	NOUN
ejpam-6729	100	8	,	,	PUNCT
ejpam-6729	100	9	hypergraph	hypergraph	VERB
ejpam-6729	100	10	,	,	PUNCT
ejpam-6729	100	11	and	and	CCONJ
ejpam-6729	100	12	n	n	CCONJ
ejpam-6729	100	13	-	-	PUNCT
ejpam-6729	100	14	superhypergraph	superhypergraph	NOUN
ejpam-6729	100	15	.	.	PUNCT
ejpam-6729	101	1	model	model	NOUN
ejpam-6729	101	2	vertices	vertice	VERB
ejpam-6729	101	3	edges	edge	NOUN
ejpam-6729	101	4	notes	note	NOUN
ejpam-6729	101	5	graph	graph	VERB
ejpam-6729	101	6	v	v	NOUN
ejpam-6729	101	7	(	(	PUNCT
ejpam-6729	101	8	finite	finite	PROPN
ejpam-6729	101	9	)	)	PUNCT
ejpam-6729	101	10	e	e	NOUN
ejpam-6729	102	1	⊆	⊆	NUM
ejpam-6729	102	2	v	v	NUM
ejpam-6729	102	3	×	×	NOUN
ejpam-6729	102	4	v	v	NOUN
ejpam-6729	102	5	or	or	CCONJ
ejpam-6729	102	6	e	e	NOUN
ejpam-6729	102	7	=	=	NOUN
ejpam-6729	102	8	{	{	PUNCT
ejpam-6729	102	9	{	{	PUNCT
ejpam-6729	102	10	u	u	NOUN
ejpam-6729	102	11	,	,	PUNCT
ejpam-6729	102	12	v	v	NOUN
ejpam-6729	102	13	}	}	PUNCT
ejpam-6729	102	14	}	}	PUNCT
ejpam-6729	102	15	each	each	DET
ejpam-6729	102	16	edge	edge	NOUN
ejpam-6729	102	17	links	link	NOUN
ejpam-6729	102	18	exactly	exactly	ADV
ejpam-6729	102	19	two	two	NUM
ejpam-6729	102	20	vertices	vertex	NOUN
ejpam-6729	102	21	;	;	PUNCT
ejpam-6729	102	22	captures	capture	VERB
ejpam-6729	102	23	pairwise	pairwise	NOUN
ejpam-6729	102	24	relations	relation	NOUN
ejpam-6729	102	25	.	.	PUNCT
ejpam-6729	103	1	hypergraph	hypergraph	VERB
ejpam-6729	103	2	v	v	NOUN
ejpam-6729	103	3	(	(	PUNCT
ejpam-6729	103	4	finite	finite	PROPN
ejpam-6729	103	5	)	)	PUNCT
ejpam-6729	103	6	e	e	NOUN
ejpam-6729	103	7	⊆	⊆	NUM
ejpam-6729	103	8	p(v	p(v	NOUN
ejpam-6729	103	9	)	)	PUNCT
ejpam-6729	103	10	\	\	NOUN
ejpam-6729	103	11	{	{	PUNCT
ejpam-6729	103	12	∅	∅	NOUN
ejpam-6729	103	13	}	}	PUNCT
ejpam-6729	103	14	hyperedges	hyperedge	NOUN
ejpam-6729	103	15	connect	connect	VERB
ejpam-6729	103	16	arbitrary	arbitrary	ADJ
ejpam-6729	103	17	nonempty	nonempty	ADJ
ejpam-6729	103	18	subsets	subset	NOUN
ejpam-6729	103	19	of	of	ADP
ejpam-6729	103	20	vertices	vertex	NOUN
ejpam-6729	103	21	.	.	PUNCT
ejpam-6729	104	1	n	n	CCONJ
ejpam-6729	104	2	-	-	PUNCT
ejpam-6729	104	3	superhypergraph	superhypergraph	NOUN
ejpam-6729	104	4	v	v	ADP
ejpam-6729	104	5	⊆	⊆	NUM
ejpam-6729	104	6	pn(v0	pn(v0	NUM
ejpam-6729	104	7	)	)	PUNCT
ejpam-6729	104	8	e	e	PROPN
ejpam-6729	104	9	⊆	⊆	NUM
ejpam-6729	104	10	p(v	p(v	NOUN
ejpam-6729	104	11	)	)	PUNCT
ejpam-6729	104	12	\	\	NOUN
ejpam-6729	104	13	{	{	PUNCT
ejpam-6729	104	14	∅	∅	NOUN
ejpam-6729	104	15	}	}	PUNCT
ejpam-6729	104	16	vertices	vertex	NOUN
ejpam-6729	104	17	lie	lie	NOUN
ejpam-6729	104	18	at	at	ADP
ejpam-6729	104	19	level	level	NOUN
ejpam-6729	104	20	n	n	CCONJ
ejpam-6729	104	21	(	(	PUNCT
ejpam-6729	104	22	iterated	iterated	ADJ
ejpam-6729	104	23	powerset	powerset	NOUN
ejpam-6729	104	24	)	)	PUNCT
ejpam-6729	104	25	;	;	PUNCT
ejpam-6729	105	1	edges	edge	NOUN
ejpam-6729	105	2	link	link	NOUN
ejpam-6729	105	3	level	level	NOUN
ejpam-6729	105	4	-	-	PUNCT
ejpam-6729	105	5	n	n	NOUN
ejpam-6729	105	6	vertices	vertex	NOUN
ejpam-6729	105	7	in	in	ADP
ejpam-6729	105	8	hierarchical	hierarchical	ADJ
ejpam-6729	105	9	groupings	grouping	NOUN
ejpam-6729	105	10	.	.	PUNCT
ejpam-6729	106	1	several	several	ADJ
ejpam-6729	106	2	concrete	concrete	ADJ
ejpam-6729	106	3	examples	example	NOUN
ejpam-6729	106	4	of	of	ADP
ejpam-6729	106	5	superhypergraphs	superhypergraph	NOUN
ejpam-6729	106	6	are	be	AUX
ejpam-6729	106	7	presented	present	VERB
ejpam-6729	106	8	below	below	ADV
ejpam-6729	106	9	.	.	PUNCT
ejpam-6729	107	1	example	example	NOUN
ejpam-6729	107	2	3	3	NUM
ejpam-6729	107	3	(	(	PUNCT
ejpam-6729	107	4	a	a	DET
ejpam-6729	107	5	2	2	NUM
ejpam-6729	107	6	-	-	PUNCT
ejpam-6729	107	7	superhypergraph	superhypergraph	NOUN
ejpam-6729	107	8	for	for	ADP
ejpam-6729	107	9	market	market	NOUN
ejpam-6729	107	10	-	-	PUNCT
ejpam-6729	107	11	basket	basket	NOUN
ejpam-6729	107	12	data	datum	NOUN
ejpam-6729	107	13	mining	mining	NOUN
ejpam-6729	107	14	)	)	PUNCT
ejpam-6729	107	15	.	.	PUNCT
ejpam-6729	108	1	we	we	PRON
ejpam-6729	108	2	show	show	VERB
ejpam-6729	108	3	that	that	SCONJ
ejpam-6729	108	4	a	a	DET
ejpam-6729	108	5	toy	toy	NOUN
ejpam-6729	108	6	transaction	transaction	NOUN
ejpam-6729	108	7	dataset	dataset	VERB
ejpam-6729	108	8	naturally	naturally	ADV
ejpam-6729	108	9	forms	form	VERB
ejpam-6729	108	10	a	a	DET
ejpam-6729	108	11	2	2	NUM
ejpam-6729	108	12	-	-	PUNCT
ejpam-6729	108	13	superhypergraph	superhypergraph	NOUN
ejpam-6729	108	14	shg(2	shg(2	NOUN
ejpam-6729	108	15	)	)	PUNCT
ejpam-6729	109	1	=	=	PRON
ejpam-6729	109	2	(	(	PUNCT
ejpam-6729	109	3	v	v	NOUN
ejpam-6729	109	4	,	,	PUNCT
ejpam-6729	109	5	e	e	NOUN
ejpam-6729	109	6	)	)	PUNCT
ejpam-6729	109	7	in	in	ADP
ejpam-6729	109	8	the	the	DET
ejpam-6729	109	9	sense	sense	NOUN
ejpam-6729	109	10	of	of	ADP
ejpam-6729	109	11	definition	definition	NOUN
ejpam-6729	109	12	5	5	NUM
ejpam-6729	109	13	.	.	PUNCT
ejpam-6729	110	1	step	step	NOUN
ejpam-6729	110	2	0	0	NUM
ejpam-6729	111	1	(	(	PUNCT
ejpam-6729	111	2	base	base	NOUN
ejpam-6729	111	3	set	set	NOUN
ejpam-6729	111	4	of	of	ADP
ejpam-6729	111	5	items	item	NOUN
ejpam-6729	111	6	)	)	PUNCT
ejpam-6729	111	7	.	.	PUNCT
ejpam-6729	112	1	let	let	VERB
ejpam-6729	112	2	v0	v0	NOUN
ejpam-6729	112	3	=	=	SYM
ejpam-6729	112	4	{	{	PUNCT
ejpam-6729	112	5	a	a	PRON
ejpam-6729	112	6	,	,	PUNCT
ejpam-6729	112	7	b	b	NOUN
ejpam-6729	112	8	,	,	PUNCT
ejpam-6729	112	9	c	c	X
ejpam-6729	112	10	,	,	PUNCT
ejpam-6729	112	11	d	d	NOUN
ejpam-6729	112	12	}	}	PUNCT
ejpam-6729	112	13	=	=	SYM
ejpam-6729	112	14	{	{	PUNCT
ejpam-6729	112	15	bread	bread	NOUN
ejpam-6729	112	16	,	,	PUNCT
ejpam-6729	112	17	milk	milk	NOUN
ejpam-6729	112	18	,	,	PUNCT
ejpam-6729	112	19	eggs	egg	NOUN
ejpam-6729	112	20	,	,	PUNCT
ejpam-6729	112	21	butter	butter	NOUN
ejpam-6729	112	22	}	}	PUNCT
ejpam-6729	112	23	.	.	PUNCT
ejpam-6729	113	1	t.	t.	PROPN
ejpam-6729	113	2	fujita	fujita	PROPN
ejpam-6729	113	3	,	,	PUNCT
ejpam-6729	113	4	f.	f.	PROPN
ejpam-6729	113	5	smarandache	smarandache	PROPN
ejpam-6729	113	6	/	/	SYM
ejpam-6729	113	7	eur	eur	PROPN
ejpam-6729	113	8	.	.	PUNCT
ejpam-6729	114	1	j.	j.	PROPN
ejpam-6729	114	2	pure	pure	PROPN
ejpam-6729	114	3	appl	appl	PROPN
ejpam-6729	114	4	.	.	PROPN
ejpam-6729	114	5	math	math	PROPN
ejpam-6729	114	6	,	,	PUNCT
ejpam-6729	114	7	18	18	NUM
ejpam-6729	114	8	(	(	PUNCT
ejpam-6729	114	9	4	4	NUM
ejpam-6729	114	10	)	)	PUNCT
ejpam-6729	114	11	(	(	PUNCT
ejpam-6729	114	12	2025	2025	NUM
ejpam-6729	114	13	)	)	PUNCT
ejpam-6729	114	14	,	,	PUNCT
ejpam-6729	114	15	6729	6729	NUM
ejpam-6729	114	16	6	6	NUM
ejpam-6729	114	17	of	of	ADP
ejpam-6729	114	18	36	36	NUM
ejpam-6729	114	19	step	step	NOUN
ejpam-6729	114	20	1	1	NUM
ejpam-6729	114	21	(	(	PUNCT
ejpam-6729	114	22	transactions	transaction	NOUN
ejpam-6729	114	23	as	as	ADP
ejpam-6729	114	24	1	1	NUM
ejpam-6729	114	25	-	-	PUNCT
ejpam-6729	114	26	supervertices	supervertice	NOUN
ejpam-6729	114	27	)	)	PUNCT
ejpam-6729	114	28	.	.	PUNCT
ejpam-6729	115	1	transactions	transaction	NOUN
ejpam-6729	115	2	are	be	AUX
ejpam-6729	115	3	subsets	subset	NOUN
ejpam-6729	115	4	of	of	ADP
ejpam-6729	115	5	v0	v0	NOUN
ejpam-6729	115	6	,	,	PUNCT
ejpam-6729	115	7	hence	hence	ADV
ejpam-6729	115	8	elements	element	NOUN
ejpam-6729	115	9	of	of	ADP
ejpam-6729	115	10	p1(v0	p1(v0	PROPN
ejpam-6729	115	11	)	)	PUNCT
ejpam-6729	115	12	=	=	PRON
ejpam-6729	115	13	p(v0	p(v0	NOUN
ejpam-6729	115	14	)	)	PUNCT
ejpam-6729	115	15	.	.	PUNCT
ejpam-6729	116	1	fix	fix	VERB
ejpam-6729	116	2	four	four	NUM
ejpam-6729	116	3	transactions	transaction	NOUN
ejpam-6729	116	4	t1	t1	NOUN
ejpam-6729	116	5	=	=	PUNCT
ejpam-6729	116	6	{	{	PUNCT
ejpam-6729	116	7	a	a	DET
ejpam-6729	116	8	,	,	PUNCT
ejpam-6729	116	9	b	b	NOUN
ejpam-6729	116	10	}	}	PUNCT
ejpam-6729	116	11	,	,	PUNCT
ejpam-6729	116	12	t2	t2	NOUN
ejpam-6729	116	13	=	=	SYM
ejpam-6729	116	14	{	{	PUNCT
ejpam-6729	116	15	b	b	PROPN
ejpam-6729	116	16	,	,	PUNCT
ejpam-6729	116	17	c	c	X
ejpam-6729	116	18	,	,	PUNCT
ejpam-6729	116	19	d	d	NOUN
ejpam-6729	116	20	}	}	PUNCT
ejpam-6729	116	21	,	,	PUNCT
ejpam-6729	116	22	t3	t3	PROPN
ejpam-6729	116	23	=	=	PUNCT
ejpam-6729	116	24	{	{	PUNCT
ejpam-6729	116	25	a	a	X
ejpam-6729	116	26	,	,	PUNCT
ejpam-6729	116	27	c	c	NOUN
ejpam-6729	116	28	,	,	PUNCT
ejpam-6729	116	29	d	d	NOUN
ejpam-6729	116	30	}	}	PUNCT
ejpam-6729	116	31	,	,	PUNCT
ejpam-6729	116	32	t4	t4	PROPN
ejpam-6729	116	33	=	=	PROPN
ejpam-6729	116	34	{	{	PUNCT
ejpam-6729	116	35	a	a	PRON
ejpam-6729	116	36	,	,	PUNCT
ejpam-6729	116	37	b	b	NOUN
ejpam-6729	116	38	,	,	PUNCT
ejpam-6729	116	39	d	d	NOUN
ejpam-6729	116	40	}	}	PUNCT
ejpam-6729	116	41	∈	∈	PROPN
ejpam-6729	116	42	p1(v0	p1(v0	PROPN
ejpam-6729	116	43	)	)	PUNCT
ejpam-6729	116	44	.	.	PUNCT
ejpam-6729	117	1	step	step	NOUN
ejpam-6729	117	2	2	2	NUM
ejpam-6729	117	3	(	(	PUNCT
ejpam-6729	117	4	pattern	pattern	NOUN
ejpam-6729	117	5	groups	group	NOUN
ejpam-6729	117	6	as	as	ADP
ejpam-6729	117	7	2	2	NUM
ejpam-6729	117	8	-	-	PUNCT
ejpam-6729	117	9	supervertices	supervertice	NOUN
ejpam-6729	117	10	)	)	PUNCT
ejpam-6729	117	11	.	.	PUNCT
ejpam-6729	118	1	sets	set	NOUN
ejpam-6729	118	2	of	of	ADP
ejpam-6729	118	3	transactions	transaction	NOUN
ejpam-6729	118	4	lie	lie	VERB
ejpam-6729	118	5	in	in	ADP
ejpam-6729	118	6	p2(v0	p2(v0	PROPN
ejpam-6729	118	7	)	)	PUNCT
ejpam-6729	118	8	=	=	SYM
ejpam-6729	119	1	p	p	NOUN
ejpam-6729	119	2	(	(	PUNCT
ejpam-6729	119	3	p(v0	p(v0	NOUN
ejpam-6729	119	4	)	)	PUNCT
ejpam-6729	119	5	)	)	PUNCT
ejpam-6729	119	6	.	.	PUNCT
ejpam-6729	120	1	define	define	VERB
ejpam-6729	120	2	g1	g1	PROPN
ejpam-6729	120	3	=	=	SYM
ejpam-6729	120	4	{	{	PUNCT
ejpam-6729	120	5	t1	t1	PROPN
ejpam-6729	120	6	,	,	PUNCT
ejpam-6729	120	7	t4	t4	PROPN
ejpam-6729	120	8	}	}	PUNCT
ejpam-6729	120	9	,	,	PUNCT
ejpam-6729	120	10	g2	g2	PROPN
ejpam-6729	120	11	=	=	PUNCT
ejpam-6729	120	12	{	{	PUNCT
ejpam-6729	120	13	t2	t2	PROPN
ejpam-6729	120	14	,	,	PUNCT
ejpam-6729	120	15	t3	t3	NOUN
ejpam-6729	120	16	}	}	PUNCT
ejpam-6729	120	17	,	,	PUNCT
ejpam-6729	120	18	g3	g3	NOUN
ejpam-6729	120	19	=	=	SYM
ejpam-6729	120	20	{	{	PUNCT
ejpam-6729	120	21	t2	t2	PROPN
ejpam-6729	120	22	,	,	PUNCT
ejpam-6729	120	23	t3	t3	PROPN
ejpam-6729	120	24	,	,	PUNCT
ejpam-6729	120	25	t4	t4	PROPN
ejpam-6729	120	26	}	}	PUNCT
ejpam-6729	120	27	,	,	PUNCT
ejpam-6729	120	28	and	and	CCONJ
ejpam-6729	120	29	set	set	VERB
ejpam-6729	120	30	v	v	NOUN
ejpam-6729	120	31	:	:	PUNCT
ejpam-6729	120	32	=	=	SYM
ejpam-6729	120	33	{	{	PUNCT
ejpam-6729	120	34	g1	g1	PROPN
ejpam-6729	120	35	,	,	PUNCT
ejpam-6729	120	36	g2	g2	PROPN
ejpam-6729	120	37	,	,	PUNCT
ejpam-6729	120	38	g3	g3	PROPN
ejpam-6729	120	39	}	}	PUNCT
ejpam-6729	120	40	⊆	⊆	NUM
ejpam-6729	120	41	p2(v0	p2(v0	NOUN
ejpam-6729	120	42	)	)	PUNCT
ejpam-6729	120	43	.	.	PUNCT
ejpam-6729	121	1	interpretation	interpretation	NOUN
ejpam-6729	121	2	:	:	PUNCT
ejpam-6729	121	3	g1	g1	PROPN
ejpam-6729	121	4	collects	collect	VERB
ejpam-6729	121	5	baskets	basket	NOUN
ejpam-6729	121	6	with	with	ADP
ejpam-6729	121	7	{	{	PUNCT
ejpam-6729	121	8	a	a	DET
ejpam-6729	121	9	,	,	PUNCT
ejpam-6729	121	10	b	b	NOUN
ejpam-6729	121	11	}	}	PUNCT
ejpam-6729	121	12	;	;	PUNCT
ejpam-6729	121	13	g2	g2	PROPN
ejpam-6729	121	14	those	those	PRON
ejpam-6729	121	15	with	with	ADP
ejpam-6729	121	16	{	{	PUNCT
ejpam-6729	121	17	c	c	NOUN
ejpam-6729	121	18	,	,	PUNCT
ejpam-6729	121	19	d	d	NOUN
ejpam-6729	121	20	}	}	PUNCT
ejpam-6729	121	21	;	;	PUNCT
ejpam-6729	121	22	g3	g3	ADJ
ejpam-6729	121	23	those	those	PRON
ejpam-6729	121	24	with	with	ADP
ejpam-6729	121	25	d	d	PROPN
ejpam-6729	121	26	plus	plus	CCONJ
ejpam-6729	121	27	at	at	ADP
ejpam-6729	121	28	least	least	ADV
ejpam-6729	121	29	one	one	NUM
ejpam-6729	121	30	additional	additional	ADJ
ejpam-6729	121	31	item	item	NOUN
ejpam-6729	121	32	.	.	PUNCT
ejpam-6729	122	1	step	step	NOUN
ejpam-6729	122	2	3	3	NUM
ejpam-6729	122	3	(	(	PUNCT
ejpam-6729	122	4	2	2	NUM
ejpam-6729	122	5	-	-	PUNCT
ejpam-6729	122	6	superedges	superedge	NOUN
ejpam-6729	122	7	via	via	ADP
ejpam-6729	122	8	overlap	overlap	NOUN
ejpam-6729	122	9	of	of	ADP
ejpam-6729	122	10	pattern	pattern	NOUN
ejpam-6729	122	11	groups	group	NOUN
ejpam-6729	122	12	)	)	PUNCT
ejpam-6729	122	13	.	.	PUNCT
ejpam-6729	123	1	define	define	VERB
ejpam-6729	123	2	a	a	DET
ejpam-6729	123	3	symmetric	symmetric	ADJ
ejpam-6729	123	4	adjacency	adjacency	NOUN
ejpam-6729	123	5	on	on	ADP
ejpam-6729	123	6	v	v	NOUN
ejpam-6729	123	7	by	by	ADP
ejpam-6729	123	8	{	{	PUNCT
ejpam-6729	123	9	gi	gi	INTJ
ejpam-6729	123	10	,	,	PUNCT
ejpam-6729	123	11	gj	gj	NOUN
ejpam-6729	123	12	}	}	PUNCT
ejpam-6729	123	13	∈	∈	PROPN
ejpam-6729	123	14	e	e	X
ejpam-6729	123	15	⇐	⇐	ADJ
ejpam-6729	123	16	⇒	⇒	PROPN
ejpam-6729	123	17	i	i	PRON
ejpam-6729	123	18	6=	6=	PROPN
ejpam-6729	123	19	j	j	PROPN
ejpam-6729	123	20	and	and	CCONJ
ejpam-6729	123	21	gi	gi	VERB
ejpam-6729	123	22	∩gj	∩gj	NOUN
ejpam-6729	123	23	6=	6=	NOUN
ejpam-6729	123	24	∅	∅	NOUN
ejpam-6729	123	25	,	,	PUNCT
ejpam-6729	123	26	and	and	CCONJ
ejpam-6729	123	27	take	take	VERB
ejpam-6729	123	28	e	e	NOUN
ejpam-6729	123	29	=	=	PRON
ejpam-6729	123	30	{	{	PUNCT
ejpam-6729	123	31	{	{	PUNCT
ejpam-6729	123	32	g1	g1	PROPN
ejpam-6729	123	33	,	,	PUNCT
ejpam-6729	123	34	g3	g3	PROPN
ejpam-6729	123	35	}	}	PUNCT
ejpam-6729	123	36	,	,	PUNCT
ejpam-6729	123	37	{	{	PUNCT
ejpam-6729	123	38	g2	g2	PROPN
ejpam-6729	123	39	,	,	PUNCT
ejpam-6729	123	40	g3	g3	PROPN
ejpam-6729	123	41	}	}	PUNCT
ejpam-6729	123	42	}	}	PUNCT
ejpam-6729	123	43	⊆	⊆	NUM
ejpam-6729	123	44	p(v	p(v	NOUN
ejpam-6729	123	45	)	)	PUNCT
ejpam-6729	123	46	\	\	NOUN
ejpam-6729	123	47	{	{	PUNCT
ejpam-6729	123	48	∅	∅	NOUN
ejpam-6729	123	49	}	}	PUNCT
ejpam-6729	123	50	.	.	PUNCT
ejpam-6729	124	1	explicitly	explicitly	ADV
ejpam-6729	124	2	,	,	PUNCT
ejpam-6729	124	3	g1	g1	PROPN
ejpam-6729	124	4	∩g3	∩g3	PROPN
ejpam-6729	125	1	=	=	SYM
ejpam-6729	125	2	{	{	PUNCT
ejpam-6729	125	3	t4	t4	PROPN
ejpam-6729	125	4	}	}	PUNCT
ejpam-6729	125	5	6=	6=	ADP
ejpam-6729	125	6	∅	∅	NOUN
ejpam-6729	125	7	and	and	CCONJ
ejpam-6729	125	8	g2	g2	PROPN
ejpam-6729	125	9	∩g3	∩g3	PROPN
ejpam-6729	126	1	=	=	PRON
ejpam-6729	126	2	{	{	PUNCT
ejpam-6729	126	3	t2	t2	PROPN
ejpam-6729	126	4	,	,	PUNCT
ejpam-6729	126	5	t3	t3	PROPN
ejpam-6729	126	6	}	}	PUNCT
ejpam-6729	126	7	6=	6=	NUM
ejpam-6729	126	8	∅	∅	NOUN
ejpam-6729	126	9	,	,	PUNCT
ejpam-6729	126	10	while	while	SCONJ
ejpam-6729	126	11	g1	g1	PROPN
ejpam-6729	126	12	∩g2	∩g2	PROPN
ejpam-6729	126	13	=	=	PUNCT
ejpam-6729	126	14	∅.	∅.	VERB
ejpam-6729	126	15	each	each	DET
ejpam-6729	126	16	ti	ti	PROPN
ejpam-6729	126	17	⊆	⊆	NUM
ejpam-6729	126	18	v0	v0	NOUN
ejpam-6729	126	19	⇒	⇒	NOUN
ejpam-6729	126	20	ti	ti	PROPN
ejpam-6729	126	21	∈	∈	PROPN
ejpam-6729	126	22	p1(v0	p1(v0	PROPN
ejpam-6729	126	23	)	)	PUNCT
ejpam-6729	126	24	.	.	PUNCT
ejpam-6729	127	1	therefore	therefore	ADV
ejpam-6729	127	2	gj	gj	VERB
ejpam-6729	127	3	⊆	⊆	NUM
ejpam-6729	127	4	{	{	PUNCT
ejpam-6729	127	5	t1	t1	NOUN
ejpam-6729	127	6	,	,	PUNCT
ejpam-6729	127	7	t2	t2	NOUN
ejpam-6729	127	8	,	,	PUNCT
ejpam-6729	127	9	t3	t3	PROPN
ejpam-6729	127	10	,	,	PUNCT
ejpam-6729	127	11	t4	t4	PROPN
ejpam-6729	127	12	}	}	PUNCT
ejpam-6729	127	13	⇒	⇒	VERB
ejpam-6729	127	14	gj	gj	PROPN
ejpam-6729	127	15	∈	∈	PROPN
ejpam-6729	127	16	p2(v0	p2(v0	PROPN
ejpam-6729	127	17	)	)	PUNCT
ejpam-6729	127	18	.	.	PUNCT
ejpam-6729	128	1	thus	thus	ADV
ejpam-6729	128	2	v	v	ADP
ejpam-6729	128	3	⊆	⊆	NUM
ejpam-6729	128	4	p2(v0	p2(v0	NOUN
ejpam-6729	128	5	)	)	PUNCT
ejpam-6729	128	6	.	.	PUNCT
ejpam-6729	129	1	moreover	moreover	ADV
ejpam-6729	129	2	,	,	PUNCT
ejpam-6729	129	3	every	every	DET
ejpam-6729	129	4	listed	list	VERB
ejpam-6729	129	5	superedge	superedge	NOUN
ejpam-6729	129	6	is	be	AUX
ejpam-6729	129	7	a	a	DET
ejpam-6729	129	8	nonempty	nonempty	ADJ
ejpam-6729	129	9	subset	subset	NOUN
ejpam-6729	129	10	of	of	ADP
ejpam-6729	129	11	v	v	NOUN
ejpam-6729	129	12	,	,	PUNCT
ejpam-6729	129	13	so	so	CCONJ
ejpam-6729	129	14	e	e	NOUN
ejpam-6729	129	15	⊆	⊆	NUM
ejpam-6729	129	16	p(v	p(v	NOUN
ejpam-6729	129	17	)	)	PUNCT
ejpam-6729	129	18	\	\	NOUN
ejpam-6729	129	19	{	{	PUNCT
ejpam-6729	129	20	∅	∅	NOUN
ejpam-6729	129	21	}	}	PUNCT
ejpam-6729	129	22	.	.	PUNCT
ejpam-6729	130	1	hence	hence	ADV
ejpam-6729	130	2	shg(2	shg(2	NOUN
ejpam-6729	130	3	)	)	PUNCT
ejpam-6729	131	1	=	=	PUNCT
ejpam-6729	131	2	(	(	PUNCT
ejpam-6729	131	3	v	v	NOUN
ejpam-6729	131	4	,	,	PUNCT
ejpam-6729	131	5	e	e	NOUN
ejpam-6729	131	6	)	)	PUNCT
ejpam-6729	131	7	is	be	AUX
ejpam-6729	131	8	a	a	DET
ejpam-6729	131	9	valid	valid	ADJ
ejpam-6729	131	10	2	2	NUM
ejpam-6729	131	11	-	-	PUNCT
ejpam-6729	131	12	superhypergraph	superhypergraph	NOUN
ejpam-6729	131	13	.	.	PUNCT
ejpam-6729	132	1	use	use	NOUN
ejpam-6729	132	2	in	in	ADP
ejpam-6729	132	3	pattern	pattern	NOUN
ejpam-6729	132	4	mining	mining	NOUN
ejpam-6729	132	5	.	.	PUNCT
ejpam-6729	133	1	vertices	vertice	VERB
ejpam-6729	133	2	gj	gj	PROPN
ejpam-6729	133	3	encode	encode	ADJ
ejpam-6729	133	4	candidate	candidate	NOUN
ejpam-6729	133	5	frequent	frequent	ADJ
ejpam-6729	133	6	pattern	pattern	NOUN
ejpam-6729	133	7	groups	group	NOUN
ejpam-6729	133	8	;	;	PUNCT
ejpam-6729	133	9	edges	edge	NOUN
ejpam-6729	133	10	record	record	VERB
ejpam-6729	133	11	higher	high	ADJ
ejpam-6729	133	12	-	-	PUNCT
ejpam-6729	133	13	order	order	NOUN
ejpam-6729	133	14	overlaps	overlap	NOUN
ejpam-6729	133	15	among	among	ADP
ejpam-6729	133	16	these	these	DET
ejpam-6729	133	17	groups	group	NOUN
ejpam-6729	133	18	.	.	PUNCT
ejpam-6729	134	1	level	level	NOUN
ejpam-6729	134	2	-	-	PUNCT
ejpam-6729	134	3	wise	wise	ADJ
ejpam-6729	134	4	algorithms	algorithm	NOUN
ejpam-6729	134	5	(	(	PUNCT
ejpam-6729	134	6	e.g.	e.g.	ADV
ejpam-6729	134	7	apriori	apriori	PRON
ejpam-6729	134	8	)	)	PUNCT
ejpam-6729	134	9	may	may	AUX
ejpam-6729	134	10	operate	operate	VERB
ejpam-6729	134	11	on	on	ADP
ejpam-6729	134	12	shg(2	shg(2	NOUN
ejpam-6729	134	13	)	)	PUNCT
ejpam-6729	134	14	to	to	PART
ejpam-6729	134	15	prune	prune	VERB
ejpam-6729	134	16	infrequent	infrequent	ADJ
ejpam-6729	134	17	groups	group	NOUN
ejpam-6729	134	18	and	and	CCONJ
ejpam-6729	134	19	derive	derive	ADJ
ejpam-6729	134	20	rules	rule	NOUN
ejpam-6729	134	21	such	such	ADJ
ejpam-6729	134	22	as	as	ADP
ejpam-6729	134	23	{	{	PUNCT
ejpam-6729	134	24	a	a	PRON
ejpam-6729	134	25	,	,	PUNCT
ejpam-6729	134	26	b	b	NOUN
ejpam-6729	134	27	}	}	PUNCT
ejpam-6729	134	28	⇒	⇒	NOUN
ejpam-6729	135	1	d	d	NOUN
ejpam-6729	135	2	when	when	SCONJ
ejpam-6729	135	3	supported	support	VERB
ejpam-6729	135	4	by	by	ADP
ejpam-6729	135	5	the	the	DET
ejpam-6729	135	6	underlying	underlie	VERB
ejpam-6729	135	7	transactions	transaction	NOUN
ejpam-6729	135	8	(	(	PUNCT
ejpam-6729	135	9	e.g.	e.g.	ADV
ejpam-6729	135	10	via	via	ADP
ejpam-6729	135	11	the	the	DET
ejpam-6729	135	12	shared	share	VERB
ejpam-6729	135	13	transaction	transaction	NOUN
ejpam-6729	135	14	t4	t4	PROPN
ejpam-6729	135	15	)	)	PUNCT
ejpam-6729	135	16	.	.	PUNCT
ejpam-6729	136	1	example	example	NOUN
ejpam-6729	136	2	4	4	NUM
ejpam-6729	136	3	(	(	PUNCT
ejpam-6729	136	4	a	a	DET
ejpam-6729	136	5	3	3	NUM
ejpam-6729	136	6	-	-	PUNCT
ejpam-6729	136	7	superhypergraph	superhypergraph	NOUN
ejpam-6729	136	8	for	for	ADP
ejpam-6729	136	9	multi	multi	ADJ
ejpam-6729	136	10	-	-	ADJ
ejpam-6729	136	11	tier	tier	ADJ
ejpam-6729	136	12	database	database	NOUN
ejpam-6729	136	13	development	development	NOUN
ejpam-6729	136	14	)	)	PUNCT
ejpam-6729	136	15	.	.	PUNCT
ejpam-6729	137	1	we	we	PRON
ejpam-6729	137	2	model	model	VERB
ejpam-6729	137	3	columns	column	NOUN
ejpam-6729	137	4	,	,	PUNCT
ejpam-6729	137	5	tables	table	NOUN
ejpam-6729	137	6	,	,	PUNCT
ejpam-6729	137	7	logical	logical	ADJ
ejpam-6729	137	8	databases	database	NOUN
ejpam-6729	137	9	,	,	PUNCT
ejpam-6729	137	10	and	and	CCONJ
ejpam-6729	137	11	services	service	NOUN
ejpam-6729	137	12	at	at	ADP
ejpam-6729	137	13	successive	successive	ADJ
ejpam-6729	137	14	powerset	powerset	NOUN
ejpam-6729	137	15	levels	level	NOUN
ejpam-6729	137	16	.	.	PUNCT
ejpam-6729	138	1	step	step	NOUN
ejpam-6729	138	2	0	0	NUM
ejpam-6729	138	3	(	(	PUNCT
ejpam-6729	138	4	v0	v0	NOUN
ejpam-6729	138	5	:	:	PUNCT
ejpam-6729	138	6	atomic	atomic	ADJ
ejpam-6729	138	7	columns	column	NOUN
ejpam-6729	138	8	)	)	PUNCT
ejpam-6729	138	9	.	.	PUNCT
ejpam-6729	139	1	v0	v0	NOUN
ejpam-6729	139	2	=	=	SYM
ejpam-6729	139	3	{	{	PUNCT
ejpam-6729	139	4	userid	userid	NOUN
ejpam-6729	139	5	,	,	PUNCT
ejpam-6729	139	6	name	name	NOUN
ejpam-6729	139	7	,	,	PUNCT
ejpam-6729	139	8	email	email	NOUN
ejpam-6729	139	9	,	,	PUNCT
ejpam-6729	139	10	orderid	orderid	ADJ
ejpam-6729	139	11	,	,	PUNCT
ejpam-6729	139	12	orderdate	orderdate	NOUN
ejpam-6729	139	13	,	,	PUNCT
ejpam-6729	139	14	productid	productid	NOUN
ejpam-6729	139	15	,	,	PUNCT
ejpam-6729	139	16	quantity	quantity	NOUN
ejpam-6729	139	17	,	,	PUNCT
ejpam-6729	139	18	price	price	NOUN
ejpam-6729	139	19	}	}	PUNCT
ejpam-6729	139	20	.	.	PUNCT
ejpam-6729	140	1	step	step	NOUN
ejpam-6729	140	2	1	1	NUM
ejpam-6729	140	3	(	(	PUNCT
ejpam-6729	140	4	p1(v0	p1(v0	PROPN
ejpam-6729	140	5	):	):	PUNCT
ejpam-6729	140	6	tables	table	NOUN
ejpam-6729	140	7	as	as	ADP
ejpam-6729	140	8	1	1	NUM
ejpam-6729	140	9	-	-	PUNCT
ejpam-6729	140	10	supervertices	supervertice	NOUN
ejpam-6729	140	11	)	)	PUNCT
ejpam-6729	140	12	.	.	PUNCT
ejpam-6729	141	1	tusers	tuser	NOUN
ejpam-6729	141	2	:	:	PUNCT
ejpam-6729	141	3	=	=	SYM
ejpam-6729	141	4	{	{	PUNCT
ejpam-6729	141	5	userid	userid	NOUN
ejpam-6729	141	6	,	,	PUNCT
ejpam-6729	141	7	name	name	NOUN
ejpam-6729	141	8	,	,	PUNCT
ejpam-6729	141	9	email	email	NOUN
ejpam-6729	141	10	}	}	PUNCT
ejpam-6729	141	11	,	,	PUNCT
ejpam-6729	141	12	torders	torder	VERB
ejpam-6729	141	13	:	:	PUNCT
ejpam-6729	141	14	=	=	PRON
ejpam-6729	141	15	{	{	PUNCT
ejpam-6729	141	16	orderid	orderid	ADJ
ejpam-6729	141	17	,	,	PUNCT
ejpam-6729	141	18	userid	userid	NOUN
ejpam-6729	141	19	,	,	PUNCT
ejpam-6729	141	20	orderdate	orderdate	PROPN
ejpam-6729	141	21	}	}	PUNCT
ejpam-6729	141	22	,	,	PUNCT
ejpam-6729	141	23	torderitems	torderitem	VERB
ejpam-6729	141	24	:	:	PUNCT
ejpam-6729	141	25	=	=	PRON
ejpam-6729	141	26	{	{	PUNCT
ejpam-6729	141	27	orderid	orderid	ADJ
ejpam-6729	141	28	,	,	PUNCT
ejpam-6729	141	29	productid	productid	NOUN
ejpam-6729	141	30	,	,	PUNCT
ejpam-6729	141	31	quantity	quantity	NOUN
ejpam-6729	141	32	,	,	PUNCT
ejpam-6729	141	33	price	price	NOUN
ejpam-6729	141	34	}	}	PUNCT
ejpam-6729	141	35	,	,	PUNCT
ejpam-6729	141	36	∈	∈	PROPN
ejpam-6729	141	37	p1(v0	p1(v0	PROPN
ejpam-6729	141	38	)	)	PUNCT
ejpam-6729	141	39	.	.	PUNCT
ejpam-6729	142	1	t.	t.	PROPN
ejpam-6729	142	2	fujita	fujita	PROPN
ejpam-6729	142	3	,	,	PUNCT
ejpam-6729	142	4	f.	f.	PROPN
ejpam-6729	142	5	smarandache	smarandache	PROPN
ejpam-6729	142	6	/	/	SYM
ejpam-6729	142	7	eur	eur	PROPN
ejpam-6729	142	8	.	.	PUNCT
ejpam-6729	143	1	j.	j.	PROPN
ejpam-6729	143	2	pure	pure	PROPN
ejpam-6729	143	3	appl	appl	PROPN
ejpam-6729	143	4	.	.	PROPN
ejpam-6729	143	5	math	math	PROPN
ejpam-6729	143	6	,	,	PUNCT
ejpam-6729	143	7	18	18	NUM
ejpam-6729	143	8	(	(	PUNCT
ejpam-6729	143	9	4	4	NUM
ejpam-6729	143	10	)	)	PUNCT
ejpam-6729	143	11	(	(	PUNCT
ejpam-6729	143	12	2025	2025	NUM
ejpam-6729	143	13	)	)	PUNCT
ejpam-6729	143	14	,	,	PUNCT
ejpam-6729	143	15	6729	6729	NUM
ejpam-6729	143	16	7	7	NUM
ejpam-6729	143	17	of	of	ADP
ejpam-6729	143	18	36	36	NUM
ejpam-6729	143	19	let	let	VERB
ejpam-6729	143	20	v1	v1	ADV
ejpam-6729	143	21	:	:	PUNCT
ejpam-6729	143	22	=	=	SYM
ejpam-6729	143	23	{	{	PUNCT
ejpam-6729	143	24	tusers	tuser	NOUN
ejpam-6729	143	25	,	,	PUNCT
ejpam-6729	143	26	torders	torder	NOUN
ejpam-6729	143	27	,	,	PUNCT
ejpam-6729	143	28	torderitems	torderitem	VERB
ejpam-6729	143	29	}	}	PUNCT
ejpam-6729	143	30	⊆	⊆	NUM
ejpam-6729	143	31	p1(v0	p1(v0	NOUN
ejpam-6729	143	32	)	)	PUNCT
ejpam-6729	143	33	.	.	PUNCT
ejpam-6729	144	1	define	define	VERB
ejpam-6729	144	2	1	1	NUM
ejpam-6729	144	3	-	-	PUNCT
ejpam-6729	144	4	superedges	superedge	NOUN
ejpam-6729	144	5	e1	e1	NOUN
ejpam-6729	144	6	:	:	PUNCT
ejpam-6729	144	7	=	=	SYM
ejpam-6729	144	8	{	{	PUNCT
ejpam-6729	144	9	{	{	PUNCT
ejpam-6729	144	10	tusers	tuser	NOUN
ejpam-6729	144	11	,	,	PUNCT
ejpam-6729	144	12	torders	torder	NOUN
ejpam-6729	144	13	}	}	PUNCT
ejpam-6729	144	14	,	,	PUNCT
ejpam-6729	144	15	{	{	PUNCT
ejpam-6729	144	16	torders	torder	NOUN
ejpam-6729	144	17	,	,	PUNCT
ejpam-6729	144	18	torderitems	torderitem	VERB
ejpam-6729	144	19	}	}	PUNCT
ejpam-6729	144	20	}	}	PUNCT
ejpam-6729	144	21	⊆	⊆	NUM
ejpam-6729	144	22	p(v1	p(v1	NOUN
ejpam-6729	144	23	)	)	PUNCT
ejpam-6729	144	24	\	\	NOUN
ejpam-6729	144	25	{	{	PUNCT
ejpam-6729	144	26	∅	∅	NOUN
ejpam-6729	144	27	}	}	PUNCT
ejpam-6729	144	28	,	,	PUNCT
ejpam-6729	144	29	encoding	encode	VERB
ejpam-6729	144	30	the	the	DET
ejpam-6729	144	31	foreign	foreign	ADJ
ejpam-6729	144	32	-	-	PUNCT
ejpam-6729	144	33	key	key	NOUN
ejpam-6729	144	34	relations	relation	NOUN
ejpam-6729	144	35	orders.userid	orders.userid	NUM
ejpam-6729	144	36	→	→	SYM
ejpam-6729	144	37	users.userid	users.userid	X
ejpam-6729	144	38	and	and	CCONJ
ejpam-6729	144	39	orderitems.orderid	orderitems.orderid	X
ejpam-6729	144	40	→	→	SYM
ejpam-6729	144	41	orders.orderid	orders.orderid	NUM
ejpam-6729	144	42	.	.	PUNCT
ejpam-6729	145	1	step	step	NOUN
ejpam-6729	145	2	2	2	NUM
ejpam-6729	145	3	(	(	PUNCT
ejpam-6729	145	4	p2(v0	p2(v0	PROPN
ejpam-6729	145	5	):	):	PUNCT
ejpam-6729	145	6	logical	logical	ADJ
ejpam-6729	145	7	databases	database	NOUN
ejpam-6729	145	8	as	as	ADP
ejpam-6729	145	9	2	2	NUM
ejpam-6729	145	10	-	-	PUNCT
ejpam-6729	145	11	supervertices	supervertice	NOUN
ejpam-6729	145	12	)	)	PUNCT
ejpam-6729	145	13	.	.	PUNCT
ejpam-6729	146	1	ecomdb	ecomdb	PROPN
ejpam-6729	146	2	:	:	PUNCT
ejpam-6729	146	3	=	=	SYM
ejpam-6729	146	4	{	{	PUNCT
ejpam-6729	146	5	tusers	tuser	NOUN
ejpam-6729	146	6	,	,	PUNCT
ejpam-6729	146	7	torders	torder	NOUN
ejpam-6729	146	8	,	,	PUNCT
ejpam-6729	146	9	torderitems	torderitem	VERB
ejpam-6729	146	10	}	}	PUNCT
ejpam-6729	146	11	,	,	PUNCT
ejpam-6729	146	12	analyticsdb	analyticsdb	NOUN
ejpam-6729	146	13	:	:	PUNCT
ejpam-6729	146	14	=	=	SYM
ejpam-6729	146	15	{	{	PUNCT
ejpam-6729	146	16	torders	torder	NOUN
ejpam-6729	146	17	,	,	PUNCT
ejpam-6729	146	18	torderitems	torderitem	VERB
ejpam-6729	146	19	}	}	PUNCT
ejpam-6729	146	20	,	,	PUNCT
ejpam-6729	146	21	so	so	ADV
ejpam-6729	146	22	v2	v2	VERB
ejpam-6729	146	23	:	:	PUNCT
ejpam-6729	146	24	=	=	SYM
ejpam-6729	146	25	{	{	PUNCT
ejpam-6729	146	26	ecomdb	ecomdb	NOUN
ejpam-6729	146	27	,	,	PUNCT
ejpam-6729	146	28	analyticsdb	analyticsdb	NOUN
ejpam-6729	146	29	}	}	PUNCT
ejpam-6729	146	30	⊆	⊆	NUM
ejpam-6729	146	31	p2(v0	p2(v0	NOUN
ejpam-6729	146	32	)	)	PUNCT
ejpam-6729	146	33	.	.	PUNCT
ejpam-6729	147	1	define	define	VERB
ejpam-6729	147	2	a	a	DET
ejpam-6729	147	3	2	2	NUM
ejpam-6729	147	4	-	-	PUNCT
ejpam-6729	147	5	superedge	superedge	NOUN
ejpam-6729	147	6	e2	e2	NOUN
ejpam-6729	147	7	:	:	PUNCT
ejpam-6729	147	8	=	=	SYM
ejpam-6729	147	9	{	{	PUNCT
ejpam-6729	147	10	{	{	PUNCT
ejpam-6729	147	11	ecomdb	ecomdb	NOUN
ejpam-6729	147	12	,	,	PUNCT
ejpam-6729	147	13	analyticsdb	analyticsdb	NOUN
ejpam-6729	147	14	}	}	PUNCT
ejpam-6729	147	15	}	}	PUNCT
ejpam-6729	147	16	⊆	⊆	NUM
ejpam-6729	147	17	p(v2	p(v2	NOUN
ejpam-6729	147	18	)	)	PUNCT
ejpam-6729	147	19	\	\	NOUN
ejpam-6729	147	20	{	{	PUNCT
ejpam-6729	147	21	∅	∅	NOUN
ejpam-6729	147	22	}	}	PUNCT
ejpam-6729	147	23	,	,	PUNCT
ejpam-6729	147	24	representing	represent	VERB
ejpam-6729	147	25	an	an	DET
ejpam-6729	147	26	etl	etl	NOUN
ejpam-6729	147	27	replication	replication	NOUN
ejpam-6729	147	28	from	from	ADP
ejpam-6729	147	29	operational	operational	ADJ
ejpam-6729	147	30	to	to	ADP
ejpam-6729	147	31	analytical	analytical	ADJ
ejpam-6729	147	32	storage	storage	NOUN
ejpam-6729	147	33	.	.	PUNCT
ejpam-6729	148	1	step	step	NOUN
ejpam-6729	148	2	3	3	NUM
ejpam-6729	148	3	(	(	PUNCT
ejpam-6729	148	4	p3(v0	p3(v0	PROPN
ejpam-6729	148	5	):	):	PUNCT
ejpam-6729	148	6	services	service	NOUN
ejpam-6729	148	7	as	as	ADP
ejpam-6729	148	8	3	3	NUM
ejpam-6729	148	9	-	-	PUNCT
ejpam-6729	148	10	supervertices	supervertice	NOUN
ejpam-6729	148	11	)	)	PUNCT
ejpam-6729	148	12	.	.	PUNCT
ejpam-6729	149	1	transactionsvc	transactionsvc	NOUN
ejpam-6729	149	2	:	:	PUNCT
ejpam-6729	150	1	=	=	SYM
ejpam-6729	150	2	{	{	PUNCT
ejpam-6729	150	3	ecomdb	ecomdb	NOUN
ejpam-6729	150	4	}	}	PUNCT
ejpam-6729	150	5	,	,	PUNCT
ejpam-6729	150	6	reportingsvc	reportingsvc	NOUN
ejpam-6729	150	7	:	:	PUNCT
ejpam-6729	150	8	=	=	SYM
ejpam-6729	150	9	{	{	PUNCT
ejpam-6729	150	10	analyticsdb	analyticsdb	NOUN
ejpam-6729	150	11	}	}	PUNCT
ejpam-6729	150	12	,	,	PUNCT
ejpam-6729	150	13	hence	hence	ADV
ejpam-6729	150	14	v3	v3	PROPN
ejpam-6729	150	15	:	:	PUNCT
ejpam-6729	150	16	=	=	SYM
ejpam-6729	150	17	{	{	PUNCT
ejpam-6729	150	18	transactionsvc	transactionsvc	NOUN
ejpam-6729	150	19	,	,	PUNCT
ejpam-6729	150	20	reportingsvc	reportingsvc	PROPN
ejpam-6729	150	21	}	}	PUNCT
ejpam-6729	150	22	⊆	⊆	NUM
ejpam-6729	150	23	p3(v0	p3(v0	PROPN
ejpam-6729	150	24	)	)	PUNCT
ejpam-6729	150	25	.	.	PUNCT
ejpam-6729	151	1	define	define	VERB
ejpam-6729	151	2	a	a	DET
ejpam-6729	151	3	3	3	NUM
ejpam-6729	151	4	-	-	PUNCT
ejpam-6729	151	5	superedge	superedge	NOUN
ejpam-6729	151	6	e3	e3	NOUN
ejpam-6729	151	7	:	:	PUNCT
ejpam-6729	151	8	=	=	SYM
ejpam-6729	151	9	{	{	PUNCT
ejpam-6729	151	10	{	{	PUNCT
ejpam-6729	151	11	transactionsvc	transactionsvc	NOUN
ejpam-6729	151	12	,	,	PUNCT
ejpam-6729	151	13	reportingsvc	reportingsvc	PROPN
ejpam-6729	151	14	}	}	PUNCT
ejpam-6729	151	15	}	}	PUNCT
ejpam-6729	151	16	⊆	⊆	NUM
ejpam-6729	151	17	p(v3	p(v3	NOUN
ejpam-6729	151	18	)	)	PUNCT
ejpam-6729	151	19	\	\	NOUN
ejpam-6729	151	20	{	{	PUNCT
ejpam-6729	151	21	∅	∅	NOUN
ejpam-6729	151	22	}	}	PUNCT
ejpam-6729	151	23	,	,	PUNCT
ejpam-6729	151	24	capturing	capture	VERB
ejpam-6729	151	25	an	an	DET
ejpam-6729	151	26	event	event	NOUN
ejpam-6729	151	27	stream	stream	NOUN
ejpam-6729	151	28	by	by	ADP
ejpam-6729	151	29	which	which	PRON
ejpam-6729	151	30	the	the	DET
ejpam-6729	151	31	transaction	transaction	NOUN
ejpam-6729	151	32	service	service	NOUN
ejpam-6729	151	33	publishes	publish	VERB
ejpam-6729	151	34	updates	update	NOUN
ejpam-6729	151	35	consumed	consume	VERB
ejpam-6729	151	36	by	by	ADP
ejpam-6729	151	37	the	the	DET
ejpam-6729	151	38	reporting	reporting	NOUN
ejpam-6729	151	39	service	service	NOUN
ejpam-6729	151	40	.	.	PUNCT
ejpam-6729	152	1	verification	verification	NOUN
ejpam-6729	152	2	(	(	PUNCT
ejpam-6729	152	3	membership	membership	NOUN
ejpam-6729	152	4	checks	check	NOUN
ejpam-6729	152	5	)	)	PUNCT
ejpam-6729	152	6	.	.	PUNCT
ejpam-6729	153	1	by	by	ADP
ejpam-6729	153	2	construction	construction	NOUN
ejpam-6729	153	3	,	,	PUNCT
ejpam-6729	153	4	vk	vk	VERB
ejpam-6729	153	5	⊆	⊆	NUM
ejpam-6729	153	6	pk(v0	pk(v0	ADJ
ejpam-6729	153	7	)	)	PUNCT
ejpam-6729	153	8	and	and	CCONJ
ejpam-6729	153	9	ek	ek	VERB
ejpam-6729	153	10	⊆	⊆	NUM
ejpam-6729	153	11	p(vk	p(vk	PROPN
ejpam-6729	153	12	)	)	PUNCT
ejpam-6729	153	13	\	\	NOUN
ejpam-6729	153	14	{	{	PUNCT
ejpam-6729	153	15	∅	∅	NOUN
ejpam-6729	153	16	}	}	PUNCT
ejpam-6729	153	17	for	for	ADP
ejpam-6729	153	18	k	k	PROPN
ejpam-6729	153	19	=	=	SYM
ejpam-6729	153	20	1	1	NUM
ejpam-6729	153	21	,	,	PUNCT
ejpam-6729	153	22	2	2	NUM
ejpam-6729	153	23	,	,	PUNCT
ejpam-6729	153	24	3	3	NUM
ejpam-6729	153	25	.	.	PUNCT
ejpam-6729	153	26	thus	thus	ADV
ejpam-6729	153	27	shg(3	shg(3	NOUN
ejpam-6729	153	28	)	)	PUNCT
ejpam-6729	154	1	=	=	SYM
ejpam-6729	154	2	(	(	PUNCT
ejpam-6729	154	3	v3	v3	PROPN
ejpam-6729	154	4	,	,	PUNCT
ejpam-6729	154	5	e3	e3	NOUN
ejpam-6729	154	6	)	)	PUNCT
ejpam-6729	154	7	satisfies	satisfie	NOUN
ejpam-6729	154	8	definition	definition	NOUN
ejpam-6729	154	9	5	5	NUM
ejpam-6729	154	10	.	.	PUNCT
ejpam-6729	155	1	interpretation	interpretation	NOUN
ejpam-6729	155	2	.	.	PUNCT
ejpam-6729	156	1	level	level	NOUN
ejpam-6729	156	2	0	0	NUM
ejpam-6729	156	3	lists	list	NOUN
ejpam-6729	156	4	columns	column	NOUN
ejpam-6729	156	5	;	;	PUNCT
ejpam-6729	156	6	level	level	NOUN
ejpam-6729	156	7	1	1	NUM
ejpam-6729	156	8	models	model	NOUN
ejpam-6729	156	9	relational	relational	ADJ
ejpam-6729	156	10	schemas	schema	NOUN
ejpam-6729	156	11	and	and	CCONJ
ejpam-6729	156	12	key	key	ADJ
ejpam-6729	156	13	constraints	constraint	NOUN
ejpam-6729	156	14	;	;	PUNCT
ejpam-6729	156	15	level	level	NOUN
ejpam-6729	156	16	2	2	NUM
ejpam-6729	156	17	groups	group	NOUN
ejpam-6729	156	18	tables	table	NOUN
ejpam-6729	156	19	into	into	ADP
ejpam-6729	156	20	logical	logical	ADJ
ejpam-6729	156	21	databases	database	NOUN
ejpam-6729	156	22	;	;	PUNCT
ejpam-6729	156	23	level	level	NOUN
ejpam-6729	156	24	3	3	NUM
ejpam-6729	156	25	groups	group	NOUN
ejpam-6729	156	26	databases	database	NOUN
ejpam-6729	156	27	into	into	ADP
ejpam-6729	156	28	services	service	NOUN
ejpam-6729	156	29	and	and	CCONJ
ejpam-6729	156	30	specifies	specifie	NOUN
ejpam-6729	156	31	inter	inter	ADJ
ejpam-6729	156	32	-	-	ADJ
ejpam-6729	156	33	service	service	ADJ
ejpam-6729	156	34	dependencies	dependency	NOUN
ejpam-6729	156	35	as	as	ADP
ejpam-6729	156	36	superedges	superedge	NOUN
ejpam-6729	156	37	.	.	PUNCT
ejpam-6729	157	1	2.2	2.2	NUM
ejpam-6729	157	2	.	.	PUNCT
ejpam-6729	157	3	property	property	NOUN
ejpam-6729	157	4	graph	graph	NOUN
ejpam-6729	157	5	a	a	DET
ejpam-6729	157	6	property	property	NOUN
ejpam-6729	157	7	graph	graph	NOUN
ejpam-6729	157	8	is	be	AUX
ejpam-6729	157	9	a	a	DET
ejpam-6729	157	10	directed	direct	VERB
ejpam-6729	157	11	multigraph	multigraph	NOUN
ejpam-6729	157	12	in	in	ADP
ejpam-6729	157	13	which	which	PRON
ejpam-6729	157	14	both	both	DET
ejpam-6729	157	15	vertices	vertice	VERB
ejpam-6729	157	16	and	and	CCONJ
ejpam-6729	157	17	edges	edge	NOUN
ejpam-6729	157	18	may	may	AUX
ejpam-6729	157	19	carry	carry	VERB
ejpam-6729	157	20	arbitrary	arbitrary	ADJ
ejpam-6729	157	21	key	key	ADJ
ejpam-6729	157	22	–	–	PUNCT
ejpam-6729	157	23	value	value	NOUN
ejpam-6729	157	24	attributes	attribute	NOUN
ejpam-6729	157	25	,	,	PUNCT
ejpam-6729	157	26	and	and	CCONJ
ejpam-6729	157	27	where	where	SCONJ
ejpam-6729	157	28	edges	edge	NOUN
ejpam-6729	157	29	are	be	AUX
ejpam-6729	157	30	additionally	additionally	ADV
ejpam-6729	157	31	assigned	assign	VERB
ejpam-6729	157	32	labels	label	NOUN
ejpam-6729	157	33	.	.	PUNCT
ejpam-6729	158	1	this	this	DET
ejpam-6729	158	2	structure	structure	NOUN
ejpam-6729	158	3	enables	enable	VERB
ejpam-6729	158	4	schema	schema	NOUN
ejpam-6729	158	5	-	-	PUNCT
ejpam-6729	158	6	flexible	flexible	ADJ
ejpam-6729	158	7	modeling	modeling	NOUN
ejpam-6729	158	8	of	of	ADP
ejpam-6729	158	9	relational	relational	ADJ
ejpam-6729	158	10	data	datum	NOUN
ejpam-6729	159	1	[	[	X
ejpam-6729	159	2	6–8	6–8	X
ejpam-6729	159	3	,	,	PUNCT
ejpam-6729	159	4	36	36	NUM
ejpam-6729	159	5	]	]	PUNCT
ejpam-6729	159	6	.	.	PUNCT
ejpam-6729	160	1	below	below	ADV
ejpam-6729	160	2	,	,	PUNCT
ejpam-6729	160	3	we	we	PRON
ejpam-6729	160	4	provide	provide	VERB
ejpam-6729	160	5	a	a	DET
ejpam-6729	160	6	concise	concise	ADJ
ejpam-6729	160	7	formal	formal	ADJ
ejpam-6729	160	8	definition	definition	NOUN
ejpam-6729	160	9	together	together	ADV
ejpam-6729	160	10	with	with	ADP
ejpam-6729	160	11	illustrative	illustrative	ADJ
ejpam-6729	160	12	examples	example	NOUN
ejpam-6729	160	13	.	.	PUNCT
ejpam-6729	161	1	definition	definition	NOUN
ejpam-6729	161	2	6	6	NUM
ejpam-6729	161	3	(	(	PUNCT
ejpam-6729	161	4	property	property	NOUN
ejpam-6729	161	5	graph	graph	NOUN
ejpam-6729	161	6	)	)	PUNCT
ejpam-6729	161	7	.	.	PUNCT
ejpam-6729	162	1	(	(	PUNCT
ejpam-6729	162	2	cf.[6–8	cf.[6–8	PROPN
ejpam-6729	162	3	,	,	PUNCT
ejpam-6729	162	4	36	36	NUM
ejpam-6729	162	5	]	]	PUNCT
ejpam-6729	162	6	)	)	PUNCT
ejpam-6729	162	7	fix	fix	VERB
ejpam-6729	162	8	three	three	NUM
ejpam-6729	162	9	(	(	PUNCT
ejpam-6729	162	10	possibly	possibly	ADV
ejpam-6729	162	11	infinite	infinite	VERB
ejpam-6729	162	12	)	)	PUNCT
ejpam-6729	162	13	sets	set	VERB
ejpam-6729	162	14	σ	σ	PROPN
ejpam-6729	162	15	(	(	PUNCT
ejpam-6729	162	16	edge	edge	NOUN
ejpam-6729	162	17	–	–	PUNCT
ejpam-6729	162	18	label	label	NOUN
ejpam-6729	162	19	alphabet	alphabet	NOUN
ejpam-6729	162	20	)	)	PUNCT
ejpam-6729	162	21	,	,	PUNCT
ejpam-6729	162	22	t.	t.	PROPN
ejpam-6729	162	23	fujita	fujita	PROPN
ejpam-6729	162	24	,	,	PUNCT
ejpam-6729	162	25	f.	f.	PROPN
ejpam-6729	162	26	smarandache	smarandache	PROPN
ejpam-6729	162	27	/	/	SYM
ejpam-6729	162	28	eur	eur	PROPN
ejpam-6729	162	29	.	.	PUNCT
ejpam-6729	163	1	j.	j.	PROPN
ejpam-6729	163	2	pure	pure	PROPN
ejpam-6729	163	3	appl	appl	PROPN
ejpam-6729	163	4	.	.	PROPN
ejpam-6729	163	5	math	math	PROPN
ejpam-6729	163	6	,	,	PUNCT
ejpam-6729	163	7	18	18	NUM
ejpam-6729	163	8	(	(	PUNCT
ejpam-6729	163	9	4	4	NUM
ejpam-6729	163	10	)	)	PUNCT
ejpam-6729	163	11	(	(	PUNCT
ejpam-6729	163	12	2025	2025	NUM
ejpam-6729	163	13	)	)	PUNCT
ejpam-6729	163	14	,	,	PUNCT
ejpam-6729	163	15	6729	6729	NUM
ejpam-6729	163	16	8	8	NUM
ejpam-6729	163	17	of	of	ADP
ejpam-6729	163	18	36	36	NUM
ejpam-6729	163	19	k	k	NOUN
ejpam-6729	163	20	(	(	PUNCT
ejpam-6729	163	21	property	property	NOUN
ejpam-6729	163	22	keys	key	NOUN
ejpam-6729	163	23	)	)	PUNCT
ejpam-6729	163	24	,	,	PUNCT
ejpam-6729	163	25	s	s	X
ejpam-6729	163	26	(	(	PUNCT
ejpam-6729	163	27	property	property	NOUN
ejpam-6729	163	28	values	value	NOUN
ejpam-6729	163	29	)	)	PUNCT
ejpam-6729	163	30	.	.	PUNCT
ejpam-6729	164	1	a	a	DET
ejpam-6729	164	2	property	property	NOUN
ejpam-6729	164	3	graph†	graph†	NOUN
ejpam-6729	164	4	is	be	AUX
ejpam-6729	164	5	a	a	DET
ejpam-6729	164	6	septuple	septuple	NOUN
ejpam-6729	164	7	g	g	NOUN
ejpam-6729	164	8	=	=	PUNCT
ejpam-6729	164	9	(	(	PUNCT
ejpam-6729	164	10	v	v	NOUN
ejpam-6729	164	11	,	,	PUNCT
ejpam-6729	164	12	e	e	NOUN
ejpam-6729	164	13	,	,	PUNCT
ejpam-6729	164	14	s	s	PROPN
ejpam-6729	164	15	,	,	PUNCT
ejpam-6729	164	16	t	t	PROPN
ejpam-6729	164	17	,	,	PUNCT
ejpam-6729	164	18	λ	λ	PROPN
ejpam-6729	164	19	,	,	PUNCT
ejpam-6729	164	20	µ	µ	PRON
ejpam-6729	164	21	,	,	PUNCT
ejpam-6729	164	22	⊥	⊥	NOUN
ejpam-6729	164	23	)	)	PUNCT
ejpam-6729	164	24	whose	whose	DET
ejpam-6729	164	25	components	component	NOUN
ejpam-6729	164	26	satisfy	satisfy	VERB
ejpam-6729	164	27	the	the	DET
ejpam-6729	164	28	following	follow	VERB
ejpam-6729	164	29	conditions	condition	NOUN
ejpam-6729	164	30	:	:	PUNCT
ejpam-6729	164	31	(	(	PUNCT
ejpam-6729	164	32	a	a	X
ejpam-6729	164	33	)	)	PUNCT
ejpam-6729	164	34	v	v	NOUN
ejpam-6729	164	35	is	be	AUX
ejpam-6729	164	36	a	a	DET
ejpam-6729	164	37	finite	finite	NOUN
ejpam-6729	164	38	(	(	PUNCT
ejpam-6729	164	39	or	or	CCONJ
ejpam-6729	164	40	at	at	ADP
ejpam-6729	164	41	most	most	ADV
ejpam-6729	164	42	countable	countable	ADJ
ejpam-6729	164	43	)	)	PUNCT
ejpam-6729	164	44	set	set	VERB
ejpam-6729	164	45	whose	whose	DET
ejpam-6729	164	46	elements	element	NOUN
ejpam-6729	164	47	are	be	AUX
ejpam-6729	164	48	called	call	VERB
ejpam-6729	164	49	vertices	vertex	NOUN
ejpam-6729	164	50	(	(	PUNCT
ejpam-6729	164	51	or	or	CCONJ
ejpam-6729	164	52	nodes	node	NOUN
ejpam-6729	164	53	)	)	PUNCT
ejpam-6729	164	54	.	.	PUNCT
ejpam-6729	165	1	(	(	PUNCT
ejpam-6729	165	2	b	b	X
ejpam-6729	165	3	)	)	PUNCT
ejpam-6729	165	4	e	e	NOUN
ejpam-6729	165	5	is	be	AUX
ejpam-6729	165	6	a	a	DET
ejpam-6729	165	7	finite	finite	NOUN
ejpam-6729	165	8	(	(	PUNCT
ejpam-6729	165	9	or	or	CCONJ
ejpam-6729	165	10	at	at	ADP
ejpam-6729	165	11	most	most	ADV
ejpam-6729	165	12	countable	countable	ADJ
ejpam-6729	165	13	)	)	PUNCT
ejpam-6729	165	14	set	set	VERB
ejpam-6729	165	15	whose	whose	DET
ejpam-6729	165	16	elements	element	NOUN
ejpam-6729	165	17	are	be	AUX
ejpam-6729	165	18	called	call	VERB
ejpam-6729	165	19	edges	edge	NOUN
ejpam-6729	165	20	.	.	PUNCT
ejpam-6729	166	1	distinct	distinct	ADJ
ejpam-6729	166	2	edges	edge	NOUN
ejpam-6729	166	3	may	may	AUX
ejpam-6729	166	4	share	share	VERB
ejpam-6729	166	5	the	the	DET
ejpam-6729	166	6	same	same	ADJ
ejpam-6729	166	7	endpoints	endpoint	NOUN
ejpam-6729	166	8	,	,	PUNCT
ejpam-6729	166	9	so	so	CCONJ
ejpam-6729	166	10	(	(	PUNCT
ejpam-6729	166	11	v	v	NOUN
ejpam-6729	166	12	,	,	PUNCT
ejpam-6729	166	13	e	e	NOUN
ejpam-6729	166	14	)	)	PUNCT
ejpam-6729	166	15	is	be	AUX
ejpam-6729	166	16	a	a	DET
ejpam-6729	166	17	multigraph	multigraph	NOUN
ejpam-6729	166	18	.	.	PUNCT
ejpam-6729	167	1	(	(	PUNCT
ejpam-6729	167	2	c	c	X
ejpam-6729	167	3	)	)	PUNCT
ejpam-6729	167	4	s	s	PROPN
ejpam-6729	167	5	,	,	PUNCT
ejpam-6729	167	6	t	t	NOUN
ejpam-6729	167	7	:	:	PUNCT
ejpam-6729	167	8	e	e	X
ejpam-6729	167	9	→	→	SYM
ejpam-6729	167	10	v	v	NUM
ejpam-6729	167	11	are	be	AUX
ejpam-6729	167	12	the	the	DET
ejpam-6729	167	13	source	source	NOUN
ejpam-6729	167	14	and	and	CCONJ
ejpam-6729	167	15	target	target	NOUN
ejpam-6729	167	16	functions	function	NOUN
ejpam-6729	167	17	.	.	PUNCT
ejpam-6729	168	1	for	for	ADP
ejpam-6729	168	2	e	e	PROPN
ejpam-6729	168	3	∈	∈	PROPN
ejpam-6729	168	4	e	e	X
ejpam-6729	168	5	we	we	PRON
ejpam-6729	168	6	write	write	VERB
ejpam-6729	168	7	s(e	s(e	PROPN
ejpam-6729	168	8	)	)	PUNCT
ejpam-6729	168	9	e−→	e−→	PROPN
ejpam-6729	168	10	t(e	t(e	PROPN
ejpam-6729	168	11	)	)	PUNCT
ejpam-6729	168	12	.	.	PUNCT
ejpam-6729	169	1	(	(	PUNCT
ejpam-6729	169	2	d	d	X
ejpam-6729	169	3	)	)	PUNCT
ejpam-6729	169	4	λ	λ	NOUN
ejpam-6729	169	5	:	:	PUNCT
ejpam-6729	169	6	e	e	X
ejpam-6729	169	7	→	→	SYM
ejpam-6729	169	8	σ	σ	PROPN
ejpam-6729	169	9	assigns	assign	VERB
ejpam-6729	169	10	a	a	DET
ejpam-6729	169	11	label	label	NOUN
ejpam-6729	169	12	(	(	PUNCT
ejpam-6729	169	13	drawn	draw	VERB
ejpam-6729	169	14	from	from	ADP
ejpam-6729	169	15	the	the	DET
ejpam-6729	169	16	alphabet	alphabet	PROPN
ejpam-6729	169	17	σ	σ	PROPN
ejpam-6729	169	18	)	)	PUNCT
ejpam-6729	169	19	to	to	ADP
ejpam-6729	169	20	every	every	DET
ejpam-6729	169	21	edge	edge	NOUN
ejpam-6729	169	22	.	.	PUNCT
ejpam-6729	170	1	(	(	PUNCT
ejpam-6729	170	2	e	e	NOUN
ejpam-6729	170	3	)	)	PUNCT
ejpam-6729	170	4	µ	µ	NOUN
ejpam-6729	170	5	:	:	PUNCT
ejpam-6729	170	6	(	(	PUNCT
ejpam-6729	170	7	v	v	NOUN
ejpam-6729	170	8	∪	∪	VERB
ejpam-6729	170	9	e)×k	e)×k	NOUN
ejpam-6729	170	10	−→	−→	NOUN
ejpam-6729	170	11	s	s	NOUN
ejpam-6729	170	12	∪	∪	X
ejpam-6729	170	13	{	{	PUNCT
ejpam-6729	170	14	⊥	⊥	NOUN
ejpam-6729	170	15	}	}	PUNCT
ejpam-6729	170	16	is	be	AUX
ejpam-6729	170	17	the	the	DET
ejpam-6729	170	18	property	property	NOUN
ejpam-6729	170	19	map	map	NOUN
ejpam-6729	170	20	.	.	PUNCT
ejpam-6729	171	1	for	for	ADP
ejpam-6729	171	2	an	an	DET
ejpam-6729	171	3	entity	entity	NOUN
ejpam-6729	171	4	x	x	SYM
ejpam-6729	171	5	∈	∈	NOUN
ejpam-6729	171	6	v	v	NOUN
ejpam-6729	171	7	∪	∪	NOUN
ejpam-6729	171	8	e	e	NOUN
ejpam-6729	171	9	and	and	CCONJ
ejpam-6729	171	10	a	a	DET
ejpam-6729	171	11	key	key	ADJ
ejpam-6729	171	12	k	k	PROPN
ejpam-6729	171	13	∈	∈	PROPN
ejpam-6729	171	14	k	k	PROPN
ejpam-6729	171	15	,	,	PUNCT
ejpam-6729	171	16	the	the	DET
ejpam-6729	171	17	value	value	NOUN
ejpam-6729	171	18	µ(x	µ(x	VERB
ejpam-6729	171	19	,	,	PUNCT
ejpam-6729	171	20	k	k	NOUN
ejpam-6729	171	21	)	)	PUNCT
ejpam-6729	171	22	is	be	AUX
ejpam-6729	171	23	either	either	CCONJ
ejpam-6729	171	24	a	a	DET
ejpam-6729	171	25	member	member	NOUN
ejpam-6729	171	26	of	of	ADP
ejpam-6729	171	27	s	s	PRON
ejpam-6729	171	28	or	or	CCONJ
ejpam-6729	171	29	the	the	DET
ejpam-6729	171	30	distinguished	distinguished	ADJ
ejpam-6729	171	31	symbol	symbol	NOUN
ejpam-6729	171	32	⊥	⊥	NOUN
ejpam-6729	171	33	indicating	indicate	VERB
ejpam-6729	171	34	that	that	SCONJ
ejpam-6729	171	35	x	x	PRON
ejpam-6729	171	36	has	have	VERB
ejpam-6729	171	37	no	no	DET
ejpam-6729	171	38	value	value	NOUN
ejpam-6729	171	39	for	for	ADP
ejpam-6729	171	40	key	key	ADJ
ejpam-6729	171	41	k.	k.	PROPN
ejpam-6729	171	42	(	(	PUNCT
ejpam-6729	171	43	f	f	X
ejpam-6729	171	44	)	)	PUNCT
ejpam-6729	171	45	the	the	DET
ejpam-6729	171	46	symbol	symbol	NOUN
ejpam-6729	171	47	⊥	⊥	PROPN
ejpam-6729	171	48	/∈	/∈	PUNCT
ejpam-6729	172	1	s	s	PART
ejpam-6729	172	2	is	be	AUX
ejpam-6729	172	3	fixed	fix	VERB
ejpam-6729	172	4	once	once	ADV
ejpam-6729	172	5	and	and	CCONJ
ejpam-6729	172	6	for	for	ADP
ejpam-6729	172	7	all	all	PRON
ejpam-6729	172	8	and	and	CCONJ
ejpam-6729	172	9	is	be	AUX
ejpam-6729	172	10	not	not	PART
ejpam-6729	172	11	considered	consider	VERB
ejpam-6729	172	12	a	a	DET
ejpam-6729	172	13	valid	valid	ADJ
ejpam-6729	172	14	property	property	NOUN
ejpam-6729	172	15	value	value	NOUN
ejpam-6729	172	16	.	.	PUNCT
ejpam-6729	173	1	we	we	PRON
ejpam-6729	173	2	write	write	VERB
ejpam-6729	173	3	keyset(x	keyset(x	PROPN
ejpam-6729	173	4	)	)	PUNCT
ejpam-6729	173	5	:	:	PUNCT
ejpam-6729	174	1	=	=	PRON
ejpam-6729	174	2	{	{	PUNCT
ejpam-6729	174	3	k	k	PROPN
ejpam-6729	174	4	∈	∈	PROPN
ejpam-6729	174	5	k	k	PROPN
ejpam-6729	175	1	|	|	PROPN
ejpam-6729	175	2	µ(x	µ(x	PROPN
ejpam-6729	175	3	,	,	PUNCT
ejpam-6729	175	4	k	k	NOUN
ejpam-6729	175	5	)	)	PUNCT
ejpam-6729	175	6	6=	6=	ADP
ejpam-6729	176	1	⊥	⊥	NUM
ejpam-6729	176	2	}	}	PUNCT
ejpam-6729	176	3	,	,	PUNCT
ejpam-6729	176	4	val(x	val(x	PROPN
ejpam-6729	176	5	,	,	PUNCT
ejpam-6729	176	6	k	k	NOUN
ejpam-6729	176	7	)	)	PUNCT
ejpam-6729	176	8	:	:	PUNCT
ejpam-6729	177	1	=	=	SYM
ejpam-6729	177	2	µ(x	µ(x	X
ejpam-6729	177	3	,	,	PUNCT
ejpam-6729	177	4	k	k	NOUN
ejpam-6729	177	5	)	)	PUNCT
ejpam-6729	177	6	(	(	PUNCT
ejpam-6729	177	7	k	k	PROPN
ejpam-6729	177	8	∈	∈	PROPN
ejpam-6729	177	9	keyset(x	keyset(x	PROPN
ejpam-6729	177	10	)	)	PUNCT
ejpam-6729	177	11	)	)	PUNCT
ejpam-6729	177	12	,	,	PUNCT
ejpam-6729	177	13	and	and	CCONJ
ejpam-6729	177	14	call	call	VERB
ejpam-6729	177	15	〈	〈	PROPN
ejpam-6729	177	16	k	k	PROPN
ejpam-6729	177	17	,	,	PUNCT
ejpam-6729	177	18	µ(x	µ(x	ADJ
ejpam-6729	177	19	,	,	PUNCT
ejpam-6729	177	20	k	k	NOUN
ejpam-6729	177	21	)	)	PUNCT
ejpam-6729	177	22	〉	〉	NOUN
ejpam-6729	177	23	an	an	DET
ejpam-6729	177	24	attribute	attribute	NOUN
ejpam-6729	177	25	of	of	ADP
ejpam-6729	177	26	x.	x.	PROPN
ejpam-6729	177	27	remark	remark	PROPN
ejpam-6729	177	28	1	1	NUM
ejpam-6729	177	29	.	.	PUNCT
ejpam-6729	178	1	(	(	PUNCT
ejpam-6729	178	2	i	i	NOUN
ejpam-6729	178	3	)	)	PUNCT
ejpam-6729	178	4	allowing	allow	VERB
ejpam-6729	178	5	e	e	NOUN
ejpam-6729	178	6	to	to	PART
ejpam-6729	178	7	be	be	AUX
ejpam-6729	178	8	a	a	DET
ejpam-6729	178	9	multiset	multiset	NOUN
ejpam-6729	178	10	(	(	PUNCT
ejpam-6729	178	11	or	or	CCONJ
ejpam-6729	178	12	,	,	PUNCT
ejpam-6729	178	13	equivalently	equivalently	ADV
ejpam-6729	178	14	,	,	PUNCT
ejpam-6729	178	15	introducing	introduce	VERB
ejpam-6729	178	16	edge	edge	NOUN
ejpam-6729	178	17	identifiers	identifier	NOUN
ejpam-6729	178	18	)	)	PUNCT
ejpam-6729	178	19	lets	let	VERB
ejpam-6729	178	20	two	two	NUM
ejpam-6729	178	21	vertices	vertex	NOUN
ejpam-6729	178	22	be	be	AUX
ejpam-6729	178	23	joined	join	VERB
ejpam-6729	178	24	by	by	ADP
ejpam-6729	178	25	arbitrarily	arbitrarily	ADV
ejpam-6729	178	26	many	many	ADJ
ejpam-6729	178	27	edges	edge	NOUN
ejpam-6729	178	28	—	—	PUNCT
ejpam-6729	178	29	even	even	ADV
ejpam-6729	178	30	with	with	ADP
ejpam-6729	178	31	identical	identical	ADJ
ejpam-6729	178	32	labels	label	NOUN
ejpam-6729	178	33	and	and	CCONJ
ejpam-6729	178	34	attributes	attribute	NOUN
ejpam-6729	178	35	.	.	PUNCT
ejpam-6729	179	1	(	(	PUNCT
ejpam-6729	179	2	ii	ii	NOUN
ejpam-6729	179	3	)	)	PUNCT
ejpam-6729	179	4	if	if	SCONJ
ejpam-6729	179	5	λ	λ	NOUN
ejpam-6729	179	6	is	be	AUX
ejpam-6729	179	7	constant	constant	ADJ
ejpam-6729	179	8	(	(	PUNCT
ejpam-6729	179	9	all	all	DET
ejpam-6729	179	10	edges	edge	NOUN
ejpam-6729	179	11	share	share	VERB
ejpam-6729	179	12	one	one	NUM
ejpam-6729	179	13	label	label	NOUN
ejpam-6729	179	14	)	)	PUNCT
ejpam-6729	179	15	and	and	CCONJ
ejpam-6729	179	16	µ	µ	PRON
ejpam-6729	179	17	≡	≡	PROPN
ejpam-6729	179	18	⊥	⊥	PROPN
ejpam-6729	179	19	,	,	PUNCT
ejpam-6729	179	20	definition	definition	NOUN
ejpam-6729	179	21	6	6	NUM
ejpam-6729	179	22	collapses	collapse	VERB
ejpam-6729	179	23	to	to	ADP
ejpam-6729	179	24	the	the	DET
ejpam-6729	179	25	usual	usual	ADJ
ejpam-6729	179	26	concept	concept	NOUN
ejpam-6729	179	27	of	of	ADP
ejpam-6729	179	28	a	a	DET
ejpam-6729	179	29	directed	direct	VERB
ejpam-6729	179	30	multigraph	multigraph	NOUN
ejpam-6729	179	31	.	.	PUNCT
ejpam-6729	180	1	(	(	PUNCT
ejpam-6729	180	2	iii	iii	X
ejpam-6729	180	3	)	)	PUNCT
ejpam-6729	180	4	many	many	ADJ
ejpam-6729	180	5	graph	graph	NOUN
ejpam-6729	180	6	-	-	PUNCT
ejpam-6729	180	7	database	database	NOUN
ejpam-6729	180	8	operations	operation	NOUN
ejpam-6729	180	9	(	(	PUNCT
ejpam-6729	180	10	e.g.	e.g.	ADV
ejpam-6729	180	11	gremlin	gremlin	NOUN
ejpam-6729	180	12	traversals	traversal	NOUN
ejpam-6729	180	13	)	)	PUNCT
ejpam-6729	180	14	can	can	AUX
ejpam-6729	180	15	be	be	AUX
ejpam-6729	180	16	formalised	formalise	VERB
ejpam-6729	180	17	as	as	ADP
ejpam-6729	180	18	functions	function	NOUN
ejpam-6729	180	19	t	t	NOUN
ejpam-6729	180	20	:	:	PUNCT
ejpam-6729	180	21	p(v	p(v	NOUN
ejpam-6729	180	22	)	)	PUNCT
ejpam-6729	180	23	→p(v	→p(v	PROPN
ejpam-6729	180	24	)	)	PUNCT
ejpam-6729	180	25	;	;	PUNCT
ejpam-6729	180	26	see	see	VERB
ejpam-6729	180	27	yamaguchi	yamaguchi	PROPN
ejpam-6729	180	28	et	et	PROPN
ejpam-6729	180	29	al	al	PROPN
ejpam-6729	180	30	.	.	PROPN
ejpam-6729	181	1	for	for	ADP
ejpam-6729	181	2	a	a	DET
ejpam-6729	181	3	standard	standard	ADJ
ejpam-6729	181	4	treatment	treatment	NOUN
ejpam-6729	181	5	.	.	PUNCT
ejpam-6729	182	1	example	example	NOUN
ejpam-6729	182	2	5	5	NUM
ejpam-6729	182	3	(	(	PUNCT
ejpam-6729	182	4	property	property	NOUN
ejpam-6729	182	5	graph	graph	NOUN
ejpam-6729	182	6	for	for	ADP
ejpam-6729	182	7	a	a	DET
ejpam-6729	182	8	streaming	streaming	NOUN
ejpam-6729	182	9	-	-	PUNCT
ejpam-6729	182	10	platform	platform	NOUN
ejpam-6729	182	11	dataset	dataset	NOUN
ejpam-6729	182	12	)	)	PUNCT
ejpam-6729	182	13	.	.	PUNCT
ejpam-6729	183	1	we	we	PRON
ejpam-6729	183	2	illustrate	illustrate	VERB
ejpam-6729	183	3	definition	definition	NOUN
ejpam-6729	183	4	6	6	NUM
ejpam-6729	183	5	with	with	ADP
ejpam-6729	183	6	a	a	DET
ejpam-6729	183	7	concrete	concrete	ADJ
ejpam-6729	183	8	,	,	PUNCT
ejpam-6729	183	9	small	small	ADJ
ejpam-6729	183	10	-	-	PUNCT
ejpam-6729	183	11	scale	scale	NOUN
ejpam-6729	183	12	model	model	NOUN
ejpam-6729	183	13	of	of	ADP
ejpam-6729	183	14	an	an	DET
ejpam-6729	183	15	on	on	ADP
ejpam-6729	183	16	-	-	PUNCT
ejpam-6729	183	17	line	line	NOUN
ejpam-6729	183	18	movie	movie	NOUN
ejpam-6729	183	19	-	-	PUNCT
ejpam-6729	183	20	streaming	streaming	NOUN
ejpam-6729	183	21	service	service	NOUN
ejpam-6729	183	22	.	.	PUNCT
ejpam-6729	184	1	label	label	NOUN
ejpam-6729	184	2	alphabet	alphabet	PROPN
ejpam-6729	184	3	,	,	PUNCT
ejpam-6729	184	4	keys	key	NOUN
ejpam-6729	184	5	,	,	PUNCT
ejpam-6729	184	6	and	and	CCONJ
ejpam-6729	184	7	value	value	NOUN
ejpam-6729	184	8	domain	domain	NOUN
ejpam-6729	184	9	.	.	PUNCT
ejpam-6729	185	1	σ	σ	NOUN
ejpam-6729	185	2	=	=	PUNCT
ejpam-6729	185	3	{	{	PUNCT
ejpam-6729	185	4	follows	follow	VERB
ejpam-6729	185	5	,	,	PUNCT
ejpam-6729	185	6	rated	rate	VERB
ejpam-6729	185	7	,	,	PUNCT
ejpam-6729	185	8	has_genre	has_genre	NOUN
ejpam-6729	185	9	}	}	PUNCT
ejpam-6729	185	10	,	,	PUNCT
ejpam-6729	185	11	k	k	PROPN
ejpam-6729	185	12	=	=	PRON
ejpam-6729	185	13	{	{	PUNCT
ejpam-6729	185	14	type	type	NOUN
ejpam-6729	185	15	,	,	PUNCT
ejpam-6729	185	16	name	name	NOUN
ejpam-6729	185	17	,	,	PUNCT
ejpam-6729	185	18	age	age	NOUN
ejpam-6729	185	19	,	,	PUNCT
ejpam-6729	185	20	city	city	NOUN
ejpam-6729	185	21	,	,	PUNCT
ejpam-6729	185	22	title	title	NOUN
ejpam-6729	185	23	,	,	PUNCT
ejpam-6729	185	24	year	year	NOUN
ejpam-6729	185	25	,	,	PUNCT
ejpam-6729	185	26	rating	rating	NOUN
ejpam-6729	185	27	,	,	PUNCT
ejpam-6729	185	28	date	date	NOUN
ejpam-6729	185	29	}	}	PUNCT
ejpam-6729	185	30	,	,	PUNCT
ejpam-6729	185	31	s	s	VERB
ejpam-6729	185	32	=	=	SYM
ejpam-6729	185	33	n	n	PRON
ejpam-6729	185	34	∪	∪	NOUN
ejpam-6729	185	35	r	r	NOUN
ejpam-6729	185	36	∪	∪	ADJ
ejpam-6729	185	37	strings	string	NOUN
ejpam-6729	185	38	.	.	PUNCT
ejpam-6729	186	1	†equivalent	†equivalent	NOUN
ejpam-6729	186	2	to	to	ADP
ejpam-6729	186	3	“	"	PUNCT
ejpam-6729	186	4	directed	direct	VERB
ejpam-6729	186	5	,	,	PUNCT
ejpam-6729	186	6	edge	edge	NOUN
ejpam-6729	186	7	-	-	PUNCT
ejpam-6729	186	8	labelled	label	VERB
ejpam-6729	186	9	,	,	PUNCT
ejpam-6729	186	10	attributed	attribute	VERB
ejpam-6729	186	11	multigraph	multigraph	NOUN
ejpam-6729	186	12	”	"	PUNCT
ejpam-6729	186	13	in	in	ADP
ejpam-6729	186	14	the	the	DET
ejpam-6729	186	15	graph	graph	NOUN
ejpam-6729	186	16	-	-	PUNCT
ejpam-6729	186	17	database	database	NOUN
ejpam-6729	186	18	literature	literature	NOUN
ejpam-6729	186	19	.	.	PUNCT
ejpam-6729	187	1	t.	t.	PROPN
ejpam-6729	187	2	fujita	fujita	PROPN
ejpam-6729	187	3	,	,	PUNCT
ejpam-6729	187	4	f.	f.	PROPN
ejpam-6729	187	5	smarandache	smarandache	PROPN
ejpam-6729	187	6	/	/	SYM
ejpam-6729	187	7	eur	eur	PROPN
ejpam-6729	187	8	.	.	PUNCT
ejpam-6729	188	1	j.	j.	PROPN
ejpam-6729	188	2	pure	pure	PROPN
ejpam-6729	188	3	appl	appl	PROPN
ejpam-6729	188	4	.	.	PROPN
ejpam-6729	188	5	math	math	PROPN
ejpam-6729	188	6	,	,	PUNCT
ejpam-6729	188	7	18	18	NUM
ejpam-6729	188	8	(	(	PUNCT
ejpam-6729	188	9	4	4	NUM
ejpam-6729	188	10	)	)	PUNCT
ejpam-6729	188	11	(	(	PUNCT
ejpam-6729	188	12	2025	2025	NUM
ejpam-6729	188	13	)	)	PUNCT
ejpam-6729	188	14	,	,	PUNCT
ejpam-6729	188	15	6729	6729	NUM
ejpam-6729	188	16	9	9	NUM
ejpam-6729	188	17	of	of	ADP
ejpam-6729	188	18	36	36	NUM
ejpam-6729	188	19	vertices	vertex	NOUN
ejpam-6729	188	20	.	.	PUNCT
ejpam-6729	189	1	the	the	DET
ejpam-6729	189	2	vertex	vertex	NOUN
ejpam-6729	189	3	set	set	VERB
ejpam-6729	189	4	v	v	NOUN
ejpam-6729	189	5	=	=	SYM
ejpam-6729	189	6	{	{	PUNCT
ejpam-6729	189	7	p1	p1	PROPN
ejpam-6729	189	8	,	,	PUNCT
ejpam-6729	189	9	p2,m1,m2	p2,m1,m2	NOUN
ejpam-6729	189	10	,	,	PUNCT
ejpam-6729	189	11	g1	g1	PROPN
ejpam-6729	189	12	}	}	PUNCT
ejpam-6729	189	13	is	be	AUX
ejpam-6729	189	14	partitioned	partition	VERB
ejpam-6729	189	15	by	by	ADP
ejpam-6729	189	16	the	the	DET
ejpam-6729	189	17	attribute	attribute	NOUN
ejpam-6729	189	18	type	type	NOUN
ejpam-6729	189	19	:	:	PUNCT
ejpam-6729	189	20	µ(pi	µ(pi	NOUN
ejpam-6729	189	21	,	,	PUNCT
ejpam-6729	189	22	type	type	NOUN
ejpam-6729	189	23	)	)	PUNCT
ejpam-6729	189	24	=	=	PUNCT
ejpam-6729	189	25	“	"	PUNCT
ejpam-6729	189	26	person	person	NOUN
ejpam-6729	189	27	”	"	PUNCT
ejpam-6729	189	28	(	(	PUNCT
ejpam-6729	189	29	i	i	NOUN
ejpam-6729	189	30	=	=	NOUN
ejpam-6729	189	31	1	1	NUM
ejpam-6729	189	32	,	,	PUNCT
ejpam-6729	189	33	2	2	NUM
ejpam-6729	189	34	)	)	PUNCT
ejpam-6729	189	35	,	,	PUNCT
ejpam-6729	189	36	µ(mj	µ(mj	X
ejpam-6729	189	37	,	,	PUNCT
ejpam-6729	189	38	type	type	NOUN
ejpam-6729	189	39	)	)	PUNCT
ejpam-6729	189	40	=	=	PUNCT
ejpam-6729	189	41	“	"	PUNCT
ejpam-6729	189	42	movie	movie	NOUN
ejpam-6729	189	43	”	"	PUNCT
ejpam-6729	189	44	(	(	PUNCT
ejpam-6729	189	45	j	j	NOUN
ejpam-6729	189	46	=	=	SYM
ejpam-6729	189	47	1	1	NUM
ejpam-6729	189	48	,	,	PUNCT
ejpam-6729	189	49	2	2	NUM
ejpam-6729	189	50	)	)	PUNCT
ejpam-6729	189	51	,	,	PUNCT
ejpam-6729	189	52	µ(g1	µ(g1	NOUN
ejpam-6729	189	53	,	,	PUNCT
ejpam-6729	189	54	type	type	NOUN
ejpam-6729	189	55	)	)	PUNCT
ejpam-6729	189	56	=	=	PUNCT
ejpam-6729	189	57	“	"	PUNCT
ejpam-6729	189	58	genre	genre	NOUN
ejpam-6729	189	59	”	"	PUNCT
ejpam-6729	189	60	.	.	PUNCT
ejpam-6729	190	1	selected	select	VERB
ejpam-6729	190	2	vertex	vertex	NOUN
ejpam-6729	190	3	attributes	attribute	NOUN
ejpam-6729	190	4	are	be	AUX
ejpam-6729	190	5	µ(p1	µ(p1	NOUN
ejpam-6729	190	6	,	,	PUNCT
ejpam-6729	190	7	name	name	NOUN
ejpam-6729	190	8	)	)	PUNCT
ejpam-6729	190	9	=	=	PUNCT
ejpam-6729	190	10	“	"	PUNCT
ejpam-6729	190	11	alice	alice	PROPN
ejpam-6729	190	12	”	"	PUNCT
ejpam-6729	190	13	µ(p2	µ(p2	ADJ
ejpam-6729	190	14	,	,	PUNCT
ejpam-6729	190	15	name	name	NOUN
ejpam-6729	190	16	)	)	PUNCT
ejpam-6729	190	17	=	=	PUNCT
ejpam-6729	190	18	“	"	PUNCT
ejpam-6729	190	19	bob	bob	PROPN
ejpam-6729	190	20	”	"	PUNCT
ejpam-6729	190	21	µ(p1	µ(p1	NOUN
ejpam-6729	190	22	,	,	PUNCT
ejpam-6729	190	23	age	age	NOUN
ejpam-6729	190	24	)	)	PUNCT
ejpam-6729	190	25	=	=	NOUN
ejpam-6729	190	26	27	27	NUM
ejpam-6729	190	27	µ(p2	µ(p2	ADJ
ejpam-6729	190	28	,	,	PUNCT
ejpam-6729	190	29	age	age	NOUN
ejpam-6729	190	30	)	)	PUNCT
ejpam-6729	191	1	=	=	SYM
ejpam-6729	191	2	25	25	NUM
ejpam-6729	191	3	µ(p1	µ(p1	NOUN
ejpam-6729	191	4	,	,	PUNCT
ejpam-6729	191	5	city	city	NOUN
ejpam-6729	191	6	)	)	PUNCT
ejpam-6729	191	7	=	=	PUNCT
ejpam-6729	191	8	“	"	PUNCT
ejpam-6729	191	9	tokyo	tokyo	PROPN
ejpam-6729	191	10	”	"	PUNCT
ejpam-6729	191	11	µ(p2	µ(p2	ADJ
ejpam-6729	191	12	,	,	PUNCT
ejpam-6729	191	13	city	city	NOUN
ejpam-6729	191	14	)	)	PUNCT
ejpam-6729	191	15	=	=	PUNCT
ejpam-6729	191	16	“	"	PUNCT
ejpam-6729	191	17	kyoto	kyoto	PROPN
ejpam-6729	191	18	”	"	PUNCT
ejpam-6729	191	19	µ(m1	µ(m1	NOUN
ejpam-6729	191	20	,	,	PUNCT
ejpam-6729	191	21	title	title	NOUN
ejpam-6729	191	22	)	)	PUNCT
ejpam-6729	191	23	=	=	PUNCT
ejpam-6729	191	24	“	"	PUNCT
ejpam-6729	191	25	inception	inception	NOUN
ejpam-6729	191	26	”	"	PUNCT
ejpam-6729	191	27	µ(m1	µ(m1	NOUN
ejpam-6729	191	28	,	,	PUNCT
ejpam-6729	191	29	year	year	NOUN
ejpam-6729	191	30	)	)	PUNCT
ejpam-6729	191	31	=	=	SYM
ejpam-6729	191	32	2010	2010	NUM
ejpam-6729	191	33	µ(m2	µ(m2	NOUN
ejpam-6729	191	34	,	,	PUNCT
ejpam-6729	191	35	title	title	NOUN
ejpam-6729	191	36	)	)	PUNCT
ejpam-6729	191	37	=	=	SYM
ejpam-6729	191	38	“	"	PUNCT
ejpam-6729	191	39	interstellar	interstellar	ADJ
ejpam-6729	191	40	”	"	PUNCT
ejpam-6729	191	41	µ(m2	µ(m2	NOUN
ejpam-6729	191	42	,	,	PUNCT
ejpam-6729	191	43	year	year	NOUN
ejpam-6729	191	44	)	)	PUNCT
ejpam-6729	192	1	=	=	SYM
ejpam-6729	192	2	2014	2014	NUM
ejpam-6729	192	3	µ(g1	µ(g1	NOUN
ejpam-6729	192	4	,	,	PUNCT
ejpam-6729	192	5	name	name	NOUN
ejpam-6729	192	6	)	)	PUNCT
ejpam-6729	192	7	=	=	PUNCT
ejpam-6729	192	8	“	"	PUNCT
ejpam-6729	192	9	sci	sci	PROPN
ejpam-6729	192	10	-	-	PUNCT
ejpam-6729	192	11	fi	fi	NOUN
ejpam-6729	192	12	”	"	PUNCT
ejpam-6729	192	13	.	.	PUNCT
ejpam-6729	193	1	edges	edge	NOUN
ejpam-6729	193	2	,	,	PUNCT
ejpam-6729	193	3	endpoints	endpoint	NOUN
ejpam-6729	193	4	,	,	PUNCT
ejpam-6729	193	5	labels	label	NOUN
ejpam-6729	193	6	.	.	PUNCT
ejpam-6729	194	1	e	e	X
ejpam-6729	194	2	=	=	PRON
ejpam-6729	194	3	{	{	PUNCT
ejpam-6729	194	4	e1	e1	PROPN
ejpam-6729	194	5	,	,	PUNCT
ejpam-6729	194	6	e2	e2	PROPN
ejpam-6729	194	7	,	,	PUNCT
ejpam-6729	194	8	e3	e3	NOUN
ejpam-6729	194	9	,	,	PUNCT
ejpam-6729	194	10	e4	e4	PROPN
ejpam-6729	194	11	,	,	PUNCT
ejpam-6729	194	12	e5	e5	PROPN
ejpam-6729	194	13	}	}	PUNCT
ejpam-6729	194	14	,	,	PUNCT
ejpam-6729	194	15	s(e1	s(e1	NOUN
ejpam-6729	194	16	)	)	PUNCT
ejpam-6729	194	17	=	=	SYM
ejpam-6729	194	18	p1	p1	NOUN
ejpam-6729	194	19	,	,	PUNCT
ejpam-6729	194	20	t(e1	t(e1	NOUN
ejpam-6729	194	21	)	)	PUNCT
ejpam-6729	194	22	=	=	SYM
ejpam-6729	194	23	p2	p2	X
ejpam-6729	194	24	,	,	PUNCT
ejpam-6729	194	25	λ(e1	λ(e1	NUM
ejpam-6729	194	26	)	)	PUNCT
ejpam-6729	195	1	=	=	PRON
ejpam-6729	195	2	follows	follow	VERB
ejpam-6729	195	3	,	,	PUNCT
ejpam-6729	195	4	s(e2	s(e2	NOUN
ejpam-6729	195	5	)	)	PUNCT
ejpam-6729	195	6	=	=	SYM
ejpam-6729	195	7	p1	p1	NOUN
ejpam-6729	195	8	,	,	PUNCT
ejpam-6729	195	9	t(e2	t(e2	NOUN
ejpam-6729	195	10	)	)	PUNCT
ejpam-6729	195	11	=	=	SYM
ejpam-6729	195	12	m1	m1	NOUN
ejpam-6729	195	13	,	,	PUNCT
ejpam-6729	195	14	λ(e2	λ(e2	PROPN
ejpam-6729	195	15	)	)	PUNCT
ejpam-6729	195	16	=	=	PRON
ejpam-6729	195	17	rated	rate	VERB
ejpam-6729	195	18	,	,	PUNCT
ejpam-6729	195	19	s(e3	s(e3	NOUN
ejpam-6729	195	20	)	)	PUNCT
ejpam-6729	195	21	=	=	SYM
ejpam-6729	195	22	p1	p1	PROPN
ejpam-6729	195	23	,	,	PUNCT
ejpam-6729	195	24	t(e3	t(e3	NUM
ejpam-6729	195	25	)	)	PUNCT
ejpam-6729	195	26	=	=	SYM
ejpam-6729	195	27	m2	m2	PROPN
ejpam-6729	195	28	,	,	PUNCT
ejpam-6729	195	29	λ(e3	λ(e3	NUM
ejpam-6729	195	30	)	)	PUNCT
ejpam-6729	195	31	=	=	VERB
ejpam-6729	195	32	rated	rate	VERB
ejpam-6729	195	33	,	,	PUNCT
ejpam-6729	195	34	s(e4	s(e4	NUM
ejpam-6729	195	35	)	)	PUNCT
ejpam-6729	196	1	=	=	SYM
ejpam-6729	196	2	m1	m1	NOUN
ejpam-6729	196	3	,	,	PUNCT
ejpam-6729	196	4	t(e4	t(e4	NOUN
ejpam-6729	196	5	)	)	PUNCT
ejpam-6729	196	6	=	=	SYM
ejpam-6729	196	7	g1	g1	PROPN
ejpam-6729	196	8	,	,	PUNCT
ejpam-6729	196	9	λ(e4	λ(e4	PROPN
ejpam-6729	196	10	)	)	PUNCT
ejpam-6729	196	11	=	=	SYM
ejpam-6729	196	12	has_genre	has_genre	NOUN
ejpam-6729	196	13	,	,	PUNCT
ejpam-6729	196	14	s(e5	s(e5	PROPN
ejpam-6729	196	15	)	)	PUNCT
ejpam-6729	196	16	=	=	SYM
ejpam-6729	196	17	m2	m2	PROPN
ejpam-6729	196	18	,	,	PUNCT
ejpam-6729	196	19	t(e5	t(e5	NOUN
ejpam-6729	196	20	)	)	PUNCT
ejpam-6729	196	21	=	=	SYM
ejpam-6729	196	22	g1	g1	NOUN
ejpam-6729	196	23	,	,	PUNCT
ejpam-6729	196	24	λ(e5	λ(e5	NOUN
ejpam-6729	196	25	)	)	PUNCT
ejpam-6729	196	26	=	=	PUNCT
ejpam-6729	196	27	has_genre	has_genre	NOUN
ejpam-6729	196	28	.	.	PUNCT
ejpam-6729	197	1	edge	edge	NOUN
ejpam-6729	197	2	attributes	attribute	NOUN
ejpam-6729	197	3	.	.	PUNCT
ejpam-6729	198	1	µ(e1	µ(e1	NOUN
ejpam-6729	198	2	,	,	PUNCT
ejpam-6729	198	3	date	date	NOUN
ejpam-6729	198	4	)	)	PUNCT
ejpam-6729	198	5	=	=	PUNCT
ejpam-6729	199	1	“	"	PUNCT
ejpam-6729	199	2	2025	2025	NUM
ejpam-6729	199	3	-	-	SYM
ejpam-6729	199	4	05	05	NUM
ejpam-6729	199	5	-	-	PUNCT
ejpam-6729	199	6	12	12	NUM
ejpam-6729	199	7	”	"	PUNCT
ejpam-6729	199	8	,	,	PUNCT
ejpam-6729	199	9	µ(e2	µ(e2	NOUN
ejpam-6729	199	10	,	,	PUNCT
ejpam-6729	199	11	rating	rating	NOUN
ejpam-6729	199	12	)	)	PUNCT
ejpam-6729	199	13	=	=	SYM
ejpam-6729	199	14	5	5	NUM
ejpam-6729	199	15	,	,	PUNCT
ejpam-6729	199	16	µ(e2	µ(e2	NOUN
ejpam-6729	199	17	,	,	PUNCT
ejpam-6729	199	18	date	date	NOUN
ejpam-6729	199	19	)	)	PUNCT
ejpam-6729	199	20	=	=	PUNCT
ejpam-6729	199	21	“	"	PUNCT
ejpam-6729	199	22	2025	2025	NUM
ejpam-6729	199	23	-	-	SYM
ejpam-6729	199	24	05	05	NUM
ejpam-6729	199	25	-	-	PUNCT
ejpam-6729	199	26	13	13	NUM
ejpam-6729	199	27	”	"	PUNCT
ejpam-6729	199	28	,	,	PUNCT
ejpam-6729	199	29	µ(e3	µ(e3	ADJ
ejpam-6729	199	30	,	,	PUNCT
ejpam-6729	199	31	rating	rating	NOUN
ejpam-6729	199	32	)	)	PUNCT
ejpam-6729	199	33	=	=	SYM
ejpam-6729	199	34	4	4	NUM
ejpam-6729	199	35	,	,	PUNCT
ejpam-6729	199	36	µ(e3	µ(e3	ADJ
ejpam-6729	199	37	,	,	PUNCT
ejpam-6729	199	38	date	date	NOUN
ejpam-6729	199	39	)	)	PUNCT
ejpam-6729	199	40	=	=	PUNCT
ejpam-6729	199	41	“	"	PUNCT
ejpam-6729	199	42	2025	2025	NUM
ejpam-6729	199	43	-	-	SYM
ejpam-6729	199	44	05	05	NUM
ejpam-6729	199	45	-	-	PUNCT
ejpam-6729	199	46	14	14	NUM
ejpam-6729	199	47	”	"	PUNCT
ejpam-6729	199	48	.	.	PUNCT
ejpam-6729	200	1	all	all	DET
ejpam-6729	200	2	other	other	ADJ
ejpam-6729	200	3	µ(x	µ(x	ADJ
ejpam-6729	200	4	,	,	PUNCT
ejpam-6729	200	5	k	k	NOUN
ejpam-6729	200	6	)	)	PUNCT
ejpam-6729	200	7	not	not	PART
ejpam-6729	200	8	listed	list	VERB
ejpam-6729	200	9	are	be	AUX
ejpam-6729	200	10	set	set	VERB
ejpam-6729	200	11	to	to	ADP
ejpam-6729	200	12	the	the	DET
ejpam-6729	200	13	distinguished	distinguished	ADJ
ejpam-6729	200	14	value	value	NOUN
ejpam-6729	200	15	⊥.	⊥.	NUM
ejpam-6729	200	16	the	the	DET
ejpam-6729	200	17	septuple	septuple	NOUN
ejpam-6729	200	18	g	g	PROPN
ejpam-6729	200	19	=	=	SYM
ejpam-6729	200	20	(	(	PUNCT
ejpam-6729	200	21	v	v	NOUN
ejpam-6729	200	22	,	,	PUNCT
ejpam-6729	200	23	e	e	NOUN
ejpam-6729	200	24	,	,	PUNCT
ejpam-6729	200	25	s	s	PROPN
ejpam-6729	200	26	,	,	PUNCT
ejpam-6729	200	27	t	t	PROPN
ejpam-6729	200	28	,	,	PUNCT
ejpam-6729	200	29	λ	λ	NOUN
ejpam-6729	200	30	,	,	PUNCT
ejpam-6729	200	31	µ,⊥	µ,⊥	NOUN
ejpam-6729	200	32	)	)	PUNCT
ejpam-6729	200	33	thus	thus	ADV
ejpam-6729	200	34	obtained	obtain	VERB
ejpam-6729	200	35	satisfies	satisfie	NOUN
ejpam-6729	200	36	every	every	DET
ejpam-6729	200	37	clause	clause	NOUN
ejpam-6729	200	38	of	of	ADP
ejpam-6729	200	39	definition	definition	NOUN
ejpam-6729	200	40	6	6	NUM
ejpam-6729	200	41	.	.	PUNCT
ejpam-6729	201	1	it	it	PRON
ejpam-6729	201	2	captures	capture	VERB
ejpam-6729	201	3	users	user	NOUN
ejpam-6729	201	4	(	(	PUNCT
ejpam-6729	201	5	persons	person	NOUN
ejpam-6729	201	6	)	)	PUNCT
ejpam-6729	201	7	,	,	PUNCT
ejpam-6729	201	8	movies	movie	NOUN
ejpam-6729	201	9	,	,	PUNCT
ejpam-6729	201	10	and	and	CCONJ
ejpam-6729	201	11	genres	genre	NOUN
ejpam-6729	201	12	as	as	ADP
ejpam-6729	201	13	vertices	vertex	NOUN
ejpam-6729	201	14	;	;	PUNCT
ejpam-6729	201	15	user	user	NOUN
ejpam-6729	201	16	-	-	PUNCT
ejpam-6729	201	17	to	to	ADP
ejpam-6729	201	18	-	-	PUNCT
ejpam-6729	201	19	user	user	NOUN
ejpam-6729	201	20	follows	follow	VERB
ejpam-6729	201	21	relationships	relationship	NOUN
ejpam-6729	201	22	,	,	PUNCT
ejpam-6729	201	23	user	user	NOUN
ejpam-6729	201	24	ratings	rating	NOUN
ejpam-6729	201	25	of	of	ADP
ejpam-6729	201	26	movies	movie	NOUN
ejpam-6729	201	27	,	,	PUNCT
ejpam-6729	201	28	and	and	CCONJ
ejpam-6729	201	29	movie	movie	NOUN
ejpam-6729	201	30	-	-	PUNCT
ejpam-6729	201	31	to	to	ADP
ejpam-6729	201	32	-	-	PUNCT
ejpam-6729	201	33	genre	genre	NOUN
ejpam-6729	201	34	links	link	NOUN
ejpam-6729	201	35	as	as	ADP
ejpam-6729	201	36	labelled	label	VERB
ejpam-6729	201	37	,	,	PUNCT
ejpam-6729	201	38	attributed	attribute	VERB
ejpam-6729	201	39	edges	edge	NOUN
ejpam-6729	201	40	.	.	PUNCT
ejpam-6729	202	1	additional	additional	ADJ
ejpam-6729	202	2	properties	property	NOUN
ejpam-6729	202	3	or	or	CCONJ
ejpam-6729	202	4	vertex	vertex	NOUN
ejpam-6729	202	5	types	type	NOUN
ejpam-6729	202	6	(	(	PUNCT
ejpam-6729	202	7	e.g.	e.g.	ADV
ejpam-6729	202	8	director	director	NOUN
ejpam-6729	202	9	,	,	PUNCT
ejpam-6729	202	10	studio	studio	NOUN
ejpam-6729	202	11	)	)	PUNCT
ejpam-6729	202	12	can	can	AUX
ejpam-6729	202	13	be	be	AUX
ejpam-6729	202	14	incorporated	incorporate	VERB
ejpam-6729	202	15	seamlessly	seamlessly	ADV
ejpam-6729	202	16	by	by	ADP
ejpam-6729	202	17	extending	extend	VERB
ejpam-6729	202	18	the	the	DET
ejpam-6729	202	19	key	key	ADJ
ejpam-6729	202	20	set	set	NOUN
ejpam-6729	202	21	k	k	PROPN
ejpam-6729	202	22	and	and	CCONJ
ejpam-6729	202	23	adding	add	VERB
ejpam-6729	202	24	new	new	ADJ
ejpam-6729	202	25	vertices	vertex	NOUN
ejpam-6729	202	26	and	and	CCONJ
ejpam-6729	202	27	edges	edge	NOUN
ejpam-6729	202	28	.	.	PUNCT
ejpam-6729	203	1	t.	t.	PROPN
ejpam-6729	203	2	fujita	fujita	PROPN
ejpam-6729	203	3	,	,	PUNCT
ejpam-6729	203	4	f.	f.	PROPN
ejpam-6729	203	5	smarandache	smarandache	PROPN
ejpam-6729	203	6	/	/	SYM
ejpam-6729	203	7	eur	eur	PROPN
ejpam-6729	203	8	.	.	PUNCT
ejpam-6729	204	1	j.	j.	PROPN
ejpam-6729	204	2	pure	pure	PROPN
ejpam-6729	204	3	appl	appl	PROPN
ejpam-6729	204	4	.	.	PROPN
ejpam-6729	204	5	math	math	PROPN
ejpam-6729	204	6	,	,	PUNCT
ejpam-6729	204	7	18	18	NUM
ejpam-6729	204	8	(	(	PUNCT
ejpam-6729	204	9	4	4	NUM
ejpam-6729	204	10	)	)	PUNCT
ejpam-6729	204	11	(	(	PUNCT
ejpam-6729	204	12	2025	2025	NUM
ejpam-6729	204	13	)	)	PUNCT
ejpam-6729	204	14	,	,	PUNCT
ejpam-6729	204	15	6729	6729	NUM
ejpam-6729	204	16	10	10	NUM
ejpam-6729	204	17	of	of	ADP
ejpam-6729	204	18	36	36	NUM
ejpam-6729	204	19	3	3	NUM
ejpam-6729	204	20	.	.	NOUN
ejpam-6729	204	21	results	result	NOUN
ejpam-6729	204	22	and	and	CCONJ
ejpam-6729	204	23	revisits	revisit	VERB
ejpam-6729	204	24	:	:	PUNCT
ejpam-6729	204	25	property	property	NOUN
ejpam-6729	204	26	hypergraphs	hypergraphs	PROPN
ejpam-6729	204	27	property	property	NOUN
ejpam-6729	204	28	hypergraphs	hypergraph	NOUN
ejpam-6729	204	29	generalize	generalize	VERB
ejpam-6729	204	30	hypergraphs	hypergraph	NOUN
ejpam-6729	204	31	by	by	ADP
ejpam-6729	204	32	allowing	allow	VERB
ejpam-6729	204	33	vertices	vertex	NOUN
ejpam-6729	204	34	and	and	CCONJ
ejpam-6729	204	35	hyperedges	hyperedge	NOUN
ejpam-6729	204	36	to	to	PART
ejpam-6729	204	37	carry	carry	VERB
ejpam-6729	204	38	key	key	ADJ
ejpam-6729	204	39	–	–	PUNCT
ejpam-6729	204	40	value	value	NOUN
ejpam-6729	204	41	properties	property	NOUN
ejpam-6729	204	42	and	and	CCONJ
ejpam-6729	204	43	labels	label	NOUN
ejpam-6729	204	44	,	,	PUNCT
ejpam-6729	204	45	supporting	support	VERB
ejpam-6729	204	46	flexible	flexible	ADJ
ejpam-6729	204	47	modeling	modeling	NOUN
ejpam-6729	204	48	.	.	PUNCT
ejpam-6729	205	1	notation	notation	NOUN
ejpam-6729	205	2	1	1	NUM
ejpam-6729	205	3	.	.	PUNCT
ejpam-6729	206	1	fix	fix	VERB
ejpam-6729	206	2	three	three	NUM
ejpam-6729	206	3	(	(	PUNCT
ejpam-6729	206	4	possibly	possibly	ADV
ejpam-6729	206	5	infinite	infinite	VERB
ejpam-6729	206	6	)	)	PUNCT
ejpam-6729	206	7	sets	set	VERB
ejpam-6729	206	8	σ	σ	PROPN
ejpam-6729	206	9	(	(	PUNCT
ejpam-6729	206	10	hyperedge‐label	hyperedge‐label	PROPN
ejpam-6729	206	11	alphabet	alphabet	NOUN
ejpam-6729	206	12	)	)	PUNCT
ejpam-6729	206	13	,	,	PUNCT
ejpam-6729	206	14	k	k	PROPN
ejpam-6729	206	15	(	(	PUNCT
ejpam-6729	206	16	property	property	NOUN
ejpam-6729	206	17	keys	key	NOUN
ejpam-6729	206	18	)	)	PUNCT
ejpam-6729	206	19	,	,	PUNCT
ejpam-6729	206	20	s	s	X
ejpam-6729	206	21	(	(	PUNCT
ejpam-6729	206	22	property	property	NOUN
ejpam-6729	206	23	values	value	NOUN
ejpam-6729	206	24	)	)	PUNCT
ejpam-6729	206	25	,	,	PUNCT
ejpam-6729	206	26	and	and	CCONJ
ejpam-6729	206	27	let	let	VERB
ejpam-6729	206	28	⊥	⊥	NOUN
ejpam-6729	206	29	/∈	/∈	PUNCT
ejpam-6729	207	1	s	s	VERB
ejpam-6729	207	2	be	be	AUX
ejpam-6729	207	3	a	a	DET
ejpam-6729	207	4	distinguished	distinguished	ADJ
ejpam-6729	207	5	symbol	symbol	NOUN
ejpam-6729	207	6	.	.	PUNCT
ejpam-6729	208	1	definition	definition	NOUN
ejpam-6729	208	2	7	7	NUM
ejpam-6729	208	3	(	(	PUNCT
ejpam-6729	208	4	property	property	NOUN
ejpam-6729	208	5	hypergraph	hypergraph	NOUN
ejpam-6729	208	6	)	)	PUNCT
ejpam-6729	208	7	.	.	PUNCT
ejpam-6729	209	1	a	a	DET
ejpam-6729	209	2	property	property	NOUN
ejpam-6729	209	3	hypergraph	hypergraph	NOUN
ejpam-6729	209	4	is	be	AUX
ejpam-6729	209	5	a	a	DET
ejpam-6729	209	6	quadruple	quadruple	NOUN
ejpam-6729	209	7	h	h	NOUN
ejpam-6729	210	1	=	=	PUNCT
ejpam-6729	210	2	(	(	PUNCT
ejpam-6729	210	3	v	v	NOUN
ejpam-6729	210	4	,	,	PUNCT
ejpam-6729	210	5	e	e	NOUN
ejpam-6729	210	6	,	,	PUNCT
ejpam-6729	210	7	λ	λ	PROPN
ejpam-6729	210	8	,	,	PUNCT
ejpam-6729	210	9	µ	µ	NOUN
ejpam-6729	210	10	)	)	PUNCT
ejpam-6729	210	11	satisfying	satisfying	NOUN
ejpam-6729	210	12	:	:	PUNCT
ejpam-6729	210	13	(	(	PUNCT
ejpam-6729	210	14	a	a	X
ejpam-6729	210	15	)	)	PUNCT
ejpam-6729	210	16	v	v	NOUN
ejpam-6729	210	17	is	be	AUX
ejpam-6729	210	18	a	a	DET
ejpam-6729	210	19	finite	finite	NOUN
ejpam-6729	210	20	(	(	PUNCT
ejpam-6729	210	21	or	or	CCONJ
ejpam-6729	210	22	at	at	ADP
ejpam-6729	210	23	most	most	ADV
ejpam-6729	210	24	countable	countable	ADJ
ejpam-6729	210	25	)	)	PUNCT
ejpam-6729	210	26	set	set	NOUN
ejpam-6729	210	27	of	of	ADP
ejpam-6729	210	28	vertices	vertex	NOUN
ejpam-6729	210	29	.	.	PUNCT
ejpam-6729	211	1	(	(	PUNCT
ejpam-6729	211	2	b	b	X
ejpam-6729	211	3	)	)	PUNCT
ejpam-6729	211	4	e	e	NOUN
ejpam-6729	211	5	is	be	AUX
ejpam-6729	211	6	a	a	DET
ejpam-6729	211	7	finite	finite	ADJ
ejpam-6729	211	8	family	family	NOUN
ejpam-6729	211	9	of	of	ADP
ejpam-6729	211	10	non‐empty	non‐empty	PROPN
ejpam-6729	211	11	subsets	subset	NOUN
ejpam-6729	211	12	of	of	ADP
ejpam-6729	211	13	v	v	NOUN
ejpam-6729	211	14	,	,	PUNCT
ejpam-6729	211	15	called	call	VERB
ejpam-6729	211	16	hyperedges	hyperedge	NOUN
ejpam-6729	211	17	.	.	PUNCT
ejpam-6729	212	1	(	(	PUNCT
ejpam-6729	212	2	c	c	X
ejpam-6729	212	3	)	)	PUNCT
ejpam-6729	212	4	λ	λ	NOUN
ejpam-6729	212	5	:	:	PUNCT
ejpam-6729	212	6	e	e	X
ejpam-6729	212	7	→	→	SYM
ejpam-6729	212	8	σ	σ	NOUN
ejpam-6729	212	9	assigns	assign	NOUN
ejpam-6729	212	10	to	to	PART
ejpam-6729	212	11	each	each	DET
ejpam-6729	212	12	hyperedge	hyperedge	VERB
ejpam-6729	212	13	a	a	DET
ejpam-6729	212	14	label	label	NOUN
ejpam-6729	212	15	.	.	PUNCT
ejpam-6729	213	1	(	(	PUNCT
ejpam-6729	213	2	d	d	X
ejpam-6729	213	3	)	)	PUNCT
ejpam-6729	213	4	µ	µ	NOUN
ejpam-6729	213	5	:	:	PUNCT
ejpam-6729	213	6	(	(	PUNCT
ejpam-6729	213	7	v	v	NOUN
ejpam-6729	213	8	∪	∪	VERB
ejpam-6729	213	9	e)×k	e)×k	NOUN
ejpam-6729	213	10	→	→	SYM
ejpam-6729	213	11	s	s	NOUN
ejpam-6729	213	12	∪	∪	X
ejpam-6729	213	13	{	{	PUNCT
ejpam-6729	213	14	⊥	⊥	NOUN
ejpam-6729	213	15	}	}	PUNCT
ejpam-6729	213	16	is	be	AUX
ejpam-6729	213	17	the	the	DET
ejpam-6729	213	18	property	property	NOUN
ejpam-6729	213	19	map	map	NOUN
ejpam-6729	213	20	,	,	PUNCT
ejpam-6729	213	21	where	where	SCONJ
ejpam-6729	213	22	µ(x	µ(x	VERB
ejpam-6729	213	23	,	,	PUNCT
ejpam-6729	213	24	k	k	NOUN
ejpam-6729	213	25	)	)	PUNCT
ejpam-6729	213	26	=	=	NOUN
ejpam-6729	213	27	{	{	PUNCT
ejpam-6729	213	28	s	s	NOUN
ejpam-6729	213	29	∈	∈	NOUN
ejpam-6729	213	30	s	s	NOUN
ejpam-6729	213	31	,	,	PUNCT
ejpam-6729	213	32	if	if	SCONJ
ejpam-6729	213	33	x	x	PRON
ejpam-6729	213	34	has	have	VERB
ejpam-6729	213	35	property	property	NOUN
ejpam-6729	213	36	k	k	PROPN
ejpam-6729	213	37	with	with	ADP
ejpam-6729	213	38	value	value	NOUN
ejpam-6729	213	39	s	s	PROPN
ejpam-6729	213	40	,	,	PUNCT
ejpam-6729	213	41	⊥	⊥	NOUN
ejpam-6729	213	42	,	,	PUNCT
ejpam-6729	213	43	if	if	SCONJ
ejpam-6729	213	44	no	no	DET
ejpam-6729	213	45	value	value	NOUN
ejpam-6729	213	46	is	be	AUX
ejpam-6729	213	47	assigned	assign	VERB
ejpam-6729	213	48	.	.	PUNCT
ejpam-6729	214	1	we	we	PRON
ejpam-6729	214	2	write	write	VERB
ejpam-6729	214	3	(	(	PUNCT
ejpam-6729	214	4	x	x	NOUN
ejpam-6729	214	5	)	)	PUNCT
ejpam-6729	214	6	:	:	PUNCT
ejpam-6729	215	1	=	=	SYM
ejpam-6729	215	2	{	{	PUNCT
ejpam-6729	215	3	k	k	PROPN
ejpam-6729	215	4	∈	∈	PROPN
ejpam-6729	215	5	k	k	PROPN
ejpam-6729	216	1	|	|	PROPN
ejpam-6729	216	2	µ(x	µ(x	PROPN
ejpam-6729	216	3	,	,	PUNCT
ejpam-6729	216	4	k	k	NOUN
ejpam-6729	216	5	)	)	PUNCT
ejpam-6729	216	6	6=	6=	ADP
ejpam-6729	217	1	⊥	⊥	NOUN
ejpam-6729	217	2	}	}	PUNCT
ejpam-6729	217	3	,	,	PUNCT
ejpam-6729	217	4	(	(	PUNCT
ejpam-6729	217	5	x	x	X
ejpam-6729	217	6	,	,	PUNCT
ejpam-6729	217	7	k	k	NOUN
ejpam-6729	217	8	)	)	PUNCT
ejpam-6729	217	9	:	:	PUNCT
ejpam-6729	217	10	=	=	SYM
ejpam-6729	217	11	µ(x	µ(x	X
ejpam-6729	217	12	,	,	PUNCT
ejpam-6729	217	13	k	k	NOUN
ejpam-6729	217	14	)	)	PUNCT
ejpam-6729	217	15	(	(	PUNCT
ejpam-6729	217	16	k	k	PROPN
ejpam-6729	217	17	∈	∈	PROPN
ejpam-6729	217	18	(	(	PUNCT
ejpam-6729	217	19	x	x	NOUN
ejpam-6729	217	20	)	)	PUNCT
ejpam-6729	217	21	)	)	PUNCT
ejpam-6729	217	22	.	.	PUNCT
ejpam-6729	218	1	example	example	NOUN
ejpam-6729	218	2	6	6	NUM
ejpam-6729	218	3	(	(	PUNCT
ejpam-6729	218	4	property	property	NOUN
ejpam-6729	218	5	hypergraph	hypergraph	NOUN
ejpam-6729	218	6	for	for	ADP
ejpam-6729	218	7	patient	patient	ADJ
ejpam-6729	218	8	–	–	PUNCT
ejpam-6729	218	9	symptom	symptom	NOUN
ejpam-6729	218	10	dataset	dataset	NOUN
ejpam-6729	218	11	)	)	PUNCT
ejpam-6729	218	12	.	.	PUNCT
ejpam-6729	219	1	we	we	PRON
ejpam-6729	219	2	illustrate	illustrate	VERB
ejpam-6729	219	3	definition	definition	NOUN
ejpam-6729	219	4	7	7	NUM
ejpam-6729	219	5	by	by	ADP
ejpam-6729	219	6	modelling	model	VERB
ejpam-6729	219	7	a	a	DET
ejpam-6729	219	8	clinical	clinical	ADJ
ejpam-6729	219	9	dataset	dataset	NOUN
ejpam-6729	219	10	in	in	ADP
ejpam-6729	219	11	which	which	PRON
ejpam-6729	219	12	each	each	DET
ejpam-6729	219	13	patient	patient	ADJ
ejpam-6729	219	14	record	record	NOUN
ejpam-6729	219	15	links	link	NOUN
ejpam-6729	219	16	the	the	DET
ejpam-6729	219	17	symptoms	symptom	NOUN
ejpam-6729	219	18	they	they	PRON
ejpam-6729	219	19	exhibit	exhibit	VERB
ejpam-6729	219	20	and	and	CCONJ
ejpam-6729	219	21	carries	carry	VERB
ejpam-6729	219	22	patient	patient	ADJ
ejpam-6729	219	23	metadata	metadata	NOUN
ejpam-6729	219	24	.	.	PUNCT
ejpam-6729	220	1	label	label	NOUN
ejpam-6729	220	2	alphabet	alphabet	NOUN
ejpam-6729	220	3	,	,	PUNCT
ejpam-6729	220	4	keys	key	NOUN
ejpam-6729	220	5	,	,	PUNCT
ejpam-6729	220	6	and	and	CCONJ
ejpam-6729	220	7	value	value	NOUN
ejpam-6729	220	8	domain	domain	NOUN
ejpam-6729	220	9	.	.	PUNCT
ejpam-6729	221	1	σ	σ	NOUN
ejpam-6729	221	2	=	=	PUNCT
ejpam-6729	221	3	{	{	PUNCT
ejpam-6729	221	4	covid19	covid19	NOUN
ejpam-6729	221	5	,	,	PUNCT
ejpam-6729	221	6	influenza	influenza	NOUN
ejpam-6729	221	7	,	,	PUNCT
ejpam-6729	221	8	migraine	migraine	NOUN
ejpam-6729	221	9	}	}	PUNCT
ejpam-6729	221	10	,	,	PUNCT
ejpam-6729	221	11	k	k	X
ejpam-6729	221	12	=	=	PRON
ejpam-6729	221	13	{	{	PUNCT
ejpam-6729	221	14	category	category	NOUN
ejpam-6729	221	15	,	,	PUNCT
ejpam-6729	221	16	icd_code	icd_code	NOUN
ejpam-6729	221	17	,	,	PUNCT
ejpam-6729	221	18	age	age	NOUN
ejpam-6729	221	19	,	,	PUNCT
ejpam-6729	221	20	gender	gender	NOUN
ejpam-6729	221	21	,	,	PUNCT
ejpam-6729	221	22	severity	severity	NOUN
ejpam-6729	221	23	}	}	PUNCT
ejpam-6729	221	24	,	,	PUNCT
ejpam-6729	221	25	s	s	X
ejpam-6729	221	26	=	=	PUNCT
ejpam-6729	221	27	{	{	PUNCT
ejpam-6729	221	28	“	"	PUNCT
ejpam-6729	221	29	constitutional	constitutional	ADJ
ejpam-6729	221	30	”	"	PUNCT
ejpam-6729	221	31	,	,	PUNCT
ejpam-6729	221	32	“	"	PUNCT
ejpam-6729	221	33	respiratory	respiratory	ADJ
ejpam-6729	221	34	”	"	PUNCT
ejpam-6729	221	35	,	,	PUNCT
ejpam-6729	221	36	“	"	PUNCT
ejpam-6729	221	37	neurological	neurological	ADJ
ejpam-6729	221	38	”	"	PUNCT
ejpam-6729	221	39	}	}	PUNCT
ejpam-6729	221	40	∪	∪	NOUN
ejpam-6729	221	41	{	{	PUNCT
ejpam-6729	221	42	strings	string	NOUN
ejpam-6729	221	43	}	}	PUNCT
ejpam-6729	221	44	∪	∪	ADP
ejpam-6729	221	45	n.	n.	PROPN
ejpam-6729	221	46	t.	t.	PROPN
ejpam-6729	221	47	fujita	fujita	PROPN
ejpam-6729	221	48	,	,	PUNCT
ejpam-6729	221	49	f.	f.	PROPN
ejpam-6729	221	50	smarandache	smarandache	PROPN
ejpam-6729	221	51	/	/	SYM
ejpam-6729	221	52	eur	eur	PROPN
ejpam-6729	221	53	.	.	PUNCT
ejpam-6729	222	1	j.	j.	PROPN
ejpam-6729	222	2	pure	pure	PROPN
ejpam-6729	222	3	appl	appl	PROPN
ejpam-6729	222	4	.	.	PROPN
ejpam-6729	222	5	math	math	PROPN
ejpam-6729	222	6	,	,	PUNCT
ejpam-6729	222	7	18	18	NUM
ejpam-6729	222	8	(	(	PUNCT
ejpam-6729	222	9	4	4	NUM
ejpam-6729	222	10	)	)	PUNCT
ejpam-6729	222	11	(	(	PUNCT
ejpam-6729	222	12	2025	2025	NUM
ejpam-6729	222	13	)	)	PUNCT
ejpam-6729	222	14	,	,	PUNCT
ejpam-6729	222	15	6729	6729	NUM
ejpam-6729	222	16	11	11	NUM
ejpam-6729	222	17	of	of	ADP
ejpam-6729	222	18	36	36	NUM
ejpam-6729	222	19	vertices	vertex	NOUN
ejpam-6729	222	20	(	(	PUNCT
ejpam-6729	222	21	symptoms	symptom	NOUN
ejpam-6729	222	22	)	)	PUNCT
ejpam-6729	222	23	.	.	PUNCT
ejpam-6729	223	1	let	let	VERB
ejpam-6729	223	2	v	v	VERB
ejpam-6729	223	3	=	=	SYM
ejpam-6729	223	4	{	{	PUNCT
ejpam-6729	223	5	v1	v1	PROPN
ejpam-6729	223	6	,	,	PUNCT
ejpam-6729	223	7	v2	v2	PROPN
ejpam-6729	223	8	,	,	PUNCT
ejpam-6729	223	9	v3	v3	PROPN
ejpam-6729	223	10	,	,	PUNCT
ejpam-6729	223	11	v4	v4	PROPN
ejpam-6729	223	12	,	,	PUNCT
ejpam-6729	223	13	v5	v5	PROPN
ejpam-6729	223	14	}	}	PUNCT
ejpam-6729	223	15	,	,	PUNCT
ejpam-6729	223	16	where	where	SCONJ
ejpam-6729	223	17	µ(v1	µ(v1	ADJ
ejpam-6729	223	18	,	,	PUNCT
ejpam-6729	223	19	category	category	NOUN
ejpam-6729	223	20	)	)	PUNCT
ejpam-6729	223	21	=	=	PUNCT
ejpam-6729	223	22	“	"	PUNCT
ejpam-6729	223	23	constitutional	constitutional	ADJ
ejpam-6729	223	24	”	"	PUNCT
ejpam-6729	223	25	,	,	PUNCT
ejpam-6729	223	26	µ(v1	µ(v1	NOUN
ejpam-6729	223	27	,	,	PUNCT
ejpam-6729	223	28	icd_code	icd_code	NOUN
ejpam-6729	223	29	)	)	PUNCT
ejpam-6729	223	30	=	=	PUNCT
ejpam-6729	223	31	“	"	PUNCT
ejpam-6729	223	32	r50.9	r50.9	PROPN
ejpam-6729	223	33	”	"	PUNCT
ejpam-6729	223	34	,	,	PUNCT
ejpam-6729	223	35	µ(v2	µ(v2	NOUN
ejpam-6729	223	36	,	,	PUNCT
ejpam-6729	223	37	category	category	NOUN
ejpam-6729	223	38	)	)	PUNCT
ejpam-6729	223	39	=	=	PUNCT
ejpam-6729	224	1	“	"	PUNCT
ejpam-6729	224	2	respiratory	respiratory	ADJ
ejpam-6729	224	3	”	"	PUNCT
ejpam-6729	224	4	,	,	PUNCT
ejpam-6729	224	5	µ(v2	µ(v2	PROPN
ejpam-6729	224	6	,	,	PUNCT
ejpam-6729	224	7	icd_code	icd_code	NOUN
ejpam-6729	224	8	)	)	PUNCT
ejpam-6729	224	9	=	=	PUNCT
ejpam-6729	224	10	“	"	PUNCT
ejpam-6729	224	11	r05	r05	NOUN
ejpam-6729	224	12	”	"	PUNCT
ejpam-6729	224	13	,	,	PUNCT
ejpam-6729	224	14	µ(v3	µ(v3	NOUN
ejpam-6729	224	15	,	,	PUNCT
ejpam-6729	224	16	category	category	NOUN
ejpam-6729	224	17	)	)	PUNCT
ejpam-6729	224	18	=	=	PUNCT
ejpam-6729	224	19	“	"	PUNCT
ejpam-6729	224	20	constitutional	constitutional	ADJ
ejpam-6729	224	21	”	"	PUNCT
ejpam-6729	224	22	,	,	PUNCT
ejpam-6729	224	23	µ(v3	µ(v3	NOUN
ejpam-6729	224	24	,	,	PUNCT
ejpam-6729	224	25	icd_code	icd_code	NOUN
ejpam-6729	224	26	)	)	PUNCT
ejpam-6729	224	27	=	=	PUNCT
ejpam-6729	224	28	“	"	PUNCT
ejpam-6729	224	29	r53.83	r53.83	VERB
ejpam-6729	224	30	”	"	PUNCT
ejpam-6729	224	31	,	,	PUNCT
ejpam-6729	224	32	µ(v4	µ(v4	PROPN
ejpam-6729	224	33	,	,	PUNCT
ejpam-6729	224	34	category	category	NOUN
ejpam-6729	224	35	)	)	PUNCT
ejpam-6729	224	36	=	=	PUNCT
ejpam-6729	224	37	“	"	PUNCT
ejpam-6729	224	38	neurological	neurological	ADJ
ejpam-6729	224	39	”	"	PUNCT
ejpam-6729	224	40	,	,	PUNCT
ejpam-6729	224	41	µ(v4	µ(v4	PROPN
ejpam-6729	224	42	,	,	PUNCT
ejpam-6729	224	43	icd_code	icd_code	NOUN
ejpam-6729	224	44	)	)	PUNCT
ejpam-6729	224	45	=	=	PUNCT
ejpam-6729	224	46	“	"	PUNCT
ejpam-6729	224	47	r51	r51	NOUN
ejpam-6729	224	48	”	"	PUNCT
ejpam-6729	224	49	,	,	PUNCT
ejpam-6729	224	50	µ(v5	µ(v5	NOUN
ejpam-6729	224	51	,	,	PUNCT
ejpam-6729	224	52	category	category	NOUN
ejpam-6729	224	53	)	)	PUNCT
ejpam-6729	224	54	=	=	PUNCT
ejpam-6729	224	55	“	"	PUNCT
ejpam-6729	224	56	respiratory	respiratory	ADJ
ejpam-6729	224	57	”	"	PUNCT
ejpam-6729	224	58	,	,	PUNCT
ejpam-6729	224	59	µ(v5	µ(v5	NOUN
ejpam-6729	224	60	,	,	PUNCT
ejpam-6729	224	61	icd_code	icd_code	NOUN
ejpam-6729	224	62	)	)	PUNCT
ejpam-6729	224	63	=	=	PUNCT
ejpam-6729	224	64	“	"	PUNCT
ejpam-6729	224	65	r06.02	r06.02	NOUN
ejpam-6729	224	66	”	"	PUNCT
ejpam-6729	224	67	.	.	PUNCT
ejpam-6729	225	1	hyperedges	hyperedge	NOUN
ejpam-6729	225	2	(	(	PUNCT
ejpam-6729	225	3	patient	patient	NOUN
ejpam-6729	225	4	records	record	NOUN
ejpam-6729	225	5	)	)	PUNCT
ejpam-6729	225	6	.	.	PUNCT
ejpam-6729	226	1	define	define	VERB
ejpam-6729	226	2	three	three	NUM
ejpam-6729	226	3	patient	patient	ADJ
ejpam-6729	226	4	hyperedges	hyperedge	NOUN
ejpam-6729	226	5	:	:	PUNCT
ejpam-6729	227	1	e	e	X
ejpam-6729	227	2	=	=	PRON
ejpam-6729	227	3	{	{	PUNCT
ejpam-6729	227	4	e1	e1	PROPN
ejpam-6729	227	5	,	,	PUNCT
ejpam-6729	227	6	e2	e2	PROPN
ejpam-6729	227	7	,	,	PUNCT
ejpam-6729	227	8	e3	e3	NOUN
ejpam-6729	227	9	}	}	PUNCT
ejpam-6729	227	10	,	,	PUNCT
ejpam-6729	227	11	with	with	ADP
ejpam-6729	227	12	e1	e1	NOUN
ejpam-6729	227	13	=	=	SYM
ejpam-6729	227	14	{	{	PUNCT
ejpam-6729	227	15	v1	v1	PROPN
ejpam-6729	227	16	,	,	PUNCT
ejpam-6729	227	17	v2	v2	PROPN
ejpam-6729	227	18	,	,	PUNCT
ejpam-6729	227	19	v3	v3	PROPN
ejpam-6729	227	20	}	}	PUNCT
ejpam-6729	227	21	,	,	PUNCT
ejpam-6729	227	22	e2	e2	PROPN
ejpam-6729	227	23	=	=	PUNCT
ejpam-6729	227	24	{	{	PUNCT
ejpam-6729	227	25	v2	v2	PROPN
ejpam-6729	227	26	,	,	PUNCT
ejpam-6729	227	27	v3	v3	PROPN
ejpam-6729	227	28	,	,	PUNCT
ejpam-6729	227	29	v4	v4	PROPN
ejpam-6729	227	30	}	}	PUNCT
ejpam-6729	227	31	,	,	PUNCT
ejpam-6729	227	32	e3	e3	NOUN
ejpam-6729	227	33	=	=	SYM
ejpam-6729	227	34	{	{	PUNCT
ejpam-6729	227	35	v1	v1	PROPN
ejpam-6729	227	36	,	,	PUNCT
ejpam-6729	227	37	v4	v4	NOUN
ejpam-6729	227	38	,	,	PUNCT
ejpam-6729	227	39	v5	v5	PROPN
ejpam-6729	227	40	}	}	PUNCT
ejpam-6729	227	41	.	.	PUNCT
ejpam-6729	228	1	labels	label	NOUN
ejpam-6729	228	2	and	and	CCONJ
ejpam-6729	228	3	properties	property	NOUN
ejpam-6729	228	4	.	.	PUNCT
ejpam-6729	229	1	assign	assign	VERB
ejpam-6729	229	2	each	each	DET
ejpam-6729	229	3	record	record	NOUN
ejpam-6729	229	4	a	a	DET
ejpam-6729	229	5	diagnosis	diagnosis	NOUN
ejpam-6729	229	6	label	label	NOUN
ejpam-6729	229	7	and	and	CCONJ
ejpam-6729	229	8	patient	patient	ADJ
ejpam-6729	229	9	metadata	metadata	NOUN
ejpam-6729	229	10	:	:	PUNCT
ejpam-6729	229	11	λ(e1	λ(e1	X
ejpam-6729	229	12	)	)	PUNCT
ejpam-6729	229	13	=	=	SYM
ejpam-6729	229	14	covid19	covid19	NOUN
ejpam-6729	229	15	,	,	PUNCT
ejpam-6729	229	16	µ(e1	µ(e1	NOUN
ejpam-6729	229	17	,	,	PUNCT
ejpam-6729	229	18	age	age	NOUN
ejpam-6729	229	19	)	)	PUNCT
ejpam-6729	229	20	=	=	SYM
ejpam-6729	229	21	45	45	NUM
ejpam-6729	229	22	,	,	PUNCT
ejpam-6729	229	23	µ(e1	µ(e1	NOUN
ejpam-6729	229	24	,	,	PUNCT
ejpam-6729	229	25	gender	gender	NOUN
ejpam-6729	229	26	)	)	PUNCT
ejpam-6729	229	27	=	=	PUNCT
ejpam-6729	229	28	“	"	PUNCT
ejpam-6729	229	29	male	male	NOUN
ejpam-6729	229	30	”	"	PUNCT
ejpam-6729	229	31	,	,	PUNCT
ejpam-6729	229	32	µ(e1	µ(e1	NOUN
ejpam-6729	229	33	,	,	PUNCT
ejpam-6729	229	34	severity	severity	NOUN
ejpam-6729	229	35	)	)	PUNCT
ejpam-6729	229	36	=	=	SYM
ejpam-6729	229	37	“	"	PUNCT
ejpam-6729	229	38	moderate	moderate	ADJ
ejpam-6729	229	39	”	"	PUNCT
ejpam-6729	229	40	,	,	PUNCT
ejpam-6729	229	41	λ(e2	λ(e2	PROPN
ejpam-6729	229	42	)	)	PUNCT
ejpam-6729	229	43	=	=	SYM
ejpam-6729	229	44	influenza	influenza	NOUN
ejpam-6729	229	45	,	,	PUNCT
ejpam-6729	229	46	µ(e2	µ(e2	NOUN
ejpam-6729	229	47	,	,	PUNCT
ejpam-6729	229	48	age	age	NOUN
ejpam-6729	229	49	)	)	PUNCT
ejpam-6729	229	50	=	=	SYM
ejpam-6729	229	51	30	30	NUM
ejpam-6729	229	52	,	,	PUNCT
ejpam-6729	229	53	µ(e2	µ(e2	NOUN
ejpam-6729	229	54	,	,	PUNCT
ejpam-6729	229	55	gender	gender	NOUN
ejpam-6729	229	56	)	)	PUNCT
ejpam-6729	229	57	=	=	NUM
ejpam-6729	229	58	“	"	PUNCT
ejpam-6729	229	59	female	female	NOUN
ejpam-6729	229	60	”	"	PUNCT
ejpam-6729	229	61	,	,	PUNCT
ejpam-6729	229	62	µ(e2	µ(e2	NOUN
ejpam-6729	229	63	,	,	PUNCT
ejpam-6729	229	64	severity	severity	NOUN
ejpam-6729	229	65	)	)	PUNCT
ejpam-6729	229	66	=	=	SYM
ejpam-6729	229	67	“	"	PUNCT
ejpam-6729	229	68	mild	mild	ADJ
ejpam-6729	229	69	”	"	PUNCT
ejpam-6729	229	70	,	,	PUNCT
ejpam-6729	229	71	λ(e3	λ(e3	NUM
ejpam-6729	229	72	)	)	PUNCT
ejpam-6729	229	73	=	=	SYM
ejpam-6729	229	74	migraine	migraine	NOUN
ejpam-6729	229	75	,	,	PUNCT
ejpam-6729	229	76	µ(e3	µ(e3	ADJ
ejpam-6729	229	77	,	,	PUNCT
ejpam-6729	229	78	age	age	NOUN
ejpam-6729	229	79	)	)	PUNCT
ejpam-6729	229	80	=	=	SYM
ejpam-6729	229	81	25	25	NUM
ejpam-6729	229	82	,	,	PUNCT
ejpam-6729	229	83	µ(e3	µ(e3	ADJ
ejpam-6729	229	84	,	,	PUNCT
ejpam-6729	229	85	gender	gender	NOUN
ejpam-6729	229	86	)	)	PUNCT
ejpam-6729	229	87	=	=	NUM
ejpam-6729	229	88	“	"	PUNCT
ejpam-6729	229	89	female	female	NOUN
ejpam-6729	229	90	”	"	PUNCT
ejpam-6729	229	91	,	,	PUNCT
ejpam-6729	229	92	µ(e3	µ(e3	ADJ
ejpam-6729	229	93	,	,	PUNCT
ejpam-6729	229	94	severity	severity	NOUN
ejpam-6729	229	95	)	)	PUNCT
ejpam-6729	229	96	=	=	PUNCT
ejpam-6729	229	97	“	"	PUNCT
ejpam-6729	229	98	severe	severe	ADJ
ejpam-6729	229	99	”	"	PUNCT
ejpam-6729	229	100	.	.	PUNCT
ejpam-6729	230	1	keysets	keyset	NOUN
ejpam-6729	230	2	and	and	CCONJ
ejpam-6729	230	3	values	value	NOUN
ejpam-6729	230	4	.	.	PUNCT
ejpam-6729	231	1	for	for	ADP
ejpam-6729	231	2	example	example	NOUN
ejpam-6729	231	3	,	,	PUNCT
ejpam-6729	231	4	(	(	PUNCT
ejpam-6729	231	5	v4	v4	NOUN
ejpam-6729	231	6	)	)	PUNCT
ejpam-6729	231	7	=	=	SYM
ejpam-6729	232	1	{	{	PUNCT
ejpam-6729	232	2	category	category	NOUN
ejpam-6729	232	3	,	,	PUNCT
ejpam-6729	232	4	icd_code	icd_code	NOUN
ejpam-6729	232	5	}	}	PUNCT
ejpam-6729	232	6	,	,	PUNCT
ejpam-6729	232	7	(	(	PUNCT
ejpam-6729	232	8	v4	v4	NOUN
ejpam-6729	232	9	,	,	PUNCT
ejpam-6729	232	10	icd_code	icd_code	NOUN
ejpam-6729	232	11	)	)	PUNCT
ejpam-6729	232	12	=	=	PUNCT
ejpam-6729	232	13	“	"	PUNCT
ejpam-6729	232	14	r51	r51	NOUN
ejpam-6729	232	15	”	"	PUNCT
ejpam-6729	232	16	,	,	PUNCT
ejpam-6729	232	17	(	(	PUNCT
ejpam-6729	232	18	e2	e2	PROPN
ejpam-6729	232	19	)	)	PUNCT
ejpam-6729	232	20	=	=	SYM
ejpam-6729	232	21	{	{	PUNCT
ejpam-6729	232	22	age	age	NOUN
ejpam-6729	232	23	,	,	PUNCT
ejpam-6729	232	24	gender	gender	NOUN
ejpam-6729	232	25	,	,	PUNCT
ejpam-6729	232	26	severity	severity	NOUN
ejpam-6729	232	27	}	}	PUNCT
ejpam-6729	232	28	,	,	PUNCT
ejpam-6729	232	29	(	(	PUNCT
ejpam-6729	232	30	e2	e2	PROPN
ejpam-6729	232	31	,	,	PUNCT
ejpam-6729	232	32	severity	severity	NOUN
ejpam-6729	232	33	)	)	PUNCT
ejpam-6729	232	34	=	=	SYM
ejpam-6729	232	35	“	"	PUNCT
ejpam-6729	232	36	mild	mild	ADJ
ejpam-6729	232	37	”	"	PUNCT
ejpam-6729	232	38	.	.	PUNCT
ejpam-6729	233	1	the	the	DET
ejpam-6729	233	2	quadruple	quadruple	NOUN
ejpam-6729	233	3	h	h	NOUN
ejpam-6729	233	4	=	=	SYM
ejpam-6729	233	5	(	(	PUNCT
ejpam-6729	233	6	v	v	NOUN
ejpam-6729	233	7	,	,	PUNCT
ejpam-6729	233	8	e	e	NOUN
ejpam-6729	233	9	,	,	PUNCT
ejpam-6729	233	10	λ	λ	PROPN
ejpam-6729	233	11	,	,	PUNCT
ejpam-6729	233	12	µ	µ	NOUN
ejpam-6729	233	13	)	)	PUNCT
ejpam-6729	233	14	thus	thus	ADV
ejpam-6729	233	15	satisfies	satisfy	VERB
ejpam-6729	233	16	definition	definition	NOUN
ejpam-6729	233	17	7	7	NUM
ejpam-6729	233	18	,	,	PUNCT
ejpam-6729	233	19	modelling	model	VERB
ejpam-6729	233	20	a	a	DET
ejpam-6729	233	21	patient‐symptom	patient‐symptom	NOUN
ejpam-6729	233	22	dataset	dataset	NOUN
ejpam-6729	233	23	in	in	ADP
ejpam-6729	233	24	which	which	PRON
ejpam-6729	233	25	each	each	DET
ejpam-6729	233	26	record	record	NOUN
ejpam-6729	233	27	links	link	NOUN
ejpam-6729	233	28	multiple	multiple	ADJ
ejpam-6729	233	29	symptoms	symptom	NOUN
ejpam-6729	233	30	and	and	CCONJ
ejpam-6729	233	31	carries	carry	VERB
ejpam-6729	233	32	patient	patient	ADJ
ejpam-6729	233	33	attributes	attribute	NOUN
ejpam-6729	233	34	.	.	PUNCT
ejpam-6729	234	1	example	example	NOUN
ejpam-6729	234	2	7	7	NUM
ejpam-6729	234	3	(	(	PUNCT
ejpam-6729	234	4	property	property	NOUN
ejpam-6729	234	5	hypergraph	hypergraph	NOUN
ejpam-6729	234	6	for	for	ADP
ejpam-6729	234	7	university	university	NOUN
ejpam-6729	234	8	course	course	NOUN
ejpam-6729	234	9	enrollment	enrollment	NOUN
ejpam-6729	234	10	)	)	PUNCT
ejpam-6729	234	11	.	.	PUNCT
ejpam-6729	235	1	we	we	PRON
ejpam-6729	235	2	illustrate	illustrate	VERB
ejpam-6729	235	3	definition	definition	NOUN
ejpam-6729	235	4	7	7	NUM
ejpam-6729	235	5	by	by	ADP
ejpam-6729	235	6	modelling	model	VERB
ejpam-6729	235	7	a	a	DET
ejpam-6729	235	8	university	university	NOUN
ejpam-6729	235	9	’s	’s	PART
ejpam-6729	235	10	course‐enrollment	course‐enrollment	ADJ
ejpam-6729	235	11	system	system	NOUN
ejpam-6729	235	12	.	.	PUNCT
ejpam-6729	236	1	t.	t.	PROPN
ejpam-6729	236	2	fujita	fujita	PROPN
ejpam-6729	236	3	,	,	PUNCT
ejpam-6729	236	4	f.	f.	PROPN
ejpam-6729	236	5	smarandache	smarandache	PROPN
ejpam-6729	236	6	/	/	SYM
ejpam-6729	236	7	eur	eur	PROPN
ejpam-6729	236	8	.	.	PUNCT
ejpam-6729	237	1	j.	j.	PROPN
ejpam-6729	237	2	pure	pure	PROPN
ejpam-6729	237	3	appl	appl	PROPN
ejpam-6729	237	4	.	.	PROPN
ejpam-6729	237	5	math	math	PROPN
ejpam-6729	237	6	,	,	PUNCT
ejpam-6729	237	7	18	18	NUM
ejpam-6729	237	8	(	(	PUNCT
ejpam-6729	237	9	4	4	NUM
ejpam-6729	237	10	)	)	PUNCT
ejpam-6729	237	11	(	(	PUNCT
ejpam-6729	237	12	2025	2025	NUM
ejpam-6729	237	13	)	)	PUNCT
ejpam-6729	237	14	,	,	PUNCT
ejpam-6729	237	15	6729	6729	NUM
ejpam-6729	237	16	12	12	NUM
ejpam-6729	237	17	of	of	ADP
ejpam-6729	237	18	36	36	NUM
ejpam-6729	237	19	label	label	NOUN
ejpam-6729	237	20	alphabet	alphabet	NOUN
ejpam-6729	237	21	,	,	PUNCT
ejpam-6729	237	22	keys	key	NOUN
ejpam-6729	237	23	,	,	PUNCT
ejpam-6729	237	24	and	and	CCONJ
ejpam-6729	237	25	value	value	NOUN
ejpam-6729	237	26	domain	domain	NOUN
ejpam-6729	237	27	.	.	PUNCT
ejpam-6729	238	1	σ	σ	NOUN
ejpam-6729	238	2	=	=	SYM
ejpam-6729	238	3	{	{	PUNCT
ejpam-6729	238	4	cse101	cse101	PROPN
ejpam-6729	238	5	,	,	PUNCT
ejpam-6729	238	6	math202	math202	PROPN
ejpam-6729	238	7	,	,	PUNCT
ejpam-6729	238	8	hist303	hist303	PROPN
ejpam-6729	238	9	}	}	PUNCT
ejpam-6729	238	10	,	,	PUNCT
ejpam-6729	238	11	k	k	X
ejpam-6729	238	12	=	=	PUNCT
ejpam-6729	238	13	{	{	PUNCT
ejpam-6729	238	14	role	role	NOUN
ejpam-6729	238	15	,	,	PUNCT
ejpam-6729	238	16	name	name	NOUN
ejpam-6729	238	17	,	,	PUNCT
ejpam-6729	238	18	semester	semester	NOUN
ejpam-6729	238	19	,	,	PUNCT
ejpam-6729	238	20	credits	credit	NOUN
ejpam-6729	238	21	}	}	PUNCT
ejpam-6729	238	22	,	,	PUNCT
ejpam-6729	238	23	s	s	AUX
ejpam-6729	238	24	=	=	PUNCT
ejpam-6729	238	25	{	{	PUNCT
ejpam-6729	238	26	“	"	PUNCT
ejpam-6729	238	27	instructor	instructor	NOUN
ejpam-6729	238	28	”	"	PUNCT
ejpam-6729	238	29	,	,	PUNCT
ejpam-6729	238	30	“	"	PUNCT
ejpam-6729	238	31	student	student	NOUN
ejpam-6729	238	32	”	"	PUNCT
ejpam-6729	238	33	,	,	PUNCT
ejpam-6729	238	34	“	"	PUNCT
ejpam-6729	238	35	ta	ta	X
ejpam-6729	238	36	”	"	PUNCT
ejpam-6729	238	37	}	}	PUNCT
ejpam-6729	238	38	∪	∪	ADJ
ejpam-6729	238	39	{	{	PUNCT
ejpam-6729	238	40	strings	string	NOUN
ejpam-6729	238	41	}	}	PUNCT
ejpam-6729	238	42	∪	∪	ADJ
ejpam-6729	238	43	n.	n.	NOUN
ejpam-6729	238	44	vertices	vertex	NOUN
ejpam-6729	238	45	.	.	PUNCT
ejpam-6729	239	1	let	let	VERB
ejpam-6729	239	2	v	v	VERB
ejpam-6729	239	3	=	=	PUNCT
ejpam-6729	239	4	{	{	PUNCT
ejpam-6729	239	5	v1	v1	PROPN
ejpam-6729	239	6	,	,	PUNCT
ejpam-6729	239	7	v2	v2	PROPN
ejpam-6729	239	8	,	,	PUNCT
ejpam-6729	239	9	v3	v3	PROPN
ejpam-6729	239	10	,	,	PUNCT
ejpam-6729	239	11	v4	v4	PROPN
ejpam-6729	239	12	,	,	PUNCT
ejpam-6729	239	13	v5	v5	PROPN
ejpam-6729	239	14	}	}	PUNCT
ejpam-6729	239	15	where	where	SCONJ
ejpam-6729	239	16	µ(v1	µ(v1	ADJ
ejpam-6729	239	17	,	,	PUNCT
ejpam-6729	239	18	name	name	NOUN
ejpam-6729	239	19	)	)	PUNCT
ejpam-6729	239	20	=	=	PUNCT
ejpam-6729	239	21	“	"	PUNCT
ejpam-6729	239	22	dr	dr	PROPN
ejpam-6729	239	23	.	.	PROPN
ejpam-6729	239	24	smith	smith	PROPN
ejpam-6729	239	25	”	"	PUNCT
ejpam-6729	239	26	,	,	PUNCT
ejpam-6729	239	27	µ(v1	µ(v1	ADJ
ejpam-6729	239	28	,	,	PUNCT
ejpam-6729	239	29	role	role	NOUN
ejpam-6729	239	30	)	)	PUNCT
ejpam-6729	239	31	=	=	PUNCT
ejpam-6729	240	1	“	"	PUNCT
ejpam-6729	240	2	instructor	instructor	NOUN
ejpam-6729	240	3	”	"	PUNCT
ejpam-6729	240	4	,	,	PUNCT
ejpam-6729	240	5	µ(v2	µ(v2	NOUN
ejpam-6729	240	6	,	,	PUNCT
ejpam-6729	240	7	name	name	NOUN
ejpam-6729	240	8	)	)	PUNCT
ejpam-6729	240	9	=	=	PUNCT
ejpam-6729	240	10	“	"	PUNCT
ejpam-6729	240	11	alice	alice	PROPN
ejpam-6729	240	12	”	"	PUNCT
ejpam-6729	240	13	,	,	PUNCT
ejpam-6729	240	14	µ(v2	µ(v2	NOUN
ejpam-6729	240	15	,	,	PUNCT
ejpam-6729	240	16	role	role	NOUN
ejpam-6729	240	17	)	)	PUNCT
ejpam-6729	240	18	=	=	PUNCT
ejpam-6729	240	19	“	"	PUNCT
ejpam-6729	240	20	student	student	NOUN
ejpam-6729	240	21	”	"	PUNCT
ejpam-6729	240	22	,	,	PUNCT
ejpam-6729	240	23	µ(v3	µ(v3	NOUN
ejpam-6729	240	24	,	,	PUNCT
ejpam-6729	240	25	name	name	NOUN
ejpam-6729	240	26	)	)	PUNCT
ejpam-6729	240	27	=	=	PUNCT
ejpam-6729	240	28	“	"	PUNCT
ejpam-6729	240	29	bob	bob	PROPN
ejpam-6729	240	30	”	"	PUNCT
ejpam-6729	240	31	,	,	PUNCT
ejpam-6729	240	32	µ(v3	µ(v3	NOUN
ejpam-6729	240	33	,	,	PUNCT
ejpam-6729	240	34	role	role	NOUN
ejpam-6729	240	35	)	)	PUNCT
ejpam-6729	240	36	=	=	PUNCT
ejpam-6729	240	37	“	"	PUNCT
ejpam-6729	240	38	student	student	NOUN
ejpam-6729	240	39	”	"	PUNCT
ejpam-6729	240	40	,	,	PUNCT
ejpam-6729	240	41	µ(v4	µ(v4	PROPN
ejpam-6729	240	42	,	,	PUNCT
ejpam-6729	240	43	name	name	NOUN
ejpam-6729	240	44	)	)	PUNCT
ejpam-6729	240	45	=	=	PUNCT
ejpam-6729	240	46	“	"	PUNCT
ejpam-6729	240	47	carol	carol	NOUN
ejpam-6729	240	48	”	"	PUNCT
ejpam-6729	240	49	,	,	PUNCT
ejpam-6729	240	50	µ(v4	µ(v4	PROPN
ejpam-6729	240	51	,	,	PUNCT
ejpam-6729	240	52	role	role	NOUN
ejpam-6729	240	53	)	)	PUNCT
ejpam-6729	240	54	=	=	PUNCT
ejpam-6729	241	1	“	"	PUNCT
ejpam-6729	241	2	ta	ta	X
ejpam-6729	241	3	”	"	PUNCT
ejpam-6729	241	4	,	,	PUNCT
ejpam-6729	241	5	µ(v5	µ(v5	NOUN
ejpam-6729	241	6	,	,	PUNCT
ejpam-6729	241	7	name	name	NOUN
ejpam-6729	241	8	)	)	PUNCT
ejpam-6729	241	9	=	=	PUNCT
ejpam-6729	241	10	“	"	PUNCT
ejpam-6729	241	11	dave	dave	PROPN
ejpam-6729	241	12	”	"	PUNCT
ejpam-6729	241	13	,	,	PUNCT
ejpam-6729	241	14	µ(v5	µ(v5	NOUN
ejpam-6729	241	15	,	,	PUNCT
ejpam-6729	241	16	role	role	NOUN
ejpam-6729	241	17	)	)	PUNCT
ejpam-6729	241	18	=	=	PUNCT
ejpam-6729	241	19	“	"	PUNCT
ejpam-6729	241	20	student	student	NOUN
ejpam-6729	241	21	”	"	PUNCT
ejpam-6729	241	22	.	.	PUNCT
ejpam-6729	242	1	hyperedges	hyperedge	NOUN
ejpam-6729	242	2	.	.	PUNCT
ejpam-6729	243	1	define	define	VERB
ejpam-6729	243	2	three	three	NUM
ejpam-6729	243	3	hyperedges	hyperedge	NOUN
ejpam-6729	243	4	,	,	PUNCT
ejpam-6729	243	5	one	one	NUM
ejpam-6729	243	6	per	per	ADP
ejpam-6729	243	7	course	course	NOUN
ejpam-6729	243	8	:	:	PUNCT
ejpam-6729	243	9	e	e	X
ejpam-6729	243	10	=	=	PRON
ejpam-6729	243	11	{	{	PUNCT
ejpam-6729	243	12	e1	e1	PROPN
ejpam-6729	243	13	,	,	PUNCT
ejpam-6729	243	14	e2	e2	PROPN
ejpam-6729	243	15	,	,	PUNCT
ejpam-6729	243	16	e3	e3	PROPN
ejpam-6729	243	17	}	}	PUNCT
ejpam-6729	243	18	,	,	PUNCT
ejpam-6729	243	19	with	with	ADP
ejpam-6729	243	20	e1	e1	NOUN
ejpam-6729	243	21	=	=	SYM
ejpam-6729	243	22	{	{	PUNCT
ejpam-6729	243	23	v1	v1	PROPN
ejpam-6729	243	24	,	,	PUNCT
ejpam-6729	243	25	v2	v2	PROPN
ejpam-6729	243	26	,	,	PUNCT
ejpam-6729	243	27	v3	v3	PROPN
ejpam-6729	243	28	,	,	PUNCT
ejpam-6729	243	29	v4	v4	PROPN
ejpam-6729	243	30	}	}	PUNCT
ejpam-6729	243	31	,	,	PUNCT
ejpam-6729	243	32	e2	e2	PROPN
ejpam-6729	243	33	=	=	SYM
ejpam-6729	243	34	{	{	PUNCT
ejpam-6729	243	35	v1	v1	PROPN
ejpam-6729	243	36	,	,	PUNCT
ejpam-6729	243	37	v2	v2	PROPN
ejpam-6729	243	38	,	,	PUNCT
ejpam-6729	243	39	v5	v5	PROPN
ejpam-6729	243	40	}	}	PUNCT
ejpam-6729	243	41	,	,	PUNCT
ejpam-6729	243	42	e3	e3	NOUN
ejpam-6729	243	43	=	=	SYM
ejpam-6729	243	44	{	{	PUNCT
ejpam-6729	243	45	v1	v1	PROPN
ejpam-6729	243	46	,	,	PUNCT
ejpam-6729	243	47	v3	v3	PROPN
ejpam-6729	243	48	,	,	PUNCT
ejpam-6729	243	49	v5	v5	PROPN
ejpam-6729	243	50	}	}	PUNCT
ejpam-6729	243	51	.	.	PUNCT
ejpam-6729	244	1	labels	label	NOUN
ejpam-6729	244	2	and	and	CCONJ
ejpam-6729	244	3	properties	property	NOUN
ejpam-6729	244	4	.	.	PUNCT
ejpam-6729	245	1	for	for	ADP
ejpam-6729	245	2	each	each	DET
ejpam-6729	245	3	course	course	NOUN
ejpam-6729	245	4	hyperedge	hyperedge	NOUN
ejpam-6729	245	5	ei	ei	INTJ
ejpam-6729	245	6	we	we	PRON
ejpam-6729	245	7	set	set	VERB
ejpam-6729	245	8	λ(e1	λ(e1	ADV
ejpam-6729	245	9	)	)	PUNCT
ejpam-6729	246	1	=	=	SYM
ejpam-6729	246	2	cse101	cse101	PROPN
ejpam-6729	246	3	,	,	PUNCT
ejpam-6729	246	4	λ(e2	λ(e2	PROPN
ejpam-6729	246	5	)	)	PUNCT
ejpam-6729	246	6	=	=	SYM
ejpam-6729	246	7	math202	math202	PROPN
ejpam-6729	246	8	,	,	PUNCT
ejpam-6729	246	9	λ(e3	λ(e3	PROPN
ejpam-6729	246	10	)	)	PUNCT
ejpam-6729	246	11	=	=	SYM
ejpam-6729	246	12	hist303	hist303	PROPN
ejpam-6729	246	13	,	,	PUNCT
ejpam-6729	246	14	and	and	CCONJ
ejpam-6729	246	15	assign	assign	VERB
ejpam-6729	246	16	µ(e1	µ(e1	NOUN
ejpam-6729	246	17	,	,	PUNCT
ejpam-6729	246	18	semester	semester	NOUN
ejpam-6729	246	19	)	)	PUNCT
ejpam-6729	246	20	=	=	PUNCT
ejpam-6729	246	21	“	"	PUNCT
ejpam-6729	246	22	fall	fall	VERB
ejpam-6729	246	23	2025	2025	NUM
ejpam-6729	246	24	”	"	PUNCT
ejpam-6729	246	25	,	,	PUNCT
ejpam-6729	246	26	µ(e1	µ(e1	NOUN
ejpam-6729	246	27	,	,	PUNCT
ejpam-6729	246	28	credits	credit	NOUN
ejpam-6729	246	29	)	)	PUNCT
ejpam-6729	246	30	=	=	SYM
ejpam-6729	246	31	4	4	NUM
ejpam-6729	246	32	,	,	PUNCT
ejpam-6729	246	33	µ(e2	µ(e2	NOUN
ejpam-6729	246	34	,	,	PUNCT
ejpam-6729	246	35	semester	semester	NOUN
ejpam-6729	246	36	)	)	PUNCT
ejpam-6729	246	37	=	=	PUNCT
ejpam-6729	246	38	“	"	PUNCT
ejpam-6729	246	39	spring	spring	NOUN
ejpam-6729	246	40	2025	2025	NUM
ejpam-6729	246	41	”	"	PUNCT
ejpam-6729	246	42	,	,	PUNCT
ejpam-6729	246	43	µ(e2	µ(e2	NOUN
ejpam-6729	246	44	,	,	PUNCT
ejpam-6729	246	45	credits	credit	NOUN
ejpam-6729	246	46	)	)	PUNCT
ejpam-6729	246	47	=	=	SYM
ejpam-6729	246	48	3	3	NUM
ejpam-6729	246	49	,	,	PUNCT
ejpam-6729	246	50	µ(e3	µ(e3	ADJ
ejpam-6729	246	51	,	,	PUNCT
ejpam-6729	246	52	semester	semester	NOUN
ejpam-6729	246	53	)	)	PUNCT
ejpam-6729	246	54	=	=	PUNCT
ejpam-6729	246	55	“	"	PUNCT
ejpam-6729	246	56	fall	fall	VERB
ejpam-6729	246	57	2025	2025	NUM
ejpam-6729	246	58	”	"	PUNCT
ejpam-6729	246	59	,	,	PUNCT
ejpam-6729	246	60	µ(e3	µ(e3	ADJ
ejpam-6729	246	61	,	,	PUNCT
ejpam-6729	246	62	credits	credit	NOUN
ejpam-6729	246	63	)	)	PUNCT
ejpam-6729	246	64	=	=	SYM
ejpam-6729	247	1	3	3	X
ejpam-6729	247	2	.	.	X
ejpam-6729	247	3	keysets	keyset	NOUN
ejpam-6729	247	4	and	and	CCONJ
ejpam-6729	247	5	values	value	NOUN
ejpam-6729	247	6	.	.	PUNCT
ejpam-6729	248	1	for	for	ADP
ejpam-6729	248	2	example	example	NOUN
ejpam-6729	248	3	,	,	PUNCT
ejpam-6729	248	4	(	(	PUNCT
ejpam-6729	248	5	v2	v2	NOUN
ejpam-6729	248	6	)	)	PUNCT
ejpam-6729	248	7	=	=	SYM
ejpam-6729	248	8	{	{	PUNCT
ejpam-6729	248	9	name	name	NOUN
ejpam-6729	248	10	,	,	PUNCT
ejpam-6729	248	11	role	role	NOUN
ejpam-6729	248	12	}	}	PUNCT
ejpam-6729	248	13	,	,	PUNCT
ejpam-6729	248	14	(	(	PUNCT
ejpam-6729	248	15	v2	v2	NOUN
ejpam-6729	248	16	,	,	PUNCT
ejpam-6729	248	17	name	name	NOUN
ejpam-6729	248	18	)	)	PUNCT
ejpam-6729	248	19	=	=	PUNCT
ejpam-6729	248	20	“	"	PUNCT
ejpam-6729	248	21	alice	alice	PROPN
ejpam-6729	248	22	”	"	PUNCT
ejpam-6729	248	23	,	,	PUNCT
ejpam-6729	248	24	(	(	PUNCT
ejpam-6729	248	25	e1	e1	PROPN
ejpam-6729	248	26	)	)	PUNCT
ejpam-6729	248	27	=	=	PRON
ejpam-6729	248	28	{	{	PUNCT
ejpam-6729	248	29	semester	semester	NOUN
ejpam-6729	248	30	,	,	PUNCT
ejpam-6729	248	31	credits	credit	NOUN
ejpam-6729	248	32	}	}	PUNCT
ejpam-6729	248	33	,	,	PUNCT
ejpam-6729	248	34	(	(	PUNCT
ejpam-6729	248	35	e1	e1	NOUN
ejpam-6729	248	36	,	,	PUNCT
ejpam-6729	248	37	credits	credit	NOUN
ejpam-6729	248	38	)	)	PUNCT
ejpam-6729	248	39	=	=	SYM
ejpam-6729	249	1	4	4	X
ejpam-6729	249	2	.	.	X
ejpam-6729	249	3	the	the	DET
ejpam-6729	249	4	quadruple	quadruple	NOUN
ejpam-6729	249	5	h	h	NOUN
ejpam-6729	249	6	=	=	SYM
ejpam-6729	249	7	(	(	PUNCT
ejpam-6729	249	8	v	v	NOUN
ejpam-6729	249	9	,	,	PUNCT
ejpam-6729	249	10	e	e	NOUN
ejpam-6729	249	11	,	,	PUNCT
ejpam-6729	249	12	λ	λ	PROPN
ejpam-6729	249	13	,	,	PUNCT
ejpam-6729	249	14	µ	µ	NOUN
ejpam-6729	249	15	)	)	PUNCT
ejpam-6729	249	16	thus	thus	ADV
ejpam-6729	249	17	satisfies	satisfy	VERB
ejpam-6729	249	18	all	all	DET
ejpam-6729	249	19	clauses	clause	NOUN
ejpam-6729	249	20	of	of	ADP
ejpam-6729	249	21	definition	definition	NOUN
ejpam-6729	249	22	7	7	NUM
ejpam-6729	249	23	:	:	PUNCT
ejpam-6729	249	24	vertices	vertex	NOUN
ejpam-6729	249	25	represent	represent	VERB
ejpam-6729	249	26	people	people	NOUN
ejpam-6729	249	27	with	with	ADP
ejpam-6729	249	28	roles	role	NOUN
ejpam-6729	249	29	,	,	PUNCT
ejpam-6729	249	30	hyperedges	hyperedge	NOUN
ejpam-6729	249	31	represent	represent	VERB
ejpam-6729	249	32	courses	course	NOUN
ejpam-6729	249	33	linking	link	VERB
ejpam-6729	249	34	instructor	instructor	NOUN
ejpam-6729	249	35	,	,	PUNCT
ejpam-6729	249	36	students	student	NOUN
ejpam-6729	249	37	,	,	PUNCT
ejpam-6729	249	38	and	and	CCONJ
ejpam-6729	249	39	tas	ta	NOUN
ejpam-6729	249	40	,	,	PUNCT
ejpam-6729	249	41	each	each	DET
ejpam-6729	249	42	course	course	NOUN
ejpam-6729	249	43	carries	carry	VERB
ejpam-6729	249	44	a	a	DET
ejpam-6729	249	45	label	label	NOUN
ejpam-6729	249	46	(	(	PUNCT
ejpam-6729	249	47	course	course	NOUN
ejpam-6729	249	48	code	code	NOUN
ejpam-6729	249	49	)	)	PUNCT
ejpam-6729	249	50	and	and	CCONJ
ejpam-6729	249	51	properties	property	NOUN
ejpam-6729	249	52	(	(	PUNCT
ejpam-6729	249	53	semester	semester	NOUN
ejpam-6729	249	54	,	,	PUNCT
ejpam-6729	249	55	credits	credit	NOUN
ejpam-6729	249	56	)	)	PUNCT
ejpam-6729	249	57	.	.	PUNCT
ejpam-6729	250	1	example	example	NOUN
ejpam-6729	250	2	8	8	NUM
ejpam-6729	250	3	(	(	PUNCT
ejpam-6729	250	4	property	property	NOUN
ejpam-6729	250	5	hypergraph	hypergraph	NOUN
ejpam-6729	250	6	for	for	ADP
ejpam-6729	250	7	film	film	NOUN
ejpam-6729	250	8	productions	production	NOUN
ejpam-6729	250	9	)	)	PUNCT
ejpam-6729	250	10	.	.	PUNCT
ejpam-6729	251	1	we	we	PRON
ejpam-6729	251	2	illustrate	illustrate	VERB
ejpam-6729	251	3	definition	definition	NOUN
ejpam-6729	251	4	7	7	NUM
ejpam-6729	251	5	by	by	ADP
ejpam-6729	251	6	modelling	model	VERB
ejpam-6729	251	7	a	a	DET
ejpam-6729	251	8	film‐production	film‐production	NOUN
ejpam-6729	251	9	scenario	scenario	NOUN
ejpam-6729	251	10	.	.	PUNCT
ejpam-6729	252	1	t.	t.	PROPN
ejpam-6729	252	2	fujita	fujita	PROPN
ejpam-6729	252	3	,	,	PUNCT
ejpam-6729	252	4	f.	f.	PROPN
ejpam-6729	252	5	smarandache	smarandache	PROPN
ejpam-6729	252	6	/	/	SYM
ejpam-6729	252	7	eur	eur	PROPN
ejpam-6729	252	8	.	.	PUNCT
ejpam-6729	253	1	j.	j.	PROPN
ejpam-6729	253	2	pure	pure	PROPN
ejpam-6729	253	3	appl	appl	PROPN
ejpam-6729	253	4	.	.	PROPN
ejpam-6729	253	5	math	math	PROPN
ejpam-6729	253	6	,	,	PUNCT
ejpam-6729	253	7	18	18	NUM
ejpam-6729	253	8	(	(	PUNCT
ejpam-6729	253	9	4	4	NUM
ejpam-6729	253	10	)	)	PUNCT
ejpam-6729	253	11	(	(	PUNCT
ejpam-6729	253	12	2025	2025	NUM
ejpam-6729	253	13	)	)	PUNCT
ejpam-6729	253	14	,	,	PUNCT
ejpam-6729	253	15	6729	6729	NUM
ejpam-6729	253	16	13	13	NUM
ejpam-6729	253	17	of	of	ADP
ejpam-6729	253	18	36	36	NUM
ejpam-6729	253	19	label	label	NOUN
ejpam-6729	253	20	alphabet	alphabet	NOUN
ejpam-6729	253	21	,	,	PUNCT
ejpam-6729	253	22	keys	key	NOUN
ejpam-6729	253	23	,	,	PUNCT
ejpam-6729	253	24	and	and	CCONJ
ejpam-6729	253	25	value	value	NOUN
ejpam-6729	253	26	domain	domain	NOUN
ejpam-6729	253	27	.	.	PUNCT
ejpam-6729	254	1	σ	σ	NOUN
ejpam-6729	254	2	=	=	PUNCT
ejpam-6729	254	3	{	{	PUNCT
ejpam-6729	254	4	thegreatadventure	thegreatadventure	NOUN
ejpam-6729	254	5	,	,	PUNCT
ejpam-6729	254	6	mysterynight	mysterynight	NOUN
ejpam-6729	254	7	}	}	PUNCT
ejpam-6729	254	8	,	,	PUNCT
ejpam-6729	254	9	k	k	X
ejpam-6729	254	10	=	=	PUNCT
ejpam-6729	254	11	{	{	PUNCT
ejpam-6729	254	12	roletype	roletype	NOUN
ejpam-6729	254	13	,	,	PUNCT
ejpam-6729	254	14	name	name	NOUN
ejpam-6729	254	15	,	,	PUNCT
ejpam-6729	254	16	birthyear	birthyear	ADJ
ejpam-6729	254	17	,	,	PUNCT
ejpam-6729	254	18	nationality	nationality	NOUN
ejpam-6729	254	19	,	,	PUNCT
ejpam-6729	254	20	releaseyear	releaseyear	ADJ
ejpam-6729	254	21	,	,	PUNCT
ejpam-6729	254	22	genre	genre	NOUN
ejpam-6729	254	23	,	,	PUNCT
ejpam-6729	254	24	boxoffice	boxoffice	NOUN
ejpam-6729	254	25	}	}	PUNCT
ejpam-6729	254	26	,	,	PUNCT
ejpam-6729	254	27	s	s	AUX
ejpam-6729	254	28	=	=	PUNCT
ejpam-6729	254	29	{	{	PUNCT
ejpam-6729	254	30	“	"	PUNCT
ejpam-6729	254	31	actor	actor	NOUN
ejpam-6729	254	32	”	"	PUNCT
ejpam-6729	254	33	,	,	PUNCT
ejpam-6729	254	34	“	"	PUNCT
ejpam-6729	254	35	director	director	NOUN
ejpam-6729	254	36	”	"	PUNCT
ejpam-6729	254	37	,	,	PUNCT
ejpam-6729	254	38	“	"	PUNCT
ejpam-6729	254	39	producer	producer	NOUN
ejpam-6729	254	40	”	"	PUNCT
ejpam-6729	254	41	}	}	PUNCT
ejpam-6729	254	42	∪	∪	VERB
ejpam-6729	254	43	strings	string	NOUN
ejpam-6729	254	44	∪	∪	ADP
ejpam-6729	254	45	n.	n.	NOUN
ejpam-6729	254	46	vertices	vertex	NOUN
ejpam-6729	254	47	.	.	PUNCT
ejpam-6729	255	1	let	let	VERB
ejpam-6729	255	2	v	v	VERB
ejpam-6729	255	3	=	=	PUNCT
ejpam-6729	255	4	{	{	PUNCT
ejpam-6729	255	5	v1	v1	PROPN
ejpam-6729	255	6	,	,	PUNCT
ejpam-6729	255	7	v2	v2	PROPN
ejpam-6729	255	8	,	,	PUNCT
ejpam-6729	255	9	v3	v3	PROPN
ejpam-6729	255	10	,	,	PUNCT
ejpam-6729	255	11	v4	v4	PROPN
ejpam-6729	255	12	,	,	PUNCT
ejpam-6729	255	13	v5	v5	PROPN
ejpam-6729	255	14	}	}	PUNCT
ejpam-6729	255	15	,	,	PUNCT
ejpam-6729	255	16	with	with	ADP
ejpam-6729	255	17	properties	property	NOUN
ejpam-6729	255	18	µ(v1	µ(v1	VERB
ejpam-6729	255	19	,	,	PUNCT
ejpam-6729	255	20	name	name	NOUN
ejpam-6729	255	21	)	)	PUNCT
ejpam-6729	255	22	=	=	PUNCT
ejpam-6729	256	1	“	"	PUNCT
ejpam-6729	256	2	alice	alice	PROPN
ejpam-6729	256	3	johnson	johnson	PROPN
ejpam-6729	256	4	”	"	PUNCT
ejpam-6729	256	5	,	,	PUNCT
ejpam-6729	256	6	µ(v1	µ(v1	ADJ
ejpam-6729	256	7	,	,	PUNCT
ejpam-6729	256	8	roletype	roletype	NOUN
ejpam-6729	256	9	)	)	PUNCT
ejpam-6729	256	10	=	=	PUNCT
ejpam-6729	256	11	“	"	PUNCT
ejpam-6729	256	12	actor	actor	NOUN
ejpam-6729	256	13	”	"	PUNCT
ejpam-6729	256	14	,	,	PUNCT
ejpam-6729	256	15	µ(v1	µ(v1	ADJ
ejpam-6729	256	16	,	,	PUNCT
ejpam-6729	256	17	birthyear	birthyear	ADJ
ejpam-6729	256	18	)	)	PUNCT
ejpam-6729	256	19	=	=	SYM
ejpam-6729	256	20	1985	1985	NUM
ejpam-6729	256	21	,	,	PUNCT
ejpam-6729	256	22	µ(v2	µ(v2	NOUN
ejpam-6729	256	23	,	,	PUNCT
ejpam-6729	256	24	name	name	NOUN
ejpam-6729	256	25	)	)	PUNCT
ejpam-6729	256	26	=	=	PUNCT
ejpam-6729	256	27	“	"	PUNCT
ejpam-6729	256	28	bob	bob	PROPN
ejpam-6729	256	29	lee	lee	PROPN
ejpam-6729	256	30	”	"	PUNCT
ejpam-6729	256	31	,	,	PUNCT
ejpam-6729	256	32	µ(v2	µ(v2	PROPN
ejpam-6729	256	33	,	,	PUNCT
ejpam-6729	256	34	roletype	roletype	NOUN
ejpam-6729	256	35	)	)	PUNCT
ejpam-6729	256	36	=	=	PUNCT
ejpam-6729	256	37	“	"	PUNCT
ejpam-6729	256	38	actor	actor	NOUN
ejpam-6729	256	39	”	"	PUNCT
ejpam-6729	256	40	,	,	PUNCT
ejpam-6729	256	41	µ(v2	µ(v2	PROPN
ejpam-6729	256	42	,	,	PUNCT
ejpam-6729	256	43	birthyear	birthyear	ADJ
ejpam-6729	256	44	)	)	PUNCT
ejpam-6729	256	45	=	=	SYM
ejpam-6729	256	46	1978	1978	NUM
ejpam-6729	256	47	,	,	PUNCT
ejpam-6729	256	48	µ(v3	µ(v3	NOUN
ejpam-6729	256	49	,	,	PUNCT
ejpam-6729	256	50	name	name	NOUN
ejpam-6729	256	51	)	)	PUNCT
ejpam-6729	256	52	=	=	PUNCT
ejpam-6729	256	53	“	"	PUNCT
ejpam-6729	256	54	carol	carol	PROPN
ejpam-6729	256	55	smith	smith	PROPN
ejpam-6729	256	56	”	"	PUNCT
ejpam-6729	256	57	,	,	PUNCT
ejpam-6729	256	58	µ(v3	µ(v3	NOUN
ejpam-6729	256	59	,	,	PUNCT
ejpam-6729	256	60	roletype	roletype	NOUN
ejpam-6729	256	61	)	)	PUNCT
ejpam-6729	256	62	=	=	PUNCT
ejpam-6729	256	63	“	"	PUNCT
ejpam-6729	256	64	director	director	NOUN
ejpam-6729	256	65	”	"	PUNCT
ejpam-6729	256	66	,	,	PUNCT
ejpam-6729	256	67	µ(v3	µ(v3	NOUN
ejpam-6729	256	68	,	,	PUNCT
ejpam-6729	256	69	nationality	nationality	NOUN
ejpam-6729	256	70	)	)	PUNCT
ejpam-6729	256	71	=	=	PUNCT
ejpam-6729	256	72	“	"	PUNCT
ejpam-6729	256	73	usa	usa	PROPN
ejpam-6729	256	74	”	"	PUNCT
ejpam-6729	256	75	,	,	PUNCT
ejpam-6729	256	76	µ(v4	µ(v4	PROPN
ejpam-6729	256	77	,	,	PUNCT
ejpam-6729	256	78	name	name	NOUN
ejpam-6729	256	79	)	)	PUNCT
ejpam-6729	256	80	=	=	PUNCT
ejpam-6729	256	81	“	"	PUNCT
ejpam-6729	256	82	david	david	PROPN
ejpam-6729	256	83	kumar	kumar	PROPN
ejpam-6729	256	84	”	"	PUNCT
ejpam-6729	256	85	,	,	PUNCT
ejpam-6729	256	86	µ(v4	µ(v4	PROPN
ejpam-6729	256	87	,	,	PUNCT
ejpam-6729	256	88	roletype	roletype	NOUN
ejpam-6729	256	89	)	)	PUNCT
ejpam-6729	256	90	=	=	PUNCT
ejpam-6729	256	91	“	"	PUNCT
ejpam-6729	256	92	producer	producer	NOUN
ejpam-6729	256	93	”	"	PUNCT
ejpam-6729	256	94	,	,	PUNCT
ejpam-6729	256	95	µ(v4	µ(v4	PROPN
ejpam-6729	256	96	,	,	PUNCT
ejpam-6729	256	97	nationality	nationality	NOUN
ejpam-6729	256	98	)	)	PUNCT
ejpam-6729	256	99	=	=	PUNCT
ejpam-6729	256	100	“	"	PUNCT
ejpam-6729	256	101	uk	uk	PROPN
ejpam-6729	256	102	”	"	PUNCT
ejpam-6729	256	103	,	,	PUNCT
ejpam-6729	256	104	µ(v5	µ(v5	NOUN
ejpam-6729	256	105	,	,	PUNCT
ejpam-6729	256	106	name	name	NOUN
ejpam-6729	256	107	)	)	PUNCT
ejpam-6729	256	108	=	=	PUNCT
ejpam-6729	256	109	“	"	PUNCT
ejpam-6729	256	110	eva	eva	PROPN
ejpam-6729	256	111	zhang	zhang	PROPN
ejpam-6729	256	112	”	"	PUNCT
ejpam-6729	256	113	,	,	PUNCT
ejpam-6729	256	114	µ(v5	µ(v5	NOUN
ejpam-6729	256	115	,	,	PUNCT
ejpam-6729	256	116	roletype	roletype	NOUN
ejpam-6729	256	117	)	)	PUNCT
ejpam-6729	256	118	=	=	PUNCT
ejpam-6729	256	119	“	"	PUNCT
ejpam-6729	256	120	actor	actor	NOUN
ejpam-6729	256	121	”	"	PUNCT
ejpam-6729	256	122	,	,	PUNCT
ejpam-6729	256	123	µ(v5	µ(v5	NOUN
ejpam-6729	256	124	,	,	PUNCT
ejpam-6729	256	125	birthyear	birthyear	ADJ
ejpam-6729	256	126	)	)	PUNCT
ejpam-6729	256	127	=	=	SYM
ejpam-6729	256	128	1990	1990	NUM
ejpam-6729	256	129	.	.	PUNCT
ejpam-6729	257	1	hyperedges	hyperedge	NOUN
ejpam-6729	257	2	.	.	PUNCT
ejpam-6729	258	1	define	define	VERB
ejpam-6729	258	2	two	two	NUM
ejpam-6729	258	3	film	film	NOUN
ejpam-6729	258	4	hyperedges	hyperedge	NOUN
ejpam-6729	258	5	:	:	PUNCT
ejpam-6729	258	6	e	e	X
ejpam-6729	258	7	=	=	PRON
ejpam-6729	258	8	{	{	PUNCT
ejpam-6729	258	9	e1	e1	PROPN
ejpam-6729	258	10	,	,	PUNCT
ejpam-6729	258	11	e2	e2	PROPN
ejpam-6729	258	12	}	}	PUNCT
ejpam-6729	258	13	,	,	PUNCT
ejpam-6729	258	14	where	where	SCONJ
ejpam-6729	258	15	e1	e1	NOUN
ejpam-6729	258	16	=	=	SYM
ejpam-6729	258	17	{	{	PUNCT
ejpam-6729	258	18	v1	v1	PROPN
ejpam-6729	258	19	,	,	PUNCT
ejpam-6729	258	20	v2	v2	PROPN
ejpam-6729	258	21	,	,	PUNCT
ejpam-6729	258	22	v3	v3	PROPN
ejpam-6729	258	23	,	,	PUNCT
ejpam-6729	258	24	v4	v4	PROPN
ejpam-6729	258	25	}	}	PUNCT
ejpam-6729	258	26	(	(	PUNCT
ejpam-6729	258	27	the	the	DET
ejpam-6729	258	28	great	great	ADJ
ejpam-6729	258	29	adventure	adventure	NOUN
ejpam-6729	258	30	cast	cast	NOUN
ejpam-6729	258	31	/	/	SYM
ejpam-6729	258	32	crew	crew	NOUN
ejpam-6729	258	33	)	)	PUNCT
ejpam-6729	258	34	,	,	PUNCT
ejpam-6729	258	35	e2	e2	PROPN
ejpam-6729	258	36	=	=	PUNCT
ejpam-6729	258	37	{	{	PUNCT
ejpam-6729	258	38	v2	v2	PROPN
ejpam-6729	258	39	,	,	PUNCT
ejpam-6729	258	40	v3	v3	PROPN
ejpam-6729	258	41	,	,	PUNCT
ejpam-6729	258	42	v5	v5	PROPN
ejpam-6729	258	43	}	}	PUNCT
ejpam-6729	258	44	(	(	PUNCT
ejpam-6729	258	45	mystery	mystery	NOUN
ejpam-6729	258	46	night	night	NOUN
ejpam-6729	258	47	cast	cast	NOUN
ejpam-6729	258	48	/	/	SYM
ejpam-6729	258	49	crew	crew	NOUN
ejpam-6729	258	50	)	)	PUNCT
ejpam-6729	258	51	.	.	PUNCT
ejpam-6729	259	1	t.	t.	PROPN
ejpam-6729	259	2	fujita	fujita	PROPN
ejpam-6729	259	3	,	,	PUNCT
ejpam-6729	259	4	f.	f.	PROPN
ejpam-6729	259	5	smarandache	smarandache	PROPN
ejpam-6729	259	6	/	/	SYM
ejpam-6729	259	7	eur	eur	PROPN
ejpam-6729	259	8	.	.	PUNCT
ejpam-6729	260	1	j.	j.	PROPN
ejpam-6729	260	2	pure	pure	PROPN
ejpam-6729	260	3	appl	appl	PROPN
ejpam-6729	260	4	.	.	PROPN
ejpam-6729	260	5	math	math	PROPN
ejpam-6729	260	6	,	,	PUNCT
ejpam-6729	260	7	18	18	NUM
ejpam-6729	260	8	(	(	PUNCT
ejpam-6729	260	9	4	4	NUM
ejpam-6729	260	10	)	)	PUNCT
ejpam-6729	260	11	(	(	PUNCT
ejpam-6729	260	12	2025	2025	NUM
ejpam-6729	260	13	)	)	PUNCT
ejpam-6729	260	14	,	,	PUNCT
ejpam-6729	260	15	6729	6729	NUM
ejpam-6729	260	16	14	14	NUM
ejpam-6729	260	17	of	of	ADP
ejpam-6729	260	18	36	36	NUM
ejpam-6729	260	19	labels	label	NOUN
ejpam-6729	260	20	and	and	CCONJ
ejpam-6729	260	21	properties	property	NOUN
ejpam-6729	260	22	.	.	PUNCT
ejpam-6729	261	1	for	for	ADP
ejpam-6729	261	2	each	each	DET
ejpam-6729	261	3	film	film	NOUN
ejpam-6729	261	4	hyperedge	hyperedge	NOUN
ejpam-6729	261	5	:	:	PUNCT
ejpam-6729	261	6	λ(e1	λ(e1	NUM
ejpam-6729	261	7	)	)	PUNCT
ejpam-6729	261	8	=	=	SYM
ejpam-6729	261	9	thegreatadventure	thegreatadventure	NOUN
ejpam-6729	261	10	,	,	PUNCT
ejpam-6729	261	11	µ(e1	µ(e1	NOUN
ejpam-6729	261	12	,	,	PUNCT
ejpam-6729	261	13	releaseyear	releaseyear	ADJ
ejpam-6729	261	14	)	)	PUNCT
ejpam-6729	261	15	=	=	SYM
ejpam-6729	261	16	2024	2024	NUM
ejpam-6729	261	17	,	,	PUNCT
ejpam-6729	261	18	µ(e1	µ(e1	NOUN
ejpam-6729	261	19	,	,	PUNCT
ejpam-6729	261	20	genre	genre	NOUN
ejpam-6729	261	21	)	)	PUNCT
ejpam-6729	261	22	=	=	PUNCT
ejpam-6729	261	23	“	"	PUNCT
ejpam-6729	261	24	action	action	NOUN
ejpam-6729	261	25	”	"	PUNCT
ejpam-6729	261	26	,	,	PUNCT
ejpam-6729	261	27	µ(e1	µ(e1	NOUN
ejpam-6729	261	28	,	,	PUNCT
ejpam-6729	261	29	boxoffice	boxoffice	NOUN
ejpam-6729	261	30	)	)	PUNCT
ejpam-6729	261	31	=	=	SYM
ejpam-6729	261	32	120000000	120000000	NUM
ejpam-6729	261	33	,	,	PUNCT
ejpam-6729	261	34	λ(e2	λ(e2	NOUN
ejpam-6729	261	35	)	)	PUNCT
ejpam-6729	261	36	=	=	SYM
ejpam-6729	261	37	mysterynight	mysterynight	NOUN
ejpam-6729	261	38	,	,	PUNCT
ejpam-6729	261	39	µ(e2	µ(e2	NOUN
ejpam-6729	261	40	,	,	PUNCT
ejpam-6729	261	41	releaseyear	releaseyear	ADJ
ejpam-6729	261	42	)	)	PUNCT
ejpam-6729	261	43	=	=	SYM
ejpam-6729	261	44	2023	2023	NUM
ejpam-6729	261	45	,	,	PUNCT
ejpam-6729	261	46	µ(e2	µ(e2	NOUN
ejpam-6729	261	47	,	,	PUNCT
ejpam-6729	261	48	genre	genre	NOUN
ejpam-6729	261	49	)	)	PUNCT
ejpam-6729	261	50	=	=	PUNCT
ejpam-6729	261	51	“	"	PUNCT
ejpam-6729	261	52	mystery	mystery	NOUN
ejpam-6729	261	53	”	"	PUNCT
ejpam-6729	261	54	,	,	PUNCT
ejpam-6729	261	55	µ(e2	µ(e2	NOUN
ejpam-6729	261	56	,	,	PUNCT
ejpam-6729	261	57	boxoffice	boxoffice	NOUN
ejpam-6729	261	58	)	)	PUNCT
ejpam-6729	261	59	=	=	SYM
ejpam-6729	261	60	85000000	85000000	NUM
ejpam-6729	261	61	.	.	PUNCT
ejpam-6729	262	1	keysets	keyset	NOUN
ejpam-6729	262	2	and	and	CCONJ
ejpam-6729	262	3	values	value	NOUN
ejpam-6729	262	4	.	.	PUNCT
ejpam-6729	263	1	for	for	ADP
ejpam-6729	263	2	example	example	NOUN
ejpam-6729	263	3	,	,	PUNCT
ejpam-6729	263	4	(	(	PUNCT
ejpam-6729	263	5	v3	v3	PROPN
ejpam-6729	263	6	)	)	PUNCT
ejpam-6729	263	7	=	=	PRON
ejpam-6729	263	8	{	{	PUNCT
ejpam-6729	263	9	name	name	NOUN
ejpam-6729	263	10	,	,	PUNCT
ejpam-6729	263	11	roletype	roletype	NOUN
ejpam-6729	263	12	,	,	PUNCT
ejpam-6729	263	13	nationality	nationality	NOUN
ejpam-6729	263	14	}	}	PUNCT
ejpam-6729	263	15	,	,	PUNCT
ejpam-6729	263	16	(	(	PUNCT
ejpam-6729	263	17	v3	v3	NOUN
ejpam-6729	263	18	,	,	PUNCT
ejpam-6729	263	19	roletype	roletype	NOUN
ejpam-6729	263	20	)	)	PUNCT
ejpam-6729	263	21	=	=	PUNCT
ejpam-6729	263	22	“	"	PUNCT
ejpam-6729	263	23	director	director	NOUN
ejpam-6729	263	24	”	"	PUNCT
ejpam-6729	263	25	,	,	PUNCT
ejpam-6729	263	26	(	(	PUNCT
ejpam-6729	263	27	e1	e1	PROPN
ejpam-6729	263	28	)	)	PUNCT
ejpam-6729	263	29	=	=	PRON
ejpam-6729	264	1	{	{	PUNCT
ejpam-6729	264	2	releaseyear	releaseyear	ADJ
ejpam-6729	264	3	,	,	PUNCT
ejpam-6729	264	4	genre	genre	NOUN
ejpam-6729	264	5	,	,	PUNCT
ejpam-6729	264	6	boxoffice	boxoffice	NOUN
ejpam-6729	264	7	}	}	PUNCT
ejpam-6729	264	8	,	,	PUNCT
ejpam-6729	264	9	(	(	PUNCT
ejpam-6729	264	10	e1	e1	NOUN
ejpam-6729	264	11	,	,	PUNCT
ejpam-6729	264	12	genre	genre	NOUN
ejpam-6729	264	13	)	)	PUNCT
ejpam-6729	264	14	=	=	PUNCT
ejpam-6729	264	15	“	"	PUNCT
ejpam-6729	264	16	action	action	NOUN
ejpam-6729	264	17	”	"	PUNCT
ejpam-6729	264	18	.	.	PUNCT
ejpam-6729	265	1	the	the	DET
ejpam-6729	265	2	quadruple	quadruple	NOUN
ejpam-6729	265	3	h	h	NOUN
ejpam-6729	265	4	=	=	SYM
ejpam-6729	265	5	(	(	PUNCT
ejpam-6729	265	6	v	v	NOUN
ejpam-6729	265	7	,	,	PUNCT
ejpam-6729	265	8	e	e	NOUN
ejpam-6729	265	9	,	,	PUNCT
ejpam-6729	265	10	λ	λ	PROPN
ejpam-6729	265	11	,	,	PUNCT
ejpam-6729	265	12	µ	µ	NOUN
ejpam-6729	265	13	)	)	PUNCT
ejpam-6729	265	14	thus	thus	ADV
ejpam-6729	265	15	satisfies	satisfy	VERB
ejpam-6729	265	16	all	all	DET
ejpam-6729	265	17	requirements	requirement	NOUN
ejpam-6729	265	18	of	of	ADP
ejpam-6729	265	19	definition	definition	NOUN
ejpam-6729	265	20	7	7	NUM
ejpam-6729	265	21	:	:	PUNCT
ejpam-6729	265	22	vertices	vertex	NOUN
ejpam-6729	265	23	represent	represent	VERB
ejpam-6729	265	24	cast	cast	NOUN
ejpam-6729	265	25	and	and	CCONJ
ejpam-6729	265	26	crew	crew	NOUN
ejpam-6729	265	27	with	with	ADP
ejpam-6729	265	28	personal	personal	ADJ
ejpam-6729	265	29	attributes	attribute	NOUN
ejpam-6729	265	30	;	;	PUNCT
ejpam-6729	265	31	hyperedges	hyperedge	NOUN
ejpam-6729	265	32	represent	represent	VERB
ejpam-6729	265	33	films	film	NOUN
ejpam-6729	265	34	linking	link	VERB
ejpam-6729	265	35	multiple	multiple	ADJ
ejpam-6729	265	36	participants	participant	NOUN
ejpam-6729	265	37	,	,	PUNCT
ejpam-6729	265	38	each	each	PRON
ejpam-6729	265	39	carrying	carry	VERB
ejpam-6729	265	40	a	a	DET
ejpam-6729	265	41	label	label	NOUN
ejpam-6729	265	42	(	(	PUNCT
ejpam-6729	265	43	film	film	NOUN
ejpam-6729	265	44	title	title	NOUN
ejpam-6729	265	45	)	)	PUNCT
ejpam-6729	265	46	and	and	CCONJ
ejpam-6729	265	47	properties	property	NOUN
ejpam-6729	265	48	(	(	PUNCT
ejpam-6729	265	49	release	release	NOUN
ejpam-6729	265	50	year	year	NOUN
ejpam-6729	265	51	,	,	PUNCT
ejpam-6729	265	52	genre	genre	NOUN
ejpam-6729	265	53	,	,	PUNCT
ejpam-6729	265	54	box	box	NOUN
ejpam-6729	265	55	office	office	PROPN
ejpam-6729	265	56	)	)	PUNCT
ejpam-6729	265	57	.	.	PUNCT
ejpam-6729	266	1	theorem	theorem	ADJ
ejpam-6729	266	2	1	1	NUM
ejpam-6729	266	3	(	(	PUNCT
ejpam-6729	266	4	generalisation	generalisation	NOUN
ejpam-6729	266	5	of	of	ADP
ejpam-6729	266	6	property	property	NOUN
ejpam-6729	266	7	graphs	graph	NOUN
ejpam-6729	266	8	and	and	CCONJ
ejpam-6729	266	9	hypergraphs	hypergraph	NOUN
ejpam-6729	266	10	)	)	PUNCT
ejpam-6729	266	11	.	.	PUNCT
ejpam-6729	267	1	let	let	VERB
ejpam-6729	267	2	h	h	NOUN
ejpam-6729	267	3	=	=	PUNCT
ejpam-6729	267	4	(	(	PUNCT
ejpam-6729	267	5	v	v	NOUN
ejpam-6729	267	6	,	,	PUNCT
ejpam-6729	267	7	e	e	NOUN
ejpam-6729	267	8	,	,	PUNCT
ejpam-6729	267	9	λ	λ	PROPN
ejpam-6729	267	10	,	,	PUNCT
ejpam-6729	267	11	µ	µ	NOUN
ejpam-6729	267	12	)	)	PUNCT
ejpam-6729	267	13	be	be	VERB
ejpam-6729	267	14	a	a	DET
ejpam-6729	267	15	property	property	NOUN
ejpam-6729	267	16	hypergraph	hypergraph	NOUN
ejpam-6729	267	17	over	over	ADP
ejpam-6729	267	18	(	(	PUNCT
ejpam-6729	267	19	σ	σ	PROPN
ejpam-6729	267	20	,	,	PUNCT
ejpam-6729	267	21	k	k	NOUN
ejpam-6729	267	22	,	,	PUNCT
ejpam-6729	267	23	s,⊥	s,⊥	ADJ
ejpam-6729	267	24	)	)	PUNCT
ejpam-6729	267	25	.	.	PUNCT
ejpam-6729	268	1	then	then	ADV
ejpam-6729	268	2	:	:	PUNCT
ejpam-6729	268	3	(	(	PUNCT
ejpam-6729	268	4	i	i	NOUN
ejpam-6729	268	5	)	)	PUNCT
ejpam-6729	268	6	if	if	SCONJ
ejpam-6729	268	7	every	every	DET
ejpam-6729	268	8	hyperedge	hyperedge	NOUN
ejpam-6729	268	9	e	e	X
ejpam-6729	268	10	∈	∈	NOUN
ejpam-6729	268	11	e	e	NOUN
ejpam-6729	268	12	satisfies	satisfy	VERB
ejpam-6729	268	13	|e|	|e|	PRON
ejpam-6729	268	14	=	=	SYM
ejpam-6729	268	15	2	2	NUM
ejpam-6729	268	16	and	and	CCONJ
ejpam-6729	268	17	we	we	PRON
ejpam-6729	268	18	equip	equip	VERB
ejpam-6729	268	19	e	e	NOUN
ejpam-6729	268	20	=	=	PUNCT
ejpam-6729	268	21	{	{	PUNCT
ejpam-6729	268	22	u	u	NOUN
ejpam-6729	268	23	,	,	PUNCT
ejpam-6729	268	24	v	v	NOUN
ejpam-6729	268	25	}	}	PUNCT
ejpam-6729	268	26	with	with	ADP
ejpam-6729	268	27	an	an	DET
ejpam-6729	268	28	arbitrary	arbitrary	ADJ
ejpam-6729	268	29	orientation	orientation	NOUN
ejpam-6729	268	30	u	u	NOUN
ejpam-6729	268	31	→	→	SYM
ejpam-6729	268	32	v	v	PROPN
ejpam-6729	268	33	,	,	PUNCT
ejpam-6729	268	34	then	then	ADV
ejpam-6729	268	35	(	(	PUNCT
ejpam-6729	268	36	v	v	NOUN
ejpam-6729	268	37	,	,	PUNCT
ejpam-6729	268	38	e	e	NOUN
ejpam-6729	268	39	,	,	PUNCT
ejpam-6729	268	40	s	s	PROPN
ejpam-6729	268	41	,	,	PUNCT
ejpam-6729	268	42	t	t	PROPN
ejpam-6729	268	43	,	,	PUNCT
ejpam-6729	268	44	λ	λ	NOUN
ejpam-6729	268	45	,	,	PUNCT
ejpam-6729	268	46	µ,⊥	µ,⊥	NOUN
ejpam-6729	268	47	)	)	PUNCT
ejpam-6729	268	48	is	be	AUX
ejpam-6729	268	49	precisely	precisely	ADV
ejpam-6729	268	50	a	a	DET
ejpam-6729	268	51	property	property	NOUN
ejpam-6729	268	52	graph	graph	NOUN
ejpam-6729	268	53	as	as	ADP
ejpam-6729	268	54	in	in	ADP
ejpam-6729	268	55	definition	definition	NOUN
ejpam-6729	268	56	6	6	NUM
ejpam-6729	268	57	.	.	PUNCT
ejpam-6729	269	1	(	(	PUNCT
ejpam-6729	269	2	ii	ii	NOUN
ejpam-6729	269	3	)	)	PUNCT
ejpam-6729	269	4	if	if	SCONJ
ejpam-6729	269	5	σ	σ	NOUN
ejpam-6729	269	6	=	=	SYM
ejpam-6729	269	7	{	{	PUNCT
ejpam-6729	269	8	σ0	σ0	NOUN
ejpam-6729	269	9	}	}	PUNCT
ejpam-6729	269	10	is	be	AUX
ejpam-6729	269	11	a	a	DET
ejpam-6729	269	12	singleton	singleton	NOUN
ejpam-6729	269	13	and	and	CCONJ
ejpam-6729	269	14	µ(x	µ(x	ADJ
ejpam-6729	269	15	,	,	PUNCT
ejpam-6729	269	16	k	k	NOUN
ejpam-6729	269	17	)	)	PUNCT
ejpam-6729	269	18	≡	≡	PROPN
ejpam-6729	269	19	⊥	⊥	PROPN
ejpam-6729	269	20	for	for	ADP
ejpam-6729	269	21	all	all	PRON
ejpam-6729	269	22	(	(	PUNCT
ejpam-6729	269	23	x	x	NOUN
ejpam-6729	269	24	,	,	PUNCT
ejpam-6729	269	25	k	k	NOUN
ejpam-6729	269	26	)	)	PUNCT
ejpam-6729	269	27	,	,	PUNCT
ejpam-6729	269	28	then	then	ADV
ejpam-6729	269	29	h	h	NOUN
ejpam-6729	269	30	=	=	SYM
ejpam-6729	269	31	(	(	PUNCT
ejpam-6729	269	32	v	v	NOUN
ejpam-6729	269	33	,	,	PUNCT
ejpam-6729	269	34	e	e	NOUN
ejpam-6729	269	35	)	)	PUNCT
ejpam-6729	269	36	collapses	collapse	VERB
ejpam-6729	269	37	to	to	ADP
ejpam-6729	269	38	an	an	DET
ejpam-6729	269	39	ordinary	ordinary	ADJ
ejpam-6729	269	40	hypergraph	hypergraph	NOUN
ejpam-6729	269	41	as	as	ADP
ejpam-6729	269	42	in	in	ADP
ejpam-6729	269	43	definition	definition	NOUN
ejpam-6729	269	44	3	3	NUM
ejpam-6729	269	45	.	.	PUNCT
ejpam-6729	270	1	proof	proof	NOUN
ejpam-6729	270	2	.	.	PUNCT
ejpam-6729	271	1	for	for	ADP
ejpam-6729	271	2	(	(	PUNCT
ejpam-6729	271	3	i	i	NOUN
ejpam-6729	271	4	)	)	PUNCT
ejpam-6729	271	5	,	,	PUNCT
ejpam-6729	271	6	restrict	restrict	VERB
ejpam-6729	271	7	every	every	DET
ejpam-6729	271	8	2‐element	2‐element	NUM
ejpam-6729	271	9	hyperedge	hyperedge	NOUN
ejpam-6729	271	10	e	e	NOUN
ejpam-6729	271	11	=	=	SYM
ejpam-6729	271	12	{	{	PUNCT
ejpam-6729	271	13	u	u	NOUN
ejpam-6729	271	14	,	,	PUNCT
ejpam-6729	271	15	v	v	NOUN
ejpam-6729	271	16	}	}	PUNCT
ejpam-6729	271	17	to	to	ADP
ejpam-6729	271	18	a	a	DET
ejpam-6729	271	19	directed	direct	VERB
ejpam-6729	271	20	edge	edge	NOUN
ejpam-6729	271	21	by	by	ADP
ejpam-6729	271	22	choosing	choose	VERB
ejpam-6729	271	23	one	one	NUM
ejpam-6729	271	24	of	of	ADP
ejpam-6729	271	25	the	the	DET
ejpam-6729	271	26	two	two	NUM
ejpam-6729	271	27	orderings	ordering	NOUN
ejpam-6729	271	28	(	(	PUNCT
ejpam-6729	271	29	u	u	NOUN
ejpam-6729	271	30	,	,	PUNCT
ejpam-6729	271	31	v	v	NOUN
ejpam-6729	271	32	)	)	PUNCT
ejpam-6729	271	33	or	or	CCONJ
ejpam-6729	271	34	(	(	PUNCT
ejpam-6729	271	35	v	v	NOUN
ejpam-6729	271	36	,	,	PUNCT
ejpam-6729	271	37	u	u	NOUN
ejpam-6729	271	38	)	)	PUNCT
ejpam-6729	271	39	.	.	PUNCT
ejpam-6729	272	1	the	the	DET
ejpam-6729	272	2	label	label	NOUN
ejpam-6729	272	3	map	map	NOUN
ejpam-6729	272	4	λ	λ	X
ejpam-6729	272	5	:	:	PUNCT
ejpam-6729	272	6	e	e	X
ejpam-6729	272	7	→	→	SYM
ejpam-6729	272	8	σ	σ	NOUN
ejpam-6729	272	9	and	and	CCONJ
ejpam-6729	272	10	the	the	DET
ejpam-6729	272	11	property	property	NOUN
ejpam-6729	272	12	map	map	NOUN
ejpam-6729	272	13	µ	µ	X
ejpam-6729	272	14	coincide	coincide	NOUN
ejpam-6729	272	15	with	with	ADP
ejpam-6729	272	16	those	those	PRON
ejpam-6729	272	17	of	of	ADP
ejpam-6729	272	18	a	a	DET
ejpam-6729	272	19	property	property	NOUN
ejpam-6729	272	20	graph	graph	NOUN
ejpam-6729	272	21	.	.	PUNCT
ejpam-6729	273	1	all	all	DET
ejpam-6729	273	2	axioms	axiom	NOUN
ejpam-6729	273	3	(	(	PUNCT
ejpam-6729	273	4	a)–(f	a)–(f	NOUN
ejpam-6729	273	5	)	)	PUNCT
ejpam-6729	273	6	of	of	ADP
ejpam-6729	273	7	definition	definition	NOUN
ejpam-6729	273	8	6	6	NUM
ejpam-6729	273	9	follow	follow	VERB
ejpam-6729	273	10	immediately	immediately	ADV
ejpam-6729	273	11	.	.	PUNCT
ejpam-6729	274	1	for	for	ADP
ejpam-6729	274	2	(	(	PUNCT
ejpam-6729	274	3	ii	ii	NOUN
ejpam-6729	274	4	)	)	PUNCT
ejpam-6729	274	5	,	,	PUNCT
ejpam-6729	274	6	since	since	SCONJ
ejpam-6729	274	7	σ	σ	PROPN
ejpam-6729	274	8	has	have	VERB
ejpam-6729	274	9	only	only	ADV
ejpam-6729	274	10	one	one	NUM
ejpam-6729	274	11	element	element	NOUN
ejpam-6729	274	12	,	,	PUNCT
ejpam-6729	274	13	λ	λ	PROPN
ejpam-6729	274	14	carries	carry	VERB
ejpam-6729	274	15	no	no	DET
ejpam-6729	274	16	additional	additional	ADJ
ejpam-6729	274	17	information	information	NOUN
ejpam-6729	274	18	;	;	PUNCT
ejpam-6729	274	19	and	and	CCONJ
ejpam-6729	274	20	because	because	SCONJ
ejpam-6729	274	21	µ	µ	PRON
ejpam-6729	274	22	≡	≡	PROPN
ejpam-6729	274	23	⊥	⊥	PROPN
ejpam-6729	274	24	,	,	PUNCT
ejpam-6729	274	25	no	no	DET
ejpam-6729	274	26	vertex	vertex	NOUN
ejpam-6729	274	27	or	or	CCONJ
ejpam-6729	274	28	hyperedge	hyperedge	NOUN
ejpam-6729	274	29	carries	carry	VERB
ejpam-6729	274	30	a	a	DET
ejpam-6729	274	31	property	property	NOUN
ejpam-6729	274	32	.	.	PUNCT
ejpam-6729	275	1	thus	thus	ADV
ejpam-6729	275	2	h	h	NOUN
ejpam-6729	275	3	=	=	SYM
ejpam-6729	275	4	(	(	PUNCT
ejpam-6729	275	5	v	v	NOUN
ejpam-6729	275	6	,	,	PUNCT
ejpam-6729	275	7	e	e	NOUN
ejpam-6729	275	8	)	)	PUNCT
ejpam-6729	275	9	satisfies	satisfy	VERB
ejpam-6729	275	10	exactly	exactly	ADV
ejpam-6729	275	11	the	the	DET
ejpam-6729	275	12	conditions	condition	NOUN
ejpam-6729	275	13	of	of	ADP
ejpam-6729	275	14	definition	definition	NOUN
ejpam-6729	275	15	3	3	NUM
ejpam-6729	275	16	,	,	PUNCT
ejpam-6729	275	17	concluding	conclude	VERB
ejpam-6729	275	18	the	the	DET
ejpam-6729	275	19	proof	proof	NOUN
ejpam-6729	275	20	.	.	PUNCT
ejpam-6729	276	1	theorem	theorem	ADJ
ejpam-6729	276	2	2	2	NUM
ejpam-6729	276	3	(	(	PUNCT
ejpam-6729	276	4	vertex	vertex	NOUN
ejpam-6729	276	5	-	-	PUNCT
ejpam-6729	276	6	induced	induce	VERB
ejpam-6729	276	7	sub	sub	ADJ
ejpam-6729	276	8	-	-	ADJ
ejpam-6729	276	9	property	property	ADJ
ejpam-6729	276	10	hypergraph	hypergraph	NOUN
ejpam-6729	276	11	)	)	PUNCT
ejpam-6729	276	12	.	.	PUNCT
ejpam-6729	277	1	let	let	VERB
ejpam-6729	277	2	h	h	NOUN
ejpam-6729	277	3	=	=	PUNCT
ejpam-6729	277	4	(	(	PUNCT
ejpam-6729	277	5	v	v	NOUN
ejpam-6729	277	6	,	,	PUNCT
ejpam-6729	277	7	e	e	NOUN
ejpam-6729	277	8	,	,	PUNCT
ejpam-6729	277	9	λ	λ	PROPN
ejpam-6729	277	10	,	,	PUNCT
ejpam-6729	277	11	µ	µ	NOUN
ejpam-6729	277	12	)	)	PUNCT
ejpam-6729	277	13	be	be	VERB
ejpam-6729	277	14	a	a	DET
ejpam-6729	277	15	property	property	NOUN
ejpam-6729	277	16	hypergraph	hypergraph	NOUN
ejpam-6729	277	17	and	and	CCONJ
ejpam-6729	277	18	let	let	VERB
ejpam-6729	277	19	u	u	PRON
ejpam-6729	277	20	⊆	⊆	NUM
ejpam-6729	277	21	v	v	NOUN
ejpam-6729	277	22	.	.	PUNCT
ejpam-6729	278	1	define	define	VERB
ejpam-6729	278	2	vu	vu	NOUN
ejpam-6729	278	3	:	:	PUNCT
ejpam-6729	278	4	=	=	SYM
ejpam-6729	278	5	u	u	NOUN
ejpam-6729	278	6	,	,	PUNCT
ejpam-6729	278	7	eu	eu	PROPN
ejpam-6729	278	8	:	:	PUNCT
ejpam-6729	278	9	=	=	X
ejpam-6729	278	10	{	{	PUNCT
ejpam-6729	278	11	e	e	X
ejpam-6729	278	12	∈	∈	PROPN
ejpam-6729	278	13	e	e	NOUN
ejpam-6729	278	14	|	|	NOUN
ejpam-6729	278	15	e	e	NOUN
ejpam-6729	278	16	⊆	⊆	NUM
ejpam-6729	278	17	u	u	NOUN
ejpam-6729	278	18	}	}	PUNCT
ejpam-6729	278	19	,	,	PUNCT
ejpam-6729	278	20	and	and	CCONJ
ejpam-6729	278	21	restrict	restrict	VERB
ejpam-6729	278	22	the	the	DET
ejpam-6729	278	23	maps	map	NOUN
ejpam-6729	278	24	by	by	ADP
ejpam-6729	278	25	λu	λu	X
ejpam-6729	278	26	:	:	PUNCT
ejpam-6729	278	27	=	=	SYM
ejpam-6729	278	28	λ|eu	λ|eu	NOUN
ejpam-6729	278	29	and	and	CCONJ
ejpam-6729	278	30	µu	µu	ADP
ejpam-6729	278	31	:	:	PUNCT
ejpam-6729	278	32	=	=	SYM
ejpam-6729	278	33	µ|(u∪eu	µ|(u∪eu	ADJ
ejpam-6729	278	34	)	)	PUNCT
ejpam-6729	278	35	×k	×k	NOUN
ejpam-6729	278	36	.	.	PUNCT
ejpam-6729	279	1	then	then	ADV
ejpam-6729	279	2	hu	hu	PROPN
ejpam-6729	279	3	:	:	PUNCT
ejpam-6729	280	1	=	=	SYM
ejpam-6729	280	2	(	(	PUNCT
ejpam-6729	280	3	vu	vu	INTJ
ejpam-6729	280	4	,	,	PUNCT
ejpam-6729	280	5	eu	eu	PROPN
ejpam-6729	280	6	,	,	PUNCT
ejpam-6729	280	7	λu	λu	INTJ
ejpam-6729	280	8	,	,	PUNCT
ejpam-6729	280	9	µu	µu	NUM
ejpam-6729	280	10	)	)	PUNCT
ejpam-6729	280	11	is	be	AUX
ejpam-6729	280	12	a	a	DET
ejpam-6729	280	13	property	property	NOUN
ejpam-6729	280	14	hypergraph	hypergraph	NOUN
ejpam-6729	280	15	.	.	PUNCT
ejpam-6729	281	1	t.	t.	PROPN
ejpam-6729	281	2	fujita	fujita	PROPN
ejpam-6729	281	3	,	,	PUNCT
ejpam-6729	281	4	f.	f.	PROPN
ejpam-6729	281	5	smarandache	smarandache	PROPN
ejpam-6729	281	6	/	/	SYM
ejpam-6729	281	7	eur	eur	PROPN
ejpam-6729	281	8	.	.	PUNCT
ejpam-6729	282	1	j.	j.	PROPN
ejpam-6729	282	2	pure	pure	PROPN
ejpam-6729	282	3	appl	appl	PROPN
ejpam-6729	282	4	.	.	PROPN
ejpam-6729	282	5	math	math	PROPN
ejpam-6729	282	6	,	,	PUNCT
ejpam-6729	282	7	18	18	NUM
ejpam-6729	282	8	(	(	PUNCT
ejpam-6729	282	9	4	4	NUM
ejpam-6729	282	10	)	)	PUNCT
ejpam-6729	282	11	(	(	PUNCT
ejpam-6729	282	12	2025	2025	NUM
ejpam-6729	282	13	)	)	PUNCT
ejpam-6729	282	14	,	,	PUNCT
ejpam-6729	282	15	6729	6729	NUM
ejpam-6729	282	16	15	15	NUM
ejpam-6729	282	17	of	of	ADP
ejpam-6729	282	18	36	36	NUM
ejpam-6729	282	19	proof	proof	NOUN
ejpam-6729	282	20	.	.	PUNCT
ejpam-6729	283	1	we	we	PRON
ejpam-6729	283	2	check	check	VERB
ejpam-6729	283	3	the	the	DET
ejpam-6729	283	4	items	item	NOUN
ejpam-6729	283	5	of	of	ADP
ejpam-6729	283	6	definition	definition	NOUN
ejpam-6729	283	7	7	7	NUM
ejpam-6729	283	8	.	.	PUNCT
ejpam-6729	284	1	(	(	PUNCT
ejpam-6729	284	2	a	a	X
ejpam-6729	284	3	)	)	PUNCT
ejpam-6729	284	4	by	by	ADP
ejpam-6729	284	5	construction	construction	NOUN
ejpam-6729	284	6	vu	vu	NOUN
ejpam-6729	284	7	⊆	⊆	NUM
ejpam-6729	284	8	v	v	NOUN
ejpam-6729	284	9	.	.	PUNCT
ejpam-6729	285	1	(	(	PUNCT
ejpam-6729	285	2	b	b	X
ejpam-6729	285	3	)	)	PUNCT
ejpam-6729	285	4	each	each	DET
ejpam-6729	285	5	e	e	PROPN
ejpam-6729	285	6	∈	∈	PROPN
ejpam-6729	285	7	eu	eu	PROPN
ejpam-6729	285	8	is	be	AUX
ejpam-6729	285	9	nonempty	nonempty	ADJ
ejpam-6729	285	10	and	and	CCONJ
ejpam-6729	285	11	e	e	NOUN
ejpam-6729	285	12	⊆	⊆	NUM
ejpam-6729	285	13	u	u	NOUN
ejpam-6729	285	14	=	=	X
ejpam-6729	285	15	vu	vu	X
ejpam-6729	285	16	,	,	PUNCT
ejpam-6729	285	17	hence	hence	ADV
ejpam-6729	285	18	eu	eu	PROPN
ejpam-6729	285	19	⊆	⊆	NUM
ejpam-6729	285	20	p(vu	p(vu	PROPN
ejpam-6729	285	21	)	)	PUNCT
ejpam-6729	285	22	\	\	PROPN
ejpam-6729	285	23	{	{	PUNCT
ejpam-6729	285	24	∅	∅	NOUN
ejpam-6729	285	25	}	}	PUNCT
ejpam-6729	285	26	.	.	PUNCT
ejpam-6729	286	1	(	(	PUNCT
ejpam-6729	286	2	c	c	X
ejpam-6729	286	3	)	)	PUNCT
ejpam-6729	286	4	λu	λu	PROPN
ejpam-6729	286	5	maps	map	VERB
ejpam-6729	286	6	eu	eu	PROPN
ejpam-6729	286	7	into	into	ADP
ejpam-6729	286	8	σ	σ	NUM
ejpam-6729	286	9	by	by	ADP
ejpam-6729	286	10	restriction	restriction	NOUN
ejpam-6729	286	11	.	.	PUNCT
ejpam-6729	287	1	(	(	PUNCT
ejpam-6729	287	2	d	d	X
ejpam-6729	287	3	)	)	PUNCT
ejpam-6729	287	4	µu	µu	ADP
ejpam-6729	287	5	maps	map	NOUN
ejpam-6729	287	6	(	(	PUNCT
ejpam-6729	287	7	vu	vu	PROPN
ejpam-6729	287	8	∪	∪	PROPN
ejpam-6729	287	9	eu	eu	PROPN
ejpam-6729	287	10	)	)	PUNCT
ejpam-6729	287	11	×	×	PROPN
ejpam-6729	287	12	k	k	PROPN
ejpam-6729	287	13	into	into	ADP
ejpam-6729	287	14	s	s	PRON
ejpam-6729	287	15	∪	∪	X
ejpam-6729	287	16	{	{	PUNCT
ejpam-6729	287	17	⊥	⊥	NOUN
ejpam-6729	287	18	}	}	PUNCT
ejpam-6729	287	19	by	by	ADP
ejpam-6729	287	20	restriction	restriction	NOUN
ejpam-6729	287	21	.	.	PUNCT
ejpam-6729	288	1	all	all	DET
ejpam-6729	288	2	conditions	condition	NOUN
ejpam-6729	288	3	hold	hold	VERB
ejpam-6729	288	4	.	.	PUNCT
ejpam-6729	289	1	theorem	theorem	ADJ
ejpam-6729	289	2	3	3	NUM
ejpam-6729	289	3	(	(	PUNCT
ejpam-6729	289	4	edge	edge	NOUN
ejpam-6729	289	5	-	-	PUNCT
ejpam-6729	289	6	induced	induce	VERB
ejpam-6729	289	7	sub	sub	ADJ
ejpam-6729	289	8	-	-	ADJ
ejpam-6729	289	9	property	property	ADJ
ejpam-6729	289	10	hypergraph	hypergraph	NOUN
ejpam-6729	289	11	)	)	PUNCT
ejpam-6729	289	12	.	.	PUNCT
ejpam-6729	290	1	let	let	VERB
ejpam-6729	290	2	h	h	NOUN
ejpam-6729	290	3	=	=	PUNCT
ejpam-6729	290	4	(	(	PUNCT
ejpam-6729	290	5	v	v	NOUN
ejpam-6729	290	6	,	,	PUNCT
ejpam-6729	290	7	e	e	NOUN
ejpam-6729	290	8	,	,	PUNCT
ejpam-6729	290	9	λ	λ	PROPN
ejpam-6729	290	10	,	,	PUNCT
ejpam-6729	290	11	µ	µ	NOUN
ejpam-6729	290	12	)	)	PUNCT
ejpam-6729	290	13	be	be	VERB
ejpam-6729	290	14	a	a	DET
ejpam-6729	290	15	property	property	NOUN
ejpam-6729	290	16	hypergraph	hypergraph	NOUN
ejpam-6729	290	17	and	and	CCONJ
ejpam-6729	290	18	let	let	VERB
ejpam-6729	290	19	f	f	PROPN
ejpam-6729	290	20	⊆	⊆	NUM
ejpam-6729	290	21	e.	e.	PROPN
ejpam-6729	290	22	set	set	PROPN
ejpam-6729	290	23	vf	vf	PROPN
ejpam-6729	290	24	:	:	PUNCT
ejpam-6729	290	25	=	=	SYM
ejpam-6729	290	26	⋃	⋃	NOUN
ejpam-6729	290	27	e∈f	e∈f	ADJ
ejpam-6729	290	28	e	e	NOUN
ejpam-6729	290	29	,	,	PUNCT
ejpam-6729	290	30	ef	ef	X
ejpam-6729	290	31	:	:	PUNCT
ejpam-6729	290	32	=	=	SYM
ejpam-6729	290	33	f	f	X
ejpam-6729	290	34	,	,	PUNCT
ejpam-6729	290	35	and	and	CCONJ
ejpam-6729	290	36	restrict	restrict	VERB
ejpam-6729	290	37	λf	λf	X
ejpam-6729	290	38	:	:	PUNCT
ejpam-6729	290	39	=	=	SYM
ejpam-6729	290	40	λ|ef	λ|ef	NOUN
ejpam-6729	290	41	and	and	CCONJ
ejpam-6729	290	42	µf	µf	X
ejpam-6729	290	43	:	:	PUNCT
ejpam-6729	290	44	=	=	SYM
ejpam-6729	290	45	µ|(vf∪ef	µ|(vf∪ef	X
ejpam-6729	290	46	)	)	PUNCT
ejpam-6729	290	47	×k	×k	NOUN
ejpam-6729	290	48	.	.	PUNCT
ejpam-6729	291	1	then	then	ADV
ejpam-6729	291	2	hf	hf	VERB
ejpam-6729	291	3	:	:	PUNCT
ejpam-6729	291	4	=	=	SYM
ejpam-6729	291	5	(	(	PUNCT
ejpam-6729	291	6	vf	vf	X
ejpam-6729	291	7	,	,	PUNCT
ejpam-6729	291	8	ef	ef	PROPN
ejpam-6729	291	9	,	,	PUNCT
ejpam-6729	291	10	λf	λf	INTJ
ejpam-6729	291	11	,	,	PUNCT
ejpam-6729	291	12	µf	µf	PROPN
ejpam-6729	291	13	)	)	PUNCT
ejpam-6729	291	14	is	be	AUX
ejpam-6729	291	15	a	a	DET
ejpam-6729	291	16	property	property	NOUN
ejpam-6729	291	17	hypergraph	hypergraph	NOUN
ejpam-6729	291	18	.	.	PUNCT
ejpam-6729	292	1	proof	proof	NOUN
ejpam-6729	292	2	.	.	PUNCT
ejpam-6729	293	1	(	(	PUNCT
ejpam-6729	293	2	a	a	X
ejpam-6729	293	3	)	)	PUNCT
ejpam-6729	293	4	vf	vf	PROPN
ejpam-6729	293	5	⊆	⊆	NUM
ejpam-6729	293	6	v	v	NOUN
ejpam-6729	293	7	by	by	ADP
ejpam-6729	293	8	definition	definition	NOUN
ejpam-6729	293	9	.	.	PUNCT
ejpam-6729	294	1	(	(	PUNCT
ejpam-6729	294	2	b	b	X
ejpam-6729	294	3	)	)	PUNCT
ejpam-6729	294	4	every	every	DET
ejpam-6729	294	5	e	e	PROPN
ejpam-6729	294	6	∈	∈	PROPN
ejpam-6729	294	7	ef	ef	PROPN
ejpam-6729	294	8	is	be	AUX
ejpam-6729	294	9	nonempty	nonempty	ADJ
ejpam-6729	294	10	and	and	CCONJ
ejpam-6729	294	11	satisfies	satisfie	NOUN
ejpam-6729	294	12	e	e	PROPN
ejpam-6729	294	13	⊆	⊆	NUM
ejpam-6729	294	14	vf	vf	X
ejpam-6729	294	15	,	,	PUNCT
ejpam-6729	294	16	hence	hence	ADV
ejpam-6729	294	17	ef	ef	VERB
ejpam-6729	294	18	⊆	⊆	NUM
ejpam-6729	294	19	p(vf	p(vf	NOUN
ejpam-6729	294	20	)	)	PUNCT
ejpam-6729	294	21	\	\	NOUN
ejpam-6729	294	22	{	{	PUNCT
ejpam-6729	294	23	∅	∅	NOUN
ejpam-6729	294	24	}	}	PUNCT
ejpam-6729	294	25	.	.	PUNCT
ejpam-6729	295	1	(	(	PUNCT
ejpam-6729	295	2	c)–(d	c)–(d	NOUN
ejpam-6729	295	3	)	)	PUNCT
ejpam-6729	295	4	follow	follow	VERB
ejpam-6729	295	5	immediately	immediately	ADV
ejpam-6729	295	6	from	from	ADP
ejpam-6729	295	7	restricting	restrict	VERB
ejpam-6729	295	8	λ	λ	PROPN
ejpam-6729	295	9	and	and	CCONJ
ejpam-6729	295	10	µ	µ	X
ejpam-6729	295	11	to	to	ADP
ejpam-6729	295	12	the	the	DET
ejpam-6729	295	13	new	new	ADJ
ejpam-6729	295	14	domains	domain	NOUN
ejpam-6729	295	15	/	/	SYM
ejpam-6729	295	16	codomains	codomain	NOUN
ejpam-6729	295	17	.	.	PUNCT
ejpam-6729	296	1	theorem	theorem	VERB
ejpam-6729	296	2	4	4	NUM
ejpam-6729	296	3	(	(	PUNCT
ejpam-6729	296	4	uniformity	uniformity	NOUN
ejpam-6729	296	5	and	and	CCONJ
ejpam-6729	296	6	inheritance	inheritance	NOUN
ejpam-6729	296	7	)	)	PUNCT
ejpam-6729	296	8	.	.	PUNCT
ejpam-6729	297	1	suppose	suppose	VERB
ejpam-6729	297	2	h	h	NOUN
ejpam-6729	297	3	=	=	SYM
ejpam-6729	297	4	(	(	PUNCT
ejpam-6729	297	5	v	v	NOUN
ejpam-6729	297	6	,	,	PUNCT
ejpam-6729	297	7	e	e	NOUN
ejpam-6729	297	8	,	,	PUNCT
ejpam-6729	297	9	λ	λ	PROPN
ejpam-6729	297	10	,	,	PUNCT
ejpam-6729	297	11	µ	µ	NOUN
ejpam-6729	297	12	)	)	PUNCT
ejpam-6729	297	13	is	be	AUX
ejpam-6729	297	14	such	such	ADJ
ejpam-6729	297	15	that	that	SCONJ
ejpam-6729	297	16	there	there	PRON
ejpam-6729	297	17	exists	exist	VERB
ejpam-6729	297	18	k	k	PROPN
ejpam-6729	297	19	≥	≥	NUM
ejpam-6729	297	20	1	1	NUM
ejpam-6729	297	21	with	with	ADP
ejpam-6729	297	22	|e|	|e|	PRON
ejpam-6729	297	23	=	=	SYM
ejpam-6729	297	24	k	k	PROPN
ejpam-6729	297	25	for	for	ADP
ejpam-6729	297	26	all	all	DET
ejpam-6729	297	27	e	e	PROPN
ejpam-6729	297	28	∈	∈	PROPN
ejpam-6729	297	29	e.	e.	PROPN
ejpam-6729	297	30	then	then	ADV
ejpam-6729	297	31	h	h	PROPN
ejpam-6729	297	32	is	be	AUX
ejpam-6729	297	33	k	k	NOUN
ejpam-6729	297	34	-	-	NOUN
ejpam-6729	297	35	uniform	uniform	NOUN
ejpam-6729	297	36	.	.	PUNCT
ejpam-6729	298	1	moreover	moreover	ADV
ejpam-6729	298	2	,	,	PUNCT
ejpam-6729	298	3	every	every	DET
ejpam-6729	298	4	subfamily	subfamily	ADV
ejpam-6729	298	5	f	f	NOUN
ejpam-6729	298	6	⊆	⊆	NUM
ejpam-6729	298	7	e	e	NOUN
ejpam-6729	298	8	yields	yield	VERB
ejpam-6729	298	9	a	a	DET
ejpam-6729	298	10	k	k	ADJ
ejpam-6729	298	11	-	-	PUNCT
ejpam-6729	298	12	uniform	uniform	ADJ
ejpam-6729	298	13	edge	edge	NOUN
ejpam-6729	298	14	-	-	PUNCT
ejpam-6729	298	15	induced	induce	VERB
ejpam-6729	298	16	sub	sub	ADJ
ejpam-6729	298	17	-	-	ADJ
ejpam-6729	298	18	property	property	ADJ
ejpam-6729	298	19	hypergraph	hypergraph	NOUN
ejpam-6729	298	20	hf	hf	NOUN
ejpam-6729	298	21	.	.	PUNCT
ejpam-6729	299	1	proof	proof	NOUN
ejpam-6729	299	2	.	.	PUNCT
ejpam-6729	300	1	by	by	ADP
ejpam-6729	300	2	hypothesis	hypothesis	NOUN
ejpam-6729	300	3	,	,	PUNCT
ejpam-6729	300	4	for	for	ADP
ejpam-6729	300	5	each	each	DET
ejpam-6729	300	6	e	e	NOUN
ejpam-6729	300	7	∈	∈	PROPN
ejpam-6729	300	8	e	e	NOUN
ejpam-6729	300	9	we	we	PRON
ejpam-6729	300	10	have	have	VERB
ejpam-6729	300	11	e	e	NOUN
ejpam-6729	300	12	⊆	⊆	PROPN
ejpam-6729	300	13	v	v	NOUN
ejpam-6729	300	14	and	and	CCONJ
ejpam-6729	300	15	|e|	|e|	NOUN
ejpam-6729	300	16	=	=	SYM
ejpam-6729	300	17	k	k	NOUN
ejpam-6729	300	18	,	,	PUNCT
ejpam-6729	300	19	which	which	PRON
ejpam-6729	300	20	is	be	AUX
ejpam-6729	300	21	precisely	precisely	ADV
ejpam-6729	300	22	the	the	DET
ejpam-6729	300	23	definition	definition	NOUN
ejpam-6729	300	24	of	of	ADP
ejpam-6729	300	25	k	k	NOUN
ejpam-6729	300	26	-	-	NOUN
ejpam-6729	300	27	uniformity	uniformity	NOUN
ejpam-6729	300	28	.	.	PUNCT
ejpam-6729	301	1	if	if	SCONJ
ejpam-6729	301	2	f	f	PROPN
ejpam-6729	301	3	⊆	⊆	NUM
ejpam-6729	301	4	e	e	NOUN
ejpam-6729	301	5	,	,	PUNCT
ejpam-6729	301	6	then	then	ADV
ejpam-6729	301	7	every	every	DET
ejpam-6729	301	8	e	e	NOUN
ejpam-6729	301	9	∈	∈	PROPN
ejpam-6729	301	10	f	f	X
ejpam-6729	301	11	still	still	ADV
ejpam-6729	301	12	satisfies	satisfy	VERB
ejpam-6729	301	13	|e|	|e|	PROPN
ejpam-6729	301	14	=	=	SYM
ejpam-6729	301	15	k	k	PROPN
ejpam-6729	301	16	,	,	PUNCT
ejpam-6729	301	17	so	so	ADV
ejpam-6729	301	18	theorem	theorem	ADJ
ejpam-6729	301	19	3	3	NUM
ejpam-6729	301	20	gives	give	VERB
ejpam-6729	301	21	a	a	DET
ejpam-6729	301	22	k	k	ADJ
ejpam-6729	301	23	-	-	PUNCT
ejpam-6729	301	24	uniform	uniform	ADJ
ejpam-6729	301	25	sub	sub	ADJ
ejpam-6729	301	26	-	-	ADJ
ejpam-6729	301	27	property	property	ADJ
ejpam-6729	301	28	hypergraph	hypergraph	NOUN
ejpam-6729	301	29	.	.	PUNCT
ejpam-6729	302	1	theorem	theorem	NOUN
ejpam-6729	302	2	5	5	NUM
ejpam-6729	302	3	(	(	PUNCT
ejpam-6729	302	4	disjoint	disjoint	NOUN
ejpam-6729	302	5	union	union	NOUN
ejpam-6729	302	6	)	)	PUNCT
ejpam-6729	302	7	.	.	PUNCT
ejpam-6729	303	1	let	let	VERB
ejpam-6729	303	2	h1	h1	VERB
ejpam-6729	303	3	=	=	SYM
ejpam-6729	303	4	(	(	PUNCT
ejpam-6729	303	5	v1	v1	PROPN
ejpam-6729	303	6	,	,	PUNCT
ejpam-6729	303	7	e1	e1	NOUN
ejpam-6729	303	8	,	,	PUNCT
ejpam-6729	303	9	λ1	λ1	ADJ
ejpam-6729	303	10	,	,	PUNCT
ejpam-6729	303	11	µ1	µ1	PROPN
ejpam-6729	303	12	)	)	PUNCT
ejpam-6729	303	13	and	and	CCONJ
ejpam-6729	303	14	h2	h2	NOUN
ejpam-6729	303	15	=	=	SYM
ejpam-6729	303	16	(	(	PUNCT
ejpam-6729	303	17	v2	v2	PROPN
ejpam-6729	303	18	,	,	PUNCT
ejpam-6729	303	19	e2	e2	PROPN
ejpam-6729	303	20	,	,	PUNCT
ejpam-6729	303	21	λ2	λ2	PROPN
ejpam-6729	303	22	,	,	PUNCT
ejpam-6729	303	23	µ2	µ2	PROPN
ejpam-6729	303	24	)	)	PUNCT
ejpam-6729	303	25	be	be	VERB
ejpam-6729	303	26	property	property	NOUN
ejpam-6729	303	27	hypergraphs	hypergraph	NOUN
ejpam-6729	303	28	with	with	ADP
ejpam-6729	303	29	disjoint	disjoint	ADJ
ejpam-6729	303	30	vertex	vertex	NOUN
ejpam-6729	303	31	sets	set	VERB
ejpam-6729	303	32	v1	v1	NOUN
ejpam-6729	303	33	∩	∩	ADJ
ejpam-6729	303	34	v2	v2	NOUN
ejpam-6729	303	35	=	=	PUNCT
ejpam-6729	303	36	∅.	∅.	AUX
ejpam-6729	303	37	define	define	VERB
ejpam-6729	303	38	v	v	ADP
ejpam-6729	303	39	:	:	PUNCT
ejpam-6729	303	40	=	=	SYM
ejpam-6729	303	41	v1	v1	VERB
ejpam-6729	303	42	∪	∪	NOUN
ejpam-6729	303	43	v2	v2	NOUN
ejpam-6729	303	44	,	,	PUNCT
ejpam-6729	303	45	e	e	NOUN
ejpam-6729	303	46	:	:	PUNCT
ejpam-6729	303	47	=	=	SYM
ejpam-6729	303	48	e1	e1	PROPN
ejpam-6729	303	49	∪	∪	ADJ
ejpam-6729	303	50	e2	e2	PROPN
ejpam-6729	303	51	,	,	PUNCT
ejpam-6729	303	52	and	and	CCONJ
ejpam-6729	303	53	the	the	DET
ejpam-6729	303	54	piecewise	piecewise	NOUN
ejpam-6729	303	55	maps	map	NOUN
ejpam-6729	303	56	λ(e	λ(e	VERB
ejpam-6729	303	57	)	)	PUNCT
ejpam-6729	303	58	:	:	PUNCT
ejpam-6729	303	59	=	=	X
ejpam-6729	303	60	{	{	PUNCT
ejpam-6729	303	61	λ1(e	λ1(e	PROPN
ejpam-6729	303	62	)	)	PUNCT
ejpam-6729	303	63	,	,	PUNCT
ejpam-6729	303	64	e	e	PROPN
ejpam-6729	303	65	∈	∈	PROPN
ejpam-6729	303	66	e1	e1	PROPN
ejpam-6729	303	67	,	,	PUNCT
ejpam-6729	303	68	λ2(e	λ2(e	NOUN
ejpam-6729	303	69	)	)	PUNCT
ejpam-6729	303	70	,	,	PUNCT
ejpam-6729	303	71	e	e	PROPN
ejpam-6729	303	72	∈	∈	PROPN
ejpam-6729	303	73	e2	e2	PROPN
ejpam-6729	303	74	,	,	PUNCT
ejpam-6729	303	75	µ(x	µ(x	ADJ
ejpam-6729	303	76	,	,	PUNCT
ejpam-6729	303	77	k	k	NOUN
ejpam-6729	303	78	)	)	PUNCT
ejpam-6729	303	79	:	:	PUNCT
ejpam-6729	304	1	=	=	X
ejpam-6729	304	2	{	{	PUNCT
ejpam-6729	304	3	µ1(x	µ1(x	PROPN
ejpam-6729	304	4	,	,	PUNCT
ejpam-6729	304	5	k	k	NOUN
ejpam-6729	304	6	)	)	PUNCT
ejpam-6729	304	7	,	,	PUNCT
ejpam-6729	304	8	x	x	PUNCT
ejpam-6729	304	9	∈	∈	NOUN
ejpam-6729	304	10	v1	v1	NOUN
ejpam-6729	304	11	∪	∪	NOUN
ejpam-6729	304	12	e1	e1	NOUN
ejpam-6729	304	13	,	,	PUNCT
ejpam-6729	304	14	µ2(x	µ2(x	PROPN
ejpam-6729	304	15	,	,	PUNCT
ejpam-6729	304	16	k	k	NOUN
ejpam-6729	304	17	)	)	PUNCT
ejpam-6729	304	18	,	,	PUNCT
ejpam-6729	304	19	x	x	PUNCT
ejpam-6729	304	20	∈	∈	NOUN
ejpam-6729	304	21	v2	v2	NOUN
ejpam-6729	304	22	∪	∪	PROPN
ejpam-6729	304	23	e2	e2	PROPN
ejpam-6729	304	24	.	.	PUNCT
ejpam-6729	305	1	then	then	ADV
ejpam-6729	305	2	h	h	NOUN
ejpam-6729	305	3	:	:	PUNCT
ejpam-6729	305	4	=	=	SYM
ejpam-6729	305	5	(	(	PUNCT
ejpam-6729	305	6	v	v	NOUN
ejpam-6729	305	7	,	,	PUNCT
ejpam-6729	305	8	e	e	NOUN
ejpam-6729	305	9	,	,	PUNCT
ejpam-6729	305	10	λ	λ	PROPN
ejpam-6729	305	11	,	,	PUNCT
ejpam-6729	305	12	µ	µ	NOUN
ejpam-6729	305	13	)	)	PUNCT
ejpam-6729	305	14	is	be	AUX
ejpam-6729	305	15	a	a	DET
ejpam-6729	305	16	property	property	NOUN
ejpam-6729	305	17	hypergraph	hypergraph	NOUN
ejpam-6729	305	18	.	.	PUNCT
ejpam-6729	306	1	proof	proof	NOUN
ejpam-6729	306	2	.	.	PUNCT
ejpam-6729	307	1	(	(	PUNCT
ejpam-6729	307	2	a	a	X
ejpam-6729	307	3	)	)	PUNCT
ejpam-6729	307	4	v	v	NOUN
ejpam-6729	307	5	is	be	AUX
ejpam-6729	307	6	a	a	DET
ejpam-6729	307	7	set	set	NOUN
ejpam-6729	307	8	of	of	ADP
ejpam-6729	307	9	vertices	vertex	NOUN
ejpam-6729	307	10	.	.	PUNCT
ejpam-6729	308	1	(	(	PUNCT
ejpam-6729	308	2	b	b	X
ejpam-6729	308	3	)	)	PUNCT
ejpam-6729	308	4	each	each	DET
ejpam-6729	308	5	e	e	PROPN
ejpam-6729	308	6	∈	∈	NOUN
ejpam-6729	308	7	ei	ei	X
ejpam-6729	308	8	is	be	AUX
ejpam-6729	308	9	nonempty	nonempty	ADJ
ejpam-6729	308	10	and	and	CCONJ
ejpam-6729	308	11	e	e	NOUN
ejpam-6729	308	12	⊆	⊆	NUM
ejpam-6729	308	13	vi	vi	PROPN
ejpam-6729	308	14	⊆	⊆	NUM
ejpam-6729	308	15	v	v	NOUN
ejpam-6729	308	16	,	,	PUNCT
ejpam-6729	308	17	hence	hence	ADV
ejpam-6729	308	18	e	e	NOUN
ejpam-6729	308	19	⊆	⊆	NUM
ejpam-6729	308	20	p(v	p(v	NOUN
ejpam-6729	308	21	)	)	PUNCT
ejpam-6729	308	22	\	\	NOUN
ejpam-6729	308	23	{	{	PUNCT
ejpam-6729	308	24	∅	∅	NOUN
ejpam-6729	308	25	}	}	PUNCT
ejpam-6729	308	26	.	.	PUNCT
ejpam-6729	309	1	(	(	PUNCT
ejpam-6729	309	2	c)–(d	c)–(d	NOUN
ejpam-6729	309	3	)	)	PUNCT
ejpam-6729	309	4	disjointness	disjointness	NOUN
ejpam-6729	309	5	of	of	ADP
ejpam-6729	309	6	v1	v1	NOUN
ejpam-6729	309	7	,	,	PUNCT
ejpam-6729	309	8	v2	v2	PROPN
ejpam-6729	309	9	makes	make	VERB
ejpam-6729	309	10	λ	λ	NOUN
ejpam-6729	309	11	and	and	CCONJ
ejpam-6729	309	12	µ	µ	PRON
ejpam-6729	309	13	well	well	ADV
ejpam-6729	309	14	-	-	PUNCT
ejpam-6729	309	15	defined	define	VERB
ejpam-6729	309	16	with	with	ADP
ejpam-6729	309	17	the	the	DET
ejpam-6729	309	18	same	same	ADJ
ejpam-6729	309	19	codomains	codomain	NOUN
ejpam-6729	309	20	as	as	ADP
ejpam-6729	309	21	before	before	ADV
ejpam-6729	309	22	.	.	PUNCT
ejpam-6729	310	1	theorem	theorem	NOUN
ejpam-6729	310	2	6	6	NUM
ejpam-6729	310	3	(	(	PUNCT
ejpam-6729	310	4	incidence	incidence	NOUN
ejpam-6729	310	5	representation	representation	NOUN
ejpam-6729	310	6	as	as	ADP
ejpam-6729	310	7	a	a	DET
ejpam-6729	310	8	property	property	NOUN
ejpam-6729	310	9	graph	graph	NOUN
ejpam-6729	310	10	)	)	PUNCT
ejpam-6729	310	11	.	.	PUNCT
ejpam-6729	311	1	let	let	VERB
ejpam-6729	311	2	h	h	NOUN
ejpam-6729	311	3	=	=	PUNCT
ejpam-6729	311	4	(	(	PUNCT
ejpam-6729	311	5	v	v	NOUN
ejpam-6729	311	6	,	,	PUNCT
ejpam-6729	311	7	e	e	NOUN
ejpam-6729	311	8	,	,	PUNCT
ejpam-6729	311	9	λ	λ	PROPN
ejpam-6729	311	10	,	,	PUNCT
ejpam-6729	311	11	µ	µ	NOUN
ejpam-6729	311	12	)	)	PUNCT
ejpam-6729	311	13	be	be	AUX
ejpam-6729	311	14	a	a	DET
ejpam-6729	311	15	property	property	NOUN
ejpam-6729	311	16	hypergraph	hypergraph	NOUN
ejpam-6729	311	17	.	.	PUNCT
ejpam-6729	312	1	form	form	VERB
ejpam-6729	312	2	a	a	DET
ejpam-6729	312	3	(	(	PUNCT
ejpam-6729	312	4	directed	directed	ADJ
ejpam-6729	312	5	)	)	PUNCT
ejpam-6729	312	6	property	property	NOUN
ejpam-6729	312	7	graph	graph	NOUN
ejpam-6729	312	8	g	g	PROPN
ejpam-6729	312	9	=	=	PUNCT
ejpam-6729	312	10	(	(	PUNCT
ejpam-6729	312	11	vg	vg	NOUN
ejpam-6729	312	12	,	,	PUNCT
ejpam-6729	312	13	eg	eg	NOUN
ejpam-6729	312	14	,	,	PUNCT
ejpam-6729	312	15	s	s	PROPN
ejpam-6729	312	16	,	,	PUNCT
ejpam-6729	312	17	t	t	PROPN
ejpam-6729	312	18	,	,	PUNCT
ejpam-6729	312	19	λg	λg	NOUN
ejpam-6729	312	20	,	,	PUNCT
ejpam-6729	312	21	µg,⊥	µg,⊥	NUM
ejpam-6729	312	22	)	)	PUNCT
ejpam-6729	312	23	t.	t.	PROPN
ejpam-6729	312	24	fujita	fujita	PROPN
ejpam-6729	312	25	,	,	PUNCT
ejpam-6729	312	26	f.	f.	PROPN
ejpam-6729	312	27	smarandache	smarandache	PROPN
ejpam-6729	312	28	/	/	SYM
ejpam-6729	312	29	eur	eur	PROPN
ejpam-6729	312	30	.	.	PUNCT
ejpam-6729	313	1	j.	j.	PROPN
ejpam-6729	313	2	pure	pure	PROPN
ejpam-6729	313	3	appl	appl	PROPN
ejpam-6729	313	4	.	.	PROPN
ejpam-6729	313	5	math	math	PROPN
ejpam-6729	313	6	,	,	PUNCT
ejpam-6729	313	7	18	18	NUM
ejpam-6729	313	8	(	(	PUNCT
ejpam-6729	313	9	4	4	NUM
ejpam-6729	313	10	)	)	PUNCT
ejpam-6729	313	11	(	(	PUNCT
ejpam-6729	313	12	2025	2025	NUM
ejpam-6729	313	13	)	)	PUNCT
ejpam-6729	313	14	,	,	PUNCT
ejpam-6729	313	15	6729	6729	NUM
ejpam-6729	313	16	16	16	NUM
ejpam-6729	313	17	of	of	ADP
ejpam-6729	313	18	36	36	NUM
ejpam-6729	313	19	by	by	ADP
ejpam-6729	313	20	taking	take	VERB
ejpam-6729	313	21	vg	vg	NOUN
ejpam-6729	313	22	:	:	PUNCT
ejpam-6729	313	23	=	=	SYM
ejpam-6729	313	24	v	v	NOUN
ejpam-6729	313	25	∪	∪	X
ejpam-6729	313	26	e	e	X
ejpam-6729	313	27	(	(	PUNCT
ejpam-6729	313	28	disjoint	disjoint	PROPN
ejpam-6729	313	29	union	union	NOUN
ejpam-6729	313	30	of	of	ADP
ejpam-6729	313	31	tags	tag	NOUN
ejpam-6729	313	32	“	"	PUNCT
ejpam-6729	313	33	vertex	vertex	NOUN
ejpam-6729	313	34	”	"	PUNCT
ejpam-6729	313	35	and	and	CCONJ
ejpam-6729	313	36	“	"	PUNCT
ejpam-6729	313	37	edge	edge	NOUN
ejpam-6729	313	38	”	"	PUNCT
ejpam-6729	313	39	)	)	PUNCT
ejpam-6729	313	40	,	,	PUNCT
ejpam-6729	313	41	eg	eg	NOUN
ejpam-6729	313	42	:	:	PUNCT
ejpam-6729	314	1	=	=	SYM
ejpam-6729	314	2	{	{	PUNCT
ejpam-6729	314	3	(	(	PUNCT
ejpam-6729	314	4	e	e	NOUN
ejpam-6729	314	5	,	,	PUNCT
ejpam-6729	314	6	v	v	NOUN
ejpam-6729	314	7	)	)	PUNCT
ejpam-6729	314	8	∈	∈	PROPN
ejpam-6729	314	9	e	e	NOUN
ejpam-6729	314	10	×	×	NOUN
ejpam-6729	314	11	v	v	INTJ
ejpam-6729	314	12	|	|	ADV
ejpam-6729	314	13	v	v	NOUN
ejpam-6729	314	14	∈	∈	NOUN
ejpam-6729	314	15	e	e	X
ejpam-6729	314	16	}	}	PUNCT
ejpam-6729	314	17	,	,	PUNCT
ejpam-6729	314	18	s(e	s(e	PROPN
ejpam-6729	314	19	,	,	PUNCT
ejpam-6729	314	20	v	v	NOUN
ejpam-6729	314	21	)	)	PUNCT
ejpam-6729	314	22	=	=	SYM
ejpam-6729	314	23	e	e	NOUN
ejpam-6729	314	24	,	,	PUNCT
ejpam-6729	314	25	t(e	t(e	PROPN
ejpam-6729	314	26	,	,	PUNCT
ejpam-6729	314	27	v	v	NOUN
ejpam-6729	314	28	)	)	PUNCT
ejpam-6729	314	29	=	=	SYM
ejpam-6729	314	30	v	v	NOUN
ejpam-6729	314	31	,	,	PUNCT
ejpam-6729	314	32	and	and	CCONJ
ejpam-6729	314	33	define	define	VERB
ejpam-6729	314	34	λg(e	λg(e	NUM
ejpam-6729	314	35	,	,	PUNCT
ejpam-6729	314	36	v	v	NOUN
ejpam-6729	314	37	)	)	PUNCT
ejpam-6729	314	38	:	:	PUNCT
ejpam-6729	314	39	=	=	SYM
ejpam-6729	314	40	λ(e	λ(e	ADJ
ejpam-6729	314	41	)	)	PUNCT
ejpam-6729	314	42	∈	∈	PROPN
ejpam-6729	314	43	σ	σ	PROPN
ejpam-6729	314	44	,	,	PUNCT
ejpam-6729	314	45	µg(x	µg(x	ADV
ejpam-6729	314	46	,	,	PUNCT
ejpam-6729	314	47	k	k	NOUN
ejpam-6729	314	48	)	)	PUNCT
ejpam-6729	314	49	:	:	PUNCT
ejpam-6729	314	50	=	=	PRON
ejpam-6729	314	51	{	{	PUNCT
ejpam-6729	314	52	µ(x	µ(x	PROPN
ejpam-6729	314	53	,	,	PUNCT
ejpam-6729	314	54	k	k	NOUN
ejpam-6729	314	55	)	)	PUNCT
ejpam-6729	314	56	,	,	PUNCT
ejpam-6729	314	57	x	x	PUNCT
ejpam-6729	314	58	∈	∈	NOUN
ejpam-6729	314	59	v	v	ADP
ejpam-6729	314	60	∪	∪	NOUN
ejpam-6729	314	61	e	e	NOUN
ejpam-6729	314	62	(=	(=	NOUN
ejpam-6729	314	63	vg	vg	NOUN
ejpam-6729	314	64	)	)	PUNCT
ejpam-6729	314	65	,	,	PUNCT
ejpam-6729	314	66	⊥	⊥	PROPN
ejpam-6729	314	67	,	,	PUNCT
ejpam-6729	314	68	x	x	SYM
ejpam-6729	314	69	∈	∈	PROPN
ejpam-6729	314	70	eg	eg	NOUN
ejpam-6729	314	71	.	.	PUNCT
ejpam-6729	315	1	then	then	ADV
ejpam-6729	315	2	g	g	PROPN
ejpam-6729	315	3	is	be	AUX
ejpam-6729	315	4	a	a	DET
ejpam-6729	315	5	property	property	NOUN
ejpam-6729	315	6	graph	graph	NOUN
ejpam-6729	315	7	(	(	PUNCT
ejpam-6729	315	8	in	in	ADP
ejpam-6729	315	9	the	the	DET
ejpam-6729	315	10	sense	sense	NOUN
ejpam-6729	315	11	of	of	ADP
ejpam-6729	315	12	a	a	DET
ejpam-6729	315	13	directed	direct	VERB
ejpam-6729	315	14	,	,	PUNCT
ejpam-6729	315	15	edge	edge	NOUN
ejpam-6729	315	16	-	-	PUNCT
ejpam-6729	315	17	labelled	label	VERB
ejpam-6729	315	18	,	,	PUNCT
ejpam-6729	315	19	attributed	attribute	VERB
ejpam-6729	315	20	multigraph	multigraph	NOUN
ejpam-6729	315	21	)	)	PUNCT
ejpam-6729	315	22	.	.	PUNCT
ejpam-6729	316	1	proof	proof	NOUN
ejpam-6729	316	2	.	.	PUNCT
ejpam-6729	317	1	by	by	ADP
ejpam-6729	317	2	construction	construction	NOUN
ejpam-6729	317	3	vg	vg	NOUN
ejpam-6729	317	4	is	be	AUX
ejpam-6729	317	5	a	a	DET
ejpam-6729	317	6	set	set	NOUN
ejpam-6729	317	7	and	and	CCONJ
ejpam-6729	317	8	eg	eg	VERB
ejpam-6729	317	9	⊆	⊆	NUM
ejpam-6729	317	10	vg	vg	ADP
ejpam-6729	317	11	×	×	NOUN
ejpam-6729	317	12	vg	vg	NOUN
ejpam-6729	317	13	.	.	PUNCT
ejpam-6729	318	1	the	the	DET
ejpam-6729	318	2	maps	map	NOUN
ejpam-6729	318	3	s	s	PROPN
ejpam-6729	318	4	,	,	PUNCT
ejpam-6729	318	5	t	t	PROPN
ejpam-6729	318	6	are	be	AUX
ejpam-6729	318	7	projections	projection	NOUN
ejpam-6729	318	8	,	,	PUNCT
ejpam-6729	318	9	hence	hence	ADV
ejpam-6729	318	10	well	well	ADV
ejpam-6729	318	11	-	-	PUNCT
ejpam-6729	318	12	defined	define	VERB
ejpam-6729	318	13	.	.	PUNCT
ejpam-6729	319	1	the	the	DET
ejpam-6729	319	2	edge	edge	NOUN
ejpam-6729	319	3	-	-	PUNCT
ejpam-6729	319	4	labelling	labelling	NOUN
ejpam-6729	319	5	λg	λg	NOUN
ejpam-6729	319	6	uses	use	VERB
ejpam-6729	319	7	the	the	DET
ejpam-6729	319	8	hyperedge	hyperedge	NOUN
ejpam-6729	319	9	label	label	NOUN
ejpam-6729	319	10	λ(e	λ(e	VERB
ejpam-6729	319	11	)	)	PUNCT
ejpam-6729	319	12	;	;	PUNCT
ejpam-6729	319	13	the	the	DET
ejpam-6729	319	14	property	property	NOUN
ejpam-6729	319	15	map	map	NOUN
ejpam-6729	319	16	µg	µg	ADV
ejpam-6729	319	17	agrees	agree	VERB
ejpam-6729	319	18	with	with	ADP
ejpam-6729	319	19	µ	µ	NOUN
ejpam-6729	319	20	on	on	ADP
ejpam-6729	319	21	all	all	DET
ejpam-6729	319	22	vertices	vertex	NOUN
ejpam-6729	319	23	of	of	ADP
ejpam-6729	319	24	g	g	NOUN
ejpam-6729	319	25	(	(	PUNCT
ejpam-6729	319	26	i.e.	i.e.	X
ejpam-6729	319	27	original	original	ADJ
ejpam-6729	319	28	vertices	vertex	NOUN
ejpam-6729	319	29	and	and	CCONJ
ejpam-6729	319	30	hyperedges	hyperedge	NOUN
ejpam-6729	319	31	)	)	PUNCT
ejpam-6729	319	32	and	and	CCONJ
ejpam-6729	319	33	assigns	assign	VERB
ejpam-6729	319	34	the	the	DET
ejpam-6729	319	35	sentinel	sentinel	NOUN
ejpam-6729	319	36	⊥	⊥	X
ejpam-6729	319	37	to	to	ADP
ejpam-6729	319	38	edges	edge	NOUN
ejpam-6729	319	39	,	,	PUNCT
ejpam-6729	319	40	ensuring	ensure	VERB
ejpam-6729	319	41	µg	µg	ADV
ejpam-6729	319	42	:	:	PUNCT
ejpam-6729	319	43	(	(	PUNCT
ejpam-6729	319	44	vg	vg	SCONJ
ejpam-6729	319	45	∪	∪	VERB
ejpam-6729	319	46	eg)×k	eg)×k	NOUN
ejpam-6729	319	47	→	→	SYM
ejpam-6729	319	48	s	s	NOUN
ejpam-6729	319	49	∪	∪	X
ejpam-6729	319	50	{	{	PUNCT
ejpam-6729	319	51	⊥	⊥	NOUN
ejpam-6729	319	52	}	}	PUNCT
ejpam-6729	319	53	.	.	PUNCT
ejpam-6729	320	1	thus	thus	ADV
ejpam-6729	320	2	all	all	DET
ejpam-6729	320	3	clauses	clause	NOUN
ejpam-6729	320	4	of	of	ADP
ejpam-6729	320	5	the	the	DET
ejpam-6729	320	6	property	property	NOUN
ejpam-6729	320	7	graph	graph	NOUN
ejpam-6729	320	8	definition	definition	NOUN
ejpam-6729	320	9	are	be	AUX
ejpam-6729	320	10	satisfied	satisfied	ADJ
ejpam-6729	320	11	.	.	PUNCT
ejpam-6729	321	1	theorem	theorem	ADJ
ejpam-6729	321	2	7	7	NUM
ejpam-6729	321	3	(	(	PUNCT
ejpam-6729	321	4	forgetting	forget	VERB
ejpam-6729	321	5	labels	label	NOUN
ejpam-6729	321	6	and	and	CCONJ
ejpam-6729	321	7	properties	property	NOUN
ejpam-6729	321	8	)	)	PUNCT
ejpam-6729	321	9	.	.	PUNCT
ejpam-6729	322	1	if	if	SCONJ
ejpam-6729	322	2	σ	σ	NOUN
ejpam-6729	322	3	=	=	SYM
ejpam-6729	322	4	{	{	PUNCT
ejpam-6729	322	5	σ0	σ0	NOUN
ejpam-6729	322	6	}	}	PUNCT
ejpam-6729	322	7	is	be	AUX
ejpam-6729	322	8	a	a	DET
ejpam-6729	322	9	singleton	singleton	NOUN
ejpam-6729	322	10	and	and	CCONJ
ejpam-6729	322	11	µ	µ	PRON
ejpam-6729	322	12	≡	≡	PROPN
ejpam-6729	322	13	⊥	⊥	NOUN
ejpam-6729	322	14	,	,	PUNCT
ejpam-6729	322	15	then	then	ADV
ejpam-6729	322	16	any	any	DET
ejpam-6729	322	17	property	property	NOUN
ejpam-6729	322	18	hypergraph	hypergraph	NOUN
ejpam-6729	322	19	h	h	NOUN
ejpam-6729	322	20	=	=	SYM
ejpam-6729	322	21	(	(	PUNCT
ejpam-6729	322	22	v	v	NOUN
ejpam-6729	322	23	,	,	PUNCT
ejpam-6729	322	24	e	e	NOUN
ejpam-6729	322	25	,	,	PUNCT
ejpam-6729	322	26	λ	λ	PROPN
ejpam-6729	322	27	,	,	PUNCT
ejpam-6729	322	28	µ	µ	NOUN
ejpam-6729	322	29	)	)	PUNCT
ejpam-6729	322	30	reduces	reduce	VERB
ejpam-6729	322	31	to	to	ADP
ejpam-6729	322	32	the	the	DET
ejpam-6729	322	33	ordinary	ordinary	ADJ
ejpam-6729	322	34	hypergraph	hypergraph	NOUN
ejpam-6729	322	35	(	(	PUNCT
ejpam-6729	322	36	v	v	NOUN
ejpam-6729	322	37	,	,	PUNCT
ejpam-6729	322	38	e	e	NOUN
ejpam-6729	322	39	)	)	PUNCT
ejpam-6729	322	40	.	.	PUNCT
ejpam-6729	323	1	proof	proof	NOUN
ejpam-6729	323	2	.	.	PUNCT
ejpam-6729	324	1	with	with	ADP
ejpam-6729	324	2	σ	σ	PROPN
ejpam-6729	324	3	a	a	DET
ejpam-6729	324	4	singleton	singleton	NOUN
ejpam-6729	324	5	,	,	PUNCT
ejpam-6729	324	6	λ	λ	PROPN
ejpam-6729	324	7	carries	carry	VERB
ejpam-6729	324	8	no	no	DET
ejpam-6729	324	9	information	information	NOUN
ejpam-6729	324	10	beyond	beyond	ADP
ejpam-6729	324	11	existence	existence	NOUN
ejpam-6729	324	12	,	,	PUNCT
ejpam-6729	324	13	and	and	CCONJ
ejpam-6729	324	14	with	with	ADP
ejpam-6729	324	15	µ	µ	PROPN
ejpam-6729	324	16	≡	≡	PROPN
ejpam-6729	324	17	⊥	⊥	NOUN
ejpam-6729	324	18	there	there	PRON
ejpam-6729	324	19	are	be	VERB
ejpam-6729	324	20	no	no	DET
ejpam-6729	324	21	attributes	attribute	NOUN
ejpam-6729	324	22	on	on	ADP
ejpam-6729	324	23	vertices	vertex	NOUN
ejpam-6729	324	24	or	or	CCONJ
ejpam-6729	324	25	hyperedges	hyperedge	NOUN
ejpam-6729	324	26	.	.	PUNCT
ejpam-6729	325	1	the	the	DET
ejpam-6729	325	2	remaining	remain	VERB
ejpam-6729	325	3	data	datum	NOUN
ejpam-6729	325	4	are	be	AUX
ejpam-6729	325	5	precisely	precisely	ADV
ejpam-6729	325	6	v	v	ADJ
ejpam-6729	325	7	and	and	CCONJ
ejpam-6729	325	8	e	e	NOUN
ejpam-6729	325	9	⊆	⊆	NUM
ejpam-6729	325	10	p(v	p(v	NOUN
ejpam-6729	325	11	)	)	PUNCT
ejpam-6729	325	12	\	\	NOUN
ejpam-6729	325	13	{	{	PUNCT
ejpam-6729	325	14	∅	∅	NOUN
ejpam-6729	325	15	}	}	PUNCT
ejpam-6729	325	16	,	,	PUNCT
ejpam-6729	325	17	which	which	PRON
ejpam-6729	325	18	is	be	AUX
ejpam-6729	325	19	the	the	DET
ejpam-6729	325	20	definition	definition	NOUN
ejpam-6729	325	21	of	of	ADP
ejpam-6729	325	22	a	a	DET
ejpam-6729	325	23	hypergraph	hypergraph	NOUN
ejpam-6729	325	24	.	.	PUNCT
ejpam-6729	326	1	4	4	X
ejpam-6729	326	2	.	.	X
ejpam-6729	326	3	main	main	ADJ
ejpam-6729	326	4	result	result	NOUN
ejpam-6729	326	5	:	:	PUNCT
ejpam-6729	326	6	property	property	NOUN
ejpam-6729	326	7	superhypergraphs	superhypergraph	NOUN
ejpam-6729	326	8	we	we	PRON
ejpam-6729	326	9	introduce	introduce	VERB
ejpam-6729	326	10	and	and	CCONJ
ejpam-6729	326	11	formalise	formalise	VERB
ejpam-6729	326	12	the	the	DET
ejpam-6729	326	13	concept	concept	NOUN
ejpam-6729	326	14	of	of	ADP
ejpam-6729	326	15	a	a	DET
ejpam-6729	326	16	property	property	NOUN
ejpam-6729	326	17	superhypergraph	superhypergraph	NOUN
ejpam-6729	326	18	.	.	PUNCT
ejpam-6729	327	1	property	property	NOUN
ejpam-6729	327	2	superhypergraphs	superhypergraph	NOUN
ejpam-6729	327	3	extend	extend	VERB
ejpam-6729	327	4	superhypergraphs	superhypergraph	NOUN
ejpam-6729	327	5	with	with	ADP
ejpam-6729	327	6	labels	label	NOUN
ejpam-6729	327	7	and	and	CCONJ
ejpam-6729	327	8	key	key	ADJ
ejpam-6729	327	9	–	–	PUNCT
ejpam-6729	327	10	value	value	NOUN
ejpam-6729	327	11	attributes	attribute	VERB
ejpam-6729	327	12	on	on	ADP
ejpam-6729	327	13	supervertices	supervertice	NOUN
ejpam-6729	327	14	and	and	CCONJ
ejpam-6729	327	15	superedges	superedge	NOUN
ejpam-6729	327	16	,	,	PUNCT
ejpam-6729	327	17	supporting	support	VERB
ejpam-6729	327	18	hierarchical	hierarchical	ADJ
ejpam-6729	327	19	attributed	attribute	VERB
ejpam-6729	327	20	modeling	modeling	NOUN
ejpam-6729	327	21	.	.	PUNCT
ejpam-6729	328	1	definition	definition	NOUN
ejpam-6729	328	2	8	8	NUM
ejpam-6729	328	3	(	(	PUNCT
ejpam-6729	328	4	iterated	iterated	ADJ
ejpam-6729	328	5	powerset	powerset	NOUN
ejpam-6729	328	6	(	(	PUNCT
ejpam-6729	328	7	recall	recall	NOUN
ejpam-6729	328	8	)	)	PUNCT
ejpam-6729	328	9	)	)	PUNCT
ejpam-6729	328	10	.	.	PUNCT
ejpam-6729	329	1	let	let	VERB
ejpam-6729	329	2	v0	v0	NOUN
ejpam-6729	329	3	be	be	AUX
ejpam-6729	329	4	a	a	DET
ejpam-6729	329	5	finite	finite	NOUN
ejpam-6729	329	6	,	,	PUNCT
ejpam-6729	329	7	nonempty	nonempty	ADJ
ejpam-6729	329	8	base	base	NOUN
ejpam-6729	329	9	set	set	NOUN
ejpam-6729	329	10	.	.	PUNCT
ejpam-6729	330	1	define	define	VERB
ejpam-6729	330	2	p0(v0	p0(v0	VERB
ejpam-6729	330	3	)	)	PUNCT
ejpam-6729	330	4	:	:	PUNCT
ejpam-6729	331	1	=	=	SYM
ejpam-6729	331	2	v0	v0	PROPN
ejpam-6729	331	3	,	,	PUNCT
ejpam-6729	331	4	pk+1(v0	pk+1(v0	NUM
ejpam-6729	331	5	)	)	PUNCT
ejpam-6729	331	6	:	:	PUNCT
ejpam-6729	332	1	=	=	SYM
ejpam-6729	332	2	p	p	X
ejpam-6729	332	3	(	(	PUNCT
ejpam-6729	332	4	pk(v0	pk(v0	PROPN
ejpam-6729	332	5	)	)	PUNCT
ejpam-6729	332	6	)	)	PUNCT
ejpam-6729	333	1	(	(	PUNCT
ejpam-6729	333	2	k	k	PROPN
ejpam-6729	333	3	∈	∈	PROPN
ejpam-6729	333	4	n	n	CCONJ
ejpam-6729	333	5	)	)	PUNCT
ejpam-6729	333	6	.	.	PUNCT
ejpam-6729	334	1	for	for	ADP
ejpam-6729	334	2	n	n	PRON
ejpam-6729	334	3	∈	∈	PROPN
ejpam-6729	334	4	n	n	CCONJ
ejpam-6729	334	5	,	,	PUNCT
ejpam-6729	334	6	the	the	DET
ejpam-6729	334	7	elements	element	NOUN
ejpam-6729	334	8	of	of	ADP
ejpam-6729	334	9	pn(v0	pn(v0	NOUN
ejpam-6729	334	10	)	)	PUNCT
ejpam-6729	334	11	are	be	AUX
ejpam-6729	334	12	called	call	VERB
ejpam-6729	334	13	level	level	NOUN
ejpam-6729	334	14	-	-	PUNCT
ejpam-6729	334	15	n	n	NOUN
ejpam-6729	334	16	carriers	carrier	NOUN
ejpam-6729	334	17	(	(	PUNCT
ejpam-6729	334	18	or	or	CCONJ
ejpam-6729	334	19	n	n	CCONJ
ejpam-6729	334	20	-	-	PUNCT
ejpam-6729	334	21	carriers	carrier	NOUN
ejpam-6729	334	22	)	)	PUNCT
ejpam-6729	334	23	.	.	PUNCT
ejpam-6729	335	1	definition	definition	NOUN
ejpam-6729	335	2	9	9	NUM
ejpam-6729	335	3	(	(	PUNCT
ejpam-6729	335	4	property	property	NOUN
ejpam-6729	335	5	n	n	CCONJ
ejpam-6729	335	6	-	-	PUNCT
ejpam-6729	335	7	superhypergraph	superhypergraph	NOUN
ejpam-6729	335	8	)	)	PUNCT
ejpam-6729	335	9	.	.	PUNCT
ejpam-6729	336	1	fix	fix	NOUN
ejpam-6729	336	2	alphabets	alphabet	NOUN
ejpam-6729	336	3	/	/	SYM
ejpam-6729	336	4	sets	set	NOUN
ejpam-6729	336	5	σ	σ	NOUN
ejpam-6729	336	6	(	(	PUNCT
ejpam-6729	336	7	edge	edge	NOUN
ejpam-6729	336	8	-	-	PUNCT
ejpam-6729	336	9	label	label	NOUN
ejpam-6729	336	10	alphabet	alphabet	NOUN
ejpam-6729	336	11	)	)	PUNCT
ejpam-6729	336	12	,	,	PUNCT
ejpam-6729	336	13	k	k	PROPN
ejpam-6729	336	14	(	(	PUNCT
ejpam-6729	336	15	property	property	NOUN
ejpam-6729	336	16	keys	key	NOUN
ejpam-6729	336	17	)	)	PUNCT
ejpam-6729	336	18	,	,	PUNCT
ejpam-6729	336	19	s	s	X
ejpam-6729	336	20	(	(	PUNCT
ejpam-6729	336	21	property	property	NOUN
ejpam-6729	336	22	values	value	NOUN
ejpam-6729	336	23	)	)	PUNCT
ejpam-6729	336	24	,	,	PUNCT
ejpam-6729	336	25	and	and	CCONJ
ejpam-6729	336	26	a	a	DET
ejpam-6729	336	27	distinguished	distinguished	ADJ
ejpam-6729	336	28	symbol	symbol	NOUN
ejpam-6729	336	29	⊥	⊥	PROPN
ejpam-6729	336	30	/∈	/∈	PUNCT
ejpam-6729	337	1	s.	s.	PROPN
ejpam-6729	337	2	for	for	ADP
ejpam-6729	337	3	n	n	PROPN
ejpam-6729	337	4	∈	∈	PROPN
ejpam-6729	337	5	n	n	CCONJ
ejpam-6729	337	6	,	,	PUNCT
ejpam-6729	337	7	a	a	DET
ejpam-6729	337	8	property	property	NOUN
ejpam-6729	337	9	n	n	CCONJ
ejpam-6729	337	10	-	-	PUNCT
ejpam-6729	337	11	superhypergraph	superhypergraph	NOUN
ejpam-6729	337	12	(	(	PUNCT
ejpam-6729	337	13	over	over	ADP
ejpam-6729	337	14	v0	v0	NOUN
ejpam-6729	337	15	)	)	PUNCT
ejpam-6729	337	16	is	be	AUX
ejpam-6729	337	17	a	a	DET
ejpam-6729	337	18	quadruple	quadruple	NOUN
ejpam-6729	337	19	h(n	h(n	NUM
ejpam-6729	337	20	)	)	PUNCT
ejpam-6729	338	1	=	=	PRON
ejpam-6729	338	2	(	(	PUNCT
ejpam-6729	338	3	v	v	NOUN
ejpam-6729	338	4	(	(	PUNCT
ejpam-6729	338	5	n	n	CCONJ
ejpam-6729	338	6	)	)	PUNCT
ejpam-6729	338	7	,	,	PUNCT
ejpam-6729	338	8	e(n	e(n	PROPN
ejpam-6729	338	9	)	)	PUNCT
ejpam-6729	338	10	,	,	PUNCT
ejpam-6729	338	11	λ	λ	PROPN
ejpam-6729	338	12	,	,	PUNCT
ejpam-6729	338	13	µ	µ	NOUN
ejpam-6729	338	14	)	)	PUNCT
ejpam-6729	338	15	consisting	consist	VERB
ejpam-6729	338	16	of	of	ADP
ejpam-6729	338	17	:	:	PUNCT
ejpam-6729	338	18	t.	t.	PROPN
ejpam-6729	338	19	fujita	fujita	PROPN
ejpam-6729	338	20	,	,	PUNCT
ejpam-6729	338	21	f.	f.	PROPN
ejpam-6729	338	22	smarandache	smarandache	PROPN
ejpam-6729	338	23	/	/	SYM
ejpam-6729	338	24	eur	eur	PROPN
ejpam-6729	338	25	.	.	PUNCT
ejpam-6729	339	1	j.	j.	PROPN
ejpam-6729	339	2	pure	pure	PROPN
ejpam-6729	339	3	appl	appl	PROPN
ejpam-6729	339	4	.	.	PROPN
ejpam-6729	339	5	math	math	PROPN
ejpam-6729	339	6	,	,	PUNCT
ejpam-6729	339	7	18	18	NUM
ejpam-6729	339	8	(	(	PUNCT
ejpam-6729	339	9	4	4	NUM
ejpam-6729	339	10	)	)	PUNCT
ejpam-6729	339	11	(	(	PUNCT
ejpam-6729	339	12	2025	2025	NUM
ejpam-6729	339	13	)	)	PUNCT
ejpam-6729	339	14	,	,	PUNCT
ejpam-6729	339	15	6729	6729	NUM
ejpam-6729	339	16	17	17	NUM
ejpam-6729	339	17	of	of	ADP
ejpam-6729	339	18	36	36	NUM
ejpam-6729	339	19	(	(	PUNCT
ejpam-6729	339	20	i	i	NOUN
ejpam-6729	339	21	)	)	PUNCT
ejpam-6729	339	22	a	a	DET
ejpam-6729	339	23	vertex	vertex	NOUN
ejpam-6729	339	24	set	set	VERB
ejpam-6729	339	25	v	v	NOUN
ejpam-6729	339	26	(	(	PUNCT
ejpam-6729	339	27	n	n	CCONJ
ejpam-6729	339	28	)	)	PUNCT
ejpam-6729	339	29	⊆	⊆	NUM
ejpam-6729	339	30	pn(v0	pn(v0	NUM
ejpam-6729	339	31	)	)	PUNCT
ejpam-6729	339	32	;	;	PUNCT
ejpam-6729	339	33	(	(	PUNCT
ejpam-6729	339	34	ii	ii	NOUN
ejpam-6729	339	35	)	)	PUNCT
ejpam-6729	339	36	a	a	DET
ejpam-6729	339	37	finite	finite	ADJ
ejpam-6729	339	38	family	family	NOUN
ejpam-6729	339	39	of	of	ADP
ejpam-6729	339	40	nonempty	nonempty	X
ejpam-6729	339	41	superedges	superedge	NOUN
ejpam-6729	339	42	e(n	e(n	PROPN
ejpam-6729	339	43	)	)	PUNCT
ejpam-6729	339	44	⊆	⊆	NUM
ejpam-6729	339	45	p	p	NOUN
ejpam-6729	339	46	(	(	PUNCT
ejpam-6729	339	47	v	v	NOUN
ejpam-6729	339	48	(	(	PUNCT
ejpam-6729	339	49	n	n	CCONJ
ejpam-6729	339	50	)	)	PUNCT
ejpam-6729	339	51	)	)	PUNCT
ejpam-6729	339	52	\	\	NOUN
ejpam-6729	339	53	{	{	PUNCT
ejpam-6729	339	54	∅	∅	NOUN
ejpam-6729	339	55	}	}	PUNCT
ejpam-6729	339	56	;	;	PUNCT
ejpam-6729	339	57	(	(	PUNCT
ejpam-6729	339	58	iii	iii	X
ejpam-6729	339	59	)	)	PUNCT
ejpam-6729	339	60	an	an	DET
ejpam-6729	339	61	edge	edge	NOUN
ejpam-6729	339	62	-	-	PUNCT
ejpam-6729	339	63	labelling	labelling	NOUN
ejpam-6729	339	64	map	map	NOUN
ejpam-6729	339	65	λ	λ	X
ejpam-6729	339	66	:	:	PUNCT
ejpam-6729	339	67	e(n	e(n	ADJ
ejpam-6729	339	68	)	)	PUNCT
ejpam-6729	339	69	→	→	SYM
ejpam-6729	339	70	σ	σ	PROPN
ejpam-6729	339	71	;	;	PUNCT
ejpam-6729	339	72	(	(	PUNCT
ejpam-6729	339	73	iv	iv	X
ejpam-6729	339	74	)	)	PUNCT
ejpam-6729	339	75	a	a	DET
ejpam-6729	339	76	property	property	NOUN
ejpam-6729	339	77	map	map	NOUN
ejpam-6729	339	78	µ	µ	X
ejpam-6729	339	79	:	:	PUNCT
ejpam-6729	339	80	(	(	PUNCT
ejpam-6729	339	81	d(n	d(n	PROPN
ejpam-6729	339	82	)	)	PUNCT
ejpam-6729	339	83	×k	×k	NOUN
ejpam-6729	339	84	)	)	PUNCT
ejpam-6729	340	1	−→	−→	NOUN
ejpam-6729	340	2	s	s	NOUN
ejpam-6729	340	3	∪	∪	X
ejpam-6729	340	4	{	{	PUNCT
ejpam-6729	340	5	⊥	⊥	NOUN
ejpam-6729	340	6	}	}	PUNCT
ejpam-6729	340	7	,	,	PUNCT
ejpam-6729	340	8	d(n	d(n	NOUN
ejpam-6729	340	9	)	)	PUNCT
ejpam-6729	340	10	:	:	PUNCT
ejpam-6729	341	1	=	=	SYM
ejpam-6729	341	2	(	(	PUNCT
ejpam-6729	341	3	n⋃	n⋃	X
ejpam-6729	341	4	k=0	k=0	PROPN
ejpam-6729	341	5	pk(v0	pk(v0	VERB
ejpam-6729	341	6	)	)	PUNCT
ejpam-6729	341	7	)	)	PUNCT
ejpam-6729	341	8	∪	∪	ADP
ejpam-6729	341	9	e(n	e(n	PROPN
ejpam-6729	341	10	)	)	PUNCT
ejpam-6729	341	11	,	,	PUNCT
ejpam-6729	341	12	interpreted	interpret	VERB
ejpam-6729	341	13	by	by	ADP
ejpam-6729	341	14	µ(x	µ(x	NOUN
ejpam-6729	341	15	,	,	PUNCT
ejpam-6729	341	16	k	k	NOUN
ejpam-6729	341	17	)	)	PUNCT
ejpam-6729	341	18	=	=	SYM
ejpam-6729	341	19	s	s	PART
ejpam-6729	341	20	∈	∈	NOUN
ejpam-6729	341	21	s	s	VERB
ejpam-6729	341	22	when	when	SCONJ
ejpam-6729	341	23	object	object	NOUN
ejpam-6729	341	24	x	x	PUNCT
ejpam-6729	341	25	carries	carry	VERB
ejpam-6729	341	26	key	key	ADJ
ejpam-6729	341	27	k	k	PROPN
ejpam-6729	341	28	with	with	ADP
ejpam-6729	341	29	value	value	NOUN
ejpam-6729	341	30	s	s	PROPN
ejpam-6729	341	31	,	,	PUNCT
ejpam-6729	341	32	and	and	CCONJ
ejpam-6729	341	33	µ(x	µ(x	ADJ
ejpam-6729	341	34	,	,	PUNCT
ejpam-6729	341	35	k	k	NOUN
ejpam-6729	341	36	)	)	PUNCT
ejpam-6729	341	37	=	=	VERB
ejpam-6729	342	1	⊥	⊥	NOUN
ejpam-6729	342	2	otherwise	otherwise	ADV
ejpam-6729	342	3	.	.	PUNCT
ejpam-6729	343	1	we	we	PRON
ejpam-6729	343	2	set	set	VERB
ejpam-6729	343	3	(	(	PUNCT
ejpam-6729	343	4	x	x	NOUN
ejpam-6729	343	5	)	)	PUNCT
ejpam-6729	343	6	:	:	PUNCT
ejpam-6729	344	1	=	=	SYM
ejpam-6729	344	2	{	{	PUNCT
ejpam-6729	344	3	k	k	PROPN
ejpam-6729	344	4	∈	∈	PROPN
ejpam-6729	344	5	k	k	PROPN
ejpam-6729	345	1	|	|	PROPN
ejpam-6729	345	2	µ(x	µ(x	PROPN
ejpam-6729	345	3	,	,	PUNCT
ejpam-6729	345	4	k	k	NOUN
ejpam-6729	345	5	)	)	PUNCT
ejpam-6729	345	6	6=	6=	ADP
ejpam-6729	346	1	⊥	⊥	NOUN
ejpam-6729	346	2	}	}	PUNCT
ejpam-6729	346	3	,	,	PUNCT
ejpam-6729	346	4	(	(	PUNCT
ejpam-6729	346	5	x	x	X
ejpam-6729	346	6	,	,	PUNCT
ejpam-6729	346	7	k	k	NOUN
ejpam-6729	346	8	)	)	PUNCT
ejpam-6729	346	9	:	:	PUNCT
ejpam-6729	346	10	=	=	SYM
ejpam-6729	346	11	µ(x	µ(x	X
ejpam-6729	346	12	,	,	PUNCT
ejpam-6729	346	13	k	k	NOUN
ejpam-6729	346	14	)	)	PUNCT
ejpam-6729	346	15	(	(	PUNCT
ejpam-6729	346	16	k	k	PROPN
ejpam-6729	346	17	∈	∈	PROPN
ejpam-6729	346	18	(	(	PUNCT
ejpam-6729	346	19	x	x	NOUN
ejpam-6729	346	20	)	)	PUNCT
ejpam-6729	346	21	)	)	PUNCT
ejpam-6729	346	22	.	.	PUNCT
ejpam-6729	347	1	elements	element	NOUN
ejpam-6729	347	2	of	of	ADP
ejpam-6729	347	3	v	v	NOUN
ejpam-6729	347	4	(	(	PUNCT
ejpam-6729	347	5	n	n	CCONJ
ejpam-6729	347	6	)	)	PUNCT
ejpam-6729	347	7	are	be	AUX
ejpam-6729	347	8	n	n	PRON
ejpam-6729	347	9	-	-	PUNCT
ejpam-6729	347	10	supervertices	supervertice	NOUN
ejpam-6729	347	11	;	;	PUNCT
ejpam-6729	347	12	elements	element	NOUN
ejpam-6729	347	13	of	of	ADP
ejpam-6729	347	14	e(n	e(n	PROPN
ejpam-6729	347	15	)	)	PUNCT
ejpam-6729	347	16	are	be	AUX
ejpam-6729	347	17	n	n	PRON
ejpam-6729	347	18	-	-	PUNCT
ejpam-6729	347	19	superedges	superedge	NOUN
ejpam-6729	347	20	.	.	PUNCT
ejpam-6729	348	1	example	example	NOUN
ejpam-6729	348	2	9	9	NUM
ejpam-6729	348	3	(	(	PUNCT
ejpam-6729	348	4	property	property	NOUN
ejpam-6729	348	5	3	3	NUM
ejpam-6729	348	6	-	-	PUNCT
ejpam-6729	348	7	superhypergraph	superhypergraph	NOUN
ejpam-6729	348	8	for	for	ADP
ejpam-6729	348	9	an	an	DET
ejpam-6729	348	10	image	image	NOUN
ejpam-6729	348	11	-	-	PUNCT
ejpam-6729	348	12	classification	classification	NOUN
ejpam-6729	348	13	dataset	dataset	NOUN
ejpam-6729	348	14	)	)	PUNCT
ejpam-6729	348	15	.	.	PUNCT
ejpam-6729	349	1	we	we	PRON
ejpam-6729	349	2	organise	organise	VERB
ejpam-6729	349	3	a	a	DET
ejpam-6729	349	4	hierarchical	hierarchical	ADJ
ejpam-6729	349	5	dataset	dataset	NOUN
ejpam-6729	349	6	with	with	ADP
ejpam-6729	349	7	images	image	NOUN
ejpam-6729	349	8	(	(	PUNCT
ejpam-6729	349	9	level	level	NOUN
ejpam-6729	349	10	0	0	NUM
ejpam-6729	349	11	)	)	PUNCT
ejpam-6729	349	12	,	,	PUNCT
ejpam-6729	349	13	species	species	NOUN
ejpam-6729	349	14	classes	class	NOUN
ejpam-6729	349	15	(	(	PUNCT
ejpam-6729	349	16	level	level	NOUN
ejpam-6729	349	17	1	1	NUM
ejpam-6729	349	18	)	)	PUNCT
ejpam-6729	349	19	,	,	PUNCT
ejpam-6729	349	20	genera	genera	NOUN
ejpam-6729	349	21	(	(	PUNCT
ejpam-6729	349	22	level	level	NOUN
ejpam-6729	349	23	2	2	NUM
ejpam-6729	349	24	)	)	PUNCT
ejpam-6729	349	25	,	,	PUNCT
ejpam-6729	349	26	and	and	CCONJ
ejpam-6729	349	27	dataset	dataset	NOUN
ejpam-6729	349	28	splits	split	NOUN
ejpam-6729	349	29	(	(	PUNCT
ejpam-6729	349	30	level	level	NOUN
ejpam-6729	349	31	3	3	NUM
ejpam-6729	349	32	)	)	PUNCT
ejpam-6729	349	33	.	.	PUNCT
ejpam-6729	350	1	level	level	NOUN
ejpam-6729	350	2	0	0	NUM
ejpam-6729	350	3	(	(	PUNCT
ejpam-6729	350	4	images	image	NOUN
ejpam-6729	350	5	)	)	PUNCT
ejpam-6729	350	6	.	.	PUNCT
ejpam-6729	351	1	let	let	VERB
ejpam-6729	351	2	v0	v0	NOUN
ejpam-6729	351	3	=	=	SYM
ejpam-6729	351	4	{	{	PUNCT
ejpam-6729	351	5	i1	i1	PROPN
ejpam-6729	351	6	,	,	PUNCT
ejpam-6729	351	7	i2	i2	PROPN
ejpam-6729	351	8	,	,	PUNCT
ejpam-6729	351	9	i3	i3	NOUN
ejpam-6729	351	10	,	,	PUNCT
ejpam-6729	351	11	i4	i4	PROPN
ejpam-6729	351	12	,	,	PUNCT
ejpam-6729	351	13	i5	i5	NOUN
ejpam-6729	351	14	,	,	PUNCT
ejpam-6729	351	15	i6	i6	NOUN
ejpam-6729	351	16	}	}	PUNCT
ejpam-6729	351	17	.	.	PUNCT
ejpam-6729	352	1	assign	assign	VERB
ejpam-6729	352	2	base	base	NOUN
ejpam-6729	352	3	-	-	PUNCT
ejpam-6729	352	4	level	level	NOUN
ejpam-6729	352	5	properties	property	NOUN
ejpam-6729	352	6	(	(	PUNCT
ejpam-6729	352	7	allowed	allow	VERB
ejpam-6729	352	8	since	since	SCONJ
ejpam-6729	352	9	v0	v0	NOUN
ejpam-6729	352	10	⊆	⊆	NUM
ejpam-6729	352	11	d(3	d(3	NOUN
ejpam-6729	352	12	)	)	PUNCT
ejpam-6729	352	13	):	):	PUNCT
ejpam-6729	352	14	µ(ij	µ(ij	PRON
ejpam-6729	352	15	,	,	PUNCT
ejpam-6729	352	16	resolution	resolution	NOUN
ejpam-6729	352	17	)	)	PUNCT
ejpam-6729	352	18	=	=	PUNCT
ejpam-6729	352	19	“	"	PUNCT
ejpam-6729	352	20	1024×768	1024×768	NUM
ejpam-6729	352	21	”	"	PUNCT
ejpam-6729	352	22	,	,	PUNCT
ejpam-6729	352	23	µ(ij	µ(ij	NUM
ejpam-6729	352	24	,	,	PUNCT
ejpam-6729	352	25	date	date	NOUN
ejpam-6729	352	26	)	)	PUNCT
ejpam-6729	352	27	=	=	PUNCT
ejpam-6729	352	28	“	"	PUNCT
ejpam-6729	352	29	2025	2025	NUM
ejpam-6729	352	30	-	-	SYM
ejpam-6729	352	31	06	06	NUM
ejpam-6729	352	32	-	-	PUNCT
ejpam-6729	352	33	01	01	NUM
ejpam-6729	352	34	”	"	PUNCT
ejpam-6729	352	35	(	(	PUNCT
ejpam-6729	352	36	j	j	NOUN
ejpam-6729	352	37	=	=	SYM
ejpam-6729	352	38	1	1	NUM
ejpam-6729	352	39	,	,	PUNCT
ejpam-6729	352	40	.	.	PUNCT
ejpam-6729	352	41	.	.	PUNCT
ejpam-6729	352	42	.	.	PUNCT
ejpam-6729	353	1	,	,	PUNCT
ejpam-6729	353	2	6	6	NUM
ejpam-6729	353	3	)	)	PUNCT
ejpam-6729	353	4	.	.	PUNCT
ejpam-6729	354	1	level	level	NOUN
ejpam-6729	354	2	1	1	NUM
ejpam-6729	354	3	(	(	PUNCT
ejpam-6729	354	4	species	specie	NOUN
ejpam-6729	354	5	;	;	PUNCT
ejpam-6729	354	6	1	1	NUM
ejpam-6729	354	7	-	-	PUNCT
ejpam-6729	354	8	supervertices	supervertice	NOUN
ejpam-6729	354	9	)	)	PUNCT
ejpam-6729	354	10	.	.	PUNCT
ejpam-6729	355	1	ccat	ccat	NOUN
ejpam-6729	355	2	=	=	SYM
ejpam-6729	355	3	{	{	PUNCT
ejpam-6729	355	4	i1	i1	PROPN
ejpam-6729	355	5	,	,	PUNCT
ejpam-6729	355	6	i2	i2	PROPN
ejpam-6729	355	7	}	}	PUNCT
ejpam-6729	355	8	,	,	PUNCT
ejpam-6729	355	9	cdog	cdog	NOUN
ejpam-6729	355	10	=	=	SYM
ejpam-6729	355	11	{	{	PUNCT
ejpam-6729	355	12	i3	i3	NOUN
ejpam-6729	355	13	,	,	PUNCT
ejpam-6729	355	14	i4	i4	PROPN
ejpam-6729	355	15	}	}	PUNCT
ejpam-6729	355	16	,	,	PUNCT
ejpam-6729	355	17	cbird	cbird	NOUN
ejpam-6729	355	18	=	=	SYM
ejpam-6729	355	19	{	{	PUNCT
ejpam-6729	355	20	i5	i5	NOUN
ejpam-6729	355	21	,	,	PUNCT
ejpam-6729	355	22	i6	i6	NOUN
ejpam-6729	355	23	}	}	PUNCT
ejpam-6729	355	24	∈	∈	PROPN
ejpam-6729	355	25	p1(v0	p1(v0	PROPN
ejpam-6729	355	26	)	)	PUNCT
ejpam-6729	355	27	.	.	PUNCT
ejpam-6729	356	1	set	set	VERB
ejpam-6729	356	2	v	v	NOUN
ejpam-6729	356	3	(	(	PUNCT
ejpam-6729	356	4	1	1	NUM
ejpam-6729	356	5	)	)	PUNCT
ejpam-6729	356	6	=	=	NOUN
ejpam-6729	356	7	{	{	PUNCT
ejpam-6729	356	8	ccat	ccat	NOUN
ejpam-6729	356	9	,	,	PUNCT
ejpam-6729	356	10	cdog	cdog	ADJ
ejpam-6729	356	11	,	,	PUNCT
ejpam-6729	356	12	cbird	cbird	NOUN
ejpam-6729	356	13	}	}	PUNCT
ejpam-6729	356	14	and	and	CCONJ
ejpam-6729	356	15	µ(ccat	µ(ccat	PROPN
ejpam-6729	356	16	,	,	PUNCT
ejpam-6729	356	17	species	specie	NOUN
ejpam-6729	356	18	)	)	PUNCT
ejpam-6729	356	19	=	=	PUNCT
ejpam-6729	356	20	“	"	PUNCT
ejpam-6729	356	21	felis	felis	NOUN
ejpam-6729	356	22	catus	catus	NOUN
ejpam-6729	356	23	”	"	PUNCT
ejpam-6729	356	24	,	,	PUNCT
ejpam-6729	356	25	µ(ccat	µ(ccat	PROPN
ejpam-6729	356	26	,	,	PUNCT
ejpam-6729	356	27	count	count	NOUN
ejpam-6729	356	28	)	)	PUNCT
ejpam-6729	356	29	=	=	SYM
ejpam-6729	356	30	2	2	NUM
ejpam-6729	356	31	,	,	PUNCT
ejpam-6729	356	32	µ(cdog	µ(cdog	NOUN
ejpam-6729	356	33	,	,	PUNCT
ejpam-6729	356	34	species	specie	NOUN
ejpam-6729	356	35	)	)	PUNCT
ejpam-6729	356	36	=	=	PUNCT
ejpam-6729	357	1	“	"	PUNCT
ejpam-6729	357	2	canis	canis	X
ejpam-6729	357	3	lupus	lupus	NOUN
ejpam-6729	357	4	”	"	PUNCT
ejpam-6729	357	5	,	,	PUNCT
ejpam-6729	357	6	µ(cdog	µ(cdog	NOUN
ejpam-6729	357	7	,	,	PUNCT
ejpam-6729	357	8	count	count	NOUN
ejpam-6729	357	9	)	)	PUNCT
ejpam-6729	357	10	=	=	SYM
ejpam-6729	357	11	2	2	NUM
ejpam-6729	357	12	,	,	PUNCT
ejpam-6729	357	13	µ(cbird	µ(cbird	ADJ
ejpam-6729	357	14	,	,	PUNCT
ejpam-6729	357	15	species	specie	NOUN
ejpam-6729	357	16	)	)	PUNCT
ejpam-6729	357	17	=	=	PUNCT
ejpam-6729	357	18	“	"	PUNCT
ejpam-6729	357	19	passer	passer	ADJ
ejpam-6729	357	20	domesticus	domesticus	NOUN
ejpam-6729	357	21	”	"	PUNCT
ejpam-6729	357	22	,	,	PUNCT
ejpam-6729	357	23	µ(cbird	µ(cbird	ADJ
ejpam-6729	357	24	,	,	PUNCT
ejpam-6729	357	25	count	count	NOUN
ejpam-6729	357	26	)	)	PUNCT
ejpam-6729	357	27	=	=	SYM
ejpam-6729	357	28	2	2	X
ejpam-6729	357	29	.	.	PUNCT
ejpam-6729	357	30	level	level	NOUN
ejpam-6729	357	31	2	2	NUM
ejpam-6729	357	32	(	(	PUNCT
ejpam-6729	357	33	genera	genera	NOUN
ejpam-6729	357	34	;	;	PUNCT
ejpam-6729	357	35	2	2	NUM
ejpam-6729	357	36	-	-	PUNCT
ejpam-6729	357	37	supervertices	supervertice	NOUN
ejpam-6729	357	38	)	)	PUNCT
ejpam-6729	357	39	.	.	PUNCT
ejpam-6729	358	1	gfelidae	gfelidae	NOUN
ejpam-6729	358	2	=	=	PUNCT
ejpam-6729	358	3	{	{	PUNCT
ejpam-6729	358	4	ccat	ccat	NOUN
ejpam-6729	358	5	}	}	PUNCT
ejpam-6729	358	6	,	,	PUNCT
ejpam-6729	358	7	gcanidae	gcanidae	NOUN
ejpam-6729	358	8	=	=	PUNCT
ejpam-6729	358	9	{	{	PUNCT
ejpam-6729	358	10	cdog	cdog	NOUN
ejpam-6729	358	11	}	}	PUNCT
ejpam-6729	358	12	,	,	PUNCT
ejpam-6729	358	13	gpasseridae	gpasseridae	NOUN
ejpam-6729	358	14	=	=	SYM
ejpam-6729	358	15	{	{	PUNCT
ejpam-6729	358	16	cbird	cbird	NOUN
ejpam-6729	358	17	}	}	PUNCT
ejpam-6729	358	18	∈	∈	PROPN
ejpam-6729	358	19	p2(v0	p2(v0	PROPN
ejpam-6729	358	20	)	)	PUNCT
ejpam-6729	358	21	,	,	PUNCT
ejpam-6729	358	22	with	with	ADP
ejpam-6729	358	23	v	v	NUM
ejpam-6729	358	24	(	(	PUNCT
ejpam-6729	358	25	2	2	NUM
ejpam-6729	358	26	)	)	PUNCT
ejpam-6729	358	27	=	=	NOUN
ejpam-6729	358	28	{	{	PUNCT
ejpam-6729	358	29	gfelidae	gfelidae	NOUN
ejpam-6729	358	30	,	,	PUNCT
ejpam-6729	358	31	gcanidae	gcanidae	NOUN
ejpam-6729	358	32	,	,	PUNCT
ejpam-6729	358	33	gpasseridae	gpasseridae	NOUN
ejpam-6729	358	34	}	}	PUNCT
ejpam-6729	358	35	and	and	CCONJ
ejpam-6729	358	36	µ(gfelidae	µ(gfelidae	NOUN
ejpam-6729	358	37	,	,	PUNCT
ejpam-6729	358	38	genus	genus	NOUN
ejpam-6729	358	39	)	)	PUNCT
ejpam-6729	358	40	=	=	PUNCT
ejpam-6729	358	41	“	"	PUNCT
ejpam-6729	358	42	felis	felis	NOUN
ejpam-6729	358	43	”	"	PUNCT
ejpam-6729	358	44	,	,	PUNCT
ejpam-6729	358	45	µ(gfelidae	µ(gfelidae	NOUN
ejpam-6729	358	46	,	,	PUNCT
ejpam-6729	358	47	numspecies	numspecie	NOUN
ejpam-6729	358	48	)	)	PUNCT
ejpam-6729	358	49	=	=	SYM
ejpam-6729	358	50	1	1	NUM
ejpam-6729	358	51	,	,	PUNCT
ejpam-6729	358	52	µ(gcanidae	µ(gcanidae	ADJ
ejpam-6729	358	53	,	,	PUNCT
ejpam-6729	358	54	genus	genus	NOUN
ejpam-6729	358	55	)	)	PUNCT
ejpam-6729	358	56	=	=	PUNCT
ejpam-6729	358	57	“	"	PUNCT
ejpam-6729	358	58	canis	canis	X
ejpam-6729	358	59	”	"	PUNCT
ejpam-6729	358	60	,	,	PUNCT
ejpam-6729	358	61	µ(gcanidae	µ(gcanidae	ADJ
ejpam-6729	358	62	,	,	PUNCT
ejpam-6729	358	63	numspecies	numspecie	NOUN
ejpam-6729	358	64	)	)	PUNCT
ejpam-6729	358	65	=	=	SYM
ejpam-6729	358	66	1	1	NUM
ejpam-6729	358	67	,	,	PUNCT
ejpam-6729	358	68	µ(gpasseridae	µ(gpasseridae	ADJ
ejpam-6729	358	69	,	,	PUNCT
ejpam-6729	358	70	genus	genus	NOUN
ejpam-6729	358	71	)	)	PUNCT
ejpam-6729	358	72	=	=	PUNCT
ejpam-6729	358	73	“	"	PUNCT
ejpam-6729	358	74	passer	passer	X
ejpam-6729	358	75	”	"	PUNCT
ejpam-6729	358	76	,	,	PUNCT
ejpam-6729	358	77	µ(gpasseridae	µ(gpasseridae	NOUN
ejpam-6729	358	78	,	,	PUNCT
ejpam-6729	358	79	numspecies	numspecie	NOUN
ejpam-6729	358	80	)	)	PUNCT
ejpam-6729	358	81	=	=	SYM
ejpam-6729	359	1	1	1	X
ejpam-6729	359	2	.	.	PUNCT
ejpam-6729	359	3	t.	t.	PROPN
ejpam-6729	359	4	fujita	fujita	PROPN
ejpam-6729	359	5	,	,	PUNCT
ejpam-6729	359	6	f.	f.	PROPN
ejpam-6729	359	7	smarandache	smarandache	PROPN
ejpam-6729	359	8	/	/	SYM
ejpam-6729	359	9	eur	eur	PROPN
ejpam-6729	359	10	.	.	PUNCT
ejpam-6729	360	1	j.	j.	PROPN
ejpam-6729	360	2	pure	pure	PROPN
ejpam-6729	360	3	appl	appl	PROPN
ejpam-6729	360	4	.	.	PROPN
ejpam-6729	360	5	math	math	PROPN
ejpam-6729	360	6	,	,	PUNCT
ejpam-6729	360	7	18	18	NUM
ejpam-6729	360	8	(	(	PUNCT
ejpam-6729	360	9	4	4	NUM
ejpam-6729	360	10	)	)	PUNCT
ejpam-6729	360	11	(	(	PUNCT
ejpam-6729	360	12	2025	2025	NUM
ejpam-6729	360	13	)	)	PUNCT
ejpam-6729	360	14	,	,	PUNCT
ejpam-6729	360	15	6729	6729	NUM
ejpam-6729	360	16	18	18	NUM
ejpam-6729	360	17	of	of	ADP
ejpam-6729	360	18	36	36	NUM
ejpam-6729	360	19	level	level	NOUN
ejpam-6729	360	20	3	3	NUM
ejpam-6729	360	21	(	(	PUNCT
ejpam-6729	360	22	splits	split	NOUN
ejpam-6729	360	23	;	;	PUNCT
ejpam-6729	360	24	3	3	NUM
ejpam-6729	360	25	-	-	PUNCT
ejpam-6729	360	26	supervertices	supervertice	NOUN
ejpam-6729	360	27	)	)	PUNCT
ejpam-6729	360	28	.	.	PUNCT
ejpam-6729	361	1	strain	strain	NOUN
ejpam-6729	361	2	=	=	SYM
ejpam-6729	361	3	{	{	PUNCT
ejpam-6729	361	4	gfelidae	gfelidae	NOUN
ejpam-6729	361	5	,	,	PUNCT
ejpam-6729	361	6	gcanidae	gcanidae	NOUN
ejpam-6729	361	7	}	}	PUNCT
ejpam-6729	361	8	,	,	PUNCT
ejpam-6729	361	9	stest	st	ADJ
ejpam-6729	361	10	=	=	SYM
ejpam-6729	361	11	{	{	PUNCT
ejpam-6729	361	12	gpasseridae	gpasseridae	NOUN
ejpam-6729	361	13	}	}	PUNCT
ejpam-6729	361	14	∈	∈	NOUN
ejpam-6729	361	15	p3(v0	p3(v0	VERB
ejpam-6729	361	16	)	)	PUNCT
ejpam-6729	361	17	,	,	PUNCT
ejpam-6729	361	18	with	with	ADP
ejpam-6729	361	19	v	v	NUM
ejpam-6729	361	20	(	(	PUNCT
ejpam-6729	361	21	3	3	NUM
ejpam-6729	361	22	)	)	PUNCT
ejpam-6729	361	23	=	=	NOUN
ejpam-6729	361	24	{	{	PUNCT
ejpam-6729	361	25	strain	strain	NOUN
ejpam-6729	361	26	,	,	PUNCT
ejpam-6729	361	27	stest	st	ADJ
ejpam-6729	361	28	}	}	PUNCT
ejpam-6729	361	29	and	and	CCONJ
ejpam-6729	361	30	µ(strain	µ(strain	NOUN
ejpam-6729	361	31	,	,	PUNCT
ejpam-6729	361	32	split	split	NOUN
ejpam-6729	361	33	)	)	PUNCT
ejpam-6729	361	34	=	=	PUNCT
ejpam-6729	362	1	“	"	PUNCT
ejpam-6729	362	2	train	train	NOUN
ejpam-6729	362	3	”	"	PUNCT
ejpam-6729	362	4	,	,	PUNCT
ejpam-6729	362	5	µ(strain	µ(strain	NOUN
ejpam-6729	362	6	,	,	PUNCT
ejpam-6729	362	7	fraction	fraction	NOUN
ejpam-6729	362	8	)	)	PUNCT
ejpam-6729	362	9	=	=	SYM
ejpam-6729	362	10	0.8	0.8	NUM
ejpam-6729	362	11	,	,	PUNCT
ejpam-6729	362	12	µ(stest	µ(stest	NOUN
ejpam-6729	362	13	,	,	PUNCT
ejpam-6729	362	14	split	split	NOUN
ejpam-6729	362	15	)	)	PUNCT
ejpam-6729	362	16	=	=	PUNCT
ejpam-6729	362	17	“	"	PUNCT
ejpam-6729	362	18	test	test	NOUN
ejpam-6729	362	19	”	"	PUNCT
ejpam-6729	362	20	,	,	PUNCT
ejpam-6729	362	21	µ(stest	µ(st	ADJ
ejpam-6729	362	22	,	,	PUNCT
ejpam-6729	362	23	fraction	fraction	NOUN
ejpam-6729	362	24	)	)	PUNCT
ejpam-6729	362	25	=	=	PUNCT
ejpam-6729	363	1	0.2	0.2	NUM
ejpam-6729	363	2	.	.	PUNCT
ejpam-6729	364	1	3	3	NUM
ejpam-6729	364	2	-	-	NOUN
ejpam-6729	364	3	superedges	superedge	NOUN
ejpam-6729	364	4	.	.	PUNCT
ejpam-6729	365	1	let	let	VERB
ejpam-6729	365	2	efull	efull	VERB
ejpam-6729	365	3	=	=	PUNCT
ejpam-6729	365	4	{	{	PUNCT
ejpam-6729	365	5	strain	strain	NOUN
ejpam-6729	365	6	,	,	PUNCT
ejpam-6729	365	7	stest	st	ADJ
ejpam-6729	365	8	}	}	PUNCT
ejpam-6729	365	9	∈	∈	PROPN
ejpam-6729	365	10	p	p	X
ejpam-6729	365	11	(	(	PUNCT
ejpam-6729	365	12	v	v	NOUN
ejpam-6729	365	13	(	(	PUNCT
ejpam-6729	365	14	3	3	NUM
ejpam-6729	365	15	)	)	PUNCT
ejpam-6729	365	16	)	)	PUNCT
ejpam-6729	365	17	\	\	NOUN
ejpam-6729	366	1	{	{	PUNCT
ejpam-6729	366	2	∅	∅	NOUN
ejpam-6729	366	3	}	}	PUNCT
ejpam-6729	366	4	,	,	PUNCT
ejpam-6729	366	5	e(3	e(3	PROPN
ejpam-6729	366	6	)	)	PUNCT
ejpam-6729	366	7	=	=	PRON
ejpam-6729	366	8	{	{	PUNCT
ejpam-6729	366	9	efull	efull	NOUN
ejpam-6729	366	10	}	}	PUNCT
ejpam-6729	366	11	.	.	PUNCT
ejpam-6729	367	1	with	with	ADP
ejpam-6729	367	2	σ	σ	PROPN
ejpam-6729	367	3	=	=	SYM
ejpam-6729	367	4	{	{	PUNCT
ejpam-6729	367	5	imagenetsubset	imagenetsubset	NOUN
ejpam-6729	367	6	}	}	PUNCT
ejpam-6729	367	7	,	,	PUNCT
ejpam-6729	367	8	λ(efull	λ(efull	ADJ
ejpam-6729	367	9	)	)	PUNCT
ejpam-6729	367	10	=	=	VERB
ejpam-6729	367	11	imagenetsubset	imagenetsubset	VERB
ejpam-6729	367	12	,	,	PUNCT
ejpam-6729	367	13	µ(efull	µ(efull	ADJ
ejpam-6729	367	14	,	,	PUNCT
ejpam-6729	367	15	version	version	NOUN
ejpam-6729	367	16	)	)	PUNCT
ejpam-6729	367	17	=	=	PUNCT
ejpam-6729	367	18	“	"	PUNCT
ejpam-6729	367	19	v1.0	v1.0	PROPN
ejpam-6729	367	20	”	"	PUNCT
ejpam-6729	367	21	.	.	PUNCT
ejpam-6729	368	1	keysets	keyset	NOUN
ejpam-6729	368	2	.	.	PUNCT
ejpam-6729	369	1	for	for	ADP
ejpam-6729	369	2	instance	instance	NOUN
ejpam-6729	369	3	,	,	PUNCT
ejpam-6729	369	4	(	(	PUNCT
ejpam-6729	369	5	cdog	cdog	NOUN
ejpam-6729	369	6	)	)	PUNCT
ejpam-6729	369	7	=	=	SYM
ejpam-6729	369	8	{	{	PUNCT
ejpam-6729	369	9	species	specie	NOUN
ejpam-6729	369	10	,	,	PUNCT
ejpam-6729	369	11	count	count	NOUN
ejpam-6729	369	12	}	}	PUNCT
ejpam-6729	369	13	and	and	CCONJ
ejpam-6729	369	14	(	(	PUNCT
ejpam-6729	369	15	cdog	cdog	ADJ
ejpam-6729	369	16	,	,	PUNCT
ejpam-6729	369	17	species	specie	NOUN
ejpam-6729	369	18	)	)	PUNCT
ejpam-6729	369	19	=	=	PUNCT
ejpam-6729	369	20	“	"	PUNCT
ejpam-6729	369	21	canis	canis	X
ejpam-6729	369	22	lupus	lupus	NOUN
ejpam-6729	369	23	”	"	PUNCT
ejpam-6729	369	24	.	.	PUNCT
ejpam-6729	370	1	thus	thus	ADV
ejpam-6729	370	2	h(3	h(3	NOUN
ejpam-6729	370	3	)	)	PUNCT
ejpam-6729	370	4	=	=	PUNCT
ejpam-6729	370	5	(	(	PUNCT
ejpam-6729	370	6	v	v	NOUN
ejpam-6729	370	7	(	(	PUNCT
ejpam-6729	370	8	3	3	NUM
ejpam-6729	370	9	)	)	PUNCT
ejpam-6729	370	10	,	,	PUNCT
ejpam-6729	370	11	e(3	e(3	PROPN
ejpam-6729	370	12	)	)	PUNCT
ejpam-6729	370	13	,	,	PUNCT
ejpam-6729	370	14	λ	λ	PROPN
ejpam-6729	370	15	,	,	PUNCT
ejpam-6729	370	16	µ	µ	NOUN
ejpam-6729	370	17	)	)	PUNCT
ejpam-6729	370	18	satisfies	satisfie	NOUN
ejpam-6729	370	19	definition	definition	NOUN
ejpam-6729	370	20	9	9	NUM
ejpam-6729	370	21	.	.	PUNCT
ejpam-6729	370	22	example	example	NOUN
ejpam-6729	370	23	10	10	NUM
ejpam-6729	370	24	(	(	PUNCT
ejpam-6729	370	25	property	property	NOUN
ejpam-6729	370	26	3	3	NUM
ejpam-6729	370	27	-	-	PUNCT
ejpam-6729	370	28	superhypergraph	superhypergraph	NOUN
ejpam-6729	370	29	for	for	ADP
ejpam-6729	370	30	multi	multi	ADJ
ejpam-6729	370	31	-	-	ADJ
ejpam-6729	370	32	tier	tier	ADJ
ejpam-6729	370	33	database	database	NOUN
ejpam-6729	370	34	systems	system	NOUN
ejpam-6729	370	35	)	)	PUNCT
ejpam-6729	370	36	.	.	PUNCT
ejpam-6729	371	1	we	we	PRON
ejpam-6729	371	2	model	model	VERB
ejpam-6729	371	3	columns	column	NOUN
ejpam-6729	371	4	(	(	PUNCT
ejpam-6729	371	5	level	level	NOUN
ejpam-6729	371	6	0	0	NUM
ejpam-6729	371	7	)	)	PUNCT
ejpam-6729	371	8	,	,	PUNCT
ejpam-6729	371	9	tables	table	NOUN
ejpam-6729	371	10	(	(	PUNCT
ejpam-6729	371	11	1	1	NUM
ejpam-6729	371	12	)	)	PUNCT
ejpam-6729	371	13	,	,	PUNCT
ejpam-6729	371	14	schemas	schema	NOUN
ejpam-6729	371	15	(	(	PUNCT
ejpam-6729	371	16	2	2	NUM
ejpam-6729	371	17	)	)	PUNCT
ejpam-6729	371	18	,	,	PUNCT
ejpam-6729	371	19	and	and	CCONJ
ejpam-6729	371	20	clusters	cluster	NOUN
ejpam-6729	371	21	(	(	PUNCT
ejpam-6729	371	22	3	3	NUM
ejpam-6729	371	23	)	)	PUNCT
ejpam-6729	371	24	.	.	PUNCT
ejpam-6729	372	1	level	level	NOUN
ejpam-6729	372	2	0	0	PUNCT
ejpam-6729	373	1	(	(	PUNCT
ejpam-6729	373	2	columns	column	NOUN
ejpam-6729	373	3	)	)	PUNCT
ejpam-6729	373	4	.	.	PUNCT
ejpam-6729	374	1	v0	v0	NOUN
ejpam-6729	374	2	=	=	SYM
ejpam-6729	374	3	{	{	PUNCT
ejpam-6729	374	4	user_id	user_id	PROPN
ejpam-6729	374	5	,	,	PUNCT
ejpam-6729	374	6	username	username	NOUN
ejpam-6729	374	7	,	,	PUNCT
ejpam-6729	374	8	email	email	NOUN
ejpam-6729	374	9	,	,	PUNCT
ejpam-6729	374	10	order_id	order_id	PROPN
ejpam-6729	374	11	,	,	PUNCT
ejpam-6729	374	12	order_date	order_date	ADJ
ejpam-6729	374	13	,	,	PUNCT
ejpam-6729	374	14	product_id	product_id	NOUN
ejpam-6729	374	15	,	,	PUNCT
ejpam-6729	374	16	quantity	quantity	NOUN
ejpam-6729	374	17	,	,	PUNCT
ejpam-6729	374	18	price	price	NOUN
ejpam-6729	374	19	}	}	PUNCT
ejpam-6729	374	20	.	.	PUNCT
ejpam-6729	375	1	assign	assign	VERB
ejpam-6729	375	2	µ(c	µ(c	PROPN
ejpam-6729	375	3	,	,	PUNCT
ejpam-6729	375	4	name	name	NOUN
ejpam-6729	375	5	)	)	PUNCT
ejpam-6729	375	6	=	=	SYM
ejpam-6729	375	7	c	c	NOUN
ejpam-6729	375	8	and	and	CCONJ
ejpam-6729	375	9	µ(c	µ(c	PROPN
ejpam-6729	375	10	,	,	PUNCT
ejpam-6729	375	11	datatype	datatype	NOUN
ejpam-6729	375	12	)	)	PUNCT
ejpam-6729	375	13	∈	∈	PROPN
ejpam-6729	375	14	{	{	PUNCT
ejpam-6729	375	15	int	int	NOUN
ejpam-6729	375	16	,	,	PUNCT
ejpam-6729	375	17	varchar	varchar	NOUN
ejpam-6729	375	18	,	,	PUNCT
ejpam-6729	375	19	date	date	NOUN
ejpam-6729	375	20	,	,	PUNCT
ejpam-6729	375	21	decimal	decimal	NOUN
ejpam-6729	375	22	}	}	PUNCT
ejpam-6729	375	23	.	.	PUNCT
ejpam-6729	376	1	level	level	NOUN
ejpam-6729	376	2	1	1	NUM
ejpam-6729	376	3	(	(	PUNCT
ejpam-6729	376	4	tables	table	NOUN
ejpam-6729	376	5	;	;	PUNCT
ejpam-6729	376	6	1	1	NUM
ejpam-6729	376	7	-	-	PUNCT
ejpam-6729	376	8	supervertices	supervertice	NOUN
ejpam-6729	376	9	)	)	PUNCT
ejpam-6729	376	10	.	.	PUNCT
ejpam-6729	377	1	tusers	tuser	NOUN
ejpam-6729	377	2	=	=	SYM
ejpam-6729	377	3	{	{	PUNCT
ejpam-6729	377	4	user_id	user_id	PROPN
ejpam-6729	377	5	,	,	PUNCT
ejpam-6729	377	6	username	username	NOUN
ejpam-6729	377	7	,	,	PUNCT
ejpam-6729	377	8	email	email	NOUN
ejpam-6729	377	9	}	}	PUNCT
ejpam-6729	377	10	,	,	PUNCT
ejpam-6729	377	11	torders	torder	NOUN
ejpam-6729	377	12	=	=	SYM
ejpam-6729	377	13	{	{	PUNCT
ejpam-6729	377	14	order_id	order_id	PROPN
ejpam-6729	377	15	,	,	PUNCT
ejpam-6729	377	16	user_id	user_id	PROPN
ejpam-6729	377	17	,	,	PUNCT
ejpam-6729	377	18	order_date	order_date	ADJ
ejpam-6729	377	19	}	}	PUNCT
ejpam-6729	377	20	,	,	PUNCT
ejpam-6729	377	21	titems	titem	NOUN
ejpam-6729	377	22	=	=	SYM
ejpam-6729	377	23	{	{	PUNCT
ejpam-6729	377	24	order_id	order_id	PROPN
ejpam-6729	377	25	,	,	PUNCT
ejpam-6729	377	26	product_id	product_id	NOUN
ejpam-6729	377	27	,	,	PUNCT
ejpam-6729	377	28	quantity	quantity	NOUN
ejpam-6729	377	29	,	,	PUNCT
ejpam-6729	377	30	price	price	NOUN
ejpam-6729	377	31	}	}	PUNCT
ejpam-6729	377	32	,	,	PUNCT
ejpam-6729	377	33	v	v	X
ejpam-6729	377	34	(	(	PUNCT
ejpam-6729	377	35	1	1	NUM
ejpam-6729	377	36	)	)	PUNCT
ejpam-6729	377	37	=	=	PRON
ejpam-6729	377	38	{	{	PUNCT
ejpam-6729	377	39	tusers	tuser	NOUN
ejpam-6729	377	40	,	,	PUNCT
ejpam-6729	377	41	torders	torder	NOUN
ejpam-6729	377	42	,	,	PUNCT
ejpam-6729	377	43	titems	titem	NOUN
ejpam-6729	377	44	}	}	PUNCT
ejpam-6729	377	45	,	,	PUNCT
ejpam-6729	377	46	with	with	ADP
ejpam-6729	377	47	µ(tusers	µ(tuser	NOUN
ejpam-6729	377	48	,	,	PUNCT
ejpam-6729	377	49	tablename	tablename	PROPN
ejpam-6729	377	50	)	)	PUNCT
ejpam-6729	377	51	=	=	PUNCT
ejpam-6729	377	52	“	"	PUNCT
ejpam-6729	377	53	users	user	NOUN
ejpam-6729	377	54	”	"	PUNCT
ejpam-6729	377	55	,	,	PUNCT
ejpam-6729	377	56	µ(tusers	µ(tuser	NOUN
ejpam-6729	377	57	,	,	PUNCT
ejpam-6729	377	58	rowcount	rowcount	NOUN
ejpam-6729	377	59	)	)	PUNCT
ejpam-6729	377	60	=	=	SYM
ejpam-6729	377	61	120000	120000	NUM
ejpam-6729	377	62	,	,	PUNCT
ejpam-6729	377	63	µ(torders	µ(torder	NOUN
ejpam-6729	377	64	,	,	PUNCT
ejpam-6729	377	65	tablename	tablename	NOUN
ejpam-6729	377	66	)	)	PUNCT
ejpam-6729	377	67	=	=	PUNCT
ejpam-6729	377	68	“	"	PUNCT
ejpam-6729	377	69	orders	order	NOUN
ejpam-6729	377	70	”	"	PUNCT
ejpam-6729	377	71	,	,	PUNCT
ejpam-6729	377	72	µ(torders	µ(torder	NOUN
ejpam-6729	377	73	,	,	PUNCT
ejpam-6729	377	74	rowcount	rowcount	NOUN
ejpam-6729	377	75	)	)	PUNCT
ejpam-6729	377	76	=	=	SYM
ejpam-6729	377	77	450000	450000	NUM
ejpam-6729	377	78	,	,	PUNCT
ejpam-6729	377	79	µ(titems	µ(titem	NOUN
ejpam-6729	377	80	,	,	PUNCT
ejpam-6729	377	81	tablename	tablename	NOUN
ejpam-6729	377	82	)	)	PUNCT
ejpam-6729	377	83	=	=	PUNCT
ejpam-6729	377	84	“	"	PUNCT
ejpam-6729	377	85	items	item	NOUN
ejpam-6729	377	86	”	"	PUNCT
ejpam-6729	377	87	,	,	PUNCT
ejpam-6729	377	88	µ(titems	µ(titem	NOUN
ejpam-6729	377	89	,	,	PUNCT
ejpam-6729	377	90	rowcount	rowcount	NOUN
ejpam-6729	377	91	)	)	PUNCT
ejpam-6729	377	92	=	=	SYM
ejpam-6729	377	93	950000	950000	NUM
ejpam-6729	377	94	.	.	PUNCT
ejpam-6729	378	1	t.	t.	PROPN
ejpam-6729	378	2	fujita	fujita	PROPN
ejpam-6729	378	3	,	,	PUNCT
ejpam-6729	378	4	f.	f.	PROPN
ejpam-6729	378	5	smarandache	smarandache	PROPN
ejpam-6729	378	6	/	/	SYM
ejpam-6729	378	7	eur	eur	PROPN
ejpam-6729	378	8	.	.	PUNCT
ejpam-6729	379	1	j.	j.	PROPN
ejpam-6729	379	2	pure	pure	PROPN
ejpam-6729	379	3	appl	appl	PROPN
ejpam-6729	379	4	.	.	PROPN
ejpam-6729	379	5	math	math	PROPN
ejpam-6729	379	6	,	,	PUNCT
ejpam-6729	379	7	18	18	NUM
ejpam-6729	379	8	(	(	PUNCT
ejpam-6729	379	9	4	4	NUM
ejpam-6729	379	10	)	)	PUNCT
ejpam-6729	379	11	(	(	PUNCT
ejpam-6729	379	12	2025	2025	NUM
ejpam-6729	379	13	)	)	PUNCT
ejpam-6729	379	14	,	,	PUNCT
ejpam-6729	379	15	6729	6729	NUM
ejpam-6729	379	16	19	19	NUM
ejpam-6729	379	17	of	of	ADP
ejpam-6729	379	18	36	36	NUM
ejpam-6729	379	19	level	level	NOUN
ejpam-6729	379	20	2	2	NUM
ejpam-6729	379	21	(	(	PUNCT
ejpam-6729	379	22	schemas	schema	NOUN
ejpam-6729	379	23	;	;	PUNCT
ejpam-6729	379	24	2	2	NUM
ejpam-6729	379	25	-	-	PUNCT
ejpam-6729	379	26	supervertices	supervertice	NOUN
ejpam-6729	379	27	)	)	PUNCT
ejpam-6729	379	28	.	.	PUNCT
ejpam-6729	380	1	ssales	ssale	NOUN
ejpam-6729	380	2	=	=	SYM
ejpam-6729	380	3	{	{	PUNCT
ejpam-6729	380	4	tusers	tuser	NOUN
ejpam-6729	380	5	,	,	PUNCT
ejpam-6729	380	6	torders	torder	NOUN
ejpam-6729	380	7	,	,	PUNCT
ejpam-6729	380	8	titems	titem	NOUN
ejpam-6729	380	9	}	}	PUNCT
ejpam-6729	380	10	,	,	PUNCT
ejpam-6729	380	11	v	v	X
ejpam-6729	380	12	(	(	PUNCT
ejpam-6729	380	13	2	2	NUM
ejpam-6729	380	14	)	)	PUNCT
ejpam-6729	380	15	=	=	PRON
ejpam-6729	380	16	{	{	PUNCT
ejpam-6729	380	17	ssales	ssale	NOUN
ejpam-6729	380	18	}	}	PUNCT
ejpam-6729	380	19	,	,	PUNCT
ejpam-6729	380	20	µ(ssales	µ(ssale	NOUN
ejpam-6729	380	21	,	,	PUNCT
ejpam-6729	380	22	schemaname	schemaname	NOUN
ejpam-6729	380	23	)	)	PUNCT
ejpam-6729	380	24	=	=	PUNCT
ejpam-6729	380	25	“	"	PUNCT
ejpam-6729	380	26	salesdb	salesdb	NOUN
ejpam-6729	380	27	”	"	PUNCT
ejpam-6729	380	28	,	,	PUNCT
ejpam-6729	380	29	µ(ssales	µ(ssale	NOUN
ejpam-6729	380	30	,	,	PUNCT
ejpam-6729	380	31	version	version	NOUN
ejpam-6729	380	32	)	)	PUNCT
ejpam-6729	380	33	=	=	PUNCT
ejpam-6729	380	34	“	"	PUNCT
ejpam-6729	380	35	v1.2	v1.2	ADJ
ejpam-6729	380	36	”	"	PUNCT
ejpam-6729	380	37	.	.	PUNCT
ejpam-6729	381	1	level	level	NOUN
ejpam-6729	381	2	3	3	NUM
ejpam-6729	381	3	(	(	PUNCT
ejpam-6729	381	4	clusters	cluster	NOUN
ejpam-6729	381	5	;	;	PUNCT
ejpam-6729	381	6	3	3	NUM
ejpam-6729	381	7	-	-	PUNCT
ejpam-6729	381	8	supervertices	supervertice	NOUN
ejpam-6729	381	9	)	)	PUNCT
ejpam-6729	381	10	.	.	PUNCT
ejpam-6729	382	1	cprimary	cprimary	NOUN
ejpam-6729	383	1	=	=	PRON
ejpam-6729	383	2	{	{	PUNCT
ejpam-6729	383	3	ssales	ssale	NOUN
ejpam-6729	383	4	}	}	PUNCT
ejpam-6729	383	5	,	,	PUNCT
ejpam-6729	383	6	creplica	creplica	NOUN
ejpam-6729	383	7	=	=	SYM
ejpam-6729	383	8	{	{	PUNCT
ejpam-6729	383	9	ssales	ssale	NOUN
ejpam-6729	383	10	}	}	PUNCT
ejpam-6729	383	11	,	,	PUNCT
ejpam-6729	383	12	v	v	X
ejpam-6729	383	13	(	(	PUNCT
ejpam-6729	383	14	3	3	NUM
ejpam-6729	383	15	)	)	PUNCT
ejpam-6729	383	16	=	=	NOUN
ejpam-6729	383	17	{	{	PUNCT
ejpam-6729	383	18	cprimary	cprimary	NOUN
ejpam-6729	383	19	,	,	PUNCT
ejpam-6729	383	20	creplica	creplica	NOUN
ejpam-6729	383	21	}	}	PUNCT
ejpam-6729	383	22	,	,	PUNCT
ejpam-6729	383	23	with	with	ADP
ejpam-6729	383	24	µ(cprimary	µ(cprimary	NOUN
ejpam-6729	383	25	,	,	PUNCT
ejpam-6729	383	26	clusterrole	clusterrole	NOUN
ejpam-6729	383	27	)	)	PUNCT
ejpam-6729	383	28	=	=	PUNCT
ejpam-6729	383	29	“	"	PUNCT
ejpam-6729	383	30	primary	primary	ADJ
ejpam-6729	383	31	”	"	PUNCT
ejpam-6729	383	32	,	,	PUNCT
ejpam-6729	383	33	µ(cprimary	µ(cprimary	ADJ
ejpam-6729	383	34	,	,	PUNCT
ejpam-6729	383	35	region	region	NOUN
ejpam-6729	383	36	)	)	PUNCT
ejpam-6729	383	37	=	=	PUNCT
ejpam-6729	383	38	“	"	PUNCT
ejpam-6729	383	39	us	us	PROPN
ejpam-6729	383	40	-	-	PUNCT
ejpam-6729	383	41	east-1	east-1	PROPN
ejpam-6729	383	42	”	"	PUNCT
ejpam-6729	383	43	,	,	PUNCT
ejpam-6729	383	44	µ(creplica	µ(creplica	ADJ
ejpam-6729	383	45	,	,	PUNCT
ejpam-6729	383	46	clusterrole	clusterrole	NOUN
ejpam-6729	383	47	)	)	PUNCT
ejpam-6729	383	48	=	=	PUNCT
ejpam-6729	383	49	“	"	PUNCT
ejpam-6729	383	50	replica	replica	NOUN
ejpam-6729	383	51	”	"	PUNCT
ejpam-6729	383	52	,	,	PUNCT
ejpam-6729	383	53	µ(creplica	µ(creplica	ADJ
ejpam-6729	383	54	,	,	PUNCT
ejpam-6729	383	55	region	region	NOUN
ejpam-6729	383	56	)	)	PUNCT
ejpam-6729	383	57	=	=	PUNCT
ejpam-6729	383	58	“	"	PUNCT
ejpam-6729	383	59	us	us	PROPN
ejpam-6729	383	60	-	-	PUNCT
ejpam-6729	383	61	west-2	west-2	PROPN
ejpam-6729	383	62	”	"	PUNCT
ejpam-6729	383	63	.	.	PUNCT
ejpam-6729	384	1	3	3	NUM
ejpam-6729	384	2	-	-	NUM
ejpam-6729	384	3	superedges	superedge	NOUN
ejpam-6729	384	4	.	.	PUNCT
ejpam-6729	385	1	let	let	VERB
ejpam-6729	385	2	eenterprise	eenterprise	NOUN
ejpam-6729	385	3	=	=	SYM
ejpam-6729	385	4	{	{	PUNCT
ejpam-6729	385	5	cprimary	cprimary	ADJ
ejpam-6729	385	6	,	,	PUNCT
ejpam-6729	385	7	creplica	creplica	NOUN
ejpam-6729	385	8	}	}	PUNCT
ejpam-6729	385	9	,	,	PUNCT
ejpam-6729	385	10	e(3	e(3	PROPN
ejpam-6729	385	11	)	)	PUNCT
ejpam-6729	386	1	=	=	PRON
ejpam-6729	386	2	{	{	PUNCT
ejpam-6729	386	3	eenterprise	eenterprise	NOUN
ejpam-6729	386	4	}	}	PUNCT
ejpam-6729	386	5	,	,	PUNCT
ejpam-6729	386	6	σ	σ	PROPN
ejpam-6729	386	7	=	=	SYM
ejpam-6729	386	8	{	{	PUNCT
ejpam-6729	386	9	enterprisedb	enterprisedb	NOUN
ejpam-6729	386	10	}	}	PUNCT
ejpam-6729	386	11	,	,	PUNCT
ejpam-6729	386	12	and	and	CCONJ
ejpam-6729	386	13	set	set	VERB
ejpam-6729	386	14	λ(eenterprise	λ(eenterprise	NOUN
ejpam-6729	386	15	)	)	PUNCT
ejpam-6729	386	16	=	=	SYM
ejpam-6729	386	17	enterprisedb	enterprisedb	NOUN
ejpam-6729	386	18	,	,	PUNCT
ejpam-6729	386	19	µ(eenterprise	µ(eenterprise	NOUN
ejpam-6729	386	20	,	,	PUNCT
ejpam-6729	386	21	admin	admin	ADJ
ejpam-6729	386	22	)	)	PUNCT
ejpam-6729	386	23	=	=	PUNCT
ejpam-6729	386	24	“	"	PUNCT
ejpam-6729	386	25	dba	dba	ADJ
ejpam-6729	386	26	team	team	NOUN
ejpam-6729	386	27	”	"	PUNCT
ejpam-6729	386	28	,	,	PUNCT
ejpam-6729	386	29	µ(eenterprise	µ(eenterprise	NOUN
ejpam-6729	386	30	,	,	PUNCT
ejpam-6729	386	31	uptime_sla	uptime_sla	NUM
ejpam-6729	386	32	)	)	PUNCT
ejpam-6729	386	33	=	=	PUNCT
ejpam-6729	387	1	99.99	99.99	NUM
ejpam-6729	387	2	.	.	PUNCT
ejpam-6729	388	1	then	then	ADV
ejpam-6729	388	2	h(3	h(3	PROPN
ejpam-6729	388	3	)	)	PUNCT
ejpam-6729	388	4	=	=	PRON
ejpam-6729	388	5	(	(	PUNCT
ejpam-6729	388	6	v	v	NOUN
ejpam-6729	388	7	(	(	PUNCT
ejpam-6729	388	8	3	3	NUM
ejpam-6729	388	9	)	)	PUNCT
ejpam-6729	388	10	,	,	PUNCT
ejpam-6729	388	11	e(3	e(3	PROPN
ejpam-6729	388	12	)	)	PUNCT
ejpam-6729	388	13	,	,	PUNCT
ejpam-6729	388	14	λ	λ	PROPN
ejpam-6729	388	15	,	,	PUNCT
ejpam-6729	388	16	µ	µ	NOUN
ejpam-6729	388	17	)	)	PUNCT
ejpam-6729	388	18	is	be	AUX
ejpam-6729	388	19	a	a	DET
ejpam-6729	388	20	property	property	NOUN
ejpam-6729	388	21	3	3	NUM
ejpam-6729	388	22	-	-	PUNCT
ejpam-6729	388	23	shg	shg	NOUN
ejpam-6729	388	24	.	.	PUNCT
ejpam-6729	388	25	example	example	NOUN
ejpam-6729	389	1	11	11	NUM
ejpam-6729	389	2	(	(	PUNCT
ejpam-6729	389	3	a	a	DET
ejpam-6729	389	4	3	3	NUM
ejpam-6729	389	5	-	-	PUNCT
ejpam-6729	389	6	level	level	NOUN
ejpam-6729	389	7	property	property	NOUN
ejpam-6729	389	8	superhypergraph	superhypergraph	NOUN
ejpam-6729	389	9	for	for	ADP
ejpam-6729	389	10	urban	urban	ADJ
ejpam-6729	389	11	transit	transit	NOUN
ejpam-6729	389	12	)	)	PUNCT
ejpam-6729	389	13	.	.	PUNCT
ejpam-6729	390	1	we	we	PRON
ejpam-6729	390	2	model	model	VERB
ejpam-6729	390	3	an	an	DET
ejpam-6729	390	4	urban	urban	ADJ
ejpam-6729	390	5	transit	transit	NOUN
ejpam-6729	390	6	system	system	NOUN
ejpam-6729	390	7	with	with	ADP
ejpam-6729	390	8	stops	stop	NOUN
ejpam-6729	390	9	(	(	PUNCT
ejpam-6729	390	10	level	level	NOUN
ejpam-6729	390	11	0	0	NUM
ejpam-6729	390	12	)	)	PUNCT
ejpam-6729	390	13	,	,	PUNCT
ejpam-6729	390	14	routes	route	NOUN
ejpam-6729	390	15	(	(	PUNCT
ejpam-6729	390	16	level	level	NOUN
ejpam-6729	390	17	1	1	NUM
ejpam-6729	390	18	)	)	PUNCT
ejpam-6729	390	19	,	,	PUNCT
ejpam-6729	390	20	lines	line	NOUN
ejpam-6729	390	21	(	(	PUNCT
ejpam-6729	390	22	level	level	NOUN
ejpam-6729	390	23	2	2	NUM
ejpam-6729	390	24	)	)	PUNCT
ejpam-6729	390	25	,	,	PUNCT
ejpam-6729	390	26	and	and	CCONJ
ejpam-6729	390	27	networks	network	NOUN
ejpam-6729	390	28	(	(	PUNCT
ejpam-6729	390	29	level	level	NOUN
ejpam-6729	390	30	3	3	NUM
ejpam-6729	390	31	)	)	PUNCT
ejpam-6729	390	32	.	.	PUNCT
ejpam-6729	391	1	level	level	NOUN
ejpam-6729	391	2	0	0	PUNCT
ejpam-6729	392	1	(	(	PUNCT
ejpam-6729	392	2	base	base	NOUN
ejpam-6729	392	3	stops	stop	VERB
ejpam-6729	392	4	)	)	PUNCT
ejpam-6729	392	5	.	.	PUNCT
ejpam-6729	393	1	let	let	VERB
ejpam-6729	393	2	v0	v0	NOUN
ejpam-6729	393	3	=	=	SYM
ejpam-6729	393	4	{	{	PUNCT
ejpam-6729	393	5	s1	s1	NOUN
ejpam-6729	393	6	,	,	PUNCT
ejpam-6729	393	7	s2	s2	PROPN
ejpam-6729	393	8	,	,	PUNCT
ejpam-6729	393	9	s3	s3	PROPN
ejpam-6729	393	10	,	,	PUNCT
ejpam-6729	393	11	s4	s4	PROPN
ejpam-6729	393	12	,	,	PUNCT
ejpam-6729	393	13	s5	s5	PROPN
ejpam-6729	393	14	,	,	PUNCT
ejpam-6729	393	15	s6	s6	PROPN
ejpam-6729	393	16	}	}	PUNCT
ejpam-6729	393	17	.	.	PUNCT
ejpam-6729	394	1	assign	assign	VERB
ejpam-6729	394	2	stop	stop	NOUN
ejpam-6729	394	3	properties	property	NOUN
ejpam-6729	394	4	(	(	PUNCT
ejpam-6729	394	5	allowed	allow	VERB
ejpam-6729	394	6	since	since	SCONJ
ejpam-6729	394	7	v0	v0	NOUN
ejpam-6729	394	8	⊆	⊆	NUM
ejpam-6729	394	9	d(3	d(3	NOUN
ejpam-6729	394	10	)	)	PUNCT
ejpam-6729	394	11	):	):	PUNCT
ejpam-6729	394	12	µ(s1	µ(s1	ADJ
ejpam-6729	394	13	,	,	PUNCT
ejpam-6729	394	14	zone	zone	NOUN
ejpam-6729	394	15	)	)	PUNCT
ejpam-6729	394	16	=	=	PUNCT
ejpam-6729	395	1	“	"	PUNCT
ejpam-6729	395	2	1	1	NUM
ejpam-6729	395	3	”	"	PUNCT
ejpam-6729	395	4	,	,	PUNCT
ejpam-6729	395	5	µ(s1	µ(s1	ADV
ejpam-6729	395	6	,	,	PUNCT
ejpam-6729	395	7	lat	lat	NOUN
ejpam-6729	395	8	)	)	PUNCT
ejpam-6729	395	9	=	=	PUNCT
ejpam-6729	396	1	35.69	35.69	NUM
ejpam-6729	396	2	,	,	PUNCT
ejpam-6729	396	3	µ(s1	µ(s1	ADV
ejpam-6729	396	4	,	,	PUNCT
ejpam-6729	396	5	lon	lon	PROPN
ejpam-6729	396	6	)	)	PUNCT
ejpam-6729	396	7	=	=	NOUN
ejpam-6729	397	1	139.70	139.70	NUM
ejpam-6729	397	2	,	,	PUNCT
ejpam-6729	397	3	µ(s2	µ(s2	NOUN
ejpam-6729	397	4	,	,	PUNCT
ejpam-6729	397	5	zone	zone	NOUN
ejpam-6729	397	6	)	)	PUNCT
ejpam-6729	397	7	=	=	PUNCT
ejpam-6729	398	1	“	"	PUNCT
ejpam-6729	398	2	1	1	NUM
ejpam-6729	398	3	”	"	PUNCT
ejpam-6729	398	4	,	,	PUNCT
ejpam-6729	398	5	.	.	PUNCT
ejpam-6729	398	6	.	.	PUNCT
ejpam-6729	398	7	.	.	PUNCT
ejpam-6729	399	1	level	level	NOUN
ejpam-6729	399	2	1	1	NUM
ejpam-6729	399	3	(	(	PUNCT
ejpam-6729	399	4	routes	route	NOUN
ejpam-6729	399	5	as	as	ADP
ejpam-6729	399	6	sets	set	NOUN
ejpam-6729	399	7	of	of	ADP
ejpam-6729	399	8	stops	stop	NOUN
ejpam-6729	399	9	;	;	PUNCT
ejpam-6729	399	10	1	1	NUM
ejpam-6729	399	11	-	-	PUNCT
ejpam-6729	399	12	supervertices	supervertice	NOUN
ejpam-6729	399	13	)	)	PUNCT
ejpam-6729	399	14	.	.	PUNCT
ejpam-6729	400	1	define	define	VERB
ejpam-6729	400	2	ra	ra	PROPN
ejpam-6729	400	3	=	=	PUNCT
ejpam-6729	400	4	{	{	PUNCT
ejpam-6729	400	5	s1	s1	PROPN
ejpam-6729	400	6	,	,	PUNCT
ejpam-6729	400	7	s2	s2	PROPN
ejpam-6729	400	8	,	,	PUNCT
ejpam-6729	400	9	s3	s3	PROPN
ejpam-6729	400	10	}	}	PUNCT
ejpam-6729	400	11	,	,	PUNCT
ejpam-6729	400	12	rb	rb	NOUN
ejpam-6729	400	13	=	=	SYM
ejpam-6729	400	14	{	{	PUNCT
ejpam-6729	400	15	s3	s3	PROPN
ejpam-6729	400	16	,	,	PUNCT
ejpam-6729	400	17	s4	s4	PROPN
ejpam-6729	400	18	,	,	PUNCT
ejpam-6729	400	19	s5	s5	PROPN
ejpam-6729	400	20	}	}	PUNCT
ejpam-6729	400	21	,	,	PUNCT
ejpam-6729	400	22	rc	rc	PROPN
ejpam-6729	400	23	=	=	PROPN
ejpam-6729	400	24	{	{	PUNCT
ejpam-6729	400	25	s5	s5	PROPN
ejpam-6729	400	26	,	,	PUNCT
ejpam-6729	400	27	s6	s6	PROPN
ejpam-6729	400	28	}	}	PUNCT
ejpam-6729	400	29	∈	∈	PROPN
ejpam-6729	400	30	p1(v0	p1(v0	PROPN
ejpam-6729	400	31	)	)	PUNCT
ejpam-6729	400	32	.	.	PUNCT
ejpam-6729	401	1	set	set	VERB
ejpam-6729	401	2	v	v	NOUN
ejpam-6729	401	3	(	(	PUNCT
ejpam-6729	401	4	1	1	NUM
ejpam-6729	401	5	)	)	PUNCT
ejpam-6729	401	6	=	=	PRON
ejpam-6729	401	7	{	{	PUNCT
ejpam-6729	401	8	ra	ra	PROPN
ejpam-6729	401	9	,	,	PUNCT
ejpam-6729	401	10	rb	rb	PROPN
ejpam-6729	401	11	,	,	PUNCT
ejpam-6729	401	12	rc	rc	NOUN
ejpam-6729	401	13	}	}	PUNCT
ejpam-6729	401	14	and	and	CCONJ
ejpam-6729	401	15	assign	assign	VERB
ejpam-6729	401	16	µ(ra	µ(ra	PROPN
ejpam-6729	401	17	,	,	PUNCT
ejpam-6729	401	18	routeid	routeid	NOUN
ejpam-6729	401	19	)	)	PUNCT
ejpam-6729	401	20	=	=	PUNCT
ejpam-6729	402	1	“	"	PUNCT
ejpam-6729	402	2	a	a	DET
ejpam-6729	402	3	”	"	PUNCT
ejpam-6729	402	4	,	,	PUNCT
ejpam-6729	402	5	µ(ra	µ(ra	PROPN
ejpam-6729	402	6	,	,	PUNCT
ejpam-6729	402	7	headwaymin	headwaymin	NOUN
ejpam-6729	402	8	)	)	PUNCT
ejpam-6729	402	9	=	=	SYM
ejpam-6729	402	10	6	6	NUM
ejpam-6729	402	11	,	,	PUNCT
ejpam-6729	402	12	µ(rb	µ(rb	PRON
ejpam-6729	402	13	,	,	PUNCT
ejpam-6729	402	14	routeid	routeid	NOUN
ejpam-6729	402	15	)	)	PUNCT
ejpam-6729	402	16	=	=	PUNCT
ejpam-6729	402	17	“	"	PUNCT
ejpam-6729	402	18	b	b	NOUN
ejpam-6729	402	19	”	"	PUNCT
ejpam-6729	402	20	,	,	PUNCT
ejpam-6729	402	21	µ(rb	µ(rb	PROPN
ejpam-6729	402	22	,	,	PUNCT
ejpam-6729	402	23	headwaymin	headwaymin	NOUN
ejpam-6729	402	24	)	)	PUNCT
ejpam-6729	402	25	=	=	SYM
ejpam-6729	402	26	8	8	NUM
ejpam-6729	402	27	,	,	PUNCT
ejpam-6729	402	28	µ(rc	µ(rc	NOUN
ejpam-6729	402	29	,	,	PUNCT
ejpam-6729	402	30	routeid	routeid	NOUN
ejpam-6729	402	31	)	)	PUNCT
ejpam-6729	402	32	=	=	PUNCT
ejpam-6729	403	1	“	"	PUNCT
ejpam-6729	403	2	c	c	X
ejpam-6729	403	3	”	"	PUNCT
ejpam-6729	403	4	,	,	PUNCT
ejpam-6729	403	5	µ(rc	µ(rc	PROPN
ejpam-6729	403	6	,	,	PUNCT
ejpam-6729	403	7	headwaymin	headwaymin	PROPN
ejpam-6729	403	8	)	)	PUNCT
ejpam-6729	403	9	=	=	NOUN
ejpam-6729	404	1	12	12	NUM
ejpam-6729	404	2	.	.	PUNCT
ejpam-6729	405	1	t.	t.	PROPN
ejpam-6729	405	2	fujita	fujita	PROPN
ejpam-6729	405	3	,	,	PUNCT
ejpam-6729	405	4	f.	f.	PROPN
ejpam-6729	405	5	smarandache	smarandache	PROPN
ejpam-6729	405	6	/	/	SYM
ejpam-6729	405	7	eur	eur	PROPN
ejpam-6729	405	8	.	.	PUNCT
ejpam-6729	406	1	j.	j.	PROPN
ejpam-6729	406	2	pure	pure	PROPN
ejpam-6729	406	3	appl	appl	PROPN
ejpam-6729	406	4	.	.	PROPN
ejpam-6729	406	5	math	math	PROPN
ejpam-6729	406	6	,	,	PUNCT
ejpam-6729	406	7	18	18	NUM
ejpam-6729	406	8	(	(	PUNCT
ejpam-6729	406	9	4	4	NUM
ejpam-6729	406	10	)	)	PUNCT
ejpam-6729	406	11	(	(	PUNCT
ejpam-6729	406	12	2025	2025	NUM
ejpam-6729	406	13	)	)	PUNCT
ejpam-6729	406	14	,	,	PUNCT
ejpam-6729	406	15	6729	6729	NUM
ejpam-6729	406	16	20	20	NUM
ejpam-6729	406	17	of	of	ADP
ejpam-6729	406	18	36	36	NUM
ejpam-6729	406	19	level	level	NOUN
ejpam-6729	406	20	2	2	NUM
ejpam-6729	406	21	(	(	PUNCT
ejpam-6729	406	22	lines	line	NOUN
ejpam-6729	406	23	as	as	ADP
ejpam-6729	406	24	sets	set	NOUN
ejpam-6729	406	25	of	of	ADP
ejpam-6729	406	26	routes	route	NOUN
ejpam-6729	406	27	;	;	PUNCT
ejpam-6729	406	28	2	2	NUM
ejpam-6729	406	29	-	-	PUNCT
ejpam-6729	406	30	supervertices	supervertice	NOUN
ejpam-6729	406	31	)	)	PUNCT
ejpam-6729	406	32	.	.	PUNCT
ejpam-6729	407	1	let	let	AUX
ejpam-6729	407	2	lred	lre	VERB
ejpam-6729	407	3	=	=	SYM
ejpam-6729	407	4	{	{	PUNCT
ejpam-6729	407	5	ra	ra	PROPN
ejpam-6729	407	6	,	,	PUNCT
ejpam-6729	407	7	rb	rb	PROPN
ejpam-6729	407	8	}	}	PUNCT
ejpam-6729	407	9	,	,	PUNCT
ejpam-6729	407	10	lblue	lblue	NOUN
ejpam-6729	407	11	=	=	SYM
ejpam-6729	407	12	{	{	PUNCT
ejpam-6729	407	13	rc	rc	PROPN
ejpam-6729	407	14	}	}	PUNCT
ejpam-6729	407	15	∈	∈	PROPN
ejpam-6729	407	16	p2(v0	p2(v0	PROPN
ejpam-6729	407	17	)	)	PUNCT
ejpam-6729	407	18	.	.	PUNCT
ejpam-6729	408	1	set	set	VERB
ejpam-6729	408	2	v	v	NOUN
ejpam-6729	408	3	(	(	PUNCT
ejpam-6729	408	4	2	2	NUM
ejpam-6729	408	5	)	)	PUNCT
ejpam-6729	408	6	=	=	PRON
ejpam-6729	408	7	{	{	PUNCT
ejpam-6729	408	8	lred	lre	VERB
ejpam-6729	408	9	,	,	PUNCT
ejpam-6729	408	10	lblue	lblue	NOUN
ejpam-6729	408	11	}	}	PUNCT
ejpam-6729	408	12	with	with	ADP
ejpam-6729	408	13	µ(lred	µ(lre	VERB
ejpam-6729	408	14	,	,	PUNCT
ejpam-6729	408	15	color	color	NOUN
ejpam-6729	408	16	)	)	PUNCT
ejpam-6729	408	17	=	=	PUNCT
ejpam-6729	408	18	“	"	PUNCT
ejpam-6729	408	19	red	red	ADJ
ejpam-6729	408	20	”	"	PUNCT
ejpam-6729	408	21	,	,	PUNCT
ejpam-6729	408	22	µ(lred	µ(lre	VERB
ejpam-6729	408	23	,	,	PUNCT
ejpam-6729	408	24	operator	operator	NOUN
ejpam-6729	408	25	)	)	PUNCT
ejpam-6729	408	26	=	=	PUNCT
ejpam-6729	408	27	“	"	PUNCT
ejpam-6729	408	28	metroco	metroco	PROPN
ejpam-6729	408	29	”	"	PUNCT
ejpam-6729	408	30	,	,	PUNCT
ejpam-6729	408	31	µ(lblue	µ(lblue	NOUN
ejpam-6729	408	32	,	,	PUNCT
ejpam-6729	408	33	color	color	NOUN
ejpam-6729	408	34	)	)	PUNCT
ejpam-6729	408	35	=	=	PUNCT
ejpam-6729	408	36	“	"	PUNCT
ejpam-6729	408	37	blue	blue	ADJ
ejpam-6729	408	38	”	"	PUNCT
ejpam-6729	408	39	,	,	PUNCT
ejpam-6729	408	40	µ(lblue	µ(lblue	NOUN
ejpam-6729	408	41	,	,	PUNCT
ejpam-6729	408	42	operator	operator	NOUN
ejpam-6729	408	43	)	)	PUNCT
ejpam-6729	408	44	=	=	PUNCT
ejpam-6729	408	45	“	"	PUNCT
ejpam-6729	408	46	metroco	metroco	PROPN
ejpam-6729	408	47	”	"	PUNCT
ejpam-6729	408	48	.	.	PUNCT
ejpam-6729	409	1	level	level	NOUN
ejpam-6729	409	2	3	3	NUM
ejpam-6729	409	3	(	(	PUNCT
ejpam-6729	409	4	networks	network	NOUN
ejpam-6729	409	5	as	as	ADP
ejpam-6729	409	6	sets	set	NOUN
ejpam-6729	409	7	of	of	ADP
ejpam-6729	409	8	lines	line	NOUN
ejpam-6729	409	9	;	;	PUNCT
ejpam-6729	409	10	3	3	NUM
ejpam-6729	409	11	-	-	PUNCT
ejpam-6729	409	12	supervertices	supervertice	NOUN
ejpam-6729	409	13	)	)	PUNCT
ejpam-6729	409	14	.	.	PUNCT
ejpam-6729	410	1	define	define	VERB
ejpam-6729	410	2	ncity	ncity	NOUN
ejpam-6729	410	3	=	=	SYM
ejpam-6729	410	4	{	{	PUNCT
ejpam-6729	410	5	lred	lre	VERB
ejpam-6729	410	6	,	,	PUNCT
ejpam-6729	410	7	lblue	lblue	PROPN
ejpam-6729	410	8	}	}	PUNCT
ejpam-6729	410	9	,	,	PUNCT
ejpam-6729	410	10	nregional	nregional	ADJ
ejpam-6729	410	11	=	=	X
ejpam-6729	410	12	{	{	PUNCT
ejpam-6729	410	13	lblue	lblue	ADJ
ejpam-6729	410	14	}	}	PUNCT
ejpam-6729	410	15	∈	∈	NOUN
ejpam-6729	410	16	p3(v0	p3(v0	PROPN
ejpam-6729	410	17	)	)	PUNCT
ejpam-6729	410	18	.	.	PUNCT
ejpam-6729	411	1	set	set	VERB
ejpam-6729	411	2	v	v	NOUN
ejpam-6729	411	3	(	(	PUNCT
ejpam-6729	411	4	3	3	NUM
ejpam-6729	411	5	)	)	PUNCT
ejpam-6729	411	6	=	=	SYM
ejpam-6729	411	7	{	{	PUNCT
ejpam-6729	411	8	ncity	ncity	NOUN
ejpam-6729	411	9	,	,	PUNCT
ejpam-6729	411	10	nregional	nregional	ADJ
ejpam-6729	411	11	}	}	PUNCT
ejpam-6729	411	12	and	and	CCONJ
ejpam-6729	411	13	assign	assign	VERB
ejpam-6729	411	14	µ(ncity	µ(ncity	ADV
ejpam-6729	411	15	,	,	PUNCT
ejpam-6729	411	16	name	name	NOUN
ejpam-6729	411	17	)	)	PUNCT
ejpam-6729	411	18	=	=	PUNCT
ejpam-6729	411	19	“	"	PUNCT
ejpam-6729	411	20	city	city	NOUN
ejpam-6729	411	21	network	network	NOUN
ejpam-6729	411	22	”	"	PUNCT
ejpam-6729	411	23	,	,	PUNCT
ejpam-6729	411	24	µ(ncity	µ(ncity	ADV
ejpam-6729	411	25	,	,	PUNCT
ejpam-6729	411	26	rev	rev	ADJ
ejpam-6729	411	27	)	)	PUNCT
ejpam-6729	411	28	=	=	SYM
ejpam-6729	411	29	“	"	PUNCT
ejpam-6729	411	30	2025q3	2025q3	PROPN
ejpam-6729	411	31	”	"	PUNCT
ejpam-6729	411	32	,	,	PUNCT
ejpam-6729	411	33	µ(nregional	µ(nregional	ADJ
ejpam-6729	411	34	,	,	PUNCT
ejpam-6729	411	35	name	name	NOUN
ejpam-6729	411	36	)	)	PUNCT
ejpam-6729	411	37	=	=	PUNCT
ejpam-6729	411	38	“	"	PUNCT
ejpam-6729	411	39	regional	regional	ADJ
ejpam-6729	411	40	link	link	NOUN
ejpam-6729	411	41	”	"	PUNCT
ejpam-6729	411	42	.	.	PUNCT
ejpam-6729	412	1	3	3	NUM
ejpam-6729	412	2	-	-	PUNCT
ejpam-6729	412	3	superedges	superedge	NOUN
ejpam-6729	412	4	and	and	CCONJ
ejpam-6729	412	5	labels	label	NOUN
ejpam-6729	412	6	.	.	PUNCT
ejpam-6729	413	1	let	let	VERB
ejpam-6729	413	2	the	the	DET
ejpam-6729	413	3	label	label	NOUN
ejpam-6729	413	4	alphabet	alphabet	NOUN
ejpam-6729	413	5	σ	σ	PROPN
ejpam-6729	414	1	=	=	PUNCT
ejpam-6729	415	1	{	{	PUNCT
ejpam-6729	415	2	fareagreement	fareagreement	NOUN
ejpam-6729	415	3	,	,	PUNCT
ejpam-6729	415	4	interchange	interchange	NOUN
ejpam-6729	415	5	}	}	PUNCT
ejpam-6729	415	6	.	.	PUNCT
ejpam-6729	416	1	define	define	VERB
ejpam-6729	416	2	e1	e1	NOUN
ejpam-6729	416	3	=	=	SYM
ejpam-6729	416	4	{	{	PUNCT
ejpam-6729	416	5	ncity	ncity	NOUN
ejpam-6729	416	6	,	,	PUNCT
ejpam-6729	416	7	nregional	nregional	ADJ
ejpam-6729	416	8	}	}	PUNCT
ejpam-6729	416	9	,	,	PUNCT
ejpam-6729	416	10	e2	e2	PROPN
ejpam-6729	416	11	=	=	SYM
ejpam-6729	416	12	{	{	PUNCT
ejpam-6729	416	13	ncity	ncity	NOUN
ejpam-6729	416	14	}	}	PUNCT
ejpam-6729	416	15	,	,	PUNCT
ejpam-6729	416	16	and	and	CCONJ
ejpam-6729	416	17	e(3	e(3	PROPN
ejpam-6729	416	18	)	)	PUNCT
ejpam-6729	417	1	=	=	PRON
ejpam-6729	417	2	{	{	PUNCT
ejpam-6729	417	3	e1	e1	PROPN
ejpam-6729	417	4	,	,	PUNCT
ejpam-6729	417	5	e2	e2	NOUN
ejpam-6729	417	6	}	}	PUNCT
ejpam-6729	417	7	⊆	⊆	PROPN
ejpam-6729	417	8	p	p	NOUN
ejpam-6729	417	9	(	(	PUNCT
ejpam-6729	417	10	v	v	NOUN
ejpam-6729	417	11	(	(	PUNCT
ejpam-6729	417	12	3	3	NUM
ejpam-6729	417	13	)	)	PUNCT
ejpam-6729	417	14	)	)	PUNCT
ejpam-6729	417	15	\	\	NOUN
ejpam-6729	417	16	{	{	PUNCT
ejpam-6729	417	17	∅	∅	NOUN
ejpam-6729	417	18	}	}	PUNCT
ejpam-6729	417	19	.	.	PUNCT
ejpam-6729	418	1	set	set	VERB
ejpam-6729	418	2	λ(e1	λ(e1	NOUN
ejpam-6729	418	3	)	)	PUNCT
ejpam-6729	418	4	=	=	SYM
ejpam-6729	418	5	fareagreement	fareagreement	NOUN
ejpam-6729	418	6	,	,	PUNCT
ejpam-6729	418	7	µ(e1	µ(e1	NOUN
ejpam-6729	418	8	,	,	PUNCT
ejpam-6729	418	9	year	year	NOUN
ejpam-6729	418	10	)	)	PUNCT
ejpam-6729	418	11	=	=	SYM
ejpam-6729	418	12	2025	2025	NUM
ejpam-6729	418	13	,	,	PUNCT
ejpam-6729	418	14	λ(e2	λ(e2	NOUN
ejpam-6729	418	15	)	)	PUNCT
ejpam-6729	418	16	=	=	SYM
ejpam-6729	419	1	interchange	interchange	NOUN
ejpam-6729	419	2	,	,	PUNCT
ejpam-6729	419	3	µ(e2	µ(e2	NOUN
ejpam-6729	419	4	,	,	PUNCT
ejpam-6729	419	5	hub	hub	NOUN
ejpam-6729	419	6	)	)	PUNCT
ejpam-6729	420	1	=	=	PUNCT
ejpam-6729	420	2	“	"	PUNCT
ejpam-6729	420	3	central	central	ADJ
ejpam-6729	420	4	”	"	PUNCT
ejpam-6729	420	5	.	.	PUNCT
ejpam-6729	420	6	verification	verification	NOUN
ejpam-6729	420	7	.	.	PUNCT
ejpam-6729	421	1	each	each	DET
ejpam-6729	421	2	route	route	NOUN
ejpam-6729	421	3	is	be	AUX
ejpam-6729	421	4	a	a	DET
ejpam-6729	421	5	subset	subset	NOUN
ejpam-6729	421	6	of	of	ADP
ejpam-6729	421	7	v0	v0	NOUN
ejpam-6729	421	8	⇒	⇒	NOUN
ejpam-6729	421	9	v	v	PROPN
ejpam-6729	421	10	(	(	PUNCT
ejpam-6729	421	11	1	1	NUM
ejpam-6729	421	12	)	)	PUNCT
ejpam-6729	421	13	⊆	⊆	NUM
ejpam-6729	421	14	p1(v0	p1(v0	NOUN
ejpam-6729	421	15	)	)	PUNCT
ejpam-6729	421	16	.	.	PUNCT
ejpam-6729	422	1	each	each	DET
ejpam-6729	422	2	line	line	NOUN
ejpam-6729	422	3	is	be	AUX
ejpam-6729	422	4	a	a	DET
ejpam-6729	422	5	set	set	NOUN
ejpam-6729	422	6	of	of	ADP
ejpam-6729	422	7	routes	route	NOUN
ejpam-6729	422	8	⇒	⇒	VERB
ejpam-6729	422	9	v	v	NUM
ejpam-6729	422	10	(	(	PUNCT
ejpam-6729	422	11	2	2	NUM
ejpam-6729	422	12	)	)	PUNCT
ejpam-6729	422	13	⊆	⊆	NUM
ejpam-6729	422	14	p2(v0	p2(v0	NOUN
ejpam-6729	422	15	)	)	PUNCT
ejpam-6729	422	16	.	.	PUNCT
ejpam-6729	423	1	each	each	DET
ejpam-6729	423	2	network	network	NOUN
ejpam-6729	423	3	is	be	AUX
ejpam-6729	423	4	a	a	DET
ejpam-6729	423	5	set	set	NOUN
ejpam-6729	423	6	of	of	ADP
ejpam-6729	423	7	lines	line	NOUN
ejpam-6729	423	8	⇒	⇒	VERB
ejpam-6729	423	9	v	v	NUM
ejpam-6729	423	10	(	(	PUNCT
ejpam-6729	423	11	3	3	NUM
ejpam-6729	423	12	)	)	PUNCT
ejpam-6729	423	13	⊆	⊆	NUM
ejpam-6729	423	14	p3(v0	p3(v0	NOUN
ejpam-6729	423	15	)	)	PUNCT
ejpam-6729	423	16	.	.	PUNCT
ejpam-6729	424	1	finally	finally	ADV
ejpam-6729	424	2	,	,	PUNCT
ejpam-6729	424	3	e1	e1	PROPN
ejpam-6729	424	4	,	,	PUNCT
ejpam-6729	424	5	e2	e2	PROPN
ejpam-6729	424	6	are	be	AUX
ejpam-6729	424	7	nonempty	nonempty	ADJ
ejpam-6729	424	8	subsets	subset	NOUN
ejpam-6729	424	9	of	of	ADP
ejpam-6729	424	10	v	v	NOUN
ejpam-6729	424	11	(	(	PUNCT
ejpam-6729	424	12	3	3	NUM
ejpam-6729	424	13	)	)	PUNCT
ejpam-6729	424	14	.	.	PUNCT
ejpam-6729	425	1	thus	thus	ADV
ejpam-6729	425	2	h(3	h(3	NOUN
ejpam-6729	425	3	)	)	PUNCT
ejpam-6729	425	4	=	=	PRON
ejpam-6729	425	5	(	(	PUNCT
ejpam-6729	425	6	v	v	NOUN
ejpam-6729	425	7	(	(	PUNCT
ejpam-6729	425	8	3	3	NUM
ejpam-6729	425	9	)	)	PUNCT
ejpam-6729	425	10	,	,	PUNCT
ejpam-6729	425	11	e(3	e(3	PROPN
ejpam-6729	425	12	)	)	PUNCT
ejpam-6729	425	13	,	,	PUNCT
ejpam-6729	425	14	λ	λ	PROPN
ejpam-6729	425	15	,	,	PUNCT
ejpam-6729	425	16	µ	µ	NOUN
ejpam-6729	425	17	)	)	PUNCT
ejpam-6729	425	18	is	be	AUX
ejpam-6729	425	19	a	a	DET
ejpam-6729	425	20	property	property	NOUN
ejpam-6729	425	21	3	3	NUM
ejpam-6729	425	22	-	-	PUNCT
ejpam-6729	425	23	superhypergraph	superhypergraph	NOUN
ejpam-6729	425	24	.	.	PUNCT
ejpam-6729	425	25	example	example	NOUN
ejpam-6729	425	26	12	12	NUM
ejpam-6729	425	27	(	(	PUNCT
ejpam-6729	425	28	a	a	DET
ejpam-6729	425	29	3	3	NUM
ejpam-6729	425	30	-	-	PUNCT
ejpam-6729	425	31	level	level	NOUN
ejpam-6729	425	32	property	property	NOUN
ejpam-6729	425	33	superhypergraph	superhypergraph	NOUN
ejpam-6729	425	34	for	for	ADP
ejpam-6729	425	35	academic	academic	ADJ
ejpam-6729	425	36	collections	collection	NOUN
ejpam-6729	425	37	)	)	PUNCT
ejpam-6729	425	38	.	.	PUNCT
ejpam-6729	426	1	we	we	PRON
ejpam-6729	426	2	model	model	VERB
ejpam-6729	426	3	academic	academic	ADJ
ejpam-6729	426	4	artifacts	artifact	NOUN
ejpam-6729	426	5	with	with	ADP
ejpam-6729	426	6	papers	paper	NOUN
ejpam-6729	426	7	(	(	PUNCT
ejpam-6729	426	8	level	level	NOUN
ejpam-6729	426	9	0	0	NUM
ejpam-6729	426	10	)	)	PUNCT
ejpam-6729	426	11	,	,	PUNCT
ejpam-6729	426	12	venues	venue	NOUN
ejpam-6729	426	13	(	(	PUNCT
ejpam-6729	426	14	level	level	NOUN
ejpam-6729	426	15	1	1	NUM
ejpam-6729	426	16	)	)	PUNCT
ejpam-6729	426	17	,	,	PUNCT
ejpam-6729	426	18	fields	field	NOUN
ejpam-6729	426	19	(	(	PUNCT
ejpam-6729	426	20	level	level	NOUN
ejpam-6729	426	21	2	2	NUM
ejpam-6729	426	22	)	)	PUNCT
ejpam-6729	426	23	,	,	PUNCT
ejpam-6729	426	24	and	and	CCONJ
ejpam-6729	426	25	programs	program	NOUN
ejpam-6729	426	26	/	/	SYM
ejpam-6729	426	27	consortia	consortia	NOUN
ejpam-6729	426	28	(	(	PUNCT
ejpam-6729	426	29	level	level	NOUN
ejpam-6729	426	30	3	3	NUM
ejpam-6729	426	31	)	)	PUNCT
ejpam-6729	426	32	.	.	PUNCT
ejpam-6729	427	1	t.	t.	PROPN
ejpam-6729	427	2	fujita	fujita	PROPN
ejpam-6729	427	3	,	,	PUNCT
ejpam-6729	427	4	f.	f.	PROPN
ejpam-6729	427	5	smarandache	smarandache	PROPN
ejpam-6729	427	6	/	/	SYM
ejpam-6729	427	7	eur	eur	PROPN
ejpam-6729	427	8	.	.	PUNCT
ejpam-6729	428	1	j.	j.	PROPN
ejpam-6729	428	2	pure	pure	PROPN
ejpam-6729	428	3	appl	appl	PROPN
ejpam-6729	428	4	.	.	PROPN
ejpam-6729	428	5	math	math	PROPN
ejpam-6729	428	6	,	,	PUNCT
ejpam-6729	428	7	18	18	NUM
ejpam-6729	428	8	(	(	PUNCT
ejpam-6729	428	9	4	4	NUM
ejpam-6729	428	10	)	)	PUNCT
ejpam-6729	428	11	(	(	PUNCT
ejpam-6729	428	12	2025	2025	NUM
ejpam-6729	428	13	)	)	PUNCT
ejpam-6729	428	14	,	,	PUNCT
ejpam-6729	428	15	6729	6729	NUM
ejpam-6729	428	16	21	21	NUM
ejpam-6729	428	17	of	of	ADP
ejpam-6729	428	18	36	36	NUM
ejpam-6729	428	19	level	level	NOUN
ejpam-6729	428	20	0	0	NUM
ejpam-6729	428	21	(	(	PUNCT
ejpam-6729	428	22	papers	paper	NOUN
ejpam-6729	428	23	)	)	PUNCT
ejpam-6729	428	24	.	.	PUNCT
ejpam-6729	429	1	let	let	VERB
ejpam-6729	429	2	v0	v0	NOUN
ejpam-6729	429	3	=	=	SYM
ejpam-6729	429	4	{	{	PUNCT
ejpam-6729	429	5	p1	p1	NOUN
ejpam-6729	429	6	,	,	PUNCT
ejpam-6729	429	7	p2	p2	NOUN
ejpam-6729	429	8	,	,	PUNCT
ejpam-6729	429	9	p3	p3	NOUN
ejpam-6729	429	10	,	,	PUNCT
ejpam-6729	429	11	p4	p4	ADJ
ejpam-6729	429	12	,	,	PUNCT
ejpam-6729	429	13	p5	p5	ADJ
ejpam-6729	429	14	}	}	PUNCT
ejpam-6729	429	15	.	.	PUNCT
ejpam-6729	430	1	assign	assign	VERB
ejpam-6729	430	2	basic	basic	ADJ
ejpam-6729	430	3	properties	property	NOUN
ejpam-6729	430	4	:	:	PUNCT
ejpam-6729	430	5	µ(p1	µ(p1	NOUN
ejpam-6729	430	6	,	,	PUNCT
ejpam-6729	430	7	title	title	NOUN
ejpam-6729	430	8	)	)	PUNCT
ejpam-6729	430	9	=	=	PUNCT
ejpam-6729	431	1	“	"	PUNCT
ejpam-6729	431	2	a	a	DET
ejpam-6729	431	3	study	study	NOUN
ejpam-6729	431	4	on	on	ADP
ejpam-6729	431	5	x	x	X
ejpam-6729	431	6	”	"	PUNCT
ejpam-6729	431	7	,	,	PUNCT
ejpam-6729	431	8	µ(p1	µ(p1	NOUN
ejpam-6729	431	9	,	,	PUNCT
ejpam-6729	431	10	year	year	NOUN
ejpam-6729	431	11	)	)	PUNCT
ejpam-6729	431	12	=	=	SYM
ejpam-6729	431	13	2023	2023	NUM
ejpam-6729	431	14	,	,	PUNCT
ejpam-6729	431	15	µ(p2	µ(p2	ADJ
ejpam-6729	431	16	,	,	PUNCT
ejpam-6729	431	17	title	title	NOUN
ejpam-6729	431	18	)	)	PUNCT
ejpam-6729	431	19	=	=	PUNCT
ejpam-6729	431	20	“	"	PUNCT
ejpam-6729	431	21	learning	learn	VERB
ejpam-6729	431	22	y	y	PROPN
ejpam-6729	431	23	”	"	PUNCT
ejpam-6729	431	24	,	,	PUNCT
ejpam-6729	431	25	µ(p2	µ(p2	ADJ
ejpam-6729	431	26	,	,	PUNCT
ejpam-6729	431	27	year	year	NOUN
ejpam-6729	431	28	)	)	PUNCT
ejpam-6729	431	29	=	=	SYM
ejpam-6729	431	30	2024	2024	NUM
ejpam-6729	431	31	,	,	PUNCT
ejpam-6729	431	32	.	.	PUNCT
ejpam-6729	431	33	.	.	PUNCT
ejpam-6729	431	34	.	.	PUNCT
ejpam-6729	432	1	level	level	NOUN
ejpam-6729	432	2	1	1	NUM
ejpam-6729	432	3	(	(	PUNCT
ejpam-6729	432	4	venues	venue	NOUN
ejpam-6729	432	5	;	;	PUNCT
ejpam-6729	432	6	1	1	NUM
ejpam-6729	432	7	-	-	PUNCT
ejpam-6729	432	8	supervertices	supervertice	NOUN
ejpam-6729	432	9	)	)	PUNCT
ejpam-6729	432	10	.	.	PUNCT
ejpam-6729	433	1	group	group	NOUN
ejpam-6729	433	2	papers	paper	NOUN
ejpam-6729	433	3	by	by	ADP
ejpam-6729	433	4	publication	publication	NOUN
ejpam-6729	433	5	venue	venue	NOUN
ejpam-6729	433	6	:	:	PUNCT
ejpam-6729	433	7	vconfa	vconfa	NOUN
ejpam-6729	433	8	=	=	SYM
ejpam-6729	433	9	{	{	PUNCT
ejpam-6729	433	10	p1	p1	NOUN
ejpam-6729	433	11	,	,	PUNCT
ejpam-6729	433	12	p2	p2	NOUN
ejpam-6729	433	13	}	}	PUNCT
ejpam-6729	433	14	,	,	PUNCT
ejpam-6729	433	15	vconfb	vconfb	NOUN
ejpam-6729	433	16	=	=	SYM
ejpam-6729	433	17	{	{	PUNCT
ejpam-6729	433	18	p3	p3	PROPN
ejpam-6729	433	19	,	,	PUNCT
ejpam-6729	433	20	p4	p4	ADJ
ejpam-6729	433	21	}	}	PUNCT
ejpam-6729	433	22	,	,	PUNCT
ejpam-6729	433	23	vjournalc	vjournalc	ADJ
ejpam-6729	433	24	=	=	CCONJ
ejpam-6729	433	25	{	{	PUNCT
ejpam-6729	433	26	p5	p5	PROPN
ejpam-6729	433	27	}	}	PUNCT
ejpam-6729	433	28	∈	∈	PROPN
ejpam-6729	433	29	p1(v0	p1(v0	PROPN
ejpam-6729	433	30	)	)	PUNCT
ejpam-6729	433	31	.	.	PUNCT
ejpam-6729	434	1	set	set	VERB
ejpam-6729	434	2	v	v	NOUN
ejpam-6729	434	3	(	(	PUNCT
ejpam-6729	434	4	1	1	NUM
ejpam-6729	434	5	)	)	PUNCT
ejpam-6729	434	6	=	=	PRON
ejpam-6729	434	7	{	{	PUNCT
ejpam-6729	434	8	vconfa	vconfa	NOUN
ejpam-6729	434	9	,	,	PUNCT
ejpam-6729	434	10	vconfb	vconfb	NOUN
ejpam-6729	434	11	,	,	PUNCT
ejpam-6729	434	12	vjournalc	vjournalc	ADJ
ejpam-6729	434	13	}	}	PUNCT
ejpam-6729	434	14	and	and	CCONJ
ejpam-6729	434	15	assign	assign	VERB
ejpam-6729	434	16	µ(vconfa	µ(vconfa	PROPN
ejpam-6729	434	17	,	,	PUNCT
ejpam-6729	434	18	abbr	abbr	PROPN
ejpam-6729	434	19	)	)	PUNCT
ejpam-6729	434	20	=	=	PUNCT
ejpam-6729	434	21	“	"	PUNCT
ejpam-6729	434	22	confa	confa	PROPN
ejpam-6729	434	23	”	"	PUNCT
ejpam-6729	434	24	,	,	PUNCT
ejpam-6729	434	25	µ(vconfa	µ(vconfa	PROPN
ejpam-6729	434	26	,	,	PUNCT
ejpam-6729	434	27	issn	issn	PROPN
ejpam-6729	434	28	)	)	PUNCT
ejpam-6729	434	29	=	=	PUNCT
ejpam-6729	434	30	“	"	PUNCT
ejpam-6729	434	31	1111	1111	NUM
ejpam-6729	434	32	-	-	SYM
ejpam-6729	434	33	1111	1111	NUM
ejpam-6729	434	34	”	"	PUNCT
ejpam-6729	434	35	,	,	PUNCT
ejpam-6729	434	36	µ(vconfb	µ(vconfb	PROPN
ejpam-6729	434	37	,	,	PUNCT
ejpam-6729	434	38	abbr	abbr	PROPN
ejpam-6729	434	39	)	)	PUNCT
ejpam-6729	434	40	=	=	PUNCT
ejpam-6729	434	41	“	"	PUNCT
ejpam-6729	434	42	confb	confb	NOUN
ejpam-6729	434	43	”	"	PUNCT
ejpam-6729	434	44	,	,	PUNCT
ejpam-6729	434	45	µ(vconfb	µ(vconfb	PROPN
ejpam-6729	434	46	,	,	PUNCT
ejpam-6729	434	47	issn	issn	PROPN
ejpam-6729	434	48	)	)	PUNCT
ejpam-6729	434	49	=	=	PUNCT
ejpam-6729	434	50	“	"	PUNCT
ejpam-6729	434	51	2222	2222	NUM
ejpam-6729	434	52	-	-	SYM
ejpam-6729	434	53	2222	2222	NUM
ejpam-6729	434	54	”	"	PUNCT
ejpam-6729	434	55	,	,	PUNCT
ejpam-6729	434	56	µ(vjournalc	µ(vjournalc	PROPN
ejpam-6729	434	57	,	,	PUNCT
ejpam-6729	434	58	abbr	abbr	PROPN
ejpam-6729	434	59	)	)	PUNCT
ejpam-6729	434	60	=	=	PUNCT
ejpam-6729	434	61	“	"	PUNCT
ejpam-6729	434	62	jrnc	jrnc	PROPN
ejpam-6729	434	63	”	"	PUNCT
ejpam-6729	434	64	,	,	PUNCT
ejpam-6729	434	65	µ(vjournalc	µ(vjournalc	PROPN
ejpam-6729	434	66	,	,	PUNCT
ejpam-6729	434	67	issn	issn	PROPN
ejpam-6729	434	68	)	)	PUNCT
ejpam-6729	434	69	=	=	PUNCT
ejpam-6729	434	70	“	"	PUNCT
ejpam-6729	434	71	3333	3333	NUM
ejpam-6729	434	72	-	-	SYM
ejpam-6729	434	73	3333	3333	NUM
ejpam-6729	434	74	”	"	PUNCT
ejpam-6729	434	75	.	.	PUNCT
ejpam-6729	435	1	level	level	NOUN
ejpam-6729	435	2	2	2	NUM
ejpam-6729	435	3	(	(	PUNCT
ejpam-6729	435	4	fields	field	NOUN
ejpam-6729	435	5	;	;	PUNCT
ejpam-6729	435	6	2	2	NUM
ejpam-6729	435	7	-	-	PUNCT
ejpam-6729	435	8	supervertices	supervertice	NOUN
ejpam-6729	435	9	)	)	PUNCT
ejpam-6729	435	10	.	.	PUNCT
ejpam-6729	436	1	group	group	NOUN
ejpam-6729	436	2	venues	venue	NOUN
ejpam-6729	436	3	by	by	ADP
ejpam-6729	436	4	field	field	NOUN
ejpam-6729	436	5	:	:	PUNCT
ejpam-6729	436	6	fml	fml	X
ejpam-6729	437	1	=	=	PRON
ejpam-6729	437	2	{	{	PUNCT
ejpam-6729	437	3	vconfa	vconfa	NOUN
ejpam-6729	437	4	,	,	PUNCT
ejpam-6729	437	5	vconfb	vconfb	NOUN
ejpam-6729	437	6	}	}	PUNCT
ejpam-6729	437	7	,	,	PUNCT
ejpam-6729	437	8	ftheory	ftheory	NOUN
ejpam-6729	437	9	=	=	SYM
ejpam-6729	437	10	{	{	PUNCT
ejpam-6729	437	11	vjournalc	vjournalc	PROPN
ejpam-6729	437	12	}	}	PUNCT
ejpam-6729	437	13	∈	∈	PROPN
ejpam-6729	437	14	p2(v0	p2(v0	PROPN
ejpam-6729	437	15	)	)	PUNCT
ejpam-6729	437	16	,	,	PUNCT
ejpam-6729	437	17	with	with	ADP
ejpam-6729	437	18	v	v	NUM
ejpam-6729	437	19	(	(	PUNCT
ejpam-6729	437	20	2	2	NUM
ejpam-6729	437	21	)	)	PUNCT
ejpam-6729	437	22	=	=	PRON
ejpam-6729	437	23	{	{	PUNCT
ejpam-6729	437	24	fml	fml	PROPN
ejpam-6729	437	25	,	,	PUNCT
ejpam-6729	437	26	ftheory	ftheory	ADJ
ejpam-6729	437	27	}	}	PUNCT
ejpam-6729	437	28	and	and	CCONJ
ejpam-6729	437	29	µ(fml	µ(fml	PROPN
ejpam-6729	437	30	,	,	PUNCT
ejpam-6729	437	31	fieldname	fieldname	PROPN
ejpam-6729	437	32	)	)	PUNCT
ejpam-6729	437	33	=	=	PUNCT
ejpam-6729	438	1	“	"	PUNCT
ejpam-6729	438	2	machine	machine	NOUN
ejpam-6729	438	3	learning	learning	NOUN
ejpam-6729	438	4	”	"	PUNCT
ejpam-6729	438	5	,	,	PUNCT
ejpam-6729	438	6	µ(fml	µ(fml	NOUN
ejpam-6729	438	7	,	,	PUNCT
ejpam-6729	438	8	hindex	hindex	NOUN
ejpam-6729	438	9	)	)	PUNCT
ejpam-6729	438	10	=	=	SYM
ejpam-6729	438	11	120	120	NUM
ejpam-6729	438	12	,	,	PUNCT
ejpam-6729	438	13	µ(ftheory	µ(ftheory	ADJ
ejpam-6729	438	14	,	,	PUNCT
ejpam-6729	438	15	fieldname	fieldname	PROPN
ejpam-6729	438	16	)	)	PUNCT
ejpam-6729	438	17	=	=	PUNCT
ejpam-6729	438	18	“	"	PUNCT
ejpam-6729	438	19	theory	theory	NOUN
ejpam-6729	438	20	”	"	PUNCT
ejpam-6729	438	21	,	,	PUNCT
ejpam-6729	438	22	µ(ftheory	µ(ftheory	NOUN
ejpam-6729	438	23	,	,	PUNCT
ejpam-6729	438	24	hindex	hindex	NOUN
ejpam-6729	438	25	)	)	PUNCT
ejpam-6729	438	26	=	=	SYM
ejpam-6729	438	27	85	85	NUM
ejpam-6729	438	28	.	.	PUNCT
ejpam-6729	438	29	level	level	NOUN
ejpam-6729	438	30	3	3	NUM
ejpam-6729	438	31	(	(	PUNCT
ejpam-6729	438	32	programs	program	NOUN
ejpam-6729	438	33	/	/	SYM
ejpam-6729	438	34	consortia	consortium	NOUN
ejpam-6729	438	35	;	;	PUNCT
ejpam-6729	438	36	3	3	NUM
ejpam-6729	438	37	-	-	PUNCT
ejpam-6729	438	38	supervertices	supervertice	NOUN
ejpam-6729	438	39	)	)	PUNCT
ejpam-6729	438	40	.	.	PUNCT
ejpam-6729	439	1	paialliance	paialliance	NOUN
ejpam-6729	439	2	=	=	SYM
ejpam-6729	439	3	{	{	PUNCT
ejpam-6729	439	4	fml	fml	INTJ
ejpam-6729	439	5	}	}	PUNCT
ejpam-6729	439	6	,	,	PUNCT
ejpam-6729	439	7	pscicouncil	pscicouncil	NOUN
ejpam-6729	439	8	=	=	NOUN
ejpam-6729	439	9	{	{	PUNCT
ejpam-6729	439	10	ftheory	ftheory	ADJ
ejpam-6729	439	11	}	}	PUNCT
ejpam-6729	439	12	∈	∈	PROPN
ejpam-6729	439	13	p3(v0	p3(v0	VERB
ejpam-6729	439	14	)	)	PUNCT
ejpam-6729	439	15	,	,	PUNCT
ejpam-6729	439	16	and	and	CCONJ
ejpam-6729	439	17	v	v	X
ejpam-6729	439	18	(	(	PUNCT
ejpam-6729	439	19	3	3	NUM
ejpam-6729	439	20	)	)	PUNCT
ejpam-6729	439	21	=	=	NOUN
ejpam-6729	439	22	{	{	PUNCT
ejpam-6729	439	23	paialliance	paialliance	NOUN
ejpam-6729	439	24	,	,	PUNCT
ejpam-6729	439	25	pscicouncil	pscicouncil	NOUN
ejpam-6729	439	26	}	}	PUNCT
ejpam-6729	439	27	with	with	ADP
ejpam-6729	439	28	µ(paialliance	µ(paialliance	NOUN
ejpam-6729	439	29	,	,	PUNCT
ejpam-6729	439	30	program	program	NOUN
ejpam-6729	439	31	)	)	PUNCT
ejpam-6729	439	32	=	=	PUNCT
ejpam-6729	440	1	“	"	PUNCT
ejpam-6729	440	2	ai	ai	PROPN
ejpam-6729	440	3	alliance	alliance	NOUN
ejpam-6729	440	4	”	"	PUNCT
ejpam-6729	440	5	,	,	PUNCT
ejpam-6729	440	6	µ(pscicouncil	µ(pscicouncil	NOUN
ejpam-6729	440	7	,	,	PUNCT
ejpam-6729	440	8	program	program	NOUN
ejpam-6729	440	9	)	)	PUNCT
ejpam-6729	440	10	=	=	PUNCT
ejpam-6729	440	11	“	"	PUNCT
ejpam-6729	440	12	science	science	NOUN
ejpam-6729	440	13	council	council	PROPN
ejpam-6729	440	14	”	"	PUNCT
ejpam-6729	440	15	.	.	PUNCT
ejpam-6729	441	1	t.	t.	PROPN
ejpam-6729	441	2	fujita	fujita	PROPN
ejpam-6729	441	3	,	,	PUNCT
ejpam-6729	441	4	f.	f.	PROPN
ejpam-6729	441	5	smarandache	smarandache	PROPN
ejpam-6729	441	6	/	/	SYM
ejpam-6729	441	7	eur	eur	PROPN
ejpam-6729	441	8	.	.	PUNCT
ejpam-6729	442	1	j.	j.	PROPN
ejpam-6729	442	2	pure	pure	PROPN
ejpam-6729	442	3	appl	appl	PROPN
ejpam-6729	442	4	.	.	PROPN
ejpam-6729	442	5	math	math	PROPN
ejpam-6729	442	6	,	,	PUNCT
ejpam-6729	442	7	18	18	NUM
ejpam-6729	442	8	(	(	PUNCT
ejpam-6729	442	9	4	4	NUM
ejpam-6729	442	10	)	)	PUNCT
ejpam-6729	442	11	(	(	PUNCT
ejpam-6729	442	12	2025	2025	NUM
ejpam-6729	442	13	)	)	PUNCT
ejpam-6729	442	14	,	,	PUNCT
ejpam-6729	442	15	6729	6729	NUM
ejpam-6729	442	16	22	22	NUM
ejpam-6729	442	17	of	of	ADP
ejpam-6729	442	18	36	36	NUM
ejpam-6729	442	19	3	3	NUM
ejpam-6729	442	20	-	-	PUNCT
ejpam-6729	442	21	superedges	superedge	NOUN
ejpam-6729	442	22	and	and	CCONJ
ejpam-6729	442	23	labels	label	NOUN
ejpam-6729	442	24	.	.	PUNCT
ejpam-6729	443	1	let	let	VERB
ejpam-6729	443	2	σ	σ	NOUN
ejpam-6729	443	3	=	=	PUNCT
ejpam-6729	443	4	{	{	PUNCT
ejpam-6729	443	5	consortium	consortium	NOUN
ejpam-6729	443	6	,	,	PUNCT
ejpam-6729	443	7	datasharing	datasharing	NOUN
ejpam-6729	443	8	}	}	PUNCT
ejpam-6729	443	9	.	.	PUNCT
ejpam-6729	444	1	define	define	VERB
ejpam-6729	444	2	econs	econ	NOUN
ejpam-6729	444	3	=	=	PUNCT
ejpam-6729	444	4	{	{	PUNCT
ejpam-6729	444	5	paialliance	paialliance	NOUN
ejpam-6729	444	6	,	,	PUNCT
ejpam-6729	444	7	pscicouncil	pscicouncil	NOUN
ejpam-6729	444	8	}	}	PUNCT
ejpam-6729	444	9	,	,	PUNCT
ejpam-6729	444	10	eshare	eshare	VERB
ejpam-6729	444	11	=	=	SYM
ejpam-6729	444	12	{	{	PUNCT
ejpam-6729	444	13	paialliance	paialliance	NOUN
ejpam-6729	444	14	}	}	PUNCT
ejpam-6729	444	15	,	,	PUNCT
ejpam-6729	444	16	e(3	e(3	PROPN
ejpam-6729	444	17	)	)	PUNCT
ejpam-6729	445	1	=	=	PRON
ejpam-6729	445	2	{	{	PUNCT
ejpam-6729	445	3	econs	econ	NOUN
ejpam-6729	445	4	,	,	PUNCT
ejpam-6729	445	5	eshare	eshare	VERB
ejpam-6729	445	6	}	}	PUNCT
ejpam-6729	445	7	⊆	⊆	PROPN
ejpam-6729	445	8	p	p	NOUN
ejpam-6729	445	9	(	(	PUNCT
ejpam-6729	445	10	v	v	NOUN
ejpam-6729	445	11	(	(	PUNCT
ejpam-6729	445	12	3	3	NUM
ejpam-6729	445	13	)	)	PUNCT
ejpam-6729	445	14	)	)	PUNCT
ejpam-6729	445	15	\	\	NOUN
ejpam-6729	446	1	{	{	PUNCT
ejpam-6729	446	2	∅	∅	NOUN
ejpam-6729	446	3	}	}	PUNCT
ejpam-6729	446	4	.	.	PUNCT
ejpam-6729	447	1	set	set	VERB
ejpam-6729	447	2	λ(econs	λ(econ	NOUN
ejpam-6729	447	3	)	)	PUNCT
ejpam-6729	447	4	=	=	SYM
ejpam-6729	447	5	consortium	consortium	NOUN
ejpam-6729	447	6	,	,	PUNCT
ejpam-6729	447	7	µ(econs	µ(econ	NOUN
ejpam-6729	447	8	,	,	PUNCT
ejpam-6729	447	9	agreementyear	agreementyear	NOUN
ejpam-6729	447	10	)	)	PUNCT
ejpam-6729	447	11	=	=	SYM
ejpam-6729	447	12	2025	2025	NUM
ejpam-6729	447	13	,	,	PUNCT
ejpam-6729	447	14	λ(eshare	λ(eshare	NOUN
ejpam-6729	447	15	)	)	PUNCT
ejpam-6729	447	16	=	=	SYM
ejpam-6729	447	17	datasharing	datasharing	NOUN
ejpam-6729	447	18	,	,	PUNCT
ejpam-6729	447	19	µ(eshare	µ(eshare	NOUN
ejpam-6729	447	20	,	,	PUNCT
ejpam-6729	447	21	scope	scope	NOUN
ejpam-6729	447	22	)	)	PUNCT
ejpam-6729	447	23	=	=	PUNCT
ejpam-6729	447	24	“	"	PUNCT
ejpam-6729	447	25	anonymized	anonymize	VERB
ejpam-6729	447	26	-	-	PUNCT
ejpam-6729	447	27	metadata	metadata	NOUN
ejpam-6729	447	28	”	"	PUNCT
ejpam-6729	447	29	.	.	PUNCT
ejpam-6729	448	1	verification	verification	NOUN
ejpam-6729	448	2	.	.	PUNCT
ejpam-6729	449	1	each	each	DET
ejpam-6729	449	2	venue	venue	NOUN
ejpam-6729	449	3	is	be	AUX
ejpam-6729	449	4	a	a	DET
ejpam-6729	449	5	subset	subset	NOUN
ejpam-6729	449	6	of	of	ADP
ejpam-6729	449	7	v0	v0	NOUN
ejpam-6729	449	8	⇒	⇒	NOUN
ejpam-6729	449	9	v	v	PROPN
ejpam-6729	449	10	(	(	PUNCT
ejpam-6729	449	11	1	1	NUM
ejpam-6729	449	12	)	)	PUNCT
ejpam-6729	449	13	⊆	⊆	NUM
ejpam-6729	449	14	p1(v0	p1(v0	NOUN
ejpam-6729	449	15	)	)	PUNCT
ejpam-6729	449	16	.	.	PUNCT
ejpam-6729	450	1	each	each	DET
ejpam-6729	450	2	field	field	NOUN
ejpam-6729	450	3	is	be	AUX
ejpam-6729	450	4	a	a	DET
ejpam-6729	450	5	set	set	NOUN
ejpam-6729	450	6	of	of	ADP
ejpam-6729	450	7	venues	venue	NOUN
ejpam-6729	450	8	⇒	⇒	X
ejpam-6729	450	9	v	v	NUM
ejpam-6729	450	10	(	(	PUNCT
ejpam-6729	450	11	2	2	NUM
ejpam-6729	450	12	)	)	PUNCT
ejpam-6729	450	13	⊆	⊆	NUM
ejpam-6729	450	14	p2(v0	p2(v0	NOUN
ejpam-6729	450	15	)	)	PUNCT
ejpam-6729	450	16	.	.	PUNCT
ejpam-6729	451	1	each	each	DET
ejpam-6729	451	2	program	program	NOUN
ejpam-6729	451	3	is	be	AUX
ejpam-6729	451	4	a	a	DET
ejpam-6729	451	5	set	set	NOUN
ejpam-6729	451	6	of	of	ADP
ejpam-6729	451	7	fields	field	NOUN
ejpam-6729	451	8	⇒	⇒	PROPN
ejpam-6729	451	9	v	v	NUM
ejpam-6729	451	10	(	(	PUNCT
ejpam-6729	451	11	3	3	NUM
ejpam-6729	451	12	)	)	PUNCT
ejpam-6729	451	13	⊆	⊆	NUM
ejpam-6729	451	14	p3(v0	p3(v0	NOUN
ejpam-6729	451	15	)	)	PUNCT
ejpam-6729	451	16	.	.	PUNCT
ejpam-6729	452	1	the	the	DET
ejpam-6729	452	2	listed	list	VERB
ejpam-6729	452	3	edges	edge	NOUN
ejpam-6729	452	4	are	be	AUX
ejpam-6729	452	5	nonempty	nonempty	ADJ
ejpam-6729	452	6	subsets	subset	NOUN
ejpam-6729	452	7	of	of	ADP
ejpam-6729	452	8	v	v	NOUN
ejpam-6729	452	9	(	(	PUNCT
ejpam-6729	452	10	3	3	NUM
ejpam-6729	452	11	)	)	PUNCT
ejpam-6729	452	12	.	.	PUNCT
ejpam-6729	453	1	hence	hence	ADV
ejpam-6729	453	2	h(3	h(3	PROPN
ejpam-6729	453	3	)	)	PUNCT
ejpam-6729	454	1	=	=	PRON
ejpam-6729	454	2	(	(	PUNCT
ejpam-6729	454	3	v	v	NOUN
ejpam-6729	454	4	(	(	PUNCT
ejpam-6729	454	5	3	3	NUM
ejpam-6729	454	6	)	)	PUNCT
ejpam-6729	454	7	,	,	PUNCT
ejpam-6729	454	8	e(3	e(3	PROPN
ejpam-6729	454	9	)	)	PUNCT
ejpam-6729	454	10	,	,	PUNCT
ejpam-6729	454	11	λ	λ	PROPN
ejpam-6729	454	12	,	,	PUNCT
ejpam-6729	454	13	µ	µ	NOUN
ejpam-6729	454	14	)	)	PUNCT
ejpam-6729	454	15	is	be	AUX
ejpam-6729	454	16	a	a	DET
ejpam-6729	454	17	property	property	NOUN
ejpam-6729	454	18	3	3	NUM
ejpam-6729	454	19	-	-	PUNCT
ejpam-6729	454	20	superhypergraph	superhypergraph	NOUN
ejpam-6729	454	21	.	.	PUNCT
ejpam-6729	455	1	theorem	theorem	ADJ
ejpam-6729	455	2	8	8	NUM
ejpam-6729	455	3	(	(	PUNCT
ejpam-6729	455	4	generalisation	generalisation	NOUN
ejpam-6729	455	5	)	)	PUNCT
ejpam-6729	455	6	.	.	PUNCT
ejpam-6729	456	1	let	let	VERB
ejpam-6729	456	2	h(n	h(n	PRON
ejpam-6729	456	3	)	)	PUNCT
ejpam-6729	457	1	=	=	PRON
ejpam-6729	457	2	(	(	PUNCT
ejpam-6729	457	3	v	v	NOUN
ejpam-6729	457	4	(	(	PUNCT
ejpam-6729	457	5	n	n	CCONJ
ejpam-6729	457	6	)	)	PUNCT
ejpam-6729	457	7	,	,	PUNCT
ejpam-6729	457	8	e(n	e(n	PROPN
ejpam-6729	457	9	)	)	PUNCT
ejpam-6729	457	10	,	,	PUNCT
ejpam-6729	457	11	λ	λ	PROPN
ejpam-6729	457	12	,	,	PUNCT
ejpam-6729	457	13	µ	µ	NOUN
ejpam-6729	457	14	)	)	PUNCT
ejpam-6729	457	15	be	be	AUX
ejpam-6729	457	16	a	a	DET
ejpam-6729	457	17	property	property	NOUN
ejpam-6729	457	18	n	n	CCONJ
ejpam-6729	457	19	-	-	PUNCT
ejpam-6729	457	20	superhypergraph	superhypergraph	NOUN
ejpam-6729	457	21	over	over	ADP
ejpam-6729	457	22	the	the	DET
ejpam-6729	457	23	base	base	NOUN
ejpam-6729	457	24	v0	v0	NOUN
ejpam-6729	457	25	.	.	PUNCT
ejpam-6729	458	1	then	then	ADV
ejpam-6729	458	2	:	:	PUNCT
ejpam-6729	458	3	(	(	PUNCT
ejpam-6729	458	4	i	i	NOUN
ejpam-6729	458	5	)	)	PUNCT
ejpam-6729	458	6	if	if	SCONJ
ejpam-6729	458	7	n	n	NOUN
ejpam-6729	458	8	=	=	SYM
ejpam-6729	458	9	1	1	NUM
ejpam-6729	458	10	,	,	PUNCT
ejpam-6729	458	11	every	every	DET
ejpam-6729	458	12	e	e	PROPN
ejpam-6729	458	13	∈	∈	PROPN
ejpam-6729	458	14	e(1	e(1	PROPN
ejpam-6729	458	15	)	)	PUNCT
ejpam-6729	458	16	has	have	VERB
ejpam-6729	458	17	|e|	|e|	DET
ejpam-6729	458	18	=	=	SYM
ejpam-6729	458	19	2	2	NUM
ejpam-6729	458	20	,	,	PUNCT
ejpam-6729	458	21	and	and	CCONJ
ejpam-6729	458	22	an	an	DET
ejpam-6729	458	23	orientation	orientation	NOUN
ejpam-6729	458	24	is	be	AUX
ejpam-6729	458	25	chosen	choose	VERB
ejpam-6729	458	26	on	on	ADP
ejpam-6729	458	27	each	each	DET
ejpam-6729	458	28	such	such	ADJ
ejpam-6729	458	29	pair	pair	NOUN
ejpam-6729	458	30	,	,	PUNCT
ejpam-6729	458	31	then	then	ADV
ejpam-6729	458	32	h(1	h(1	PROPN
ejpam-6729	458	33	)	)	PUNCT
ejpam-6729	458	34	induces	induce	VERB
ejpam-6729	458	35	a	a	DET
ejpam-6729	458	36	property	property	NOUN
ejpam-6729	458	37	graph	graph	NOUN
ejpam-6729	458	38	in	in	ADP
ejpam-6729	458	39	the	the	DET
ejpam-6729	458	40	sense	sense	NOUN
ejpam-6729	458	41	of	of	ADP
ejpam-6729	458	42	definition	definition	NOUN
ejpam-6729	458	43	6	6	NUM
ejpam-6729	458	44	.	.	PUNCT
ejpam-6729	459	1	(	(	PUNCT
ejpam-6729	459	2	ii	ii	NOUN
ejpam-6729	459	3	)	)	PUNCT
ejpam-6729	459	4	if	if	SCONJ
ejpam-6729	459	5	n	n	NOUN
ejpam-6729	459	6	=	=	SYM
ejpam-6729	459	7	1	1	NUM
ejpam-6729	459	8	,	,	PUNCT
ejpam-6729	459	9	σ	σ	NOUN
ejpam-6729	459	10	=	=	SYM
ejpam-6729	459	11	{	{	PUNCT
ejpam-6729	459	12	σ0	σ0	NOUN
ejpam-6729	459	13	}	}	PUNCT
ejpam-6729	459	14	is	be	AUX
ejpam-6729	459	15	a	a	DET
ejpam-6729	459	16	singleton	singleton	NOUN
ejpam-6729	459	17	and	and	CCONJ
ejpam-6729	459	18	µ	µ	PRON
ejpam-6729	459	19	≡	≡	PROPN
ejpam-6729	459	20	⊥	⊥	PROPN
ejpam-6729	459	21	,	,	PUNCT
ejpam-6729	459	22	then	then	ADV
ejpam-6729	459	23	h(1	h(1	PROPN
ejpam-6729	459	24	)	)	PUNCT
ejpam-6729	459	25	reduces	reduce	VERB
ejpam-6729	459	26	to	to	ADP
ejpam-6729	459	27	the	the	DET
ejpam-6729	459	28	classical	classical	ADJ
ejpam-6729	459	29	hypergraph	hypergraph	NOUN
ejpam-6729	459	30	(	(	PUNCT
ejpam-6729	459	31	v	v	NOUN
ejpam-6729	459	32	(	(	PUNCT
ejpam-6729	459	33	1	1	NUM
ejpam-6729	459	34	)	)	PUNCT
ejpam-6729	459	35	,	,	PUNCT
ejpam-6729	459	36	e(1	e(1	PROPN
ejpam-6729	459	37	)	)	PUNCT
ejpam-6729	459	38	)	)	PUNCT
ejpam-6729	459	39	.	.	PUNCT
ejpam-6729	460	1	(	(	PUNCT
ejpam-6729	460	2	iii	iii	X
ejpam-6729	460	3	)	)	PUNCT
ejpam-6729	460	4	if	if	SCONJ
ejpam-6729	460	5	σ	σ	NOUN
ejpam-6729	460	6	=	=	SYM
ejpam-6729	460	7	{	{	PUNCT
ejpam-6729	460	8	σ0	σ0	NOUN
ejpam-6729	460	9	}	}	PUNCT
ejpam-6729	460	10	and	and	CCONJ
ejpam-6729	460	11	µ	µ	PRON
ejpam-6729	460	12	≡	≡	PROPN
ejpam-6729	460	13	⊥	⊥	PROPN
ejpam-6729	460	14	(	(	PUNCT
ejpam-6729	460	15	for	for	ADP
ejpam-6729	460	16	arbitrary	arbitrary	ADJ
ejpam-6729	460	17	n	n	CCONJ
ejpam-6729	460	18	)	)	PUNCT
ejpam-6729	460	19	,	,	PUNCT
ejpam-6729	460	20	then	then	ADV
ejpam-6729	460	21	h(n	h(n	PROPN
ejpam-6729	460	22	)	)	PUNCT
ejpam-6729	460	23	reduces	reduce	VERB
ejpam-6729	460	24	to	to	ADP
ejpam-6729	460	25	the	the	DET
ejpam-6729	460	26	ordinary	ordinary	ADJ
ejpam-6729	460	27	nsuperhypergraph	nsuperhypergraph	NOUN
ejpam-6729	460	28	(	(	PUNCT
ejpam-6729	460	29	v	v	NOUN
ejpam-6729	460	30	(	(	PUNCT
ejpam-6729	460	31	n	n	CCONJ
ejpam-6729	460	32	)	)	PUNCT
ejpam-6729	460	33	,	,	PUNCT
ejpam-6729	460	34	e(n	e(n	PROPN
ejpam-6729	460	35	)	)	PUNCT
ejpam-6729	460	36	)	)	PUNCT
ejpam-6729	460	37	.	.	PUNCT
ejpam-6729	461	1	proof	proof	NOUN
ejpam-6729	461	2	.	.	PUNCT
ejpam-6729	462	1	(	(	PUNCT
ejpam-6729	462	2	1	1	X
ejpam-6729	462	3	)	)	PUNCT
ejpam-6729	462	4	since	since	SCONJ
ejpam-6729	462	5	e(1	e(1	PROPN
ejpam-6729	462	6	)	)	PUNCT
ejpam-6729	462	7	⊆	⊆	NUM
ejpam-6729	462	8	p(v	p(v	NOUN
ejpam-6729	462	9	(	(	PUNCT
ejpam-6729	462	10	1	1	NUM
ejpam-6729	462	11	)	)	PUNCT
ejpam-6729	462	12	)	)	PUNCT
ejpam-6729	462	13	and	and	CCONJ
ejpam-6729	462	14	|e|	|e|	PRON
ejpam-6729	462	15	=	=	SYM
ejpam-6729	462	16	2	2	NUM
ejpam-6729	462	17	for	for	ADP
ejpam-6729	462	18	each	each	DET
ejpam-6729	462	19	e	e	PROPN
ejpam-6729	462	20	∈	∈	PROPN
ejpam-6729	462	21	e(1	e(1	PROPN
ejpam-6729	462	22	)	)	PUNCT
ejpam-6729	462	23	,	,	PUNCT
ejpam-6729	462	24	every	every	DET
ejpam-6729	462	25	edge	edge	NOUN
ejpam-6729	462	26	is	be	AUX
ejpam-6729	462	27	a	a	DET
ejpam-6729	462	28	2	2	NUM
ejpam-6729	462	29	–	–	PUNCT
ejpam-6729	462	30	element	element	NOUN
ejpam-6729	462	31	subset	subset	NOUN
ejpam-6729	462	32	{	{	PUNCT
ejpam-6729	462	33	u	u	NOUN
ejpam-6729	462	34	,	,	PUNCT
ejpam-6729	462	35	v	v	NOUN
ejpam-6729	462	36	}	}	PUNCT
ejpam-6729	462	37	⊆	⊆	NUM
ejpam-6729	462	38	v	v	NOUN
ejpam-6729	462	39	(	(	PUNCT
ejpam-6729	462	40	1	1	NUM
ejpam-6729	462	41	)	)	PUNCT
ejpam-6729	462	42	.	.	PUNCT
ejpam-6729	463	1	fix	fix	NOUN
ejpam-6729	463	2	,	,	PUNCT
ejpam-6729	463	3	once	once	ADV
ejpam-6729	463	4	and	and	CCONJ
ejpam-6729	463	5	for	for	ADP
ejpam-6729	463	6	all	all	PRON
ejpam-6729	463	7	,	,	PUNCT
ejpam-6729	463	8	a	a	DET
ejpam-6729	463	9	choice	choice	NOUN
ejpam-6729	463	10	of	of	ADP
ejpam-6729	463	11	orientation	orientation	NOUN
ejpam-6729	463	12	for	for	ADP
ejpam-6729	463	13	each	each	DET
ejpam-6729	463	14	unordered	unordered	ADJ
ejpam-6729	463	15	pair	pair	NOUN
ejpam-6729	463	16	:	:	PUNCT
ejpam-6729	463	17	θ	θ	NOUN
ejpam-6729	463	18	:	:	PUNCT
ejpam-6729	463	19	e(1	e(1	NOUN
ejpam-6729	463	20	)	)	PUNCT
ejpam-6729	463	21	−→	−→	NOUN
ejpam-6729	463	22	v	v	NOUN
ejpam-6729	463	23	(	(	PUNCT
ejpam-6729	463	24	1	1	NUM
ejpam-6729	463	25	)	)	PUNCT
ejpam-6729	463	26	×	×	NOUN
ejpam-6729	463	27	v	v	NOUN
ejpam-6729	463	28	(	(	PUNCT
ejpam-6729	463	29	1	1	NUM
ejpam-6729	463	30	)	)	PUNCT
ejpam-6729	463	31	,	,	PUNCT
ejpam-6729	463	32	θ({u	θ({u	PROPN
ejpam-6729	463	33	,	,	PUNCT
ejpam-6729	463	34	v	v	NOUN
ejpam-6729	463	35	}	}	PUNCT
ejpam-6729	463	36	)	)	PUNCT
ejpam-6729	463	37	=	=	SYM
ejpam-6729	463	38	(	(	PUNCT
ejpam-6729	463	39	u	u	NOUN
ejpam-6729	463	40	,	,	PUNCT
ejpam-6729	463	41	v	v	NOUN
ejpam-6729	463	42	)	)	PUNCT
ejpam-6729	463	43	or	or	CCONJ
ejpam-6729	463	44	(	(	PUNCT
ejpam-6729	463	45	v	v	NOUN
ejpam-6729	463	46	,	,	PUNCT
ejpam-6729	463	47	u	u	NOUN
ejpam-6729	463	48	)	)	PUNCT
ejpam-6729	463	49	.	.	PUNCT
ejpam-6729	464	1	define	define	VERB
ejpam-6729	464	2	the	the	DET
ejpam-6729	464	3	directed	direct	VERB
ejpam-6729	464	4	edge	edge	NOUN
ejpam-6729	464	5	set	set	VERB
ejpam-6729	464	6	eg	eg	NOUN
ejpam-6729	464	7	:	:	PUNCT
ejpam-6729	464	8	=	=	SYM
ejpam-6729	464	9	{	{	PUNCT
ejpam-6729	464	10	θ(e	θ(e	NUM
ejpam-6729	464	11	)	)	PUNCT
ejpam-6729	464	12	|	|	ADV
ejpam-6729	464	13	e	e	PROPN
ejpam-6729	464	14	∈	∈	PROPN
ejpam-6729	464	15	e(1	e(1	PROPN
ejpam-6729	464	16	)	)	PUNCT
ejpam-6729	464	17	}	}	PUNCT
ejpam-6729	464	18	⊆	⊆	NUM
ejpam-6729	464	19	v	v	NOUN
ejpam-6729	464	20	(	(	PUNCT
ejpam-6729	464	21	1	1	NUM
ejpam-6729	464	22	)	)	PUNCT
ejpam-6729	464	23	×	×	NOUN
ejpam-6729	464	24	v	v	NOUN
ejpam-6729	464	25	(	(	PUNCT
ejpam-6729	464	26	1	1	NUM
ejpam-6729	464	27	)	)	PUNCT
ejpam-6729	464	28	.	.	PUNCT
ejpam-6729	465	1	set	set	VERB
ejpam-6729	465	2	vg	vg	NOUN
ejpam-6729	465	3	:	:	PUNCT
ejpam-6729	465	4	=	=	SYM
ejpam-6729	465	5	v	v	X
ejpam-6729	465	6	(	(	PUNCT
ejpam-6729	465	7	1	1	NUM
ejpam-6729	465	8	)	)	PUNCT
ejpam-6729	465	9	and	and	CCONJ
ejpam-6729	465	10	define	define	VERB
ejpam-6729	465	11	source	source	NOUN
ejpam-6729	465	12	/	/	SYM
ejpam-6729	465	13	target	target	NOUN
ejpam-6729	465	14	maps	map	NOUN
ejpam-6729	465	15	by	by	ADP
ejpam-6729	465	16	s(u	s(u	PROPN
ejpam-6729	465	17	,	,	PUNCT
ejpam-6729	465	18	v	v	NOUN
ejpam-6729	465	19	)	)	PUNCT
ejpam-6729	465	20	=	=	SYM
ejpam-6729	465	21	u	u	NOUN
ejpam-6729	465	22	,	,	PUNCT
ejpam-6729	465	23	t(u	t(u	PROPN
ejpam-6729	465	24	,	,	PUNCT
ejpam-6729	465	25	v	v	NOUN
ejpam-6729	465	26	)	)	PUNCT
ejpam-6729	465	27	=	=	PUNCT
ejpam-6729	466	1	v.	v.	CCONJ
ejpam-6729	466	2	let	let	VERB
ejpam-6729	466	3	π	π	NOUN
ejpam-6729	466	4	:	:	PUNCT
ejpam-6729	466	5	eg	eg	PROPN
ejpam-6729	466	6	→	→	SYM
ejpam-6729	466	7	e(1	e(1	PROPN
ejpam-6729	466	8	)	)	PUNCT
ejpam-6729	466	9	be	be	VERB
ejpam-6729	466	10	the	the	DET
ejpam-6729	466	11	forgetful	forgetful	ADJ
ejpam-6729	466	12	map	map	NOUN
ejpam-6729	466	13	π(u	π(u	PROPN
ejpam-6729	466	14	,	,	PUNCT
ejpam-6729	466	15	v	v	NOUN
ejpam-6729	466	16	)	)	PUNCT
ejpam-6729	466	17	=	=	SYM
ejpam-6729	466	18	{	{	PUNCT
ejpam-6729	466	19	u	u	NOUN
ejpam-6729	466	20	,	,	PUNCT
ejpam-6729	466	21	v	v	NOUN
ejpam-6729	466	22	}	}	PUNCT
ejpam-6729	466	23	.	.	PUNCT
ejpam-6729	467	1	define	define	VERB
ejpam-6729	467	2	the	the	DET
ejpam-6729	467	3	label	label	NOUN
ejpam-6729	467	4	and	and	CCONJ
ejpam-6729	467	5	property	property	NOUN
ejpam-6729	467	6	maps	map	NOUN
ejpam-6729	467	7	by	by	ADP
ejpam-6729	467	8	λg(a	λg(a	NOUN
ejpam-6729	467	9	)	)	PUNCT
ejpam-6729	467	10	:	:	PUNCT
ejpam-6729	467	11	=	=	SYM
ejpam-6729	467	12	λ	λ	X
ejpam-6729	467	13	(	(	PUNCT
ejpam-6729	467	14	π(a	π(a	PROPN
ejpam-6729	467	15	)	)	PUNCT
ejpam-6729	467	16	)	)	PUNCT
ejpam-6729	468	1	∈	∈	PROPN
ejpam-6729	468	2	σ	σ	PROPN
ejpam-6729	468	3	,	,	PUNCT
ejpam-6729	468	4	µg(x	µg(x	ADV
ejpam-6729	468	5	,	,	PUNCT
ejpam-6729	468	6	k	k	NOUN
ejpam-6729	468	7	)	)	PUNCT
ejpam-6729	468	8	:	:	PUNCT
ejpam-6729	469	1	=	=	PRON
ejpam-6729	469	2	{	{	PUNCT
ejpam-6729	469	3	µ(x	µ(x	PROPN
ejpam-6729	469	4	,	,	PUNCT
ejpam-6729	469	5	k	k	NOUN
ejpam-6729	469	6	)	)	PUNCT
ejpam-6729	469	7	,	,	PUNCT
ejpam-6729	469	8	x	x	PUNCT
ejpam-6729	469	9	∈	∈	NOUN
ejpam-6729	469	10	vg	vg	NOUN
ejpam-6729	469	11	=	=	SYM
ejpam-6729	469	12	v	v	NOUN
ejpam-6729	469	13	(	(	PUNCT
ejpam-6729	469	14	1	1	NUM
ejpam-6729	469	15	)	)	PUNCT
ejpam-6729	469	16	,	,	PUNCT
ejpam-6729	469	17	µ	µ	X
ejpam-6729	469	18	(	(	PUNCT
ejpam-6729	469	19	π(x	π(x	NOUN
ejpam-6729	469	20	)	)	PUNCT
ejpam-6729	469	21	,	,	PUNCT
ejpam-6729	469	22	k	k	PROPN
ejpam-6729	469	23	)	)	PUNCT
ejpam-6729	469	24	,	,	PUNCT
ejpam-6729	469	25	x	x	PUNCT
ejpam-6729	469	26	∈	∈	NOUN
ejpam-6729	469	27	eg	eg	NOUN
ejpam-6729	469	28	.	.	PUNCT
ejpam-6729	470	1	t.	t.	PROPN
ejpam-6729	470	2	fujita	fujita	PROPN
ejpam-6729	470	3	,	,	PUNCT
ejpam-6729	470	4	f.	f.	PROPN
ejpam-6729	470	5	smarandache	smarandache	PROPN
ejpam-6729	470	6	/	/	SYM
ejpam-6729	470	7	eur	eur	PROPN
ejpam-6729	470	8	.	.	PUNCT
ejpam-6729	471	1	j.	j.	PROPN
ejpam-6729	471	2	pure	pure	PROPN
ejpam-6729	471	3	appl	appl	PROPN
ejpam-6729	471	4	.	.	PROPN
ejpam-6729	471	5	math	math	PROPN
ejpam-6729	471	6	,	,	PUNCT
ejpam-6729	471	7	18	18	NUM
ejpam-6729	471	8	(	(	PUNCT
ejpam-6729	471	9	4	4	NUM
ejpam-6729	471	10	)	)	PUNCT
ejpam-6729	471	11	(	(	PUNCT
ejpam-6729	471	12	2025	2025	NUM
ejpam-6729	471	13	)	)	PUNCT
ejpam-6729	471	14	,	,	PUNCT
ejpam-6729	471	15	6729	6729	NUM
ejpam-6729	471	16	23	23	NUM
ejpam-6729	471	17	of	of	ADP
ejpam-6729	471	18	36	36	NUM
ejpam-6729	471	19	then	then	ADV
ejpam-6729	471	20	g	g	PROPN
ejpam-6729	471	21	=	=	PUNCT
ejpam-6729	471	22	(	(	PUNCT
ejpam-6729	471	23	vg	vg	NOUN
ejpam-6729	471	24	,	,	PUNCT
ejpam-6729	471	25	eg	eg	NOUN
ejpam-6729	471	26	,	,	PUNCT
ejpam-6729	471	27	s	s	PROPN
ejpam-6729	471	28	,	,	PUNCT
ejpam-6729	471	29	t	t	PROPN
ejpam-6729	471	30	,	,	PUNCT
ejpam-6729	471	31	λg	λg	NOUN
ejpam-6729	471	32	,	,	PUNCT
ejpam-6729	471	33	µg,⊥	µg,⊥	NUM
ejpam-6729	471	34	)	)	PUNCT
ejpam-6729	471	35	satisfies	satisfy	VERB
ejpam-6729	471	36	all	all	DET
ejpam-6729	471	37	clauses	clause	NOUN
ejpam-6729	471	38	of	of	ADP
ejpam-6729	471	39	definition	definition	NOUN
ejpam-6729	471	40	6	6	NUM
ejpam-6729	471	41	:	:	PUNCT
ejpam-6729	471	42	vg	vg	NOUN
ejpam-6729	471	43	is	be	AUX
ejpam-6729	471	44	the	the	DET
ejpam-6729	471	45	vertex	vertex	NOUN
ejpam-6729	471	46	set	set	NOUN
ejpam-6729	471	47	,	,	PUNCT
ejpam-6729	471	48	eg	eg	ADP
ejpam-6729	471	49	⊆	⊆	NUM
ejpam-6729	471	50	vg	vg	ADP
ejpam-6729	471	51	×	×	NOUN
ejpam-6729	471	52	vg	vg	NOUN
ejpam-6729	471	53	,	,	PUNCT
ejpam-6729	471	54	s	s	PROPN
ejpam-6729	471	55	,	,	PUNCT
ejpam-6729	471	56	t	t	PROPN
ejpam-6729	471	57	are	be	AUX
ejpam-6729	471	58	well	well	ADV
ejpam-6729	471	59	-	-	PUNCT
ejpam-6729	471	60	defined	define	VERB
ejpam-6729	471	61	,	,	PUNCT
ejpam-6729	471	62	λg	λg	NOUN
ejpam-6729	471	63	labels	label	NOUN
ejpam-6729	471	64	directed	direct	VERB
ejpam-6729	471	65	edges	edge	NOUN
ejpam-6729	471	66	via	via	ADP
ejpam-6729	471	67	their	their	PRON
ejpam-6729	471	68	underlying	underlying	ADJ
ejpam-6729	471	69	undirected	undirected	ADJ
ejpam-6729	471	70	pairs	pair	NOUN
ejpam-6729	471	71	,	,	PUNCT
ejpam-6729	471	72	and	and	CCONJ
ejpam-6729	471	73	µg	µg	ADV
ejpam-6729	471	74	is	be	VERB
ejpam-6729	471	75	a	a	DET
ejpam-6729	471	76	property	property	NOUN
ejpam-6729	471	77	map	map	NOUN
ejpam-6729	471	78	with	with	ADP
ejpam-6729	471	79	codomain	codomain	NOUN
ejpam-6729	471	80	s	s	NOUN
ejpam-6729	471	81	∪	∪	X
ejpam-6729	471	82	{	{	PUNCT
ejpam-6729	471	83	⊥	⊥	NOUN
ejpam-6729	471	84	}	}	PUNCT
ejpam-6729	471	85	(	(	PUNCT
ejpam-6729	471	86	using	use	VERB
ejpam-6729	471	87	the	the	DET
ejpam-6729	471	88	original	original	ADJ
ejpam-6729	471	89	µ	µ	NOUN
ejpam-6729	471	90	on	on	ADP
ejpam-6729	471	91	vertices	vertex	NOUN
ejpam-6729	471	92	and	and	CCONJ
ejpam-6729	471	93	pulling	pull	VERB
ejpam-6729	471	94	back	back	ADV
ejpam-6729	471	95	along	along	ADP
ejpam-6729	471	96	π	π	PROPN
ejpam-6729	471	97	on	on	ADP
ejpam-6729	471	98	edges	edge	NOUN
ejpam-6729	471	99	)	)	PUNCT
ejpam-6729	471	100	.	.	PUNCT
ejpam-6729	472	1	hence	hence	ADV
ejpam-6729	472	2	h(1	h(1	PROPN
ejpam-6729	472	3	)	)	PUNCT
ejpam-6729	472	4	yields	yield	VERB
ejpam-6729	472	5	a	a	DET
ejpam-6729	472	6	property	property	NOUN
ejpam-6729	472	7	graph	graph	NOUN
ejpam-6729	472	8	.	.	PUNCT
ejpam-6729	473	1	(	(	PUNCT
ejpam-6729	473	2	2	2	X
ejpam-6729	473	3	)	)	PUNCT
ejpam-6729	473	4	if	if	SCONJ
ejpam-6729	473	5	n	n	NOUN
ejpam-6729	473	6	=	=	SYM
ejpam-6729	473	7	1	1	NUM
ejpam-6729	473	8	,	,	PUNCT
ejpam-6729	473	9	σ	σ	NOUN
ejpam-6729	473	10	=	=	SYM
ejpam-6729	473	11	{	{	PUNCT
ejpam-6729	473	12	σ0	σ0	NOUN
ejpam-6729	473	13	}	}	PUNCT
ejpam-6729	473	14	and	and	CCONJ
ejpam-6729	473	15	µ	µ	PRON
ejpam-6729	473	16	≡	≡	PROPN
ejpam-6729	473	17	⊥	⊥	NOUN
ejpam-6729	473	18	,	,	PUNCT
ejpam-6729	473	19	then	then	ADV
ejpam-6729	473	20	labels	label	NOUN
ejpam-6729	473	21	carry	carry	VERB
ejpam-6729	473	22	no	no	DET
ejpam-6729	473	23	information	information	NOUN
ejpam-6729	473	24	and	and	CCONJ
ejpam-6729	473	25	no	no	DET
ejpam-6729	473	26	vertex	vertex	NOUN
ejpam-6729	473	27	/	/	SYM
ejpam-6729	473	28	edge	edge	NOUN
ejpam-6729	473	29	has	have	VERB
ejpam-6729	473	30	a	a	DET
ejpam-6729	473	31	nontrivial	nontrivial	ADJ
ejpam-6729	473	32	property	property	NOUN
ejpam-6729	473	33	.	.	PUNCT
ejpam-6729	474	1	the	the	DET
ejpam-6729	474	2	structure	structure	NOUN
ejpam-6729	474	3	h(1	h(1	NOUN
ejpam-6729	474	4	)	)	PUNCT
ejpam-6729	474	5	reduces	reduce	VERB
ejpam-6729	474	6	to	to	ADP
ejpam-6729	474	7	its	its	PRON
ejpam-6729	474	8	underlying	underlie	VERB
ejpam-6729	474	9	pair	pair	NOUN
ejpam-6729	474	10	(	(	PUNCT
ejpam-6729	474	11	v	v	NOUN
ejpam-6729	474	12	(	(	PUNCT
ejpam-6729	474	13	1	1	NUM
ejpam-6729	474	14	)	)	PUNCT
ejpam-6729	474	15	,	,	PUNCT
ejpam-6729	474	16	e(1	e(1	PROPN
ejpam-6729	474	17	)	)	PUNCT
ejpam-6729	474	18	)	)	PUNCT
ejpam-6729	474	19	,	,	PUNCT
ejpam-6729	474	20	with	with	ADP
ejpam-6729	474	21	e(1	e(1	NOUN
ejpam-6729	474	22	)	)	PUNCT
ejpam-6729	474	23	⊆	⊆	NUM
ejpam-6729	474	24	p(v	p(v	NOUN
ejpam-6729	474	25	(	(	PUNCT
ejpam-6729	474	26	1	1	NUM
ejpam-6729	474	27	)	)	PUNCT
ejpam-6729	474	28	)	)	PUNCT
ejpam-6729	474	29	\	\	NOUN
ejpam-6729	474	30	{	{	PUNCT
ejpam-6729	474	31	∅	∅	NOUN
ejpam-6729	474	32	}	}	PUNCT
ejpam-6729	474	33	,	,	PUNCT
ejpam-6729	474	34	which	which	PRON
ejpam-6729	474	35	is	be	AUX
ejpam-6729	474	36	precisely	precisely	ADV
ejpam-6729	474	37	the	the	DET
ejpam-6729	474	38	definition	definition	NOUN
ejpam-6729	474	39	of	of	ADP
ejpam-6729	474	40	a	a	DET
ejpam-6729	474	41	hypergraph	hypergraph	NOUN
ejpam-6729	474	42	.	.	PUNCT
ejpam-6729	475	1	(	(	PUNCT
ejpam-6729	475	2	3	3	X
ejpam-6729	475	3	)	)	PUNCT
ejpam-6729	475	4	the	the	DET
ejpam-6729	475	5	same	same	ADJ
ejpam-6729	475	6	argument	argument	NOUN
ejpam-6729	475	7	applies	apply	VERB
ejpam-6729	475	8	verbatim	verbatim	ADJ
ejpam-6729	475	9	for	for	ADP
ejpam-6729	475	10	general	general	ADJ
ejpam-6729	475	11	n	n	CCONJ
ejpam-6729	475	12	:	:	PUNCT
ejpam-6729	475	13	with	with	ADP
ejpam-6729	475	14	a	a	DET
ejpam-6729	475	15	trivial	trivial	ADJ
ejpam-6729	475	16	label	label	NOUN
ejpam-6729	475	17	alphabet	alphabet	NOUN
ejpam-6729	475	18	and	and	CCONJ
ejpam-6729	475	19	µ	µ	PRON
ejpam-6729	475	20	≡	≡	PROPN
ejpam-6729	475	21	⊥	⊥	NOUN
ejpam-6729	475	22	,	,	PUNCT
ejpam-6729	475	23	only	only	ADV
ejpam-6729	475	24	v	v	NUM
ejpam-6729	475	25	(	(	PUNCT
ejpam-6729	475	26	n	n	CCONJ
ejpam-6729	475	27	)	)	PUNCT
ejpam-6729	475	28	⊆	⊆	NUM
ejpam-6729	475	29	pn(v0	pn(v0	NUM
ejpam-6729	475	30	)	)	PUNCT
ejpam-6729	475	31	and	and	CCONJ
ejpam-6729	475	32	e(n	e(n	PROPN
ejpam-6729	475	33	)	)	PUNCT
ejpam-6729	475	34	⊆	⊆	NUM
ejpam-6729	475	35	p(v	p(v	NOUN
ejpam-6729	475	36	(	(	PUNCT
ejpam-6729	475	37	n	n	CCONJ
ejpam-6729	475	38	)	)	PUNCT
ejpam-6729	475	39	)	)	PUNCT
ejpam-6729	476	1	\	\	NOUN
ejpam-6729	476	2	{	{	PUNCT
ejpam-6729	476	3	∅	∅	NOUN
ejpam-6729	476	4	}	}	PUNCT
ejpam-6729	476	5	remain	remain	VERB
ejpam-6729	476	6	.	.	PUNCT
ejpam-6729	477	1	this	this	PRON
ejpam-6729	477	2	is	be	AUX
ejpam-6729	477	3	exactly	exactly	ADV
ejpam-6729	477	4	an	an	DET
ejpam-6729	477	5	n	n	CCONJ
ejpam-6729	477	6	-	-	PUNCT
ejpam-6729	477	7	superhypergraph	superhypergraph	NOUN
ejpam-6729	477	8	.	.	PUNCT
ejpam-6729	478	1	theorem	theorem	NOUN
ejpam-6729	478	2	9	9	NUM
ejpam-6729	478	3	(	(	PUNCT
ejpam-6729	478	4	induced	induce	VERB
ejpam-6729	478	5	sub	sub	ADJ
ejpam-6729	478	6	-	-	ADJ
ejpam-6729	478	7	n	n	CCONJ
ejpam-6729	478	8	-	-	PUNCT
ejpam-6729	478	9	superhypergraph	superhypergraph	NOUN
ejpam-6729	478	10	)	)	PUNCT
ejpam-6729	478	11	.	.	PUNCT
ejpam-6729	479	1	let	let	VERB
ejpam-6729	479	2	h(n	h(n	PRON
ejpam-6729	479	3	)	)	PUNCT
ejpam-6729	480	1	=	=	PRON
ejpam-6729	480	2	(	(	PUNCT
ejpam-6729	480	3	v	v	NOUN
ejpam-6729	480	4	(	(	PUNCT
ejpam-6729	480	5	n	n	CCONJ
ejpam-6729	480	6	)	)	PUNCT
ejpam-6729	480	7	,	,	PUNCT
ejpam-6729	480	8	e(n	e(n	PROPN
ejpam-6729	480	9	)	)	PUNCT
ejpam-6729	480	10	,	,	PUNCT
ejpam-6729	480	11	λ	λ	PROPN
ejpam-6729	480	12	,	,	PUNCT
ejpam-6729	480	13	µ	µ	NOUN
ejpam-6729	480	14	)	)	PUNCT
ejpam-6729	480	15	be	be	AUX
ejpam-6729	480	16	a	a	DET
ejpam-6729	480	17	property	property	NOUN
ejpam-6729	480	18	n	n	CCONJ
ejpam-6729	480	19	-	-	PUNCT
ejpam-6729	480	20	superhypergraph	superhypergraph	NOUN
ejpam-6729	480	21	over	over	ADP
ejpam-6729	480	22	the	the	DET
ejpam-6729	480	23	base	base	NOUN
ejpam-6729	480	24	v0	v0	NOUN
ejpam-6729	480	25	,	,	PUNCT
ejpam-6729	480	26	and	and	CCONJ
ejpam-6729	480	27	let	let	VERB
ejpam-6729	480	28	u0	u0	VERB
ejpam-6729	480	29	⊆	⊆	NUM
ejpam-6729	480	30	v0	v0	NOUN
ejpam-6729	480	31	.	.	PUNCT
ejpam-6729	481	1	define	define	VERB
ejpam-6729	481	2	v	v	ADP
ejpam-6729	481	3	(	(	PUNCT
ejpam-6729	481	4	n	n	CCONJ
ejpam-6729	481	5	)	)	PUNCT
ejpam-6729	481	6	u	u	NOUN
ejpam-6729	481	7	:	:	PUNCT
ejpam-6729	481	8	=	=	SYM
ejpam-6729	481	9	{	{	PUNCT
ejpam-6729	481	10	x	x	PROPN
ejpam-6729	481	11	∈	∈	PROPN
ejpam-6729	481	12	v	v	NOUN
ejpam-6729	481	13	(	(	PUNCT
ejpam-6729	481	14	n	n	CCONJ
ejpam-6729	481	15	)	)	PUNCT
ejpam-6729	482	1	|	|	ADV
ejpam-6729	482	2	x	x	SYM
ejpam-6729	482	3	⊆	⊆	NUM
ejpam-6729	482	4	pn−1(u0	pn−1(u0	PROPN
ejpam-6729	482	5	)	)	PUNCT
ejpam-6729	482	6	}	}	PUNCT
ejpam-6729	482	7	,	,	PUNCT
ejpam-6729	482	8	e	e	X
ejpam-6729	482	9	(	(	PUNCT
ejpam-6729	482	10	n	n	CCONJ
ejpam-6729	482	11	)	)	PUNCT
ejpam-6729	482	12	u	u	NOUN
ejpam-6729	482	13	:	:	PUNCT
ejpam-6729	482	14	=	=	SYM
ejpam-6729	482	15	{	{	PUNCT
ejpam-6729	482	16	e	e	X
ejpam-6729	482	17	∈	∈	PROPN
ejpam-6729	482	18	e(n	e(n	PROPN
ejpam-6729	482	19	)	)	PUNCT
ejpam-6729	482	20	|	|	ADV
ejpam-6729	482	21	e	e	X
ejpam-6729	482	22	⊆	⊆	NUM
ejpam-6729	482	23	v	v	ADP
ejpam-6729	482	24	(	(	PUNCT
ejpam-6729	482	25	n	n	CCONJ
ejpam-6729	482	26	)	)	PUNCT
ejpam-6729	482	27	u	u	NOUN
ejpam-6729	482	28	}	}	PUNCT
ejpam-6729	482	29	.	.	PUNCT
ejpam-6729	483	1	let	let	VERB
ejpam-6729	483	2	d	d	NOUN
ejpam-6729	483	3	(	(	PUNCT
ejpam-6729	483	4	n	n	CCONJ
ejpam-6729	483	5	)	)	PUNCT
ejpam-6729	483	6	u	u	NOUN
ejpam-6729	483	7	:	:	PUNCT
ejpam-6729	483	8	=	=	SYM
ejpam-6729	483	9	(	(	PUNCT
ejpam-6729	483	10	n⋃	n⋃	PROPN
ejpam-6729	483	11	r=0	r=0	PROPN
ejpam-6729	483	12	pr(u0	pr(u0	NOUN
ejpam-6729	483	13	)	)	PUNCT
ejpam-6729	483	14	)	)	PUNCT
ejpam-6729	483	15	∪	∪	ADP
ejpam-6729	483	16	e	e	X
ejpam-6729	483	17	(	(	PUNCT
ejpam-6729	483	18	n	n	CCONJ
ejpam-6729	483	19	)	)	PUNCT
ejpam-6729	483	20	u	u	NOUN
ejpam-6729	483	21	,	,	PUNCT
ejpam-6729	483	22	and	and	CCONJ
ejpam-6729	483	23	set	set	VERB
ejpam-6729	483	24	h(n	h(n	PROPN
ejpam-6729	483	25	)	)	PUNCT
ejpam-6729	483	26	u	u	NOUN
ejpam-6729	483	27	:	:	PUNCT
ejpam-6729	483	28	=	=	SYM
ejpam-6729	483	29	(	(	PUNCT
ejpam-6729	483	30	v	v	NOUN
ejpam-6729	483	31	(	(	PUNCT
ejpam-6729	483	32	n	n	CCONJ
ejpam-6729	483	33	)	)	PUNCT
ejpam-6729	483	34	u	u	NOUN
ejpam-6729	483	35	,	,	PUNCT
ejpam-6729	483	36	e	e	X
ejpam-6729	483	37	(	(	PUNCT
ejpam-6729	483	38	n	n	CCONJ
ejpam-6729	483	39	)	)	PUNCT
ejpam-6729	483	40	u	u	NOUN
ejpam-6729	483	41	,	,	PUNCT
ejpam-6729	483	42	λ|	λ|	PROPN
ejpam-6729	483	43	e	e	PROPN
ejpam-6729	483	44	(	(	PUNCT
ejpam-6729	483	45	n	n	CCONJ
ejpam-6729	483	46	)	)	PUNCT
ejpam-6729	483	47	u	u	NOUN
ejpam-6729	483	48	,	,	PUNCT
ejpam-6729	483	49	µ|	µ|	PROPN
ejpam-6729	483	50	d	d	PROPN
ejpam-6729	483	51	(	(	PUNCT
ejpam-6729	483	52	n	n	CCONJ
ejpam-6729	483	53	)	)	PUNCT
ejpam-6729	483	54	u	u	NOUN
ejpam-6729	483	55	×k	×k	NOUN
ejpam-6729	483	56	)	)	PUNCT
ejpam-6729	483	57	.	.	PUNCT
ejpam-6729	484	1	then	then	ADV
ejpam-6729	484	2	h	h	PROPN
ejpam-6729	484	3	(	(	PUNCT
ejpam-6729	484	4	n	n	CCONJ
ejpam-6729	484	5	)	)	PUNCT
ejpam-6729	484	6	u	u	NOUN
ejpam-6729	484	7	is	be	AUX
ejpam-6729	484	8	a	a	DET
ejpam-6729	484	9	property	property	NOUN
ejpam-6729	484	10	n	n	CCONJ
ejpam-6729	484	11	-	-	PUNCT
ejpam-6729	484	12	superhypergraph	superhypergraph	NOUN
ejpam-6729	484	13	over	over	ADP
ejpam-6729	484	14	u0	u0	ADJ
ejpam-6729	484	15	.	.	PUNCT
ejpam-6729	485	1	proof	proof	NOUN
ejpam-6729	485	2	.	.	PUNCT
ejpam-6729	486	1	we	we	PRON
ejpam-6729	486	2	verify	verify	VERB
ejpam-6729	486	3	each	each	DET
ejpam-6729	486	4	clause	clause	NOUN
ejpam-6729	486	5	of	of	ADP
ejpam-6729	486	6	the	the	DET
ejpam-6729	486	7	definition	definition	NOUN
ejpam-6729	486	8	.	.	PUNCT
ejpam-6729	487	1	(	(	PUNCT
ejpam-6729	487	2	i	i	NOUN
ejpam-6729	487	3	)	)	PUNCT
ejpam-6729	487	4	vertex	vertex	NOUN
ejpam-6729	487	5	condition	condition	NOUN
ejpam-6729	487	6	.	.	PUNCT
ejpam-6729	488	1	we	we	PRON
ejpam-6729	488	2	first	first	ADV
ejpam-6729	488	3	note	note	VERB
ejpam-6729	488	4	the	the	DET
ejpam-6729	488	5	monotonicity	monotonicity	NOUN
ejpam-6729	488	6	of	of	ADP
ejpam-6729	488	7	iterated	iterated	ADJ
ejpam-6729	488	8	powersets	powerset	NOUN
ejpam-6729	488	9	:	:	PUNCT
ejpam-6729	488	10	if	if	SCONJ
ejpam-6729	488	11	a	a	DET
ejpam-6729	488	12	⊆	⊆	NUM
ejpam-6729	488	13	b	b	NOUN
ejpam-6729	488	14	,	,	PUNCT
ejpam-6729	488	15	then	then	ADV
ejpam-6729	488	16	pr(a	pr(a	PUNCT
ejpam-6729	488	17	)	)	PUNCT
ejpam-6729	488	18	⊆	⊆	NUM
ejpam-6729	488	19	pr(b	pr(b	X
ejpam-6729	488	20	)	)	PUNCT
ejpam-6729	488	21	for	for	ADP
ejpam-6729	488	22	all	all	DET
ejpam-6729	488	23	r	r	NOUN
ejpam-6729	488	24	≥	≥	NOUN
ejpam-6729	488	25	0	0	NUM
ejpam-6729	488	26	.	.	PUNCT
ejpam-6729	489	1	this	this	PRON
ejpam-6729	489	2	is	be	AUX
ejpam-6729	489	3	proved	prove	VERB
ejpam-6729	489	4	by	by	ADP
ejpam-6729	489	5	induction	induction	NOUN
ejpam-6729	489	6	on	on	ADP
ejpam-6729	489	7	r	r	NOUN
ejpam-6729	489	8	:	:	PUNCT
ejpam-6729	489	9	for	for	ADP
ejpam-6729	489	10	r	r	NOUN
ejpam-6729	489	11	=	=	SYM
ejpam-6729	489	12	0	0	NUM
ejpam-6729	489	13	it	it	PRON
ejpam-6729	489	14	is	be	AUX
ejpam-6729	489	15	a	a	DET
ejpam-6729	489	16	⊆	⊆	NUM
ejpam-6729	489	17	b	b	NOUN
ejpam-6729	489	18	;	;	PUNCT
ejpam-6729	489	19	if	if	SCONJ
ejpam-6729	489	20	pr(a	pr(a	VERB
ejpam-6729	489	21	)	)	PUNCT
ejpam-6729	489	22	⊆	⊆	NUM
ejpam-6729	489	23	pr(b	pr(b	NOUN
ejpam-6729	489	24	)	)	PUNCT
ejpam-6729	489	25	,	,	PUNCT
ejpam-6729	489	26	then	then	ADV
ejpam-6729	489	27	pr+1(a	pr+1(a	ADV
ejpam-6729	489	28	)	)	PUNCT
ejpam-6729	490	1	=	=	SYM
ejpam-6729	491	1	p	p	X
ejpam-6729	491	2	(	(	PUNCT
ejpam-6729	491	3	pr(a	pr(a	NOUN
ejpam-6729	491	4	)	)	PUNCT
ejpam-6729	491	5	)	)	PUNCT
ejpam-6729	492	1	⊆	⊆	NUM
ejpam-6729	492	2	p	p	NOUN
ejpam-6729	492	3	(	(	PUNCT
ejpam-6729	492	4	pr(b	pr(b	X
ejpam-6729	492	5	)	)	PUNCT
ejpam-6729	492	6	)	)	PUNCT
ejpam-6729	493	1	=	=	PUNCT
ejpam-6729	493	2	pr+1(b	pr+1(b	PROPN
ejpam-6729	493	3	)	)	PUNCT
ejpam-6729	493	4	.	.	PUNCT
ejpam-6729	494	1	applying	apply	VERB
ejpam-6729	494	2	this	this	PRON
ejpam-6729	494	3	with	with	ADP
ejpam-6729	494	4	a	a	DET
ejpam-6729	494	5	=	=	X
ejpam-6729	494	6	u0	u0	ADJ
ejpam-6729	494	7	⊆	⊆	NUM
ejpam-6729	494	8	b	b	NOUN
ejpam-6729	494	9	=	=	SYM
ejpam-6729	494	10	v0	v0	PROPN
ejpam-6729	494	11	and	and	CCONJ
ejpam-6729	494	12	r	r	NOUN
ejpam-6729	494	13	=	=	SYM
ejpam-6729	494	14	n	n	CCONJ
ejpam-6729	494	15	−	−	PROPN
ejpam-6729	494	16	1	1	NUM
ejpam-6729	494	17	,	,	PUNCT
ejpam-6729	494	18	we	we	PRON
ejpam-6729	494	19	get	get	VERB
ejpam-6729	494	20	pn−1(u0	pn−1(u0	PROPN
ejpam-6729	494	21	)	)	PUNCT
ejpam-6729	494	22	⊆	⊆	NUM
ejpam-6729	494	23	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	494	24	)	)	PUNCT
ejpam-6729	494	25	.	.	PUNCT
ejpam-6729	495	1	hence	hence	ADV
ejpam-6729	495	2	every	every	DET
ejpam-6729	495	3	x	x	SYM
ejpam-6729	495	4	∈	∈	PROPN
ejpam-6729	495	5	v	v	NOUN
ejpam-6729	495	6	(	(	PUNCT
ejpam-6729	495	7	n	n	CCONJ
ejpam-6729	495	8	)	)	PUNCT
ejpam-6729	495	9	u	u	NOUN
ejpam-6729	495	10	lies	lie	VERB
ejpam-6729	495	11	in	in	ADP
ejpam-6729	495	12	pn(u0	pn(u0	NOUN
ejpam-6729	495	13	)	)	PUNCT
ejpam-6729	495	14	(	(	PUNCT
ejpam-6729	495	15	because	because	SCONJ
ejpam-6729	495	16	x	x	PRON
ejpam-6729	495	17	is	be	AUX
ejpam-6729	495	18	by	by	ADP
ejpam-6729	495	19	definition	definition	NOUN
ejpam-6729	495	20	a	a	DET
ejpam-6729	495	21	subset	subset	NOUN
ejpam-6729	495	22	of	of	ADP
ejpam-6729	495	23	pn−1(u0	pn−1(u0	PROPN
ejpam-6729	495	24	)	)	PUNCT
ejpam-6729	495	25	)	)	PUNCT
ejpam-6729	495	26	,	,	PUNCT
ejpam-6729	495	27	so	so	ADV
ejpam-6729	495	28	v	v	ADP
ejpam-6729	495	29	(	(	PUNCT
ejpam-6729	495	30	n	n	CCONJ
ejpam-6729	495	31	)	)	PUNCT
ejpam-6729	495	32	u	u	NOUN
ejpam-6729	495	33	⊆	⊆	NUM
ejpam-6729	495	34	pn(u0	pn(u0	NUM
ejpam-6729	495	35	)	)	PUNCT
ejpam-6729	495	36	.	.	PUNCT
ejpam-6729	496	1	(	(	PUNCT
ejpam-6729	496	2	ii	ii	NOUN
ejpam-6729	496	3	)	)	PUNCT
ejpam-6729	496	4	edge	edge	NOUN
ejpam-6729	496	5	condition	condition	NOUN
ejpam-6729	496	6	.	.	PUNCT
ejpam-6729	497	1	by	by	ADP
ejpam-6729	497	2	construction	construction	NOUN
ejpam-6729	497	3	,	,	PUNCT
ejpam-6729	497	4	every	every	DET
ejpam-6729	497	5	e	e	NOUN
ejpam-6729	497	6	∈	∈	PROPN
ejpam-6729	497	7	e	e	X
ejpam-6729	497	8	(	(	PUNCT
ejpam-6729	497	9	n	n	CCONJ
ejpam-6729	497	10	)	)	PUNCT
ejpam-6729	497	11	u	u	NOUN
ejpam-6729	497	12	satisfies	satisfy	VERB
ejpam-6729	497	13	e	e	X
ejpam-6729	497	14	⊆	⊆	NUM
ejpam-6729	497	15	v	v	ADP
ejpam-6729	497	16	(	(	PUNCT
ejpam-6729	497	17	n	n	CCONJ
ejpam-6729	497	18	)	)	PUNCT
ejpam-6729	497	19	u	u	NOUN
ejpam-6729	497	20	and	and	CCONJ
ejpam-6729	497	21	e	e	NOUN
ejpam-6729	497	22	6=	6=	NOUN
ejpam-6729	497	23	∅	∅	NOUN
ejpam-6729	497	24	(	(	PUNCT
ejpam-6729	497	25	because	because	SCONJ
ejpam-6729	497	26	e(n	e(n	PROPN
ejpam-6729	497	27	)	)	PUNCT
ejpam-6729	497	28	consisted	consist	VERB
ejpam-6729	497	29	of	of	ADP
ejpam-6729	497	30	nonempty	nonempty	ADJ
ejpam-6729	497	31	subsets	subset	NOUN
ejpam-6729	497	32	of	of	ADP
ejpam-6729	497	33	v	v	NOUN
ejpam-6729	497	34	(	(	PUNCT
ejpam-6729	497	35	n	n	CCONJ
ejpam-6729	497	36	)	)	PUNCT
ejpam-6729	497	37	,	,	PUNCT
ejpam-6729	497	38	and	and	CCONJ
ejpam-6729	497	39	we	we	PRON
ejpam-6729	497	40	only	only	ADV
ejpam-6729	497	41	removed	remove	VERB
ejpam-6729	497	42	vertices	vertex	NOUN
ejpam-6729	497	43	)	)	PUNCT
ejpam-6729	497	44	.	.	PUNCT
ejpam-6729	498	1	thus	thus	ADV
ejpam-6729	498	2	e	e	X
ejpam-6729	498	3	(	(	PUNCT
ejpam-6729	498	4	n	n	CCONJ
ejpam-6729	498	5	)	)	PUNCT
ejpam-6729	498	6	u	u	NOUN
ejpam-6729	498	7	⊆	⊆	NUM
ejpam-6729	498	8	p	p	PROPN
ejpam-6729	498	9	(	(	PUNCT
ejpam-6729	498	10	v	v	NOUN
ejpam-6729	498	11	(	(	PUNCT
ejpam-6729	498	12	n	n	CCONJ
ejpam-6729	498	13	)	)	PUNCT
ejpam-6729	498	14	u	u	NOUN
ejpam-6729	498	15	)	)	PUNCT
ejpam-6729	498	16	\	\	NOUN
ejpam-6729	498	17	{	{	PUNCT
ejpam-6729	498	18	∅	∅	NOUN
ejpam-6729	498	19	}	}	PUNCT
ejpam-6729	498	20	.	.	PUNCT
ejpam-6729	499	1	(	(	PUNCT
ejpam-6729	499	2	iii	iii	X
ejpam-6729	499	3	)	)	PUNCT
ejpam-6729	499	4	label	label	NOUN
ejpam-6729	499	5	map	map	NOUN
ejpam-6729	499	6	.	.	PUNCT
ejpam-6729	500	1	the	the	DET
ejpam-6729	500	2	restriction	restriction	NOUN
ejpam-6729	500	3	λ|	λ|	PROPN
ejpam-6729	500	4	e	e	PROPN
ejpam-6729	500	5	(	(	PUNCT
ejpam-6729	500	6	n	n	CCONJ
ejpam-6729	500	7	)	)	PUNCT
ejpam-6729	500	8	u	u	NOUN
ejpam-6729	500	9	:	:	PUNCT
ejpam-6729	500	10	e	e	NOUN
ejpam-6729	500	11	(	(	PUNCT
ejpam-6729	500	12	n	n	CCONJ
ejpam-6729	500	13	)	)	PUNCT
ejpam-6729	500	14	u	u	NOUN
ejpam-6729	500	15	→	→	PROPN
ejpam-6729	500	16	σ	σ	PROPN
ejpam-6729	500	17	is	be	AUX
ejpam-6729	500	18	well	well	ADV
ejpam-6729	500	19	-	-	PUNCT
ejpam-6729	500	20	defined	define	VERB
ejpam-6729	500	21	with	with	ADP
ejpam-6729	500	22	the	the	DET
ejpam-6729	500	23	same	same	ADJ
ejpam-6729	500	24	codomain	codomain	NOUN
ejpam-6729	500	25	σ	σ	PROPN
ejpam-6729	500	26	.	.	PUNCT
ejpam-6729	500	27	(	(	PUNCT
ejpam-6729	500	28	iv	iv	X
ejpam-6729	500	29	)	)	PUNCT
ejpam-6729	500	30	property	property	NOUN
ejpam-6729	500	31	map	map	NOUN
ejpam-6729	500	32	.	.	PUNCT
ejpam-6729	501	1	since	since	SCONJ
ejpam-6729	501	2	d	d	PROPN
ejpam-6729	501	3	(	(	PUNCT
ejpam-6729	501	4	n	n	CCONJ
ejpam-6729	501	5	)	)	PUNCT
ejpam-6729	501	6	u	u	NOUN
ejpam-6729	501	7	⊆	⊆	NUM
ejpam-6729	501	8	(	(	PUNCT
ejpam-6729	501	9	⋃n	⋃n	NOUN
ejpam-6729	501	10	r=0	r=0	PROPN
ejpam-6729	501	11	pr(v0	pr(v0	NOUN
ejpam-6729	501	12	)	)	PUNCT
ejpam-6729	501	13	)	)	PUNCT
ejpam-6729	501	14	∪	∪	ADP
ejpam-6729	501	15	e(n	e(n	PROPN
ejpam-6729	501	16	)	)	PUNCT
ejpam-6729	501	17	by	by	ADP
ejpam-6729	501	18	monotonicity	monotonicity	NOUN
ejpam-6729	501	19	and	and	CCONJ
ejpam-6729	501	20	by	by	ADP
ejpam-6729	501	21	the	the	DET
ejpam-6729	501	22	definition	definition	NOUN
ejpam-6729	501	23	of	of	ADP
ejpam-6729	501	24	e(n	e(n	PROPN
ejpam-6729	501	25	)	)	PUNCT
ejpam-6729	501	26	u	u	NOUN
ejpam-6729	501	27	,	,	PUNCT
ejpam-6729	501	28	the	the	DET
ejpam-6729	501	29	restricted	restricted	ADJ
ejpam-6729	501	30	map	map	NOUN
ejpam-6729	501	31	µ|	µ|	PROPN
ejpam-6729	501	32	d	d	PROPN
ejpam-6729	501	33	(	(	PUNCT
ejpam-6729	501	34	n	n	CCONJ
ejpam-6729	501	35	)	)	PUNCT
ejpam-6729	501	36	u	u	NOUN
ejpam-6729	501	37	×k	×k	NOUN
ejpam-6729	501	38	:	:	PUNCT
ejpam-6729	501	39	d	d	X
ejpam-6729	501	40	(	(	PUNCT
ejpam-6729	501	41	n	n	CCONJ
ejpam-6729	501	42	)	)	PUNCT
ejpam-6729	501	43	u	u	NOUN
ejpam-6729	501	44	×k	×k	NOUN
ejpam-6729	501	45	→	→	SYM
ejpam-6729	501	46	s	s	NOUN
ejpam-6729	501	47	∪	∪	X
ejpam-6729	501	48	{	{	PUNCT
ejpam-6729	501	49	⊥	⊥	NOUN
ejpam-6729	501	50	}	}	PUNCT
ejpam-6729	501	51	is	be	AUX
ejpam-6729	501	52	well	well	ADV
ejpam-6729	501	53	-	-	PUNCT
ejpam-6729	501	54	defined	define	VERB
ejpam-6729	501	55	with	with	ADP
ejpam-6729	501	56	the	the	DET
ejpam-6729	501	57	same	same	ADJ
ejpam-6729	501	58	codomain	codomain	NOUN
ejpam-6729	501	59	.	.	PUNCT
ejpam-6729	502	1	all	all	DET
ejpam-6729	502	2	axioms	axiom	NOUN
ejpam-6729	502	3	are	be	AUX
ejpam-6729	502	4	satisfied	satisfied	ADJ
ejpam-6729	502	5	,	,	PUNCT
ejpam-6729	502	6	hence	hence	ADV
ejpam-6729	502	7	h	h	NOUN
ejpam-6729	502	8	(	(	PUNCT
ejpam-6729	502	9	n	n	CCONJ
ejpam-6729	502	10	)	)	PUNCT
ejpam-6729	502	11	u	u	NOUN
ejpam-6729	502	12	is	be	AUX
ejpam-6729	502	13	a	a	DET
ejpam-6729	502	14	property	property	NOUN
ejpam-6729	502	15	n	n	CCONJ
ejpam-6729	502	16	-	-	PUNCT
ejpam-6729	502	17	superhypergraph	superhypergraph	NOUN
ejpam-6729	502	18	over	over	ADP
ejpam-6729	502	19	u0	u0	PROPN
ejpam-6729	502	20	.	.	PUNCT
ejpam-6729	502	21	example	example	NOUN
ejpam-6729	502	22	13	13	NUM
ejpam-6729	502	23	(	(	PUNCT
ejpam-6729	502	24	induced	induce	VERB
ejpam-6729	502	25	sub	sub	ADJ
ejpam-6729	502	26	-	-	ADJ
ejpam-6729	502	27	n	n	CCONJ
ejpam-6729	502	28	-	-	PUNCT
ejpam-6729	502	29	superhypergraph	superhypergraph	NOUN
ejpam-6729	502	30	:	:	PUNCT
ejpam-6729	502	31	a	a	DET
ejpam-6729	502	32	concrete	concrete	ADJ
ejpam-6729	502	33	n	n	NOUN
ejpam-6729	502	34	=	=	SYM
ejpam-6729	502	35	2	2	NUM
ejpam-6729	502	36	instance	instance	NOUN
ejpam-6729	502	37	)	)	PUNCT
ejpam-6729	502	38	.	.	PUNCT
ejpam-6729	503	1	fix	fix	NOUN
ejpam-6729	503	2	σ	σ	NOUN
ejpam-6729	503	3	=	=	SYM
ejpam-6729	503	4	{	{	PUNCT
ejpam-6729	503	5	link	link	NOUN
ejpam-6729	503	6	}	}	PUNCT
ejpam-6729	503	7	,	,	PUNCT
ejpam-6729	503	8	k	k	PROPN
ejpam-6729	503	9	=	=	PRON
ejpam-6729	503	10	{	{	PUNCT
ejpam-6729	503	11	tag	tag	NOUN
ejpam-6729	503	12	}	}	PUNCT
ejpam-6729	503	13	,	,	PUNCT
ejpam-6729	503	14	s	s	VERB
ejpam-6729	503	15	=	=	PUNCT
ejpam-6729	503	16	n	n	CCONJ
ejpam-6729	503	17	∪	∪	ADJ
ejpam-6729	503	18	strings	string	NOUN
ejpam-6729	503	19	,	,	PUNCT
ejpam-6729	503	20	⊥	⊥	PROPN
ejpam-6729	503	21	/∈	/∈	PUNCT
ejpam-6729	504	1	s	s	X
ejpam-6729	504	2	,	,	PUNCT
ejpam-6729	504	3	t.	t.	PROPN
ejpam-6729	504	4	fujita	fujita	PROPN
ejpam-6729	504	5	,	,	PUNCT
ejpam-6729	504	6	f.	f.	PROPN
ejpam-6729	504	7	smarandache	smarandache	PROPN
ejpam-6729	504	8	/	/	SYM
ejpam-6729	504	9	eur	eur	PROPN
ejpam-6729	504	10	.	.	PUNCT
ejpam-6729	505	1	j.	j.	PROPN
ejpam-6729	505	2	pure	pure	PROPN
ejpam-6729	505	3	appl	appl	PROPN
ejpam-6729	505	4	.	.	PROPN
ejpam-6729	505	5	math	math	PROPN
ejpam-6729	505	6	,	,	PUNCT
ejpam-6729	505	7	18	18	NUM
ejpam-6729	505	8	(	(	PUNCT
ejpam-6729	505	9	4	4	NUM
ejpam-6729	505	10	)	)	PUNCT
ejpam-6729	505	11	(	(	PUNCT
ejpam-6729	505	12	2025	2025	NUM
ejpam-6729	505	13	)	)	PUNCT
ejpam-6729	505	14	,	,	PUNCT
ejpam-6729	505	15	6729	6729	NUM
ejpam-6729	505	16	24	24	NUM
ejpam-6729	505	17	of	of	ADP
ejpam-6729	505	18	36	36	NUM
ejpam-6729	505	19	and	and	CCONJ
ejpam-6729	505	20	let	let	VERB
ejpam-6729	505	21	the	the	DET
ejpam-6729	505	22	base	base	NOUN
ejpam-6729	505	23	be	be	AUX
ejpam-6729	505	24	v0	v0	NOUN
ejpam-6729	505	25	=	=	SYM
ejpam-6729	505	26	{	{	PUNCT
ejpam-6729	505	27	a	a	PRON
ejpam-6729	505	28	,	,	PUNCT
ejpam-6729	505	29	b	b	NOUN
ejpam-6729	505	30	,	,	PUNCT
ejpam-6729	505	31	c	c	NOUN
ejpam-6729	505	32	,	,	PUNCT
ejpam-6729	505	33	d	d	NOUN
ejpam-6729	505	34	}	}	PUNCT
ejpam-6729	505	35	.	.	PUNCT
ejpam-6729	506	1	define	define	VERB
ejpam-6729	506	2	1	1	NUM
ejpam-6729	506	3	-	-	PUNCT
ejpam-6729	506	4	level	level	NOUN
ejpam-6729	506	5	carriers	carrier	NOUN
ejpam-6729	506	6	(	(	PUNCT
ejpam-6729	506	7	subsets	subset	NOUN
ejpam-6729	506	8	of	of	ADP
ejpam-6729	506	9	v0	v0	NOUN
ejpam-6729	506	10	)	)	PUNCT
ejpam-6729	506	11	a1	a1	NOUN
ejpam-6729	506	12	=	=	PUNCT
ejpam-6729	506	13	{	{	PUNCT
ejpam-6729	506	14	a	a	PRON
ejpam-6729	506	15	,	,	PUNCT
ejpam-6729	506	16	b	b	NOUN
ejpam-6729	506	17	}	}	PUNCT
ejpam-6729	506	18	,	,	PUNCT
ejpam-6729	506	19	a2	a2	PROPN
ejpam-6729	506	20	=	=	PUNCT
ejpam-6729	506	21	{	{	PUNCT
ejpam-6729	506	22	b	b	PROPN
ejpam-6729	506	23	,	,	PUNCT
ejpam-6729	506	24	c	c	NOUN
ejpam-6729	506	25	}	}	PUNCT
ejpam-6729	506	26	,	,	PUNCT
ejpam-6729	506	27	a3	a3	NOUN
ejpam-6729	506	28	=	=	SYM
ejpam-6729	506	29	{	{	PUNCT
ejpam-6729	506	30	c	c	NOUN
ejpam-6729	506	31	,	,	PUNCT
ejpam-6729	506	32	d	d	NOUN
ejpam-6729	506	33	}	}	PUNCT
ejpam-6729	506	34	∈	∈	PROPN
ejpam-6729	506	35	p1(v0	p1(v0	PROPN
ejpam-6729	506	36	)	)	PUNCT
ejpam-6729	506	37	,	,	PUNCT
ejpam-6729	506	38	and	and	CCONJ
ejpam-6729	506	39	2	2	NUM
ejpam-6729	506	40	-	-	PUNCT
ejpam-6729	506	41	supervertices	supervertice	NOUN
ejpam-6729	506	42	g1	g1	NOUN
ejpam-6729	506	43	=	=	SYM
ejpam-6729	506	44	{	{	PUNCT
ejpam-6729	506	45	a1	a1	PROPN
ejpam-6729	506	46	,	,	PUNCT
ejpam-6729	506	47	a2	a2	PROPN
ejpam-6729	506	48	}	}	PUNCT
ejpam-6729	506	49	,	,	PUNCT
ejpam-6729	506	50	g2	g2	PROPN
ejpam-6729	506	51	=	=	PUNCT
ejpam-6729	506	52	{	{	PUNCT
ejpam-6729	506	53	a2	a2	PROPN
ejpam-6729	506	54	,	,	PUNCT
ejpam-6729	506	55	a3	a3	NOUN
ejpam-6729	506	56	}	}	PUNCT
ejpam-6729	506	57	∈	∈	PROPN
ejpam-6729	506	58	p2(v0	p2(v0	PROPN
ejpam-6729	506	59	)	)	PUNCT
ejpam-6729	506	60	.	.	PUNCT
ejpam-6729	507	1	set	set	VERB
ejpam-6729	507	2	v	v	NOUN
ejpam-6729	507	3	(	(	PUNCT
ejpam-6729	507	4	2	2	NUM
ejpam-6729	507	5	)	)	PUNCT
ejpam-6729	507	6	=	=	PRON
ejpam-6729	507	7	{	{	PUNCT
ejpam-6729	507	8	g1	g1	PROPN
ejpam-6729	507	9	,	,	PUNCT
ejpam-6729	507	10	g2	g2	PROPN
ejpam-6729	507	11	}	}	PUNCT
ejpam-6729	507	12	⊆	⊆	NUM
ejpam-6729	507	13	p2(v0	p2(v0	NOUN
ejpam-6729	507	14	)	)	PUNCT
ejpam-6729	507	15	and	and	CCONJ
ejpam-6729	507	16	e(2	e(2	NOUN
ejpam-6729	507	17	)	)	PUNCT
ejpam-6729	507	18	=	=	PRON
ejpam-6729	507	19	{	{	PUNCT
ejpam-6729	507	20	e	e	NOUN
ejpam-6729	507	21	}	}	PUNCT
ejpam-6729	507	22	,	,	PUNCT
ejpam-6729	507	23	e	e	X
ejpam-6729	507	24	=	=	PRON
ejpam-6729	507	25	{	{	PUNCT
ejpam-6729	507	26	g1	g1	PROPN
ejpam-6729	507	27	,	,	PUNCT
ejpam-6729	507	28	g2	g2	PROPN
ejpam-6729	507	29	}	}	PUNCT
ejpam-6729	507	30	∈	∈	PROPN
ejpam-6729	507	31	p(v	p(v	NOUN
ejpam-6729	507	32	(	(	PUNCT
ejpam-6729	507	33	2	2	NUM
ejpam-6729	507	34	)	)	PUNCT
ejpam-6729	507	35	)	)	PUNCT
ejpam-6729	507	36	\	\	NOUN
ejpam-6729	508	1	{	{	PUNCT
ejpam-6729	508	2	∅	∅	NOUN
ejpam-6729	508	3	}	}	PUNCT
ejpam-6729	508	4	.	.	PUNCT
ejpam-6729	509	1	label	label	NOUN
ejpam-6729	509	2	and	and	CCONJ
ejpam-6729	509	3	properties	property	NOUN
ejpam-6729	509	4	:	:	PUNCT
ejpam-6729	509	5	λ(e	λ(e	ADJ
ejpam-6729	509	6	)	)	PUNCT
ejpam-6729	509	7	=	=	SYM
ejpam-6729	509	8	link	link	NOUN
ejpam-6729	509	9	,	,	PUNCT
ejpam-6729	509	10	µ(g1	µ(g1	NOUN
ejpam-6729	509	11	,	,	PUNCT
ejpam-6729	509	12	tag	tag	NOUN
ejpam-6729	509	13	)	)	PUNCT
ejpam-6729	509	14	=	=	PUNCT
ejpam-6729	509	15	“	"	PUNCT
ejpam-6729	509	16	north	north	NOUN
ejpam-6729	509	17	”	"	PUNCT
ejpam-6729	509	18	,	,	PUNCT
ejpam-6729	509	19	µ(g2	µ(g2	ADV
ejpam-6729	509	20	,	,	PUNCT
ejpam-6729	509	21	tag	tag	NOUN
ejpam-6729	509	22	)	)	PUNCT
ejpam-6729	509	23	=	=	PUNCT
ejpam-6729	509	24	“	"	PUNCT
ejpam-6729	509	25	south	south	PROPN
ejpam-6729	509	26	”	"	PUNCT
ejpam-6729	509	27	,	,	PUNCT
ejpam-6729	509	28	µ(e	µ(e	PROPN
ejpam-6729	509	29	,	,	PUNCT
ejpam-6729	509	30	tag	tag	NOUN
ejpam-6729	509	31	)	)	PUNCT
ejpam-6729	509	32	=	=	PUNCT
ejpam-6729	509	33	“	"	PUNCT
ejpam-6729	509	34	overlap	overlap	NOUN
ejpam-6729	509	35	”	"	PUNCT
ejpam-6729	509	36	.	.	PUNCT
ejpam-6729	510	1	thus	thus	ADV
ejpam-6729	510	2	h(2	h(2	NOUN
ejpam-6729	510	3	)	)	PUNCT
ejpam-6729	510	4	=	=	PUNCT
ejpam-6729	511	1	(	(	PUNCT
ejpam-6729	511	2	v	v	NOUN
ejpam-6729	511	3	(	(	PUNCT
ejpam-6729	511	4	2	2	NUM
ejpam-6729	511	5	)	)	PUNCT
ejpam-6729	511	6	,	,	PUNCT
ejpam-6729	511	7	e(2	e(2	PROPN
ejpam-6729	511	8	)	)	PUNCT
ejpam-6729	511	9	,	,	PUNCT
ejpam-6729	511	10	λ	λ	PROPN
ejpam-6729	511	11	,	,	PUNCT
ejpam-6729	511	12	µ	µ	NOUN
ejpam-6729	511	13	)	)	PUNCT
ejpam-6729	511	14	is	be	AUX
ejpam-6729	511	15	a	a	DET
ejpam-6729	511	16	property	property	NOUN
ejpam-6729	511	17	2	2	NUM
ejpam-6729	511	18	-	-	PUNCT
ejpam-6729	511	19	shg	shg	NOUN
ejpam-6729	511	20	over	over	ADP
ejpam-6729	511	21	v0	v0	PROPN
ejpam-6729	511	22	.	.	PUNCT
ejpam-6729	512	1	now	now	ADV
ejpam-6729	512	2	take	take	VERB
ejpam-6729	512	3	u0	u0	ADJ
ejpam-6729	512	4	=	=	PUNCT
ejpam-6729	512	5	{	{	PUNCT
ejpam-6729	512	6	a	a	PRON
ejpam-6729	512	7	,	,	PUNCT
ejpam-6729	512	8	b	b	NOUN
ejpam-6729	512	9	,	,	PUNCT
ejpam-6729	512	10	c	c	NOUN
ejpam-6729	512	11	}	}	PUNCT
ejpam-6729	512	12	⊆	⊆	NUM
ejpam-6729	512	13	v0	v0	NOUN
ejpam-6729	512	14	.	.	PUNCT
ejpam-6729	513	1	then	then	ADV
ejpam-6729	513	2	p1(u0	p1(u0	VERB
ejpam-6729	513	3	)	)	PUNCT
ejpam-6729	514	1	=	=	SYM
ejpam-6729	514	2	p(u0	p(u0	NOUN
ejpam-6729	514	3	)	)	PUNCT
ejpam-6729	514	4	,	,	PUNCT
ejpam-6729	514	5	and	and	CCONJ
ejpam-6729	514	6	we	we	PRON
ejpam-6729	514	7	check	check	VERB
ejpam-6729	514	8	membership	membership	NOUN
ejpam-6729	514	9	:	:	PUNCT
ejpam-6729	514	10	a1	a1	NOUN
ejpam-6729	514	11	,	,	PUNCT
ejpam-6729	514	12	a2	a2	PROPN
ejpam-6729	514	13	⊆	⊆	NUM
ejpam-6729	514	14	u0	u0	ADJ
ejpam-6729	514	15	⇒	⇒	NOUN
ejpam-6729	514	16	g1	g1	PROPN
ejpam-6729	514	17	⊆	⊆	NUM
ejpam-6729	514	18	p1(u0	p1(u0	NOUN
ejpam-6729	514	19	)	)	PUNCT
ejpam-6729	514	20	,	,	PUNCT
ejpam-6729	514	21	a3	a3	NOUN
ejpam-6729	514	22	*	*	PUNCT
ejpam-6729	514	23	u0	u0	PROPN
ejpam-6729	514	24	⇒	⇒	PROPN
ejpam-6729	514	25	g2	g2	PROPN
ejpam-6729	514	26	*	*	PUNCT
ejpam-6729	514	27	p1(u0	p1(u0	NOUN
ejpam-6729	514	28	)	)	PUNCT
ejpam-6729	514	29	.	.	PUNCT
ejpam-6729	515	1	hence	hence	ADV
ejpam-6729	515	2	v	v	NOUN
ejpam-6729	515	3	(	(	PUNCT
ejpam-6729	515	4	2	2	NUM
ejpam-6729	515	5	)	)	PUNCT
ejpam-6729	515	6	u	u	NOUN
ejpam-6729	515	7	=	=	PUNCT
ejpam-6729	515	8	{	{	PUNCT
ejpam-6729	515	9	g1	g1	PROPN
ejpam-6729	515	10	}	}	PUNCT
ejpam-6729	515	11	,	,	PUNCT
ejpam-6729	515	12	e	e	X
ejpam-6729	515	13	(	(	PUNCT
ejpam-6729	515	14	2	2	X
ejpam-6729	515	15	)	)	PUNCT
ejpam-6729	515	16	u	u	NOUN
ejpam-6729	515	17	=	=	NOUN
ejpam-6729	515	18	∅	∅	NOUN
ejpam-6729	515	19	,	,	PUNCT
ejpam-6729	515	20	and	and	CCONJ
ejpam-6729	515	21	with	with	ADP
ejpam-6729	515	22	d	d	PROPN
ejpam-6729	515	23	(	(	PUNCT
ejpam-6729	515	24	2	2	NUM
ejpam-6729	515	25	)	)	PUNCT
ejpam-6729	515	26	u	u	NOUN
ejpam-6729	515	27	=	=	PROPN
ejpam-6729	515	28	p0(u0	p0(u0	NOUN
ejpam-6729	515	29	)	)	PUNCT
ejpam-6729	515	30	∪	∪	ADP
ejpam-6729	515	31	p1(u0	p1(u0	NOUN
ejpam-6729	515	32	)	)	PUNCT
ejpam-6729	515	33	∪	∪	ADP
ejpam-6729	515	34	p2(u0	p2(u0	NOUN
ejpam-6729	515	35	)	)	PUNCT
ejpam-6729	515	36	∪	∪	NOUN
ejpam-6729	515	37	e	e	X
ejpam-6729	515	38	(	(	PUNCT
ejpam-6729	515	39	2	2	X
ejpam-6729	515	40	)	)	PUNCT
ejpam-6729	515	41	u	u	NOUN
ejpam-6729	515	42	we	we	PRON
ejpam-6729	515	43	obtain	obtain	VERB
ejpam-6729	515	44	the	the	DET
ejpam-6729	515	45	induced	induced	ADJ
ejpam-6729	515	46	substructure	substructure	NOUN
ejpam-6729	515	47	h	h	NOUN
ejpam-6729	515	48	(	(	PUNCT
ejpam-6729	515	49	2	2	NUM
ejpam-6729	515	50	)	)	PUNCT
ejpam-6729	515	51	u	u	NOUN
ejpam-6729	515	52	=	=	PUNCT
ejpam-6729	515	53	(	(	PUNCT
ejpam-6729	515	54	v	v	NOUN
ejpam-6729	515	55	(	(	PUNCT
ejpam-6729	515	56	2	2	NUM
ejpam-6729	515	57	)	)	PUNCT
ejpam-6729	515	58	u	u	NOUN
ejpam-6729	515	59	,	,	PUNCT
ejpam-6729	515	60	e	e	X
ejpam-6729	515	61	(	(	PUNCT
ejpam-6729	515	62	2	2	NUM
ejpam-6729	515	63	)	)	PUNCT
ejpam-6729	515	64	u	u	NOUN
ejpam-6729	515	65	,	,	PUNCT
ejpam-6729	515	66	λ|	λ|	PROPN
ejpam-6729	515	67	e	e	PROPN
ejpam-6729	515	68	(	(	PUNCT
ejpam-6729	515	69	2	2	NUM
ejpam-6729	515	70	)	)	PUNCT
ejpam-6729	515	71	u	u	NOUN
ejpam-6729	515	72	,	,	PUNCT
ejpam-6729	515	73	µ|	µ|	PROPN
ejpam-6729	515	74	d	d	PROPN
ejpam-6729	515	75	(	(	PUNCT
ejpam-6729	515	76	2	2	NUM
ejpam-6729	515	77	)	)	PUNCT
ejpam-6729	515	78	u	u	NOUN
ejpam-6729	515	79	×k	×k	NOUN
ejpam-6729	515	80	)	)	PUNCT
ejpam-6729	515	81	,	,	PUNCT
ejpam-6729	515	82	which	which	PRON
ejpam-6729	515	83	is	be	AUX
ejpam-6729	515	84	(	(	PUNCT
ejpam-6729	515	85	by	by	ADP
ejpam-6729	515	86	theorem	theorem	NOUN
ejpam-6729	515	87	9	9	NUM
ejpam-6729	515	88	)	)	PUNCT
ejpam-6729	515	89	a	a	DET
ejpam-6729	515	90	property	property	NOUN
ejpam-6729	515	91	2	2	NUM
ejpam-6729	515	92	-	-	PUNCT
ejpam-6729	515	93	superhypergraph	superhypergraph	NOUN
ejpam-6729	515	94	over	over	ADP
ejpam-6729	515	95	the	the	DET
ejpam-6729	515	96	base	base	NOUN
ejpam-6729	515	97	u0	u0	PROPN
ejpam-6729	515	98	.	.	PUNCT
ejpam-6729	516	1	theorem	theorem	ADJ
ejpam-6729	516	2	10	10	NUM
ejpam-6729	516	3	(	(	PUNCT
ejpam-6729	516	4	flattening	flattening	NOUN
ejpam-6729	516	5	projection	projection	NOUN
ejpam-6729	516	6	)	)	PUNCT
ejpam-6729	516	7	.	.	PUNCT
ejpam-6729	517	1	let	let	VERB
ejpam-6729	517	2	h(n	h(n	PRON
ejpam-6729	517	3	)	)	PUNCT
ejpam-6729	518	1	=	=	PRON
ejpam-6729	518	2	(	(	PUNCT
ejpam-6729	518	3	v	v	NOUN
ejpam-6729	518	4	(	(	PUNCT
ejpam-6729	518	5	n	n	CCONJ
ejpam-6729	518	6	)	)	PUNCT
ejpam-6729	518	7	,	,	PUNCT
ejpam-6729	518	8	e(n	e(n	PROPN
ejpam-6729	518	9	)	)	PUNCT
ejpam-6729	518	10	,	,	PUNCT
ejpam-6729	518	11	λ	λ	PROPN
ejpam-6729	518	12	,	,	PUNCT
ejpam-6729	518	13	µ	µ	NOUN
ejpam-6729	518	14	)	)	PUNCT
ejpam-6729	518	15	be	be	AUX
ejpam-6729	518	16	a	a	DET
ejpam-6729	518	17	property	property	NOUN
ejpam-6729	518	18	n	n	CCONJ
ejpam-6729	518	19	-	-	PUNCT
ejpam-6729	518	20	superhypergraph	superhypergraph	NOUN
ejpam-6729	518	21	with	with	ADP
ejpam-6729	518	22	n	n	PRON
ejpam-6729	518	23	≥	≥	NUM
ejpam-6729	518	24	1	1	NUM
ejpam-6729	518	25	.	.	PUNCT
ejpam-6729	519	1	define	define	VERB
ejpam-6729	519	2	the	the	DET
ejpam-6729	519	3	vertex	vertex	NOUN
ejpam-6729	519	4	-	-	PUNCT
ejpam-6729	519	5	flattening	flattening	NOUN
ejpam-6729	519	6	map	map	NOUN
ejpam-6729	519	7	ϕv	ϕv	ADP
ejpam-6729	519	8	:	:	PUNCT
ejpam-6729	519	9	pn(v0	pn(v0	VERB
ejpam-6729	519	10	)	)	PUNCT
ejpam-6729	519	11	−→	−→	PROPN
ejpam-6729	519	12	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	519	13	)	)	PUNCT
ejpam-6729	519	14	,	,	PUNCT
ejpam-6729	519	15	ϕv	ϕv	PROPN
ejpam-6729	519	16	(	(	PUNCT
ejpam-6729	519	17	x	x	X
ejpam-6729	519	18	)	)	PUNCT
ejpam-6729	519	19	=	=	SYM
ejpam-6729	519	20	⋃	⋃	NOUN
ejpam-6729	519	21	x∈x	x∈x	NOUN
ejpam-6729	519	22	x	x	NOUN
ejpam-6729	519	23	,	,	PUNCT
ejpam-6729	519	24	and	and	CCONJ
ejpam-6729	519	25	its	its	PRON
ejpam-6729	519	26	action	action	NOUN
ejpam-6729	519	27	on	on	ADP
ejpam-6729	519	28	edges	edge	NOUN
ejpam-6729	519	29	by	by	ADP
ejpam-6729	519	30	image	image	NOUN
ejpam-6729	519	31	ϕe	ϕe	NOUN
ejpam-6729	519	32	:	:	PUNCT
ejpam-6729	519	33	p	p	X
ejpam-6729	519	34	(	(	PUNCT
ejpam-6729	519	35	v	v	NOUN
ejpam-6729	519	36	(	(	PUNCT
ejpam-6729	519	37	n	n	CCONJ
ejpam-6729	519	38	)	)	PUNCT
ejpam-6729	519	39	)	)	PUNCT
ejpam-6729	519	40	\	\	NOUN
ejpam-6729	520	1	{	{	PUNCT
ejpam-6729	520	2	∅	∅	NOUN
ejpam-6729	520	3	}	}	PUNCT
ejpam-6729	520	4	−→	−→	NOUN
ejpam-6729	520	5	p	p	NOUN
ejpam-6729	520	6	(	(	PUNCT
ejpam-6729	520	7	ϕv	ϕv	ADP
ejpam-6729	521	1	[	[	X
ejpam-6729	521	2	v	v	X
ejpam-6729	521	3	(	(	PUNCT
ejpam-6729	521	4	n	n	CCONJ
ejpam-6729	521	5	)	)	PUNCT
ejpam-6729	521	6	]	]	PUNCT
ejpam-6729	521	7	)	)	PUNCT
ejpam-6729	521	8	\	\	NOUN
ejpam-6729	521	9	{	{	PUNCT
ejpam-6729	521	10	∅	∅	NOUN
ejpam-6729	521	11	}	}	PUNCT
ejpam-6729	521	12	,	,	PUNCT
ejpam-6729	521	13	ϕe(e	ϕe(e	NUM
ejpam-6729	521	14	)	)	PUNCT
ejpam-6729	521	15	=	=	PRON
ejpam-6729	521	16	{	{	PUNCT
ejpam-6729	521	17	ϕv	ϕv	PROPN
ejpam-6729	521	18	(	(	PUNCT
ejpam-6729	521	19	v	v	NOUN
ejpam-6729	521	20	)	)	PUNCT
ejpam-6729	522	1	|	|	ADV
ejpam-6729	522	2	v	v	NOUN
ejpam-6729	522	3	∈	∈	NOUN
ejpam-6729	522	4	e	e	X
ejpam-6729	522	5	}	}	PUNCT
ejpam-6729	522	6	.	.	PUNCT
ejpam-6729	523	1	assume	assume	VERB
ejpam-6729	523	2	the	the	DET
ejpam-6729	523	3	following	follow	VERB
ejpam-6729	523	4	compatibility	compatibility	NOUN
ejpam-6729	523	5	on	on	ADP
ejpam-6729	523	6	fibres	fibre	NOUN
ejpam-6729	523	7	:	:	PUNCT
ejpam-6729	523	8	(	(	PUNCT
ejpam-6729	523	9	labels	label	NOUN
ejpam-6729	523	10	on	on	ADP
ejpam-6729	523	11	edges	edge	NOUN
ejpam-6729	523	12	)	)	PUNCT
ejpam-6729	523	13	ϕe(e	ϕe(e	NUM
ejpam-6729	523	14	)	)	PUNCT
ejpam-6729	524	1	=	=	PRON
ejpam-6729	524	2	ϕe(e	ϕe(e	NUM
ejpam-6729	524	3	′	′	NUM
ejpam-6729	524	4	)	)	PUNCT
ejpam-6729	525	1	=	=	VERB
ejpam-6729	525	2	⇒	⇒	NOUN
ejpam-6729	525	3	λ(e	λ(e	ADJ
ejpam-6729	525	4	)	)	PUNCT
ejpam-6729	525	5	=	=	PUNCT
ejpam-6729	525	6	λ(e′	λ(e′	ADJ
ejpam-6729	525	7	)	)	PUNCT
ejpam-6729	525	8	,	,	PUNCT
ejpam-6729	525	9	t.	t.	PROPN
ejpam-6729	525	10	fujita	fujita	PROPN
ejpam-6729	525	11	,	,	PUNCT
ejpam-6729	525	12	f.	f.	PROPN
ejpam-6729	525	13	smarandache	smarandache	PROPN
ejpam-6729	525	14	/	/	SYM
ejpam-6729	525	15	eur	eur	PROPN
ejpam-6729	525	16	.	.	PUNCT
ejpam-6729	526	1	j.	j.	PROPN
ejpam-6729	526	2	pure	pure	PROPN
ejpam-6729	526	3	appl	appl	PROPN
ejpam-6729	526	4	.	.	PROPN
ejpam-6729	526	5	math	math	PROPN
ejpam-6729	526	6	,	,	PUNCT
ejpam-6729	526	7	18	18	NUM
ejpam-6729	526	8	(	(	PUNCT
ejpam-6729	526	9	4	4	NUM
ejpam-6729	526	10	)	)	PUNCT
ejpam-6729	526	11	(	(	PUNCT
ejpam-6729	526	12	2025	2025	NUM
ejpam-6729	526	13	)	)	PUNCT
ejpam-6729	526	14	,	,	PUNCT
ejpam-6729	526	15	6729	6729	NUM
ejpam-6729	526	16	25	25	NUM
ejpam-6729	526	17	of	of	ADP
ejpam-6729	526	18	36	36	NUM
ejpam-6729	526	19	(	(	PUNCT
ejpam-6729	526	20	properties	property	NOUN
ejpam-6729	526	21	on	on	ADP
ejpam-6729	526	22	vertices	vertex	NOUN
ejpam-6729	526	23	)	)	PUNCT
ejpam-6729	526	24	ϕv	ϕv	ADP
ejpam-6729	526	25	(	(	PUNCT
ejpam-6729	526	26	v	v	NOUN
ejpam-6729	526	27	)	)	PUNCT
ejpam-6729	526	28	=	=	PUNCT
ejpam-6729	526	29	ϕv	ϕv	PROPN
ejpam-6729	526	30	(	(	PUNCT
ejpam-6729	526	31	v	v	NOUN
ejpam-6729	526	32	′	′	NOUN
ejpam-6729	526	33	)	)	PUNCT
ejpam-6729	527	1	=	=	NOUN
ejpam-6729	527	2	⇒	⇒	NOUN
ejpam-6729	527	3	µ(v	µ(v	PROPN
ejpam-6729	527	4	,	,	PUNCT
ejpam-6729	527	5	k	k	NOUN
ejpam-6729	527	6	)	)	PUNCT
ejpam-6729	527	7	=	=	SYM
ejpam-6729	527	8	µ(v′	µ(v′	PROPN
ejpam-6729	527	9	,	,	PUNCT
ejpam-6729	527	10	k	k	NOUN
ejpam-6729	527	11	)	)	PUNCT
ejpam-6729	527	12	∀k	∀k	NOUN
ejpam-6729	527	13	∈	∈	PROPN
ejpam-6729	527	14	k	k	X
ejpam-6729	527	15	,	,	PUNCT
ejpam-6729	527	16	(	(	PUNCT
ejpam-6729	527	17	properties	property	NOUN
ejpam-6729	527	18	on	on	ADP
ejpam-6729	527	19	edges	edge	NOUN
ejpam-6729	527	20	)	)	PUNCT
ejpam-6729	527	21	ϕe(e	ϕe(e	NUM
ejpam-6729	527	22	)	)	PUNCT
ejpam-6729	527	23	=	=	PRON
ejpam-6729	527	24	ϕe(e	ϕe(e	NUM
ejpam-6729	527	25	′	′	NUM
ejpam-6729	527	26	)	)	PUNCT
ejpam-6729	528	1	=	=	NOUN
ejpam-6729	528	2	⇒	⇒	PROPN
ejpam-6729	528	3	µ(e	µ(e	PROPN
ejpam-6729	528	4	,	,	PUNCT
ejpam-6729	528	5	k	k	NOUN
ejpam-6729	528	6	)	)	PUNCT
ejpam-6729	528	7	=	=	PUNCT
ejpam-6729	528	8	µ(e′	µ(e′	PROPN
ejpam-6729	528	9	,	,	PUNCT
ejpam-6729	528	10	k	k	NOUN
ejpam-6729	528	11	)	)	PUNCT
ejpam-6729	528	12	∀k	∀k	NOUN
ejpam-6729	528	13	∈	∈	PROPN
ejpam-6729	529	1	k.	k.	NOUN
ejpam-6729	529	2	then	then	ADV
ejpam-6729	529	3	with	with	ADP
ejpam-6729	529	4	v	v	NOUN
ejpam-6729	529	5	′	′	NUM
ejpam-6729	529	6	:	:	PUNCT
ejpam-6729	530	1	=	=	PUNCT
ejpam-6729	530	2	ϕv	ϕv	ADP
ejpam-6729	531	1	[	[	X
ejpam-6729	531	2	v	v	X
ejpam-6729	531	3	(	(	PUNCT
ejpam-6729	531	4	n	n	CCONJ
ejpam-6729	531	5	)	)	PUNCT
ejpam-6729	531	6	]	]	PUNCT
ejpam-6729	531	7	⊆	⊆	NUM
ejpam-6729	531	8	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	531	9	)	)	PUNCT
ejpam-6729	531	10	,	,	PUNCT
ejpam-6729	531	11	e′	e′	X
ejpam-6729	531	12	:	:	PUNCT
ejpam-6729	531	13	=	=	PRON
ejpam-6729	531	14	{	{	PUNCT
ejpam-6729	531	15	ϕe(e	ϕe(e	NOUN
ejpam-6729	531	16	)	)	PUNCT
ejpam-6729	532	1	|	|	ADV
ejpam-6729	532	2	e	e	X
ejpam-6729	532	3	∈	∈	PROPN
ejpam-6729	532	4	e(n	e(n	PROPN
ejpam-6729	532	5	)	)	PUNCT
ejpam-6729	532	6	}	}	PUNCT
ejpam-6729	532	7	⊆	⊆	NUM
ejpam-6729	532	8	p(v	p(v	NOUN
ejpam-6729	532	9	′	′	NUM
ejpam-6729	532	10	)	)	PUNCT
ejpam-6729	532	11	\	\	NOUN
ejpam-6729	532	12	{	{	PUNCT
ejpam-6729	532	13	∅	∅	NOUN
ejpam-6729	532	14	}	}	PUNCT
ejpam-6729	532	15	,	,	PUNCT
ejpam-6729	532	16	and	and	CCONJ
ejpam-6729	532	17	with	with	ADP
ejpam-6729	532	18	λ′(ϕe(e	λ′(ϕe(e	NOUN
ejpam-6729	532	19	)	)	PUNCT
ejpam-6729	532	20	)	)	PUNCT
ejpam-6729	532	21	:	:	PUNCT
ejpam-6729	532	22	=	=	PUNCT
ejpam-6729	532	23	λ(e	λ(e	PROPN
ejpam-6729	532	24	)	)	PUNCT
ejpam-6729	532	25	,	,	PUNCT
ejpam-6729	532	26	µ′(z′	µ′(z′	NOUN
ejpam-6729	532	27	,	,	PUNCT
ejpam-6729	532	28	k	k	NOUN
ejpam-6729	532	29	)	)	PUNCT
ejpam-6729	532	30	:	:	PUNCT
ejpam-6729	532	31	=	=	X
ejpam-6729	532	32	{	{	PUNCT
ejpam-6729	532	33	µ(v	µ(v	PROPN
ejpam-6729	532	34	,	,	PUNCT
ejpam-6729	532	35	k	k	NOUN
ejpam-6729	532	36	)	)	PUNCT
ejpam-6729	532	37	,	,	PUNCT
ejpam-6729	532	38	z′	z′	NUM
ejpam-6729	532	39	=	=	SYM
ejpam-6729	532	40	ϕv	ϕv	PROPN
ejpam-6729	532	41	(	(	PUNCT
ejpam-6729	532	42	v	v	NOUN
ejpam-6729	532	43	)	)	PUNCT
ejpam-6729	532	44	∈	∈	PROPN
ejpam-6729	532	45	v	v	ADP
ejpam-6729	532	46	′	′	NUM
ejpam-6729	532	47	,	,	PUNCT
ejpam-6729	532	48	µ(e	µ(e	PROPN
ejpam-6729	532	49	,	,	PUNCT
ejpam-6729	532	50	k	k	PROPN
ejpam-6729	532	51	)	)	PUNCT
ejpam-6729	532	52	,	,	PUNCT
ejpam-6729	532	53	z′	z′	NUM
ejpam-6729	532	54	=	=	SYM
ejpam-6729	532	55	ϕe(e	ϕe(e	X
ejpam-6729	532	56	)	)	PUNCT
ejpam-6729	532	57	∈	∈	PROPN
ejpam-6729	532	58	e′	e′	PROPN
ejpam-6729	532	59	,	,	PUNCT
ejpam-6729	532	60	the	the	DET
ejpam-6729	532	61	quadruple	quadruple	NOUN
ejpam-6729	532	62	h	h	NOUN
ejpam-6729	532	63	′	′	NUM
ejpam-6729	533	1	=	=	PUNCT
ejpam-6729	534	1	(	(	PUNCT
ejpam-6729	534	2	v	v	NOUN
ejpam-6729	534	3	′	′	NUM
ejpam-6729	534	4	,	,	PUNCT
ejpam-6729	534	5	e′	e′	PROPN
ejpam-6729	534	6	,	,	PUNCT
ejpam-6729	534	7	λ′	λ′	NOUN
ejpam-6729	534	8	,	,	PUNCT
ejpam-6729	534	9	µ′	µ′	NUM
ejpam-6729	534	10	)	)	PUNCT
ejpam-6729	534	11	is	be	AUX
ejpam-6729	534	12	a	a	DET
ejpam-6729	534	13	property	property	NOUN
ejpam-6729	534	14	(	(	PUNCT
ejpam-6729	534	15	n−	n−	NOUN
ejpam-6729	534	16	1)-superhypergraph	1)-superhypergraph	VERB
ejpam-6729	534	17	over	over	ADP
ejpam-6729	534	18	v0	v0	NOUN
ejpam-6729	534	19	.	.	PUNCT
ejpam-6729	535	1	proof	proof	NOUN
ejpam-6729	535	2	.	.	PUNCT
ejpam-6729	536	1	(	(	PUNCT
ejpam-6729	536	2	i	i	NOUN
ejpam-6729	536	3	)	)	PUNCT
ejpam-6729	536	4	vertex	vertex	NOUN
ejpam-6729	536	5	condition	condition	NOUN
ejpam-6729	536	6	.	.	PUNCT
ejpam-6729	537	1	by	by	ADP
ejpam-6729	537	2	definition	definition	NOUN
ejpam-6729	537	3	of	of	ADP
ejpam-6729	537	4	ϕv	ϕv	ADV
ejpam-6729	537	5	,	,	PUNCT
ejpam-6729	537	6	we	we	PRON
ejpam-6729	537	7	have	have	VERB
ejpam-6729	537	8	ϕv	ϕv	NUM
ejpam-6729	537	9	(	(	PUNCT
ejpam-6729	537	10	x	x	X
ejpam-6729	537	11	)	)	PUNCT
ejpam-6729	537	12	∈	∈	PROPN
ejpam-6729	537	13	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	537	14	)	)	PUNCT
ejpam-6729	537	15	for	for	ADP
ejpam-6729	537	16	every	every	DET
ejpam-6729	537	17	x	x	PROPN
ejpam-6729	537	18	∈	∈	PROPN
ejpam-6729	537	19	pn(v0	pn(v0	VERB
ejpam-6729	537	20	)	)	PUNCT
ejpam-6729	537	21	.	.	PUNCT
ejpam-6729	538	1	hence	hence	ADV
ejpam-6729	538	2	v	v	ADP
ejpam-6729	538	3	′	′	NUM
ejpam-6729	539	1	=	=	PUNCT
ejpam-6729	539	2	ϕv	ϕv	ADP
ejpam-6729	540	1	[	[	X
ejpam-6729	540	2	v	v	X
ejpam-6729	540	3	(	(	PUNCT
ejpam-6729	540	4	n	n	CCONJ
ejpam-6729	540	5	)	)	PUNCT
ejpam-6729	540	6	]	]	PUNCT
ejpam-6729	540	7	⊆	⊆	NUM
ejpam-6729	540	8	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	540	9	)	)	PUNCT
ejpam-6729	540	10	.	.	PUNCT
ejpam-6729	541	1	(	(	PUNCT
ejpam-6729	541	2	ii	ii	NOUN
ejpam-6729	541	3	)	)	PUNCT
ejpam-6729	541	4	edge	edge	NOUN
ejpam-6729	541	5	condition	condition	NOUN
ejpam-6729	541	6	.	.	PUNCT
ejpam-6729	542	1	let	let	VERB
ejpam-6729	542	2	e	e	PRON
ejpam-6729	542	3	∈	∈	PROPN
ejpam-6729	542	4	e(n	e(n	PROPN
ejpam-6729	542	5	)	)	PUNCT
ejpam-6729	542	6	.	.	PUNCT
ejpam-6729	543	1	since	since	SCONJ
ejpam-6729	543	2	e	e	PROPN
ejpam-6729	543	3	⊆	⊆	NUM
ejpam-6729	543	4	v	v	ADP
ejpam-6729	543	5	(	(	PUNCT
ejpam-6729	543	6	n	n	CCONJ
ejpam-6729	543	7	)	)	PUNCT
ejpam-6729	543	8	and	and	CCONJ
ejpam-6729	543	9	e	e	NOUN
ejpam-6729	543	10	6=	6=	PROPN
ejpam-6729	543	11	∅	∅	NOUN
ejpam-6729	543	12	,	,	PUNCT
ejpam-6729	543	13	its	its	PRON
ejpam-6729	543	14	image	image	NOUN
ejpam-6729	543	15	ϕe(e	ϕe(e	NOUN
ejpam-6729	543	16	)	)	PUNCT
ejpam-6729	543	17	=	=	PRON
ejpam-6729	543	18	{	{	PUNCT
ejpam-6729	543	19	ϕv	ϕv	PROPN
ejpam-6729	543	20	(	(	PUNCT
ejpam-6729	543	21	v	v	NOUN
ejpam-6729	543	22	)	)	PUNCT
ejpam-6729	543	23	|	|	ADV
ejpam-6729	543	24	v	v	ADP
ejpam-6729	543	25	∈	∈	NOUN
ejpam-6729	543	26	e	e	X
ejpam-6729	543	27	}	}	PUNCT
ejpam-6729	543	28	is	be	AUX
ejpam-6729	543	29	a	a	DET
ejpam-6729	543	30	nonempty	nonempty	ADJ
ejpam-6729	543	31	subset	subset	NOUN
ejpam-6729	543	32	of	of	ADP
ejpam-6729	543	33	v	v	NUM
ejpam-6729	543	34	′.	′.	NOUN
ejpam-6729	543	35	thus	thus	ADV
ejpam-6729	543	36	e′	e′	X
ejpam-6729	543	37	⊆	⊆	NUM
ejpam-6729	543	38	p(v	p(v	PROPN
ejpam-6729	543	39	′	′	NUM
ejpam-6729	543	40	)	)	PUNCT
ejpam-6729	543	41	\	\	NOUN
ejpam-6729	543	42	{	{	PUNCT
ejpam-6729	543	43	∅	∅	NOUN
ejpam-6729	543	44	}	}	PUNCT
ejpam-6729	543	45	.	.	PUNCT
ejpam-6729	544	1	(	(	PUNCT
ejpam-6729	544	2	iii	iii	NOUN
ejpam-6729	544	3	)	)	PUNCT
ejpam-6729	544	4	labels	label	NOUN
ejpam-6729	544	5	.	.	PUNCT
ejpam-6729	545	1	if	if	SCONJ
ejpam-6729	545	2	ϕe(e	ϕe(e	NUM
ejpam-6729	545	3	)	)	PUNCT
ejpam-6729	546	1	=	=	PRON
ejpam-6729	546	2	ϕe(e	ϕe(e	NUM
ejpam-6729	546	3	′	′	NUM
ejpam-6729	546	4	)	)	PUNCT
ejpam-6729	547	1	,	,	PUNCT
ejpam-6729	547	2	the	the	DET
ejpam-6729	547	3	label	label	NOUN
ejpam-6729	547	4	-	-	PUNCT
ejpam-6729	547	5	compatibility	compatibility	NOUN
ejpam-6729	547	6	assumption	assumption	NOUN
ejpam-6729	547	7	gives	give	VERB
ejpam-6729	547	8	λ(e	λ(e	PROPN
ejpam-6729	547	9	)	)	PUNCT
ejpam-6729	547	10	=	=	PUNCT
ejpam-6729	547	11	λ(e′	λ(e′	ADJ
ejpam-6729	547	12	)	)	PUNCT
ejpam-6729	547	13	,	,	PUNCT
ejpam-6729	547	14	so	so	CCONJ
ejpam-6729	547	15	λ′	λ′	NOUN
ejpam-6729	547	16	is	be	AUX
ejpam-6729	547	17	well	well	ADV
ejpam-6729	547	18	-	-	PUNCT
ejpam-6729	547	19	defined	define	VERB
ejpam-6729	547	20	on	on	ADP
ejpam-6729	547	21	e′	e′	PROPN
ejpam-6729	547	22	and	and	CCONJ
ejpam-6729	547	23	λ′	λ′	X
ejpam-6729	547	24	:	:	PUNCT
ejpam-6729	547	25	e′	e′	X
ejpam-6729	547	26	→	→	SYM
ejpam-6729	547	27	σ	σ	PROPN
ejpam-6729	547	28	.	.	PROPN
ejpam-6729	547	29	(	(	PUNCT
ejpam-6729	547	30	iv	iv	X
ejpam-6729	547	31	)	)	PUNCT
ejpam-6729	547	32	properties	property	NOUN
ejpam-6729	547	33	.	.	PUNCT
ejpam-6729	548	1	if	if	SCONJ
ejpam-6729	548	2	ϕv	ϕv	PROPN
ejpam-6729	548	3	(	(	PUNCT
ejpam-6729	548	4	v	v	NOUN
ejpam-6729	548	5	)	)	PUNCT
ejpam-6729	548	6	=	=	PUNCT
ejpam-6729	548	7	ϕv	ϕv	PROPN
ejpam-6729	548	8	(	(	PUNCT
ejpam-6729	548	9	v	v	NOUN
ejpam-6729	548	10	′	′	NOUN
ejpam-6729	548	11	)	)	PUNCT
ejpam-6729	548	12	then	then	ADV
ejpam-6729	548	13	µ(v	µ(v	PROPN
ejpam-6729	548	14	,	,	PUNCT
ejpam-6729	548	15	k	k	NOUN
ejpam-6729	548	16	)	)	PUNCT
ejpam-6729	549	1	=	=	SYM
ejpam-6729	549	2	µ(v′	µ(v′	PROPN
ejpam-6729	549	3	,	,	PUNCT
ejpam-6729	549	4	k	k	NOUN
ejpam-6729	549	5	)	)	PUNCT
ejpam-6729	549	6	for	for	ADP
ejpam-6729	549	7	all	all	DET
ejpam-6729	549	8	k	k	PROPN
ejpam-6729	549	9	∈	∈	PROPN
ejpam-6729	549	10	k	k	NOUN
ejpam-6729	549	11	,	,	PUNCT
ejpam-6729	549	12	and	and	CCONJ
ejpam-6729	549	13	if	if	SCONJ
ejpam-6729	549	14	ϕe(e	ϕe(e	NUM
ejpam-6729	549	15	)	)	PUNCT
ejpam-6729	549	16	=	=	PRON
ejpam-6729	549	17	ϕe(e	ϕe(e	NUM
ejpam-6729	549	18	′	′	NUM
ejpam-6729	549	19	)	)	PUNCT
ejpam-6729	549	20	then	then	ADV
ejpam-6729	549	21	µ(e	µ(e	PROPN
ejpam-6729	549	22	,	,	PUNCT
ejpam-6729	549	23	k	k	NOUN
ejpam-6729	549	24	)	)	PUNCT
ejpam-6729	549	25	=	=	PUNCT
ejpam-6729	549	26	µ(e′	µ(e′	PROPN
ejpam-6729	549	27	,	,	PUNCT
ejpam-6729	549	28	k	k	NOUN
ejpam-6729	549	29	)	)	PUNCT
ejpam-6729	549	30	for	for	ADP
ejpam-6729	549	31	all	all	DET
ejpam-6729	549	32	k	k	PROPN
ejpam-6729	549	33	∈	∈	PROPN
ejpam-6729	549	34	k.	k.	NOUN
ejpam-6729	549	35	hence	hence	ADV
ejpam-6729	549	36	µ′	µ′	PUNCT
ejpam-6729	549	37	is	be	AUX
ejpam-6729	549	38	well	well	ADV
ejpam-6729	549	39	-	-	PUNCT
ejpam-6729	549	40	defined	define	VERB
ejpam-6729	549	41	on	on	ADP
ejpam-6729	549	42	(	(	PUNCT
ejpam-6729	549	43	v	v	NOUN
ejpam-6729	549	44	′∪e′)×k	′∪e′)×k	NOUN
ejpam-6729	549	45	with	with	ADP
ejpam-6729	549	46	codomain	codomain	NOUN
ejpam-6729	549	47	s	s	NOUN
ejpam-6729	549	48	∪	∪	X
ejpam-6729	549	49	{	{	PUNCT
ejpam-6729	549	50	⊥	⊥	NOUN
ejpam-6729	549	51	}	}	PUNCT
ejpam-6729	549	52	.	.	PUNCT
ejpam-6729	550	1	all	all	DET
ejpam-6729	550	2	clauses	clause	NOUN
ejpam-6729	550	3	of	of	ADP
ejpam-6729	550	4	the	the	DET
ejpam-6729	550	5	definition	definition	NOUN
ejpam-6729	550	6	of	of	ADP
ejpam-6729	550	7	a	a	DET
ejpam-6729	550	8	property	property	NOUN
ejpam-6729	550	9	(	(	PUNCT
ejpam-6729	550	10	n−	n−	NOUN
ejpam-6729	550	11	1)-superhypergraph	1)-superhypergraph	NUM
ejpam-6729	550	12	are	be	AUX
ejpam-6729	550	13	satisfied	satisfied	ADJ
ejpam-6729	550	14	.	.	PUNCT
ejpam-6729	551	1	example	example	NOUN
ejpam-6729	551	2	14	14	NUM
ejpam-6729	551	3	(	(	PUNCT
ejpam-6729	551	4	flattening	flattening	NOUN
ejpam-6729	551	5	projection	projection	NOUN
ejpam-6729	551	6	:	:	PUNCT
ejpam-6729	551	7	a	a	DET
ejpam-6729	551	8	concrete	concrete	ADJ
ejpam-6729	551	9	2	2	NUM
ejpam-6729	551	10	→	→	SYM
ejpam-6729	551	11	1	1	NUM
ejpam-6729	551	12	instance	instance	NOUN
ejpam-6729	551	13	)	)	PUNCT
ejpam-6729	551	14	.	.	PUNCT
ejpam-6729	552	1	let	let	VERB
ejpam-6729	552	2	the	the	DET
ejpam-6729	552	3	base	base	NOUN
ejpam-6729	552	4	set	set	NOUN
ejpam-6729	552	5	be	be	AUX
ejpam-6729	552	6	v0	v0	NOUN
ejpam-6729	552	7	=	=	SYM
ejpam-6729	552	8	{	{	PUNCT
ejpam-6729	552	9	a	a	DET
ejpam-6729	552	10	,	,	PUNCT
ejpam-6729	552	11	b	b	NOUN
ejpam-6729	552	12	,	,	PUNCT
ejpam-6729	552	13	c	c	NOUN
ejpam-6729	552	14	}	}	PUNCT
ejpam-6729	552	15	.	.	PUNCT
ejpam-6729	553	1	consider	consider	VERB
ejpam-6729	553	2	the	the	DET
ejpam-6729	553	3	property	property	NOUN
ejpam-6729	553	4	2	2	NUM
ejpam-6729	553	5	-	-	PUNCT
ejpam-6729	553	6	superhypergraph	superhypergraph	NOUN
ejpam-6729	553	7	h(2	h(2	NOUN
ejpam-6729	553	8	)	)	PUNCT
ejpam-6729	554	1	=	=	PUNCT
ejpam-6729	554	2	(	(	PUNCT
ejpam-6729	554	3	v	v	NOUN
ejpam-6729	554	4	(	(	PUNCT
ejpam-6729	554	5	2	2	NUM
ejpam-6729	554	6	)	)	PUNCT
ejpam-6729	554	7	,	,	PUNCT
ejpam-6729	554	8	e(2	e(2	PROPN
ejpam-6729	554	9	)	)	PUNCT
ejpam-6729	554	10	,	,	PUNCT
ejpam-6729	554	11	λ	λ	PROPN
ejpam-6729	554	12	,	,	PUNCT
ejpam-6729	554	13	µ	µ	NOUN
ejpam-6729	554	14	)	)	PUNCT
ejpam-6729	554	15	with	with	ADP
ejpam-6729	554	16	v	v	NUM
ejpam-6729	554	17	(	(	PUNCT
ejpam-6729	554	18	2	2	NUM
ejpam-6729	554	19	)	)	PUNCT
ejpam-6729	554	20	=	=	NOUN
ejpam-6729	554	21	{	{	PUNCT
ejpam-6729	554	22	v1	v1	PROPN
ejpam-6729	554	23	=	=	SYM
ejpam-6729	554	24	{	{	PUNCT
ejpam-6729	554	25	{	{	PUNCT
ejpam-6729	554	26	a	a	PROPN
ejpam-6729	554	27	,	,	PUNCT
ejpam-6729	554	28	b	b	NOUN
ejpam-6729	554	29	}	}	PUNCT
ejpam-6729	554	30	,	,	PUNCT
ejpam-6729	554	31	{	{	PUNCT
ejpam-6729	554	32	b	b	X
ejpam-6729	554	33	,	,	PUNCT
ejpam-6729	554	34	c	c	NOUN
ejpam-6729	554	35	}	}	PUNCT
ejpam-6729	554	36	}	}	PUNCT
ejpam-6729	554	37	,	,	PUNCT
ejpam-6729	554	38	v2	v2	PROPN
ejpam-6729	554	39	=	=	SYM
ejpam-6729	554	40	{	{	PUNCT
ejpam-6729	554	41	{	{	PUNCT
ejpam-6729	554	42	a	a	NOUN
ejpam-6729	554	43	}	}	PUNCT
ejpam-6729	554	44	,	,	PUNCT
ejpam-6729	554	45	{	{	PUNCT
ejpam-6729	554	46	a	a	PRON
ejpam-6729	554	47	,	,	PUNCT
ejpam-6729	554	48	c	c	NOUN
ejpam-6729	554	49	}	}	PUNCT
ejpam-6729	554	50	}	}	PUNCT
ejpam-6729	554	51	}	}	PUNCT
ejpam-6729	554	52	⊆	⊆	NUM
ejpam-6729	554	53	p2(v0	p2(v0	NOUN
ejpam-6729	554	54	)	)	PUNCT
ejpam-6729	554	55	,	,	PUNCT
ejpam-6729	554	56	e(2	e(2	NOUN
ejpam-6729	554	57	)	)	PUNCT
ejpam-6729	554	58	=	=	PRON
ejpam-6729	554	59	{	{	PUNCT
ejpam-6729	554	60	e	e	NOUN
ejpam-6729	554	61	=	=	NOUN
ejpam-6729	554	62	{	{	PUNCT
ejpam-6729	554	63	v1	v1	PROPN
ejpam-6729	554	64	,	,	PUNCT
ejpam-6729	554	65	v2	v2	NOUN
ejpam-6729	554	66	}	}	PUNCT
ejpam-6729	554	67	}	}	PUNCT
ejpam-6729	554	68	⊆	⊆	NUM
ejpam-6729	554	69	p(v	p(v	NOUN
ejpam-6729	554	70	(	(	PUNCT
ejpam-6729	554	71	2	2	NUM
ejpam-6729	554	72	)	)	PUNCT
ejpam-6729	554	73	)	)	PUNCT
ejpam-6729	554	74	\	\	NOUN
ejpam-6729	555	1	{	{	PUNCT
ejpam-6729	555	2	∅	∅	NOUN
ejpam-6729	555	3	}	}	PUNCT
ejpam-6729	555	4	.	.	PUNCT
ejpam-6729	556	1	let	let	VERB
ejpam-6729	556	2	the	the	DET
ejpam-6729	556	3	label	label	NOUN
ejpam-6729	556	4	alphabet	alphabet	NOUN
ejpam-6729	556	5	be	be	AUX
ejpam-6729	556	6	σ	σ	NOUN
ejpam-6729	556	7	=	=	PUNCT
ejpam-6729	556	8	{	{	PUNCT
ejpam-6729	556	9	α	α	NOUN
ejpam-6729	556	10	}	}	PUNCT
ejpam-6729	556	11	and	and	CCONJ
ejpam-6729	556	12	set	set	VERB
ejpam-6729	556	13	λ(e	λ(e	NOUN
ejpam-6729	556	14	)	)	PUNCT
ejpam-6729	556	15	=	=	SYM
ejpam-6729	556	16	α	α	X
ejpam-6729	556	17	.	.	PUNCT
ejpam-6729	557	1	fix	fix	NOUN
ejpam-6729	557	2	keys	key	NOUN
ejpam-6729	557	3	k	k	X
ejpam-6729	558	1	=	=	PRON
ejpam-6729	558	2	{	{	PUNCT
ejpam-6729	558	3	tag	tag	NOUN
ejpam-6729	558	4	,	,	PUNCT
ejpam-6729	558	5	weight	weight	NOUN
ejpam-6729	558	6	}	}	PUNCT
ejpam-6729	558	7	and	and	CCONJ
ejpam-6729	558	8	a	a	DET
ejpam-6729	558	9	value	value	NOUN
ejpam-6729	558	10	domain	domain	NOUN
ejpam-6729	558	11	s	s	AUX
ejpam-6729	558	12	containing	contain	VERB
ejpam-6729	558	13	strings	string	NOUN
ejpam-6729	558	14	and	and	CCONJ
ejpam-6729	558	15	integers	integer	NOUN
ejpam-6729	558	16	;	;	PUNCT
ejpam-6729	558	17	take	take	VERB
ejpam-6729	558	18	⊥	⊥	NOUN
ejpam-6729	558	19	/∈	/∈	PUNCT
ejpam-6729	559	1	s.	s.	PROPN
ejpam-6729	559	2	define	define	VERB
ejpam-6729	559	3	the	the	DET
ejpam-6729	559	4	property	property	NOUN
ejpam-6729	559	5	map	map	NOUN
ejpam-6729	559	6	by	by	ADP
ejpam-6729	559	7	µ(v1	µ(v1	NOUN
ejpam-6729	559	8	,	,	PUNCT
ejpam-6729	559	9	tag	tag	NOUN
ejpam-6729	559	10	)	)	PUNCT
ejpam-6729	559	11	=	=	PUNCT
ejpam-6729	559	12	“	"	PUNCT
ejpam-6729	559	13	t1	t1	PROPN
ejpam-6729	559	14	”	"	PUNCT
ejpam-6729	559	15	,	,	PUNCT
ejpam-6729	559	16	µ(v2	µ(v2	NOUN
ejpam-6729	559	17	,	,	PUNCT
ejpam-6729	559	18	tag	tag	NOUN
ejpam-6729	559	19	)	)	PUNCT
ejpam-6729	559	20	=	=	PUNCT
ejpam-6729	559	21	“	"	PUNCT
ejpam-6729	559	22	t2	t2	PROPN
ejpam-6729	559	23	”	"	PUNCT
ejpam-6729	559	24	,	,	PUNCT
ejpam-6729	559	25	µ(e	µ(e	PROPN
ejpam-6729	559	26	,	,	PUNCT
ejpam-6729	559	27	weight	weight	NOUN
ejpam-6729	559	28	)	)	PUNCT
ejpam-6729	559	29	=	=	SYM
ejpam-6729	560	1	3	3	NUM
ejpam-6729	560	2	,	,	PUNCT
ejpam-6729	560	3	and	and	CCONJ
ejpam-6729	560	4	µ	µ	X
ejpam-6729	560	5	(	(	PUNCT
ejpam-6729	560	6	·	·	PUNCT
ejpam-6729	560	7	,	,	PUNCT
ejpam-6729	560	8	·	·	PUNCT
ejpam-6729	560	9	)	)	PUNCT
ejpam-6729	561	1	=	=	PUNCT
ejpam-6729	561	2	⊥	⊥	NOUN
ejpam-6729	561	3	for	for	ADP
ejpam-6729	561	4	all	all	DET
ejpam-6729	561	5	other	other	ADJ
ejpam-6729	561	6	key	key	ADJ
ejpam-6729	561	7	–	–	PUNCT
ejpam-6729	561	8	object	object	NOUN
ejpam-6729	561	9	pairs	pair	NOUN
ejpam-6729	561	10	.	.	PUNCT
ejpam-6729	562	1	the	the	DET
ejpam-6729	562	2	vertex	vertex	NOUN
ejpam-6729	562	3	–	–	PUNCT
ejpam-6729	562	4	flattening	flattening	NOUN
ejpam-6729	562	5	map	map	NOUN
ejpam-6729	562	6	ϕv	ϕv	ADP
ejpam-6729	562	7	:	:	PUNCT
ejpam-6729	562	8	p2(v0	p2(v0	PROPN
ejpam-6729	562	9	)	)	PUNCT
ejpam-6729	562	10	→	→	SYM
ejpam-6729	562	11	p1(v0	p1(v0	PROPN
ejpam-6729	562	12	)	)	PUNCT
ejpam-6729	562	13	yields	yield	NOUN
ejpam-6729	562	14	ϕv	ϕv	ADP
ejpam-6729	562	15	(	(	PUNCT
ejpam-6729	562	16	v1	v1	NOUN
ejpam-6729	562	17	)	)	PUNCT
ejpam-6729	562	18	=	=	PRON
ejpam-6729	562	19	{	{	PUNCT
ejpam-6729	562	20	a	a	PRON
ejpam-6729	562	21	,	,	PUNCT
ejpam-6729	562	22	b	b	NOUN
ejpam-6729	562	23	}	}	PUNCT
ejpam-6729	562	24	∪	∪	ADJ
ejpam-6729	562	25	{	{	PUNCT
ejpam-6729	562	26	b	b	NOUN
ejpam-6729	562	27	,	,	PUNCT
ejpam-6729	562	28	c	c	NOUN
ejpam-6729	562	29	}	}	PUNCT
ejpam-6729	562	30	=	=	SYM
ejpam-6729	562	31	{	{	PUNCT
ejpam-6729	562	32	a	a	DET
ejpam-6729	562	33	,	,	PUNCT
ejpam-6729	562	34	b	b	NOUN
ejpam-6729	562	35	,	,	PUNCT
ejpam-6729	562	36	c	c	NOUN
ejpam-6729	562	37	}	}	PUNCT
ejpam-6729	562	38	,	,	PUNCT
ejpam-6729	562	39	ϕv	ϕv	ADP
ejpam-6729	562	40	(	(	PUNCT
ejpam-6729	562	41	v2	v2	NOUN
ejpam-6729	562	42	)	)	PUNCT
ejpam-6729	562	43	=	=	PRON
ejpam-6729	562	44	{	{	PUNCT
ejpam-6729	562	45	a	a	PRON
ejpam-6729	562	46	}	}	PUNCT
ejpam-6729	562	47	∪	∪	NOUN
ejpam-6729	562	48	{	{	PUNCT
ejpam-6729	562	49	a	a	PRON
ejpam-6729	562	50	,	,	PUNCT
ejpam-6729	562	51	c	c	NOUN
ejpam-6729	562	52	}	}	PUNCT
ejpam-6729	562	53	=	=	SYM
ejpam-6729	562	54	{	{	PUNCT
ejpam-6729	562	55	a	a	X
ejpam-6729	562	56	,	,	PUNCT
ejpam-6729	562	57	c	c	NOUN
ejpam-6729	562	58	}	}	PUNCT
ejpam-6729	562	59	.	.	PUNCT
ejpam-6729	563	1	the	the	DET
ejpam-6729	563	2	induced	induce	VERB
ejpam-6729	563	3	edge	edge	NOUN
ejpam-6729	563	4	map	map	NOUN
ejpam-6729	563	5	ϕe	ϕe	PRON
ejpam-6729	563	6	gives	give	VERB
ejpam-6729	563	7	ϕe(e	ϕe(e	NOUN
ejpam-6729	563	8	)	)	PUNCT
ejpam-6729	564	1	=	=	PRON
ejpam-6729	564	2	{	{	PUNCT
ejpam-6729	564	3	ϕv	ϕv	PROPN
ejpam-6729	564	4	(	(	PUNCT
ejpam-6729	564	5	v1	v1	NOUN
ejpam-6729	564	6	)	)	PUNCT
ejpam-6729	564	7	,	,	PUNCT
ejpam-6729	564	8	ϕv	ϕv	PROPN
ejpam-6729	564	9	(	(	PUNCT
ejpam-6729	564	10	v2	v2	NOUN
ejpam-6729	564	11	)	)	PUNCT
ejpam-6729	564	12	}	}	PUNCT
ejpam-6729	564	13	=	=	SYM
ejpam-6729	564	14	{	{	PUNCT
ejpam-6729	564	15	{	{	PUNCT
ejpam-6729	564	16	a	a	PROPN
ejpam-6729	564	17	,	,	PUNCT
ejpam-6729	564	18	b	b	NOUN
ejpam-6729	564	19	,	,	PUNCT
ejpam-6729	564	20	c	c	NOUN
ejpam-6729	564	21	}	}	PUNCT
ejpam-6729	564	22	,	,	PUNCT
ejpam-6729	564	23	{	{	PUNCT
ejpam-6729	564	24	a	a	PRON
ejpam-6729	564	25	,	,	PUNCT
ejpam-6729	564	26	c	c	NOUN
ejpam-6729	564	27	}	}	PUNCT
ejpam-6729	564	28	}	}	PUNCT
ejpam-6729	564	29	.	.	PUNCT
ejpam-6729	565	1	t.	t.	PROPN
ejpam-6729	565	2	fujita	fujita	PROPN
ejpam-6729	565	3	,	,	PUNCT
ejpam-6729	565	4	f.	f.	PROPN
ejpam-6729	565	5	smarandache	smarandache	PROPN
ejpam-6729	565	6	/	/	SYM
ejpam-6729	565	7	eur	eur	PROPN
ejpam-6729	565	8	.	.	PUNCT
ejpam-6729	566	1	j.	j.	PROPN
ejpam-6729	566	2	pure	pure	PROPN
ejpam-6729	566	3	appl	appl	PROPN
ejpam-6729	566	4	.	.	PROPN
ejpam-6729	566	5	math	math	PROPN
ejpam-6729	566	6	,	,	PUNCT
ejpam-6729	566	7	18	18	NUM
ejpam-6729	566	8	(	(	PUNCT
ejpam-6729	566	9	4	4	NUM
ejpam-6729	566	10	)	)	PUNCT
ejpam-6729	566	11	(	(	PUNCT
ejpam-6729	566	12	2025	2025	NUM
ejpam-6729	566	13	)	)	PUNCT
ejpam-6729	566	14	,	,	PUNCT
ejpam-6729	566	15	6729	6729	NUM
ejpam-6729	566	16	26	26	NUM
ejpam-6729	566	17	of	of	ADP
ejpam-6729	566	18	36	36	NUM
ejpam-6729	566	19	hence	hence	ADV
ejpam-6729	566	20	the	the	DET
ejpam-6729	566	21	flattened	flatten	VERB
ejpam-6729	566	22	structure	structure	NOUN
ejpam-6729	566	23	h	h	NOUN
ejpam-6729	566	24	′	′	NUM
ejpam-6729	567	1	=	=	PUNCT
ejpam-6729	568	1	(	(	PUNCT
ejpam-6729	568	2	v	v	NOUN
ejpam-6729	568	3	′	′	NUM
ejpam-6729	568	4	,	,	PUNCT
ejpam-6729	568	5	e′	e′	PROPN
ejpam-6729	568	6	,	,	PUNCT
ejpam-6729	568	7	λ′	λ′	NOUN
ejpam-6729	568	8	,	,	PUNCT
ejpam-6729	568	9	µ′	µ′	NUM
ejpam-6729	568	10	)	)	PUNCT
ejpam-6729	568	11	is	be	AUX
ejpam-6729	568	12	a	a	DET
ejpam-6729	568	13	property	property	NOUN
ejpam-6729	568	14	1	1	NUM
ejpam-6729	568	15	-	-	PUNCT
ejpam-6729	568	16	superhypergraph	superhypergraph	NOUN
ejpam-6729	568	17	with	with	ADP
ejpam-6729	568	18	v	v	NOUN
ejpam-6729	568	19	′	′	NUM
ejpam-6729	569	1	=	=	PUNCT
ejpam-6729	570	1	ϕv	ϕv	ADP
ejpam-6729	571	1	[	[	X
ejpam-6729	571	2	v	v	X
ejpam-6729	571	3	(	(	PUNCT
ejpam-6729	571	4	2	2	NUM
ejpam-6729	571	5	)	)	PUNCT
ejpam-6729	571	6	]	]	PUNCT
ejpam-6729	572	1	=	=	X
ejpam-6729	572	2	{	{	PUNCT
ejpam-6729	572	3	{	{	PUNCT
ejpam-6729	572	4	a	a	PROPN
ejpam-6729	572	5	,	,	PUNCT
ejpam-6729	572	6	b	b	NOUN
ejpam-6729	572	7	,	,	PUNCT
ejpam-6729	572	8	c	c	NOUN
ejpam-6729	572	9	}	}	PUNCT
ejpam-6729	572	10	,	,	PUNCT
ejpam-6729	572	11	{	{	PUNCT
ejpam-6729	572	12	a	a	PRON
ejpam-6729	572	13	,	,	PUNCT
ejpam-6729	572	14	c	c	NOUN
ejpam-6729	572	15	}	}	PUNCT
ejpam-6729	572	16	}	}	PUNCT
ejpam-6729	572	17	⊆	⊆	NUM
ejpam-6729	572	18	p1(v0	p1(v0	NOUN
ejpam-6729	572	19	)	)	PUNCT
ejpam-6729	572	20	,	,	PUNCT
ejpam-6729	572	21	e′	e′	X
ejpam-6729	572	22	=	=	X
ejpam-6729	572	23	{	{	PUNCT
ejpam-6729	572	24	ϕe(e	ϕe(e	PROPN
ejpam-6729	572	25	)	)	PUNCT
ejpam-6729	572	26	}	}	PUNCT
ejpam-6729	572	27	.	.	PUNCT
ejpam-6729	573	1	by	by	ADP
ejpam-6729	573	2	the	the	DET
ejpam-6729	573	3	theorem	theorem	NOUN
ejpam-6729	573	4	,	,	PUNCT
ejpam-6729	573	5	we	we	PRON
ejpam-6729	573	6	set	set	VERB
ejpam-6729	573	7	λ′(ϕe(e	λ′(ϕe(e	NOUN
ejpam-6729	573	8	)	)	PUNCT
ejpam-6729	573	9	)	)	PUNCT
ejpam-6729	574	1	=	=	PUNCT
ejpam-6729	574	2	λ(e	λ(e	VERB
ejpam-6729	574	3	)	)	PUNCT
ejpam-6729	574	4	=	=	SYM
ejpam-6729	574	5	α	α	PROPN
ejpam-6729	574	6	,	,	PUNCT
ejpam-6729	574	7	µ′({a	µ′({a	PROPN
ejpam-6729	574	8	,	,	PUNCT
ejpam-6729	574	9	b	b	NOUN
ejpam-6729	574	10	,	,	PUNCT
ejpam-6729	574	11	c	c	NOUN
ejpam-6729	574	12	}	}	PUNCT
ejpam-6729	574	13	,	,	PUNCT
ejpam-6729	574	14	tag	tag	NOUN
ejpam-6729	574	15	)	)	PUNCT
ejpam-6729	574	16	=	=	SYM
ejpam-6729	574	17	µ(v1	µ(v1	ADJ
ejpam-6729	574	18	,	,	PUNCT
ejpam-6729	574	19	tag	tag	NOUN
ejpam-6729	574	20	)	)	PUNCT
ejpam-6729	574	21	=	=	PUNCT
ejpam-6729	574	22	“	"	PUNCT
ejpam-6729	574	23	t1	t1	PROPN
ejpam-6729	574	24	”	"	PUNCT
ejpam-6729	574	25	,	,	PUNCT
ejpam-6729	574	26	µ′({a	µ′({a	INTJ
ejpam-6729	574	27	,	,	PUNCT
ejpam-6729	574	28	c	c	NOUN
ejpam-6729	574	29	}	}	PUNCT
ejpam-6729	574	30	,	,	PUNCT
ejpam-6729	574	31	tag	tag	NOUN
ejpam-6729	574	32	)	)	PUNCT
ejpam-6729	574	33	=	=	SYM
ejpam-6729	574	34	µ(v2	µ(v2	NOUN
ejpam-6729	574	35	,	,	PUNCT
ejpam-6729	574	36	tag	tag	NOUN
ejpam-6729	574	37	)	)	PUNCT
ejpam-6729	574	38	=	=	PUNCT
ejpam-6729	574	39	“	"	PUNCT
ejpam-6729	574	40	t2	t2	NOUN
ejpam-6729	574	41	”	"	PUNCT
ejpam-6729	574	42	,	,	PUNCT
ejpam-6729	574	43	µ′(ϕe(e	µ′(ϕe(e	ADV
ejpam-6729	574	44	)	)	PUNCT
ejpam-6729	574	45	,	,	PUNCT
ejpam-6729	574	46	weight	weight	NOUN
ejpam-6729	574	47	)	)	PUNCT
ejpam-6729	575	1	=	=	SYM
ejpam-6729	575	2	µ(e	µ(e	PROPN
ejpam-6729	575	3	,	,	PUNCT
ejpam-6729	575	4	weight	weight	NOUN
ejpam-6729	575	5	)	)	PUNCT
ejpam-6729	575	6	=	=	SYM
ejpam-6729	575	7	3	3	NUM
ejpam-6729	575	8	,	,	PUNCT
ejpam-6729	575	9	and	and	CCONJ
ejpam-6729	575	10	µ′	µ′	PROPN
ejpam-6729	575	11	(	(	PUNCT
ejpam-6729	575	12	·	·	PUNCT
ejpam-6729	575	13	,	,	PUNCT
ejpam-6729	575	14	·	·	PUNCT
ejpam-6729	575	15	)	)	PUNCT
ejpam-6729	575	16	=	=	PUNCT
ejpam-6729	576	1	⊥	⊥	X
ejpam-6729	576	2	otherwise	otherwise	ADV
ejpam-6729	576	3	.	.	PUNCT
ejpam-6729	577	1	since	since	SCONJ
ejpam-6729	577	2	no	no	DET
ejpam-6729	577	3	two	two	NUM
ejpam-6729	577	4	distinct	distinct	ADJ
ejpam-6729	577	5	vertices	vertex	NOUN
ejpam-6729	577	6	(	(	PUNCT
ejpam-6729	577	7	resp	resp	NOUN
ejpam-6729	577	8	.	.	PUNCT
ejpam-6729	577	9	edges	edge	NOUN
ejpam-6729	577	10	)	)	PUNCT
ejpam-6729	577	11	of	of	ADP
ejpam-6729	577	12	h(2	h(2	NOUN
ejpam-6729	577	13	)	)	PUNCT
ejpam-6729	577	14	share	share	VERB
ejpam-6729	577	15	the	the	DET
ejpam-6729	577	16	same	same	ADJ
ejpam-6729	577	17	ϕv	ϕv	ADP
ejpam-6729	577	18	-image	-image	NOUN
ejpam-6729	577	19	(	(	PUNCT
ejpam-6729	577	20	resp	resp	NOUN
ejpam-6729	577	21	.	.	PUNCT
ejpam-6729	578	1	ϕe	ϕe	NOUN
ejpam-6729	578	2	-	-	PUNCT
ejpam-6729	578	3	image	image	NOUN
ejpam-6729	578	4	)	)	PUNCT
ejpam-6729	579	1	,	,	PUNCT
ejpam-6729	579	2	the	the	DET
ejpam-6729	579	3	fibre	fibre	NOUN
ejpam-6729	579	4	–	–	PUNCT
ejpam-6729	579	5	compatibility	compatibility	NOUN
ejpam-6729	579	6	conditions	condition	NOUN
ejpam-6729	579	7	hold	hold	VERB
ejpam-6729	579	8	trivially	trivially	ADV
ejpam-6729	579	9	,	,	PUNCT
ejpam-6729	579	10	and	and	CCONJ
ejpam-6729	579	11	theorem	theorem	VERB
ejpam-6729	579	12	10	10	NUM
ejpam-6729	579	13	applies	applie	NOUN
ejpam-6729	579	14	.	.	PUNCT
ejpam-6729	580	1	theorem	theorem	ADJ
ejpam-6729	580	2	11	11	NUM
ejpam-6729	580	3	(	(	PUNCT
ejpam-6729	580	4	iterated	iterate	VERB
ejpam-6729	580	5	flattening	flattening	NOUN
ejpam-6729	580	6	)	)	PUNCT
ejpam-6729	580	7	.	.	PUNCT
ejpam-6729	581	1	with	with	ADP
ejpam-6729	581	2	notation	notation	NOUN
ejpam-6729	581	3	as	as	ADP
ejpam-6729	581	4	above	above	ADV
ejpam-6729	581	5	,	,	PUNCT
ejpam-6729	581	6	for	for	ADP
ejpam-6729	581	7	1	1	NUM
ejpam-6729	581	8	≤	≤	NUM
ejpam-6729	581	9	k	k	NOUN
ejpam-6729	581	10	≤	≤	NOUN
ejpam-6729	582	1	n	n	PRON
ejpam-6729	582	2	define	define	VERB
ejpam-6729	582	3	ϕ	ϕ	X
ejpam-6729	582	4	(	(	PUNCT
ejpam-6729	582	5	k	k	NOUN
ejpam-6729	582	6	)	)	PUNCT
ejpam-6729	582	7	v	v	NOUN
ejpam-6729	582	8	:	:	PUNCT
ejpam-6729	582	9	=	=	SYM
ejpam-6729	582	10	ϕv	ϕv	ADP
ejpam-6729	582	11	◦	◦	NOUN
ejpam-6729	582	12	·	·	PUNCT
ejpam-6729	582	13	·	·	PUNCT
ejpam-6729	582	14	·	·	PUNCT
ejpam-6729	583	1	◦	◦	VERB
ejpam-6729	583	2	ϕv︸	ϕv︸	PROPN
ejpam-6729	583	3	︷︷	︷︷	PROPN
ejpam-6729	584	1	︸	︸	X
ejpam-6729	585	1	k	k	PROPN
ejpam-6729	585	2	times	time	NOUN
ejpam-6729	585	3	:	:	PUNCT
ejpam-6729	585	4	pn(v0	pn(v0	X
ejpam-6729	585	5	)	)	PUNCT
ejpam-6729	585	6	→	→	SYM
ejpam-6729	585	7	pn−k(v0	pn−k(v0	NUM
ejpam-6729	585	8	)	)	PUNCT
ejpam-6729	585	9	,	,	PUNCT
ejpam-6729	585	10	and	and	CCONJ
ejpam-6729	585	11	extend	extend	VERB
ejpam-6729	585	12	to	to	ADP
ejpam-6729	585	13	edges	edge	NOUN
ejpam-6729	585	14	by	by	ADP
ejpam-6729	585	15	ϕ	ϕ	X
ejpam-6729	585	16	(	(	PUNCT
ejpam-6729	585	17	k	k	NOUN
ejpam-6729	585	18	)	)	PUNCT
ejpam-6729	585	19	e	e	NOUN
ejpam-6729	585	20	(	(	PUNCT
ejpam-6729	585	21	e	e	NOUN
ejpam-6729	585	22	)	)	PUNCT
ejpam-6729	585	23	:	:	PUNCT
ejpam-6729	586	1	=	=	PRON
ejpam-6729	586	2	{	{	PUNCT
ejpam-6729	586	3	ϕ	ϕ	X
ejpam-6729	586	4	(	(	PUNCT
ejpam-6729	586	5	k	k	NOUN
ejpam-6729	586	6	)	)	PUNCT
ejpam-6729	586	7	v	v	NOUN
ejpam-6729	586	8	(	(	PUNCT
ejpam-6729	586	9	v	v	NOUN
ejpam-6729	586	10	)	)	PUNCT
ejpam-6729	586	11	|	|	ADV
ejpam-6729	586	12	v	v	NOUN
ejpam-6729	586	13	∈	∈	NOUN
ejpam-6729	586	14	e	e	X
ejpam-6729	586	15	}	}	PUNCT
ejpam-6729	586	16	.	.	PUNCT
ejpam-6729	587	1	if	if	SCONJ
ejpam-6729	587	2	the	the	DET
ejpam-6729	587	3	label	label	NOUN
ejpam-6729	587	4	/	/	SYM
ejpam-6729	587	5	property	property	NOUN
ejpam-6729	587	6	compatibilities	compatibility	NOUN
ejpam-6729	587	7	hold	hold	VERB
ejpam-6729	587	8	at	at	ADP
ejpam-6729	587	9	each	each	DET
ejpam-6729	587	10	intermediate	intermediate	ADJ
ejpam-6729	587	11	stage	stage	NOUN
ejpam-6729	587	12	,	,	PUNCT
ejpam-6729	587	13	then	then	ADV
ejpam-6729	587	14	h(n−k	h(n−k	PROPN
ejpam-6729	587	15	)	)	PUNCT
ejpam-6729	587	16	:	:	PUNCT
ejpam-6729	588	1	=	=	SYM
ejpam-6729	588	2	(	(	PUNCT
ejpam-6729	588	3	ϕ	ϕ	X
ejpam-6729	588	4	(	(	PUNCT
ejpam-6729	588	5	k	k	NOUN
ejpam-6729	588	6	)	)	PUNCT
ejpam-6729	588	7	v	v	ADP
ejpam-6729	588	8	[	[	X
ejpam-6729	588	9	v	v	X
ejpam-6729	588	10	(	(	PUNCT
ejpam-6729	588	11	n	n	CCONJ
ejpam-6729	588	12	)	)	PUNCT
ejpam-6729	588	13	]	]	PUNCT
ejpam-6729	588	14	,	,	PUNCT
ejpam-6729	588	15	{	{	PUNCT
ejpam-6729	588	16	ϕ(k	ϕ(k	NOUN
ejpam-6729	588	17	)	)	PUNCT
ejpam-6729	588	18	e	e	NOUN
ejpam-6729	588	19	(	(	PUNCT
ejpam-6729	588	20	e	e	NOUN
ejpam-6729	588	21	)	)	PUNCT
ejpam-6729	588	22	|	|	ADV
ejpam-6729	588	23	e	e	X
ejpam-6729	588	24	∈	∈	PROPN
ejpam-6729	588	25	e(n	e(n	PROPN
ejpam-6729	588	26	)	)	PUNCT
ejpam-6729	588	27	}	}	PUNCT
ejpam-6729	588	28	,	,	PUNCT
ejpam-6729	588	29	λ(k	λ(k	PROPN
ejpam-6729	588	30	)	)	PUNCT
ejpam-6729	588	31	,	,	PUNCT
ejpam-6729	588	32	µ(k	µ(k	NOUN
ejpam-6729	588	33	)	)	PUNCT
ejpam-6729	588	34	)	)	PUNCT
ejpam-6729	588	35	is	be	AUX
ejpam-6729	588	36	a	a	DET
ejpam-6729	588	37	property	property	NOUN
ejpam-6729	588	38	(	(	PUNCT
ejpam-6729	588	39	n−	n−	NOUN
ejpam-6729	588	40	k)-superhypergraph	k)-superhypergraph	NOUN
ejpam-6729	588	41	.	.	PUNCT
ejpam-6729	589	1	proof	proof	NOUN
ejpam-6729	589	2	.	.	PUNCT
ejpam-6729	590	1	fix	fix	VERB
ejpam-6729	590	2	n	n	PRON
ejpam-6729	590	3	∈	∈	PROPN
ejpam-6729	590	4	n	n	NOUN
ejpam-6729	590	5	and	and	CCONJ
ejpam-6729	590	6	1	1	NUM
ejpam-6729	590	7	≤	≤	NUM
ejpam-6729	590	8	k	k	PROPN
ejpam-6729	590	9	≤	≤	PROPN
ejpam-6729	590	10	n.	n.	NOUN
ejpam-6729	590	11	recall	recall	VERB
ejpam-6729	590	12	the	the	DET
ejpam-6729	590	13	vertex	vertex	NOUN
ejpam-6729	590	14	–	–	PUNCT
ejpam-6729	590	15	flattening	flattening	NOUN
ejpam-6729	590	16	map	map	NOUN
ejpam-6729	590	17	ϕv	ϕv	ADP
ejpam-6729	590	18	:	:	PUNCT
ejpam-6729	590	19	pr(v0	pr(v0	NOUN
ejpam-6729	590	20	)	)	PUNCT
ejpam-6729	590	21	→	→	SYM
ejpam-6729	590	22	pr−1(v0	pr−1(v0	PROPN
ejpam-6729	590	23	)	)	PUNCT
ejpam-6729	590	24	,	,	PUNCT
ejpam-6729	590	25	x	x	X
ejpam-6729	590	26	7→	7→	ADV
ejpam-6729	591	1	⋃	⋃	NOUN
ejpam-6729	591	2	x∈x	x∈x	NOUN
ejpam-6729	591	3	x	x	PUNCT
ejpam-6729	591	4	for	for	ADP
ejpam-6729	591	5	r	r	NOUN
ejpam-6729	591	6	≥	≥	NUM
ejpam-6729	591	7	1	1	NUM
ejpam-6729	591	8	,	,	PUNCT
ejpam-6729	591	9	and	and	CCONJ
ejpam-6729	591	10	its	its	PRON
ejpam-6729	591	11	extension	extension	NOUN
ejpam-6729	591	12	to	to	ADP
ejpam-6729	591	13	(	(	PUNCT
ejpam-6729	591	14	nonempty	nonempty	X
ejpam-6729	591	15	)	)	PUNCT
ejpam-6729	591	16	edge	edge	NOUN
ejpam-6729	591	17	-	-	PUNCT
ejpam-6729	591	18	sets	set	VERB
ejpam-6729	591	19	ϕe	ϕe	NOUN
ejpam-6729	591	20	:	:	PUNCT
ejpam-6729	591	21	p(v	p(v	NOUN
ejpam-6729	591	22	(	(	PUNCT
ejpam-6729	591	23	r))\	r))\	X
ejpam-6729	591	24	{	{	PUNCT
ejpam-6729	591	25	∅	∅	NOUN
ejpam-6729	591	26	}	}	PUNCT
ejpam-6729	591	27	→	→	SYM
ejpam-6729	591	28	p	p	X
ejpam-6729	591	29	(	(	PUNCT
ejpam-6729	591	30	ϕv	ϕv	ADP
ejpam-6729	592	1	[	[	X
ejpam-6729	592	2	v	v	X
ejpam-6729	592	3	(	(	PUNCT
ejpam-6729	592	4	r	r	NOUN
ejpam-6729	592	5	)	)	PUNCT
ejpam-6729	592	6	]	]	PUNCT
ejpam-6729	592	7	)	)	PUNCT
ejpam-6729	592	8	\	\	NOUN
ejpam-6729	592	9	{	{	PUNCT
ejpam-6729	592	10	∅	∅	NOUN
ejpam-6729	592	11	}	}	PUNCT
ejpam-6729	592	12	,	,	PUNCT
ejpam-6729	592	13	ϕe(e	ϕe(e	NUM
ejpam-6729	592	14	)	)	PUNCT
ejpam-6729	592	15	:	:	PUNCT
ejpam-6729	593	1	=	=	X
ejpam-6729	593	2	{	{	PUNCT
ejpam-6729	593	3	ϕv	ϕv	PROPN
ejpam-6729	593	4	(	(	PUNCT
ejpam-6729	593	5	v	v	NOUN
ejpam-6729	593	6	)	)	PUNCT
ejpam-6729	593	7	|	|	ADV
ejpam-6729	593	8	v	v	NOUN
ejpam-6729	593	9	∈	∈	NOUN
ejpam-6729	593	10	e	e	X
ejpam-6729	593	11	}	}	PUNCT
ejpam-6729	593	12	.	.	PUNCT
ejpam-6729	594	1	for	for	ADP
ejpam-6729	594	2	k	k	PROPN
ejpam-6729	594	3	≥	≥	PROPN
ejpam-6729	594	4	1	1	NUM
ejpam-6729	594	5	,	,	PUNCT
ejpam-6729	594	6	define	define	VERB
ejpam-6729	594	7	the	the	DET
ejpam-6729	594	8	k	k	ADJ
ejpam-6729	594	9	-	-	ADJ
ejpam-6729	594	10	fold	fold	ADJ
ejpam-6729	594	11	compositions	composition	NOUN
ejpam-6729	594	12	ϕ	ϕ	X
ejpam-6729	594	13	(	(	PUNCT
ejpam-6729	594	14	k	k	NOUN
ejpam-6729	594	15	)	)	PUNCT
ejpam-6729	594	16	v	v	NOUN
ejpam-6729	594	17	:	:	PUNCT
ejpam-6729	594	18	=	=	SYM
ejpam-6729	594	19	ϕv	ϕv	ADP
ejpam-6729	594	20	◦	◦	NOUN
ejpam-6729	594	21	·	·	PUNCT
ejpam-6729	594	22	·	·	PUNCT
ejpam-6729	594	23	·	·	PUNCT
ejpam-6729	595	1	◦	◦	VERB
ejpam-6729	595	2	ϕv︸	ϕv︸	PROPN
ejpam-6729	595	3	︷︷	︷︷	PROPN
ejpam-6729	596	1	︸	︸	X
ejpam-6729	597	1	k	k	PROPN
ejpam-6729	597	2	times	time	NOUN
ejpam-6729	597	3	:	:	PUNCT
ejpam-6729	597	4	pn(v0	pn(v0	X
ejpam-6729	597	5	)	)	PUNCT
ejpam-6729	597	6	−→	−→	NOUN
ejpam-6729	597	7	pn−k(v0	pn−k(v0	ADV
ejpam-6729	597	8	)	)	PUNCT
ejpam-6729	597	9	,	,	PUNCT
ejpam-6729	597	10	ϕ	ϕ	X
ejpam-6729	597	11	(	(	PUNCT
ejpam-6729	597	12	k	k	NOUN
ejpam-6729	597	13	)	)	PUNCT
ejpam-6729	597	14	e	e	NOUN
ejpam-6729	597	15	(	(	PUNCT
ejpam-6729	597	16	e	e	NOUN
ejpam-6729	597	17	)	)	PUNCT
ejpam-6729	597	18	:	:	PUNCT
ejpam-6729	597	19	=	=	PRON
ejpam-6729	597	20	{	{	PUNCT
ejpam-6729	597	21	ϕ	ϕ	X
ejpam-6729	597	22	(	(	PUNCT
ejpam-6729	597	23	k	k	NOUN
ejpam-6729	597	24	)	)	PUNCT
ejpam-6729	597	25	v	v	NOUN
ejpam-6729	597	26	(	(	PUNCT
ejpam-6729	597	27	v	v	NOUN
ejpam-6729	597	28	)	)	PUNCT
ejpam-6729	597	29	|	|	ADV
ejpam-6729	597	30	v	v	NOUN
ejpam-6729	597	31	∈	∈	NOUN
ejpam-6729	597	32	e	e	X
ejpam-6729	597	33	}	}	PUNCT
ejpam-6729	597	34	.	.	PUNCT
ejpam-6729	598	1	we	we	PRON
ejpam-6729	598	2	prove	prove	VERB
ejpam-6729	598	3	by	by	ADP
ejpam-6729	598	4	induction	induction	NOUN
ejpam-6729	598	5	on	on	ADP
ejpam-6729	598	6	k	k	PROPN
ejpam-6729	598	7	that	that	SCONJ
ejpam-6729	598	8	h(n−k	h(n−k	NOUN
ejpam-6729	598	9	)	)	PUNCT
ejpam-6729	598	10	:	:	PUNCT
ejpam-6729	599	1	=	=	SYM
ejpam-6729	599	2	(	(	PUNCT
ejpam-6729	599	3	v	v	NOUN
ejpam-6729	599	4	(	(	PUNCT
ejpam-6729	599	5	n−k	n−k	NOUN
ejpam-6729	599	6	)	)	PUNCT
ejpam-6729	599	7	,	,	PUNCT
ejpam-6729	599	8	e(n−k	e(n−k	PROPN
ejpam-6729	599	9	)	)	PUNCT
ejpam-6729	599	10	,	,	PUNCT
ejpam-6729	599	11	λ(k	λ(k	PROPN
ejpam-6729	599	12	)	)	PUNCT
ejpam-6729	599	13	,	,	PUNCT
ejpam-6729	599	14	µ(k	µ(k	NOUN
ejpam-6729	599	15	)	)	PUNCT
ejpam-6729	599	16	)	)	PUNCT
ejpam-6729	599	17	:	:	PUNCT
ejpam-6729	600	1	=	=	SYM
ejpam-6729	600	2	(	(	PUNCT
ejpam-6729	600	3	ϕ	ϕ	X
ejpam-6729	600	4	(	(	PUNCT
ejpam-6729	600	5	k	k	NOUN
ejpam-6729	600	6	)	)	PUNCT
ejpam-6729	600	7	v	v	ADP
ejpam-6729	600	8	[	[	X
ejpam-6729	600	9	v	v	X
ejpam-6729	600	10	(	(	PUNCT
ejpam-6729	600	11	n	n	CCONJ
ejpam-6729	600	12	)	)	PUNCT
ejpam-6729	600	13	]	]	PUNCT
ejpam-6729	600	14	,	,	PUNCT
ejpam-6729	600	15	{	{	PUNCT
ejpam-6729	600	16	ϕ(k	ϕ(k	NOUN
ejpam-6729	600	17	)	)	PUNCT
ejpam-6729	600	18	e	e	NOUN
ejpam-6729	600	19	(	(	PUNCT
ejpam-6729	600	20	e	e	NOUN
ejpam-6729	600	21	)	)	PUNCT
ejpam-6729	600	22	|	|	ADV
ejpam-6729	600	23	e	e	X
ejpam-6729	600	24	∈	∈	PROPN
ejpam-6729	600	25	e(n	e(n	PROPN
ejpam-6729	600	26	)	)	PUNCT
ejpam-6729	600	27	}	}	PUNCT
ejpam-6729	600	28	,	,	PUNCT
ejpam-6729	600	29	λ(k	λ(k	PROPN
ejpam-6729	600	30	)	)	PUNCT
ejpam-6729	600	31	,	,	PUNCT
ejpam-6729	600	32	µ(k	µ(k	NOUN
ejpam-6729	600	33	)	)	PUNCT
ejpam-6729	600	34	)	)	PUNCT
ejpam-6729	600	35	is	be	AUX
ejpam-6729	600	36	a	a	DET
ejpam-6729	600	37	property	property	NOUN
ejpam-6729	600	38	(	(	PUNCT
ejpam-6729	600	39	n−	n−	NOUN
ejpam-6729	600	40	k)-superhypergraph	k)-superhypergraph	VERB
ejpam-6729	600	41	,	,	PUNCT
ejpam-6729	600	42	provided	provide	VERB
ejpam-6729	600	43	the	the	DET
ejpam-6729	600	44	label	label	NOUN
ejpam-6729	600	45	/	/	SYM
ejpam-6729	600	46	property	property	NOUN
ejpam-6729	600	47	compatibilities	compatibility	NOUN
ejpam-6729	600	48	hold	hold	VERB
ejpam-6729	600	49	at	at	ADP
ejpam-6729	600	50	each	each	DET
ejpam-6729	600	51	intermediate	intermediate	ADJ
ejpam-6729	600	52	stage	stage	NOUN
ejpam-6729	600	53	.	.	PUNCT
ejpam-6729	601	1	base	base	NOUN
ejpam-6729	601	2	case	case	NOUN
ejpam-6729	601	3	k	k	NOUN
ejpam-6729	602	1	=	=	SYM
ejpam-6729	602	2	1	1	X
ejpam-6729	602	3	.	.	PUNCT
ejpam-6729	602	4	set	set	VERB
ejpam-6729	602	5	v	v	NOUN
ejpam-6729	602	6	′	′	NUM
ejpam-6729	602	7	:	:	PUNCT
ejpam-6729	603	1	=	=	PUNCT
ejpam-6729	603	2	ϕv	ϕv	ADP
ejpam-6729	604	1	[	[	X
ejpam-6729	604	2	v	v	X
ejpam-6729	604	3	(	(	PUNCT
ejpam-6729	604	4	n	n	CCONJ
ejpam-6729	604	5	)	)	PUNCT
ejpam-6729	604	6	]	]	PUNCT
ejpam-6729	604	7	⊆	⊆	NUM
ejpam-6729	604	8	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	604	9	)	)	PUNCT
ejpam-6729	604	10	,	,	PUNCT
ejpam-6729	604	11	e′	e′	X
ejpam-6729	604	12	:	:	PUNCT
ejpam-6729	604	13	=	=	PRON
ejpam-6729	604	14	{	{	PUNCT
ejpam-6729	604	15	ϕe(e	ϕe(e	NOUN
ejpam-6729	604	16	)	)	PUNCT
ejpam-6729	605	1	|	|	ADV
ejpam-6729	605	2	e	e	X
ejpam-6729	605	3	∈	∈	PROPN
ejpam-6729	605	4	e(n	e(n	PROPN
ejpam-6729	605	5	)	)	PUNCT
ejpam-6729	605	6	}	}	PUNCT
ejpam-6729	605	7	⊆	⊆	NUM
ejpam-6729	605	8	p(v	p(v	NOUN
ejpam-6729	605	9	′	′	NUM
ejpam-6729	605	10	)	)	PUNCT
ejpam-6729	605	11	\	\	NOUN
ejpam-6729	605	12	{	{	PUNCT
ejpam-6729	605	13	∅	∅	NOUN
ejpam-6729	605	14	}	}	PUNCT
ejpam-6729	605	15	.	.	PUNCT
ejpam-6729	606	1	t.	t.	PROPN
ejpam-6729	606	2	fujita	fujita	PROPN
ejpam-6729	606	3	,	,	PUNCT
ejpam-6729	606	4	f.	f.	PROPN
ejpam-6729	606	5	smarandache	smarandache	PROPN
ejpam-6729	606	6	/	/	SYM
ejpam-6729	606	7	eur	eur	PROPN
ejpam-6729	606	8	.	.	PUNCT
ejpam-6729	607	1	j.	j.	PROPN
ejpam-6729	607	2	pure	pure	PROPN
ejpam-6729	607	3	appl	appl	PROPN
ejpam-6729	607	4	.	.	PROPN
ejpam-6729	607	5	math	math	PROPN
ejpam-6729	607	6	,	,	PUNCT
ejpam-6729	607	7	18	18	NUM
ejpam-6729	607	8	(	(	PUNCT
ejpam-6729	607	9	4	4	NUM
ejpam-6729	607	10	)	)	PUNCT
ejpam-6729	607	11	(	(	PUNCT
ejpam-6729	607	12	2025	2025	NUM
ejpam-6729	607	13	)	)	PUNCT
ejpam-6729	607	14	,	,	PUNCT
ejpam-6729	607	15	6729	6729	NUM
ejpam-6729	607	16	27	27	NUM
ejpam-6729	607	17	of	of	ADP
ejpam-6729	607	18	36	36	NUM
ejpam-6729	607	19	the	the	DET
ejpam-6729	607	20	inclusion	inclusion	NOUN
ejpam-6729	607	21	v	v	ADP
ejpam-6729	607	22	′	′	NUM
ejpam-6729	607	23	⊆	⊆	X
ejpam-6729	607	24	pn−1(v0	pn−1(v0	PROPN
ejpam-6729	607	25	)	)	PUNCT
ejpam-6729	607	26	is	be	AUX
ejpam-6729	607	27	immediate	immediate	ADJ
ejpam-6729	607	28	from	from	ADP
ejpam-6729	607	29	the	the	DET
ejpam-6729	607	30	codomain	codomain	NOUN
ejpam-6729	607	31	of	of	ADP
ejpam-6729	607	32	ϕv	ϕv	PROPN
ejpam-6729	607	33	.	.	PUNCT
ejpam-6729	608	1	nonemptiness	nonemptiness	NOUN
ejpam-6729	608	2	of	of	ADP
ejpam-6729	608	3	each	each	DET
ejpam-6729	608	4	ϕe(e	ϕe(e	NUM
ejpam-6729	608	5	)	)	PUNCT
ejpam-6729	608	6	holds	hold	VERB
ejpam-6729	608	7	because	because	SCONJ
ejpam-6729	608	8	e	e	PROPN
ejpam-6729	608	9	6=	6=	NUM
ejpam-6729	608	10	∅	∅	NOUN
ejpam-6729	608	11	and	and	CCONJ
ejpam-6729	608	12	ϕv	ϕv	ADV
ejpam-6729	608	13	is	be	AUX
ejpam-6729	608	14	total	total	ADJ
ejpam-6729	608	15	.	.	PUNCT
ejpam-6729	609	1	by	by	ADP
ejpam-6729	609	2	the	the	DET
ejpam-6729	609	3	assumed	assume	VERB
ejpam-6729	609	4	edge	edge	NOUN
ejpam-6729	609	5	-	-	PUNCT
ejpam-6729	609	6	label	label	NOUN
ejpam-6729	609	7	compatibility	compatibility	NOUN
ejpam-6729	609	8	ϕe(e	ϕe(e	NOUN
ejpam-6729	609	9	)	)	PUNCT
ejpam-6729	609	10	=	=	PRON
ejpam-6729	609	11	ϕe(e	ϕe(e	NUM
ejpam-6729	609	12	′	′	NUM
ejpam-6729	609	13	)	)	PUNCT
ejpam-6729	610	1	=	=	VERB
ejpam-6729	610	2	⇒	⇒	NOUN
ejpam-6729	610	3	λ(e	λ(e	ADJ
ejpam-6729	610	4	)	)	PUNCT
ejpam-6729	610	5	=	=	PUNCT
ejpam-6729	610	6	λ(e′	λ(e′	NUM
ejpam-6729	610	7	)	)	PUNCT
ejpam-6729	610	8	,	,	PUNCT
ejpam-6729	610	9	the	the	DET
ejpam-6729	610	10	map	map	NOUN
ejpam-6729	610	11	λ′	λ′	X
ejpam-6729	610	12	:	:	PUNCT
ejpam-6729	610	13	e′	e′	X
ejpam-6729	610	14	→	→	SYM
ejpam-6729	610	15	σ	σ	PROPN
ejpam-6729	610	16	,	,	PUNCT
ejpam-6729	610	17	λ′(ϕe(e	λ′(ϕe(e	NOUN
ejpam-6729	610	18	)	)	PUNCT
ejpam-6729	610	19	)	)	PUNCT
ejpam-6729	610	20	:	:	PUNCT
ejpam-6729	611	1	=	=	PUNCT
ejpam-6729	611	2	λ(e	λ(e	VERB
ejpam-6729	611	3	)	)	PUNCT
ejpam-6729	611	4	is	be	AUX
ejpam-6729	611	5	well	well	ADV
ejpam-6729	611	6	-	-	PUNCT
ejpam-6729	611	7	defined	define	VERB
ejpam-6729	611	8	.	.	PUNCT
ejpam-6729	612	1	by	by	ADP
ejpam-6729	612	2	the	the	DET
ejpam-6729	612	3	assumed	assume	VERB
ejpam-6729	612	4	property	property	NOUN
ejpam-6729	612	5	compatibility	compatibility	NOUN
ejpam-6729	612	6	(	(	PUNCT
ejpam-6729	612	7	for	for	ADP
ejpam-6729	612	8	both	both	DET
ejpam-6729	612	9	vertices	vertex	NOUN
ejpam-6729	612	10	and	and	CCONJ
ejpam-6729	612	11	edges	edge	NOUN
ejpam-6729	612	12	)	)	PUNCT
ejpam-6729	612	13	ϕv	ϕv	ADP
ejpam-6729	612	14	(	(	PUNCT
ejpam-6729	612	15	v	v	NOUN
ejpam-6729	612	16	)	)	PUNCT
ejpam-6729	612	17	=	=	PUNCT
ejpam-6729	612	18	ϕv	ϕv	PROPN
ejpam-6729	612	19	(	(	PUNCT
ejpam-6729	612	20	v	v	NOUN
ejpam-6729	612	21	′	′	NOUN
ejpam-6729	612	22	)	)	PUNCT
ejpam-6729	613	1	=	=	NOUN
ejpam-6729	613	2	⇒	⇒	NOUN
ejpam-6729	613	3	µ(v	µ(v	PROPN
ejpam-6729	613	4	,	,	PUNCT
ejpam-6729	613	5	k	k	NOUN
ejpam-6729	613	6	)	)	PUNCT
ejpam-6729	613	7	=	=	SYM
ejpam-6729	613	8	µ(v′	µ(v′	PROPN
ejpam-6729	613	9	,	,	PUNCT
ejpam-6729	613	10	k	k	NOUN
ejpam-6729	613	11	)	)	PUNCT
ejpam-6729	613	12	,	,	PUNCT
ejpam-6729	613	13	ϕe(e	ϕe(e	NUM
ejpam-6729	613	14	)	)	PUNCT
ejpam-6729	613	15	=	=	PRON
ejpam-6729	613	16	ϕe(e	ϕe(e	NUM
ejpam-6729	613	17	′	′	NUM
ejpam-6729	613	18	)	)	PUNCT
ejpam-6729	614	1	=	=	NOUN
ejpam-6729	614	2	⇒	⇒	PROPN
ejpam-6729	614	3	µ(e	µ(e	PROPN
ejpam-6729	614	4	,	,	PUNCT
ejpam-6729	614	5	k	k	NOUN
ejpam-6729	614	6	)	)	PUNCT
ejpam-6729	614	7	=	=	PUNCT
ejpam-6729	614	8	µ(e′	µ(e′	PROPN
ejpam-6729	614	9	,	,	PUNCT
ejpam-6729	614	10	k	k	NOUN
ejpam-6729	614	11	)	)	PUNCT
ejpam-6729	614	12	,	,	PUNCT
ejpam-6729	614	13	the	the	DET
ejpam-6729	614	14	map	map	NOUN
ejpam-6729	614	15	µ′	µ′	NOUN
ejpam-6729	614	16	:	:	PUNCT
ejpam-6729	614	17	(	(	PUNCT
ejpam-6729	614	18	v	v	X
ejpam-6729	614	19	′	′	NUM
ejpam-6729	614	20	∪	∪	X
ejpam-6729	614	21	e′)×k	e′)×k	NOUN
ejpam-6729	614	22	→	→	SYM
ejpam-6729	614	23	s	s	NOUN
ejpam-6729	614	24	∪	∪	X
ejpam-6729	614	25	{	{	PUNCT
ejpam-6729	614	26	⊥	⊥	NOUN
ejpam-6729	614	27	}	}	PUNCT
ejpam-6729	614	28	defined	define	VERB
ejpam-6729	614	29	by	by	ADP
ejpam-6729	614	30	µ′(ϕv	µ′(ϕv	PROPN
ejpam-6729	614	31	(	(	PUNCT
ejpam-6729	614	32	v	v	NOUN
ejpam-6729	614	33	)	)	PUNCT
ejpam-6729	614	34	,	,	PUNCT
ejpam-6729	614	35	k	k	NOUN
ejpam-6729	614	36	)	)	PUNCT
ejpam-6729	614	37	:	:	PUNCT
ejpam-6729	614	38	=	=	SYM
ejpam-6729	614	39	µ(v	µ(v	PROPN
ejpam-6729	614	40	,	,	PUNCT
ejpam-6729	614	41	k	k	NOUN
ejpam-6729	614	42	)	)	PUNCT
ejpam-6729	614	43	,	,	PUNCT
ejpam-6729	614	44	µ′(ϕe(e	µ′(ϕe(e	PROPN
ejpam-6729	614	45	)	)	PUNCT
ejpam-6729	614	46	,	,	PUNCT
ejpam-6729	614	47	k	k	NOUN
ejpam-6729	614	48	)	)	PUNCT
ejpam-6729	614	49	:	:	PUNCT
ejpam-6729	614	50	=	=	SYM
ejpam-6729	614	51	µ(e	µ(e	PROPN
ejpam-6729	614	52	,	,	PUNCT
ejpam-6729	614	53	k	k	NOUN
ejpam-6729	614	54	)	)	PUNCT
ejpam-6729	614	55	is	be	AUX
ejpam-6729	614	56	well	well	ADV
ejpam-6729	614	57	-	-	PUNCT
ejpam-6729	614	58	defined	define	VERB
ejpam-6729	614	59	.	.	PUNCT
ejpam-6729	615	1	consequently	consequently	ADV
ejpam-6729	615	2	(	(	PUNCT
ejpam-6729	615	3	v	v	NOUN
ejpam-6729	615	4	′	′	NUM
ejpam-6729	615	5	,	,	PUNCT
ejpam-6729	615	6	e′	e′	PROPN
ejpam-6729	615	7	,	,	PUNCT
ejpam-6729	615	8	λ′	λ′	NOUN
ejpam-6729	615	9	,	,	PUNCT
ejpam-6729	615	10	µ′	µ′	NUM
ejpam-6729	615	11	)	)	PUNCT
ejpam-6729	615	12	is	be	AUX
ejpam-6729	615	13	a	a	DET
ejpam-6729	615	14	property	property	NOUN
ejpam-6729	615	15	(	(	PUNCT
ejpam-6729	615	16	n−	n−	NOUN
ejpam-6729	615	17	1)-superhypergraph	1)-superhypergraph	VERB
ejpam-6729	615	18	.	.	PUNCT
ejpam-6729	616	1	induction	induction	NOUN
ejpam-6729	616	2	step	step	NOUN
ejpam-6729	616	3	.	.	PUNCT
ejpam-6729	617	1	assume	assume	VERB
ejpam-6729	617	2	the	the	DET
ejpam-6729	617	3	claim	claim	NOUN
ejpam-6729	617	4	holds	hold	VERB
ejpam-6729	617	5	for	for	ADP
ejpam-6729	617	6	some	some	DET
ejpam-6729	617	7	k	k	NOUN
ejpam-6729	617	8	with	with	ADP
ejpam-6729	617	9	1	1	NUM
ejpam-6729	617	10	≤	≤	NUM
ejpam-6729	617	11	k	k	X
ejpam-6729	617	12	<	<	X
ejpam-6729	617	13	n	n	CCONJ
ejpam-6729	617	14	:	:	PUNCT
ejpam-6729	617	15	that	that	PRON
ejpam-6729	617	16	is	be	AUX
ejpam-6729	617	17	,	,	PUNCT
ejpam-6729	617	18	h(n−k	h(n−k	PROPN
ejpam-6729	617	19	)	)	PUNCT
ejpam-6729	618	1	=	=	PRON
ejpam-6729	618	2	(	(	PUNCT
ejpam-6729	618	3	v	v	NOUN
ejpam-6729	618	4	(	(	PUNCT
ejpam-6729	618	5	n−k	n−k	NOUN
ejpam-6729	618	6	)	)	PUNCT
ejpam-6729	618	7	,	,	PUNCT
ejpam-6729	618	8	e(n−k	e(n−k	PROPN
ejpam-6729	618	9	)	)	PUNCT
ejpam-6729	618	10	,	,	PUNCT
ejpam-6729	618	11	λ(k	λ(k	PROPN
ejpam-6729	618	12	)	)	PUNCT
ejpam-6729	618	13	,	,	PUNCT
ejpam-6729	618	14	µ(k	µ(k	NOUN
ejpam-6729	618	15	)	)	PUNCT
ejpam-6729	618	16	)	)	PUNCT
ejpam-6729	618	17	=	=	PRON
ejpam-6729	619	1	(	(	PUNCT
ejpam-6729	619	2	ϕ	ϕ	X
ejpam-6729	619	3	(	(	PUNCT
ejpam-6729	619	4	k	k	NOUN
ejpam-6729	619	5	)	)	PUNCT
ejpam-6729	619	6	v	v	ADP
ejpam-6729	620	1	[	[	X
ejpam-6729	620	2	v	v	X
ejpam-6729	620	3	(	(	PUNCT
ejpam-6729	620	4	n	n	CCONJ
ejpam-6729	620	5	)	)	PUNCT
ejpam-6729	620	6	]	]	PUNCT
ejpam-6729	620	7	,	,	PUNCT
ejpam-6729	620	8	{	{	PUNCT
ejpam-6729	620	9	ϕ(k	ϕ(k	NOUN
ejpam-6729	620	10	)	)	PUNCT
ejpam-6729	620	11	e	e	NOUN
ejpam-6729	620	12	(	(	PUNCT
ejpam-6729	620	13	e	e	NOUN
ejpam-6729	620	14	)	)	PUNCT
ejpam-6729	620	15	|	|	ADV
ejpam-6729	620	16	e	e	X
ejpam-6729	620	17	∈	∈	PROPN
ejpam-6729	620	18	e(n	e(n	PROPN
ejpam-6729	620	19	)	)	PUNCT
ejpam-6729	620	20	}	}	PUNCT
ejpam-6729	620	21	,	,	PUNCT
ejpam-6729	620	22	λ(k	λ(k	PROPN
ejpam-6729	620	23	)	)	PUNCT
ejpam-6729	620	24	,	,	PUNCT
ejpam-6729	620	25	µ(k	µ(k	NOUN
ejpam-6729	620	26	)	)	PUNCT
ejpam-6729	620	27	)	)	PUNCT
ejpam-6729	620	28	is	be	AUX
ejpam-6729	620	29	a	a	DET
ejpam-6729	620	30	property	property	NOUN
ejpam-6729	620	31	(	(	PUNCT
ejpam-6729	620	32	n−	n−	NOUN
ejpam-6729	620	33	k)-superhypergraph	k)-superhypergraph	NOUN
ejpam-6729	620	34	.	.	PUNCT
ejpam-6729	621	1	by	by	ADP
ejpam-6729	621	2	the	the	DET
ejpam-6729	621	3	hypothesis	hypothesis	NOUN
ejpam-6729	621	4	“	"	PUNCT
ejpam-6729	621	5	label	label	NOUN
ejpam-6729	621	6	/	/	SYM
ejpam-6729	621	7	property	property	NOUN
ejpam-6729	621	8	compatibilities	compatibility	NOUN
ejpam-6729	621	9	hold	hold	VERB
ejpam-6729	621	10	at	at	ADP
ejpam-6729	621	11	each	each	DET
ejpam-6729	621	12	intermediate	intermediate	ADJ
ejpam-6729	621	13	stage	stage	NOUN
ejpam-6729	621	14	”	"	PUNCT
ejpam-6729	621	15	,	,	PUNCT
ejpam-6729	621	16	we	we	PRON
ejpam-6729	621	17	have	have	VERB
ejpam-6729	621	18	,	,	PUNCT
ejpam-6729	621	19	for	for	ADP
ejpam-6729	621	20	the	the	DET
ejpam-6729	621	21	(	(	PUNCT
ejpam-6729	621	22	k+1)-st	k+1)-st	NOUN
ejpam-6729	621	23	stage	stage	NOUN
ejpam-6729	621	24	,	,	PUNCT
ejpam-6729	621	25	the	the	DET
ejpam-6729	621	26	compatibilities	compatibility	NOUN
ejpam-6729	621	27	on	on	ADP
ejpam-6729	621	28	h(n−k	h(n−k	PROPN
ejpam-6729	621	29	):	):	PUNCT
ejpam-6729	621	30	ϕv	ϕv	PROPN
ejpam-6729	621	31	(	(	PUNCT
ejpam-6729	621	32	x	x	X
ejpam-6729	621	33	)	)	PUNCT
ejpam-6729	621	34	=	=	SYM
ejpam-6729	622	1	ϕv	ϕv	PROPN
ejpam-6729	622	2	(	(	PUNCT
ejpam-6729	622	3	y	y	NOUN
ejpam-6729	622	4	)	)	PUNCT
ejpam-6729	622	5	=	=	NOUN
ejpam-6729	622	6	⇒	⇒	NOUN
ejpam-6729	622	7	µ(k)(x	µ(k)(x	PROPN
ejpam-6729	622	8	,	,	PUNCT
ejpam-6729	622	9	·	·	PUNCT
ejpam-6729	622	10	)	)	PUNCT
ejpam-6729	622	11	=	=	PUNCT
ejpam-6729	622	12	µ(k)(y	µ(k)(y	PROPN
ejpam-6729	622	13	,	,	PUNCT
ejpam-6729	622	14	·	·	PUNCT
ejpam-6729	622	15	)	)	PUNCT
ejpam-6729	622	16	,	,	PUNCT
ejpam-6729	622	17	ϕe(a	ϕe(a	NUM
ejpam-6729	622	18	)	)	PUNCT
ejpam-6729	622	19	=	=	NOUN
ejpam-6729	622	20	ϕe(b	ϕe(b	X
ejpam-6729	622	21	)	)	PUNCT
ejpam-6729	623	1	=	=	NOUN
ejpam-6729	623	2	⇒	⇒	NOUN
ejpam-6729	623	3	λ(k)(a	λ(k)(a	ADV
ejpam-6729	623	4	)	)	PUNCT
ejpam-6729	623	5	=	=	SYM
ejpam-6729	623	6	λ(k)(b	λ(k)(b	PUNCT
ejpam-6729	623	7	)	)	PUNCT
ejpam-6729	623	8	,	,	PUNCT
ejpam-6729	623	9	µ(k)(a	µ(k)(a	NUM
ejpam-6729	623	10	,	,	PUNCT
ejpam-6729	623	11	·	·	PUNCT
ejpam-6729	623	12	)	)	PUNCT
ejpam-6729	623	13	=	=	SYM
ejpam-6729	623	14	µ(k)(b	µ(k)(b	PROPN
ejpam-6729	623	15	,	,	PUNCT
ejpam-6729	623	16	·	·	PUNCT
ejpam-6729	623	17	)	)	PUNCT
ejpam-6729	623	18	.	.	PUNCT
ejpam-6729	624	1	applying	apply	VERB
ejpam-6729	624	2	the	the	DET
ejpam-6729	624	3	base	base	NOUN
ejpam-6729	624	4	case	case	NOUN
ejpam-6729	624	5	to	to	ADP
ejpam-6729	624	6	h(n−k	h(n−k	PROPN
ejpam-6729	624	7	)	)	PUNCT
ejpam-6729	624	8	yields	yield	VERB
ejpam-6729	624	9	a	a	DET
ejpam-6729	624	10	property	property	NOUN
ejpam-6729	624	11	(	(	PUNCT
ejpam-6729	624	12	n−	n−	NOUN
ejpam-6729	624	13	k	k	X
ejpam-6729	624	14	−	−	PROPN
ejpam-6729	624	15	1)-superhypergraph	1)-superhypergraph	NUM
ejpam-6729	624	16	ĥ	ĥ	X
ejpam-6729	625	1	=	=	PUNCT
ejpam-6729	626	1	(	(	PUNCT
ejpam-6729	626	2	ϕv	ϕv	ADP
ejpam-6729	626	3	[	[	X
ejpam-6729	626	4	v	v	X
ejpam-6729	626	5	(	(	PUNCT
ejpam-6729	626	6	n−k	n−k	NOUN
ejpam-6729	626	7	)	)	PUNCT
ejpam-6729	626	8	]	]	PUNCT
ejpam-6729	626	9	,	,	PUNCT
ejpam-6729	626	10	{	{	PUNCT
ejpam-6729	626	11	ϕe(e	ϕe(e	NOUN
ejpam-6729	626	12	?	?	PUNCT
ejpam-6729	626	13	)	)	PUNCT
ejpam-6729	627	1	|	|	ADV
ejpam-6729	627	2	e	e	X
ejpam-6729	627	3	?	?	PUNCT
ejpam-6729	627	4	∈	∈	PROPN
ejpam-6729	627	5	e(n−k	e(n−k	PROPN
ejpam-6729	627	6	)	)	PUNCT
ejpam-6729	627	7	}	}	PUNCT
ejpam-6729	627	8	,	,	PUNCT
ejpam-6729	627	9	λ̂	λ̂	X
ejpam-6729	627	10	,	,	PUNCT
ejpam-6729	627	11	µ̂	µ̂	PRON
ejpam-6729	627	12	)	)	PUNCT
ejpam-6729	627	13	.	.	PUNCT
ejpam-6729	628	1	using	use	VERB
ejpam-6729	628	2	v	v	NOUN
ejpam-6729	628	3	(	(	PUNCT
ejpam-6729	628	4	n−k	n−k	NOUN
ejpam-6729	628	5	)	)	PUNCT
ejpam-6729	629	1	=	=	SYM
ejpam-6729	629	2	ϕ	ϕ	X
ejpam-6729	629	3	(	(	PUNCT
ejpam-6729	629	4	k	k	NOUN
ejpam-6729	629	5	)	)	PUNCT
ejpam-6729	629	6	v	v	ADP
ejpam-6729	630	1	[	[	X
ejpam-6729	630	2	v	v	X
ejpam-6729	630	3	(	(	PUNCT
ejpam-6729	630	4	n	n	CCONJ
ejpam-6729	630	5	)	)	PUNCT
ejpam-6729	630	6	]	]	PUNCT
ejpam-6729	630	7	and	and	CCONJ
ejpam-6729	630	8	e(n−k	e(n−k	NOUN
ejpam-6729	630	9	)	)	PUNCT
ejpam-6729	630	10	=	=	PRON
ejpam-6729	630	11	{	{	PUNCT
ejpam-6729	630	12	ϕ(k	ϕ(k	PROPN
ejpam-6729	630	13	)	)	PUNCT
ejpam-6729	630	14	e	e	NOUN
ejpam-6729	630	15	(	(	PUNCT
ejpam-6729	630	16	e	e	NOUN
ejpam-6729	630	17	)	)	PUNCT
ejpam-6729	630	18	|	|	ADV
ejpam-6729	630	19	e	e	X
ejpam-6729	630	20	∈	∈	PROPN
ejpam-6729	630	21	e(n	e(n	PROPN
ejpam-6729	630	22	)	)	PUNCT
ejpam-6729	630	23	}	}	PUNCT
ejpam-6729	630	24	,	,	PUNCT
ejpam-6729	630	25	we	we	PRON
ejpam-6729	630	26	compute	compute	VERB
ejpam-6729	630	27	ϕv	ϕv	ADP
ejpam-6729	631	1	[	[	X
ejpam-6729	631	2	v	v	X
ejpam-6729	631	3	(	(	PUNCT
ejpam-6729	631	4	n−k	n−k	NOUN
ejpam-6729	631	5	)	)	PUNCT
ejpam-6729	631	6	]	]	PUNCT
ejpam-6729	632	1	=	=	PUNCT
ejpam-6729	632	2	ϕv	ϕv	PROPN
ejpam-6729	632	3	[	[	PUNCT
ejpam-6729	632	4	ϕ	ϕ	X
ejpam-6729	632	5	(	(	PUNCT
ejpam-6729	632	6	k	k	NOUN
ejpam-6729	632	7	)	)	PUNCT
ejpam-6729	632	8	v	v	ADP
ejpam-6729	633	1	[	[	X
ejpam-6729	633	2	v	v	X
ejpam-6729	633	3	(	(	PUNCT
ejpam-6729	633	4	n	n	CCONJ
ejpam-6729	633	5	)	)	PUNCT
ejpam-6729	633	6	]	]	PUNCT
ejpam-6729	633	7	]	]	PUNCT
ejpam-6729	634	1	=	=	SYM
ejpam-6729	634	2	ϕ	ϕ	X
ejpam-6729	634	3	(	(	PUNCT
ejpam-6729	634	4	k+1	k+1	NOUN
ejpam-6729	634	5	)	)	PUNCT
ejpam-6729	634	6	v	v	NOUN
ejpam-6729	634	7	[	[	X
ejpam-6729	634	8	v	v	X
ejpam-6729	634	9	(	(	PUNCT
ejpam-6729	634	10	n	n	CCONJ
ejpam-6729	634	11	)	)	PUNCT
ejpam-6729	634	12	]	]	PUNCT
ejpam-6729	634	13	,	,	PUNCT
ejpam-6729	634	14	and	and	CCONJ
ejpam-6729	634	15	for	for	ADP
ejpam-6729	634	16	each	each	DET
ejpam-6729	634	17	e	e	PROPN
ejpam-6729	634	18	∈	∈	PROPN
ejpam-6729	634	19	e(n	e(n	PROPN
ejpam-6729	634	20	)	)	PUNCT
ejpam-6729	634	21	,	,	PUNCT
ejpam-6729	634	22	ϕe	ϕe	PROPN
ejpam-6729	634	23	(	(	PUNCT
ejpam-6729	634	24	ϕ	ϕ	X
ejpam-6729	634	25	(	(	PUNCT
ejpam-6729	634	26	k	k	NOUN
ejpam-6729	634	27	)	)	PUNCT
ejpam-6729	634	28	e	e	NOUN
ejpam-6729	634	29	(	(	PUNCT
ejpam-6729	634	30	e	e	NOUN
ejpam-6729	634	31	)	)	PUNCT
ejpam-6729	634	32	)	)	PUNCT
ejpam-6729	635	1	=	=	PRON
ejpam-6729	635	2	{	{	PUNCT
ejpam-6729	635	3	ϕv	ϕv	X
ejpam-6729	635	4	(	(	PUNCT
ejpam-6729	635	5	w	w	NOUN
ejpam-6729	635	6	)	)	PUNCT
ejpam-6729	635	7	∣∣	∣∣	X
ejpam-6729	635	8	w	w	PROPN
ejpam-6729	635	9	∈	∈	PROPN
ejpam-6729	635	10	{	{	PUNCT
ejpam-6729	635	11	ϕ(k	ϕ(k	PROPN
ejpam-6729	635	12	)	)	PUNCT
ejpam-6729	635	13	v	v	NOUN
ejpam-6729	635	14	(	(	PUNCT
ejpam-6729	635	15	v	v	NOUN
ejpam-6729	635	16	)	)	PUNCT
ejpam-6729	635	17	|	|	ADV
ejpam-6729	635	18	v	v	ADP
ejpam-6729	635	19	∈	∈	NOUN
ejpam-6729	635	20	e	e	NOUN
ejpam-6729	635	21	}	}	PUNCT
ejpam-6729	635	22	}	}	PUNCT
ejpam-6729	635	23	=	=	SYM
ejpam-6729	635	24	{	{	PUNCT
ejpam-6729	635	25	ϕ	ϕ	X
ejpam-6729	635	26	(	(	PUNCT
ejpam-6729	635	27	k+1	k+1	NOUN
ejpam-6729	635	28	)	)	PUNCT
ejpam-6729	635	29	v	v	NOUN
ejpam-6729	635	30	(	(	PUNCT
ejpam-6729	635	31	v	v	NOUN
ejpam-6729	635	32	)	)	PUNCT
ejpam-6729	635	33	∣∣	∣∣	X
ejpam-6729	635	34	v	v	ADP
ejpam-6729	635	35	∈	∈	NOUN
ejpam-6729	635	36	e	e	NOUN
ejpam-6729	635	37	}	}	PUNCT
ejpam-6729	635	38	=	=	SYM
ejpam-6729	635	39	ϕ	ϕ	X
ejpam-6729	635	40	(	(	PUNCT
ejpam-6729	635	41	k+1	k+1	NOUN
ejpam-6729	635	42	)	)	PUNCT
ejpam-6729	635	43	e	e	NOUN
ejpam-6729	635	44	(	(	PUNCT
ejpam-6729	635	45	e	e	NOUN
ejpam-6729	635	46	)	)	PUNCT
ejpam-6729	635	47	.	.	PUNCT
ejpam-6729	636	1	hence	hence	ADV
ejpam-6729	636	2	ĥ	ĥ	PROPN
ejpam-6729	636	3	coincides	coincide	VERB
ejpam-6729	636	4	with	with	ADP
ejpam-6729	636	5	(	(	PUNCT
ejpam-6729	636	6	ϕ	ϕ	X
ejpam-6729	636	7	(	(	PUNCT
ejpam-6729	636	8	k+1	k+1	NOUN
ejpam-6729	636	9	)	)	PUNCT
ejpam-6729	636	10	v	v	NOUN
ejpam-6729	637	1	[	[	X
ejpam-6729	637	2	v	v	X
ejpam-6729	637	3	(	(	PUNCT
ejpam-6729	637	4	n	n	CCONJ
ejpam-6729	637	5	)	)	PUNCT
ejpam-6729	637	6	]	]	PUNCT
ejpam-6729	637	7	,	,	PUNCT
ejpam-6729	637	8	{	{	PUNCT
ejpam-6729	637	9	ϕ(k+1	ϕ(k+1	NUM
ejpam-6729	637	10	)	)	PUNCT
ejpam-6729	637	11	e	e	NOUN
ejpam-6729	637	12	(	(	PUNCT
ejpam-6729	637	13	e	e	NOUN
ejpam-6729	637	14	)	)	PUNCT
ejpam-6729	637	15	|	|	ADV
ejpam-6729	637	16	e	e	X
ejpam-6729	637	17	∈	∈	PROPN
ejpam-6729	637	18	e(n	e(n	PROPN
ejpam-6729	637	19	)	)	PUNCT
ejpam-6729	637	20	}	}	PUNCT
ejpam-6729	637	21	,	,	PUNCT
ejpam-6729	637	22	λ(k+1	λ(k+1	NOUN
ejpam-6729	637	23	)	)	PUNCT
ejpam-6729	637	24	,	,	PUNCT
ejpam-6729	637	25	µ(k+1	µ(k+1	PUNCT
ejpam-6729	637	26	)	)	PUNCT
ejpam-6729	637	27	)	)	PUNCT
ejpam-6729	637	28	,	,	PUNCT
ejpam-6729	637	29	where	where	SCONJ
ejpam-6729	637	30	λ(k+1	λ(k+1	NOUN
ejpam-6729	637	31	)	)	PUNCT
ejpam-6729	637	32	and	and	CCONJ
ejpam-6729	637	33	µ(k+1	µ(k+1	NOUN
ejpam-6729	637	34	)	)	PUNCT
ejpam-6729	637	35	are	be	AUX
ejpam-6729	637	36	the	the	DET
ejpam-6729	637	37	induced	induce	VERB
ejpam-6729	637	38	maps	map	NOUN
ejpam-6729	637	39	defined	define	VERB
ejpam-6729	637	40	by	by	ADP
ejpam-6729	637	41	λ(k+1	λ(k+1	NOUN
ejpam-6729	637	42	)	)	PUNCT
ejpam-6729	637	43	(	(	PUNCT
ejpam-6729	637	44	ϕ	ϕ	X
ejpam-6729	637	45	(	(	PUNCT
ejpam-6729	637	46	k+1	k+1	NOUN
ejpam-6729	637	47	)	)	PUNCT
ejpam-6729	637	48	e	e	NOUN
ejpam-6729	637	49	(	(	PUNCT
ejpam-6729	637	50	e	e	NOUN
ejpam-6729	637	51	)	)	PUNCT
ejpam-6729	637	52	)	)	PUNCT
ejpam-6729	637	53	:	:	PUNCT
ejpam-6729	637	54	=	=	PUNCT
ejpam-6729	637	55	λ(e	λ(e	PROPN
ejpam-6729	637	56	)	)	PUNCT
ejpam-6729	637	57	,	,	PUNCT
ejpam-6729	637	58	t.	t.	PROPN
ejpam-6729	637	59	fujita	fujita	PROPN
ejpam-6729	637	60	,	,	PUNCT
ejpam-6729	637	61	f.	f.	PROPN
ejpam-6729	637	62	smarandache	smarandache	PROPN
ejpam-6729	637	63	/	/	SYM
ejpam-6729	637	64	eur	eur	PROPN
ejpam-6729	637	65	.	.	PUNCT
ejpam-6729	638	1	j.	j.	PROPN
ejpam-6729	638	2	pure	pure	PROPN
ejpam-6729	638	3	appl	appl	PROPN
ejpam-6729	638	4	.	.	PROPN
ejpam-6729	638	5	math	math	PROPN
ejpam-6729	638	6	,	,	PUNCT
ejpam-6729	638	7	18	18	NUM
ejpam-6729	638	8	(	(	PUNCT
ejpam-6729	638	9	4	4	NUM
ejpam-6729	638	10	)	)	PUNCT
ejpam-6729	638	11	(	(	PUNCT
ejpam-6729	638	12	2025	2025	NUM
ejpam-6729	638	13	)	)	PUNCT
ejpam-6729	638	14	,	,	PUNCT
ejpam-6729	638	15	6729	6729	NUM
ejpam-6729	638	16	28	28	NUM
ejpam-6729	638	17	of	of	ADP
ejpam-6729	638	18	36	36	NUM
ejpam-6729	638	19	µ(k+1	µ(k+1	NOUN
ejpam-6729	638	20	)	)	PUNCT
ejpam-6729	638	21	(	(	PUNCT
ejpam-6729	638	22	ϕ	ϕ	X
ejpam-6729	638	23	(	(	PUNCT
ejpam-6729	638	24	k+1	k+1	NOUN
ejpam-6729	638	25	)	)	PUNCT
ejpam-6729	638	26	v	v	NOUN
ejpam-6729	638	27	(	(	PUNCT
ejpam-6729	638	28	v	v	NOUN
ejpam-6729	638	29	)	)	PUNCT
ejpam-6729	638	30	,	,	PUNCT
ejpam-6729	638	31	k0	k0	PROPN
ejpam-6729	638	32	)	)	PUNCT
ejpam-6729	638	33	:	:	PUNCT
ejpam-6729	638	34	=	=	SYM
ejpam-6729	638	35	µ(v	µ(v	PROPN
ejpam-6729	638	36	,	,	PUNCT
ejpam-6729	638	37	k0	k0	PROPN
ejpam-6729	638	38	)	)	PUNCT
ejpam-6729	638	39	,	,	PUNCT
ejpam-6729	638	40	µ(k+1	µ(k+1	PUNCT
ejpam-6729	638	41	)	)	PUNCT
ejpam-6729	638	42	(	(	PUNCT
ejpam-6729	638	43	ϕ	ϕ	X
ejpam-6729	638	44	(	(	PUNCT
ejpam-6729	638	45	k+1	k+1	NOUN
ejpam-6729	638	46	)	)	PUNCT
ejpam-6729	638	47	e	e	NOUN
ejpam-6729	638	48	(	(	PUNCT
ejpam-6729	638	49	e	e	NOUN
ejpam-6729	638	50	)	)	PUNCT
ejpam-6729	638	51	,	,	PUNCT
ejpam-6729	638	52	k0	k0	PROPN
ejpam-6729	638	53	)	)	PUNCT
ejpam-6729	638	54	:	:	PUNCT
ejpam-6729	638	55	=	=	SYM
ejpam-6729	638	56	µ(e	µ(e	PROPN
ejpam-6729	638	57	,	,	PUNCT
ejpam-6729	638	58	k0	k0	PROPN
ejpam-6729	638	59	)	)	PUNCT
ejpam-6729	638	60	,	,	PUNCT
ejpam-6729	638	61	which	which	PRON
ejpam-6729	638	62	are	be	AUX
ejpam-6729	638	63	well	well	ADV
ejpam-6729	638	64	-	-	PUNCT
ejpam-6729	638	65	defined	define	VERB
ejpam-6729	638	66	by	by	ADP
ejpam-6729	638	67	the	the	DET
ejpam-6729	638	68	stated	state	VERB
ejpam-6729	638	69	compatibilities	compatibility	NOUN
ejpam-6729	638	70	at	at	ADP
ejpam-6729	638	71	each	each	DET
ejpam-6729	638	72	stage	stage	NOUN
ejpam-6729	638	73	.	.	PUNCT
ejpam-6729	639	1	thus	thus	ADV
ejpam-6729	639	2	the	the	DET
ejpam-6729	639	3	statement	statement	NOUN
ejpam-6729	639	4	holds	hold	VERB
ejpam-6729	639	5	for	for	ADP
ejpam-6729	639	6	k	k	PROPN
ejpam-6729	639	7	+	+	PROPN
ejpam-6729	639	8	1	1	X
ejpam-6729	639	9	.	.	PUNCT
ejpam-6729	639	10	by	by	ADP
ejpam-6729	639	11	induction	induction	NOUN
ejpam-6729	639	12	on	on	ADP
ejpam-6729	639	13	k	k	PROPN
ejpam-6729	639	14	,	,	PUNCT
ejpam-6729	639	15	the	the	DET
ejpam-6729	639	16	structure	structure	NOUN
ejpam-6729	639	17	h(n−k	h(n−k	NOUN
ejpam-6729	639	18	)	)	PUNCT
ejpam-6729	640	1	=	=	PRON
ejpam-6729	640	2	(	(	PUNCT
ejpam-6729	640	3	ϕ	ϕ	X
ejpam-6729	640	4	(	(	PUNCT
ejpam-6729	640	5	k	k	NOUN
ejpam-6729	640	6	)	)	PUNCT
ejpam-6729	640	7	v	v	ADP
ejpam-6729	640	8	[	[	X
ejpam-6729	640	9	v	v	X
ejpam-6729	640	10	(	(	PUNCT
ejpam-6729	640	11	n	n	CCONJ
ejpam-6729	640	12	)	)	PUNCT
ejpam-6729	640	13	]	]	PUNCT
ejpam-6729	640	14	,	,	PUNCT
ejpam-6729	640	15	{	{	PUNCT
ejpam-6729	640	16	ϕ(k	ϕ(k	NOUN
ejpam-6729	640	17	)	)	PUNCT
ejpam-6729	640	18	e	e	NOUN
ejpam-6729	640	19	(	(	PUNCT
ejpam-6729	640	20	e	e	NOUN
ejpam-6729	640	21	)	)	PUNCT
ejpam-6729	640	22	|	|	ADV
ejpam-6729	640	23	e	e	X
ejpam-6729	640	24	∈	∈	PROPN
ejpam-6729	640	25	e(n	e(n	PROPN
ejpam-6729	640	26	)	)	PUNCT
ejpam-6729	640	27	}	}	PUNCT
ejpam-6729	640	28	,	,	PUNCT
ejpam-6729	640	29	λ(k	λ(k	PROPN
ejpam-6729	640	30	)	)	PUNCT
ejpam-6729	640	31	,	,	PUNCT
ejpam-6729	640	32	µ(k	µ(k	NOUN
ejpam-6729	640	33	)	)	PUNCT
ejpam-6729	640	34	)	)	PUNCT
ejpam-6729	640	35	is	be	AUX
ejpam-6729	640	36	a	a	DET
ejpam-6729	640	37	property	property	NOUN
ejpam-6729	640	38	(	(	PUNCT
ejpam-6729	640	39	n−	n−	NOUN
ejpam-6729	640	40	k)-superhypergraph	k)-superhypergraph	PUNCT
ejpam-6729	640	41	for	for	ADP
ejpam-6729	640	42	all	all	PRON
ejpam-6729	640	43	1	1	NUM
ejpam-6729	640	44	≤	≤	NUM
ejpam-6729	640	45	k	k	PROPN
ejpam-6729	640	46	≤	≤	PROPN
ejpam-6729	640	47	n.	n.	PROPN
ejpam-6729	640	48	example	example	NOUN
ejpam-6729	640	49	15	15	NUM
ejpam-6729	640	50	(	(	PUNCT
ejpam-6729	640	51	iterated	iterated	ADJ
ejpam-6729	640	52	flattening	flattening	NOUN
ejpam-6729	640	53	:	:	PUNCT
ejpam-6729	640	54	a	a	DET
ejpam-6729	640	55	concrete	concrete	ADJ
ejpam-6729	640	56	3→1	3→1	NOUN
ejpam-6729	640	57	instance	instance	NOUN
ejpam-6729	640	58	with	with	ADP
ejpam-6729	640	59	k	k	PROPN
ejpam-6729	640	60	=	=	SYM
ejpam-6729	640	61	2	2	NUM
ejpam-6729	640	62	)	)	PUNCT
ejpam-6729	640	63	.	.	PUNCT
ejpam-6729	641	1	let	let	VERB
ejpam-6729	641	2	the	the	DET
ejpam-6729	641	3	base	base	NOUN
ejpam-6729	641	4	set	set	NOUN
ejpam-6729	641	5	be	be	AUX
ejpam-6729	641	6	v0	v0	NOUN
ejpam-6729	641	7	=	=	SYM
ejpam-6729	641	8	{	{	PUNCT
ejpam-6729	641	9	x	x	PROPN
ejpam-6729	641	10	,	,	PUNCT
ejpam-6729	641	11	y	y	NOUN
ejpam-6729	641	12	}	}	PUNCT
ejpam-6729	641	13	.	.	PUNCT
ejpam-6729	642	1	build	build	VERB
ejpam-6729	642	2	a	a	DET
ejpam-6729	642	3	property	property	NOUN
ejpam-6729	642	4	3	3	NUM
ejpam-6729	642	5	-	-	PUNCT
ejpam-6729	642	6	superhypergraph	superhypergraph	NOUN
ejpam-6729	642	7	h(3	h(3	NOUN
ejpam-6729	642	8	)	)	PUNCT
ejpam-6729	643	1	=	=	PRON
ejpam-6729	643	2	(	(	PUNCT
ejpam-6729	643	3	v	v	NOUN
ejpam-6729	643	4	(	(	PUNCT
ejpam-6729	643	5	3	3	NUM
ejpam-6729	643	6	)	)	PUNCT
ejpam-6729	643	7	,	,	PUNCT
ejpam-6729	643	8	e(3	e(3	PROPN
ejpam-6729	643	9	)	)	PUNCT
ejpam-6729	643	10	,	,	PUNCT
ejpam-6729	643	11	λ	λ	PROPN
ejpam-6729	643	12	,	,	PUNCT
ejpam-6729	643	13	µ	µ	NOUN
ejpam-6729	643	14	)	)	PUNCT
ejpam-6729	643	15	as	as	SCONJ
ejpam-6729	643	16	follows	follow	VERB
ejpam-6729	643	17	.	.	PUNCT
ejpam-6729	644	1	level–1	level–1	NOUN
ejpam-6729	644	2	carriers	carrier	NOUN
ejpam-6729	644	3	are	be	AUX
ejpam-6729	644	4	{	{	PUNCT
ejpam-6729	644	5	x	x	X
ejpam-6729	644	6	}	}	PUNCT
ejpam-6729	644	7	,	,	PUNCT
ejpam-6729	644	8	{	{	PUNCT
ejpam-6729	644	9	y	y	NOUN
ejpam-6729	644	10	}	}	PUNCT
ejpam-6729	644	11	,	,	PUNCT
ejpam-6729	644	12	{	{	PUNCT
ejpam-6729	644	13	x	x	NOUN
ejpam-6729	644	14	,	,	PUNCT
ejpam-6729	644	15	y	y	NOUN
ejpam-6729	644	16	}	}	PUNCT
ejpam-6729	644	17	.	.	PUNCT
ejpam-6729	645	1	define	define	VERB
ejpam-6729	645	2	two	two	NUM
ejpam-6729	645	3	level–2	level–2	PROPN
ejpam-6729	645	4	carriers	carrier	NOUN
ejpam-6729	645	5	u1	u1	NOUN
ejpam-6729	645	6	=	=	SYM
ejpam-6729	645	7	{	{	PUNCT
ejpam-6729	645	8	{	{	PUNCT
ejpam-6729	645	9	x	x	NOUN
ejpam-6729	645	10	}	}	PUNCT
ejpam-6729	645	11	,	,	PUNCT
ejpam-6729	645	12	{	{	PUNCT
ejpam-6729	645	13	y	y	NOUN
ejpam-6729	645	14	}	}	PUNCT
ejpam-6729	645	15	}	}	PUNCT
ejpam-6729	645	16	,	,	PUNCT
ejpam-6729	645	17	u2	u2	NOUN
ejpam-6729	645	18	=	=	PUNCT
ejpam-6729	645	19	{	{	PUNCT
ejpam-6729	645	20	{	{	PUNCT
ejpam-6729	645	21	x	x	NOUN
ejpam-6729	645	22	,	,	PUNCT
ejpam-6729	645	23	y	y	NOUN
ejpam-6729	645	24	}	}	PUNCT
ejpam-6729	645	25	}	}	PUNCT
ejpam-6729	645	26	,	,	PUNCT
ejpam-6729	645	27	and	and	CCONJ
ejpam-6729	645	28	two	two	NUM
ejpam-6729	645	29	level–3	level–3	NOUN
ejpam-6729	645	30	supervertices	supervertice	NOUN
ejpam-6729	645	31	w1	w1	NOUN
ejpam-6729	645	32	=	=	SYM
ejpam-6729	645	33	{	{	PUNCT
ejpam-6729	645	34	u1	u1	NOUN
ejpam-6729	645	35	}	}	PUNCT
ejpam-6729	645	36	,	,	PUNCT
ejpam-6729	645	37	w2	w2	NOUN
ejpam-6729	645	38	=	=	SYM
ejpam-6729	645	39	{	{	PUNCT
ejpam-6729	645	40	u2	u2	PROPN
ejpam-6729	645	41	}	}	PUNCT
ejpam-6729	645	42	.	.	PUNCT
ejpam-6729	646	1	set	set	VERB
ejpam-6729	646	2	v	v	NOUN
ejpam-6729	646	3	(	(	PUNCT
ejpam-6729	646	4	3	3	NUM
ejpam-6729	646	5	)	)	PUNCT
ejpam-6729	646	6	=	=	SYM
ejpam-6729	646	7	{	{	PUNCT
ejpam-6729	646	8	w1	w1	NOUN
ejpam-6729	646	9	,	,	PUNCT
ejpam-6729	646	10	w2	w2	NOUN
ejpam-6729	646	11	}	}	PUNCT
ejpam-6729	646	12	⊆	⊆	NUM
ejpam-6729	646	13	p3(v0	p3(v0	PROPN
ejpam-6729	646	14	)	)	PUNCT
ejpam-6729	646	15	,	,	PUNCT
ejpam-6729	646	16	e(3	e(3	PROPN
ejpam-6729	646	17	)	)	PUNCT
ejpam-6729	646	18	=	=	PRON
ejpam-6729	646	19	{	{	PUNCT
ejpam-6729	646	20	e	e	X
ejpam-6729	646	21	=	=	PUNCT
ejpam-6729	646	22	{	{	PUNCT
ejpam-6729	646	23	w1	w1	NOUN
ejpam-6729	646	24	,	,	PUNCT
ejpam-6729	646	25	w2	w2	NOUN
ejpam-6729	646	26	}	}	PUNCT
ejpam-6729	646	27	}	}	PUNCT
ejpam-6729	646	28	.	.	PUNCT
ejpam-6729	647	1	take	take	VERB
ejpam-6729	647	2	σ	σ	NOUN
ejpam-6729	647	3	=	=	SYM
ejpam-6729	647	4	{	{	PUNCT
ejpam-6729	647	5	σ	σ	NOUN
ejpam-6729	647	6	}	}	PUNCT
ejpam-6729	647	7	with	with	ADP
ejpam-6729	647	8	λ(e	λ(e	PROPN
ejpam-6729	647	9	)	)	PUNCT
ejpam-6729	647	10	=	=	SYM
ejpam-6729	647	11	σ	σ	PROPN
ejpam-6729	647	12	,	,	PUNCT
ejpam-6729	647	13	and	and	CCONJ
ejpam-6729	647	14	let	let	VERB
ejpam-6729	647	15	the	the	DET
ejpam-6729	647	16	property	property	NOUN
ejpam-6729	647	17	map	map	NOUN
ejpam-6729	647	18	be	be	AUX
ejpam-6729	647	19	trivial	trivial	ADJ
ejpam-6729	647	20	:	:	PUNCT
ejpam-6729	647	21	µ	µ	X
ejpam-6729	647	22	(	(	PUNCT
ejpam-6729	647	23	·	·	PUNCT
ejpam-6729	647	24	,	,	PUNCT
ejpam-6729	647	25	·	·	PUNCT
ejpam-6729	647	26	)	)	PUNCT
ejpam-6729	647	27	≡	≡	PROPN
ejpam-6729	647	28	⊥.	⊥.	PROPN
ejpam-6729	647	29	(	(	PUNCT
ejpam-6729	647	30	this	this	DET
ejpam-6729	647	31	choice	choice	NOUN
ejpam-6729	647	32	satisfies	satisfy	VERB
ejpam-6729	647	33	the	the	DET
ejpam-6729	647	34	fibre	fibre	NOUN
ejpam-6729	647	35	–	–	PUNCT
ejpam-6729	647	36	compatibility	compatibility	NOUN
ejpam-6729	647	37	conditions	condition	NOUN
ejpam-6729	647	38	automatically	automatically	ADV
ejpam-6729	647	39	.	.	PUNCT
ejpam-6729	647	40	)	)	PUNCT
ejpam-6729	648	1	first	first	ADV
ejpam-6729	648	2	flattening	flattening	NOUN
ejpam-6729	648	3	(	(	PUNCT
ejpam-6729	648	4	k	k	NOUN
ejpam-6729	648	5	=	=	SYM
ejpam-6729	648	6	1	1	NUM
ejpam-6729	648	7	)	)	PUNCT
ejpam-6729	648	8	.	.	PUNCT
ejpam-6729	649	1	the	the	DET
ejpam-6729	649	2	map	map	NOUN
ejpam-6729	649	3	ϕv	ϕv	ADP
ejpam-6729	649	4	:	:	PUNCT
ejpam-6729	649	5	p3(v0	p3(v0	PROPN
ejpam-6729	649	6	)	)	PUNCT
ejpam-6729	649	7	→	→	SYM
ejpam-6729	649	8	p2(v0	p2(v0	PROPN
ejpam-6729	649	9	)	)	PUNCT
ejpam-6729	649	10	gives	give	VERB
ejpam-6729	649	11	ϕv	ϕv	PRON
ejpam-6729	649	12	(	(	PUNCT
ejpam-6729	649	13	w1	w1	NOUN
ejpam-6729	649	14	)	)	PUNCT
ejpam-6729	649	15	=	=	SYM
ejpam-6729	649	16	u1	u1	NOUN
ejpam-6729	649	17	=	=	SYM
ejpam-6729	649	18	{	{	PUNCT
ejpam-6729	649	19	{	{	PUNCT
ejpam-6729	649	20	x	x	NOUN
ejpam-6729	649	21	}	}	PUNCT
ejpam-6729	649	22	,	,	PUNCT
ejpam-6729	649	23	{	{	PUNCT
ejpam-6729	649	24	y	y	NOUN
ejpam-6729	649	25	}	}	PUNCT
ejpam-6729	649	26	}	}	PUNCT
ejpam-6729	649	27	,	,	PUNCT
ejpam-6729	649	28	ϕv	ϕv	PROPN
ejpam-6729	649	29	(	(	PUNCT
ejpam-6729	649	30	w2	w2	NOUN
ejpam-6729	649	31	)	)	PUNCT
ejpam-6729	649	32	=	=	SYM
ejpam-6729	649	33	u2	u2	NOUN
ejpam-6729	649	34	=	=	PUNCT
ejpam-6729	649	35	{	{	PUNCT
ejpam-6729	649	36	{	{	PUNCT
ejpam-6729	649	37	x	x	NOUN
ejpam-6729	649	38	,	,	PUNCT
ejpam-6729	649	39	y	y	NOUN
ejpam-6729	649	40	}	}	PUNCT
ejpam-6729	649	41	}	}	PUNCT
ejpam-6729	649	42	.	.	PUNCT
ejpam-6729	650	1	thus	thus	ADV
ejpam-6729	650	2	v	v	X
ejpam-6729	650	3	(	(	PUNCT
ejpam-6729	650	4	2	2	NUM
ejpam-6729	650	5	)	)	PUNCT
ejpam-6729	650	6	(	(	PUNCT
ejpam-6729	650	7	1	1	X
ejpam-6729	650	8	)	)	PUNCT
ejpam-6729	650	9	=	=	PUNCT
ejpam-6729	650	10	ϕv	ϕv	ADP
ejpam-6729	651	1	[	[	X
ejpam-6729	651	2	v	v	X
ejpam-6729	651	3	(	(	PUNCT
ejpam-6729	651	4	3	3	NUM
ejpam-6729	651	5	)	)	PUNCT
ejpam-6729	651	6	]	]	PUNCT
ejpam-6729	651	7	=	=	PRON
ejpam-6729	651	8	{	{	PUNCT
ejpam-6729	651	9	u1	u1	NOUN
ejpam-6729	651	10	,	,	PUNCT
ejpam-6729	651	11	u2	u2	PROPN
ejpam-6729	651	12	}	}	PUNCT
ejpam-6729	651	13	,	,	PUNCT
ejpam-6729	651	14	e	e	X
ejpam-6729	651	15	(	(	PUNCT
ejpam-6729	651	16	2	2	NUM
ejpam-6729	651	17	)	)	PUNCT
ejpam-6729	651	18	(	(	PUNCT
ejpam-6729	651	19	1	1	X
ejpam-6729	651	20	)	)	PUNCT
ejpam-6729	651	21	=	=	PRON
ejpam-6729	651	22	{	{	PUNCT
ejpam-6729	651	23	ϕe(e	ϕe(e	NOUN
ejpam-6729	651	24	)	)	PUNCT
ejpam-6729	651	25	=	=	PRON
ejpam-6729	651	26	{	{	PUNCT
ejpam-6729	651	27	u1	u1	NOUN
ejpam-6729	651	28	,	,	PUNCT
ejpam-6729	651	29	u2	u2	PROPN
ejpam-6729	651	30	}	}	PUNCT
ejpam-6729	651	31	}	}	PUNCT
ejpam-6729	651	32	.	.	PUNCT
ejpam-6729	652	1	with	with	ADP
ejpam-6729	652	2	λ(1	λ(1	PROPN
ejpam-6729	652	3	)	)	PUNCT
ejpam-6729	652	4	(	(	PUNCT
ejpam-6729	652	5	{	{	PUNCT
ejpam-6729	652	6	u1	u1	NOUN
ejpam-6729	652	7	,	,	PUNCT
ejpam-6729	652	8	u2	u2	NOUN
ejpam-6729	652	9	}	}	PUNCT
ejpam-6729	652	10	)	)	PUNCT
ejpam-6729	652	11	=	=	SYM
ejpam-6729	652	12	σ	σ	PROPN
ejpam-6729	652	13	and	and	CCONJ
ejpam-6729	652	14	µ(1	µ(1	PROPN
ejpam-6729	652	15	)	)	PUNCT
ejpam-6729	652	16	≡	≡	PROPN
ejpam-6729	652	17	⊥	⊥	PROPN
ejpam-6729	652	18	,	,	PUNCT
ejpam-6729	652	19	theorem	theorem	VERB
ejpam-6729	652	20	10	10	NUM
ejpam-6729	652	21	yields	yield	NOUN
ejpam-6729	652	22	a	a	DET
ejpam-6729	652	23	property	property	NOUN
ejpam-6729	652	24	2	2	NUM
ejpam-6729	652	25	-	-	PUNCT
ejpam-6729	652	26	superhypergraph	superhypergraph	NOUN
ejpam-6729	652	27	h	h	NOUN
ejpam-6729	652	28	(	(	PUNCT
ejpam-6729	652	29	2	2	NUM
ejpam-6729	652	30	)	)	PUNCT
ejpam-6729	652	31	(	(	PUNCT
ejpam-6729	652	32	1	1	NUM
ejpam-6729	652	33	)	)	PUNCT
ejpam-6729	652	34	.	.	PUNCT
ejpam-6729	653	1	second	second	ADJ
ejpam-6729	653	2	flattening	flattening	NOUN
ejpam-6729	653	3	(	(	PUNCT
ejpam-6729	653	4	k	k	NOUN
ejpam-6729	653	5	=	=	SYM
ejpam-6729	653	6	2	2	NUM
ejpam-6729	653	7	)	)	PUNCT
ejpam-6729	653	8	.	.	PUNCT
ejpam-6729	653	9	apply	apply	VERB
ejpam-6729	653	10	ϕv	ϕv	ADV
ejpam-6729	653	11	again	again	ADV
ejpam-6729	653	12	,	,	PUNCT
ejpam-6729	653	13	now	now	ADV
ejpam-6729	653	14	ϕv	ϕv	ADP
ejpam-6729	653	15	:	:	PUNCT
ejpam-6729	653	16	p2(v0	p2(v0	PROPN
ejpam-6729	653	17	)	)	PUNCT
ejpam-6729	653	18	→	→	SYM
ejpam-6729	654	1	p1(v0	p1(v0	PROPN
ejpam-6729	654	2	):	):	PUNCT
ejpam-6729	654	3	ϕv	ϕv	ADP
ejpam-6729	654	4	(	(	PUNCT
ejpam-6729	654	5	u1	u1	NOUN
ejpam-6729	654	6	)	)	PUNCT
ejpam-6729	654	7	=	=	PRON
ejpam-6729	654	8	{	{	PUNCT
ejpam-6729	654	9	x	x	NOUN
ejpam-6729	654	10	}	}	PUNCT
ejpam-6729	654	11	∪	∪	ADJ
ejpam-6729	654	12	{	{	PUNCT
ejpam-6729	654	13	y	y	NOUN
ejpam-6729	654	14	}	}	PUNCT
ejpam-6729	654	15	=	=	SYM
ejpam-6729	654	16	{	{	PUNCT
ejpam-6729	654	17	x	x	NOUN
ejpam-6729	654	18	,	,	PUNCT
ejpam-6729	654	19	y	y	PROPN
ejpam-6729	654	20	}	}	PUNCT
ejpam-6729	654	21	,	,	PUNCT
ejpam-6729	654	22	ϕv	ϕv	PROPN
ejpam-6729	654	23	(	(	PUNCT
ejpam-6729	654	24	u2	u2	NOUN
ejpam-6729	654	25	)	)	PUNCT
ejpam-6729	654	26	=	=	PUNCT
ejpam-6729	654	27	{	{	PUNCT
ejpam-6729	654	28	x	x	PROPN
ejpam-6729	654	29	,	,	PUNCT
ejpam-6729	654	30	y	y	PROPN
ejpam-6729	654	31	}	}	PUNCT
ejpam-6729	654	32	.	.	PUNCT
ejpam-6729	655	1	hence	hence	ADV
ejpam-6729	655	2	both	both	DET
ejpam-6729	655	3	level–2	level–2	PROPN
ejpam-6729	655	4	vertices	vertice	VERB
ejpam-6729	655	5	collapse	collapse	NOUN
ejpam-6729	655	6	to	to	ADP
ejpam-6729	655	7	the	the	DET
ejpam-6729	655	8	same	same	ADJ
ejpam-6729	655	9	level–1	level–1	PROPN
ejpam-6729	655	10	carrier	carrier	NOUN
ejpam-6729	655	11	,	,	PUNCT
ejpam-6729	655	12	and	and	CCONJ
ejpam-6729	655	13	v	v	NOUN
ejpam-6729	655	14	(	(	PUNCT
ejpam-6729	655	15	1	1	NUM
ejpam-6729	655	16	)	)	PUNCT
ejpam-6729	655	17	(	(	PUNCT
ejpam-6729	655	18	2	2	X
ejpam-6729	655	19	)	)	PUNCT
ejpam-6729	655	20	=	=	PRON
ejpam-6729	655	21	{	{	PUNCT
ejpam-6729	655	22	{	{	PUNCT
ejpam-6729	655	23	x	x	NOUN
ejpam-6729	655	24	,	,	PUNCT
ejpam-6729	655	25	y	y	NOUN
ejpam-6729	655	26	}	}	PUNCT
ejpam-6729	655	27	}	}	PUNCT
ejpam-6729	655	28	,	,	PUNCT
ejpam-6729	655	29	e	e	X
ejpam-6729	655	30	(	(	PUNCT
ejpam-6729	655	31	1	1	NUM
ejpam-6729	655	32	)	)	PUNCT
ejpam-6729	655	33	(	(	PUNCT
ejpam-6729	655	34	2	2	X
ejpam-6729	655	35	)	)	PUNCT
ejpam-6729	655	36	=	=	PRON
ejpam-6729	655	37	{	{	PUNCT
ejpam-6729	655	38	ϕ	ϕ	NOUN
ejpam-6729	655	39	(	(	PUNCT
ejpam-6729	655	40	2	2	NUM
ejpam-6729	655	41	)	)	PUNCT
ejpam-6729	655	42	e	e	NOUN
ejpam-6729	655	43	(	(	PUNCT
ejpam-6729	655	44	e	e	NOUN
ejpam-6729	655	45	)	)	PUNCT
ejpam-6729	655	46	=	=	SYM
ejpam-6729	655	47	{	{	PUNCT
ejpam-6729	655	48	{	{	PUNCT
ejpam-6729	655	49	x	x	NOUN
ejpam-6729	655	50	,	,	PUNCT
ejpam-6729	655	51	y	y	NOUN
ejpam-6729	655	52	}	}	PUNCT
ejpam-6729	655	53	}	}	PUNCT
ejpam-6729	655	54	}	}	PUNCT
ejpam-6729	655	55	.	.	PUNCT
ejpam-6729	656	1	t.	t.	PROPN
ejpam-6729	656	2	fujita	fujita	PROPN
ejpam-6729	656	3	,	,	PUNCT
ejpam-6729	656	4	f.	f.	PROPN
ejpam-6729	656	5	smarandache	smarandache	PROPN
ejpam-6729	656	6	/	/	SYM
ejpam-6729	656	7	eur	eur	PROPN
ejpam-6729	656	8	.	.	PUNCT
ejpam-6729	657	1	j.	j.	PROPN
ejpam-6729	657	2	pure	pure	PROPN
ejpam-6729	657	3	appl	appl	PROPN
ejpam-6729	657	4	.	.	PROPN
ejpam-6729	657	5	math	math	PROPN
ejpam-6729	657	6	,	,	PUNCT
ejpam-6729	657	7	18	18	NUM
ejpam-6729	657	8	(	(	PUNCT
ejpam-6729	657	9	4	4	NUM
ejpam-6729	657	10	)	)	PUNCT
ejpam-6729	657	11	(	(	PUNCT
ejpam-6729	657	12	2025	2025	NUM
ejpam-6729	657	13	)	)	PUNCT
ejpam-6729	657	14	,	,	PUNCT
ejpam-6729	657	15	6729	6729	NUM
ejpam-6729	657	16	29	29	NUM
ejpam-6729	657	17	of	of	ADP
ejpam-6729	657	18	36	36	NUM
ejpam-6729	657	19	define	define	NOUN
ejpam-6729	657	20	λ(2	λ(2	PROPN
ejpam-6729	657	21	)	)	PUNCT
ejpam-6729	657	22	(	(	PUNCT
ejpam-6729	657	23	{	{	PUNCT
ejpam-6729	657	24	{	{	PUNCT
ejpam-6729	657	25	x	x	NOUN
ejpam-6729	657	26	,	,	PUNCT
ejpam-6729	657	27	y	y	NOUN
ejpam-6729	657	28	}	}	PUNCT
ejpam-6729	657	29	}	}	PUNCT
ejpam-6729	657	30	)	)	PUNCT
ejpam-6729	658	1	=	=	SYM
ejpam-6729	658	2	σ	σ	NOUN
ejpam-6729	658	3	and	and	CCONJ
ejpam-6729	658	4	keep	keep	VERB
ejpam-6729	658	5	µ(2	µ(2	PROPN
ejpam-6729	658	6	)	)	PUNCT
ejpam-6729	658	7	≡	≡	PROPN
ejpam-6729	658	8	⊥.	⊥.	PROPN
ejpam-6729	658	9	the	the	DET
ejpam-6729	658	10	fibre	fibre	NOUN
ejpam-6729	658	11	–	–	PUNCT
ejpam-6729	658	12	compatibility	compatibility	NOUN
ejpam-6729	658	13	assumptions	assumption	NOUN
ejpam-6729	658	14	are	be	AUX
ejpam-6729	658	15	satisfied	satisfied	ADJ
ejpam-6729	658	16	(	(	PUNCT
ejpam-6729	658	17	both	both	PRON
ejpam-6729	658	18	labels	label	VERB
ejpam-6729	658	19	constant	constant	ADJ
ejpam-6729	658	20	and	and	CCONJ
ejpam-6729	658	21	properties	property	NOUN
ejpam-6729	658	22	trivial	trivial	ADJ
ejpam-6729	658	23	)	)	PUNCT
ejpam-6729	658	24	,	,	PUNCT
ejpam-6729	658	25	so	so	ADV
ejpam-6729	658	26	by	by	ADP
ejpam-6729	658	27	theorem	theorem	NOUN
ejpam-6729	658	28	11	11	NUM
ejpam-6729	658	29	with	with	ADP
ejpam-6729	658	30	k	k	PROPN
ejpam-6729	658	31	=	=	SYM
ejpam-6729	658	32	2	2	NUM
ejpam-6729	658	33	we	we	PRON
ejpam-6729	658	34	obtain	obtain	VERB
ejpam-6729	658	35	a	a	DET
ejpam-6729	658	36	property	property	NOUN
ejpam-6729	658	37	1	1	NUM
ejpam-6729	658	38	-	-	PUNCT
ejpam-6729	658	39	superhypergraph	superhypergraph	NOUN
ejpam-6729	658	40	h(1	h(1	PROPN
ejpam-6729	658	41	)	)	PUNCT
ejpam-6729	658	42	=	=	PRON
ejpam-6729	658	43	(	(	PUNCT
ejpam-6729	658	44	v	v	NOUN
ejpam-6729	658	45	(	(	PUNCT
ejpam-6729	658	46	1	1	NUM
ejpam-6729	658	47	)	)	PUNCT
ejpam-6729	658	48	(	(	PUNCT
ejpam-6729	658	49	2	2	NUM
ejpam-6729	658	50	)	)	PUNCT
ejpam-6729	658	51	,	,	PUNCT
ejpam-6729	659	1	e	e	X
ejpam-6729	659	2	(	(	PUNCT
ejpam-6729	659	3	1	1	NUM
ejpam-6729	659	4	)	)	PUNCT
ejpam-6729	659	5	(	(	PUNCT
ejpam-6729	659	6	2	2	NUM
ejpam-6729	659	7	)	)	PUNCT
ejpam-6729	659	8	,	,	PUNCT
ejpam-6729	659	9	λ	λ	X
ejpam-6729	659	10	(	(	PUNCT
ejpam-6729	659	11	2	2	NUM
ejpam-6729	659	12	)	)	PUNCT
ejpam-6729	659	13	,	,	PUNCT
ejpam-6729	659	14	µ(2	µ(2	PROPN
ejpam-6729	659	15	)	)	PUNCT
ejpam-6729	659	16	)	)	PUNCT
ejpam-6729	660	1	=	=	PUNCT
ejpam-6729	660	2	(	(	PUNCT
ejpam-6729	660	3	{	{	PUNCT
ejpam-6729	660	4	{	{	PUNCT
ejpam-6729	660	5	x	x	NOUN
ejpam-6729	660	6	,	,	PUNCT
ejpam-6729	660	7	y	y	NOUN
ejpam-6729	660	8	}	}	PUNCT
ejpam-6729	660	9	}	}	PUNCT
ejpam-6729	660	10	,	,	PUNCT
ejpam-6729	660	11	{	{	PUNCT
ejpam-6729	660	12	{	{	PUNCT
ejpam-6729	660	13	{	{	PUNCT
ejpam-6729	660	14	x	x	NOUN
ejpam-6729	660	15	,	,	PUNCT
ejpam-6729	660	16	y	y	NOUN
ejpam-6729	660	17	}	}	PUNCT
ejpam-6729	660	18	}	}	PUNCT
ejpam-6729	660	19	}	}	PUNCT
ejpam-6729	660	20	,	,	PUNCT
ejpam-6729	660	21	σ	σ	PROPN
ejpam-6729	660	22	,	,	PUNCT
ejpam-6729	660	23	⊥	⊥	PROPN
ejpam-6729	660	24	)	)	PUNCT
ejpam-6729	660	25	.	.	PUNCT
ejpam-6729	661	1	theorem	theorem	VERB
ejpam-6729	661	2	12	12	NUM
ejpam-6729	661	3	(	(	PUNCT
ejpam-6729	661	4	uniformity	uniformity	NOUN
ejpam-6729	661	5	)	)	PUNCT
ejpam-6729	661	6	.	.	PUNCT
ejpam-6729	662	1	let	let	VERB
ejpam-6729	662	2	h(n	h(n	PRON
ejpam-6729	662	3	)	)	PUNCT
ejpam-6729	663	1	=	=	PRON
ejpam-6729	663	2	(	(	PUNCT
ejpam-6729	663	3	v	v	NOUN
ejpam-6729	663	4	(	(	PUNCT
ejpam-6729	663	5	n	n	CCONJ
ejpam-6729	663	6	)	)	PUNCT
ejpam-6729	663	7	,	,	PUNCT
ejpam-6729	663	8	e(n	e(n	PROPN
ejpam-6729	663	9	)	)	PUNCT
ejpam-6729	663	10	,	,	PUNCT
ejpam-6729	663	11	λ	λ	PROPN
ejpam-6729	663	12	,	,	PUNCT
ejpam-6729	663	13	µ	µ	NOUN
ejpam-6729	663	14	)	)	PUNCT
ejpam-6729	663	15	be	be	AUX
ejpam-6729	663	16	a	a	DET
ejpam-6729	663	17	property	property	NOUN
ejpam-6729	663	18	n	n	CCONJ
ejpam-6729	663	19	-	-	PUNCT
ejpam-6729	663	20	superhypergraph	superhypergraph	NOUN
ejpam-6729	663	21	.	.	PUNCT
ejpam-6729	664	1	assume	assume	VERB
ejpam-6729	664	2	there	there	PRON
ejpam-6729	664	3	exists	exist	VERB
ejpam-6729	664	4	an	an	DET
ejpam-6729	664	5	integer	integer	NOUN
ejpam-6729	664	6	k	k	PROPN
ejpam-6729	664	7	≥	≥	NUM
ejpam-6729	664	8	1	1	NUM
ejpam-6729	664	9	such	such	ADJ
ejpam-6729	664	10	that	that	SCONJ
ejpam-6729	664	11	|e|	|e|	PROPN
ejpam-6729	664	12	=	=	SYM
ejpam-6729	664	13	k	k	PROPN
ejpam-6729	664	14	for	for	ADP
ejpam-6729	664	15	every	every	DET
ejpam-6729	664	16	e	e	PROPN
ejpam-6729	664	17	∈	∈	PROPN
ejpam-6729	664	18	e(n	e(n	PROPN
ejpam-6729	664	19	)	)	PUNCT
ejpam-6729	664	20	.	.	PUNCT
ejpam-6729	665	1	then	then	ADV
ejpam-6729	665	2	h(n	h(n	PROPN
ejpam-6729	665	3	)	)	PUNCT
ejpam-6729	665	4	is	be	AUX
ejpam-6729	665	5	k	k	NOUN
ejpam-6729	665	6	-	-	ADJ
ejpam-6729	665	7	uniform	uniform	ADJ
ejpam-6729	665	8	,	,	PUNCT
ejpam-6729	665	9	i.e.	i.e.	X
ejpam-6729	665	10	,	,	PUNCT
ejpam-6729	665	11	every	every	DET
ejpam-6729	665	12	level	level	NOUN
ejpam-6729	665	13	-	-	PUNCT
ejpam-6729	665	14	n	n	NOUN
ejpam-6729	665	15	superedge	superedge	NOUN
ejpam-6729	665	16	links	link	NOUN
ejpam-6729	665	17	exactly	exactly	ADV
ejpam-6729	665	18	k	k	PROPN
ejpam-6729	665	19	n	n	CCONJ
ejpam-6729	665	20	-	-	PUNCT
ejpam-6729	665	21	supervertices	supervertice	NOUN
ejpam-6729	665	22	.	.	PUNCT
ejpam-6729	666	1	moreover	moreover	ADV
ejpam-6729	666	2	,	,	PUNCT
ejpam-6729	666	3	any	any	DET
ejpam-6729	666	4	subfamily	subfamily	ADV
ejpam-6729	666	5	e′(n	e′(n	CCONJ
ejpam-6729	666	6	)	)	PUNCT
ejpam-6729	666	7	⊆	⊆	NUM
ejpam-6729	666	8	e(n	e(n	NOUN
ejpam-6729	666	9	)	)	PUNCT
ejpam-6729	666	10	inherits	inherit	VERB
ejpam-6729	666	11	k	k	NOUN
ejpam-6729	666	12	-	-	NOUN
ejpam-6729	666	13	uniformity	uniformity	NOUN
ejpam-6729	666	14	.	.	PUNCT
ejpam-6729	667	1	proof	proof	NOUN
ejpam-6729	667	2	.	.	PUNCT
ejpam-6729	668	1	by	by	ADP
ejpam-6729	668	2	hypothesis	hypothesis	NOUN
ejpam-6729	668	3	,	,	PUNCT
ejpam-6729	668	4	for	for	ADP
ejpam-6729	668	5	each	each	DET
ejpam-6729	668	6	e	e	PROPN
ejpam-6729	668	7	∈	∈	PROPN
ejpam-6729	668	8	e(n	e(n	PROPN
ejpam-6729	668	9	)	)	PUNCT
ejpam-6729	668	10	we	we	PRON
ejpam-6729	668	11	have	have	VERB
ejpam-6729	668	12	e	e	NOUN
ejpam-6729	668	13	⊆	⊆	NUM
ejpam-6729	668	14	v	v	ADP
ejpam-6729	668	15	(	(	PUNCT
ejpam-6729	668	16	n	n	CCONJ
ejpam-6729	668	17	)	)	PUNCT
ejpam-6729	668	18	and	and	CCONJ
ejpam-6729	668	19	|e|	|e|	PROPN
ejpam-6729	668	20	=	=	X
ejpam-6729	668	21	k.	k.	NOUN
ejpam-6729	668	22	by	by	ADP
ejpam-6729	668	23	the	the	DET
ejpam-6729	668	24	usual	usual	ADJ
ejpam-6729	668	25	definition	definition	NOUN
ejpam-6729	668	26	,	,	PUNCT
ejpam-6729	668	27	this	this	PRON
ejpam-6729	668	28	is	be	AUX
ejpam-6729	668	29	precisely	precisely	ADV
ejpam-6729	668	30	the	the	DET
ejpam-6729	668	31	statement	statement	NOUN
ejpam-6729	668	32	that	that	SCONJ
ejpam-6729	668	33	h(n	h(n	PROPN
ejpam-6729	668	34	)	)	PUNCT
ejpam-6729	668	35	is	be	AUX
ejpam-6729	668	36	k	k	NOUN
ejpam-6729	668	37	-	-	NOUN
ejpam-6729	668	38	uniform	uniform	NOUN
ejpam-6729	668	39	.	.	PUNCT
ejpam-6729	669	1	now	now	ADV
ejpam-6729	669	2	let	let	VERB
ejpam-6729	669	3	e′(n	e′(n	PRON
ejpam-6729	669	4	)	)	PUNCT
ejpam-6729	669	5	⊆	⊆	NUM
ejpam-6729	669	6	e(n	e(n	PROPN
ejpam-6729	669	7	)	)	PUNCT
ejpam-6729	669	8	.	.	PUNCT
ejpam-6729	670	1	for	for	ADP
ejpam-6729	670	2	any	any	DET
ejpam-6729	670	3	e	e	PROPN
ejpam-6729	670	4	∈	∈	PROPN
ejpam-6729	670	5	e′(n	e′(n	PROPN
ejpam-6729	670	6	)	)	PUNCT
ejpam-6729	670	7	we	we	PRON
ejpam-6729	670	8	still	still	ADV
ejpam-6729	670	9	have	have	VERB
ejpam-6729	670	10	e	e	NOUN
ejpam-6729	670	11	⊆	⊆	NUM
ejpam-6729	670	12	v	v	ADP
ejpam-6729	670	13	(	(	PUNCT
ejpam-6729	670	14	n	n	CCONJ
ejpam-6729	670	15	)	)	PUNCT
ejpam-6729	670	16	and	and	CCONJ
ejpam-6729	670	17	(	(	PUNCT
ejpam-6729	670	18	because	because	SCONJ
ejpam-6729	670	19	e	e	PROPN
ejpam-6729	670	20	∈	∈	PROPN
ejpam-6729	670	21	e(n	e(n	PROPN
ejpam-6729	670	22	)	)	PUNCT
ejpam-6729	670	23	)	)	PUNCT
ejpam-6729	671	1	|e|	|e|	PROPN
ejpam-6729	671	2	=	=	PUNCT
ejpam-6729	671	3	k.	k.	PROPN
ejpam-6729	671	4	hence	hence	ADV
ejpam-6729	671	5	the	the	DET
ejpam-6729	671	6	restriction	restriction	NOUN
ejpam-6729	671	7	(	(	PUNCT
ejpam-6729	671	8	v	v	NOUN
ejpam-6729	671	9	(	(	PUNCT
ejpam-6729	671	10	n	n	CCONJ
ejpam-6729	671	11	)	)	PUNCT
ejpam-6729	671	12	,	,	PUNCT
ejpam-6729	671	13	e′(n	e′(n	PROPN
ejpam-6729	671	14	)	)	PUNCT
ejpam-6729	671	15	,	,	PUNCT
ejpam-6729	671	16	λ|e′(n	λ|e′(n	X
ejpam-6729	671	17	)	)	PUNCT
ejpam-6729	671	18	,	,	PUNCT
ejpam-6729	671	19	µ|(v	µ|(v	PROPN
ejpam-6729	671	20	(	(	PUNCT
ejpam-6729	671	21	n)∪e′(n))×k	n)∪e′(n))×k	NOUN
ejpam-6729	671	22	)	)	PUNCT
ejpam-6729	671	23	is	be	AUX
ejpam-6729	671	24	again	again	ADV
ejpam-6729	671	25	k	k	ADJ
ejpam-6729	671	26	-	-	NOUN
ejpam-6729	671	27	uniform	uniform	NOUN
ejpam-6729	671	28	.	.	PUNCT
ejpam-6729	672	1	no	no	DET
ejpam-6729	672	2	further	further	ADJ
ejpam-6729	672	3	conditions	condition	NOUN
ejpam-6729	672	4	are	be	AUX
ejpam-6729	672	5	required	require	VERB
ejpam-6729	672	6	.	.	PUNCT
ejpam-6729	673	1	theorem	theorem	ADJ
ejpam-6729	673	2	13	13	NUM
ejpam-6729	673	3	(	(	PUNCT
ejpam-6729	673	4	disjoint	disjoint	NOUN
ejpam-6729	673	5	union	union	PROPN
ejpam-6729	673	6	)	)	PUNCT
ejpam-6729	673	7	.	.	PUNCT
ejpam-6729	674	1	let	let	VERB
ejpam-6729	674	2	h(n	h(n	PROPN
ejpam-6729	674	3	)	)	PUNCT
ejpam-6729	675	1	i	i	PRON
ejpam-6729	675	2	=	=	PUNCT
ejpam-6729	675	3	(	(	PUNCT
ejpam-6729	675	4	v	v	NOUN
ejpam-6729	675	5	(	(	PUNCT
ejpam-6729	675	6	n	n	CCONJ
ejpam-6729	675	7	)	)	PUNCT
ejpam-6729	675	8	i	i	PRON
ejpam-6729	675	9	,	,	PUNCT
ejpam-6729	675	10	e	e	X
ejpam-6729	675	11	(	(	PUNCT
ejpam-6729	675	12	n	n	CCONJ
ejpam-6729	675	13	)	)	PUNCT
ejpam-6729	675	14	i	i	PRON
ejpam-6729	675	15	,	,	PUNCT
ejpam-6729	675	16	λi	λi	PROPN
ejpam-6729	675	17	,	,	PUNCT
ejpam-6729	675	18	µi	µi	PROPN
ejpam-6729	675	19	)	)	PUNCT
ejpam-6729	675	20	be	be	AUX
ejpam-6729	675	21	property	property	NOUN
ejpam-6729	675	22	n	n	NOUN
ejpam-6729	675	23	-	-	PUNCT
ejpam-6729	675	24	superhypergraphs	superhypergraph	NOUN
ejpam-6729	675	25	over	over	ADP
ejpam-6729	675	26	pairwise	pairwise	NOUN
ejpam-6729	675	27	disjoint	disjoint	NOUN
ejpam-6729	675	28	base	base	NOUN
ejpam-6729	675	29	sets	set	VERB
ejpam-6729	675	30	v	v	ADP
ejpam-6729	675	31	(	(	PUNCT
ejpam-6729	675	32	i	i	NOUN
ejpam-6729	675	33	)	)	PUNCT
ejpam-6729	675	34	0	0	PUNCT
ejpam-6729	676	1	for	for	ADP
ejpam-6729	676	2	i	i	PRON
ejpam-6729	676	3	=	=	NOUN
ejpam-6729	676	4	1	1	NUM
ejpam-6729	676	5	,	,	PUNCT
ejpam-6729	676	6	2	2	NUM
ejpam-6729	676	7	(	(	PUNCT
ejpam-6729	676	8	so	so	ADV
ejpam-6729	676	9	v	v	ADJ
ejpam-6729	676	10	(	(	PUNCT
ejpam-6729	676	11	1	1	NUM
ejpam-6729	676	12	)	)	PUNCT
ejpam-6729	676	13	0	0	NUM
ejpam-6729	676	14	∩	∩	PROPN
ejpam-6729	676	15	v	v	X
ejpam-6729	676	16	(	(	PUNCT
ejpam-6729	676	17	2	2	NUM
ejpam-6729	676	18	)	)	PUNCT
ejpam-6729	676	19	0	0	NUM
ejpam-6729	676	20	=	=	SYM
ejpam-6729	676	21	∅	∅	NOUN
ejpam-6729	676	22	)	)	PUNCT
ejpam-6729	676	23	.	.	PUNCT
ejpam-6729	677	1	to	to	PART
ejpam-6729	677	2	avoid	avoid	VERB
ejpam-6729	677	3	accidental	accidental	ADJ
ejpam-6729	677	4	identifications	identification	NOUN
ejpam-6729	677	5	(	(	PUNCT
ejpam-6729	677	6	e.g.	e.g.	ADV
ejpam-6729	677	7	of	of	ADP
ejpam-6729	677	8	∅	∅	NOUN
ejpam-6729	677	9	)	)	PUNCT
ejpam-6729	677	10	across	across	ADP
ejpam-6729	677	11	levels	level	NOUN
ejpam-6729	677	12	,	,	PUNCT
ejpam-6729	677	13	form	form	VERB
ejpam-6729	677	14	tagged	tag	VERB
ejpam-6729	677	15	copies	copy	NOUN
ejpam-6729	677	16	ι	ι	X
ejpam-6729	677	17	(	(	PUNCT
ejpam-6729	677	18	r	r	NOUN
ejpam-6729	677	19	)	)	PUNCT
ejpam-6729	677	20	i	i	PRON
ejpam-6729	677	21	:	:	PUNCT
ejpam-6729	677	22	pr(v	pr(v	X
ejpam-6729	677	23	(	(	PUNCT
ejpam-6729	677	24	i	i	NOUN
ejpam-6729	677	25	)	)	PUNCT
ejpam-6729	677	26	0	0	X
ejpam-6729	677	27	)	)	PUNCT
ejpam-6729	678	1	−→	−→	NOUN
ejpam-6729	678	2	pr	pr	NOUN
ejpam-6729	678	3	(	(	PUNCT
ejpam-6729	678	4	v	v	NOUN
ejpam-6729	678	5	(	(	PUNCT
ejpam-6729	678	6	1	1	NUM
ejpam-6729	678	7	)	)	PUNCT
ejpam-6729	678	8	0	0	NUM
ejpam-6729	678	9	∪	∪	PROPN
ejpam-6729	678	10	v	v	NOUN
ejpam-6729	678	11	(	(	PUNCT
ejpam-6729	678	12	2	2	NUM
ejpam-6729	678	13	)	)	PUNCT
ejpam-6729	678	14	0	0	NUM
ejpam-6729	678	15	)	)	PUNCT
ejpam-6729	678	16	×	×	NOUN
ejpam-6729	678	17	{	{	PUNCT
ejpam-6729	678	18	i	i	NOUN
ejpam-6729	678	19	}	}	PUNCT
ejpam-6729	678	20	,	,	PUNCT
ejpam-6729	678	21	x	x	X
ejpam-6729	678	22	7→	7→	NUM
ejpam-6729	678	23	(	(	PUNCT
ejpam-6729	678	24	x	x	X
ejpam-6729	678	25	,	,	PUNCT
ejpam-6729	678	26	i	i	NOUN
ejpam-6729	678	27	)	)	PUNCT
ejpam-6729	678	28	(	(	PUNCT
ejpam-6729	678	29	0	0	NUM
ejpam-6729	678	30	≤	≤	NUM
ejpam-6729	678	31	r	r	NOUN
ejpam-6729	678	32	≤	≤	NOUN
ejpam-6729	678	33	n	n	CCONJ
ejpam-6729	678	34	)	)	PUNCT
ejpam-6729	678	35	,	,	PUNCT
ejpam-6729	678	36	and	and	CCONJ
ejpam-6729	678	37	define	define	VERB
ejpam-6729	678	38	v	v	NUM
ejpam-6729	678	39	(	(	PUNCT
ejpam-6729	678	40	n	n	CCONJ
ejpam-6729	678	41	)	)	PUNCT
ejpam-6729	678	42	=	=	SYM
ejpam-6729	678	43	ι	ι	PROPN
ejpam-6729	678	44	(	(	PUNCT
ejpam-6729	678	45	n	n	CCONJ
ejpam-6729	678	46	)	)	PUNCT
ejpam-6729	678	47	1	1	NUM
ejpam-6729	678	48	[	[	PUNCT
ejpam-6729	678	49	v	v	NOUN
ejpam-6729	678	50	(	(	PUNCT
ejpam-6729	678	51	n	n	CCONJ
ejpam-6729	678	52	)	)	PUNCT
ejpam-6729	678	53	1	1	NUM
ejpam-6729	678	54	]	]	PUNCT
ejpam-6729	678	55	∪	∪	X
ejpam-6729	678	56	ι	ι	PROPN
ejpam-6729	678	57	(	(	PUNCT
ejpam-6729	678	58	n	n	CCONJ
ejpam-6729	678	59	)	)	PUNCT
ejpam-6729	678	60	2	2	NUM
ejpam-6729	678	61	[	[	PUNCT
ejpam-6729	678	62	v	v	NOUN
ejpam-6729	678	63	(	(	PUNCT
ejpam-6729	678	64	n	n	CCONJ
ejpam-6729	678	65	)	)	PUNCT
ejpam-6729	678	66	2	2	NUM
ejpam-6729	678	67	]	]	PUNCT
ejpam-6729	678	68	,	,	PUNCT
ejpam-6729	678	69	e(n	e(n	PROPN
ejpam-6729	678	70	)	)	PUNCT
ejpam-6729	678	71	=	=	PRON
ejpam-6729	678	72	{	{	PUNCT
ejpam-6729	678	73	ι	ι	X
ejpam-6729	678	74	(	(	PUNCT
ejpam-6729	678	75	n	n	CCONJ
ejpam-6729	678	76	)	)	PUNCT
ejpam-6729	678	77	1	1	NUM
ejpam-6729	679	1	[	[	X
ejpam-6729	679	2	e	e	X
ejpam-6729	679	3	]	]	X
ejpam-6729	679	4	|	|	NOUN
ejpam-6729	679	5	e	e	X
ejpam-6729	679	6	∈	∈	PROPN
ejpam-6729	679	7	e	e	X
ejpam-6729	679	8	(	(	PUNCT
ejpam-6729	679	9	n	n	CCONJ
ejpam-6729	679	10	)	)	PUNCT
ejpam-6729	679	11	1	1	NUM
ejpam-6729	679	12	}	}	PUNCT
ejpam-6729	679	13	∪	∪	NOUN
ejpam-6729	679	14	{	{	PUNCT
ejpam-6729	679	15	ι	ι	X
ejpam-6729	679	16	(	(	PUNCT
ejpam-6729	679	17	n	n	CCONJ
ejpam-6729	679	18	)	)	PUNCT
ejpam-6729	679	19	2	2	NUM
ejpam-6729	680	1	[	[	X
ejpam-6729	680	2	e	e	X
ejpam-6729	680	3	]	]	X
ejpam-6729	680	4	|	|	NOUN
ejpam-6729	680	5	e	e	X
ejpam-6729	680	6	∈	∈	PROPN
ejpam-6729	680	7	e	e	X
ejpam-6729	680	8	(	(	PUNCT
ejpam-6729	680	9	n	n	CCONJ
ejpam-6729	680	10	)	)	PUNCT
ejpam-6729	680	11	2	2	NUM
ejpam-6729	680	12	}	}	PUNCT
ejpam-6729	680	13	.	.	PUNCT
ejpam-6729	681	1	set	set	VERB
ejpam-6729	681	2	the	the	DET
ejpam-6729	681	3	label	label	NOUN
ejpam-6729	681	4	and	and	CCONJ
ejpam-6729	681	5	property	property	NOUN
ejpam-6729	681	6	maps	map	NOUN
ejpam-6729	681	7	by	by	ADP
ejpam-6729	681	8	λ	λ	PROPN
ejpam-6729	681	9	(	(	PUNCT
ejpam-6729	681	10	ι	ι	X
ejpam-6729	681	11	(	(	PUNCT
ejpam-6729	681	12	n	n	CCONJ
ejpam-6729	681	13	)	)	PUNCT
ejpam-6729	681	14	i	i	PRON
ejpam-6729	682	1	[	[	X
ejpam-6729	682	2	e	e	X
ejpam-6729	682	3	]	]	PUNCT
ejpam-6729	682	4	)	)	PUNCT
ejpam-6729	682	5	:	:	PUNCT
ejpam-6729	682	6	=	=	SYM
ejpam-6729	682	7	λi(e	λi(e	NOUN
ejpam-6729	682	8	)	)	PUNCT
ejpam-6729	682	9	,	,	PUNCT
ejpam-6729	682	10	µ	µ	X
ejpam-6729	682	11	(	(	PUNCT
ejpam-6729	682	12	(	(	PUNCT
ejpam-6729	682	13	ι	ι	X
ejpam-6729	682	14	(	(	PUNCT
ejpam-6729	682	15	r	r	NOUN
ejpam-6729	682	16	)	)	PUNCT
ejpam-6729	682	17	i	i	PRON
ejpam-6729	682	18	(	(	PUNCT
ejpam-6729	682	19	x	x	NOUN
ejpam-6729	682	20	)	)	PUNCT
ejpam-6729	682	21	,	,	PUNCT
ejpam-6729	682	22	i	i	PROPN
ejpam-6729	682	23	)	)	PUNCT
ejpam-6729	682	24	,	,	PUNCT
ejpam-6729	682	25	k	k	PROPN
ejpam-6729	682	26	)	)	PUNCT
ejpam-6729	683	1	:	:	PUNCT
ejpam-6729	683	2	=	=	SYM
ejpam-6729	683	3	µi(x	µi(x	ADP
ejpam-6729	683	4	,	,	PUNCT
ejpam-6729	683	5	k	k	NOUN
ejpam-6729	683	6	)	)	PUNCT
ejpam-6729	683	7	,	,	PUNCT
ejpam-6729	683	8	for	for	ADP
ejpam-6729	683	9	e	e	PROPN
ejpam-6729	683	10	∈	∈	PROPN
ejpam-6729	683	11	e	e	X
ejpam-6729	683	12	(	(	PUNCT
ejpam-6729	683	13	n	n	CCONJ
ejpam-6729	683	14	)	)	PUNCT
ejpam-6729	683	15	i	i	PRON
ejpam-6729	683	16	,	,	PUNCT
ejpam-6729	683	17	x	x	PUNCT
ejpam-6729	683	18	∈	∈	NOUN
ejpam-6729	683	19	pr(v	pr(v	X
ejpam-6729	683	20	(	(	PUNCT
ejpam-6729	683	21	i	i	NOUN
ejpam-6729	683	22	)	)	PUNCT
ejpam-6729	683	23	0	0	NUM
ejpam-6729	683	24	)	)	PUNCT
ejpam-6729	683	25	,	,	PUNCT
ejpam-6729	683	26	0	0	NUM
ejpam-6729	683	27	≤	≤	NUM
ejpam-6729	683	28	r	r	NOUN
ejpam-6729	683	29	≤	≤	NUM
ejpam-6729	683	30	n.	n.	NOUN
ejpam-6729	683	31	then	then	ADV
ejpam-6729	683	32	(	(	PUNCT
ejpam-6729	683	33	v	v	NOUN
ejpam-6729	683	34	(	(	PUNCT
ejpam-6729	683	35	n	n	CCONJ
ejpam-6729	683	36	)	)	PUNCT
ejpam-6729	683	37	,	,	PUNCT
ejpam-6729	683	38	e(n	e(n	PROPN
ejpam-6729	683	39	)	)	PUNCT
ejpam-6729	683	40	,	,	PUNCT
ejpam-6729	683	41	λ	λ	PROPN
ejpam-6729	683	42	,	,	PUNCT
ejpam-6729	683	43	µ	µ	NOUN
ejpam-6729	683	44	)	)	PUNCT
ejpam-6729	683	45	is	be	AUX
ejpam-6729	683	46	a	a	DET
ejpam-6729	683	47	property	property	NOUN
ejpam-6729	683	48	nsuperhypergraph	nsuperhypergraph	NOUN
ejpam-6729	683	49	over	over	ADP
ejpam-6729	683	50	the	the	DET
ejpam-6729	683	51	disjoint	disjoint	NOUN
ejpam-6729	683	52	base	base	NOUN
ejpam-6729	683	53	v	v	NOUN
ejpam-6729	683	54	(	(	PUNCT
ejpam-6729	683	55	1	1	NUM
ejpam-6729	683	56	)	)	PUNCT
ejpam-6729	683	57	0	0	NUM
ejpam-6729	683	58	∪	∪	PROPN
ejpam-6729	683	59	v	v	NOUN
ejpam-6729	683	60	(	(	PUNCT
ejpam-6729	683	61	2	2	NUM
ejpam-6729	683	62	)	)	PUNCT
ejpam-6729	683	63	0	0	NUM
ejpam-6729	684	1	(	(	PUNCT
ejpam-6729	684	2	identifying	identify	VERB
ejpam-6729	684	3	(	(	PUNCT
ejpam-6729	684	4	v	v	NOUN
ejpam-6729	684	5	,	,	PUNCT
ejpam-6729	684	6	i	i	NOUN
ejpam-6729	684	7	)	)	PUNCT
ejpam-6729	684	8	with	with	ADP
ejpam-6729	684	9	v	v	NOUN
ejpam-6729	684	10	since	since	SCONJ
ejpam-6729	684	11	the	the	DET
ejpam-6729	684	12	bases	basis	NOUN
ejpam-6729	684	13	are	be	AUX
ejpam-6729	684	14	disjoint	disjoint	ADJ
ejpam-6729	684	15	)	)	PUNCT
ejpam-6729	684	16	.	.	PUNCT
ejpam-6729	685	1	proof	proof	NOUN
ejpam-6729	685	2	.	.	PUNCT
ejpam-6729	686	1	we	we	PRON
ejpam-6729	686	2	verify	verify	VERB
ejpam-6729	686	3	the	the	DET
ejpam-6729	686	4	clauses	clause	NOUN
ejpam-6729	686	5	of	of	ADP
ejpam-6729	686	6	the	the	DET
ejpam-6729	686	7	definition	definition	NOUN
ejpam-6729	686	8	.	.	PUNCT
ejpam-6729	687	1	(	(	PUNCT
ejpam-6729	687	2	vertices	vertex	NOUN
ejpam-6729	687	3	)	)	PUNCT
ejpam-6729	687	4	since	since	SCONJ
ejpam-6729	687	5	v	v	NOUN
ejpam-6729	687	6	(	(	PUNCT
ejpam-6729	687	7	n	n	CCONJ
ejpam-6729	687	8	)	)	PUNCT
ejpam-6729	687	9	i	i	PRON
ejpam-6729	687	10	⊆	⊆	NUM
ejpam-6729	687	11	pn(v	pn(v	X
ejpam-6729	687	12	(	(	PUNCT
ejpam-6729	687	13	i	i	NOUN
ejpam-6729	687	14	)	)	PUNCT
ejpam-6729	687	15	0	0	NUM
ejpam-6729	687	16	)	)	PUNCT
ejpam-6729	687	17	for	for	ADP
ejpam-6729	687	18	each	each	DET
ejpam-6729	687	19	i	i	PRON
ejpam-6729	687	20	,	,	PUNCT
ejpam-6729	687	21	we	we	PRON
ejpam-6729	687	22	have	have	VERB
ejpam-6729	687	23	ι	ι	X
ejpam-6729	687	24	(	(	PUNCT
ejpam-6729	687	25	n	n	CCONJ
ejpam-6729	687	26	)	)	PUNCT
ejpam-6729	687	27	i	i	PRON
ejpam-6729	688	1	[	[	X
ejpam-6729	688	2	v	v	X
ejpam-6729	688	3	(	(	PUNCT
ejpam-6729	688	4	n	n	CCONJ
ejpam-6729	688	5	)	)	PUNCT
ejpam-6729	688	6	i	i	PRON
ejpam-6729	688	7	]	]	PUNCT
ejpam-6729	688	8	⊆	⊆	NUM
ejpam-6729	688	9	pn(v	pn(v	X
ejpam-6729	688	10	(	(	PUNCT
ejpam-6729	688	11	1	1	NUM
ejpam-6729	688	12	)	)	PUNCT
ejpam-6729	688	13	0	0	NUM
ejpam-6729	688	14	∪v	∪v	NOUN
ejpam-6729	688	15	(	(	PUNCT
ejpam-6729	688	16	2	2	NUM
ejpam-6729	688	17	)	)	PUNCT
ejpam-6729	688	18	0	0	NUM
ejpam-6729	688	19	)	)	PUNCT
ejpam-6729	688	20	×{i	×{i	NOUN
ejpam-6729	688	21	}	}	PUNCT
ejpam-6729	688	22	.	.	PUNCT
ejpam-6729	689	1	hence	hence	ADV
ejpam-6729	689	2	v	v	NOUN
ejpam-6729	689	3	(	(	PUNCT
ejpam-6729	689	4	n	n	CCONJ
ejpam-6729	689	5	)	)	PUNCT
ejpam-6729	689	6	⊆	⊆	NUM
ejpam-6729	689	7	pn(v	pn(v	NUM
ejpam-6729	689	8	(	(	PUNCT
ejpam-6729	689	9	1	1	NUM
ejpam-6729	689	10	)	)	PUNCT
ejpam-6729	689	11	0	0	NUM
ejpam-6729	689	12	∪	∪	PROPN
ejpam-6729	689	13	v	v	NOUN
ejpam-6729	689	14	(	(	PUNCT
ejpam-6729	689	15	2	2	NUM
ejpam-6729	689	16	)	)	PUNCT
ejpam-6729	689	17	0	0	NUM
ejpam-6729	689	18	)	)	PUNCT
ejpam-6729	689	19	×	×	NOUN
ejpam-6729	689	20	{	{	PUNCT
ejpam-6729	689	21	1	1	NUM
ejpam-6729	689	22	,	,	PUNCT
ejpam-6729	689	23	2	2	NUM
ejpam-6729	689	24	}	}	PUNCT
ejpam-6729	689	25	,	,	PUNCT
ejpam-6729	689	26	which	which	PRON
ejpam-6729	689	27	(	(	PUNCT
ejpam-6729	689	28	via	via	ADP
ejpam-6729	689	29	the	the	DET
ejpam-6729	689	30	obvious	obvious	ADJ
ejpam-6729	689	31	identification	identification	NOUN
ejpam-6729	689	32	)	)	PUNCT
ejpam-6729	689	33	sits	sit	VERB
ejpam-6729	689	34	inside	inside	ADP
ejpam-6729	689	35	pn(v	pn(v	X
ejpam-6729	689	36	(	(	PUNCT
ejpam-6729	689	37	1	1	NUM
ejpam-6729	689	38	)	)	PUNCT
ejpam-6729	689	39	0	0	NUM
ejpam-6729	689	40	∪	∪	PROPN
ejpam-6729	689	41	v	v	NOUN
ejpam-6729	689	42	(	(	PUNCT
ejpam-6729	689	43	2	2	NUM
ejpam-6729	689	44	)	)	PUNCT
ejpam-6729	689	45	0	0	NUM
ejpam-6729	689	46	)	)	PUNCT
ejpam-6729	689	47	.	.	PUNCT
ejpam-6729	690	1	(	(	PUNCT
ejpam-6729	690	2	edges	edge	NOUN
ejpam-6729	690	3	)	)	PUNCT
ejpam-6729	690	4	for	for	ADP
ejpam-6729	690	5	each	each	DET
ejpam-6729	690	6	e	e	PROPN
ejpam-6729	690	7	∈	∈	PROPN
ejpam-6729	690	8	e	e	X
ejpam-6729	690	9	(	(	PUNCT
ejpam-6729	690	10	n	n	CCONJ
ejpam-6729	690	11	)	)	PUNCT
ejpam-6729	691	1	i	i	PRON
ejpam-6729	691	2	we	we	PRON
ejpam-6729	691	3	know	know	VERB
ejpam-6729	691	4	e	e	NOUN
ejpam-6729	691	5	⊆	⊆	NUM
ejpam-6729	691	6	v	v	ADP
ejpam-6729	691	7	(	(	PUNCT
ejpam-6729	691	8	n	n	CCONJ
ejpam-6729	691	9	)	)	PUNCT
ejpam-6729	691	10	i	i	PRON
ejpam-6729	691	11	and	and	CCONJ
ejpam-6729	691	12	e	e	PROPN
ejpam-6729	691	13	6=	6=	X
ejpam-6729	691	14	∅.	∅.	VERB
ejpam-6729	691	15	therefore	therefore	ADV
ejpam-6729	691	16	ι(n)i	ι(n)i	PUNCT
ejpam-6729	692	1	[	[	X
ejpam-6729	692	2	e	e	X
ejpam-6729	692	3	]	]	X
ejpam-6729	692	4	⊆	⊆	NUM
ejpam-6729	692	5	ι	ι	X
ejpam-6729	692	6	(	(	PUNCT
ejpam-6729	692	7	n	n	CCONJ
ejpam-6729	692	8	)	)	PUNCT
ejpam-6729	692	9	i	i	PRON
ejpam-6729	693	1	[	[	X
ejpam-6729	693	2	v	v	X
ejpam-6729	693	3	(	(	PUNCT
ejpam-6729	693	4	n	n	CCONJ
ejpam-6729	693	5	)	)	PUNCT
ejpam-6729	693	6	i	i	PRON
ejpam-6729	693	7	]	]	PUNCT
ejpam-6729	694	1	⊆	⊆	NUM
ejpam-6729	694	2	v	v	NOUN
ejpam-6729	694	3	(	(	PUNCT
ejpam-6729	694	4	n	n	CCONJ
ejpam-6729	694	5	)	)	PUNCT
ejpam-6729	694	6	,	,	PUNCT
ejpam-6729	694	7	and	and	CCONJ
ejpam-6729	694	8	ι	ι	PROPN
ejpam-6729	694	9	(	(	PUNCT
ejpam-6729	694	10	n	n	CCONJ
ejpam-6729	694	11	)	)	PUNCT
ejpam-6729	694	12	i	i	PRON
ejpam-6729	695	1	[	[	X
ejpam-6729	695	2	e	e	X
ejpam-6729	695	3	]	]	X
ejpam-6729	695	4	6=	6=	ADP
ejpam-6729	695	5	∅.	∅.	VERB
ejpam-6729	695	6	thus	thus	ADV
ejpam-6729	695	7	every	every	DET
ejpam-6729	695	8	element	element	NOUN
ejpam-6729	695	9	of	of	ADP
ejpam-6729	695	10	e(n	e(n	PROPN
ejpam-6729	695	11	)	)	PUNCT
ejpam-6729	695	12	is	be	AUX
ejpam-6729	695	13	a	a	DET
ejpam-6729	695	14	nonempty	nonempty	ADJ
ejpam-6729	695	15	subset	subset	NOUN
ejpam-6729	695	16	of	of	ADP
ejpam-6729	695	17	v	v	NOUN
ejpam-6729	695	18	(	(	PUNCT
ejpam-6729	695	19	n	n	CCONJ
ejpam-6729	695	20	)	)	PUNCT
ejpam-6729	695	21	.	.	PUNCT
ejpam-6729	696	1	(	(	PUNCT
ejpam-6729	696	2	labels	label	NOUN
ejpam-6729	696	3	)	)	PUNCT
ejpam-6729	696	4	if	if	SCONJ
ejpam-6729	696	5	ι	ι	X
ejpam-6729	696	6	(	(	PUNCT
ejpam-6729	696	7	n	n	CCONJ
ejpam-6729	696	8	)	)	PUNCT
ejpam-6729	696	9	i	i	PRON
ejpam-6729	697	1	[	[	X
ejpam-6729	697	2	e	e	X
ejpam-6729	697	3	]	]	X
ejpam-6729	697	4	=	=	SYM
ejpam-6729	697	5	ι	ι	PROPN
ejpam-6729	697	6	(	(	PUNCT
ejpam-6729	697	7	n	n	CCONJ
ejpam-6729	697	8	)	)	PUNCT
ejpam-6729	697	9	j	j	NOUN
ejpam-6729	698	1	[	[	X
ejpam-6729	698	2	e′	e′	PROPN
ejpam-6729	698	3	]	]	X
ejpam-6729	698	4	,	,	PUNCT
ejpam-6729	698	5	then	then	ADV
ejpam-6729	698	6	necessarily	necessarily	ADV
ejpam-6729	698	7	i	i	PRON
ejpam-6729	698	8	=	=	SYM
ejpam-6729	698	9	j	j	PROPN
ejpam-6729	698	10	and	and	CCONJ
ejpam-6729	698	11	e	e	X
ejpam-6729	698	12	=	=	SYM
ejpam-6729	698	13	e′	e′	PROPN
ejpam-6729	698	14	(	(	PUNCT
ejpam-6729	698	15	by	by	ADP
ejpam-6729	698	16	tagging	tag	VERB
ejpam-6729	698	17	)	)	PUNCT
ejpam-6729	698	18	,	,	PUNCT
ejpam-6729	698	19	so	so	CCONJ
ejpam-6729	698	20	the	the	DET
ejpam-6729	698	21	piecewise	piecewise	NOUN
ejpam-6729	698	22	definition	definition	NOUN
ejpam-6729	698	23	λ(ι	λ(ι	PROPN
ejpam-6729	698	24	(	(	PUNCT
ejpam-6729	698	25	n	n	CCONJ
ejpam-6729	698	26	)	)	PUNCT
ejpam-6729	698	27	i	i	PRON
ejpam-6729	699	1	[	[	X
ejpam-6729	699	2	e	e	X
ejpam-6729	699	3	]	]	X
ejpam-6729	699	4	)	)	PUNCT
ejpam-6729	699	5	=	=	SYM
ejpam-6729	699	6	λi(e	λi(e	NOUN
ejpam-6729	699	7	)	)	PUNCT
ejpam-6729	699	8	is	be	AUX
ejpam-6729	699	9	well	well	ADV
ejpam-6729	699	10	-	-	PUNCT
ejpam-6729	699	11	defined	define	VERB
ejpam-6729	699	12	and	and	CCONJ
ejpam-6729	699	13	maps	map	NOUN
ejpam-6729	699	14	into	into	ADP
ejpam-6729	699	15	σ	σ	PROPN
ejpam-6729	699	16	.	.	PUNCT
ejpam-6729	699	17	t.	t.	PROPN
ejpam-6729	699	18	fujita	fujita	PROPN
ejpam-6729	699	19	,	,	PUNCT
ejpam-6729	699	20	f.	f.	PROPN
ejpam-6729	699	21	smarandache	smarandache	PROPN
ejpam-6729	699	22	/	/	SYM
ejpam-6729	699	23	eur	eur	PROPN
ejpam-6729	699	24	.	.	PUNCT
ejpam-6729	700	1	j.	j.	PROPN
ejpam-6729	700	2	pure	pure	PROPN
ejpam-6729	700	3	appl	appl	PROPN
ejpam-6729	700	4	.	.	PROPN
ejpam-6729	700	5	math	math	PROPN
ejpam-6729	700	6	,	,	PUNCT
ejpam-6729	700	7	18	18	NUM
ejpam-6729	700	8	(	(	PUNCT
ejpam-6729	700	9	4	4	NUM
ejpam-6729	700	10	)	)	PUNCT
ejpam-6729	700	11	(	(	PUNCT
ejpam-6729	700	12	2025	2025	NUM
ejpam-6729	700	13	)	)	PUNCT
ejpam-6729	700	14	,	,	PUNCT
ejpam-6729	700	15	6729	6729	NUM
ejpam-6729	700	16	30	30	NUM
ejpam-6729	700	17	of	of	ADP
ejpam-6729	700	18	36	36	NUM
ejpam-6729	700	19	(	(	PUNCT
ejpam-6729	700	20	properties	property	NOUN
ejpam-6729	700	21	)	)	PUNCT
ejpam-6729	700	22	for	for	ADP
ejpam-6729	700	23	any	any	DET
ejpam-6729	700	24	x	x	SYM
ejpam-6729	700	25	∈	∈	PROPN
ejpam-6729	700	26	⋃n	⋃n	PROPN
ejpam-6729	700	27	r=0	r=0	PROPN
ejpam-6729	700	28	pr(v	pr(v	X
ejpam-6729	700	29	(	(	PUNCT
ejpam-6729	700	30	i	i	NOUN
ejpam-6729	700	31	)	)	PUNCT
ejpam-6729	700	32	0	0	NUM
ejpam-6729	700	33	)	)	PUNCT
ejpam-6729	700	34	or	or	CCONJ
ejpam-6729	700	35	x	x	SYM
ejpam-6729	700	36	∈	∈	NOUN
ejpam-6729	700	37	e	e	X
ejpam-6729	700	38	(	(	PUNCT
ejpam-6729	700	39	n	n	CCONJ
ejpam-6729	700	40	)	)	PUNCT
ejpam-6729	700	41	i	i	PRON
ejpam-6729	700	42	,	,	PUNCT
ejpam-6729	700	43	the	the	DET
ejpam-6729	700	44	tag	tag	NOUN
ejpam-6729	700	45	ensures	ensure	VERB
ejpam-6729	700	46	that	that	SCONJ
ejpam-6729	700	47	(	(	PUNCT
ejpam-6729	700	48	ι	ι	X
ejpam-6729	700	49	(	(	PUNCT
ejpam-6729	700	50	r	r	NOUN
ejpam-6729	700	51	)	)	PUNCT
ejpam-6729	700	52	i	i	PRON
ejpam-6729	700	53	(	(	PUNCT
ejpam-6729	700	54	x	x	NOUN
ejpam-6729	700	55	)	)	PUNCT
ejpam-6729	700	56	,	,	PUNCT
ejpam-6729	700	57	i	i	NOUN
ejpam-6729	700	58	)	)	PUNCT
ejpam-6729	700	59	determines	determine	VERB
ejpam-6729	700	60	the	the	DET
ejpam-6729	700	61	source	source	NOUN
ejpam-6729	700	62	structure	structure	NOUN
ejpam-6729	700	63	uniquely	uniquely	ADV
ejpam-6729	700	64	,	,	PUNCT
ejpam-6729	701	1	so	so	ADV
ejpam-6729	701	2	µ	µ	X
ejpam-6729	701	3	(	(	PUNCT
ejpam-6729	701	4	(	(	PUNCT
ejpam-6729	701	5	ι	ι	X
ejpam-6729	701	6	(	(	PUNCT
ejpam-6729	701	7	r	r	NOUN
ejpam-6729	701	8	)	)	PUNCT
ejpam-6729	701	9	i	i	PRON
ejpam-6729	701	10	(	(	PUNCT
ejpam-6729	701	11	x	x	NOUN
ejpam-6729	701	12	)	)	PUNCT
ejpam-6729	701	13	,	,	PUNCT
ejpam-6729	701	14	i	i	PROPN
ejpam-6729	701	15	)	)	PUNCT
ejpam-6729	701	16	,	,	PUNCT
ejpam-6729	701	17	k	k	PROPN
ejpam-6729	701	18	)	)	PUNCT
ejpam-6729	701	19	:	:	PUNCT
ejpam-6729	701	20	=	=	SYM
ejpam-6729	701	21	µi(x	µi(x	ADP
ejpam-6729	701	22	,	,	PUNCT
ejpam-6729	701	23	k	k	NOUN
ejpam-6729	701	24	)	)	PUNCT
ejpam-6729	701	25	is	be	AUX
ejpam-6729	701	26	well	well	ADV
ejpam-6729	701	27	-	-	PUNCT
ejpam-6729	701	28	defined	define	VERB
ejpam-6729	701	29	with	with	ADP
ejpam-6729	701	30	codomain	codomain	ADJ
ejpam-6729	701	31	s	s	NOUN
ejpam-6729	701	32	∪	∪	X
ejpam-6729	701	33	{	{	PUNCT
ejpam-6729	701	34	⊥	⊥	NOUN
ejpam-6729	701	35	}	}	PUNCT
ejpam-6729	701	36	.	.	PUNCT
ejpam-6729	702	1	all	all	DET
ejpam-6729	702	2	axioms	axiom	NOUN
ejpam-6729	702	3	are	be	AUX
ejpam-6729	702	4	therefore	therefore	ADV
ejpam-6729	702	5	satisfied	satisfied	ADJ
ejpam-6729	702	6	,	,	PUNCT
ejpam-6729	702	7	so	so	CCONJ
ejpam-6729	702	8	(	(	PUNCT
ejpam-6729	702	9	v	v	NOUN
ejpam-6729	702	10	(	(	PUNCT
ejpam-6729	702	11	n	n	CCONJ
ejpam-6729	702	12	)	)	PUNCT
ejpam-6729	702	13	,	,	PUNCT
ejpam-6729	702	14	e(n	e(n	PROPN
ejpam-6729	702	15	)	)	PUNCT
ejpam-6729	702	16	,	,	PUNCT
ejpam-6729	702	17	λ	λ	PROPN
ejpam-6729	702	18	,	,	PUNCT
ejpam-6729	702	19	µ	µ	NOUN
ejpam-6729	702	20	)	)	PUNCT
ejpam-6729	702	21	is	be	AUX
ejpam-6729	702	22	a	a	DET
ejpam-6729	702	23	property	property	NOUN
ejpam-6729	702	24	n	n	CCONJ
ejpam-6729	702	25	-	-	PUNCT
ejpam-6729	702	26	superhypergraph	superhypergraph	NOUN
ejpam-6729	702	27	.	.	PUNCT
ejpam-6729	703	1	if	if	SCONJ
ejpam-6729	703	2	one	one	PRON
ejpam-6729	703	3	prefers	prefer	VERB
ejpam-6729	703	4	literal	literal	ADJ
ejpam-6729	703	5	unions	union	NOUN
ejpam-6729	703	6	without	without	ADP
ejpam-6729	703	7	tags	tag	NOUN
ejpam-6729	703	8	,	,	PUNCT
ejpam-6729	703	9	the	the	DET
ejpam-6729	703	10	same	same	ADJ
ejpam-6729	703	11	construction	construction	NOUN
ejpam-6729	703	12	applies	apply	VERB
ejpam-6729	703	13	because	because	SCONJ
ejpam-6729	703	14	the	the	DET
ejpam-6729	703	15	base	base	NOUN
ejpam-6729	703	16	sets	set	NOUN
ejpam-6729	703	17	are	be	AUX
ejpam-6729	703	18	disjoint	disjoint	ADJ
ejpam-6729	703	19	;	;	PUNCT
ejpam-6729	703	20	tagging	tagging	NOUN
ejpam-6729	703	21	is	be	AUX
ejpam-6729	703	22	used	use	VERB
ejpam-6729	703	23	only	only	ADV
ejpam-6729	703	24	to	to	PART
ejpam-6729	703	25	preclude	preclude	VERB
ejpam-6729	703	26	pathological	pathological	ADJ
ejpam-6729	703	27	coincidences	coincidence	NOUN
ejpam-6729	703	28	such	such	ADJ
ejpam-6729	703	29	as	as	ADP
ejpam-6729	703	30	∅.	∅.	PRON
ejpam-6729	703	31	example	example	NOUN
ejpam-6729	703	32	16	16	NUM
ejpam-6729	703	33	(	(	PUNCT
ejpam-6729	703	34	disjoint	disjoint	PROPN
ejpam-6729	703	35	union	union	PROPN
ejpam-6729	703	36	:	:	PUNCT
ejpam-6729	703	37	a	a	DET
ejpam-6729	703	38	concrete	concrete	ADJ
ejpam-6729	703	39	n	n	NOUN
ejpam-6729	703	40	=	=	SYM
ejpam-6729	703	41	1	1	NUM
ejpam-6729	703	42	instance	instance	NOUN
ejpam-6729	703	43	)	)	PUNCT
ejpam-6729	703	44	.	.	PUNCT
ejpam-6729	704	1	fix	fix	VERB
ejpam-6729	704	2	common	common	ADJ
ejpam-6729	704	3	alphabets	alphabet	NOUN
ejpam-6729	704	4	σ	σ	X
ejpam-6729	704	5	=	=	SYM
ejpam-6729	704	6	{	{	PUNCT
ejpam-6729	704	7	α	α	NOUN
ejpam-6729	704	8	,	,	PUNCT
ejpam-6729	704	9	β	β	NOUN
ejpam-6729	704	10	}	}	PUNCT
ejpam-6729	704	11	,	,	PUNCT
ejpam-6729	704	12	k	k	X
ejpam-6729	704	13	=	=	PRON
ejpam-6729	704	14	{	{	PUNCT
ejpam-6729	704	15	info	info	NOUN
ejpam-6729	704	16	}	}	PUNCT
ejpam-6729	704	17	,	,	PUNCT
ejpam-6729	704	18	s	s	NOUN
ejpam-6729	704	19	=	=	NOUN
ejpam-6729	704	20	strings	string	NOUN
ejpam-6729	704	21	,	,	PUNCT
ejpam-6729	704	22	⊥	⊥	PROPN
ejpam-6729	704	23	/∈	/∈	PUNCT
ejpam-6729	705	1	s.	s.	PROPN
ejpam-6729	705	2	first	first	PROPN
ejpam-6729	705	3	component	component	PROPN
ejpam-6729	705	4	h	h	NOUN
ejpam-6729	705	5	(	(	PUNCT
ejpam-6729	705	6	1	1	NUM
ejpam-6729	705	7	)	)	PUNCT
ejpam-6729	705	8	1	1	NUM
ejpam-6729	705	9	.	.	PUNCT
ejpam-6729	706	1	base	base	NOUN
ejpam-6729	706	2	v	v	NOUN
ejpam-6729	706	3	(	(	PUNCT
ejpam-6729	706	4	1	1	NUM
ejpam-6729	706	5	)	)	PUNCT
ejpam-6729	706	6	0	0	NUM
ejpam-6729	707	1	=	=	SYM
ejpam-6729	707	2	{	{	PUNCT
ejpam-6729	707	3	x1	x1	PROPN
ejpam-6729	707	4	,	,	PUNCT
ejpam-6729	707	5	x2	x2	PROPN
ejpam-6729	707	6	}	}	PUNCT
ejpam-6729	707	7	(	(	PUNCT
ejpam-6729	707	8	disjoint	disjoint	NOUN
ejpam-6729	707	9	from	from	ADP
ejpam-6729	707	10	the	the	DET
ejpam-6729	707	11	other	other	ADJ
ejpam-6729	707	12	base	base	NOUN
ejpam-6729	707	13	)	)	PUNCT
ejpam-6729	707	14	.	.	PUNCT
ejpam-6729	708	1	take	take	VERB
ejpam-6729	708	2	v	v	NOUN
ejpam-6729	708	3	(	(	PUNCT
ejpam-6729	708	4	1	1	NUM
ejpam-6729	708	5	)	)	PUNCT
ejpam-6729	708	6	1	1	NUM
ejpam-6729	708	7	=	=	NOUN
ejpam-6729	708	8	{	{	PUNCT
ejpam-6729	708	9	a	a	NOUN
ejpam-6729	708	10	=	=	X
ejpam-6729	708	11	{	{	PUNCT
ejpam-6729	708	12	x1	x1	PROPN
ejpam-6729	708	13	}	}	PUNCT
ejpam-6729	708	14	,	,	PUNCT
ejpam-6729	708	15	b	b	X
ejpam-6729	708	16	=	=	PRON
ejpam-6729	708	17	{	{	PUNCT
ejpam-6729	708	18	x1	x1	PROPN
ejpam-6729	708	19	,	,	PUNCT
ejpam-6729	708	20	x2	x2	PROPN
ejpam-6729	708	21	}	}	PUNCT
ejpam-6729	708	22	}	}	PUNCT
ejpam-6729	708	23	⊆	⊆	NUM
ejpam-6729	708	24	p1	p1	NOUN
ejpam-6729	708	25	(	(	PUNCT
ejpam-6729	708	26	v	v	NOUN
ejpam-6729	708	27	(	(	PUNCT
ejpam-6729	708	28	1	1	NUM
ejpam-6729	708	29	)	)	PUNCT
ejpam-6729	708	30	0	0	NUM
ejpam-6729	708	31	)	)	PUNCT
ejpam-6729	708	32	,	,	PUNCT
ejpam-6729	709	1	e	e	X
ejpam-6729	709	2	(	(	PUNCT
ejpam-6729	709	3	1	1	NUM
ejpam-6729	709	4	)	)	SYM
ejpam-6729	709	5	1	1	NUM
ejpam-6729	709	6	=	=	SYM
ejpam-6729	709	7	{	{	PUNCT
ejpam-6729	709	8	e1	e1	PROPN
ejpam-6729	709	9	}	}	PUNCT
ejpam-6729	709	10	,	,	PUNCT
ejpam-6729	709	11	e1	e1	NOUN
ejpam-6729	709	12	=	=	SYM
ejpam-6729	709	13	{	{	PUNCT
ejpam-6729	709	14	a	a	PRON
ejpam-6729	709	15	,	,	PUNCT
ejpam-6729	709	16	b	b	NOUN
ejpam-6729	709	17	}	}	PUNCT
ejpam-6729	709	18	,	,	PUNCT
ejpam-6729	709	19	λ1(e1	λ1(e1	NOUN
ejpam-6729	709	20	)	)	PUNCT
ejpam-6729	709	21	=	=	SYM
ejpam-6729	710	1	α	α	X
ejpam-6729	710	2	,	,	PUNCT
ejpam-6729	710	3	µ1(a	µ1(a	NOUN
ejpam-6729	710	4	,	,	PUNCT
ejpam-6729	710	5	info	info	NOUN
ejpam-6729	710	6	)	)	PUNCT
ejpam-6729	710	7	=	=	PUNCT
ejpam-6729	710	8	“	"	PUNCT
ejpam-6729	710	9	single	single	ADJ
ejpam-6729	710	10	”	"	PUNCT
ejpam-6729	710	11	,	,	PUNCT
ejpam-6729	710	12	µ1(b	µ1(b	ADJ
ejpam-6729	710	13	,	,	PUNCT
ejpam-6729	710	14	info	info	NOUN
ejpam-6729	710	15	)	)	PUNCT
ejpam-6729	710	16	=	=	PUNCT
ejpam-6729	710	17	“	"	PUNCT
ejpam-6729	710	18	pair	pair	NOUN
ejpam-6729	710	19	”	"	PUNCT
ejpam-6729	710	20	,	,	PUNCT
ejpam-6729	710	21	µ1(e1	µ1(e1	NOUN
ejpam-6729	710	22	,	,	PUNCT
ejpam-6729	710	23	info	info	NOUN
ejpam-6729	710	24	)	)	PUNCT
ejpam-6729	710	25	=	=	PUNCT
ejpam-6729	710	26	“	"	PUNCT
ejpam-6729	710	27	includes	include	VERB
ejpam-6729	710	28	”	"	PUNCT
ejpam-6729	710	29	.	.	PUNCT
ejpam-6729	711	1	second	second	ADJ
ejpam-6729	711	2	component	component	NOUN
ejpam-6729	711	3	h	h	NOUN
ejpam-6729	711	4	(	(	PUNCT
ejpam-6729	711	5	1	1	NUM
ejpam-6729	711	6	)	)	SYM
ejpam-6729	711	7	2	2	NUM
ejpam-6729	711	8	.	.	PUNCT
ejpam-6729	712	1	base	base	NOUN
ejpam-6729	712	2	v	v	NOUN
ejpam-6729	712	3	(	(	PUNCT
ejpam-6729	712	4	2	2	NUM
ejpam-6729	712	5	)	)	PUNCT
ejpam-6729	712	6	0	0	NUM
ejpam-6729	713	1	=	=	SYM
ejpam-6729	713	2	{	{	PUNCT
ejpam-6729	713	3	y1	y1	PROPN
ejpam-6729	713	4	,	,	PUNCT
ejpam-6729	713	5	y2	y2	PROPN
ejpam-6729	713	6	,	,	PUNCT
ejpam-6729	713	7	y3	y3	PROPN
ejpam-6729	713	8	}	}	PUNCT
ejpam-6729	713	9	with	with	ADP
ejpam-6729	713	10	v	v	NUM
ejpam-6729	713	11	(	(	PUNCT
ejpam-6729	713	12	1	1	NUM
ejpam-6729	713	13	)	)	PUNCT
ejpam-6729	713	14	0	0	NUM
ejpam-6729	713	15	∩	∩	PROPN
ejpam-6729	713	16	v	v	X
ejpam-6729	713	17	(	(	PUNCT
ejpam-6729	713	18	2	2	NUM
ejpam-6729	713	19	)	)	PUNCT
ejpam-6729	713	20	0	0	NUM
ejpam-6729	714	1	=	=	PUNCT
ejpam-6729	714	2	∅.	∅.	NOUN
ejpam-6729	714	3	let	let	VERB
ejpam-6729	714	4	v	v	NOUN
ejpam-6729	714	5	(	(	PUNCT
ejpam-6729	714	6	1	1	NUM
ejpam-6729	714	7	)	)	SYM
ejpam-6729	714	8	2	2	NUM
ejpam-6729	714	9	=	=	SYM
ejpam-6729	714	10	{	{	PUNCT
ejpam-6729	714	11	c	c	NOUN
ejpam-6729	714	12	=	=	SYM
ejpam-6729	714	13	{	{	PUNCT
ejpam-6729	714	14	y1	y1	NOUN
ejpam-6729	714	15	,	,	PUNCT
ejpam-6729	714	16	y2	y2	PROPN
ejpam-6729	714	17	}	}	PUNCT
ejpam-6729	714	18	,	,	PUNCT
ejpam-6729	714	19	d	d	PROPN
ejpam-6729	714	20	=	=	PRON
ejpam-6729	714	21	{	{	PUNCT
ejpam-6729	714	22	y2	y2	PROPN
ejpam-6729	714	23	,	,	PUNCT
ejpam-6729	714	24	y3	y3	NOUN
ejpam-6729	714	25	}	}	PUNCT
ejpam-6729	714	26	}	}	PUNCT
ejpam-6729	714	27	⊆	⊆	NUM
ejpam-6729	714	28	p1	p1	NOUN
ejpam-6729	714	29	(	(	PUNCT
ejpam-6729	714	30	v	v	NOUN
ejpam-6729	714	31	(	(	PUNCT
ejpam-6729	714	32	2	2	NUM
ejpam-6729	714	33	)	)	PUNCT
ejpam-6729	714	34	0	0	NUM
ejpam-6729	714	35	)	)	PUNCT
ejpam-6729	714	36	,	,	PUNCT
ejpam-6729	714	37	e	e	X
ejpam-6729	714	38	(	(	PUNCT
ejpam-6729	714	39	1	1	NUM
ejpam-6729	714	40	)	)	SYM
ejpam-6729	714	41	2	2	NUM
ejpam-6729	714	42	=	=	SYM
ejpam-6729	714	43	{	{	PUNCT
ejpam-6729	714	44	e2	e2	PROPN
ejpam-6729	714	45	}	}	PUNCT
ejpam-6729	714	46	,	,	PUNCT
ejpam-6729	714	47	e2	e2	PROPN
ejpam-6729	714	48	=	=	PUNCT
ejpam-6729	714	49	{	{	PUNCT
ejpam-6729	714	50	c	c	NOUN
ejpam-6729	714	51	,	,	PUNCT
ejpam-6729	714	52	d	d	NOUN
ejpam-6729	714	53	}	}	PUNCT
ejpam-6729	714	54	,	,	PUNCT
ejpam-6729	714	55	λ2(e2	λ2(e2	PROPN
ejpam-6729	714	56	)	)	PUNCT
ejpam-6729	714	57	=	=	PUNCT
ejpam-6729	714	58	β	β	X
ejpam-6729	714	59	,	,	PUNCT
ejpam-6729	714	60	µ2(c	µ2(c	PROPN
ejpam-6729	714	61	,	,	PUNCT
ejpam-6729	714	62	info	info	NOUN
ejpam-6729	714	63	)	)	PUNCT
ejpam-6729	714	64	=	=	PUNCT
ejpam-6729	714	65	“	"	PUNCT
ejpam-6729	714	66	left	leave	VERB
ejpam-6729	714	67	”	"	PUNCT
ejpam-6729	714	68	,	,	PUNCT
ejpam-6729	714	69	µ2(d	µ2(d	NOUN
ejpam-6729	714	70	,	,	PUNCT
ejpam-6729	714	71	info	info	NOUN
ejpam-6729	714	72	)	)	PUNCT
ejpam-6729	714	73	=	=	PUNCT
ejpam-6729	715	1	“	"	PUNCT
ejpam-6729	715	2	right	right	ADJ
ejpam-6729	715	3	”	"	PUNCT
ejpam-6729	715	4	,	,	PUNCT
ejpam-6729	715	5	µ2(e2	µ2(e2	NUM
ejpam-6729	715	6	,	,	PUNCT
ejpam-6729	715	7	info	info	NOUN
ejpam-6729	715	8	)	)	PUNCT
ejpam-6729	715	9	=	=	PUNCT
ejpam-6729	715	10	“	"	PUNCT
ejpam-6729	715	11	adjacent	adjacent	ADJ
ejpam-6729	715	12	”	"	PUNCT
ejpam-6729	715	13	.	.	PUNCT
ejpam-6729	716	1	tagged	tag	VERB
ejpam-6729	716	2	disjoint	disjoint	PROPN
ejpam-6729	716	3	union	union	PROPN
ejpam-6729	716	4	.	.	PUNCT
ejpam-6729	717	1	using	use	VERB
ejpam-6729	717	2	the	the	DET
ejpam-6729	717	3	injections	injection	NOUN
ejpam-6729	717	4	ι	ι	X
ejpam-6729	717	5	(	(	PUNCT
ejpam-6729	717	6	1	1	X
ejpam-6729	717	7	)	)	PUNCT
ejpam-6729	717	8	i	i	PRON
ejpam-6729	717	9	:	:	PUNCT
ejpam-6729	717	10	p1(v	p1(v	PROPN
ejpam-6729	717	11	(	(	PUNCT
ejpam-6729	717	12	i	i	NOUN
ejpam-6729	717	13	)	)	PUNCT
ejpam-6729	717	14	0	0	NUM
ejpam-6729	717	15	)	)	PUNCT
ejpam-6729	718	1	→	→	PUNCT
ejpam-6729	718	2	p1(v	p1(v	PROPN
ejpam-6729	718	3	(	(	PUNCT
ejpam-6729	718	4	1	1	NUM
ejpam-6729	718	5	)	)	PUNCT
ejpam-6729	718	6	0	0	NUM
ejpam-6729	718	7	∪	∪	PROPN
ejpam-6729	718	8	v	v	NOUN
ejpam-6729	718	9	(	(	PUNCT
ejpam-6729	718	10	2	2	NUM
ejpam-6729	718	11	)	)	PUNCT
ejpam-6729	718	12	0	0	NUM
ejpam-6729	718	13	)	)	PUNCT
ejpam-6729	718	14	×	×	NOUN
ejpam-6729	718	15	{	{	PUNCT
ejpam-6729	718	16	i	i	NOUN
ejpam-6729	718	17	}	}	PUNCT
ejpam-6729	718	18	,	,	PUNCT
ejpam-6729	718	19	form	form	NOUN
ejpam-6729	718	20	v	v	NOUN
ejpam-6729	718	21	(	(	PUNCT
ejpam-6729	718	22	1	1	NUM
ejpam-6729	718	23	)	)	PUNCT
ejpam-6729	718	24	=	=	SYM
ejpam-6729	719	1	ι	ι	PROPN
ejpam-6729	719	2	(	(	PUNCT
ejpam-6729	719	3	1	1	NUM
ejpam-6729	719	4	)	)	PUNCT
ejpam-6729	719	5	1	1	NUM
ejpam-6729	720	1	[	[	X
ejpam-6729	720	2	v	v	X
ejpam-6729	720	3	(	(	PUNCT
ejpam-6729	720	4	1	1	NUM
ejpam-6729	720	5	)	)	PUNCT
ejpam-6729	720	6	1	1	NUM
ejpam-6729	720	7	]	]	PUNCT
ejpam-6729	720	8	∪	∪	X
ejpam-6729	720	9	ι	ι	PROPN
ejpam-6729	720	10	(	(	PUNCT
ejpam-6729	720	11	1	1	NUM
ejpam-6729	720	12	)	)	PUNCT
ejpam-6729	720	13	2	2	NUM
ejpam-6729	720	14	[	[	X
ejpam-6729	720	15	v	v	X
ejpam-6729	720	16	(	(	PUNCT
ejpam-6729	720	17	1	1	NUM
ejpam-6729	720	18	)	)	PUNCT
ejpam-6729	720	19	2	2	NUM
ejpam-6729	720	20	]	]	PUNCT
ejpam-6729	720	21	,	,	PUNCT
ejpam-6729	720	22	e(1	e(1	PROPN
ejpam-6729	720	23	)	)	PUNCT
ejpam-6729	720	24	=	=	PRON
ejpam-6729	720	25	{	{	PUNCT
ejpam-6729	720	26	ι(1)1	ι(1)1	NOUN
ejpam-6729	721	1	[	[	X
ejpam-6729	721	2	e1	e1	NOUN
ejpam-6729	721	3	]	]	PUNCT
ejpam-6729	721	4	,	,	PUNCT
ejpam-6729	721	5	ι	ι	X
ejpam-6729	721	6	(	(	PUNCT
ejpam-6729	721	7	1	1	NUM
ejpam-6729	721	8	)	)	PUNCT
ejpam-6729	721	9	2	2	NUM
ejpam-6729	722	1	[	[	X
ejpam-6729	722	2	e2	e2	X
ejpam-6729	722	3	]	]	PUNCT
ejpam-6729	722	4	}	}	PUNCT
ejpam-6729	722	5	.	.	PUNCT
ejpam-6729	723	1	define	define	VERB
ejpam-6729	723	2	λ	λ	INTJ
ejpam-6729	723	3	(	(	PUNCT
ejpam-6729	723	4	ι	ι	X
ejpam-6729	723	5	(	(	PUNCT
ejpam-6729	723	6	1	1	NUM
ejpam-6729	723	7	)	)	PUNCT
ejpam-6729	723	8	1	1	NUM
ejpam-6729	724	1	[	[	X
ejpam-6729	724	2	e1	e1	NOUN
ejpam-6729	724	3	]	]	PUNCT
ejpam-6729	724	4	)	)	PUNCT
ejpam-6729	725	1	=	=	SYM
ejpam-6729	725	2	α	α	X
ejpam-6729	725	3	,	,	PUNCT
ejpam-6729	725	4	λ	λ	PROPN
ejpam-6729	725	5	(	(	PUNCT
ejpam-6729	725	6	ι	ι	X
ejpam-6729	725	7	(	(	PUNCT
ejpam-6729	725	8	1	1	NUM
ejpam-6729	725	9	)	)	PUNCT
ejpam-6729	725	10	2	2	NUM
ejpam-6729	726	1	[	[	X
ejpam-6729	726	2	e2	e2	X
ejpam-6729	726	3	]	]	PUNCT
ejpam-6729	726	4	)	)	PUNCT
ejpam-6729	727	1	=	=	SYM
ejpam-6729	727	2	β	β	NOUN
ejpam-6729	727	3	,	,	PUNCT
ejpam-6729	727	4	and	and	CCONJ
ejpam-6729	727	5	for	for	ADP
ejpam-6729	727	6	x	x	PROPN
ejpam-6729	727	7	∈	∈	PROPN
ejpam-6729	727	8	v	v	ADP
ejpam-6729	727	9	(	(	PUNCT
ejpam-6729	727	10	1	1	NUM
ejpam-6729	727	11	)	)	PUNCT
ejpam-6729	727	12	j	j	PROPN
ejpam-6729	727	13	∪	∪	X
ejpam-6729	727	14	e	e	X
ejpam-6729	727	15	(	(	PUNCT
ejpam-6729	727	16	1	1	X
ejpam-6729	727	17	)	)	PUNCT
ejpam-6729	727	18	j	j	PROPN
ejpam-6729	727	19	,	,	PUNCT
ejpam-6729	727	20	µ	µ	X
ejpam-6729	727	21	(	(	PUNCT
ejpam-6729	727	22	(	(	PUNCT
ejpam-6729	727	23	ι	ι	X
ejpam-6729	727	24	(	(	PUNCT
ejpam-6729	727	25	1	1	NUM
ejpam-6729	727	26	)	)	PUNCT
ejpam-6729	727	27	j	j	NOUN
ejpam-6729	727	28	(	(	PUNCT
ejpam-6729	727	29	x	x	NOUN
ejpam-6729	727	30	)	)	PUNCT
ejpam-6729	727	31	,	,	PUNCT
ejpam-6729	727	32	j	j	PROPN
ejpam-6729	727	33	)	)	PUNCT
ejpam-6729	727	34	,	,	PUNCT
ejpam-6729	727	35	info	info	NOUN
ejpam-6729	727	36	)	)	PUNCT
ejpam-6729	727	37	:	:	PUNCT
ejpam-6729	728	1	=	=	SYM
ejpam-6729	728	2	µj(x	µj(x	X
ejpam-6729	728	3	,	,	PUNCT
ejpam-6729	728	4	info	info	NOUN
ejpam-6729	728	5	)	)	PUNCT
ejpam-6729	728	6	(	(	PUNCT
ejpam-6729	728	7	j	j	NOUN
ejpam-6729	728	8	=	=	SYM
ejpam-6729	728	9	1	1	NUM
ejpam-6729	728	10	,	,	PUNCT
ejpam-6729	728	11	2	2	NUM
ejpam-6729	728	12	)	)	PUNCT
ejpam-6729	728	13	.	.	PUNCT
ejpam-6729	729	1	then	then	ADV
ejpam-6729	729	2	h(1	h(1	PROPN
ejpam-6729	729	3	)	)	PUNCT
ejpam-6729	729	4	=	=	PRON
ejpam-6729	729	5	(	(	PUNCT
ejpam-6729	729	6	v	v	NOUN
ejpam-6729	729	7	(	(	PUNCT
ejpam-6729	729	8	1	1	NUM
ejpam-6729	729	9	)	)	PUNCT
ejpam-6729	729	10	,	,	PUNCT
ejpam-6729	729	11	e(1	e(1	PROPN
ejpam-6729	729	12	)	)	PUNCT
ejpam-6729	729	13	,	,	PUNCT
ejpam-6729	729	14	λ	λ	PROPN
ejpam-6729	729	15	,	,	PUNCT
ejpam-6729	729	16	µ	µ	NOUN
ejpam-6729	729	17	)	)	PUNCT
ejpam-6729	729	18	is	be	AUX
ejpam-6729	729	19	a	a	DET
ejpam-6729	729	20	property	property	NOUN
ejpam-6729	729	21	1	1	NUM
ejpam-6729	729	22	-	-	PUNCT
ejpam-6729	729	23	superhypergraph	superhypergraph	NOUN
ejpam-6729	729	24	(	(	PUNCT
ejpam-6729	729	25	property	property	NOUN
ejpam-6729	729	26	hypergraph	hypergraph	NOUN
ejpam-6729	729	27	)	)	PUNCT
ejpam-6729	729	28	over	over	ADP
ejpam-6729	729	29	the	the	DET
ejpam-6729	729	30	disjoint	disjoint	NOUN
ejpam-6729	729	31	base	base	NOUN
ejpam-6729	729	32	v	v	NOUN
ejpam-6729	729	33	(	(	PUNCT
ejpam-6729	729	34	1	1	NUM
ejpam-6729	729	35	)	)	PUNCT
ejpam-6729	729	36	0	0	NUM
ejpam-6729	729	37	∪v	∪v	NOUN
ejpam-6729	729	38	(	(	PUNCT
ejpam-6729	729	39	2	2	NUM
ejpam-6729	729	40	)	)	PUNCT
ejpam-6729	729	41	0	0	NUM
ejpam-6729	729	42	by	by	ADP
ejpam-6729	729	43	theorem	theorem	NOUN
ejpam-6729	729	44	13	13	NUM
ejpam-6729	729	45	.	.	PUNCT
ejpam-6729	730	1	if	if	SCONJ
ejpam-6729	730	2	one	one	PRON
ejpam-6729	730	3	suppresses	suppress	VERB
ejpam-6729	730	4	tags	tag	NOUN
ejpam-6729	730	5	,	,	PUNCT
ejpam-6729	730	6	disjointness	disjointness	NOUN
ejpam-6729	730	7	of	of	ADP
ejpam-6729	730	8	the	the	DET
ejpam-6729	730	9	bases	basis	NOUN
ejpam-6729	730	10	still	still	ADV
ejpam-6729	730	11	prevents	prevent	VERB
ejpam-6729	730	12	accidental	accidental	ADJ
ejpam-6729	730	13	identifications	identification	NOUN
ejpam-6729	730	14	.	.	PUNCT
ejpam-6729	731	1	t.	t.	PROPN
ejpam-6729	731	2	fujita	fujita	PROPN
ejpam-6729	731	3	,	,	PUNCT
ejpam-6729	731	4	f.	f.	PROPN
ejpam-6729	731	5	smarandache	smarandache	PROPN
ejpam-6729	731	6	/	/	SYM
ejpam-6729	731	7	eur	eur	PROPN
ejpam-6729	731	8	.	.	PUNCT
ejpam-6729	732	1	j.	j.	PROPN
ejpam-6729	732	2	pure	pure	PROPN
ejpam-6729	732	3	appl	appl	PROPN
ejpam-6729	732	4	.	.	PROPN
ejpam-6729	732	5	math	math	PROPN
ejpam-6729	732	6	,	,	PUNCT
ejpam-6729	732	7	18	18	NUM
ejpam-6729	732	8	(	(	PUNCT
ejpam-6729	732	9	4	4	NUM
ejpam-6729	732	10	)	)	PUNCT
ejpam-6729	732	11	(	(	PUNCT
ejpam-6729	732	12	2025	2025	NUM
ejpam-6729	732	13	)	)	PUNCT
ejpam-6729	732	14	,	,	PUNCT
ejpam-6729	732	15	6729	6729	NUM
ejpam-6729	732	16	31	31	NUM
ejpam-6729	732	17	of	of	ADP
ejpam-6729	732	18	36	36	NUM
ejpam-6729	732	19	theorem	theorem	VERB
ejpam-6729	732	20	14	14	NUM
ejpam-6729	732	21	(	(	PUNCT
ejpam-6729	732	22	line	line	NOUN
ejpam-6729	732	23	graph	graph	NOUN
ejpam-6729	732	24	as	as	ADP
ejpam-6729	732	25	a	a	DET
ejpam-6729	732	26	property	property	NOUN
ejpam-6729	732	27	graph	graph	NOUN
ejpam-6729	732	28	)	)	PUNCT
ejpam-6729	732	29	.	.	PUNCT
ejpam-6729	733	1	let	let	VERB
ejpam-6729	733	2	h(n	h(n	PRON
ejpam-6729	733	3	)	)	PUNCT
ejpam-6729	734	1	=	=	PRON
ejpam-6729	734	2	(	(	PUNCT
ejpam-6729	734	3	v	v	NOUN
ejpam-6729	734	4	(	(	PUNCT
ejpam-6729	734	5	n	n	CCONJ
ejpam-6729	734	6	)	)	PUNCT
ejpam-6729	734	7	,	,	PUNCT
ejpam-6729	734	8	e(n	e(n	PROPN
ejpam-6729	734	9	)	)	PUNCT
ejpam-6729	734	10	,	,	PUNCT
ejpam-6729	734	11	λ	λ	PROPN
ejpam-6729	734	12	,	,	PUNCT
ejpam-6729	734	13	µ	µ	NOUN
ejpam-6729	734	14	)	)	PUNCT
ejpam-6729	734	15	be	be	AUX
ejpam-6729	734	16	a	a	DET
ejpam-6729	734	17	property	property	NOUN
ejpam-6729	734	18	n	n	CCONJ
ejpam-6729	734	19	-	-	PUNCT
ejpam-6729	734	20	superhypergraph	superhypergraph	NOUN
ejpam-6729	734	21	.	.	PUNCT
ejpam-6729	735	1	define	define	VERB
ejpam-6729	735	2	its	its	PRON
ejpam-6729	735	3	line	line	NOUN
ejpam-6729	735	4	graph	graph	NOUN
ejpam-6729	735	5	g	g	NOUN
ejpam-6729	735	6	by	by	ADP
ejpam-6729	735	7	vg	vg	NOUN
ejpam-6729	735	8	:	:	PUNCT
ejpam-6729	735	9	=	=	SYM
ejpam-6729	735	10	e(n	e(n	PROPN
ejpam-6729	735	11	)	)	PUNCT
ejpam-6729	735	12	,	,	PUNCT
ejpam-6729	735	13	eg	eg	NOUN
ejpam-6729	735	14	:	:	PUNCT
ejpam-6729	735	15	=	=	SYM
ejpam-6729	735	16	{	{	PUNCT
ejpam-6729	735	17	(	(	PUNCT
ejpam-6729	735	18	e1	e1	PROPN
ejpam-6729	735	19	,	,	PUNCT
ejpam-6729	735	20	e2	e2	NOUN
ejpam-6729	735	21	)	)	PUNCT
ejpam-6729	735	22	∈	∈	PROPN
ejpam-6729	735	23	vg	vg	ADP
ejpam-6729	735	24	×	×	NOUN
ejpam-6729	735	25	vg	vg	NOUN
ejpam-6729	735	26	∣∣	∣∣	X
ejpam-6729	735	27	e1	e1	PROPN
ejpam-6729	735	28	6=	6=	PROPN
ejpam-6729	735	29	e2	e2	PROPN
ejpam-6729	735	30	,	,	PUNCT
ejpam-6729	735	31	e1	e1	PROPN
ejpam-6729	735	32	∩	∩	ADJ
ejpam-6729	735	33	e2	e2	PROPN
ejpam-6729	735	34	6=	6=	PRON
ejpam-6729	735	35	∅	∅	NOUN
ejpam-6729	735	36	}	}	PUNCT
ejpam-6729	735	37	.	.	PUNCT
ejpam-6729	736	1	let	let	VERB
ejpam-6729	736	2	s(e1	s(e1	NOUN
ejpam-6729	736	3	,	,	PUNCT
ejpam-6729	736	4	e2	e2	PROPN
ejpam-6729	736	5	)	)	PUNCT
ejpam-6729	736	6	=	=	SYM
ejpam-6729	736	7	e1	e1	PROPN
ejpam-6729	736	8	and	and	CCONJ
ejpam-6729	736	9	t(e1	t(e1	NOUN
ejpam-6729	736	10	,	,	PUNCT
ejpam-6729	736	11	e2	e2	PROPN
ejpam-6729	736	12	)	)	PUNCT
ejpam-6729	736	13	=	=	SYM
ejpam-6729	736	14	e2	e2	PROPN
ejpam-6729	736	15	,	,	PUNCT
ejpam-6729	736	16	set	set	VERB
ejpam-6729	736	17	λg(e1	λg(e1	ADV
ejpam-6729	736	18	,	,	PUNCT
ejpam-6729	736	19	e2	e2	PROPN
ejpam-6729	736	20	)	)	PUNCT
ejpam-6729	736	21	:	:	PUNCT
ejpam-6729	736	22	=	=	SYM
ejpam-6729	736	23	λ(e1	λ(e1	X
ejpam-6729	736	24	)	)	PUNCT
ejpam-6729	736	25	∈	∈	PROPN
ejpam-6729	736	26	σ	σ	PROPN
ejpam-6729	736	27	,	,	PUNCT
ejpam-6729	736	28	and	and	CCONJ
ejpam-6729	736	29	define	define	VERB
ejpam-6729	736	30	a	a	DET
ejpam-6729	736	31	property	property	NOUN
ejpam-6729	736	32	map	map	NOUN
ejpam-6729	736	33	µg(x	µg(x	ADV
ejpam-6729	736	34	,	,	PUNCT
ejpam-6729	736	35	k	k	NOUN
ejpam-6729	736	36	)	)	PUNCT
ejpam-6729	736	37	:	:	PUNCT
ejpam-6729	737	1	=	=	PRON
ejpam-6729	737	2	{	{	PUNCT
ejpam-6729	737	3	µ(x	µ(x	PROPN
ejpam-6729	737	4	,	,	PUNCT
ejpam-6729	737	5	k	k	NOUN
ejpam-6729	737	6	)	)	PUNCT
ejpam-6729	737	7	,	,	PUNCT
ejpam-6729	737	8	x	x	PUNCT
ejpam-6729	737	9	∈	∈	NOUN
ejpam-6729	737	10	vg(=	vg(=	NOUN
ejpam-6729	737	11	e(n	e(n	NOUN
ejpam-6729	737	12	)	)	PUNCT
ejpam-6729	737	13	)	)	PUNCT
ejpam-6729	737	14	,	,	PUNCT
ejpam-6729	737	15	⊥	⊥	PROPN
ejpam-6729	737	16	,	,	PUNCT
ejpam-6729	737	17	x	x	SYM
ejpam-6729	737	18	∈	∈	PROPN
ejpam-6729	737	19	eg	eg	NOUN
ejpam-6729	737	20	.	.	PUNCT
ejpam-6729	738	1	then	then	ADV
ejpam-6729	738	2	g	g	PROPN
ejpam-6729	738	3	=	=	PUNCT
ejpam-6729	738	4	(	(	PUNCT
ejpam-6729	738	5	vg	vg	NOUN
ejpam-6729	738	6	,	,	PUNCT
ejpam-6729	738	7	eg	eg	NOUN
ejpam-6729	738	8	,	,	PUNCT
ejpam-6729	738	9	s	s	PROPN
ejpam-6729	738	10	,	,	PUNCT
ejpam-6729	738	11	t	t	PROPN
ejpam-6729	738	12	,	,	PUNCT
ejpam-6729	738	13	λg	λg	NOUN
ejpam-6729	738	14	,	,	PUNCT
ejpam-6729	738	15	µg,⊥	µg,⊥	NUM
ejpam-6729	738	16	)	)	PUNCT
ejpam-6729	738	17	is	be	AUX
ejpam-6729	738	18	a	a	DET
ejpam-6729	738	19	property	property	NOUN
ejpam-6729	738	20	graph	graph	NOUN
ejpam-6729	738	21	.	.	PUNCT
ejpam-6729	739	1	proof	proof	NOUN
ejpam-6729	739	2	.	.	PUNCT
ejpam-6729	740	1	we	we	PRON
ejpam-6729	740	2	check	check	VERB
ejpam-6729	740	3	each	each	DET
ejpam-6729	740	4	item	item	NOUN
ejpam-6729	740	5	of	of	ADP
ejpam-6729	740	6	the	the	DET
ejpam-6729	740	7	property	property	NOUN
ejpam-6729	740	8	graph	graph	NOUN
ejpam-6729	740	9	definition	definition	NOUN
ejpam-6729	740	10	.	.	PUNCT
ejpam-6729	741	1	(	(	PUNCT
ejpam-6729	741	2	1	1	X
ejpam-6729	741	3	)	)	PUNCT
ejpam-6729	741	4	vertices	vertex	NOUN
ejpam-6729	741	5	and	and	CCONJ
ejpam-6729	741	6	edges	edge	NOUN
ejpam-6729	741	7	.	.	PUNCT
ejpam-6729	742	1	by	by	ADP
ejpam-6729	742	2	construction	construction	NOUN
ejpam-6729	742	3	vg	vg	NOUN
ejpam-6729	742	4	=	=	SYM
ejpam-6729	742	5	e(n	e(n	PROPN
ejpam-6729	742	6	)	)	PUNCT
ejpam-6729	742	7	.	.	PUNCT
ejpam-6729	743	1	every	every	DET
ejpam-6729	743	2	element	element	NOUN
ejpam-6729	743	3	of	of	ADP
ejpam-6729	743	4	eg	eg	NOUN
ejpam-6729	743	5	is	be	AUX
ejpam-6729	743	6	an	an	DET
ejpam-6729	743	7	ordered	order	VERB
ejpam-6729	743	8	pair	pair	NOUN
ejpam-6729	743	9	of	of	ADP
ejpam-6729	743	10	distinct	distinct	ADJ
ejpam-6729	743	11	superedges	superedge	NOUN
ejpam-6729	743	12	that	that	PRON
ejpam-6729	743	13	intersect	intersect	VERB
ejpam-6729	743	14	,	,	PUNCT
ejpam-6729	743	15	so	so	SCONJ
ejpam-6729	743	16	eg	eg	NOUN
ejpam-6729	743	17	⊆	⊆	NUM
ejpam-6729	743	18	vg	vg	ADP
ejpam-6729	743	19	×	×	NOUN
ejpam-6729	743	20	vg	vg	NOUN
ejpam-6729	743	21	.	.	PUNCT
ejpam-6729	744	1	(	(	PUNCT
ejpam-6729	744	2	2	2	NUM
ejpam-6729	744	3	)	)	PUNCT
ejpam-6729	744	4	source	source	NOUN
ejpam-6729	744	5	/	/	SYM
ejpam-6729	744	6	target	target	NOUN
ejpam-6729	744	7	maps	map	NOUN
ejpam-6729	744	8	.	.	PUNCT
ejpam-6729	745	1	the	the	DET
ejpam-6729	745	2	maps	map	NOUN
ejpam-6729	745	3	s	s	PROPN
ejpam-6729	745	4	,	,	PUNCT
ejpam-6729	745	5	t	t	X
ejpam-6729	745	6	:	:	PUNCT
ejpam-6729	745	7	eg	eg	PROPN
ejpam-6729	745	8	→	→	SYM
ejpam-6729	745	9	vg	vg	ADP
ejpam-6729	745	10	defined	define	VERB
ejpam-6729	745	11	by	by	ADP
ejpam-6729	745	12	s(e1	s(e1	NOUN
ejpam-6729	745	13	,	,	PUNCT
ejpam-6729	745	14	e2	e2	PROPN
ejpam-6729	745	15	)	)	PUNCT
ejpam-6729	745	16	=	=	SYM
ejpam-6729	745	17	e1	e1	PROPN
ejpam-6729	745	18	and	and	CCONJ
ejpam-6729	745	19	t(e1	t(e1	NOUN
ejpam-6729	745	20	,	,	PUNCT
ejpam-6729	745	21	e2	e2	PROPN
ejpam-6729	745	22	)	)	PUNCT
ejpam-6729	746	1	=	=	SYM
ejpam-6729	746	2	e2	e2	PROPN
ejpam-6729	746	3	are	be	AUX
ejpam-6729	746	4	well	well	ADV
ejpam-6729	746	5	-	-	PUNCT
ejpam-6729	746	6	defined	define	VERB
ejpam-6729	746	7	by	by	ADP
ejpam-6729	746	8	the	the	DET
ejpam-6729	746	9	previous	previous	ADJ
ejpam-6729	746	10	item	item	NOUN
ejpam-6729	746	11	.	.	PUNCT
ejpam-6729	747	1	(	(	PUNCT
ejpam-6729	747	2	3	3	X
ejpam-6729	747	3	)	)	PUNCT
ejpam-6729	747	4	edge	edge	NOUN
ejpam-6729	747	5	labels	label	NOUN
ejpam-6729	747	6	.	.	PUNCT
ejpam-6729	748	1	for	for	ADP
ejpam-6729	748	2	(	(	PUNCT
ejpam-6729	748	3	e1	e1	PROPN
ejpam-6729	748	4	,	,	PUNCT
ejpam-6729	748	5	e2	e2	NOUN
ejpam-6729	748	6	)	)	PUNCT
ejpam-6729	748	7	∈	∈	PROPN
ejpam-6729	748	8	eg	eg	NOUN
ejpam-6729	748	9	we	we	PRON
ejpam-6729	748	10	set	set	VERB
ejpam-6729	748	11	λg(e1	λg(e1	ADV
ejpam-6729	748	12	,	,	PUNCT
ejpam-6729	748	13	e2	e2	PROPN
ejpam-6729	748	14	)	)	PUNCT
ejpam-6729	748	15	=	=	SYM
ejpam-6729	748	16	λ(e1	λ(e1	X
ejpam-6729	748	17	)	)	PUNCT
ejpam-6729	748	18	∈	∈	PROPN
ejpam-6729	748	19	σ	σ	PROPN
ejpam-6729	748	20	.	.	PUNCT
ejpam-6729	749	1	this	this	PRON
ejpam-6729	749	2	is	be	AUX
ejpam-6729	749	3	a	a	DET
ejpam-6729	749	4	bona	bona	ADJ
ejpam-6729	749	5	fide	fide	ADJ
ejpam-6729	749	6	edge	edge	NOUN
ejpam-6729	749	7	-	-	PUNCT
ejpam-6729	749	8	labelling	labelling	NOUN
ejpam-6729	749	9	(	(	PUNCT
ejpam-6729	749	10	variants	variant	NOUN
ejpam-6729	749	11	such	such	ADJ
ejpam-6729	749	12	as	as	ADP
ejpam-6729	749	13	(	(	PUNCT
ejpam-6729	749	14	λ(e1	λ(e1	NOUN
ejpam-6729	749	15	)	)	PUNCT
ejpam-6729	749	16	,	,	PUNCT
ejpam-6729	749	17	λ(e2	λ(e2	PROPN
ejpam-6729	749	18	)	)	PUNCT
ejpam-6729	749	19	)	)	PUNCT
ejpam-6729	750	1	∈	∈	PROPN
ejpam-6729	750	2	σ×	σ×	PROPN
ejpam-6729	750	3	σ	σ	NOUN
ejpam-6729	750	4	are	be	AUX
ejpam-6729	750	5	also	also	ADV
ejpam-6729	750	6	admissible	admissible	ADJ
ejpam-6729	750	7	)	)	PUNCT
ejpam-6729	750	8	.	.	PUNCT
ejpam-6729	751	1	(	(	PUNCT
ejpam-6729	751	2	4	4	X
ejpam-6729	751	3	)	)	PUNCT
ejpam-6729	751	4	properties	property	NOUN
ejpam-6729	751	5	.	.	PUNCT
ejpam-6729	752	1	on	on	ADP
ejpam-6729	752	2	vertices	vertex	NOUN
ejpam-6729	752	3	vg	vg	X
ejpam-6729	752	4	=	=	SYM
ejpam-6729	752	5	e(n	e(n	NOUN
ejpam-6729	752	6	)	)	PUNCT
ejpam-6729	752	7	we	we	PRON
ejpam-6729	752	8	reuse	reuse	VERB
ejpam-6729	752	9	µ	µ	ADP
ejpam-6729	752	10	;	;	PUNCT
ejpam-6729	752	11	on	on	ADP
ejpam-6729	752	12	edges	edge	NOUN
ejpam-6729	752	13	we	we	PRON
ejpam-6729	752	14	assign	assign	VERB
ejpam-6729	752	15	the	the	DET
ejpam-6729	752	16	sentinel	sentinel	NOUN
ejpam-6729	752	17	⊥.	⊥.	NOUN
ejpam-6729	752	18	thus	thus	ADV
ejpam-6729	752	19	µg	µg	ADV
ejpam-6729	752	20	:	:	PUNCT
ejpam-6729	752	21	(	(	PUNCT
ejpam-6729	752	22	vg∪eg)×k	vg∪eg)×k	NOUN
ejpam-6729	752	23	→	→	PUNCT
ejpam-6729	752	24	s∪{⊥	s∪{⊥	X
ejpam-6729	752	25	}	}	PUNCT
ejpam-6729	752	26	has	have	VERB
ejpam-6729	752	27	the	the	DET
ejpam-6729	752	28	correct	correct	ADJ
ejpam-6729	752	29	codomain	codomain	NOUN
ejpam-6729	752	30	,	,	PUNCT
ejpam-6729	752	31	and	and	CCONJ
ejpam-6729	752	32	⊥	⊥	NUM
ejpam-6729	752	33	/∈	/∈	PUNCT
ejpam-6729	753	1	s	s	VERB
ejpam-6729	753	2	by	by	ADP
ejpam-6729	753	3	assumption	assumption	NOUN
ejpam-6729	753	4	.	.	PUNCT
ejpam-6729	754	1	all	all	DET
ejpam-6729	754	2	requirements	requirement	NOUN
ejpam-6729	754	3	are	be	AUX
ejpam-6729	754	4	met	meet	VERB
ejpam-6729	754	5	;	;	PUNCT
ejpam-6729	754	6	hence	hence	ADV
ejpam-6729	754	7	g	g	PROPN
ejpam-6729	754	8	is	be	AUX
ejpam-6729	754	9	a	a	DET
ejpam-6729	754	10	property	property	NOUN
ejpam-6729	754	11	graph	graph	NOUN
ejpam-6729	754	12	.	.	PUNCT
ejpam-6729	755	1	5	5	X
ejpam-6729	755	2	.	.	X
ejpam-6729	755	3	conclusion	conclusion	NOUN
ejpam-6729	755	4	and	and	CCONJ
ejpam-6729	755	5	outlook	outlook	NOUN
ejpam-6729	755	6	this	this	DET
ejpam-6729	755	7	study	study	NOUN
ejpam-6729	755	8	has	have	AUX
ejpam-6729	755	9	demonstrated	demonstrate	VERB
ejpam-6729	755	10	how	how	SCONJ
ejpam-6729	755	11	the	the	DET
ejpam-6729	755	12	expressive	expressive	ADJ
ejpam-6729	755	13	power	power	NOUN
ejpam-6729	755	14	of	of	ADP
ejpam-6729	755	15	property	property	NOUN
ejpam-6729	755	16	graphs	graph	NOUN
ejpam-6729	755	17	can	can	AUX
ejpam-6729	755	18	be	be	AUX
ejpam-6729	755	19	lifted	lift	VERB
ejpam-6729	755	20	to	to	ADP
ejpam-6729	755	21	the	the	DET
ejpam-6729	755	22	richer	rich	ADJ
ejpam-6729	755	23	settings	setting	NOUN
ejpam-6729	755	24	of	of	ADP
ejpam-6729	755	25	hypergraphs	hypergraph	NOUN
ejpam-6729	755	26	and	and	CCONJ
ejpam-6729	755	27	superhypergraphs	superhypergraph	NOUN
ejpam-6729	755	28	.	.	PUNCT
ejpam-6729	756	1	we	we	PRON
ejpam-6729	756	2	provided	provide	VERB
ejpam-6729	756	3	rigorous	rigorous	ADJ
ejpam-6729	756	4	,	,	PUNCT
ejpam-6729	756	5	uniform	uniform	ADJ
ejpam-6729	756	6	definitions	definition	NOUN
ejpam-6729	756	7	for	for	ADP
ejpam-6729	756	8	these	these	DET
ejpam-6729	756	9	generalizations	generalization	NOUN
ejpam-6729	756	10	and	and	CCONJ
ejpam-6729	756	11	presented	present	VERB
ejpam-6729	756	12	initial	initial	ADJ
ejpam-6729	756	13	results	result	NOUN
ejpam-6729	756	14	that	that	PRON
ejpam-6729	756	15	underscore	underscore	VERB
ejpam-6729	756	16	their	their	PRON
ejpam-6729	756	17	modeling	modeling	NOUN
ejpam-6729	756	18	potential	potential	NOUN
ejpam-6729	756	19	.	.	PUNCT
ejpam-6729	757	1	for	for	ADP
ejpam-6729	757	2	clarity	clarity	NOUN
ejpam-6729	757	3	and	and	CCONJ
ejpam-6729	757	4	ease	ease	NOUN
ejpam-6729	757	5	of	of	ADP
ejpam-6729	757	6	reference	reference	NOUN
ejpam-6729	757	7	,	,	PUNCT
ejpam-6729	757	8	table	table	NOUN
ejpam-6729	757	9	2	2	NUM
ejpam-6729	757	10	summarizes	summarize	NOUN
ejpam-6729	757	11	the	the	DET
ejpam-6729	757	12	concepts	concept	NOUN
ejpam-6729	757	13	introduced	introduce	VERB
ejpam-6729	757	14	and	and	CCONJ
ejpam-6729	757	15	defined	define	VERB
ejpam-6729	757	16	in	in	ADP
ejpam-6729	757	17	this	this	DET
ejpam-6729	757	18	paper	paper	NOUN
ejpam-6729	757	19	.	.	PUNCT
ejpam-6729	758	1	future	future	ADJ
ejpam-6729	758	2	work	work	NOUN
ejpam-6729	758	3	may	may	AUX
ejpam-6729	758	4	explore	explore	VERB
ejpam-6729	758	5	further	further	ADJ
ejpam-6729	758	6	extensions	extension	NOUN
ejpam-6729	758	7	based	base	VERB
ejpam-6729	758	8	on	on	ADP
ejpam-6729	758	9	advanced	advanced	ADJ
ejpam-6729	758	10	uncertainty	uncertainty	NOUN
ejpam-6729	758	11	formalisms	formalism	NOUN
ejpam-6729	758	12	—	—	PUNCT
ejpam-6729	758	13	including	include	VERB
ejpam-6729	758	14	fuzzy	fuzzy	ADJ
ejpam-6729	758	15	sets[37	sets[37	NOUN
ejpam-6729	758	16	]	]	PUNCT
ejpam-6729	758	17	,	,	PUNCT
ejpam-6729	758	18	vague	vague	ADJ
ejpam-6729	758	19	sets[38	sets[38	PROPN
ejpam-6729	758	20	]	]	PUNCT
ejpam-6729	758	21	,	,	PUNCT
ejpam-6729	758	22	intuitionistic	intuitionistic	ADJ
ejpam-6729	758	23	fuzzy	fuzzy	ADJ
ejpam-6729	758	24	sets[39	sets[39	NOUN
ejpam-6729	758	25	]	]	PUNCT
ejpam-6729	758	26	,	,	PUNCT
ejpam-6729	758	27	paraconsistent	paraconsistent	NOUN
ejpam-6729	758	28	set[40	set[40	PROPN
ejpam-6729	758	29	]	]	PUNCT
ejpam-6729	758	30	,	,	PUNCT
ejpam-6729	758	31	soft	soft	ADJ
ejpam-6729	758	32	sets[41	sets[41	NOUN
ejpam-6729	758	33	,	,	PUNCT
ejpam-6729	758	34	42	42	NUM
ejpam-6729	758	35	]	]	PUNCT
ejpam-6729	758	36	,	,	PUNCT
ejpam-6729	758	37	picture	picture	NOUN
ejpam-6729	758	38	fuzzy	fuzzy	ADJ
ejpam-6729	758	39	set[43	set[43	PROPN
ejpam-6729	758	40	,	,	PUNCT
ejpam-6729	758	41	44	44	NUM
ejpam-6729	758	42	]	]	PUNCT
ejpam-6729	758	43	,	,	PUNCT
ejpam-6729	758	44	rough	rough	ADJ
ejpam-6729	758	45	sets[45	sets[45	NOUN
ejpam-6729	758	46	,	,	PUNCT
ejpam-6729	758	47	46	46	NUM
ejpam-6729	758	48	]	]	PUNCT
ejpam-6729	758	49	,	,	PUNCT
ejpam-6729	758	50	neutrosophic	neutrosophic	ADJ
ejpam-6729	758	51	sets	set	NOUN
ejpam-6729	758	52	(	(	PUNCT
ejpam-6729	758	53	and	and	CCONJ
ejpam-6729	758	54	their	their	PRON
ejpam-6729	758	55	quadri	quadri	NOUN
ejpam-6729	758	56	-	-	PUNCT
ejpam-6729	758	57	partitioned	partition	VERB
ejpam-6729	758	58	variants	variant	NOUN
ejpam-6729	758	59	)	)	PUNCT
ejpam-6729	759	1	[	[	X
ejpam-6729	759	2	47	47	NUM
ejpam-6729	759	3	,	,	PUNCT
ejpam-6729	759	4	48	48	NUM
ejpam-6729	759	5	]	]	PUNCT
ejpam-6729	759	6	,	,	PUNCT
ejpam-6729	759	7	hesitant	hesitant	ADJ
ejpam-6729	759	8	fuzzy	fuzzy	ADJ
ejpam-6729	759	9	sets	set	NOUN
ejpam-6729	759	10	[	[	X
ejpam-6729	759	11	49	49	NUM
ejpam-6729	759	12	]	]	PUNCT
ejpam-6729	759	13	,	,	PUNCT
ejpam-6729	759	14	and	and	CCONJ
ejpam-6729	759	15	plithogenic	plithogenic	ADJ
ejpam-6729	759	16	sets	set	NOUN
ejpam-6729	759	17	[	[	X
ejpam-6729	759	18	50	50	NUM
ejpam-6729	759	19	,	,	PUNCT
ejpam-6729	759	20	51	51	NUM
ejpam-6729	759	21	]	]	PUNCT
ejpam-6729	759	22	.	.	PUNCT
ejpam-6729	760	1	each	each	PRON
ejpam-6729	760	2	of	of	ADP
ejpam-6729	760	3	these	these	DET
ejpam-6729	760	4	set	set	ADJ
ejpam-6729	760	5	-	-	PUNCT
ejpam-6729	760	6	theoretic	theoretic	NOUN
ejpam-6729	760	7	paradigms	paradigm	NOUN
ejpam-6729	760	8	already	already	ADV
ejpam-6729	760	9	possesses	possess	VERB
ejpam-6729	760	10	a	a	DET
ejpam-6729	760	11	graph	graph	NOUN
ejpam-6729	760	12	-	-	PUNCT
ejpam-6729	760	13	theoretic	theoretic	NOUN
ejpam-6729	760	14	interpretation	interpretation	NOUN
ejpam-6729	760	15	,	,	PUNCT
ejpam-6729	760	16	and	and	CCONJ
ejpam-6729	760	17	incorporating	incorporate	VERB
ejpam-6729	760	18	them	they	PRON
ejpam-6729	760	19	into	into	ADP
ejpam-6729	760	20	the	the	DET
ejpam-6729	760	21	property	property	NOUN
ejpam-6729	760	22	hypergraph	hypergraph	NOUN
ejpam-6729	760	23	and	and	CCONJ
ejpam-6729	760	24	property	property	NOUN
ejpam-6729	760	25	superhypergraph	superhypergraph	NOUN
ejpam-6729	760	26	frameworks	framework	NOUN
ejpam-6729	760	27	promises	promise	VERB
ejpam-6729	760	28	a	a	DET
ejpam-6729	760	29	fertile	fertile	ADJ
ejpam-6729	760	30	direction	direction	NOUN
ejpam-6729	760	31	for	for	ADP
ejpam-6729	760	32	research	research	NOUN
ejpam-6729	760	33	.	.	PUNCT
ejpam-6729	761	1	also	also	ADV
ejpam-6729	761	2	an	an	DET
ejpam-6729	761	3	exciting	exciting	ADJ
ejpam-6729	761	4	future	future	ADJ
ejpam-6729	761	5	direction	direction	NOUN
ejpam-6729	761	6	would	would	AUX
ejpam-6729	761	7	be	be	AUX
ejpam-6729	761	8	to	to	PART
ejpam-6729	761	9	extend	extend	VERB
ejpam-6729	761	10	property	property	NOUN
ejpam-6729	761	11	superhypergraphs	superhypergraph	NOUN
ejpam-6729	761	12	over	over	ADP
ejpam-6729	761	13	complex	complex	ADJ
ejpam-6729	761	14	algebraic	algebraic	ADJ
ejpam-6729	761	15	structures	structure	NOUN
ejpam-6729	761	16	such	such	ADJ
ejpam-6729	761	17	as	as	ADP
ejpam-6729	761	18	gaussian	gaussian	ADJ
ejpam-6729	761	19	integers	integer	NOUN
ejpam-6729	761	20	,	,	PUNCT
ejpam-6729	761	21	eisenstein	eisenstein	NOUN
ejpam-6729	761	22	integers	integer	NOUN
ejpam-6729	761	23	,	,	PUNCT
ejpam-6729	761	24	quaternion	quaternion	NOUN
ejpam-6729	761	25	integers	integer	NOUN
ejpam-6729	761	26	,	,	PUNCT
ejpam-6729	761	27	and	and	CCONJ
ejpam-6729	761	28	even	even	ADV
ejpam-6729	761	29	octonion	octonion	NOUN
ejpam-6729	761	30	algebras	algebra	NOUN
ejpam-6729	761	31	(	(	PUNCT
ejpam-6729	761	32	cf.[52	cf.[52	PROPN
ejpam-6729	761	33	,	,	PUNCT
ejpam-6729	761	34	53	53	NUM
ejpam-6729	761	35	]	]	PUNCT
ejpam-6729	761	36	)	)	PUNCT
ejpam-6729	761	37	.	.	PUNCT
ejpam-6729	762	1	these	these	DET
ejpam-6729	762	2	extensions	extension	NOUN
ejpam-6729	762	3	could	could	AUX
ejpam-6729	762	4	yield	yield	VERB
ejpam-6729	762	5	novel	novel	ADJ
ejpam-6729	762	6	frameworks	framework	NOUN
ejpam-6729	762	7	for	for	ADP
ejpam-6729	762	8	secure	secure	ADJ
ejpam-6729	762	9	data	datum	NOUN
ejpam-6729	762	10	modeling	modeling	NOUN
ejpam-6729	762	11	,	,	PUNCT
ejpam-6729	762	12	multi	multi	ADJ
ejpam-6729	762	13	-	-	ADJ
ejpam-6729	762	14	dimensional	dimensional	ADJ
ejpam-6729	762	15	coding	code	VERB
ejpam-6729	762	16	theory	theory	NOUN
ejpam-6729	762	17	,	,	PUNCT
ejpam-6729	762	18	and	and	CCONJ
ejpam-6729	762	19	advanced	advanced	ADJ
ejpam-6729	762	20	cryptographic	cryptographic	ADJ
ejpam-6729	762	21	schemes	scheme	NOUN
ejpam-6729	762	22	,	,	PUNCT
ejpam-6729	762	23	exploiting	exploit	VERB
ejpam-6729	762	24	the	the	DET
ejpam-6729	762	25	non	non	ADJ
ejpam-6729	762	26	-	-	ADJ
ejpam-6729	762	27	commutative	commutative	ADJ
ejpam-6729	762	28	,	,	PUNCT
ejpam-6729	762	29	associative	associative	ADJ
ejpam-6729	762	30	,	,	PUNCT
ejpam-6729	762	31	or	or	CCONJ
ejpam-6729	762	32	non	non	ADJ
ejpam-6729	762	33	-	-	ADJ
ejpam-6729	762	34	associative	associative	ADJ
ejpam-6729	762	35	properties	property	NOUN
ejpam-6729	762	36	of	of	ADP
ejpam-6729	762	37	such	such	ADJ
ejpam-6729	762	38	algebras	algebra	NOUN
ejpam-6729	762	39	.	.	PUNCT
ejpam-6729	763	1	t.	t.	PROPN
ejpam-6729	763	2	fujita	fujita	PROPN
ejpam-6729	763	3	,	,	PUNCT
ejpam-6729	763	4	f.	f.	PROPN
ejpam-6729	763	5	smarandache	smarandache	PROPN
ejpam-6729	763	6	/	/	SYM
ejpam-6729	763	7	eur	eur	PROPN
ejpam-6729	763	8	.	.	PUNCT
ejpam-6729	764	1	j.	j.	PROPN
ejpam-6729	764	2	pure	pure	PROPN
ejpam-6729	764	3	appl	appl	PROPN
ejpam-6729	764	4	.	.	PROPN
ejpam-6729	764	5	math	math	PROPN
ejpam-6729	764	6	,	,	PUNCT
ejpam-6729	764	7	18	18	NUM
ejpam-6729	764	8	(	(	PUNCT
ejpam-6729	764	9	4	4	NUM
ejpam-6729	764	10	)	)	PUNCT
ejpam-6729	764	11	(	(	PUNCT
ejpam-6729	764	12	2025	2025	NUM
ejpam-6729	764	13	)	)	PUNCT
ejpam-6729	764	14	,	,	PUNCT
ejpam-6729	764	15	6729	6729	NUM
ejpam-6729	764	16	32	32	NUM
ejpam-6729	764	17	of	of	ADP
ejpam-6729	764	18	36	36	NUM
ejpam-6729	764	19	table	table	NOUN
ejpam-6729	764	20	2	2	NUM
ejpam-6729	764	21	:	:	PUNCT
ejpam-6729	764	22	concise	concise	ADJ
ejpam-6729	764	23	overview	overview	NOUN
ejpam-6729	764	24	of	of	ADP
ejpam-6729	764	25	property	property	NOUN
ejpam-6729	764	26	graph	graph	NOUN
ejpam-6729	764	27	,	,	PUNCT
ejpam-6729	764	28	property	property	NOUN
ejpam-6729	764	29	hypergraph	hypergraph	NOUN
ejpam-6729	764	30	,	,	PUNCT
ejpam-6729	764	31	and	and	CCONJ
ejpam-6729	764	32	property	property	NOUN
ejpam-6729	764	33	n	n	CCONJ
ejpam-6729	764	34	-	-	PUNCT
ejpam-6729	764	35	superhypergraph	superhypergraph	NOUN
ejpam-6729	764	36	.	.	PUNCT
ejpam-6729	765	1	model	model	NOUN
ejpam-6729	765	2	labels	label	NOUN
ejpam-6729	765	3	properties	property	NOUN
ejpam-6729	765	4	notes	note	VERB
ejpam-6729	765	5	property	property	NOUN
ejpam-6729	765	6	graph	graph	NOUN
ejpam-6729	765	7	λ	λ	NOUN
ejpam-6729	765	8	:	:	PUNCT
ejpam-6729	765	9	e	e	X
ejpam-6729	765	10	→	→	SYM
ejpam-6729	765	11	σ	σ	PROPN
ejpam-6729	765	12	µ	µ	X
ejpam-6729	765	13	:	:	PUNCT
ejpam-6729	765	14	(	(	PUNCT
ejpam-6729	765	15	v	v	X
ejpam-6729	765	16	∪	∪	VERB
ejpam-6729	765	17	e	e	NOUN
ejpam-6729	765	18	)	)	PUNCT
ejpam-6729	765	19	×	×	PROPN
ejpam-6729	765	20	k	k	PROPN
ejpam-6729	765	21	→	→	SYM
ejpam-6729	765	22	s	s	NOUN
ejpam-6729	765	23	∪	∪	X
ejpam-6729	765	24	{	{	PUNCT
ejpam-6729	765	25	⊥	⊥	ADJ
ejpam-6729	765	26	}	}	PUNCT
ejpam-6729	765	27	directed	direct	VERB
ejpam-6729	765	28	multigraph	multigraph	NOUN
ejpam-6729	765	29	g	g	PROPN
ejpam-6729	765	30	=	=	SYM
ejpam-6729	765	31	(	(	PUNCT
ejpam-6729	765	32	v	v	NOUN
ejpam-6729	765	33	,	,	PUNCT
ejpam-6729	765	34	e	e	NOUN
ejpam-6729	765	35	)	)	PUNCT
ejpam-6729	765	36	;	;	PUNCT
ejpam-6729	765	37	vertices	vertex	NOUN
ejpam-6729	765	38	/	/	SYM
ejpam-6729	765	39	edges	edge	NOUN
ejpam-6729	765	40	carry	carry	VERB
ejpam-6729	765	41	attributes	attribute	NOUN
ejpam-6729	765	42	;	;	PUNCT
ejpam-6729	765	43	edges	edge	NOUN
ejpam-6729	765	44	are	be	AUX
ejpam-6729	765	45	labelled	label	VERB
ejpam-6729	765	46	.	.	PUNCT
ejpam-6729	766	1	property	property	NOUN
ejpam-6729	766	2	hypergraph	hypergraph	NOUN
ejpam-6729	766	3	λ	λ	NOUN
ejpam-6729	766	4	:	:	PUNCT
ejpam-6729	766	5	e	e	X
ejpam-6729	766	6	→	→	SYM
ejpam-6729	766	7	σ	σ	PROPN
ejpam-6729	766	8	µ	µ	X
ejpam-6729	766	9	:	:	PUNCT
ejpam-6729	766	10	(	(	PUNCT
ejpam-6729	766	11	v	v	X
ejpam-6729	766	12	∪	∪	VERB
ejpam-6729	766	13	e	e	NOUN
ejpam-6729	766	14	)	)	PUNCT
ejpam-6729	766	15	×	×	PROPN
ejpam-6729	766	16	k	k	PROPN
ejpam-6729	766	17	→	→	SYM
ejpam-6729	766	18	s	s	NOUN
ejpam-6729	766	19	∪	∪	X
ejpam-6729	766	20	{	{	PUNCT
ejpam-6729	766	21	⊥	⊥	NOUN
ejpam-6729	766	22	}	}	PUNCT
ejpam-6729	766	23	hypergraph	hypergraph	NOUN
ejpam-6729	766	24	h	h	NOUN
ejpam-6729	766	25	=	=	SYM
ejpam-6729	766	26	(	(	PUNCT
ejpam-6729	766	27	v	v	NOUN
ejpam-6729	766	28	,	,	PUNCT
ejpam-6729	766	29	e	e	NOUN
ejpam-6729	766	30	)	)	PUNCT
ejpam-6729	766	31	;	;	PUNCT
ejpam-6729	766	32	hyperedges	hyperedge	NOUN
ejpam-6729	766	33	connect	connect	VERB
ejpam-6729	766	34	arbitrary	arbitrary	ADJ
ejpam-6729	766	35	vertex	vertex	NOUN
ejpam-6729	766	36	subsets	subset	NOUN
ejpam-6729	766	37	;	;	PUNCT
ejpam-6729	766	38	attributes	attribute	NOUN
ejpam-6729	766	39	and	and	CCONJ
ejpam-6729	766	40	labels	label	NOUN
ejpam-6729	766	41	allowed	allow	VERB
ejpam-6729	766	42	.	.	PUNCT
ejpam-6729	767	1	property	property	NOUN
ejpam-6729	767	2	nsuperhypergraph	nsuperhypergraph	NOUN
ejpam-6729	767	3	λ	λ	PROPN
ejpam-6729	767	4	:	:	PUNCT
ejpam-6729	767	5	e(n	e(n	ADJ
ejpam-6729	767	6	)	)	PUNCT
ejpam-6729	767	7	→	→	PUNCT
ejpam-6729	767	8	σ	σ	PROPN
ejpam-6729	767	9	µ	µ	X
ejpam-6729	767	10	:	:	PUNCT
ejpam-6729	767	11	(	(	PUNCT
ejpam-6729	767	12	d(n)×k	d(n)×k	NOUN
ejpam-6729	767	13	)	)	PUNCT
ejpam-6729	767	14	→	→	SYM
ejpam-6729	767	15	s∪{⊥	s∪{⊥	NOUN
ejpam-6729	767	16	}	}	PUNCT
ejpam-6729	767	17	h(n	h(n	PROPN
ejpam-6729	767	18	)	)	PUNCT
ejpam-6729	767	19	=	=	SYM
ejpam-6729	767	20	(	(	PUNCT
ejpam-6729	767	21	v	v	NOUN
ejpam-6729	767	22	(	(	PUNCT
ejpam-6729	767	23	n	n	CCONJ
ejpam-6729	767	24	)	)	PUNCT
ejpam-6729	767	25	,	,	PUNCT
ejpam-6729	767	26	e(n	e(n	PROPN
ejpam-6729	767	27	)	)	PUNCT
ejpam-6729	767	28	,	,	PUNCT
ejpam-6729	767	29	λ	λ	PROPN
ejpam-6729	767	30	,	,	PUNCT
ejpam-6729	767	31	µ	µ	NOUN
ejpam-6729	767	32	)	)	PUNCT
ejpam-6729	767	33	;	;	PUNCT
ejpam-6729	767	34	supervertices	supervertice	NOUN
ejpam-6729	767	35	at	at	ADP
ejpam-6729	767	36	level	level	NOUN
ejpam-6729	767	37	n	n	CCONJ
ejpam-6729	767	38	,	,	PUNCT
ejpam-6729	767	39	edges	edge	NOUN
ejpam-6729	767	40	between	between	ADP
ejpam-6729	767	41	them	they	PRON
ejpam-6729	767	42	;	;	PUNCT
ejpam-6729	767	43	supports	support	VERB
ejpam-6729	767	44	hierarchical	hierarchical	ADJ
ejpam-6729	767	45	,	,	PUNCT
ejpam-6729	767	46	attributed	attribute	VERB
ejpam-6729	767	47	structures	structure	NOUN
ejpam-6729	767	48	.	.	PUNCT
ejpam-6729	768	1	funding	fund	VERB
ejpam-6729	768	2	this	this	DET
ejpam-6729	768	3	work	work	NOUN
ejpam-6729	768	4	was	be	AUX
ejpam-6729	768	5	carried	carry	VERB
ejpam-6729	768	6	out	out	ADP
ejpam-6729	768	7	without	without	ADP
ejpam-6729	768	8	any	any	DET
ejpam-6729	768	9	external	external	ADJ
ejpam-6729	768	10	financial	financial	ADJ
ejpam-6729	768	11	support	support	NOUN
ejpam-6729	768	12	.	.	PUNCT
ejpam-6729	769	1	acknowledgements	acknowledgement	NOUN
ejpam-6729	769	2	we	we	PRON
ejpam-6729	769	3	are	be	AUX
ejpam-6729	769	4	grateful	grateful	ADJ
ejpam-6729	769	5	to	to	ADP
ejpam-6729	769	6	all	all	DET
ejpam-6729	769	7	colleagues	colleague	NOUN
ejpam-6729	769	8	and	and	CCONJ
ejpam-6729	769	9	reviewers	reviewer	NOUN
ejpam-6729	769	10	whose	whose	DET
ejpam-6729	769	11	insights	insight	NOUN
ejpam-6729	769	12	and	and	CCONJ
ejpam-6729	769	13	encouragement	encouragement	NOUN
ejpam-6729	769	14	have	have	AUX
ejpam-6729	769	15	strengthened	strengthen	VERB
ejpam-6729	769	16	this	this	DET
ejpam-6729	769	17	work	work	NOUN
ejpam-6729	769	18	.	.	PUNCT
ejpam-6729	770	1	we	we	PRON
ejpam-6729	770	2	also	also	ADV
ejpam-6729	770	3	thank	thank	VERB
ejpam-6729	770	4	the	the	DET
ejpam-6729	770	5	authors	author	NOUN
ejpam-6729	770	6	of	of	ADP
ejpam-6729	770	7	the	the	DET
ejpam-6729	770	8	cited	cite	VERB
ejpam-6729	770	9	literature	literature	NOUN
ejpam-6729	770	10	for	for	ADP
ejpam-6729	770	11	laying	lay	VERB
ejpam-6729	770	12	the	the	DET
ejpam-6729	770	13	groundwork	groundwork	NOUN
ejpam-6729	770	14	that	that	PRON
ejpam-6729	770	15	enabled	enable	VERB
ejpam-6729	770	16	our	our	PRON
ejpam-6729	770	17	study	study	NOUN
ejpam-6729	770	18	,	,	PUNCT
ejpam-6729	770	19	and	and	CCONJ
ejpam-6729	770	20	acknowledge	acknowledge	VERB
ejpam-6729	770	21	the	the	DET
ejpam-6729	770	22	institutions	institution	NOUN
ejpam-6729	770	23	that	that	PRON
ejpam-6729	770	24	provided	provide	VERB
ejpam-6729	770	25	the	the	DET
ejpam-6729	770	26	resources	resource	NOUN
ejpam-6729	770	27	and	and	CCONJ
ejpam-6729	770	28	infrastructure	infrastructure	NOUN
ejpam-6729	770	29	essential	essential	ADJ
ejpam-6729	770	30	for	for	ADP
ejpam-6729	770	31	its	its	PRON
ejpam-6729	770	32	completion	completion	NOUN
ejpam-6729	770	33	.	.	PUNCT
ejpam-6729	771	1	author	author	NOUN
ejpam-6729	771	2	’s	’s	PART
ejpam-6729	771	3	contributions	contribution	NOUN
ejpam-6729	771	4	conceptualization	conceptualization	NOUN
ejpam-6729	771	5	,	,	PUNCT
ejpam-6729	771	6	takaaki	takaaki	NOUN
ejpam-6729	771	7	fujita	fujita	NOUN
ejpam-6729	771	8	;	;	PUNCT
ejpam-6729	771	9	investigation	investigation	NOUN
ejpam-6729	771	10	,	,	PUNCT
ejpam-6729	771	11	takaaki	takaaki	NOUN
ejpam-6729	771	12	fujita	fujita	PROPN
ejpam-6729	771	13	;	;	PUNCT
ejpam-6729	771	14	methodology	methodology	NOUN
ejpam-6729	771	15	,	,	PUNCT
ejpam-6729	771	16	takaaki	takaaki	NOUN
ejpam-6729	771	17	fujita	fujita	PROPN
ejpam-6729	771	18	;	;	PUNCT
ejpam-6729	771	19	writing	write	VERB
ejpam-6729	771	20	–	–	PUNCT
ejpam-6729	771	21	original	original	ADJ
ejpam-6729	771	22	draft	draft	NOUN
ejpam-6729	771	23	,	,	PUNCT
ejpam-6729	771	24	takaaki	takaaki	NOUN
ejpam-6729	771	25	fujita	fujita	NOUN
ejpam-6729	771	26	;	;	PUNCT
ejpam-6729	771	27	writing	write	VERB
ejpam-6729	771	28	–	–	PUNCT
ejpam-6729	771	29	review	review	NOUN
ejpam-6729	771	30	&	&	CCONJ
ejpam-6729	771	31	editing	editing	NOUN
ejpam-6729	771	32	,	,	PUNCT
ejpam-6729	771	33	all	all	DET
ejpam-6729	771	34	authors	author	NOUN
ejpam-6729	771	35	.	.	PUNCT
ejpam-6729	772	1	data	datum	NOUN
ejpam-6729	772	2	availability	availability	NOUN
ejpam-6729	772	3	this	this	PRON
ejpam-6729	772	4	is	be	AUX
ejpam-6729	772	5	a	a	DET
ejpam-6729	772	6	theoretical	theoretical	ADJ
ejpam-6729	772	7	study	study	NOUN
ejpam-6729	772	8	and	and	CCONJ
ejpam-6729	772	9	did	do	AUX
ejpam-6729	772	10	not	not	PART
ejpam-6729	772	11	produce	produce	VERB
ejpam-6729	772	12	any	any	DET
ejpam-6729	772	13	data	datum	NOUN
ejpam-6729	772	14	.	.	PUNCT
ejpam-6729	773	1	we	we	PRON
ejpam-6729	773	2	invite	invite	VERB
ejpam-6729	773	3	future	future	ADJ
ejpam-6729	773	4	researchers	researcher	NOUN
ejpam-6729	773	5	to	to	PART
ejpam-6729	773	6	perform	perform	VERB
ejpam-6729	773	7	empirical	empirical	ADJ
ejpam-6729	773	8	validations	validation	NOUN
ejpam-6729	773	9	of	of	ADP
ejpam-6729	773	10	the	the	DET
ejpam-6729	773	11	concepts	concept	NOUN
ejpam-6729	773	12	presented	present	VERB
ejpam-6729	773	13	herein	herein	NOUN
ejpam-6729	773	14	.	.	PUNCT
ejpam-6729	774	1	ethical	ethical	ADJ
ejpam-6729	774	2	approval	approval	NOUN
ejpam-6729	774	3	no	no	DET
ejpam-6729	774	4	human	human	ADJ
ejpam-6729	774	5	participants	participant	NOUN
ejpam-6729	774	6	or	or	CCONJ
ejpam-6729	774	7	animal	animal	NOUN
ejpam-6729	774	8	subjects	subject	NOUN
ejpam-6729	774	9	were	be	AUX
ejpam-6729	774	10	involved	involve	VERB
ejpam-6729	774	11	in	in	ADP
ejpam-6729	774	12	this	this	DET
ejpam-6729	774	13	research	research	NOUN
ejpam-6729	774	14	;	;	PUNCT
ejpam-6729	774	15	ethical	ethical	ADJ
ejpam-6729	774	16	approval	approval	NOUN
ejpam-6729	774	17	was	be	AUX
ejpam-6729	774	18	therefore	therefore	ADV
ejpam-6729	774	19	not	not	PART
ejpam-6729	774	20	required	require	VERB
ejpam-6729	774	21	.	.	PUNCT
ejpam-6729	775	1	t.	t.	PROPN
ejpam-6729	775	2	fujita	fujita	PROPN
ejpam-6729	775	3	,	,	PUNCT
ejpam-6729	775	4	f.	f.	PROPN
ejpam-6729	775	5	smarandache	smarandache	PROPN
ejpam-6729	775	6	/	/	SYM
ejpam-6729	775	7	eur	eur	PROPN
ejpam-6729	775	8	.	.	PUNCT
ejpam-6729	776	1	j.	j.	PROPN
ejpam-6729	776	2	pure	pure	PROPN
ejpam-6729	776	3	appl	appl	PROPN
ejpam-6729	776	4	.	.	PROPN
ejpam-6729	776	5	math	math	PROPN
ejpam-6729	776	6	,	,	PUNCT
ejpam-6729	776	7	18	18	NUM
ejpam-6729	776	8	(	(	PUNCT
ejpam-6729	776	9	4	4	NUM
ejpam-6729	776	10	)	)	PUNCT
ejpam-6729	776	11	(	(	PUNCT
ejpam-6729	776	12	2025	2025	NUM
ejpam-6729	776	13	)	)	PUNCT
ejpam-6729	776	14	,	,	PUNCT
ejpam-6729	776	15	6729	6729	NUM
ejpam-6729	776	16	33	33	NUM
ejpam-6729	776	17	of	of	ADP
ejpam-6729	776	18	36	36	NUM
ejpam-6729	776	19	conflicts	conflict	NOUN
ejpam-6729	776	20	of	of	ADP
ejpam-6729	776	21	interest	interest	NOUN
ejpam-6729	776	22	the	the	DET
ejpam-6729	776	23	authors	author	NOUN
ejpam-6729	776	24	declare	declare	VERB
ejpam-6729	776	25	that	that	SCONJ
ejpam-6729	776	26	there	there	PRON
ejpam-6729	776	27	are	be	VERB
ejpam-6729	776	28	no	no	DET
ejpam-6729	776	29	conflicts	conflict	NOUN
ejpam-6729	776	30	of	of	ADP
ejpam-6729	776	31	interest	interest	NOUN
ejpam-6729	776	32	related	relate	VERB
ejpam-6729	776	33	to	to	ADP
ejpam-6729	776	34	this	this	DET
ejpam-6729	776	35	study	study	NOUN
ejpam-6729	776	36	.	.	PUNCT
ejpam-6729	777	1	use	use	NOUN
ejpam-6729	777	2	of	of	ADP
ejpam-6729	777	3	generative	generative	ADJ
ejpam-6729	777	4	ai	ai	NOUN
ejpam-6729	777	5	and	and	CCONJ
ejpam-6729	777	6	ai	ai	ADJ
ejpam-6729	777	7	-	-	PUNCT
ejpam-6729	777	8	assisted	assist	VERB
ejpam-6729	777	9	tools	tool	NOUN
ejpam-6729	777	10	we	we	PRON
ejpam-6729	777	11	use	use	VERB
ejpam-6729	777	12	generative	generative	ADJ
ejpam-6729	777	13	ai	ai	NOUN
ejpam-6729	777	14	and	and	CCONJ
ejpam-6729	777	15	ai	ai	ADJ
ejpam-6729	777	16	-	-	PUNCT
ejpam-6729	777	17	assisted	assist	VERB
ejpam-6729	777	18	tools	tool	NOUN
ejpam-6729	777	19	for	for	ADP
ejpam-6729	777	20	tasks	task	NOUN
ejpam-6729	777	21	such	such	ADJ
ejpam-6729	777	22	as	as	ADP
ejpam-6729	777	23	english	english	ADJ
ejpam-6729	777	24	grammar	grammar	NOUN
ejpam-6729	777	25	checking	checking	NOUN
ejpam-6729	777	26	,	,	PUNCT
ejpam-6729	777	27	and	and	CCONJ
ejpam-6729	777	28	we	we	PRON
ejpam-6729	777	29	do	do	AUX
ejpam-6729	777	30	not	not	PART
ejpam-6729	777	31	employ	employ	VERB
ejpam-6729	777	32	them	they	PRON
ejpam-6729	777	33	in	in	ADP
ejpam-6729	777	34	any	any	DET
ejpam-6729	777	35	way	way	NOUN
ejpam-6729	777	36	that	that	PRON
ejpam-6729	777	37	violates	violate	VERB
ejpam-6729	777	38	ethical	ethical	ADJ
ejpam-6729	777	39	standards	standard	NOUN
ejpam-6729	777	40	.	.	PUNCT
ejpam-6729	778	1	disclaimer	disclaimer	VERB
ejpam-6729	778	2	the	the	DET
ejpam-6729	778	3	ideas	idea	NOUN
ejpam-6729	778	4	and	and	CCONJ
ejpam-6729	778	5	models	model	NOUN
ejpam-6729	778	6	presented	present	VERB
ejpam-6729	778	7	in	in	ADP
ejpam-6729	778	8	this	this	DET
ejpam-6729	778	9	paper	paper	NOUN
ejpam-6729	778	10	are	be	AUX
ejpam-6729	778	11	theoretical	theoretical	ADJ
ejpam-6729	778	12	and	and	CCONJ
ejpam-6729	778	13	have	have	AUX
ejpam-6729	778	14	not	not	PART
ejpam-6729	778	15	yet	yet	ADV
ejpam-6729	778	16	been	be	AUX
ejpam-6729	778	17	empirically	empirically	ADV
ejpam-6729	778	18	tested	test	VERB
ejpam-6729	778	19	.	.	PUNCT
ejpam-6729	779	1	while	while	SCONJ
ejpam-6729	779	2	we	we	PRON
ejpam-6729	779	3	have	have	AUX
ejpam-6729	779	4	made	make	VERB
ejpam-6729	779	5	every	every	DET
ejpam-6729	779	6	effort	effort	NOUN
ejpam-6729	779	7	to	to	PART
ejpam-6729	779	8	ensure	ensure	VERB
ejpam-6729	779	9	accuracy	accuracy	NOUN
ejpam-6729	779	10	and	and	CCONJ
ejpam-6729	779	11	proper	proper	ADJ
ejpam-6729	779	12	citation	citation	NOUN
ejpam-6729	779	13	,	,	PUNCT
ejpam-6729	779	14	unintentional	unintentional	ADJ
ejpam-6729	779	15	errors	error	NOUN
ejpam-6729	779	16	may	may	AUX
ejpam-6729	779	17	remain	remain	VERB
ejpam-6729	779	18	.	.	PUNCT
ejpam-6729	780	1	readers	reader	NOUN
ejpam-6729	780	2	should	should	AUX
ejpam-6729	780	3	verify	verify	VERB
ejpam-6729	780	4	sources	source	NOUN
ejpam-6729	780	5	independently	independently	ADV
ejpam-6729	780	6	.	.	PUNCT
ejpam-6729	781	1	the	the	DET
ejpam-6729	781	2	views	view	NOUN
ejpam-6729	781	3	expressed	express	VERB
ejpam-6729	781	4	are	be	AUX
ejpam-6729	781	5	those	those	PRON
ejpam-6729	781	6	of	of	ADP
ejpam-6729	781	7	the	the	DET
ejpam-6729	781	8	authors	author	NOUN
ejpam-6729	781	9	and	and	CCONJ
ejpam-6729	781	10	do	do	AUX
ejpam-6729	781	11	not	not	PART
ejpam-6729	781	12	necessarily	necessarily	ADV
ejpam-6729	781	13	reflect	reflect	VERB
ejpam-6729	781	14	those	those	PRON
ejpam-6729	781	15	of	of	ADP
ejpam-6729	781	16	their	their	PRON
ejpam-6729	781	17	institutions	institution	NOUN
ejpam-6729	781	18	.	.	PUNCT
ejpam-6729	782	1	consent	consent	VERB
ejpam-6729	782	2	to	to	PART
ejpam-6729	782	3	publish	publish	VERB
ejpam-6729	782	4	all	all	DET
ejpam-6729	782	5	authors	author	NOUN
ejpam-6729	782	6	have	have	AUX
ejpam-6729	782	7	reviewed	review	VERB
ejpam-6729	782	8	and	and	CCONJ
ejpam-6729	782	9	approved	approve	VERB
ejpam-6729	782	10	this	this	DET
ejpam-6729	782	11	manuscript	manuscript	NOUN
ejpam-6729	782	12	for	for	ADP
ejpam-6729	782	13	submission	submission	NOUN
ejpam-6729	782	14	.	.	PUNCT
ejpam-6729	783	1	references	reference	NOUN
ejpam-6729	783	2	[	[	X
ejpam-6729	783	3	1	1	NUM
ejpam-6729	783	4	]	]	PUNCT
ejpam-6729	783	5	reinhard	reinhard	NOUN
ejpam-6729	783	6	diestel	diestel	NOUN
ejpam-6729	783	7	.	.	PUNCT
ejpam-6729	784	1	graph	graph	NOUN
ejpam-6729	784	2	theory	theory	NOUN
ejpam-6729	784	3	.	.	PUNCT
ejpam-6729	785	1	springer	springer	NOUN
ejpam-6729	785	2	(	(	PUNCT
ejpam-6729	785	3	print	print	NOUN
ejpam-6729	785	4	edition	edition	PROPN
ejpam-6729	785	5	)	)	PUNCT
ejpam-6729	785	6	;	;	PUNCT
ejpam-6729	785	7	reinhard	reinhard	NOUN
ejpam-6729	785	8	diestel	diestel	NOUN
ejpam-6729	785	9	(	(	PUNCT
ejpam-6729	785	10	ebooks	ebooks	PROPN
ejpam-6729	785	11	)	)	PUNCT
ejpam-6729	785	12	,	,	PUNCT
ejpam-6729	785	13	2024	2024	NUM
ejpam-6729	785	14	.	.	PUNCT
ejpam-6729	786	1	[	[	X
ejpam-6729	786	2	2	2	X
ejpam-6729	786	3	]	]	X
ejpam-6729	786	4	jonathan	jonathan	PROPN
ejpam-6729	786	5	l	l	PROPN
ejpam-6729	786	6	gross	gross	PROPN
ejpam-6729	786	7	,	,	PUNCT
ejpam-6729	786	8	jay	jay	PROPN
ejpam-6729	786	9	yellen	yellen	VERB
ejpam-6729	786	10	,	,	PUNCT
ejpam-6729	786	11	and	and	CCONJ
ejpam-6729	786	12	mark	mark	PROPN
ejpam-6729	786	13	anderson	anderson	PROPN
ejpam-6729	786	14	.	.	PUNCT
ejpam-6729	787	1	graph	graph	NOUN
ejpam-6729	787	2	theory	theory	NOUN
ejpam-6729	787	3	and	and	CCONJ
ejpam-6729	787	4	its	its	PRON
ejpam-6729	787	5	applications	application	NOUN
ejpam-6729	787	6	.	.	PUNCT
ejpam-6729	788	1	chapman	chapman	NOUN
ejpam-6729	788	2	and	and	CCONJ
ejpam-6729	788	3	hall	hall	PROPN
ejpam-6729	788	4	/	/	SYM
ejpam-6729	788	5	crc	crc	NOUN
ejpam-6729	788	6	,	,	PUNCT
ejpam-6729	788	7	2018	2018	NUM
ejpam-6729	788	8	.	.	PUNCT
ejpam-6729	789	1	[	[	X
ejpam-6729	789	2	3	3	X
ejpam-6729	789	3	]	]	PUNCT
ejpam-6729	789	4	claude	claude	PROPN
ejpam-6729	789	5	berge	berge	PROPN
ejpam-6729	789	6	.	.	PUNCT
ejpam-6729	790	1	hypergraphs	hypergraph	NOUN
ejpam-6729	790	2	:	:	PUNCT
ejpam-6729	790	3	combinatorics	combinatoric	NOUN
ejpam-6729	790	4	of	of	ADP
ejpam-6729	790	5	finite	finite	PROPN
ejpam-6729	790	6	sets	set	NOUN
ejpam-6729	790	7	,	,	PUNCT
ejpam-6729	790	8	volume	volume	NOUN
ejpam-6729	790	9	45	45	NUM
ejpam-6729	790	10	.	.	PUNCT
ejpam-6729	791	1	elsevier	elsevier	NOUN
ejpam-6729	791	2	,	,	PUNCT
ejpam-6729	791	3	1984	1984	NUM
ejpam-6729	791	4	.	.	PUNCT
ejpam-6729	792	1	[	[	X
ejpam-6729	792	2	4	4	NUM
ejpam-6729	792	3	]	]	PUNCT
ejpam-6729	792	4	florentin	florentin	PROPN
ejpam-6729	792	5	smarandache	smarandache	NOUN
ejpam-6729	792	6	.	.	PUNCT
ejpam-6729	793	1	introduction	introduction	NOUN
ejpam-6729	793	2	to	to	ADP
ejpam-6729	793	3	the	the	DET
ejpam-6729	793	4	n	n	CCONJ
ejpam-6729	793	5	-	-	PUNCT
ejpam-6729	793	6	superhypergraph	superhypergraph	NOUN
ejpam-6729	793	7	-	-	PUNCT
ejpam-6729	793	8	the	the	DET
ejpam-6729	793	9	most	most	ADV
ejpam-6729	793	10	general	general	ADJ
ejpam-6729	793	11	form	form	NOUN
ejpam-6729	793	12	of	of	ADP
ejpam-6729	793	13	graph	graph	NOUN
ejpam-6729	793	14	today	today	NOUN
ejpam-6729	793	15	.	.	PUNCT
ejpam-6729	794	1	infinite	infinite	ADJ
ejpam-6729	794	2	study	study	NOUN
ejpam-6729	794	3	,	,	PUNCT
ejpam-6729	794	4	2022	2022	NUM
ejpam-6729	794	5	.	.	PUNCT
ejpam-6729	795	1	[	[	X
ejpam-6729	795	2	5	5	NUM
ejpam-6729	795	3	]	]	X
ejpam-6729	795	4	mohammad	mohammad	PROPN
ejpam-6729	795	5	hamidi	hamidi	PROPN
ejpam-6729	795	6	,	,	PUNCT
ejpam-6729	795	7	florentin	florentin	NOUN
ejpam-6729	795	8	smarandache	smarandache	NOUN
ejpam-6729	795	9	,	,	PUNCT
ejpam-6729	795	10	and	and	CCONJ
ejpam-6729	795	11	mohadeseh	mohadeseh	PROPN
ejpam-6729	795	12	taghinezhad	taghinezhad	VERB
ejpam-6729	795	13	.	.	PUNCT
ejpam-6729	796	1	decision	decision	NOUN
ejpam-6729	796	2	making	making	NOUN
ejpam-6729	796	3	based	base	VERB
ejpam-6729	796	4	on	on	ADP
ejpam-6729	796	5	valued	value	VERB
ejpam-6729	796	6	fuzzy	fuzzy	ADJ
ejpam-6729	796	7	superhypergraphs	superhypergraph	NOUN
ejpam-6729	796	8	.	.	PUNCT
ejpam-6729	797	1	infinite	infinite	ADJ
ejpam-6729	797	2	study	study	NOUN
ejpam-6729	797	3	,	,	PUNCT
ejpam-6729	797	4	2023	2023	NUM
ejpam-6729	797	5	.	.	PUNCT
ejpam-6729	798	1	[	[	X
ejpam-6729	798	2	6	6	NUM
ejpam-6729	798	3	]	]	PUNCT
ejpam-6729	798	4	oskar	oskar	PROPN
ejpam-6729	798	5	van	van	PROPN
ejpam-6729	798	6	rest	rest	PROPN
ejpam-6729	798	7	,	,	PUNCT
ejpam-6729	798	8	sungpack	sungpack	VERB
ejpam-6729	798	9	hong	hong	PROPN
ejpam-6729	798	10	,	,	PUNCT
ejpam-6729	798	11	jinha	jinha	VERB
ejpam-6729	798	12	kim	kim	PROPN
ejpam-6729	798	13	,	,	PUNCT
ejpam-6729	798	14	xuming	xume	VERB
ejpam-6729	798	15	meng	meng	PROPN
ejpam-6729	798	16	,	,	PUNCT
ejpam-6729	798	17	and	and	CCONJ
ejpam-6729	798	18	hassan	hassan	PROPN
ejpam-6729	798	19	chafi	chafi	PROPN
ejpam-6729	798	20	.	.	PUNCT
ejpam-6729	799	1	pgql	pgql	PROPN
ejpam-6729	799	2	:	:	PUNCT
ejpam-6729	799	3	a	a	DET
ejpam-6729	799	4	property	property	NOUN
ejpam-6729	799	5	graph	graph	NOUN
ejpam-6729	799	6	query	query	NOUN
ejpam-6729	799	7	language	language	NOUN
ejpam-6729	799	8	.	.	PUNCT
ejpam-6729	800	1	in	in	ADP
ejpam-6729	800	2	proceedings	proceeding	NOUN
ejpam-6729	800	3	of	of	ADP
ejpam-6729	800	4	the	the	DET
ejpam-6729	800	5	fourth	fourth	ADJ
ejpam-6729	800	6	international	international	ADJ
ejpam-6729	800	7	workshop	workshop	NOUN
ejpam-6729	800	8	on	on	ADP
ejpam-6729	800	9	graph	graph	NOUN
ejpam-6729	800	10	data	datum	NOUN
ejpam-6729	800	11	management	management	NOUN
ejpam-6729	800	12	experiences	experience	NOUN
ejpam-6729	800	13	and	and	CCONJ
ejpam-6729	800	14	systems	system	NOUN
ejpam-6729	800	15	,	,	PUNCT
ejpam-6729	800	16	pages	page	NOUN
ejpam-6729	800	17	1–6	1–6	NUM
ejpam-6729	800	18	,	,	PUNCT
ejpam-6729	800	19	2016	2016	NUM
ejpam-6729	800	20	.	.	PUNCT
ejpam-6729	801	1	[	[	X
ejpam-6729	801	2	7	7	NUM
ejpam-6729	801	3	]	]	X
ejpam-6729	801	4	wen	wen	PROPN
ejpam-6729	801	5	sun	sun	PROPN
ejpam-6729	801	6	,	,	PUNCT
ejpam-6729	801	7	achille	achille	PROPN
ejpam-6729	801	8	fokoue	fokoue	PROPN
ejpam-6729	801	9	,	,	PUNCT
ejpam-6729	801	10	kavitha	kavitha	PROPN
ejpam-6729	801	11	srinivas	srinivas	PROPN
ejpam-6729	801	12	,	,	PUNCT
ejpam-6729	801	13	anastasios	anastasios	PROPN
ejpam-6729	801	14	kementsietsidis	kementsietsidis	PROPN
ejpam-6729	801	15	,	,	PUNCT
ejpam-6729	801	16	gang	gang	PROPN
ejpam-6729	801	17	hu	hu	PROPN
ejpam-6729	801	18	,	,	PUNCT
ejpam-6729	801	19	and	and	CCONJ
ejpam-6729	801	20	guotong	guotong	PROPN
ejpam-6729	801	21	xie	xie	PROPN
ejpam-6729	801	22	.	.	PUNCT
ejpam-6729	802	1	sqlgraph	sqlgraph	PROPN
ejpam-6729	802	2	:	:	PUNCT
ejpam-6729	802	3	an	an	DET
ejpam-6729	802	4	efficient	efficient	ADJ
ejpam-6729	802	5	relational	relational	NOUN
ejpam-6729	802	6	-	-	PUNCT
ejpam-6729	802	7	based	base	VERB
ejpam-6729	802	8	property	property	NOUN
ejpam-6729	802	9	graph	graph	NOUN
ejpam-6729	802	10	store	store	NOUN
ejpam-6729	802	11	.	.	PUNCT
ejpam-6729	803	1	in	in	ADP
ejpam-6729	803	2	proceedings	proceeding	NOUN
ejpam-6729	803	3	of	of	ADP
ejpam-6729	803	4	the	the	DET
ejpam-6729	803	5	2015	2015	NUM
ejpam-6729	803	6	acm	acm	PROPN
ejpam-6729	803	7	sigmod	sigmod	PROPN
ejpam-6729	803	8	international	international	ADJ
ejpam-6729	803	9	conference	conference	NOUN
ejpam-6729	803	10	on	on	ADP
ejpam-6729	803	11	management	management	NOUN
ejpam-6729	803	12	of	of	ADP
ejpam-6729	803	13	data	datum	NOUN
ejpam-6729	803	14	,	,	PUNCT
ejpam-6729	803	15	pages	page	NOUN
ejpam-6729	803	16	1887–1901	1887–1901	NUM
ejpam-6729	803	17	,	,	PUNCT
ejpam-6729	803	18	2015	2015	NUM
ejpam-6729	803	19	.	.	PUNCT
ejpam-6729	804	1	[	[	X
ejpam-6729	804	2	8	8	NUM
ejpam-6729	804	3	]	]	PUNCT
ejpam-6729	804	4	renzo	renzo	NOUN
ejpam-6729	804	5	angles	angle	NOUN
ejpam-6729	804	6	,	,	PUNCT
ejpam-6729	804	7	angela	angela	PROPN
ejpam-6729	804	8	bonifati	bonifati	PROPN
ejpam-6729	804	9	,	,	PUNCT
ejpam-6729	804	10	stefania	stefania	PROPN
ejpam-6729	804	11	dumbrava	dumbrava	PROPN
ejpam-6729	804	12	,	,	PUNCT
ejpam-6729	804	13	george	george	PROPN
ejpam-6729	804	14	fletcher	fletcher	PROPN
ejpam-6729	804	15	,	,	PUNCT
ejpam-6729	804	16	alastair	alastair	PROPN
ejpam-6729	804	17	green	green	PROPN
ejpam-6729	804	18	,	,	PUNCT
ejpam-6729	804	19	jan	jan	PROPN
ejpam-6729	804	20	hidders	hidder	NOUN
ejpam-6729	804	21	,	,	PUNCT
ejpam-6729	804	22	bei	bei	PROPN
ejpam-6729	804	23	li	li	PROPN
ejpam-6729	804	24	,	,	PUNCT
ejpam-6729	804	25	leonid	leonid	PROPN
ejpam-6729	804	26	libkin	libkin	PROPN
ejpam-6729	804	27	,	,	PUNCT
ejpam-6729	804	28	victor	victor	PROPN
ejpam-6729	804	29	marsault	marsault	NOUN
ejpam-6729	804	30	,	,	PUNCT
ejpam-6729	804	31	wim	wim	PROPN
ejpam-6729	804	32	martens	martens	PROPN
ejpam-6729	804	33	,	,	PUNCT
ejpam-6729	804	34	et	et	PROPN
ejpam-6729	804	35	al	al	PROPN
ejpam-6729	804	36	.	.	PROPN
ejpam-6729	805	1	pg	pg	NOUN
ejpam-6729	805	2	-	-	PUNCT
ejpam-6729	805	3	schema	schema	NOUN
ejpam-6729	805	4	:	:	PUNCT
ejpam-6729	805	5	schemas	schema	NOUN
ejpam-6729	805	6	for	for	ADP
ejpam-6729	805	7	property	property	NOUN
ejpam-6729	805	8	graphs	graph	NOUN
ejpam-6729	805	9	.	.	PUNCT
ejpam-6729	806	1	proceedings	proceeding	NOUN
ejpam-6729	806	2	of	of	ADP
ejpam-6729	806	3	the	the	DET
ejpam-6729	806	4	acm	acm	NOUN
ejpam-6729	806	5	on	on	ADP
ejpam-6729	806	6	management	management	NOUN
ejpam-6729	806	7	of	of	ADP
ejpam-6729	806	8	data	datum	NOUN
ejpam-6729	806	9	,	,	PUNCT
ejpam-6729	806	10	1(2):1–25	1(2):1–25	NUM
ejpam-6729	806	11	,	,	PUNCT
ejpam-6729	806	12	2023	2023	NUM
ejpam-6729	806	13	.	.	PUNCT
ejpam-6729	807	1	t.	t.	PROPN
ejpam-6729	807	2	fujita	fujita	PROPN
ejpam-6729	807	3	,	,	PUNCT
ejpam-6729	807	4	f.	f.	PROPN
ejpam-6729	807	5	smarandache	smarandache	PROPN
ejpam-6729	807	6	/	/	SYM
ejpam-6729	807	7	eur	eur	PROPN
ejpam-6729	807	8	.	.	PUNCT
ejpam-6729	808	1	j.	j.	PROPN
ejpam-6729	808	2	pure	pure	PROPN
ejpam-6729	808	3	appl	appl	PROPN
ejpam-6729	808	4	.	.	PROPN
ejpam-6729	808	5	math	math	PROPN
ejpam-6729	808	6	,	,	PUNCT
ejpam-6729	808	7	18	18	NUM
ejpam-6729	808	8	(	(	PUNCT
ejpam-6729	808	9	4	4	NUM
ejpam-6729	808	10	)	)	PUNCT
ejpam-6729	808	11	(	(	PUNCT
ejpam-6729	808	12	2025	2025	NUM
ejpam-6729	808	13	)	)	PUNCT
ejpam-6729	808	14	,	,	PUNCT
ejpam-6729	808	15	6729	6729	NUM
ejpam-6729	808	16	34	34	NUM
ejpam-6729	808	17	of	of	ADP
ejpam-6729	808	18	36	36	NUM
ejpam-6729	808	19	[	[	X
ejpam-6729	808	20	9	9	NUM
ejpam-6729	808	21	]	]	PUNCT
ejpam-6729	808	22	reinhard	reinhard	NOUN
ejpam-6729	808	23	diestel	diestel	NOUN
ejpam-6729	808	24	.	.	PUNCT
ejpam-6729	809	1	graph	graph	NOUN
ejpam-6729	809	2	theory	theory	NOUN
ejpam-6729	809	3	3rd	3rd	PROPN
ejpam-6729	809	4	ed	ed	NOUN
ejpam-6729	809	5	.	.	PUNCT
ejpam-6729	810	1	graduate	graduate	ADJ
ejpam-6729	810	2	texts	text	NOUN
ejpam-6729	810	3	in	in	ADP
ejpam-6729	810	4	mathematics	mathematic	NOUN
ejpam-6729	810	5	,	,	PUNCT
ejpam-6729	810	6	173(33):12	173(33):12	NUM
ejpam-6729	810	7	,	,	PUNCT
ejpam-6729	810	8	2005	2005	NUM
ejpam-6729	810	9	.	.	PUNCT
ejpam-6729	811	1	[	[	X
ejpam-6729	811	2	10	10	NUM
ejpam-6729	811	3	]	]	PUNCT
ejpam-6729	811	4	yifan	yifan	PROPN
ejpam-6729	811	5	feng	feng	PROPN
ejpam-6729	811	6	,	,	PUNCT
ejpam-6729	811	7	haoxuan	haoxuan	PROPN
ejpam-6729	811	8	you	you	PRON
ejpam-6729	811	9	,	,	PUNCT
ejpam-6729	811	10	zizhao	zizhao	PROPN
ejpam-6729	811	11	zhang	zhang	PROPN
ejpam-6729	811	12	,	,	PUNCT
ejpam-6729	811	13	rongrong	rongrong	PROPN
ejpam-6729	811	14	ji	ji	PROPN
ejpam-6729	811	15	,	,	PUNCT
ejpam-6729	811	16	and	and	CCONJ
ejpam-6729	811	17	yue	yue	PROPN
ejpam-6729	811	18	gao	gao	PROPN
ejpam-6729	811	19	.	.	PUNCT
ejpam-6729	811	20	hypergraph	hypergraph	VERB
ejpam-6729	811	21	neural	neural	ADJ
ejpam-6729	811	22	networks	network	NOUN
ejpam-6729	811	23	.	.	PUNCT
ejpam-6729	812	1	in	in	ADP
ejpam-6729	812	2	proceedings	proceeding	NOUN
ejpam-6729	812	3	of	of	ADP
ejpam-6729	812	4	the	the	DET
ejpam-6729	812	5	aaai	aaai	PROPN
ejpam-6729	812	6	conference	conference	NOUN
ejpam-6729	812	7	on	on	ADP
ejpam-6729	812	8	artificial	artificial	ADJ
ejpam-6729	812	9	intelligence	intelligence	NOUN
ejpam-6729	812	10	,	,	PUNCT
ejpam-6729	812	11	volume	volume	NOUN
ejpam-6729	812	12	33	33	NUM
ejpam-6729	812	13	,	,	PUNCT
ejpam-6729	812	14	pages	page	NOUN
ejpam-6729	812	15	3558–3565	3558–3565	NUM
ejpam-6729	812	16	,	,	PUNCT
ejpam-6729	812	17	2019	2019	NUM
ejpam-6729	812	18	.	.	PUNCT
ejpam-6729	813	1	[	[	X
ejpam-6729	813	2	11	11	NUM
ejpam-6729	813	3	]	]	X
ejpam-6729	813	4	derun	derun	X
ejpam-6729	813	5	cai	cai	X
ejpam-6729	813	6	,	,	PUNCT
ejpam-6729	813	7	moxian	moxian	ADJ
ejpam-6729	813	8	song	song	NOUN
ejpam-6729	813	9	,	,	PUNCT
ejpam-6729	813	10	chenxi	chenxi	PROPN
ejpam-6729	813	11	sun	sun	PROPN
ejpam-6729	813	12	,	,	PUNCT
ejpam-6729	813	13	baofeng	baofeng	PROPN
ejpam-6729	813	14	zhang	zhang	PROPN
ejpam-6729	813	15	,	,	PUNCT
ejpam-6729	813	16	shenda	shenda	ADP
ejpam-6729	813	17	hong	hong	PROPN
ejpam-6729	813	18	,	,	PUNCT
ejpam-6729	813	19	and	and	CCONJ
ejpam-6729	813	20	hongyan	hongyan	PROPN
ejpam-6729	813	21	li	li	PROPN
ejpam-6729	813	22	.	.	PROPN
ejpam-6729	813	23	hypergraph	hypergraph	PROPN
ejpam-6729	813	24	structure	structure	NOUN
ejpam-6729	813	25	learning	learn	VERB
ejpam-6729	813	26	for	for	ADP
ejpam-6729	813	27	hypergraph	hypergraph	VERB
ejpam-6729	813	28	neural	neural	ADJ
ejpam-6729	813	29	networks	network	NOUN
ejpam-6729	813	30	.	.	PUNCT
ejpam-6729	814	1	in	in	ADP
ejpam-6729	814	2	ijcai	ijcai	PROPN
ejpam-6729	814	3	,	,	PUNCT
ejpam-6729	814	4	pages	page	NOUN
ejpam-6729	814	5	1923–1929	1923–1929	NUM
ejpam-6729	814	6	,	,	PUNCT
ejpam-6729	814	7	2022	2022	NUM
ejpam-6729	814	8	.	.	PUNCT
ejpam-6729	815	1	[	[	X
ejpam-6729	815	2	12	12	NUM
ejpam-6729	815	3	]	]	PUNCT
ejpam-6729	815	4	yifan	yifan	PROPN
ejpam-6729	815	5	feng	feng	PROPN
ejpam-6729	815	6	,	,	PUNCT
ejpam-6729	815	7	jiashu	jiashu	PROPN
ejpam-6729	815	8	han	han	PROPN
ejpam-6729	815	9	,	,	PUNCT
ejpam-6729	815	10	shihui	shihui	PROPN
ejpam-6729	815	11	ying	ying	PROPN
ejpam-6729	815	12	,	,	PUNCT
ejpam-6729	815	13	and	and	CCONJ
ejpam-6729	815	14	yue	yue	PROPN
ejpam-6729	815	15	gao	gao	PROPN
ejpam-6729	815	16	.	.	PUNCT
ejpam-6729	816	1	hypergraph	hypergraph	VERB
ejpam-6729	816	2	isomorphism	isomorphism	PROPN
ejpam-6729	816	3	computation	computation	NOUN
ejpam-6729	816	4	.	.	PUNCT
ejpam-6729	817	1	ieee	ieee	NOUN
ejpam-6729	817	2	transactions	transaction	NOUN
ejpam-6729	817	3	on	on	ADP
ejpam-6729	817	4	pattern	pattern	NOUN
ejpam-6729	817	5	analysis	analysis	NOUN
ejpam-6729	817	6	and	and	CCONJ
ejpam-6729	817	7	machine	machine	NOUN
ejpam-6729	817	8	intelligence	intelligence	NOUN
ejpam-6729	817	9	,	,	PUNCT
ejpam-6729	817	10	2024	2024	NUM
ejpam-6729	817	11	.	.	PUNCT
ejpam-6729	818	1	[	[	X
ejpam-6729	818	2	13	13	NUM
ejpam-6729	818	3	]	]	PUNCT
ejpam-6729	818	4	florentin	florentin	NOUN
ejpam-6729	818	5	smarandache	smarandache	NOUN
ejpam-6729	818	6	.	.	PUNCT
ejpam-6729	819	1	extension	extension	NOUN
ejpam-6729	819	2	of	of	ADP
ejpam-6729	819	3	hypergraph	hypergraph	NOUN
ejpam-6729	819	4	to	to	ADP
ejpam-6729	819	5	n	n	CCONJ
ejpam-6729	819	6	-	-	PUNCT
ejpam-6729	819	7	superhypergraph	superhypergraph	NOUN
ejpam-6729	819	8	and	and	CCONJ
ejpam-6729	819	9	to	to	ADP
ejpam-6729	819	10	plithogenic	plithogenic	ADJ
ejpam-6729	819	11	n	n	CCONJ
ejpam-6729	819	12	-	-	PUNCT
ejpam-6729	819	13	superhypergraph	superhypergraph	NOUN
ejpam-6729	819	14	,	,	PUNCT
ejpam-6729	819	15	and	and	CCONJ
ejpam-6729	819	16	extension	extension	NOUN
ejpam-6729	819	17	of	of	ADP
ejpam-6729	819	18	hyperalgebra	hyperalgebra	NOUN
ejpam-6729	819	19	to	to	ADP
ejpam-6729	819	20	n	n	CCONJ
ejpam-6729	819	21	-	-	PUNCT
ejpam-6729	819	22	ary	ary	PROPN
ejpam-6729	819	23	(	(	PUNCT
ejpam-6729	819	24	classical	classical	ADJ
ejpam-6729	819	25	/	/	SYM
ejpam-6729	819	26	neutro-/anti-	neutro-/anti-	NOUN
ejpam-6729	819	27	)	)	PUNCT
ejpam-6729	819	28	hyperalgebra	hyperalgebra	NOUN
ejpam-6729	819	29	.	.	PUNCT
ejpam-6729	820	1	infinite	infinite	ADJ
ejpam-6729	820	2	study	study	NOUN
ejpam-6729	820	3	,	,	PUNCT
ejpam-6729	820	4	2020	2020	NUM
ejpam-6729	820	5	.	.	PUNCT
ejpam-6729	821	1	[	[	X
ejpam-6729	821	2	14	14	NUM
ejpam-6729	821	3	]	]	X
ejpam-6729	821	4	n.	n.	PROPN
ejpam-6729	821	5	b.	b.	PROPN
ejpam-6729	821	6	nalawade	nalawade	PROPN
ejpam-6729	821	7	,	,	PUNCT
ejpam-6729	821	8	m.	m.	PROPN
ejpam-6729	821	9	s.	s.	PROPN
ejpam-6729	821	10	bapat	bapat	PROPN
ejpam-6729	821	11	,	,	PUNCT
ejpam-6729	821	12	s.	s.	PROPN
ejpam-6729	821	13	g.	g.	PROPN
ejpam-6729	821	14	jakkewad	jakkewad	PROPN
ejpam-6729	821	15	,	,	PUNCT
ejpam-6729	821	16	g.	g.	PROPN
ejpam-6729	821	17	a.	a.	PROPN
ejpam-6729	821	18	dhanorkar	dhanorkar	PROPN
ejpam-6729	821	19	,	,	PUNCT
ejpam-6729	821	20	and	and	CCONJ
ejpam-6729	821	21	d.	d.	PROPN
ejpam-6729	821	22	j.	j.	PROPN
ejpam-6729	821	23	bhosale	bhosale	PROPN
ejpam-6729	821	24	.	.	PUNCT
ejpam-6729	822	1	structural	structural	ADJ
ejpam-6729	822	2	properties	property	NOUN
ejpam-6729	822	3	of	of	ADP
ejpam-6729	822	4	zero	zero	NUM
ejpam-6729	822	5	-	-	PUNCT
ejpam-6729	822	6	divisor	divisor	NOUN
ejpam-6729	822	7	hypergraph	hypergraph	NOUN
ejpam-6729	822	8	and	and	CCONJ
ejpam-6729	822	9	superhypergraph	superhypergraph	VERB
ejpam-6729	822	10	over	over	ADP
ejpam-6729	822	11	zn	zn	PROPN
ejpam-6729	822	12	:	:	PUNCT
ejpam-6729	822	13	girth	girth	NOUN
ejpam-6729	822	14	and	and	CCONJ
ejpam-6729	822	15	helly	helly	ADV
ejpam-6729	822	16	property	property	NOUN
ejpam-6729	822	17	.	.	PUNCT
ejpam-6729	823	1	panamerican	panamerican	PROPN
ejpam-6729	823	2	mathematical	mathematical	ADJ
ejpam-6729	823	3	journal	journal	PROPN
ejpam-6729	823	4	,	,	PUNCT
ejpam-6729	823	5	35(4s):485	35(4s):485	NUM
ejpam-6729	823	6	,	,	PUNCT
ejpam-6729	823	7	2025	2025	NUM
ejpam-6729	823	8	.	.	PUNCT
ejpam-6729	824	1	[	[	X
ejpam-6729	824	2	15	15	NUM
ejpam-6729	824	3	]	]	X
ejpam-6729	824	4	mohammed	mohammed	PROPN
ejpam-6729	824	5	alqahtani	alqahtani	PROPN
ejpam-6729	824	6	.	.	PUNCT
ejpam-6729	825	1	intuitionistic	intuitionistic	ADJ
ejpam-6729	825	2	fuzzy	fuzzy	ADJ
ejpam-6729	825	3	quasi	quasi	ADJ
ejpam-6729	825	4	-	-	ADJ
ejpam-6729	825	5	supergraph	supergraph	ADJ
ejpam-6729	825	6	integration	integration	NOUN
ejpam-6729	825	7	for	for	ADP
ejpam-6729	825	8	social	social	ADJ
ejpam-6729	825	9	network	network	NOUN
ejpam-6729	825	10	decision	decision	NOUN
ejpam-6729	825	11	making	making	NOUN
ejpam-6729	825	12	.	.	PUNCT
ejpam-6729	826	1	international	international	ADJ
ejpam-6729	826	2	journal	journal	NOUN
ejpam-6729	826	3	of	of	ADP
ejpam-6729	826	4	analysis	analysis	NOUN
ejpam-6729	826	5	and	and	CCONJ
ejpam-6729	826	6	applications	application	NOUN
ejpam-6729	826	7	,	,	PUNCT
ejpam-6729	826	8	23:137–137	23:137–137	NUM
ejpam-6729	826	9	,	,	PUNCT
ejpam-6729	826	10	2025	2025	NUM
ejpam-6729	826	11	.	.	PUNCT
ejpam-6729	827	1	[	[	X
ejpam-6729	827	2	16	16	NUM
ejpam-6729	827	3	]	]	X
ejpam-6729	827	4	g	g	PROPN
ejpam-6729	827	5	deepa	deepa	PROPN
ejpam-6729	827	6	,	,	PUNCT
ejpam-6729	827	7	b	b	NOUN
ejpam-6729	827	8	praba	praba	NOUN
ejpam-6729	827	9	,	,	PUNCT
ejpam-6729	827	10	and	and	CCONJ
ejpam-6729	827	11	vm	vm	PROPN
ejpam-6729	827	12	chandrasekaran	chandrasekaran	VERB
ejpam-6729	827	13	.	.	PUNCT
ejpam-6729	828	1	a	a	DET
ejpam-6729	828	2	study	study	NOUN
ejpam-6729	828	3	on	on	ADP
ejpam-6729	828	4	energy	energy	NOUN
ejpam-6729	828	5	of	of	ADP
ejpam-6729	828	6	an	an	DET
ejpam-6729	828	7	intuitionistic	intuitionistic	ADJ
ejpam-6729	828	8	fuzzy	fuzzy	ADJ
ejpam-6729	828	9	directed	direct	VERB
ejpam-6729	828	10	graph	graph	NOUN
ejpam-6729	828	11	.	.	PUNCT
ejpam-6729	829	1	research	research	NOUN
ejpam-6729	829	2	journal	journal	PROPN
ejpam-6729	829	3	of	of	ADP
ejpam-6729	829	4	pharmacy	pharmacy	NOUN
ejpam-6729	829	5	and	and	CCONJ
ejpam-6729	829	6	technology	technology	NOUN
ejpam-6729	829	7	,	,	PUNCT
ejpam-6729	829	8	9(2):190–195	9(2):190–195	NOUN
ejpam-6729	829	9	,	,	PUNCT
ejpam-6729	829	10	2016	2016	NUM
ejpam-6729	829	11	.	.	PUNCT
ejpam-6729	830	1	[	[	X
ejpam-6729	830	2	17	17	NUM
ejpam-6729	830	3	]	]	SYM
ejpam-6729	830	4	yanna	yanna	PROPN
ejpam-6729	830	5	j	j	PROPN
ejpam-6729	830	6	kraakman	kraakman	PROPN
ejpam-6729	830	7	and	and	CCONJ
ejpam-6729	830	8	clara	clara	PROPN
ejpam-6729	830	9	stegehuis	stegehuis	PROPN
ejpam-6729	830	10	.	.	PUNCT
ejpam-6729	831	1	configuration	configuration	NOUN
ejpam-6729	831	2	models	model	NOUN
ejpam-6729	831	3	for	for	ADP
ejpam-6729	831	4	random	random	ADJ
ejpam-6729	831	5	directed	direct	VERB
ejpam-6729	831	6	hypergraphs	hypergraph	NOUN
ejpam-6729	831	7	.	.	PUNCT
ejpam-6729	832	1	arxiv	arxiv	PROPN
ejpam-6729	832	2	preprint	preprint	PROPN
ejpam-6729	832	3	arxiv:2402.06466	arxiv:2402.06466	PROPN
ejpam-6729	832	4	,	,	PUNCT
ejpam-6729	832	5	2024	2024	NUM
ejpam-6729	832	6	.	.	PUNCT
ejpam-6729	833	1	[	[	X
ejpam-6729	833	2	18	18	NUM
ejpam-6729	833	3	]	]	X
ejpam-6729	833	4	muhammad	muhammad	PROPN
ejpam-6729	833	5	akram	akram	PROPN
ejpam-6729	833	6	and	and	CCONJ
ejpam-6729	833	7	anam	anam	PROPN
ejpam-6729	833	8	luqman	luqman	PROPN
ejpam-6729	833	9	.	.	PUNCT
ejpam-6729	834	1	a	a	DET
ejpam-6729	834	2	new	new	ADJ
ejpam-6729	834	3	decision	decision	NOUN
ejpam-6729	834	4	-	-	PUNCT
ejpam-6729	834	5	making	make	VERB
ejpam-6729	834	6	method	method	NOUN
ejpam-6729	834	7	based	base	VERB
ejpam-6729	834	8	on	on	ADP
ejpam-6729	834	9	bipolar	bipolar	ADJ
ejpam-6729	834	10	neutrosophic	neutrosophic	ADJ
ejpam-6729	834	11	directed	direct	VERB
ejpam-6729	834	12	hypergraphs	hypergraph	NOUN
ejpam-6729	834	13	.	.	PUNCT
ejpam-6729	835	1	journal	journal	PROPN
ejpam-6729	835	2	of	of	ADP
ejpam-6729	835	3	applied	apply	VERB
ejpam-6729	835	4	mathematics	mathematic	NOUN
ejpam-6729	835	5	and	and	CCONJ
ejpam-6729	835	6	computing	computing	NOUN
ejpam-6729	835	7	,	,	PUNCT
ejpam-6729	835	8	57:547–575	57:547–575	PROPN
ejpam-6729	835	9	,	,	PUNCT
ejpam-6729	835	10	2018	2018	NUM
ejpam-6729	835	11	.	.	PUNCT
ejpam-6729	836	1	[	[	X
ejpam-6729	836	2	19	19	NUM
ejpam-6729	836	3	]	]	X
ejpam-6729	836	4	muhammad	muhammad	PROPN
ejpam-6729	836	5	akram	akram	PROPN
ejpam-6729	836	6	and	and	CCONJ
ejpam-6729	836	7	anam	anam	PROPN
ejpam-6729	836	8	luqman	luqman	PROPN
ejpam-6729	836	9	.	.	PUNCT
ejpam-6729	837	1	certain	certain	ADJ
ejpam-6729	837	2	networks	network	NOUN
ejpam-6729	837	3	models	model	NOUN
ejpam-6729	837	4	using	use	VERB
ejpam-6729	837	5	singlevalued	singlevalue	VERB
ejpam-6729	837	6	neutrosophic	neutrosophic	ADJ
ejpam-6729	837	7	directed	direct	VERB
ejpam-6729	837	8	hypergraphs	hypergraph	NOUN
ejpam-6729	837	9	.	.	PUNCT
ejpam-6729	838	1	journal	journal	NOUN
ejpam-6729	838	2	of	of	ADP
ejpam-6729	838	3	intelligent	intelligent	ADJ
ejpam-6729	838	4	&	&	CCONJ
ejpam-6729	838	5	fuzzy	fuzzy	ADJ
ejpam-6729	838	6	systems	system	NOUN
ejpam-6729	838	7	,	,	PUNCT
ejpam-6729	838	8	33(1):575–588	33(1):575–588	NUM
ejpam-6729	838	9	,	,	PUNCT
ejpam-6729	838	10	2017	2017	NUM
ejpam-6729	838	11	.	.	PUNCT
ejpam-6729	839	1	[	[	X
ejpam-6729	839	2	20	20	NUM
ejpam-6729	839	3	]	]	PUNCT
ejpam-6729	839	4	takaaki	takaaki	NOUN
ejpam-6729	839	5	fujita	fujita	PROPN
ejpam-6729	839	6	.	.	PUNCT
ejpam-6729	840	1	review	review	NOUN
ejpam-6729	840	2	of	of	ADP
ejpam-6729	840	3	some	some	DET
ejpam-6729	840	4	superhypergraph	superhypergraph	NOUN
ejpam-6729	840	5	classes	class	NOUN
ejpam-6729	840	6	:	:	PUNCT
ejpam-6729	840	7	directed	direct	VERB
ejpam-6729	840	8	,	,	PUNCT
ejpam-6729	840	9	bidirected	bidirected	ADJ
ejpam-6729	840	10	,	,	PUNCT
ejpam-6729	840	11	soft	soft	ADJ
ejpam-6729	840	12	,	,	PUNCT
ejpam-6729	840	13	and	and	CCONJ
ejpam-6729	840	14	rough	rough	ADJ
ejpam-6729	840	15	.	.	PUNCT
ejpam-6729	841	1	advancing	advance	VERB
ejpam-6729	841	2	uncertain	uncertain	ADJ
ejpam-6729	841	3	combinatorics	combinatoric	NOUN
ejpam-6729	841	4	through	through	ADP
ejpam-6729	841	5	graphization	graphization	NOUN
ejpam-6729	841	6	,	,	PUNCT
ejpam-6729	841	7	hyperization	hyperization	NOUN
ejpam-6729	841	8	,	,	PUNCT
ejpam-6729	841	9	and	and	CCONJ
ejpam-6729	841	10	uncertainization	uncertainization	NOUN
ejpam-6729	841	11	:	:	PUNCT
ejpam-6729	841	12	fuzzy	fuzzy	ADJ
ejpam-6729	841	13	,	,	PUNCT
ejpam-6729	841	14	neutrosophic	neutrosophic	ADJ
ejpam-6729	841	15	,	,	PUNCT
ejpam-6729	841	16	soft	soft	ADJ
ejpam-6729	841	17	,	,	PUNCT
ejpam-6729	841	18	rough	rough	ADJ
ejpam-6729	841	19	,	,	PUNCT
ejpam-6729	841	20	and	and	CCONJ
ejpam-6729	841	21	beyond	beyond	ADP
ejpam-6729	841	22	(	(	PUNCT
ejpam-6729	841	23	second	second	ADJ
ejpam-6729	841	24	volume	volume	NOUN
ejpam-6729	841	25	)	)	PUNCT
ejpam-6729	841	26	,	,	PUNCT
ejpam-6729	841	27	2024	2024	NUM
ejpam-6729	841	28	.	.	PUNCT
ejpam-6729	842	1	[	[	X
ejpam-6729	842	2	21	21	NUM
ejpam-6729	842	3	]	]	X
ejpam-6729	842	4	graeme	graeme	PROPN
ejpam-6729	842	5	simsion	simsion	PROPN
ejpam-6729	842	6	and	and	CCONJ
ejpam-6729	842	7	graham	graham	PROPN
ejpam-6729	842	8	witt	witt	PROPN
ejpam-6729	842	9	.	.	PUNCT
ejpam-6729	843	1	data	datum	NOUN
ejpam-6729	843	2	modeling	modeling	NOUN
ejpam-6729	843	3	essentials	essential	NOUN
ejpam-6729	843	4	.	.	PUNCT
ejpam-6729	844	1	elsevier	elsevier	NOUN
ejpam-6729	844	2	,	,	PUNCT
ejpam-6729	844	3	2004	2004	NUM
ejpam-6729	844	4	.	.	PUNCT
ejpam-6729	845	1	[	[	X
ejpam-6729	845	2	22	22	NUM
ejpam-6729	845	3	]	]	PUNCT
ejpam-6729	845	4	michael	michael	PROPN
ejpam-6729	845	5	blaha	blaha	PROPN
ejpam-6729	845	6	.	.	PUNCT
ejpam-6729	846	1	patterns	pattern	NOUN
ejpam-6729	846	2	of	of	ADP
ejpam-6729	846	3	data	datum	NOUN
ejpam-6729	846	4	modeling	modeling	NOUN
ejpam-6729	846	5	,	,	PUNCT
ejpam-6729	846	6	volume	volume	NOUN
ejpam-6729	846	7	1	1	NUM
ejpam-6729	846	8	.	.	PUNCT
ejpam-6729	846	9	crc	crc	PROPN
ejpam-6729	846	10	press	press	PROPN
ejpam-6729	846	11	,	,	PUNCT
ejpam-6729	846	12	2010	2010	NUM
ejpam-6729	846	13	.	.	PUNCT
ejpam-6729	847	1	[	[	X
ejpam-6729	847	2	23	23	NUM
ejpam-6729	847	3	]	]	PUNCT
ejpam-6729	847	4	andré	andré	PROPN
ejpam-6729	847	5	ribeiro	ribeiro	PROPN
ejpam-6729	847	6	,	,	PUNCT
ejpam-6729	847	7	afonso	afonso	PROPN
ejpam-6729	847	8	silva	silva	PROPN
ejpam-6729	847	9	,	,	PUNCT
ejpam-6729	847	10	alberto	alberto	PROPN
ejpam-6729	847	11	rodrigues	rodrigues	PROPN
ejpam-6729	847	12	da	da	PROPN
ejpam-6729	847	13	silva	silva	PROPN
ejpam-6729	847	14	,	,	PUNCT
ejpam-6729	847	15	et	et	PROPN
ejpam-6729	847	16	al	al	PROPN
ejpam-6729	847	17	.	.	PROPN
ejpam-6729	847	18	data	datum	NOUN
ejpam-6729	847	19	modeling	modeling	NOUN
ejpam-6729	847	20	and	and	CCONJ
ejpam-6729	847	21	data	datum	NOUN
ejpam-6729	847	22	analytics	analytic	NOUN
ejpam-6729	847	23	:	:	PUNCT
ejpam-6729	847	24	a	a	DET
ejpam-6729	847	25	survey	survey	NOUN
ejpam-6729	847	26	from	from	ADP
ejpam-6729	847	27	a	a	DET
ejpam-6729	847	28	big	big	ADJ
ejpam-6729	847	29	data	datum	NOUN
ejpam-6729	847	30	perspective	perspective	NOUN
ejpam-6729	847	31	.	.	PUNCT
ejpam-6729	848	1	journal	journal	PROPN
ejpam-6729	848	2	of	of	ADP
ejpam-6729	848	3	software	software	NOUN
ejpam-6729	848	4	engineering	engineering	NOUN
ejpam-6729	848	5	and	and	CCONJ
ejpam-6729	848	6	applications	application	NOUN
ejpam-6729	848	7	,	,	PUNCT
ejpam-6729	848	8	8(12):617	8(12):617	NUM
ejpam-6729	848	9	,	,	PUNCT
ejpam-6729	848	10	2015	2015	NUM
ejpam-6729	848	11	.	.	PUNCT
ejpam-6729	849	1	[	[	X
ejpam-6729	849	2	24	24	NUM
ejpam-6729	849	3	]	]	X
ejpam-6729	849	4	yue	yue	PROPN
ejpam-6729	849	5	gao	gao	PROPN
ejpam-6729	849	6	,	,	PUNCT
ejpam-6729	849	7	zizhao	zizhao	PROPN
ejpam-6729	849	8	zhang	zhang	PROPN
ejpam-6729	849	9	,	,	PUNCT
ejpam-6729	849	10	haojie	haojie	PROPN
ejpam-6729	849	11	lin	lin	PROPN
ejpam-6729	849	12	,	,	PUNCT
ejpam-6729	849	13	xibin	xibin	PROPN
ejpam-6729	849	14	zhao	zhao	PROPN
ejpam-6729	849	15	,	,	PUNCT
ejpam-6729	849	16	shaoyi	shaoyi	PROPN
ejpam-6729	849	17	du	du	PROPN
ejpam-6729	849	18	,	,	PUNCT
ejpam-6729	849	19	and	and	CCONJ
ejpam-6729	849	20	changqing	changqe	VERB
ejpam-6729	849	21	zou	zou	PROPN
ejpam-6729	849	22	.	.	PUNCT
ejpam-6729	849	23	hypergraph	hypergraph	PROPN
ejpam-6729	849	24	learning	learning	PROPN
ejpam-6729	849	25	:	:	PUNCT
ejpam-6729	849	26	methods	method	NOUN
ejpam-6729	849	27	and	and	CCONJ
ejpam-6729	849	28	practices	practice	NOUN
ejpam-6729	849	29	.	.	PUNCT
ejpam-6729	850	1	ieee	ieee	NOUN
ejpam-6729	850	2	transactions	transaction	NOUN
ejpam-6729	850	3	on	on	ADP
ejpam-6729	850	4	pattern	pattern	NOUN
ejpam-6729	850	5	analysis	analysis	NOUN
ejpam-6729	850	6	and	and	CCONJ
ejpam-6729	850	7	machine	machine	NOUN
ejpam-6729	850	8	intelligence	intelligence	NOUN
ejpam-6729	850	9	,	,	PUNCT
ejpam-6729	850	10	44(5):2548–2566	44(5):2548–2566	NUM
ejpam-6729	850	11	,	,	PUNCT
ejpam-6729	850	12	2020	2020	NUM
ejpam-6729	850	13	.	.	PUNCT
ejpam-6729	851	1	[	[	X
ejpam-6729	851	2	25	25	NUM
ejpam-6729	851	3	]	]	X
ejpam-6729	851	4	bibin	bibin	PROPN
ejpam-6729	851	5	k	k	PROPN
ejpam-6729	851	6	jose	jose	PROPN
ejpam-6729	851	7	and	and	CCONJ
ejpam-6729	851	8	zsolt	zsolt	PROPN
ejpam-6729	851	9	tuza	tuza	PROPN
ejpam-6729	851	10	.	.	PUNCT
ejpam-6729	852	1	hypergraph	hypergraph	VERB
ejpam-6729	852	2	domination	domination	NOUN
ejpam-6729	852	3	and	and	CCONJ
ejpam-6729	852	4	strong	strong	ADJ
ejpam-6729	852	5	independence	independence	NOUN
ejpam-6729	852	6	.	.	PUNCT
ejpam-6729	853	1	t.	t.	PROPN
ejpam-6729	853	2	fujita	fujita	PROPN
ejpam-6729	853	3	,	,	PUNCT
ejpam-6729	853	4	f.	f.	PROPN
ejpam-6729	853	5	smarandache	smarandache	PROPN
ejpam-6729	853	6	/	/	SYM
ejpam-6729	853	7	eur	eur	PROPN
ejpam-6729	853	8	.	.	PUNCT
ejpam-6729	854	1	j.	j.	PROPN
ejpam-6729	854	2	pure	pure	PROPN
ejpam-6729	854	3	appl	appl	PROPN
ejpam-6729	854	4	.	.	PROPN
ejpam-6729	854	5	math	math	PROPN
ejpam-6729	854	6	,	,	PUNCT
ejpam-6729	854	7	18	18	NUM
ejpam-6729	854	8	(	(	PUNCT
ejpam-6729	854	9	4	4	NUM
ejpam-6729	854	10	)	)	PUNCT
ejpam-6729	854	11	(	(	PUNCT
ejpam-6729	854	12	2025	2025	NUM
ejpam-6729	854	13	)	)	PUNCT
ejpam-6729	854	14	,	,	PUNCT
ejpam-6729	854	15	6729	6729	NUM
ejpam-6729	854	16	35	35	NUM
ejpam-6729	854	17	of	of	ADP
ejpam-6729	854	18	36	36	NUM
ejpam-6729	854	19	applicable	applicable	ADJ
ejpam-6729	854	20	analysis	analysis	NOUN
ejpam-6729	854	21	and	and	CCONJ
ejpam-6729	854	22	discrete	discrete	ADJ
ejpam-6729	854	23	mathematics	mathematic	NOUN
ejpam-6729	854	24	,	,	PUNCT
ejpam-6729	854	25	3(2):347–358	3(2):347–358	NOUN
ejpam-6729	854	26	,	,	PUNCT
ejpam-6729	854	27	2009	2009	NUM
ejpam-6729	854	28	.	.	PUNCT
ejpam-6729	855	1	[	[	X
ejpam-6729	855	2	26	26	NUM
ejpam-6729	855	3	]	]	PUNCT
ejpam-6729	855	4	eduardo	eduardo	PROPN
ejpam-6729	855	5	martín	martín	PROPN
ejpam-6729	855	6	campoverde	campoverde	PROPN
ejpam-6729	855	7	valencia	valencia	PROPN
ejpam-6729	855	8	,	,	PUNCT
ejpam-6729	855	9	jessica	jessica	PROPN
ejpam-6729	855	10	paola	paola	PROPN
ejpam-6729	855	11	chuisaca	chuisaca	NOUN
ejpam-6729	855	12	vásquez	vásquez	NOUN
ejpam-6729	855	13	,	,	PUNCT
ejpam-6729	855	14	and	and	CCONJ
ejpam-6729	855	15	francisco	francisco	PROPN
ejpam-6729	855	16	ángel	ángel	PROPN
ejpam-6729	855	17	becerra	becerra	PROPN
ejpam-6729	855	18	lois	lois	PROPN
ejpam-6729	855	19	.	.	PUNCT
ejpam-6729	856	1	multineutrosophic	multineutrosophic	ADJ
ejpam-6729	856	2	analysis	analysis	NOUN
ejpam-6729	856	3	of	of	ADP
ejpam-6729	856	4	the	the	DET
ejpam-6729	856	5	relationship	relationship	NOUN
ejpam-6729	856	6	between	between	ADP
ejpam-6729	856	7	survival	survival	NOUN
ejpam-6729	856	8	and	and	CCONJ
ejpam-6729	856	9	business	business	NOUN
ejpam-6729	856	10	growth	growth	NOUN
ejpam-6729	856	11	in	in	ADP
ejpam-6729	856	12	the	the	DET
ejpam-6729	856	13	manufacturing	manufacturing	NOUN
ejpam-6729	856	14	sector	sector	NOUN
ejpam-6729	856	15	of	of	ADP
ejpam-6729	856	16	azuay	azuay	NOUN
ejpam-6729	856	17	province	province	NOUN
ejpam-6729	856	18	,	,	PUNCT
ejpam-6729	856	19	2020–2023	2020–2023	NUM
ejpam-6729	856	20	,	,	PUNCT
ejpam-6729	856	21	using	use	VERB
ejpam-6729	856	22	plithogenic	plithogenic	ADJ
ejpam-6729	856	23	n	n	CCONJ
ejpam-6729	856	24	-	-	PUNCT
ejpam-6729	856	25	superhypergraphs	superhypergraph	NOUN
ejpam-6729	856	26	.	.	PUNCT
ejpam-6729	857	1	neutrosophic	neutrosophic	ADJ
ejpam-6729	857	2	sets	set	NOUN
ejpam-6729	857	3	and	and	CCONJ
ejpam-6729	857	4	systems	system	NOUN
ejpam-6729	857	5	,	,	PUNCT
ejpam-6729	857	6	84:341–355	84:341–355	NUM
ejpam-6729	857	7	,	,	PUNCT
ejpam-6729	857	8	2025	2025	NUM
ejpam-6729	857	9	.	.	PUNCT
ejpam-6729	858	1	[	[	X
ejpam-6729	858	2	27	27	NUM
ejpam-6729	858	3	]	]	PUNCT
ejpam-6729	858	4	takaaki	takaaki	NOUN
ejpam-6729	858	5	fujita	fujita	PROPN
ejpam-6729	858	6	.	.	PUNCT
ejpam-6729	859	1	advancing	advance	VERB
ejpam-6729	859	2	uncertain	uncertain	ADJ
ejpam-6729	859	3	combinatorics	combinatoric	NOUN
ejpam-6729	859	4	through	through	ADP
ejpam-6729	859	5	graphization	graphization	NOUN
ejpam-6729	859	6	,	,	PUNCT
ejpam-6729	859	7	hyperization	hyperization	NOUN
ejpam-6729	859	8	,	,	PUNCT
ejpam-6729	859	9	and	and	CCONJ
ejpam-6729	859	10	uncertainization	uncertainization	NOUN
ejpam-6729	859	11	:	:	PUNCT
ejpam-6729	859	12	fuzzy	fuzzy	ADJ
ejpam-6729	859	13	,	,	PUNCT
ejpam-6729	859	14	neutrosophic	neutrosophic	ADJ
ejpam-6729	859	15	,	,	PUNCT
ejpam-6729	859	16	soft	soft	ADJ
ejpam-6729	859	17	,	,	PUNCT
ejpam-6729	859	18	rough	rough	ADJ
ejpam-6729	859	19	,	,	PUNCT
ejpam-6729	859	20	and	and	CCONJ
ejpam-6729	859	21	beyond	beyond	ADP
ejpam-6729	859	22	.	.	PUNCT
ejpam-6729	860	1	biblio	biblio	PROPN
ejpam-6729	860	2	publishing	publishing	PROPN
ejpam-6729	860	3	,	,	PUNCT
ejpam-6729	860	4	2025	2025	NUM
ejpam-6729	860	5	.	.	PUNCT
ejpam-6729	861	1	[	[	X
ejpam-6729	861	2	28	28	NUM
ejpam-6729	861	3	]	]	X
ejpam-6729	861	4	berrocal	berrocal	ADJ
ejpam-6729	861	5	villegas	villegas	PROPN
ejpam-6729	861	6	salomón	salomón	PROPN
ejpam-6729	861	7	marcos	marcos	PROPN
ejpam-6729	861	8	,	,	PUNCT
ejpam-6729	861	9	montalvo	montalvo	PROPN
ejpam-6729	861	10	fritas	frita	VERB
ejpam-6729	861	11	willner	willn	ADJ
ejpam-6729	861	12	,	,	PUNCT
ejpam-6729	861	13	berrocal	berrocal	ADJ
ejpam-6729	861	14	villegas	villegas	PROPN
ejpam-6729	861	15	carmen	carmen	PROPN
ejpam-6729	861	16	rosa	rosa	PROPN
ejpam-6729	861	17	,	,	PUNCT
ejpam-6729	861	18	flores	flores	PROPN
ejpam-6729	861	19	fuentes	fuentes	PROPN
ejpam-6729	861	20	rivera	rivera	PROPN
ejpam-6729	861	21	maría	maría	PROPN
ejpam-6729	861	22	yissel	yissel	PROPN
ejpam-6729	861	23	,	,	PUNCT
ejpam-6729	861	24	espejo	espejo	PROPN
ejpam-6729	861	25	rivera	rivera	PROPN
ejpam-6729	861	26	roberto	roberto	PROPN
ejpam-6729	861	27	,	,	PUNCT
ejpam-6729	861	28	laura	laura	PROPN
ejpam-6729	861	29	daysi	daysi	PROPN
ejpam-6729	861	30	bautista	bautista	PROPN
ejpam-6729	861	31	puma	puma	PROPN
ejpam-6729	861	32	,	,	PUNCT
ejpam-6729	861	33	and	and	CCONJ
ejpam-6729	861	34	dante	dante	PROPN
ejpam-6729	861	35	manuel	manuel	PROPN
ejpam-6729	861	36	macazana	macazana	PROPN
ejpam-6729	861	37	fernández	fernández	PROPN
ejpam-6729	861	38	.	.	PUNCT
ejpam-6729	862	1	using	use	VERB
ejpam-6729	862	2	plithogenic	plithogenic	ADJ
ejpam-6729	862	3	n	n	CCONJ
ejpam-6729	862	4	-	-	PUNCT
ejpam-6729	862	5	superhypergraphs	superhypergraph	NOUN
ejpam-6729	862	6	to	to	PART
ejpam-6729	862	7	assess	assess	VERB
ejpam-6729	862	8	the	the	DET
ejpam-6729	862	9	degree	degree	NOUN
ejpam-6729	862	10	of	of	ADP
ejpam-6729	862	11	relationship	relationship	NOUN
ejpam-6729	862	12	between	between	ADP
ejpam-6729	862	13	information	information	NOUN
ejpam-6729	862	14	skills	skill	NOUN
ejpam-6729	862	15	and	and	CCONJ
ejpam-6729	862	16	digital	digital	ADJ
ejpam-6729	862	17	competencies	competency	NOUN
ejpam-6729	862	18	.	.	PUNCT
ejpam-6729	863	1	neutrosophic	neutrosophic	ADJ
ejpam-6729	863	2	sets	set	NOUN
ejpam-6729	863	3	and	and	CCONJ
ejpam-6729	863	4	systems	system	NOUN
ejpam-6729	863	5	,	,	PUNCT
ejpam-6729	863	6	84:513–524	84:513–524	PROPN
ejpam-6729	863	7	,	,	PUNCT
ejpam-6729	863	8	2025	2025	NUM
ejpam-6729	863	9	.	.	PUNCT
ejpam-6729	864	1	[	[	X
ejpam-6729	864	2	29	29	NUM
ejpam-6729	864	3	]	]	X
ejpam-6729	864	4	takaaki	takaaki	NOUN
ejpam-6729	864	5	fujita	fujita	PROPN
ejpam-6729	864	6	.	.	PUNCT
ejpam-6729	865	1	hypergraph	hypergraph	VERB
ejpam-6729	865	2	and	and	CCONJ
ejpam-6729	865	3	superhypergraph	superhypergraph	VERB
ejpam-6729	865	4	approaches	approach	NOUN
ejpam-6729	865	5	in	in	ADP
ejpam-6729	865	6	electronics	electronic	NOUN
ejpam-6729	865	7	:	:	PUNCT
ejpam-6729	865	8	a	a	DET
ejpam-6729	865	9	hierarchical	hierarchical	ADJ
ejpam-6729	865	10	framework	framework	NOUN
ejpam-6729	865	11	for	for	ADP
ejpam-6729	865	12	modeling	model	VERB
ejpam-6729	865	13	power	power	NOUN
ejpam-6729	865	14	-	-	PUNCT
ejpam-6729	865	15	grid	grid	NOUN
ejpam-6729	865	16	hypernetworks	hypernetwork	NOUN
ejpam-6729	865	17	and	and	CCONJ
ejpam-6729	865	18	superhypernetworks	superhypernetwork	NOUN
ejpam-6729	865	19	.	.	PUNCT
ejpam-6729	866	1	journal	journal	PROPN
ejpam-6729	866	2	of	of	ADP
ejpam-6729	866	3	energy	energy	NOUN
ejpam-6729	866	4	research	research	NOUN
ejpam-6729	866	5	and	and	CCONJ
ejpam-6729	866	6	reviews	review	NOUN
ejpam-6729	866	7	,	,	PUNCT
ejpam-6729	866	8	17(6):102–136	17(6):102–136	NUM
ejpam-6729	866	9	,	,	PUNCT
ejpam-6729	866	10	2025	2025	NUM
ejpam-6729	866	11	.	.	PUNCT
ejpam-6729	867	1	[	[	X
ejpam-6729	867	2	30	30	NUM
ejpam-6729	867	3	]	]	X
ejpam-6729	867	4	shouxian	shouxian	ADJ
ejpam-6729	867	5	zhu	zhu	PROPN
ejpam-6729	867	6	.	.	PUNCT
ejpam-6729	868	1	neutrosophic	neutrosophic	PROPN
ejpam-6729	868	2	n	n	CCONJ
ejpam-6729	868	3	-	-	PUNCT
ejpam-6729	868	4	superhypernetwork	superhypernetwork	NOUN
ejpam-6729	868	5	:	:	PUNCT
ejpam-6729	868	6	a	a	DET
ejpam-6729	868	7	new	new	ADJ
ejpam-6729	868	8	approach	approach	NOUN
ejpam-6729	868	9	for	for	ADP
ejpam-6729	868	10	evaluating	evaluate	VERB
ejpam-6729	868	11	short	short	ADJ
ejpam-6729	868	12	video	video	NOUN
ejpam-6729	868	13	communication	communication	NOUN
ejpam-6729	868	14	effectiveness	effectiveness	NOUN
ejpam-6729	868	15	in	in	ADP
ejpam-6729	868	16	media	medium	NOUN
ejpam-6729	868	17	convergence	convergence	NOUN
ejpam-6729	868	18	.	.	PUNCT
ejpam-6729	869	1	neutrosophic	neutrosophic	ADJ
ejpam-6729	869	2	sets	set	NOUN
ejpam-6729	869	3	and	and	CCONJ
ejpam-6729	869	4	systems	system	NOUN
ejpam-6729	869	5	,	,	PUNCT
ejpam-6729	869	6	85:1004–1017	85:1004–1017	NUM
ejpam-6729	869	7	,	,	PUNCT
ejpam-6729	869	8	2025	2025	NUM
ejpam-6729	869	9	.	.	PUNCT
ejpam-6729	870	1	[	[	X
ejpam-6729	870	2	31	31	NUM
ejpam-6729	870	3	]	]	PUNCT
ejpam-6729	870	4	yasar	yasar	PROPN
ejpam-6729	870	5	nacaroglu	nacaroglu	PROPN
ejpam-6729	870	6	,	,	PUNCT
ejpam-6729	870	7	nihat	nihat	PROPN
ejpam-6729	870	8	akgunes	akgune	NOUN
ejpam-6729	870	9	,	,	PUNCT
ejpam-6729	870	10	sedat	sedat	PROPN
ejpam-6729	870	11	pak	pak	PROPN
ejpam-6729	870	12	,	,	PUNCT
ejpam-6729	870	13	and	and	CCONJ
ejpam-6729	870	14	i	i	PROPN
ejpam-6729	870	15	naci	naci	PROPN
ejpam-6729	870	16	cangul	cangul	PROPN
ejpam-6729	870	17	.	.	PUNCT
ejpam-6729	871	1	some	some	DET
ejpam-6729	871	2	graph	graph	NOUN
ejpam-6729	871	3	parameters	parameter	NOUN
ejpam-6729	871	4	of	of	ADP
ejpam-6729	871	5	power	power	NOUN
ejpam-6729	871	6	set	set	NOUN
ejpam-6729	871	7	graphs	graph	NOUN
ejpam-6729	871	8	.	.	PUNCT
ejpam-6729	872	1	advances	advance	NOUN
ejpam-6729	872	2	&	&	CCONJ
ejpam-6729	872	3	applications	application	NOUN
ejpam-6729	872	4	in	in	ADP
ejpam-6729	872	5	discrete	discrete	ADJ
ejpam-6729	872	6	mathematics	mathematic	NOUN
ejpam-6729	872	7	,	,	PUNCT
ejpam-6729	872	8	26(2	26(2	NUM
ejpam-6729	872	9	)	)	PUNCT
ejpam-6729	872	10	,	,	PUNCT
ejpam-6729	872	11	2021	2021	NUM
ejpam-6729	872	12	.	.	PUNCT
ejpam-6729	873	1	[	[	X
ejpam-6729	873	2	32	32	NUM
ejpam-6729	873	3	]	]	PUNCT
ejpam-6729	873	4	ma	ma	PROPN
ejpam-6729	873	5	shalu	shalu	PROPN
ejpam-6729	873	6	and	and	CCONJ
ejpam-6729	873	7	s	s	PROPN
ejpam-6729	873	8	devi	devi	PROPN
ejpam-6729	873	9	yamini	yamini	PROPN
ejpam-6729	873	10	.	.	PUNCT
ejpam-6729	874	1	counting	count	VERB
ejpam-6729	874	2	maximal	maximal	ADJ
ejpam-6729	874	3	independent	independent	ADJ
ejpam-6729	874	4	sets	set	NOUN
ejpam-6729	874	5	in	in	ADP
ejpam-6729	874	6	power	power	NOUN
ejpam-6729	874	7	set	set	NOUN
ejpam-6729	874	8	graphs	graph	NOUN
ejpam-6729	874	9	.	.	PUNCT
ejpam-6729	875	1	indian	indian	PROPN
ejpam-6729	875	2	institute	institute	PROPN
ejpam-6729	875	3	of	of	ADP
ejpam-6729	875	4	information	information	NOUN
ejpam-6729	875	5	technology	technology	NOUN
ejpam-6729	875	6	design	design	NOUN
ejpam-6729	875	7	&	&	CCONJ
ejpam-6729	875	8	manufacturing	manufacturing	PROPN
ejpam-6729	875	9	(	(	PUNCT
ejpam-6729	875	10	iiitd&m	iiitd&m	PROPN
ejpam-6729	875	11	)	)	PUNCT
ejpam-6729	875	12	kancheepuram	kancheepuram	PROPN
ejpam-6729	875	13	,	,	PUNCT
ejpam-6729	875	14	india	india	PROPN
ejpam-6729	875	15	,	,	PUNCT
ejpam-6729	875	16	2014	2014	NUM
ejpam-6729	875	17	.	.	PUNCT
ejpam-6729	876	1	[	[	X
ejpam-6729	876	2	33	33	NUM
ejpam-6729	876	3	]	]	PUNCT
ejpam-6729	876	4	alain	alain	PROPN
ejpam-6729	876	5	bretto	bretto	PROPN
ejpam-6729	876	6	.	.	PUNCT
ejpam-6729	877	1	hypergraph	hypergraph	PROPN
ejpam-6729	877	2	theory	theory	NOUN
ejpam-6729	877	3	.	.	PUNCT
ejpam-6729	878	1	an	an	DET
ejpam-6729	878	2	introduction	introduction	NOUN
ejpam-6729	878	3	.	.	PUNCT
ejpam-6729	879	1	mathematical	mathematical	ADJ
ejpam-6729	879	2	engineering	engineering	NOUN
ejpam-6729	879	3	.	.	PUNCT
ejpam-6729	880	1	cham	cham	PROPN
ejpam-6729	880	2	:	:	PUNCT
ejpam-6729	880	3	springer	springer	NOUN
ejpam-6729	880	4	,	,	PUNCT
ejpam-6729	880	5	1	1	NUM
ejpam-6729	880	6	,	,	PUNCT
ejpam-6729	880	7	2013	2013	NUM
ejpam-6729	880	8	.	.	PUNCT
ejpam-6729	881	1	[	[	X
ejpam-6729	881	2	34	34	NUM
ejpam-6729	881	3	]	]	PUNCT
ejpam-6729	881	4	florentin	florentin	PROPN
ejpam-6729	881	5	smarandache	smarandache	PROPN
ejpam-6729	881	6	.	.	PUNCT
ejpam-6729	882	1	foundation	foundation	NOUN
ejpam-6729	882	2	of	of	ADP
ejpam-6729	882	3	superhyperstructure	superhyperstructure	PROPN
ejpam-6729	882	4	&	&	CCONJ
ejpam-6729	882	5	neutrosophic	neutrosophic	ADJ
ejpam-6729	882	6	superhyperstructure	superhyperstructure	NOUN
ejpam-6729	882	7	.	.	PUNCT
ejpam-6729	883	1	neutrosophic	neutrosophic	ADJ
ejpam-6729	883	2	sets	set	NOUN
ejpam-6729	883	3	and	and	CCONJ
ejpam-6729	883	4	systems	system	NOUN
ejpam-6729	883	5	,	,	PUNCT
ejpam-6729	883	6	63(1):21	63(1):21	NUM
ejpam-6729	883	7	,	,	PUNCT
ejpam-6729	883	8	2024	2024	NUM
ejpam-6729	883	9	.	.	PUNCT
ejpam-6729	884	1	[	[	X
ejpam-6729	884	2	35	35	NUM
ejpam-6729	884	3	]	]	X
ejpam-6729	884	4	huda	huda	PROPN
ejpam-6729	884	5	e	e	PROPN
ejpam-6729	884	6	khali	khali	PROPN
ejpam-6729	884	7	,	,	PUNCT
ejpam-6729	884	8	gonca	gonca	PROPN
ejpam-6729	884	9	d	d	NOUN
ejpam-6729	884	10	güngör	güngör	PROPN
ejpam-6729	884	11	,	,	PUNCT
ejpam-6729	884	12	and	and	CCONJ
ejpam-6729	884	13	muslim	muslim	PROPN
ejpam-6729	884	14	a	a	DET
ejpam-6729	884	15	noah	noah	PROPN
ejpam-6729	884	16	zaina	zaina	PROPN
ejpam-6729	884	17	.	.	PUNCT
ejpam-6729	884	18	neutrosophic	neutrosophic	PROPN
ejpam-6729	884	19	superhyper	superhyper	NOUN
ejpam-6729	884	20	bi	bi	ADJ
ejpam-6729	884	21	-	-	ADJ
ejpam-6729	884	22	topological	topological	ADJ
ejpam-6729	884	23	spaces	space	NOUN
ejpam-6729	884	24	:	:	PUNCT
ejpam-6729	884	25	original	original	ADJ
ejpam-6729	884	26	notions	notion	NOUN
ejpam-6729	884	27	and	and	CCONJ
ejpam-6729	884	28	new	new	ADJ
ejpam-6729	884	29	insights	insight	NOUN
ejpam-6729	884	30	.	.	PUNCT
ejpam-6729	885	1	neutrosophic	neutrosophic	ADJ
ejpam-6729	885	2	sets	set	NOUN
ejpam-6729	885	3	and	and	CCONJ
ejpam-6729	885	4	systems	system	NOUN
ejpam-6729	885	5	,	,	PUNCT
ejpam-6729	885	6	51(1):3	51(1):3	PROPN
ejpam-6729	885	7	,	,	PUNCT
ejpam-6729	885	8	2022	2022	NUM
ejpam-6729	885	9	.	.	PUNCT
ejpam-6729	886	1	[	[	X
ejpam-6729	886	2	36	36	NUM
ejpam-6729	886	3	]	]	X
ejpam-6729	886	4	eldar	eldar	NOUN
ejpam-6729	886	5	fischer	fischer	PROPN
ejpam-6729	886	6	and	and	CCONJ
ejpam-6729	886	7	ilan	ilan	PROPN
ejpam-6729	886	8	newman	newman	PROPN
ejpam-6729	886	9	.	.	PUNCT
ejpam-6729	887	1	testing	testing	NOUN
ejpam-6729	887	2	versus	versus	ADP
ejpam-6729	887	3	estimation	estimation	NOUN
ejpam-6729	887	4	of	of	ADP
ejpam-6729	887	5	graph	graph	NOUN
ejpam-6729	887	6	properties	property	NOUN
ejpam-6729	887	7	.	.	PUNCT
ejpam-6729	888	1	in	in	ADP
ejpam-6729	888	2	proceedings	proceeding	NOUN
ejpam-6729	888	3	of	of	ADP
ejpam-6729	888	4	the	the	DET
ejpam-6729	888	5	thirty	thirty	NUM
ejpam-6729	888	6	-	-	PUNCT
ejpam-6729	888	7	seventh	seventh	ADJ
ejpam-6729	888	8	annual	annual	ADJ
ejpam-6729	888	9	acm	acm	NOUN
ejpam-6729	888	10	symposium	symposium	NOUN
ejpam-6729	888	11	on	on	ADP
ejpam-6729	888	12	theory	theory	NOUN
ejpam-6729	888	13	of	of	ADP
ejpam-6729	888	14	computing	computing	NOUN
ejpam-6729	888	15	,	,	PUNCT
ejpam-6729	888	16	pages	page	NOUN
ejpam-6729	888	17	138–146	138–146	NUM
ejpam-6729	888	18	,	,	PUNCT
ejpam-6729	888	19	2005	2005	NUM
ejpam-6729	888	20	.	.	PUNCT
ejpam-6729	889	1	[	[	X
ejpam-6729	889	2	37	37	NUM
ejpam-6729	889	3	]	]	PUNCT
ejpam-6729	889	4	lotfi	lotfi	X
ejpam-6729	889	5	a	a	DET
ejpam-6729	889	6	zadeh	zadeh	PROPN
ejpam-6729	889	7	.	.	PUNCT
ejpam-6729	889	8	fuzzy	fuzzy	ADJ
ejpam-6729	889	9	sets	set	NOUN
ejpam-6729	889	10	.	.	PUNCT
ejpam-6729	890	1	information	information	NOUN
ejpam-6729	890	2	and	and	CCONJ
ejpam-6729	890	3	control	control	NOUN
ejpam-6729	890	4	,	,	PUNCT
ejpam-6729	890	5	8(3):338–353	8(3):338–353	NUM
ejpam-6729	890	6	,	,	PUNCT
ejpam-6729	890	7	1965	1965	NUM
ejpam-6729	890	8	.	.	PUNCT
ejpam-6729	891	1	[	[	X
ejpam-6729	891	2	38	38	NUM
ejpam-6729	891	3	]	]	SYM
ejpam-6729	891	4	w	w	NOUN
ejpam-6729	891	5	-	-	PUNCT
ejpam-6729	891	6	l	l	NOUN
ejpam-6729	891	7	gau	gau	NOUN
ejpam-6729	891	8	and	and	CCONJ
ejpam-6729	891	9	daniel	daniel	PROPN
ejpam-6729	891	10	j	j	PROPN
ejpam-6729	891	11	buehrer	buehrer	PROPN
ejpam-6729	891	12	.	.	PUNCT
ejpam-6729	892	1	vague	vague	ADJ
ejpam-6729	892	2	sets	set	NOUN
ejpam-6729	892	3	.	.	PUNCT
ejpam-6729	893	1	ieee	ieee	NOUN
ejpam-6729	893	2	transactions	transaction	NOUN
ejpam-6729	893	3	on	on	ADP
ejpam-6729	893	4	systems	system	NOUN
ejpam-6729	893	5	,	,	PUNCT
ejpam-6729	893	6	man	man	NOUN
ejpam-6729	893	7	,	,	PUNCT
ejpam-6729	893	8	and	and	CCONJ
ejpam-6729	893	9	cybernetics	cybernetic	NOUN
ejpam-6729	893	10	,	,	PUNCT
ejpam-6729	893	11	23(2):610–614	23(2):610–614	NUM
ejpam-6729	893	12	,	,	PUNCT
ejpam-6729	893	13	1993	1993	NUM
ejpam-6729	893	14	.	.	PUNCT
ejpam-6729	894	1	[	[	X
ejpam-6729	894	2	39	39	NUM
ejpam-6729	894	3	]	]	PUNCT
ejpam-6729	894	4	muhammad	muhammad	PROPN
ejpam-6729	894	5	akram	akram	PROPN
ejpam-6729	894	6	,	,	PUNCT
ejpam-6729	894	7	bijan	bijan	PROPN
ejpam-6729	894	8	davvaz	davvaz	NOUN
ejpam-6729	894	9	,	,	PUNCT
ejpam-6729	894	10	and	and	CCONJ
ejpam-6729	894	11	feng	feng	PROPN
ejpam-6729	894	12	feng	feng	PROPN
ejpam-6729	894	13	.	.	PUNCT
ejpam-6729	895	1	intuitionistic	intuitionistic	ADJ
ejpam-6729	895	2	fuzzy	fuzzy	ADJ
ejpam-6729	895	3	soft	soft	ADJ
ejpam-6729	895	4	k	k	NOUN
ejpam-6729	895	5	-	-	PUNCT
ejpam-6729	895	6	algebras	algebra	NOUN
ejpam-6729	895	7	.	.	PUNCT
ejpam-6729	896	1	mathematics	mathematic	NOUN
ejpam-6729	896	2	in	in	ADP
ejpam-6729	896	3	computer	computer	NOUN
ejpam-6729	896	4	science	science	NOUN
ejpam-6729	896	5	,	,	PUNCT
ejpam-6729	896	6	7:353–365	7:353–365	PROPN
ejpam-6729	896	7	,	,	PUNCT
ejpam-6729	896	8	2013	2013	NUM
ejpam-6729	896	9	.	.	PUNCT
ejpam-6729	897	1	[	[	X
ejpam-6729	897	2	40	40	NUM
ejpam-6729	897	3	]	]	X
ejpam-6729	897	4	walter	walter	PROPN
ejpam-6729	897	5	alexandre	alexandre	PROPN
ejpam-6729	897	6	carnielli	carnielli	PROPN
ejpam-6729	897	7	and	and	CCONJ
ejpam-6729	897	8	marcelo	marcelo	PROPN
ejpam-6729	897	9	esteban	esteban	PROPN
ejpam-6729	897	10	coniglio	coniglio	PROPN
ejpam-6729	897	11	.	.	PUNCT
ejpam-6729	898	1	paraconsistent	paraconsistent	NOUN
ejpam-6729	898	2	set	set	NOUN
ejpam-6729	898	3	theory	theory	NOUN
ejpam-6729	898	4	by	by	ADP
ejpam-6729	898	5	predicating	predicate	VERB
ejpam-6729	898	6	on	on	ADP
ejpam-6729	898	7	consistency	consistency	NOUN
ejpam-6729	898	8	.	.	PUNCT
ejpam-6729	899	1	j.	j.	PROPN
ejpam-6729	899	2	log	log	PROPN
ejpam-6729	899	3	.	.	PUNCT
ejpam-6729	900	1	comput	comput	PROPN
ejpam-6729	900	2	.	.	PUNCT
ejpam-6729	900	3	,	,	PUNCT
ejpam-6729	900	4	26:97–116	26:97–116	NUM
ejpam-6729	900	5	,	,	PUNCT
ejpam-6729	900	6	2016	2016	NUM
ejpam-6729	900	7	.	.	PUNCT
ejpam-6729	901	1	t.	t.	PROPN
ejpam-6729	901	2	fujita	fujita	PROPN
ejpam-6729	901	3	,	,	PUNCT
ejpam-6729	901	4	f.	f.	PROPN
ejpam-6729	901	5	smarandache	smarandache	PROPN
ejpam-6729	901	6	/	/	SYM
ejpam-6729	901	7	eur	eur	PROPN
ejpam-6729	901	8	.	.	PUNCT
ejpam-6729	902	1	j.	j.	PROPN
ejpam-6729	902	2	pure	pure	PROPN
ejpam-6729	902	3	appl	appl	PROPN
ejpam-6729	902	4	.	.	PROPN
ejpam-6729	902	5	math	math	PROPN
ejpam-6729	902	6	,	,	PUNCT
ejpam-6729	902	7	18	18	NUM
ejpam-6729	902	8	(	(	PUNCT
ejpam-6729	902	9	4	4	NUM
ejpam-6729	902	10	)	)	PUNCT
ejpam-6729	902	11	(	(	PUNCT
ejpam-6729	902	12	2025	2025	NUM
ejpam-6729	902	13	)	)	PUNCT
ejpam-6729	902	14	,	,	PUNCT
ejpam-6729	902	15	6729	6729	NUM
ejpam-6729	902	16	36	36	NUM
ejpam-6729	902	17	of	of	ADP
ejpam-6729	902	18	36	36	NUM
ejpam-6729	902	19	[	[	SYM
ejpam-6729	902	20	41	41	NUM
ejpam-6729	902	21	]	]	X
ejpam-6729	902	22	dmitriy	dmitriy	PROPN
ejpam-6729	902	23	molodtsov	molodtsov	PROPN
ejpam-6729	902	24	.	.	PUNCT
ejpam-6729	903	1	soft	soft	ADJ
ejpam-6729	903	2	set	set	NOUN
ejpam-6729	903	3	theory	theory	NOUN
ejpam-6729	903	4	-	-	PUNCT
ejpam-6729	903	5	first	first	ADJ
ejpam-6729	903	6	results	result	NOUN
ejpam-6729	903	7	.	.	PUNCT
ejpam-6729	904	1	computers	computer	NOUN
ejpam-6729	904	2	&	&	CCONJ
ejpam-6729	904	3	mathematics	mathematics	PROPN
ejpam-6729	904	4	with	with	ADP
ejpam-6729	904	5	applications	application	NOUN
ejpam-6729	904	6	,	,	PUNCT
ejpam-6729	904	7	37(4	37(4	PROPN
ejpam-6729	904	8	-	-	PUNCT
ejpam-6729	904	9	5):19–31	5):19–31	NUM
ejpam-6729	904	10	,	,	PUNCT
ejpam-6729	904	11	1999	1999	NUM
ejpam-6729	904	12	.	.	PUNCT
ejpam-6729	905	1	[	[	X
ejpam-6729	905	2	42	42	NUM
ejpam-6729	905	3	]	]	PUNCT
ejpam-6729	905	4	pradip	pradip	PROPN
ejpam-6729	905	5	kumar	kumar	PROPN
ejpam-6729	905	6	maji	maji	PROPN
ejpam-6729	905	7	,	,	PUNCT
ejpam-6729	905	8	ranjit	ranjit	PROPN
ejpam-6729	905	9	biswas	biswas	PROPN
ejpam-6729	905	10	,	,	PUNCT
ejpam-6729	905	11	and	and	CCONJ
ejpam-6729	905	12	a	a	DET
ejpam-6729	905	13	ranjan	ranjan	PROPN
ejpam-6729	905	14	roy	roy	PROPN
ejpam-6729	905	15	.	.	PROPN
ejpam-6729	905	16	soft	soft	ADJ
ejpam-6729	905	17	set	set	NOUN
ejpam-6729	905	18	theory	theory	NOUN
ejpam-6729	905	19	.	.	PUNCT
ejpam-6729	906	1	computers	computer	NOUN
ejpam-6729	906	2	&	&	CCONJ
ejpam-6729	906	3	mathematics	mathematics	PROPN
ejpam-6729	906	4	with	with	ADP
ejpam-6729	906	5	applications	application	NOUN
ejpam-6729	906	6	,	,	PUNCT
ejpam-6729	906	7	45(4	45(4	NOUN
ejpam-6729	906	8	-	-	PUNCT
ejpam-6729	906	9	5):555–562	5):555–562	NUM
ejpam-6729	906	10	,	,	PUNCT
ejpam-6729	906	11	2003	2003	NUM
ejpam-6729	906	12	.	.	PUNCT
ejpam-6729	907	1	[	[	X
ejpam-6729	907	2	43	43	NUM
ejpam-6729	907	3	]	]	X
ejpam-6729	907	4	xiaolong	xiaolong	PROPN
ejpam-6729	907	5	shi	shi	PROPN
ejpam-6729	907	6	,	,	PUNCT
ejpam-6729	907	7	saeed	saeed	PROPN
ejpam-6729	907	8	kosari	kosari	PROPN
ejpam-6729	907	9	,	,	PUNCT
ejpam-6729	907	10	ali	ali	PROPN
ejpam-6729	907	11	asghar	asghar	PROPN
ejpam-6729	907	12	talebi	talebi	PROPN
ejpam-6729	907	13	,	,	PUNCT
ejpam-6729	907	14	seyed	seyed	PROPN
ejpam-6729	907	15	hossein	hossein	PROPN
ejpam-6729	907	16	sadati	sadati	PROPN
ejpam-6729	907	17	,	,	PUNCT
ejpam-6729	907	18	and	and	CCONJ
ejpam-6729	907	19	hossein	hossein	PROPN
ejpam-6729	907	20	rashmanlou	rashmanlou	PROPN
ejpam-6729	907	21	.	.	PUNCT
ejpam-6729	908	1	investigation	investigation	NOUN
ejpam-6729	908	2	of	of	ADP
ejpam-6729	908	3	the	the	DET
ejpam-6729	908	4	main	main	ADJ
ejpam-6729	908	5	energies	energy	NOUN
ejpam-6729	908	6	of	of	ADP
ejpam-6729	908	7	picture	picture	NOUN
ejpam-6729	908	8	fuzzy	fuzzy	ADJ
ejpam-6729	908	9	graph	graph	NOUN
ejpam-6729	908	10	and	and	CCONJ
ejpam-6729	908	11	its	its	PRON
ejpam-6729	908	12	applications	application	NOUN
ejpam-6729	908	13	.	.	PUNCT
ejpam-6729	909	1	international	international	ADJ
ejpam-6729	909	2	journal	journal	NOUN
ejpam-6729	909	3	of	of	ADP
ejpam-6729	909	4	computational	computational	ADJ
ejpam-6729	909	5	intelligence	intelligence	NOUN
ejpam-6729	909	6	systems	system	NOUN
ejpam-6729	909	7	,	,	PUNCT
ejpam-6729	909	8	15(1):31	15(1):31	NUM
ejpam-6729	909	9	,	,	PUNCT
ejpam-6729	909	10	2022	2022	NUM
ejpam-6729	909	11	.	.	PUNCT
ejpam-6729	910	1	[	[	X
ejpam-6729	910	2	44	44	NUM
ejpam-6729	910	3	]	]	X
ejpam-6729	910	4	bui	bui	PROPN
ejpam-6729	910	5	cong	cong	NOUN
ejpam-6729	910	6	cuong	cuong	PROPN
ejpam-6729	910	7	and	and	CCONJ
ejpam-6729	910	8	vladik	vladik	PROPN
ejpam-6729	910	9	kreinovich	kreinovich	PROPN
ejpam-6729	910	10	.	.	PUNCT
ejpam-6729	911	1	picture	picture	NOUN
ejpam-6729	911	2	fuzzy	fuzzy	ADJ
ejpam-6729	911	3	sets	set	NOUN
ejpam-6729	911	4	-	-	PUNCT
ejpam-6729	911	5	a	a	DET
ejpam-6729	911	6	new	new	ADJ
ejpam-6729	911	7	concept	concept	NOUN
ejpam-6729	911	8	for	for	ADP
ejpam-6729	911	9	computational	computational	ADJ
ejpam-6729	911	10	intelligence	intelligence	NOUN
ejpam-6729	911	11	problems	problem	NOUN
ejpam-6729	911	12	.	.	PUNCT
ejpam-6729	912	1	in	in	ADP
ejpam-6729	912	2	2013	2013	NUM
ejpam-6729	912	3	third	third	ADJ
ejpam-6729	912	4	world	world	NOUN
ejpam-6729	912	5	congress	congress	PROPN
ejpam-6729	912	6	on	on	ADP
ejpam-6729	912	7	information	information	NOUN
ejpam-6729	912	8	and	and	CCONJ
ejpam-6729	912	9	communication	communication	NOUN
ejpam-6729	912	10	technologies	technology	NOUN
ejpam-6729	912	11	(	(	PUNCT
ejpam-6729	912	12	wict	wict	NOUN
ejpam-6729	912	13	2013	2013	NUM
ejpam-6729	912	14	)	)	PUNCT
ejpam-6729	912	15	,	,	PUNCT
ejpam-6729	912	16	pages	page	NOUN
ejpam-6729	912	17	1–6	1–6	NUM
ejpam-6729	912	18	.	.	PUNCT
ejpam-6729	912	19	ieee	ieee	PROPN
ejpam-6729	912	20	,	,	PUNCT
ejpam-6729	912	21	2013	2013	NUM
ejpam-6729	912	22	.	.	PUNCT
ejpam-6729	913	1	[	[	X
ejpam-6729	913	2	45	45	NUM
ejpam-6729	913	3	]	]	PUNCT
ejpam-6729	913	4	xuerong	xuerong	NOUN
ejpam-6729	913	5	zhao	zhao	PROPN
ejpam-6729	913	6	and	and	CCONJ
ejpam-6729	913	7	bao	bao	PROPN
ejpam-6729	913	8	qing	qing	PROPN
ejpam-6729	913	9	hu	hu	PROPN
ejpam-6729	913	10	.	.	PROPN
ejpam-6729	913	11	fuzzy	fuzzy	ADJ
ejpam-6729	913	12	and	and	CCONJ
ejpam-6729	913	13	interval	interval	NOUN
ejpam-6729	913	14	-	-	PUNCT
ejpam-6729	913	15	valued	value	VERB
ejpam-6729	913	16	fuzzy	fuzzy	ADJ
ejpam-6729	913	17	decision	decision	NOUN
ejpam-6729	913	18	-	-	PUNCT
ejpam-6729	913	19	theoretic	theoretic	NOUN
ejpam-6729	913	20	rough	rough	ADJ
ejpam-6729	913	21	set	set	NOUN
ejpam-6729	913	22	approaches	approach	NOUN
ejpam-6729	913	23	based	base	VERB
ejpam-6729	913	24	on	on	ADP
ejpam-6729	913	25	fuzzy	fuzzy	ADJ
ejpam-6729	913	26	probability	probability	NOUN
ejpam-6729	913	27	measure	measure	NOUN
ejpam-6729	913	28	.	.	PUNCT
ejpam-6729	914	1	inf	inf	PROPN
ejpam-6729	914	2	.	.	PUNCT
ejpam-6729	915	1	sci	sci	PROPN
ejpam-6729	915	2	.	.	PROPN
ejpam-6729	915	3	,	,	PUNCT
ejpam-6729	915	4	298:534–554	298:534–554	NUM
ejpam-6729	915	5	,	,	PUNCT
ejpam-6729	915	6	2015	2015	NUM
ejpam-6729	915	7	.	.	PUNCT
ejpam-6729	916	1	[	[	X
ejpam-6729	916	2	46	46	NUM
ejpam-6729	916	3	]	]	PUNCT
ejpam-6729	916	4	zdzisław	zdzisław	ADJ
ejpam-6729	916	5	pawlak	pawlak	ADJ
ejpam-6729	916	6	.	.	PUNCT
ejpam-6729	917	1	rough	rough	ADJ
ejpam-6729	917	2	sets	set	NOUN
ejpam-6729	917	3	:	:	PUNCT
ejpam-6729	917	4	theoretical	theoretical	ADJ
ejpam-6729	917	5	aspects	aspect	NOUN
ejpam-6729	917	6	of	of	ADP
ejpam-6729	917	7	reasoning	reasoning	NOUN
ejpam-6729	917	8	about	about	ADP
ejpam-6729	917	9	data	datum	NOUN
ejpam-6729	917	10	,	,	PUNCT
ejpam-6729	917	11	volume	volume	NOUN
ejpam-6729	917	12	9	9	NUM
ejpam-6729	917	13	.	.	PUNCT
ejpam-6729	917	14	springer	springer	NOUN
ejpam-6729	917	15	science	science	PROPN
ejpam-6729	917	16	&	&	CCONJ
ejpam-6729	917	17	business	business	NOUN
ejpam-6729	917	18	media	medium	NOUN
ejpam-6729	917	19	,	,	PUNCT
ejpam-6729	917	20	2012	2012	NUM
ejpam-6729	917	21	.	.	PUNCT
ejpam-6729	918	1	[	[	X
ejpam-6729	918	2	47	47	NUM
ejpam-6729	918	3	]	]	PUNCT
ejpam-6729	918	4	said	say	VERB
ejpam-6729	918	5	broumi	broumi	PROPN
ejpam-6729	918	6	,	,	PUNCT
ejpam-6729	918	7	mohamed	mohamed	PROPN
ejpam-6729	918	8	talea	talea	PROPN
ejpam-6729	918	9	,	,	PUNCT
ejpam-6729	918	10	assia	assia	PROPN
ejpam-6729	918	11	bakali	bakali	VERB
ejpam-6729	918	12	,	,	PUNCT
ejpam-6729	918	13	and	and	CCONJ
ejpam-6729	918	14	florentin	florentin	PROPN
ejpam-6729	918	15	smarandache	smarandache	NOUN
ejpam-6729	918	16	.	.	PUNCT
ejpam-6729	919	1	interval	interval	NOUN
ejpam-6729	919	2	valued	value	VERB
ejpam-6729	919	3	neutrosophic	neutrosophic	ADJ
ejpam-6729	919	4	graphs	graph	NOUN
ejpam-6729	919	5	.	.	PUNCT
ejpam-6729	920	1	critical	critical	ADJ
ejpam-6729	920	2	review	review	NOUN
ejpam-6729	920	3	,	,	PUNCT
ejpam-6729	920	4	xii	xii	PROPN
ejpam-6729	920	5	,	,	PUNCT
ejpam-6729	920	6	2016:5–33	2016:5–33	NUM
ejpam-6729	920	7	,	,	PUNCT
ejpam-6729	920	8	2016	2016	NUM
ejpam-6729	920	9	.	.	PUNCT
ejpam-6729	921	1	[	[	X
ejpam-6729	921	2	48	48	NUM
ejpam-6729	921	3	]	]	PUNCT
ejpam-6729	921	4	said	say	VERB
ejpam-6729	921	5	broumi	broumi	PROPN
ejpam-6729	921	6	,	,	PUNCT
ejpam-6729	921	7	mohamed	mohamed	PROPN
ejpam-6729	921	8	talea	talea	PROPN
ejpam-6729	921	9	,	,	PUNCT
ejpam-6729	921	10	assia	assia	PROPN
ejpam-6729	921	11	bakali	bakali	VERB
ejpam-6729	921	12	,	,	PUNCT
ejpam-6729	921	13	and	and	CCONJ
ejpam-6729	921	14	florentin	florentin	PROPN
ejpam-6729	921	15	smarandache	smarandache	NOUN
ejpam-6729	921	16	.	.	PUNCT
ejpam-6729	922	1	single	single	ADJ
ejpam-6729	922	2	valued	value	VERB
ejpam-6729	922	3	neutrosophic	neutrosophic	ADJ
ejpam-6729	922	4	graphs	graph	NOUN
ejpam-6729	922	5	.	.	PUNCT
ejpam-6729	923	1	journal	journal	NOUN
ejpam-6729	923	2	of	of	ADP
ejpam-6729	923	3	new	new	ADJ
ejpam-6729	923	4	theory	theory	NOUN
ejpam-6729	923	5	,	,	PUNCT
ejpam-6729	923	6	(	(	PUNCT
ejpam-6729	923	7	10):86–101	10):86–101	PROPN
ejpam-6729	923	8	,	,	PUNCT
ejpam-6729	923	9	2016	2016	NUM
ejpam-6729	923	10	.	.	PUNCT
ejpam-6729	924	1	[	[	X
ejpam-6729	924	2	49	49	NUM
ejpam-6729	924	3	]	]	X
ejpam-6729	924	4	vicenç	vicenç	NOUN
ejpam-6729	924	5	torra	torra	VERB
ejpam-6729	924	6	and	and	CCONJ
ejpam-6729	924	7	yasuo	yasuo	PROPN
ejpam-6729	924	8	narukawa	narukawa	NOUN
ejpam-6729	924	9	.	.	PUNCT
ejpam-6729	925	1	on	on	ADP
ejpam-6729	925	2	hesitant	hesitant	ADJ
ejpam-6729	925	3	fuzzy	fuzzy	ADJ
ejpam-6729	925	4	sets	set	NOUN
ejpam-6729	925	5	and	and	CCONJ
ejpam-6729	925	6	decision	decision	NOUN
ejpam-6729	925	7	.	.	PUNCT
ejpam-6729	926	1	in	in	ADP
ejpam-6729	926	2	2009	2009	NUM
ejpam-6729	926	3	ieee	ieee	NOUN
ejpam-6729	926	4	international	international	ADJ
ejpam-6729	926	5	conference	conference	NOUN
ejpam-6729	926	6	on	on	ADP
ejpam-6729	926	7	fuzzy	fuzzy	ADJ
ejpam-6729	926	8	systems	system	NOUN
ejpam-6729	926	9	,	,	PUNCT
ejpam-6729	926	10	pages	page	NOUN
ejpam-6729	926	11	1378–1382	1378–1382	NUM
ejpam-6729	926	12	.	.	PUNCT
ejpam-6729	927	1	ieee	ieee	PROPN
ejpam-6729	927	2	,	,	PUNCT
ejpam-6729	927	3	2009	2009	NUM
ejpam-6729	927	4	.	.	PUNCT
ejpam-6729	928	1	[	[	X
ejpam-6729	928	2	50	50	NUM
ejpam-6729	928	3	]	]	PUNCT
ejpam-6729	928	4	nivetha	nivetha	PROPN
ejpam-6729	928	5	martin	martin	PROPN
ejpam-6729	928	6	.	.	PUNCT
ejpam-6729	929	1	plithogenic	plithogenic	PROPN
ejpam-6729	929	2	swara	swara	NOUN
ejpam-6729	929	3	-	-	PUNCT
ejpam-6729	929	4	topsis	topsis	NOUN
ejpam-6729	929	5	decision	decision	NOUN
ejpam-6729	929	6	making	make	VERB
ejpam-6729	929	7	on	on	ADP
ejpam-6729	929	8	food	food	NOUN
ejpam-6729	929	9	processing	processing	NOUN
ejpam-6729	929	10	methods	method	NOUN
ejpam-6729	929	11	with	with	ADP
ejpam-6729	929	12	different	different	ADJ
ejpam-6729	929	13	normalization	normalization	NOUN
ejpam-6729	929	14	techniques	technique	NOUN
ejpam-6729	929	15	.	.	PUNCT
ejpam-6729	930	1	advances	advance	NOUN
ejpam-6729	930	2	in	in	ADP
ejpam-6729	930	3	decision	decision	NOUN
ejpam-6729	930	4	making	making	NOUN
ejpam-6729	930	5	,	,	PUNCT
ejpam-6729	930	6	69	69	NUM
ejpam-6729	930	7	,	,	PUNCT
ejpam-6729	930	8	2022	2022	NUM
ejpam-6729	930	9	.	.	PUNCT
ejpam-6729	931	1	[	[	X
ejpam-6729	931	2	51	51	NUM
ejpam-6729	931	3	]	]	X
ejpam-6729	931	4	p	p	X
ejpam-6729	931	5	sathya	sathya	PROPN
ejpam-6729	931	6	,	,	PUNCT
ejpam-6729	931	7	nivetha	nivetha	PROPN
ejpam-6729	931	8	martin	martin	PROPN
ejpam-6729	931	9	,	,	PUNCT
ejpam-6729	931	10	and	and	CCONJ
ejpam-6729	931	11	florentine	florentine	NOUN
ejpam-6729	931	12	smarandache	smarandache	NOUN
ejpam-6729	931	13	.	.	PUNCT
ejpam-6729	932	1	plithogenic	plithogenic	PROPN
ejpam-6729	932	2	forest	forest	NOUN
ejpam-6729	932	3	hypersoft	hypersoft	NOUN
ejpam-6729	932	4	sets	set	NOUN
ejpam-6729	932	5	in	in	ADP
ejpam-6729	932	6	plithogenic	plithogenic	ADJ
ejpam-6729	932	7	contradiction	contradiction	NOUN
ejpam-6729	932	8	based	base	VERB
ejpam-6729	932	9	multi	multi	ADJ
ejpam-6729	932	10	-	-	ADJ
ejpam-6729	932	11	criteria	criterion	NOUN
ejpam-6729	932	12	decision	decision	NOUN
ejpam-6729	932	13	making	making	NOUN
ejpam-6729	932	14	.	.	PUNCT
ejpam-6729	933	1	neutrosophic	neutrosophic	ADJ
ejpam-6729	933	2	sets	set	NOUN
ejpam-6729	933	3	and	and	CCONJ
ejpam-6729	933	4	systems	system	NOUN
ejpam-6729	933	5	,	,	PUNCT
ejpam-6729	933	6	73:668–693	73:668–693	NUM
ejpam-6729	933	7	,	,	PUNCT
ejpam-6729	933	8	2024	2024	NUM
ejpam-6729	933	9	.	.	PUNCT
ejpam-6729	934	1	[	[	X
ejpam-6729	934	2	52	52	NUM
ejpam-6729	934	3	]	]	PUNCT
ejpam-6729	934	4	muhammad	muhammad	PROPN
ejpam-6729	934	5	sajjad	sajjad	PROPN
ejpam-6729	934	6	,	,	PUNCT
ejpam-6729	934	7	tariq	tariq	PROPN
ejpam-6729	934	8	shah	shah	PROPN
ejpam-6729	934	9	,	,	PUNCT
ejpam-6729	934	10	maha	maha	PROPN
ejpam-6729	934	11	alammari	alammari	PROPN
ejpam-6729	934	12	,	,	PUNCT
ejpam-6729	934	13	and	and	CCONJ
ejpam-6729	934	14	huda	huda	PROPN
ejpam-6729	934	15	alsaud	alsaud	PROPN
ejpam-6729	934	16	.	.	PUNCT
ejpam-6729	935	1	construction	construction	NOUN
ejpam-6729	935	2	and	and	CCONJ
ejpam-6729	935	3	decoding	decoding	NOUN
ejpam-6729	935	4	of	of	ADP
ejpam-6729	935	5	bch	bch	NOUN
ejpam-6729	935	6	-	-	PUNCT
ejpam-6729	935	7	codes	code	NOUN
ejpam-6729	935	8	over	over	ADP
ejpam-6729	935	9	the	the	DET
ejpam-6729	935	10	gaussian	gaussian	ADJ
ejpam-6729	935	11	field	field	NOUN
ejpam-6729	935	12	.	.	PUNCT
ejpam-6729	936	1	ieee	ieee	NOUN
ejpam-6729	936	2	access	access	NOUN
ejpam-6729	936	3	,	,	PUNCT
ejpam-6729	936	4	11:71972–71980	11:71972–71980	NUM
ejpam-6729	936	5	,	,	PUNCT
ejpam-6729	936	6	2023	2023	NUM
ejpam-6729	936	7	.	.	PUNCT
ejpam-6729	937	1	[	[	X
ejpam-6729	937	2	53	53	NUM
ejpam-6729	937	3	]	]	PUNCT
ejpam-6729	937	4	muhammad	muhammad	PROPN
ejpam-6729	937	5	sajjad	sajjad	PROPN
ejpam-6729	937	6	,	,	PUNCT
ejpam-6729	937	7	tariq	tariq	PROPN
ejpam-6729	937	8	shah	shah	PROPN
ejpam-6729	937	9	,	,	PUNCT
ejpam-6729	937	10	qin	qin	PROPN
ejpam-6729	937	11	xin	xin	PROPN
ejpam-6729	937	12	,	,	PUNCT
ejpam-6729	937	13	and	and	CCONJ
ejpam-6729	937	14	bander	bander	PROPN
ejpam-6729	937	15	almutairi	almutairi	NOUN
ejpam-6729	937	16	.	.	PUNCT
ejpam-6729	938	1	eisenstein	eisenstein	PROPN
ejpam-6729	938	2	field	field	PROPN
ejpam-6729	938	3	bch	bch	PROPN
ejpam-6729	938	4	codes	code	VERB
ejpam-6729	938	5	construction	construction	NOUN
ejpam-6729	938	6	and	and	CCONJ
ejpam-6729	938	7	decoding	decoding	NOUN
ejpam-6729	938	8	.	.	PUNCT
ejpam-6729	939	1	aims	aim	VERB
ejpam-6729	939	2	math	math	NOUN
ejpam-6729	939	3	,	,	PUNCT
ejpam-6729	939	4	8(12):29453–29473	8(12):29453–29473	NUM
ejpam-6729	939	5	,	,	PUNCT
ejpam-6729	939	6	2023	2023	NUM
ejpam-6729	939	7	.	.	PUNCT