id	sid	tid	token	lemma	pos
ejpam-5016	1	1	european	european	PROPN
ejpam-5016	1	2	journal	journal	PROPN
ejpam-5016	1	3	of	of	ADP
ejpam-5016	1	4	pure	pure	ADJ
ejpam-5016	1	5	and	and	CCONJ
ejpam-5016	1	6	applied	apply	VERB
ejpam-5016	1	7	mathematics	mathematic	NOUN
ejpam-5016	1	8	vol	vol	NOUN
ejpam-5016	1	9	.	.	PROPN
ejpam-5016	2	1	17	17	NUM
ejpam-5016	2	2	,	,	PUNCT
ejpam-5016	2	3	no	no	INTJ
ejpam-5016	2	4	.	.	NOUN
ejpam-5016	2	5	4	4	NUM
ejpam-5016	2	6	,	,	PUNCT
ejpam-5016	2	7	2024	2024	NUM
ejpam-5016	2	8	,	,	PUNCT
ejpam-5016	2	9	2621	2621	NUM
ejpam-5016	2	10	-	-	SYM
ejpam-5016	2	11	2650	2650	NUM
ejpam-5016	2	12	issn	issn	PROPN
ejpam-5016	2	13	1307	1307	NUM
ejpam-5016	2	14	-	-	SYM
ejpam-5016	2	15	5543	5543	NUM
ejpam-5016	2	16	–	–	PUNCT
ejpam-5016	2	17	ejpam.com	ejpam.com	X
ejpam-5016	2	18	published	publish	VERB
ejpam-5016	2	19	by	by	ADP
ejpam-5016	2	20	new	new	PROPN
ejpam-5016	2	21	york	york	PROPN
ejpam-5016	2	22	business	business	NOUN
ejpam-5016	2	23	global	global	ADJ
ejpam-5016	2	24	binomials	binomial	NOUN
ejpam-5016	2	25	arising	arise	VERB
ejpam-5016	2	26	from	from	ADP
ejpam-5016	2	27	buchberger	buchberger	NOUN
ejpam-5016	2	28	algorithm	algorithm	NOUN
ejpam-5016	2	29	on	on	ADP
ejpam-5016	2	30	polyomino	polyomino	PROPN
ejpam-5016	2	31	ideals	ideal	NOUN
ejpam-5016	2	32	yoshua	yoshua	PROPN
ejpam-5016	2	33	yonatan	yonatan	PROPN
ejpam-5016	2	34	hamonangan1,∗	hamonangan1,∗	PROPN
ejpam-5016	2	35	,	,	PUNCT
ejpam-5016	2	36	intan	intan	PROPN
ejpam-5016	2	37	muchtadi	muchtadi	PROPN
ejpam-5016	2	38	-	-	PUNCT
ejpam-5016	2	39	alamsyah2	alamsyah2	NOUN
ejpam-5016	2	40	1	1	NUM
ejpam-5016	2	41	doctoral	doctoral	ADJ
ejpam-5016	2	42	program	program	NOUN
ejpam-5016	2	43	of	of	ADP
ejpam-5016	2	44	mathematics	mathematic	NOUN
ejpam-5016	2	45	,	,	PUNCT
ejpam-5016	2	46	faculty	faculty	NOUN
ejpam-5016	2	47	of	of	ADP
ejpam-5016	2	48	mathematics	mathematic	NOUN
ejpam-5016	2	49	and	and	CCONJ
ejpam-5016	2	50	natural	natural	ADJ
ejpam-5016	2	51	sciences	science	NOUN
ejpam-5016	2	52	,	,	PUNCT
ejpam-5016	2	53	bandung	bandung	PROPN
ejpam-5016	2	54	institute	institute	PROPN
ejpam-5016	2	55	of	of	ADP
ejpam-5016	2	56	technology	technology	PROPN
ejpam-5016	2	57	,	,	PUNCT
ejpam-5016	2	58	bandung	bandung	PROPN
ejpam-5016	2	59	,	,	PUNCT
ejpam-5016	2	60	west	west	PROPN
ejpam-5016	2	61	java	java	PROPN
ejpam-5016	2	62	,	,	PUNCT
ejpam-5016	2	63	indonesia	indonesia	PROPN
ejpam-5016	2	64	2	2	NUM
ejpam-5016	2	65	algebra	algebra	PROPN
ejpam-5016	2	66	research	research	NOUN
ejpam-5016	2	67	group	group	NOUN
ejpam-5016	2	68	,	,	PUNCT
ejpam-5016	2	69	faculty	faculty	NOUN
ejpam-5016	2	70	of	of	ADP
ejpam-5016	2	71	mathematics	mathematic	NOUN
ejpam-5016	2	72	and	and	CCONJ
ejpam-5016	2	73	natural	natural	ADJ
ejpam-5016	2	74	sciences	science	NOUN
ejpam-5016	2	75	,	,	PUNCT
ejpam-5016	2	76	bandung	bandung	PROPN
ejpam-5016	2	77	institute	institute	PROPN
ejpam-5016	2	78	of	of	ADP
ejpam-5016	2	79	technology	technology	PROPN
ejpam-5016	2	80	,	,	PUNCT
ejpam-5016	2	81	bandung	bandung	PROPN
ejpam-5016	2	82	,	,	PUNCT
ejpam-5016	2	83	west	west	PROPN
ejpam-5016	2	84	java	java	PROPN
ejpam-5016	2	85	,	,	PUNCT
ejpam-5016	2	86	indonesia	indonesia	PROPN
ejpam-5016	2	87	abstract	abstract	NOUN
ejpam-5016	2	88	.	.	PUNCT
ejpam-5016	3	1	a	a	DET
ejpam-5016	3	2	polyomino	polyomino	NOUN
ejpam-5016	3	3	is	be	AUX
ejpam-5016	3	4	a	a	DET
ejpam-5016	3	5	finite	finite	ADJ
ejpam-5016	3	6	set	set	NOUN
ejpam-5016	3	7	of	of	ADP
ejpam-5016	3	8	unit	unit	NOUN
ejpam-5016	3	9	squares	square	NOUN
ejpam-5016	3	10	joined	join	VERB
ejpam-5016	3	11	side	side	NOUN
ejpam-5016	3	12	by	by	ADP
ejpam-5016	3	13	side	side	NOUN
ejpam-5016	3	14	on	on	ADP
ejpam-5016	3	15	the	the	DET
ejpam-5016	3	16	cartesian	cartesian	ADJ
ejpam-5016	3	17	plane	plane	NOUN
ejpam-5016	3	18	.	.	PUNCT
ejpam-5016	4	1	qureshi	qureshi	PROPN
ejpam-5016	4	2	introduced	introduce	VERB
ejpam-5016	4	3	an	an	DET
ejpam-5016	4	4	ideal	ideal	NOUN
ejpam-5016	4	5	constructed	construct	VERB
ejpam-5016	4	6	from	from	ADP
ejpam-5016	4	7	a	a	DET
ejpam-5016	4	8	polyomino	polyomino	NOUN
ejpam-5016	4	9	which	which	PRON
ejpam-5016	4	10	is	be	AUX
ejpam-5016	4	11	called	call	VERB
ejpam-5016	4	12	”	"	PUNCT
ejpam-5016	4	13	polyomino	polyomino	NOUN
ejpam-5016	4	14	ideal	ideal	NOUN
ejpam-5016	4	15	”	"	PUNCT
ejpam-5016	4	16	.	.	PUNCT
ejpam-5016	5	1	in	in	ADP
ejpam-5016	5	2	this	this	DET
ejpam-5016	5	3	paper	paper	NOUN
ejpam-5016	5	4	,	,	PUNCT
ejpam-5016	5	5	we	we	PRON
ejpam-5016	5	6	study	study	VERB
ejpam-5016	5	7	the	the	DET
ejpam-5016	5	8	binomials	binomial	NOUN
ejpam-5016	5	9	arising	arise	VERB
ejpam-5016	5	10	from	from	ADP
ejpam-5016	5	11	buchberger	buchberger	NOUN
ejpam-5016	5	12	algorithm	algorithm	NOUN
ejpam-5016	5	13	on	on	ADP
ejpam-5016	5	14	polyomino	polyomino	NOUN
ejpam-5016	5	15	ideals	ideal	NOUN
ejpam-5016	5	16	.	.	PUNCT
ejpam-5016	6	1	we	we	PRON
ejpam-5016	6	2	also	also	ADV
ejpam-5016	6	3	introduce	introduce	VERB
ejpam-5016	6	4	socket	socket	NOUN
ejpam-5016	6	5	wrench	wrench	NOUN
ejpam-5016	6	6	polyominoes	polyominoe	NOUN
ejpam-5016	6	7	and	and	CCONJ
ejpam-5016	6	8	study	study	VERB
ejpam-5016	6	9	the	the	DET
ejpam-5016	6	10	gröbner	gröbner	NOUN
ejpam-5016	6	11	bases	basis	NOUN
ejpam-5016	6	12	of	of	ADP
ejpam-5016	6	13	the	the	DET
ejpam-5016	6	14	ideal	ideal	ADJ
ejpam-5016	6	15	ip	ip	NOUN
ejpam-5016	6	16	and	and	CCONJ
ejpam-5016	6	17	some	some	DET
ejpam-5016	6	18	algebraic	algebraic	ADJ
ejpam-5016	6	19	properties	property	NOUN
ejpam-5016	6	20	of	of	ADP
ejpam-5016	6	21	k[p	k[p	NOUN
ejpam-5016	6	22	]	]	PUNCT
ejpam-5016	6	23	.	.	PUNCT
ejpam-5016	7	1	2020	2020	NUM
ejpam-5016	7	2	mathematics	mathematic	NOUN
ejpam-5016	7	3	subject	subject	NOUN
ejpam-5016	7	4	classifications	classification	NOUN
ejpam-5016	7	5	:	:	PUNCT
ejpam-5016	7	6	05b50	05b50	ADJ
ejpam-5016	7	7	,	,	PUNCT
ejpam-5016	7	8	05e40	05e40	ADV
ejpam-5016	7	9	,	,	PUNCT
ejpam-5016	7	10	13c05	13c05	NUM
ejpam-5016	7	11	key	key	ADJ
ejpam-5016	7	12	words	word	NOUN
ejpam-5016	7	13	and	and	CCONJ
ejpam-5016	7	14	phrases	phrase	NOUN
ejpam-5016	7	15	:	:	PUNCT
ejpam-5016	7	16	buchberger	buchberger	NOUN
ejpam-5016	7	17	algorithm	algorithm	NOUN
ejpam-5016	7	18	,	,	PUNCT
ejpam-5016	7	19	gröbner	gröbner	NOUN
ejpam-5016	7	20	bases	basis	NOUN
ejpam-5016	7	21	,	,	PUNCT
ejpam-5016	7	22	polyomino	polyomino	NOUN
ejpam-5016	7	23	,	,	PUNCT
ejpam-5016	7	24	radical	radical	ADJ
ejpam-5016	7	25	ideal	ideal	NOUN
ejpam-5016	7	26	1	1	NUM
ejpam-5016	7	27	.	.	PUNCT
ejpam-5016	8	1	introduction	introduction	NOUN
ejpam-5016	8	2	a	a	DET
ejpam-5016	8	3	polyomino	polyomino	NOUN
ejpam-5016	8	4	is	be	AUX
ejpam-5016	8	5	a	a	DET
ejpam-5016	8	6	finite	finite	ADJ
ejpam-5016	8	7	set	set	NOUN
ejpam-5016	8	8	of	of	ADP
ejpam-5016	8	9	unit	unit	NOUN
ejpam-5016	8	10	squares	square	NOUN
ejpam-5016	8	11	joined	join	VERB
ejpam-5016	8	12	side	side	NOUN
ejpam-5016	8	13	by	by	ADP
ejpam-5016	8	14	side	side	NOUN
ejpam-5016	8	15	on	on	ADP
ejpam-5016	8	16	the	the	DET
ejpam-5016	8	17	cartesian	cartesian	ADJ
ejpam-5016	8	18	plane	plane	NOUN
ejpam-5016	8	19	.	.	PUNCT
ejpam-5016	9	1	they	they	PRON
ejpam-5016	9	2	are	be	AUX
ejpam-5016	9	3	discussed	discuss	VERB
ejpam-5016	9	4	in	in	ADP
ejpam-5016	9	5	a	a	DET
ejpam-5016	9	6	lot	lot	NOUN
ejpam-5016	9	7	of	of	ADP
ejpam-5016	9	8	papers	paper	NOUN
ejpam-5016	9	9	.	.	PUNCT
ejpam-5016	10	1	look	look	VERB
ejpam-5016	10	2	at	at	ADP
ejpam-5016	10	3	:	:	PUNCT
ejpam-5016	10	4	[	[	X
ejpam-5016	10	5	2	2	NUM
ejpam-5016	10	6	,	,	PUNCT
ejpam-5016	10	7	3	3	NUM
ejpam-5016	10	8	]	]	PUNCT
ejpam-5016	10	9	for	for	ADP
ejpam-5016	10	10	combinatorics	combinatoric	NOUN
ejpam-5016	10	11	;	;	PUNCT
ejpam-5016	10	12	[	[	X
ejpam-5016	10	13	17–19	17–19	NUM
ejpam-5016	10	14	]	]	PUNCT
ejpam-5016	10	15	for	for	ADP
ejpam-5016	10	16	its	its	PRON
ejpam-5016	10	17	relation	relation	NOUN
ejpam-5016	10	18	to	to	ADP
ejpam-5016	10	19	the	the	DET
ejpam-5016	10	20	tiling	tile	VERB
ejpam-5016	10	21	problem	problem	NOUN
ejpam-5016	10	22	on	on	ADP
ejpam-5016	10	23	the	the	DET
ejpam-5016	10	24	plane	plane	NOUN
ejpam-5016	10	25	;	;	PUNCT
ejpam-5016	10	26	[	[	X
ejpam-5016	10	27	12	12	NUM
ejpam-5016	10	28	]	]	PUNCT
ejpam-5016	10	29	for	for	ADP
ejpam-5016	10	30	the	the	DET
ejpam-5016	10	31	relation	relation	NOUN
ejpam-5016	10	32	between	between	ADP
ejpam-5016	10	33	polyominoes	polyominoe	NOUN
ejpam-5016	10	34	and	and	CCONJ
ejpam-5016	10	35	dyck	dyck	ADJ
ejpam-5016	10	36	words	word	NOUN
ejpam-5016	10	37	and	and	CCONJ
ejpam-5016	10	38	motzkin	motzkin	ADJ
ejpam-5016	10	39	word	word	NOUN
ejpam-5016	10	40	;	;	PUNCT
ejpam-5016	10	41	and	and	CCONJ
ejpam-5016	10	42	[	[	X
ejpam-5016	10	43	41	41	NUM
ejpam-5016	10	44	]	]	PUNCT
ejpam-5016	10	45	for	for	ADP
ejpam-5016	10	46	statistical	statistical	ADJ
ejpam-5016	10	47	physics	physic	NOUN
ejpam-5016	10	48	.	.	PUNCT
ejpam-5016	11	1	the	the	DET
ejpam-5016	11	2	relation	relation	NOUN
ejpam-5016	11	3	between	between	ADP
ejpam-5016	11	4	polyominoes	polyominoe	NOUN
ejpam-5016	11	5	and	and	CCONJ
ejpam-5016	11	6	commutative	commutative	ADJ
ejpam-5016	11	7	algebra	algebra	NOUN
ejpam-5016	11	8	was	be	AUX
ejpam-5016	11	9	introduced	introduce	VERB
ejpam-5016	11	10	by	by	ADP
ejpam-5016	11	11	qureshi	qureshi	PROPN
ejpam-5016	11	12	,	,	PUNCT
ejpam-5016	11	13	introducing	introduce	VERB
ejpam-5016	11	14	an	an	DET
ejpam-5016	11	15	ideal	ideal	NOUN
ejpam-5016	11	16	constructed	construct	VERB
ejpam-5016	11	17	from	from	ADP
ejpam-5016	11	18	a	a	DET
ejpam-5016	11	19	polyomino	polyomino	NOUN
ejpam-5016	11	20	which	which	PRON
ejpam-5016	11	21	is	be	AUX
ejpam-5016	11	22	called	call	VERB
ejpam-5016	11	23	polyomino	polyomino	PROPN
ejpam-5016	11	24	ideal	ideal	NOUN
ejpam-5016	12	1	[	[	X
ejpam-5016	12	2	34	34	NUM
ejpam-5016	12	3	]	]	PUNCT
ejpam-5016	12	4	.	.	PUNCT
ejpam-5016	13	1	the	the	DET
ejpam-5016	13	2	polyomino	polyomino	PROPN
ejpam-5016	13	3	ideal	ideal	NOUN
ejpam-5016	13	4	is	be	AUX
ejpam-5016	13	5	a	a	DET
ejpam-5016	13	6	generalization	generalization	NOUN
ejpam-5016	13	7	of	of	ADP
ejpam-5016	13	8	ideals	ideal	NOUN
ejpam-5016	13	9	generated	generate	VERB
ejpam-5016	13	10	by	by	ADP
ejpam-5016	13	11	the	the	DET
ejpam-5016	13	12	set	set	NOUN
ejpam-5016	13	13	of	of	ADP
ejpam-5016	13	14	2	2	NUM
ejpam-5016	13	15	-	-	PUNCT
ejpam-5016	13	16	minor	minor	NOUN
ejpam-5016	13	17	of	of	ADP
ejpam-5016	13	18	a	a	DET
ejpam-5016	13	19	matrix	matrix	NOUN
ejpam-5016	13	20	.	.	PUNCT
ejpam-5016	14	1	generally	generally	ADV
ejpam-5016	14	2	,	,	PUNCT
ejpam-5016	14	3	the	the	DET
ejpam-5016	14	4	ideal	ideal	NOUN
ejpam-5016	14	5	of	of	ADP
ejpam-5016	14	6	t	t	PROPN
ejpam-5016	14	7	-	-	PUNCT
ejpam-5016	14	8	minors	minor	NOUN
ejpam-5016	14	9	is	be	AUX
ejpam-5016	14	10	a	a	DET
ejpam-5016	14	11	central	central	ADJ
ejpam-5016	14	12	topic	topic	NOUN
ejpam-5016	14	13	in	in	ADP
ejpam-5016	14	14	commutative	commutative	ADJ
ejpam-5016	14	15	algebra	algebra	NOUN
ejpam-5016	14	16	and	and	CCONJ
ejpam-5016	14	17	has	have	VERB
ejpam-5016	14	18	some	some	DET
ejpam-5016	14	19	applications	application	NOUN
ejpam-5016	14	20	in	in	ADP
ejpam-5016	14	21	algebraic	algebraic	ADJ
ejpam-5016	14	22	statistics	statistic	NOUN
ejpam-5016	15	1	[	[	X
ejpam-5016	15	2	33	33	NUM
ejpam-5016	15	3	,	,	PUNCT
ejpam-5016	15	4	40	40	NUM
ejpam-5016	15	5	]	]	PUNCT
ejpam-5016	15	6	.	.	PUNCT
ejpam-5016	16	1	there	there	PRON
ejpam-5016	16	2	were	be	VERB
ejpam-5016	16	3	a	a	DET
ejpam-5016	16	4	lot	lot	NOUN
ejpam-5016	16	5	of	of	ADP
ejpam-5016	16	6	research	research	NOUN
ejpam-5016	16	7	related	relate	VERB
ejpam-5016	16	8	to	to	ADP
ejpam-5016	16	9	the	the	DET
ejpam-5016	16	10	ideal	ideal	NOUN
ejpam-5016	16	11	generated	generate	VERB
ejpam-5016	16	12	by	by	ADP
ejpam-5016	16	13	the	the	DET
ejpam-5016	16	14	set	set	NOUN
ejpam-5016	16	15	of	of	ADP
ejpam-5016	16	16	t−minor	t−minor	NOUN
ejpam-5016	16	17	of	of	ADP
ejpam-5016	16	18	a	a	DET
ejpam-5016	16	19	matrix	matrix	NOUN
ejpam-5016	16	20	[	[	X
ejpam-5016	16	21	22	22	NUM
ejpam-5016	16	22	,	,	PUNCT
ejpam-5016	16	23	27	27	NUM
ejpam-5016	16	24	]	]	PUNCT
ejpam-5016	16	25	.	.	PUNCT
ejpam-5016	17	1	since	since	SCONJ
ejpam-5016	17	2	it	it	PRON
ejpam-5016	17	3	was	be	AUX
ejpam-5016	17	4	introduced	introduce	VERB
ejpam-5016	17	5	by	by	ADP
ejpam-5016	17	6	qureshi	qureshi	PROPN
ejpam-5016	17	7	in	in	ADP
ejpam-5016	17	8	2012	2012	NUM
ejpam-5016	17	9	,	,	PUNCT
ejpam-5016	17	10	many	many	ADJ
ejpam-5016	17	11	interesting	interesting	ADJ
ejpam-5016	17	12	question	question	NOUN
ejpam-5016	17	13	have	have	AUX
ejpam-5016	17	14	arisen	arise	VERB
ejpam-5016	17	15	about	about	ADP
ejpam-5016	17	16	polyomino	polyomino	NOUN
ejpam-5016	17	17	ideal	ideal	NOUN
ejpam-5016	17	18	.	.	PUNCT
ejpam-5016	18	1	here	here	ADV
ejpam-5016	18	2	are	be	AUX
ejpam-5016	18	3	some	some	DET
ejpam-5016	18	4	recent	recent	ADJ
ejpam-5016	18	5	works	work	NOUN
ejpam-5016	18	6	and	and	CCONJ
ejpam-5016	18	7	related	related	ADJ
ejpam-5016	18	8	results	result	NOUN
ejpam-5016	18	9	:	:	PUNCT
ejpam-5016	18	10	∗corresponding	∗corresponde	VERB
ejpam-5016	18	11	author	author	NOUN
ejpam-5016	18	12	.	.	PUNCT
ejpam-5016	19	1	doi	doi	NOUN
ejpam-5016	19	2	:	:	PUNCT
ejpam-5016	19	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5016	https://doi.org/10.29020/nybg.ejpam.v17i4.5016	PROPN
ejpam-5016	19	4	email	email	NOUN
ejpam-5016	19	5	addresses	address	VERB
ejpam-5016	19	6	:	:	PUNCT
ejpam-5016	19	7	yoshua.yonatan.h@gmail.com	yoshua.yonatan.h@gmail.com	X
ejpam-5016	19	8	(	(	PUNCT
ejpam-5016	19	9	y.	y.	PROPN
ejpam-5016	19	10	y.	y.	PROPN
ejpam-5016	19	11	hamonangan	hamonangan	PROPN
ejpam-5016	19	12	)	)	PUNCT
ejpam-5016	19	13	,	,	PUNCT
ejpam-5016	19	14	ntan@itb.ac.id	ntan@itb.ac.id	NOUN
ejpam-5016	19	15	(	(	PUNCT
ejpam-5016	19	16	i.	i.	PROPN
ejpam-5016	19	17	muchtadi	muchtadi	NOUN
ejpam-5016	19	18	-	-	PUNCT
ejpam-5016	19	19	alamsyah	alamsyah	NOUN
ejpam-5016	19	20	)	)	PUNCT
ejpam-5016	19	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5016	19	22	2621	2621	NUM
ejpam-5016	20	1	copyright	copyright	NOUN
ejpam-5016	20	2	:	:	PUNCT
ejpam-5016	20	3	©	©	PROPN
ejpam-5016	20	4	2024	2024	NUM
ejpam-5016	20	5	the	the	DET
ejpam-5016	20	6	author(s	author(s	NOUN
ejpam-5016	20	7	)	)	PUNCT
ejpam-5016	20	8	.	.	PUNCT
ejpam-5016	21	1	(	(	PUNCT
ejpam-5016	21	2	cc	cc	NOUN
ejpam-5016	21	3	by	by	ADP
ejpam-5016	21	4	-	-	PUNCT
ejpam-5016	21	5	nc	nc	PROPN
ejpam-5016	21	6	4.0	4.0	NUM
ejpam-5016	21	7	)	)	PUNCT
ejpam-5016	21	8	y.	y.	PROPN
ejpam-5016	21	9	y.	y.	PROPN
ejpam-5016	21	10	hamonangan	hamonangan	PROPN
ejpam-5016	21	11	,	,	PUNCT
ejpam-5016	21	12	i.	i.	PROPN
ejpam-5016	21	13	muchtadi	muchtadi	PROPN
ejpam-5016	21	14	-	-	PUNCT
ejpam-5016	21	15	alamsyah	alamsyah	NOUN
ejpam-5016	21	16	/	/	SYM
ejpam-5016	21	17	eur	eur	PROPN
ejpam-5016	21	18	.	.	PUNCT
ejpam-5016	22	1	j.	j.	PROPN
ejpam-5016	22	2	pure	pure	PROPN
ejpam-5016	22	3	appl	appl	PROPN
ejpam-5016	22	4	.	.	PROPN
ejpam-5016	22	5	math	math	PROPN
ejpam-5016	22	6	,	,	PUNCT
ejpam-5016	22	7	17	17	NUM
ejpam-5016	22	8	(	(	PUNCT
ejpam-5016	22	9	4	4	NUM
ejpam-5016	22	10	)	)	PUNCT
ejpam-5016	22	11	(	(	PUNCT
ejpam-5016	22	12	2024	2024	NUM
ejpam-5016	22	13	)	)	PUNCT
ejpam-5016	22	14	,	,	PUNCT
ejpam-5016	22	15	2621	2621	NUM
ejpam-5016	22	16	-	-	SYM
ejpam-5016	22	17	2650	2650	NUM
ejpam-5016	22	18	2622	2622	NUM
ejpam-5016	22	19	•	•	ADP
ejpam-5016	22	20	the	the	DET
ejpam-5016	22	21	primality	primality	NOUN
ejpam-5016	22	22	of	of	ADP
ejpam-5016	22	23	the	the	DET
ejpam-5016	22	24	polyomino	polyomino	NOUN
ejpam-5016	22	25	ideal	ideal	NOUN
ejpam-5016	22	26	is	be	AUX
ejpam-5016	22	27	studied	study	VERB
ejpam-5016	22	28	in	in	ADP
ejpam-5016	22	29	many	many	ADJ
ejpam-5016	22	30	articles	article	NOUN
ejpam-5016	22	31	[	[	X
ejpam-5016	22	32	5	5	NUM
ejpam-5016	22	33	,	,	PUNCT
ejpam-5016	22	34	7	7	NUM
ejpam-5016	22	35	,	,	PUNCT
ejpam-5016	22	36	24–26	24–26	NUM
ejpam-5016	22	37	,	,	PUNCT
ejpam-5016	22	38	31	31	NUM
ejpam-5016	22	39	,	,	PUNCT
ejpam-5016	22	40	32	32	NUM
ejpam-5016	22	41	,	,	PUNCT
ejpam-5016	22	42	35	35	NUM
ejpam-5016	22	43	,	,	PUNCT
ejpam-5016	22	44	36	36	NUM
ejpam-5016	22	45	,	,	PUNCT
ejpam-5016	22	46	38	38	NUM
ejpam-5016	22	47	]	]	PUNCT
ejpam-5016	22	48	.	.	PUNCT
ejpam-5016	23	1	in	in	ADP
ejpam-5016	23	2	[	[	X
ejpam-5016	23	3	24	24	NUM
ejpam-5016	23	4	,	,	PUNCT
ejpam-5016	23	5	25	25	NUM
ejpam-5016	23	6	,	,	PUNCT
ejpam-5016	23	7	36	36	NUM
ejpam-5016	23	8	]	]	PUNCT
ejpam-5016	23	9	,	,	PUNCT
ejpam-5016	23	10	it	it	PRON
ejpam-5016	23	11	is	be	AUX
ejpam-5016	23	12	proved	prove	VERB
ejpam-5016	23	13	that	that	SCONJ
ejpam-5016	23	14	k[p	k[p	NOUN
ejpam-5016	23	15	]	]	X
ejpam-5016	23	16	is	be	AUX
ejpam-5016	23	17	a	a	DET
ejpam-5016	23	18	domain	domain	NOUN
ejpam-5016	23	19	if	if	SCONJ
ejpam-5016	23	20	p	p	NOUN
ejpam-5016	23	21	is	be	AUX
ejpam-5016	23	22	simple	simple	ADJ
ejpam-5016	23	23	.	.	PUNCT
ejpam-5016	24	1	in	in	ADP
ejpam-5016	24	2	[	[	X
ejpam-5016	24	3	31	31	NUM
ejpam-5016	24	4	]	]	PUNCT
ejpam-5016	24	5	,	,	PUNCT
ejpam-5016	24	6	it	it	PRON
ejpam-5016	24	7	is	be	AUX
ejpam-5016	24	8	proved	prove	VERB
ejpam-5016	24	9	that	that	SCONJ
ejpam-5016	24	10	if	if	SCONJ
ejpam-5016	24	11	k[p	k[p	NOUN
ejpam-5016	24	12	]	]	X
ejpam-5016	24	13	is	be	AUX
ejpam-5016	24	14	a	a	DET
ejpam-5016	24	15	domain	domain	NOUN
ejpam-5016	24	16	then	then	ADV
ejpam-5016	24	17	the	the	DET
ejpam-5016	24	18	polyomino	polyomino	NOUN
ejpam-5016	24	19	have	have	VERB
ejpam-5016	24	20	no	no	DET
ejpam-5016	24	21	zig	zig	VERB
ejpam-5016	24	22	-	-	PUNCT
ejpam-5016	24	23	zag	zag	NOUN
ejpam-5016	24	24	walks	walk	NOUN
ejpam-5016	24	25	.	.	PUNCT
ejpam-5016	25	1	they	they	PRON
ejpam-5016	25	2	also	also	ADV
ejpam-5016	25	3	conjectured	conjecture	VERB
ejpam-5016	25	4	that	that	SCONJ
ejpam-5016	25	5	the	the	DET
ejpam-5016	25	6	converse	converse	NOUN
ejpam-5016	25	7	direction	direction	NOUN
ejpam-5016	25	8	is	be	AUX
ejpam-5016	25	9	true	true	ADJ
ejpam-5016	25	10	.	.	PUNCT
ejpam-5016	26	1	later	later	ADV
ejpam-5016	26	2	,	,	PUNCT
ejpam-5016	26	3	it	it	PRON
ejpam-5016	26	4	was	be	AUX
ejpam-5016	26	5	proved	prove	VERB
ejpam-5016	26	6	in	in	ADP
ejpam-5016	26	7	[	[	X
ejpam-5016	26	8	5	5	NUM
ejpam-5016	26	9	]	]	PUNCT
ejpam-5016	26	10	and	and	CCONJ
ejpam-5016	26	11	[	[	X
ejpam-5016	26	12	7	7	X
ejpam-5016	26	13	]	]	PUNCT
ejpam-5016	26	14	that	that	SCONJ
ejpam-5016	26	15	the	the	DET
ejpam-5016	26	16	conjecture	conjecture	NOUN
ejpam-5016	26	17	holds	hold	VERB
ejpam-5016	26	18	for	for	ADP
ejpam-5016	26	19	two	two	NUM
ejpam-5016	26	20	special	special	ADJ
ejpam-5016	26	21	classes	class	NOUN
ejpam-5016	26	22	of	of	ADP
ejpam-5016	26	23	non	non	ADJ
ejpam-5016	26	24	-	-	ADJ
ejpam-5016	26	25	simple	simple	ADJ
ejpam-5016	26	26	polyominoes	polyominoe	NOUN
ejpam-5016	26	27	,	,	PUNCT
ejpam-5016	26	28	called	call	VERB
ejpam-5016	26	29	closed	closed	ADJ
ejpam-5016	26	30	path	path	NOUN
ejpam-5016	26	31	and	and	CCONJ
ejpam-5016	26	32	weakly	weakly	ADJ
ejpam-5016	26	33	closed	closed	ADJ
ejpam-5016	26	34	paths	path	NOUN
ejpam-5016	26	35	.	.	PUNCT
ejpam-5016	27	1	still	still	ADV
ejpam-5016	27	2	,	,	PUNCT
ejpam-5016	27	3	a	a	DET
ejpam-5016	27	4	complete	complete	ADJ
ejpam-5016	27	5	classification	classification	NOUN
ejpam-5016	27	6	of	of	ADP
ejpam-5016	27	7	polyominoes	polyominoe	NOUN
ejpam-5016	27	8	with	with	ADP
ejpam-5016	27	9	prime	prime	ADJ
ejpam-5016	27	10	polyomino	polyomino	PROPN
ejpam-5016	27	11	ideal	ideal	NOUN
ejpam-5016	27	12	is	be	AUX
ejpam-5016	27	13	not	not	PART
ejpam-5016	27	14	known	know	VERB
ejpam-5016	27	15	.	.	PUNCT
ejpam-5016	28	1	•	•	NUM
ejpam-5016	28	2	the	the	DET
ejpam-5016	28	3	algebraic	algebraic	ADJ
ejpam-5016	28	4	properties	property	NOUN
ejpam-5016	28	5	,	,	PUNCT
ejpam-5016	28	6	like	like	ADP
ejpam-5016	28	7	when	when	SCONJ
ejpam-5016	28	8	k[p	k[p	NOUN
ejpam-5016	28	9	]	]	X
ejpam-5016	28	10	is	be	AUX
ejpam-5016	28	11	cohen	cohen	NOUN
ejpam-5016	28	12	-	-	PUNCT
ejpam-5016	28	13	macaulay	macaulay	NOUN
ejpam-5016	28	14	or	or	CCONJ
ejpam-5016	28	15	gorenstein	gorenstein	NOUN
ejpam-5016	28	16	,	,	PUNCT
ejpam-5016	28	17	are	be	AUX
ejpam-5016	28	18	known	know	VERB
ejpam-5016	28	19	only	only	ADV
ejpam-5016	28	20	for	for	ADP
ejpam-5016	28	21	some	some	DET
ejpam-5016	28	22	specific	specific	ADJ
ejpam-5016	28	23	polyominoes	polyominoe	NOUN
ejpam-5016	28	24	.	.	PUNCT
ejpam-5016	29	1	in	in	ADP
ejpam-5016	29	2	[	[	X
ejpam-5016	29	3	36	36	NUM
ejpam-5016	29	4	]	]	PUNCT
ejpam-5016	29	5	the	the	DET
ejpam-5016	29	6	authors	author	NOUN
ejpam-5016	29	7	show	show	VERB
ejpam-5016	29	8	that	that	SCONJ
ejpam-5016	29	9	if	if	SCONJ
ejpam-5016	29	10	p	p	NOUN
ejpam-5016	29	11	is	be	AUX
ejpam-5016	29	12	simple	simple	ADJ
ejpam-5016	29	13	then	then	ADV
ejpam-5016	29	14	k[p	k[p	NOUN
ejpam-5016	29	15	]	]	PUNCT
ejpam-5016	29	16	is	be	AUX
ejpam-5016	29	17	a	a	DET
ejpam-5016	29	18	normal	normal	ADJ
ejpam-5016	29	19	cohen	cohen	NOUN
ejpam-5016	29	20	-	-	PUNCT
ejpam-5016	29	21	macaulay	macaulay	PROPN
ejpam-5016	29	22	domain	domain	NOUN
ejpam-5016	29	23	,	,	PUNCT
ejpam-5016	29	24	by	by	ADP
ejpam-5016	29	25	identifying	identify	VERB
ejpam-5016	29	26	their	their	PRON
ejpam-5016	29	27	quotient	quotient	NOUN
ejpam-5016	29	28	ring	ring	NOUN
ejpam-5016	29	29	with	with	ADP
ejpam-5016	29	30	the	the	DET
ejpam-5016	29	31	toric	toric	ADJ
ejpam-5016	29	32	ring	ring	NOUN
ejpam-5016	29	33	of	of	ADP
ejpam-5016	29	34	a	a	DET
ejpam-5016	29	35	weakly	weakly	ADJ
ejpam-5016	29	36	chordal	chordal	NOUN
ejpam-5016	29	37	graph	graph	NOUN
ejpam-5016	29	38	.	.	PUNCT
ejpam-5016	30	1	in	in	ADP
ejpam-5016	30	2	[	[	X
ejpam-5016	30	3	6	6	NUM
ejpam-5016	30	4	]	]	PUNCT
ejpam-5016	30	5	,	,	PUNCT
ejpam-5016	30	6	the	the	DET
ejpam-5016	30	7	authors	author	NOUN
ejpam-5016	30	8	show	show	VERB
ejpam-5016	30	9	that	that	SCONJ
ejpam-5016	30	10	if	if	SCONJ
ejpam-5016	30	11	p	p	NOUN
ejpam-5016	30	12	is	be	AUX
ejpam-5016	30	13	a	a	DET
ejpam-5016	30	14	closed	closed	ADJ
ejpam-5016	30	15	path	path	NOUN
ejpam-5016	30	16	polyomino	polyomino	NOUN
ejpam-5016	30	17	having	have	VERB
ejpam-5016	30	18	no	no	DET
ejpam-5016	30	19	zig	zig	VERB
ejpam-5016	30	20	-	-	PUNCT
ejpam-5016	30	21	zag	zag	NOUN
ejpam-5016	30	22	walks	walk	NOUN
ejpam-5016	30	23	then	then	ADV
ejpam-5016	30	24	k[p	k[p	NOUN
ejpam-5016	30	25	]	]	PUNCT
ejpam-5016	30	26	is	be	AUX
ejpam-5016	30	27	a	a	DET
ejpam-5016	30	28	cohen	cohen	NOUN
ejpam-5016	30	29	-	-	PUNCT
ejpam-5016	30	30	macaulay	macaulay	NOUN
ejpam-5016	30	31	domain	domain	NOUN
ejpam-5016	30	32	.	.	PUNCT
ejpam-5016	31	1	in	in	ADP
ejpam-5016	31	2	[	[	X
ejpam-5016	31	3	34	34	NUM
ejpam-5016	31	4	]	]	PUNCT
ejpam-5016	31	5	,	,	PUNCT
ejpam-5016	31	6	qureshi	qureshi	PROPN
ejpam-5016	31	7	established	establish	VERB
ejpam-5016	31	8	that	that	SCONJ
ejpam-5016	31	9	the	the	DET
ejpam-5016	31	10	cohen	cohen	PROPN
ejpam-5016	31	11	-	-	PUNCT
ejpam-5016	31	12	macaulay	macaulay	PROPN
ejpam-5016	31	13	property	property	NOUN
ejpam-5016	31	14	holds	hold	NOUN
ejpam-5016	31	15	for	for	ADP
ejpam-5016	31	16	convex	convex	ADJ
ejpam-5016	31	17	polyominoes	polyominoe	NOUN
ejpam-5016	31	18	and	and	CCONJ
ejpam-5016	31	19	characterized	characterize	VERB
ejpam-5016	31	20	all	all	DET
ejpam-5016	31	21	stack	stack	NOUN
ejpam-5016	31	22	polyominoes	polyominoe	NOUN
ejpam-5016	31	23	p	p	NOUN
ejpam-5016	31	24	for	for	SCONJ
ejpam-5016	31	25	which	which	DET
ejpam-5016	31	26	k[p	k[p	NOUN
ejpam-5016	31	27	]	]	X
ejpam-5016	31	28	is	be	AUX
ejpam-5016	31	29	gorenstein	gorenstein	ADJ
ejpam-5016	31	30	.	.	PUNCT
ejpam-5016	32	1	the	the	DET
ejpam-5016	32	2	gorensteiness	gorensteiness	NOUN
ejpam-5016	32	3	is	be	AUX
ejpam-5016	32	4	also	also	ADV
ejpam-5016	32	5	studied	study	VERB
ejpam-5016	32	6	in	in	ADP
ejpam-5016	32	7	[	[	X
ejpam-5016	32	8	1	1	NUM
ejpam-5016	32	9	,	,	PUNCT
ejpam-5016	32	10	8	8	NUM
ejpam-5016	32	11	,	,	PUNCT
ejpam-5016	32	12	10	10	NUM
ejpam-5016	32	13	,	,	PUNCT
ejpam-5016	32	14	16	16	NUM
ejpam-5016	32	15	,	,	PUNCT
ejpam-5016	32	16	35	35	NUM
ejpam-5016	32	17	,	,	PUNCT
ejpam-5016	32	18	37	37	NUM
ejpam-5016	32	19	]	]	PUNCT
ejpam-5016	32	20	.	.	PUNCT
ejpam-5016	33	1	•	•	NUM
ejpam-5016	33	2	gröbner	gröbner	NOUN
ejpam-5016	33	3	basis	basis	NOUN
ejpam-5016	33	4	of	of	ADP
ejpam-5016	33	5	polyomino	polyomino	NOUN
ejpam-5016	33	6	ideals	ideal	NOUN
ejpam-5016	33	7	are	be	AUX
ejpam-5016	33	8	studied	study	VERB
ejpam-5016	33	9	in	in	ADP
ejpam-5016	33	10	[	[	X
ejpam-5016	33	11	6	6	NUM
ejpam-5016	33	12	,	,	PUNCT
ejpam-5016	33	13	20	20	NUM
ejpam-5016	33	14	,	,	PUNCT
ejpam-5016	33	15	25	25	NUM
ejpam-5016	33	16	,	,	PUNCT
ejpam-5016	33	17	26	26	NUM
ejpam-5016	33	18	,	,	PUNCT
ejpam-5016	33	19	32	32	NUM
ejpam-5016	33	20	,	,	PUNCT
ejpam-5016	33	21	34	34	NUM
ejpam-5016	33	22	]	]	PUNCT
ejpam-5016	33	23	.	.	PUNCT
ejpam-5016	34	1	•	•	NUM
ejpam-5016	34	2	the	the	DET
ejpam-5016	34	3	könig	könig	PROPN
ejpam-5016	34	4	type	type	NOUN
ejpam-5016	34	5	property	property	NOUN
ejpam-5016	34	6	is	be	AUX
ejpam-5016	34	7	studied	study	VERB
ejpam-5016	34	8	for	for	ADP
ejpam-5016	34	9	simple	simple	ADJ
ejpam-5016	34	10	thin	thin	ADJ
ejpam-5016	34	11	polyominoes	polyominoe	NOUN
ejpam-5016	34	12	in	in	ADP
ejpam-5016	34	13	[	[	X
ejpam-5016	34	14	21	21	NUM
ejpam-5016	34	15	]	]	PUNCT
ejpam-5016	34	16	,	,	PUNCT
ejpam-5016	34	17	for	for	ADP
ejpam-5016	34	18	closed	closed	ADJ
ejpam-5016	34	19	path	path	NOUN
ejpam-5016	34	20	polyominoes	polyominoe	NOUN
ejpam-5016	34	21	in	in	ADP
ejpam-5016	34	22	[	[	X
ejpam-5016	34	23	13	13	NUM
ejpam-5016	34	24	]	]	PUNCT
ejpam-5016	34	25	,	,	PUNCT
ejpam-5016	34	26	and	and	CCONJ
ejpam-5016	34	27	for	for	ADP
ejpam-5016	34	28	grid	grid	NOUN
ejpam-5016	34	29	polyominoes	polyominoe	NOUN
ejpam-5016	34	30	in	in	ADP
ejpam-5016	34	31	[	[	X
ejpam-5016	34	32	14	14	NUM
ejpam-5016	34	33	]	]	PUNCT
ejpam-5016	34	34	.	.	PUNCT
ejpam-5016	35	1	•	•	NUM
ejpam-5016	35	2	the	the	DET
ejpam-5016	35	3	linearly	linearly	ADV
ejpam-5016	35	4	related	relate	VERB
ejpam-5016	35	5	polyominoes	polyominoe	NOUN
ejpam-5016	35	6	are	be	AUX
ejpam-5016	35	7	studied	study	VERB
ejpam-5016	35	8	in	in	ADP
ejpam-5016	35	9	[	[	X
ejpam-5016	35	10	15	15	NUM
ejpam-5016	35	11	]	]	PUNCT
ejpam-5016	35	12	.	.	PUNCT
ejpam-5016	36	1	•	•	NUM
ejpam-5016	36	2	the	the	DET
ejpam-5016	36	3	charney	charney	PROPN
ejpam-5016	36	4	-	-	PUNCT
ejpam-5016	36	5	davis	davis	PROPN
ejpam-5016	36	6	conjecture	conjecture	VERB
ejpam-5016	36	7	for	for	ADP
ejpam-5016	36	8	simple	simple	ADJ
ejpam-5016	36	9	thin	thin	ADJ
ejpam-5016	36	10	-	-	PUNCT
ejpam-5016	36	11	polyominoes	polyominoe	NOUN
ejpam-5016	36	12	are	be	AUX
ejpam-5016	36	13	studied	study	VERB
ejpam-5016	36	14	in	in	ADP
ejpam-5016	36	15	[	[	X
ejpam-5016	36	16	29	29	NUM
ejpam-5016	36	17	]	]	PUNCT
ejpam-5016	36	18	.	.	PUNCT
ejpam-5016	37	1	•	•	NUM
ejpam-5016	37	2	the	the	DET
ejpam-5016	37	3	primary	primary	ADJ
ejpam-5016	37	4	decomposition	decomposition	NOUN
ejpam-5016	37	5	of	of	ADP
ejpam-5016	37	6	polyomino	polyomino	NOUN
ejpam-5016	37	7	ideals	ideal	NOUN
ejpam-5016	37	8	,	,	PUNCT
ejpam-5016	37	9	like	like	ADP
ejpam-5016	37	10	closed	closed	ADJ
ejpam-5016	37	11	paths	path	NOUN
ejpam-5016	37	12	,	,	PUNCT
ejpam-5016	37	13	and	and	CCONJ
ejpam-5016	37	14	more	more	ADV
ejpam-5016	37	15	in	in	ADP
ejpam-5016	37	16	general	general	ADJ
ejpam-5016	37	17	for	for	ADP
ejpam-5016	37	18	polyocollections	polyocollection	NOUN
ejpam-5016	37	19	is	be	AUX
ejpam-5016	37	20	studied	study	VERB
ejpam-5016	37	21	in	in	ADP
ejpam-5016	37	22	[	[	PUNCT
ejpam-5016	37	23	9	9	NUM
ejpam-5016	37	24	]	]	PUNCT
ejpam-5016	37	25	.	.	PUNCT
ejpam-5016	38	1	•	•	NOUN
ejpam-5016	38	2	another	another	DET
ejpam-5016	38	3	challenging	challenging	ADJ
ejpam-5016	38	4	problem	problem	NOUN
ejpam-5016	38	5	is	be	AUX
ejpam-5016	38	6	to	to	PART
ejpam-5016	38	7	compute	compute	VERB
ejpam-5016	38	8	the	the	DET
ejpam-5016	38	9	h	h	NOUN
ejpam-5016	38	10	-	-	PUNCT
ejpam-5016	38	11	polynomial	polynomial	ADJ
ejpam-5016	38	12	of	of	ADP
ejpam-5016	38	13	k[p	k[p	NOUN
ejpam-5016	38	14	]	]	PUNCT
ejpam-5016	38	15	in	in	ADP
ejpam-5016	38	16	terms	term	NOUN
ejpam-5016	38	17	of	of	ADP
ejpam-5016	38	18	the	the	DET
ejpam-5016	38	19	rook	rook	NOUN
ejpam-5016	38	20	polynomial	polynomial	NOUN
ejpam-5016	38	21	of	of	ADP
ejpam-5016	38	22	p	p	NOUN
ejpam-5016	38	23	[	[	X
ejpam-5016	38	24	8	8	NUM
ejpam-5016	38	25	,	,	PUNCT
ejpam-5016	38	26	16	16	NUM
ejpam-5016	38	27	,	,	PUNCT
ejpam-5016	38	28	28	28	NUM
ejpam-5016	38	29	,	,	PUNCT
ejpam-5016	38	30	30	30	NUM
ejpam-5016	38	31	,	,	PUNCT
ejpam-5016	38	32	35	35	NUM
ejpam-5016	38	33	,	,	PUNCT
ejpam-5016	38	34	37	37	NUM
ejpam-5016	38	35	]	]	PUNCT
ejpam-5016	38	36	.	.	PUNCT
ejpam-5016	39	1	an	an	DET
ejpam-5016	39	2	important	important	ADJ
ejpam-5016	39	3	class	class	NOUN
ejpam-5016	39	4	of	of	ADP
ejpam-5016	39	5	ideals	ideal	NOUN
ejpam-5016	39	6	other	other	ADJ
ejpam-5016	39	7	than	than	ADP
ejpam-5016	39	8	the	the	DET
ejpam-5016	39	9	prime	prime	ADJ
ejpam-5016	39	10	ideal	ideal	NOUN
ejpam-5016	39	11	is	be	AUX
ejpam-5016	39	12	the	the	DET
ejpam-5016	39	13	radical	radical	ADJ
ejpam-5016	39	14	ideal	ideal	NOUN
ejpam-5016	39	15	.	.	PUNCT
ejpam-5016	40	1	radical	radical	ADJ
ejpam-5016	40	2	ideal	ideal	NOUN
ejpam-5016	40	3	plays	play	VERB
ejpam-5016	40	4	an	an	DET
ejpam-5016	40	5	important	important	ADJ
ejpam-5016	40	6	role	role	NOUN
ejpam-5016	40	7	in	in	ADP
ejpam-5016	40	8	algebraic	algebraic	ADJ
ejpam-5016	40	9	geometry	geometry	NOUN
ejpam-5016	40	10	,	,	PUNCT
ejpam-5016	40	11	for	for	ADP
ejpam-5016	40	12	example	example	NOUN
ejpam-5016	40	13	the	the	DET
ejpam-5016	40	14	strong	strong	ADJ
ejpam-5016	40	15	nullstellensatz	nullstellensatz	NOUN
ejpam-5016	40	16	theorem	theorem	VERB
ejpam-5016	40	17	[	[	PUNCT
ejpam-5016	40	18	11	11	NUM
ejpam-5016	40	19	]	]	PUNCT
ejpam-5016	40	20	.	.	PUNCT
ejpam-5016	41	1	qureshi	qureshi	PROPN
ejpam-5016	41	2	gave	give	VERB
ejpam-5016	41	3	an	an	DET
ejpam-5016	41	4	example	example	NOUN
ejpam-5016	41	5	of	of	ADP
ejpam-5016	41	6	a	a	DET
ejpam-5016	41	7	non	non	ADJ
ejpam-5016	41	8	-	-	ADJ
ejpam-5016	41	9	simple	simple	ADJ
ejpam-5016	41	10	polyomino	polyomino	NOUN
ejpam-5016	41	11	with	with	ADP
ejpam-5016	41	12	non	non	ADJ
ejpam-5016	41	13	-	-	ADJ
ejpam-5016	41	14	prime	prime	ADJ
ejpam-5016	41	15	polyomino	polyomino	NOUN
ejpam-5016	41	16	ideal	ideal	NOUN
ejpam-5016	41	17	[	[	X
ejpam-5016	41	18	36	36	NUM
ejpam-5016	41	19	]	]	PUNCT
ejpam-5016	41	20	that	that	PRON
ejpam-5016	41	21	is	be	AUX
ejpam-5016	41	22	radical	radical	ADJ
ejpam-5016	41	23	.	.	PUNCT
ejpam-5016	42	1	the	the	DET
ejpam-5016	42	2	radicality	radicality	NOUN
ejpam-5016	42	3	of	of	ADP
ejpam-5016	42	4	an	an	DET
ejpam-5016	42	5	ideal	ideal	NOUN
ejpam-5016	42	6	can	can	AUX
ejpam-5016	42	7	be	be	AUX
ejpam-5016	42	8	studied	study	VERB
ejpam-5016	42	9	from	from	ADP
ejpam-5016	42	10	the	the	DET
ejpam-5016	42	11	gröbner	gröbner	NOUN
ejpam-5016	42	12	bases	basis	NOUN
ejpam-5016	42	13	of	of	ADP
ejpam-5016	42	14	the	the	DET
ejpam-5016	42	15	ideal	ideal	NOUN
ejpam-5016	42	16	.	.	PUNCT
ejpam-5016	43	1	if	if	SCONJ
ejpam-5016	43	2	we	we	PRON
ejpam-5016	43	3	can	can	AUX
ejpam-5016	43	4	define	define	VERB
ejpam-5016	43	5	a	a	DET
ejpam-5016	43	6	monomial	monomial	ADJ
ejpam-5016	43	7	order	order	NOUN
ejpam-5016	43	8	such	such	ADJ
ejpam-5016	43	9	that	that	SCONJ
ejpam-5016	43	10	every	every	DET
ejpam-5016	43	11	element	element	NOUN
ejpam-5016	43	12	in	in	ADP
ejpam-5016	43	13	the	the	DET
ejpam-5016	43	14	gröbner	gröbner	NOUN
ejpam-5016	43	15	bases	basis	NOUN
ejpam-5016	43	16	has	have	VERB
ejpam-5016	43	17	square	square	ADJ
ejpam-5016	43	18	-	-	PUNCT
ejpam-5016	43	19	free	free	ADJ
ejpam-5016	43	20	initial	initial	ADJ
ejpam-5016	43	21	monomial	monomial	NOUN
ejpam-5016	43	22	then	then	ADV
ejpam-5016	43	23	the	the	DET
ejpam-5016	43	24	ideal	ideal	NOUN
ejpam-5016	43	25	is	be	AUX
ejpam-5016	43	26	radical	radical	ADJ
ejpam-5016	43	27	[	[	X
ejpam-5016	43	28	23	23	NUM
ejpam-5016	43	29	,	,	PUNCT
ejpam-5016	43	30	problem	problem	NOUN
ejpam-5016	43	31	1.8(b	1.8(b	NUM
ejpam-5016	43	32	)	)	PUNCT
ejpam-5016	43	33	]	]	PUNCT
ejpam-5016	43	34	.	.	PUNCT
ejpam-5016	44	1	the	the	DET
ejpam-5016	44	2	gröbner	gröbner	NOUN
ejpam-5016	44	3	bases	basis	NOUN
ejpam-5016	44	4	of	of	ADP
ejpam-5016	44	5	an	an	DET
ejpam-5016	44	6	ideal	ideal	NOUN
ejpam-5016	44	7	can	can	AUX
ejpam-5016	44	8	be	be	AUX
ejpam-5016	44	9	computed	compute	VERB
ejpam-5016	44	10	by	by	ADP
ejpam-5016	44	11	using	use	VERB
ejpam-5016	44	12	buchberger	buchberger	NOUN
ejpam-5016	44	13	algorithm	algorithm	NOUN
ejpam-5016	45	1	[	[	X
ejpam-5016	45	2	23	23	NUM
ejpam-5016	45	3	,	,	PUNCT
ejpam-5016	45	4	section	section	NOUN
ejpam-5016	45	5	1.3	1.3	NUM
ejpam-5016	45	6	]	]	PUNCT
ejpam-5016	45	7	.	.	PUNCT
ejpam-5016	46	1	in	in	ADP
ejpam-5016	46	2	this	this	DET
ejpam-5016	46	3	paper	paper	NOUN
ejpam-5016	46	4	,	,	PUNCT
ejpam-5016	46	5	we	we	PRON
ejpam-5016	46	6	study	study	VERB
ejpam-5016	46	7	some	some	DET
ejpam-5016	46	8	elements	element	NOUN
ejpam-5016	46	9	arising	arise	VERB
ejpam-5016	46	10	from	from	ADP
ejpam-5016	46	11	buchberger	buchberger	NOUN
ejpam-5016	46	12	algorithm	algorithm	NOUN
ejpam-5016	46	13	to	to	ADP
ejpam-5016	46	14	polyomino	polyomino	NOUN
ejpam-5016	46	15	ideals	ideal	NOUN
ejpam-5016	46	16	.	.	PUNCT
ejpam-5016	47	1	in	in	ADP
ejpam-5016	47	2	the	the	DET
ejpam-5016	47	3	second	second	ADJ
ejpam-5016	47	4	section	section	NOUN
ejpam-5016	47	5	,	,	PUNCT
ejpam-5016	47	6	polyominoes	polyominoe	NOUN
ejpam-5016	47	7	and	and	CCONJ
ejpam-5016	47	8	some	some	DET
ejpam-5016	47	9	terminologies	terminology	NOUN
ejpam-5016	47	10	related	relate	VERB
ejpam-5016	47	11	to	to	ADP
ejpam-5016	47	12	our	our	PRON
ejpam-5016	47	13	study	study	NOUN
ejpam-5016	47	14	will	will	AUX
ejpam-5016	47	15	be	be	AUX
ejpam-5016	47	16	defined	define	VERB
ejpam-5016	47	17	.	.	PUNCT
ejpam-5016	48	1	in	in	ADP
ejpam-5016	48	2	the	the	DET
ejpam-5016	48	3	third	third	ADJ
ejpam-5016	48	4	section	section	NOUN
ejpam-5016	48	5	,	,	PUNCT
ejpam-5016	48	6	we	we	PRON
ejpam-5016	48	7	will	will	AUX
ejpam-5016	48	8	perform	perform	VERB
ejpam-5016	48	9	the	the	DET
ejpam-5016	48	10	buchberger	buchberger	NOUN
ejpam-5016	48	11	algorithm	algorithm	NOUN
ejpam-5016	48	12	in	in	ADP
ejpam-5016	48	13	polyomino	polyomino	NOUN
ejpam-5016	48	14	ideals	ideal	NOUN
ejpam-5016	48	15	.	.	PUNCT
ejpam-5016	49	1	in	in	ADP
ejpam-5016	49	2	the	the	DET
ejpam-5016	49	3	fourth	fourth	ADJ
ejpam-5016	49	4	sections	section	NOUN
ejpam-5016	49	5	,	,	PUNCT
ejpam-5016	49	6	we	we	PRON
ejpam-5016	49	7	will	will	AUX
ejpam-5016	49	8	apply	apply	VERB
ejpam-5016	49	9	the	the	DET
ejpam-5016	49	10	results	result	NOUN
ejpam-5016	49	11	from	from	ADP
ejpam-5016	49	12	previous	previous	ADJ
ejpam-5016	49	13	sections	section	NOUN
ejpam-5016	49	14	to	to	ADP
ejpam-5016	49	15	a	a	DET
ejpam-5016	49	16	class	class	NOUN
ejpam-5016	49	17	of	of	ADP
ejpam-5016	49	18	polyominoes	polyominoe	NOUN
ejpam-5016	49	19	that	that	PRON
ejpam-5016	49	20	we	we	PRON
ejpam-5016	49	21	call	call	VERB
ejpam-5016	49	22	socket	socket	NOUN
ejpam-5016	49	23	wrench	wrench	NOUN
ejpam-5016	49	24	polyominoes	polyominoe	NOUN
ejpam-5016	49	25	.	.	PUNCT
ejpam-5016	50	1	we	we	PRON
ejpam-5016	50	2	prove	prove	VERB
ejpam-5016	50	3	that	that	SCONJ
ejpam-5016	50	4	for	for	ADP
ejpam-5016	50	5	the	the	DET
ejpam-5016	50	6	socket	socket	NOUN
ejpam-5016	50	7	wrench	wrench	NOUN
ejpam-5016	50	8	polyomino	polyomino	PROPN
ejpam-5016	50	9	p	p	NOUN
ejpam-5016	50	10	,	,	PUNCT
ejpam-5016	50	11	the	the	DET
ejpam-5016	50	12	ideal	ideal	ADJ
ejpam-5016	50	13	ip	ip	NOUN
ejpam-5016	50	14	has	have	VERB
ejpam-5016	50	15	square	square	ADJ
ejpam-5016	50	16	-	-	PUNCT
ejpam-5016	50	17	free	free	ADJ
ejpam-5016	50	18	quadratic	quadratic	ADJ
ejpam-5016	50	19	gröbner	gröbner	NOUN
ejpam-5016	50	20	bases	basis	NOUN
ejpam-5016	50	21	for	for	ADP
ejpam-5016	50	22	a	a	DET
ejpam-5016	50	23	suitable	suitable	ADJ
ejpam-5016	50	24	monomial	monomial	ADJ
ejpam-5016	50	25	order	order	NOUN
ejpam-5016	50	26	.	.	PUNCT
ejpam-5016	51	1	we	we	PRON
ejpam-5016	51	2	also	also	ADV
ejpam-5016	51	3	study	study	VERB
ejpam-5016	51	4	some	some	DET
ejpam-5016	51	5	algebraic	algebraic	ADJ
ejpam-5016	51	6	properties	property	NOUN
ejpam-5016	51	7	of	of	ADP
ejpam-5016	51	8	the	the	DET
ejpam-5016	51	9	k	k	NOUN
ejpam-5016	51	10	-	-	PROPN
ejpam-5016	51	11	algebra	algebra	PROPN
ejpam-5016	51	12	k[p	k[p	NOUN
ejpam-5016	51	13	]	]	X
ejpam-5016	51	14	=	=	SYM
ejpam-5016	51	15	s	s	AUX
ejpam-5016	51	16	/	/	SYM
ejpam-5016	51	17	ip	ip	NOUN
ejpam-5016	51	18	.	.	PUNCT
ejpam-5016	52	1	y.	y.	PROPN
ejpam-5016	52	2	y.	y.	PROPN
ejpam-5016	52	3	hamonangan	hamonangan	PROPN
ejpam-5016	52	4	,	,	PUNCT
ejpam-5016	52	5	i.	i.	PROPN
ejpam-5016	52	6	muchtadi	muchtadi	PROPN
ejpam-5016	52	7	-	-	PUNCT
ejpam-5016	52	8	alamsyah	alamsyah	NOUN
ejpam-5016	52	9	/	/	SYM
ejpam-5016	52	10	eur	eur	PROPN
ejpam-5016	52	11	.	.	PUNCT
ejpam-5016	53	1	j.	j.	PROPN
ejpam-5016	53	2	pure	pure	PROPN
ejpam-5016	53	3	appl	appl	PROPN
ejpam-5016	53	4	.	.	PROPN
ejpam-5016	53	5	math	math	PROPN
ejpam-5016	53	6	,	,	PUNCT
ejpam-5016	53	7	17	17	NUM
ejpam-5016	53	8	(	(	PUNCT
ejpam-5016	53	9	4	4	NUM
ejpam-5016	53	10	)	)	PUNCT
ejpam-5016	53	11	(	(	PUNCT
ejpam-5016	53	12	2024	2024	NUM
ejpam-5016	53	13	)	)	PUNCT
ejpam-5016	53	14	,	,	PUNCT
ejpam-5016	53	15	2621	2621	NUM
ejpam-5016	53	16	-	-	SYM
ejpam-5016	53	17	2650	2650	NUM
ejpam-5016	53	18	2623	2623	NUM
ejpam-5016	53	19	2	2	NUM
ejpam-5016	53	20	.	.	PUNCT
ejpam-5016	53	21	preliminaries	preliminary	NOUN
ejpam-5016	53	22	in	in	ADP
ejpam-5016	53	23	this	this	DET
ejpam-5016	53	24	section	section	NOUN
ejpam-5016	53	25	,	,	PUNCT
ejpam-5016	53	26	we	we	PRON
ejpam-5016	53	27	will	will	AUX
ejpam-5016	53	28	recall	recall	VERB
ejpam-5016	53	29	the	the	DET
ejpam-5016	53	30	definitions	definition	NOUN
ejpam-5016	53	31	and	and	CCONJ
ejpam-5016	53	32	terminologies	terminology	NOUN
ejpam-5016	53	33	about	about	ADP
ejpam-5016	53	34	polyomino	polyomino	NOUN
ejpam-5016	53	35	and	and	CCONJ
ejpam-5016	53	36	polyomino	polyomino	NOUN
ejpam-5016	53	37	ideal	ideal	NOUN
ejpam-5016	53	38	from	from	ADP
ejpam-5016	53	39	[	[	X
ejpam-5016	53	40	5	5	NUM
ejpam-5016	53	41	]	]	PUNCT
ejpam-5016	53	42	and	and	CCONJ
ejpam-5016	53	43	[	[	X
ejpam-5016	53	44	34	34	NUM
ejpam-5016	53	45	]	]	PUNCT
ejpam-5016	53	46	.	.	PUNCT
ejpam-5016	54	1	consider	consider	VERB
ejpam-5016	54	2	the	the	DET
ejpam-5016	54	3	set	set	ADJ
ejpam-5016	54	4	z2	z2	NOUN
ejpam-5016	54	5	and	and	CCONJ
ejpam-5016	54	6	define	define	VERB
ejpam-5016	54	7	the	the	DET
ejpam-5016	54	8	partial	partial	ADJ
ejpam-5016	54	9	order	order	NOUN
ejpam-5016	54	10	:	:	PUNCT
ejpam-5016	54	11	(	(	PUNCT
ejpam-5016	54	12	i	i	PRON
ejpam-5016	54	13	,	,	PUNCT
ejpam-5016	54	14	j	j	PROPN
ejpam-5016	54	15	)	)	PUNCT
ejpam-5016	54	16	≤	≤	NOUN
ejpam-5016	54	17	(	(	PUNCT
ejpam-5016	54	18	k	k	NOUN
ejpam-5016	54	19	,	,	PUNCT
ejpam-5016	54	20	ℓ	ℓ	INTJ
ejpam-5016	54	21	)	)	PUNCT
ejpam-5016	55	1	if	if	SCONJ
ejpam-5016	55	2	and	and	CCONJ
ejpam-5016	55	3	only	only	ADV
ejpam-5016	55	4	if	if	SCONJ
ejpam-5016	55	5	i	i	PRON
ejpam-5016	55	6	≤	≤	VERB
ejpam-5016	55	7	k	k	PROPN
ejpam-5016	55	8	and	and	CCONJ
ejpam-5016	55	9	j	j	PROPN
ejpam-5016	55	10	≤	≤	PROPN
ejpam-5016	55	11	ℓ.	ℓ.	NOUN
ejpam-5016	55	12	(	(	PUNCT
ejpam-5016	55	13	i	i	NOUN
ejpam-5016	55	14	)	)	PUNCT
ejpam-5016	55	15	let	let	VERB
ejpam-5016	55	16	a	a	DET
ejpam-5016	55	17	,	,	PUNCT
ejpam-5016	55	18	b	b	PROPN
ejpam-5016	55	19	∈	∈	PROPN
ejpam-5016	55	20	z2	z2	PROPN
ejpam-5016	55	21	with	with	ADP
ejpam-5016	55	22	a	a	DET
ejpam-5016	55	23	≤	≤	NUM
ejpam-5016	55	24	b.	b.	NOUN
ejpam-5016	56	1	the	the	DET
ejpam-5016	56	2	set	set	NOUN
ejpam-5016	56	3	[	[	X
ejpam-5016	56	4	a	a	X
ejpam-5016	56	5	,	,	PUNCT
ejpam-5016	56	6	b	b	NOUN
ejpam-5016	56	7	]	]	X
ejpam-5016	56	8	=	=	X
ejpam-5016	56	9	{	{	PUNCT
ejpam-5016	56	10	c	c	PROPN
ejpam-5016	56	11	∈	∈	PROPN
ejpam-5016	56	12	z2	z2	PROPN
ejpam-5016	56	13	|	|	ADV
ejpam-5016	56	14	a	a	DET
ejpam-5016	56	15	≤	≤	NUM
ejpam-5016	56	16	c	c	NOUN
ejpam-5016	56	17	≤	≤	NOUN
ejpam-5016	56	18	b	b	X
ejpam-5016	56	19	}	}	PUNCT
ejpam-5016	56	20	is	be	AUX
ejpam-5016	56	21	called	call	VERB
ejpam-5016	56	22	an	an	DET
ejpam-5016	56	23	interval	interval	NOUN
ejpam-5016	56	24	.	.	PUNCT
ejpam-5016	57	1	(	(	PUNCT
ejpam-5016	57	2	ii	ii	NOUN
ejpam-5016	57	3	)	)	PUNCT
ejpam-5016	57	4	let	let	VERB
ejpam-5016	57	5	a	a	PRON
ejpam-5016	57	6	=	=	PUNCT
ejpam-5016	57	7	(	(	PUNCT
ejpam-5016	57	8	i	i	PROPN
ejpam-5016	57	9	,	,	PUNCT
ejpam-5016	57	10	j	j	PROPN
ejpam-5016	57	11	)	)	PUNCT
ejpam-5016	57	12	and	and	CCONJ
ejpam-5016	57	13	b	b	X
ejpam-5016	57	14	=	=	SYM
ejpam-5016	57	15	(	(	PUNCT
ejpam-5016	57	16	k	k	X
ejpam-5016	57	17	,	,	PUNCT
ejpam-5016	57	18	ℓ	ℓ	NOUN
ejpam-5016	57	19	)	)	PUNCT
ejpam-5016	57	20	.	.	PUNCT
ejpam-5016	58	1	the	the	DET
ejpam-5016	58	2	elements	element	NOUN
ejpam-5016	58	3	a	a	PRON
ejpam-5016	58	4	and	and	CCONJ
ejpam-5016	58	5	b	b	NOUN
ejpam-5016	58	6	are	be	AUX
ejpam-5016	58	7	called	call	VERB
ejpam-5016	58	8	the	the	DET
ejpam-5016	58	9	diagonal	diagonal	ADJ
ejpam-5016	58	10	corners	corner	NOUN
ejpam-5016	58	11	of	of	ADP
ejpam-5016	58	12	the	the	DET
ejpam-5016	58	13	interval	interval	NOUN
ejpam-5016	58	14	[	[	X
ejpam-5016	58	15	a	a	X
ejpam-5016	58	16	,	,	PUNCT
ejpam-5016	58	17	b	b	NOUN
ejpam-5016	58	18	]	]	X
ejpam-5016	58	19	,	,	PUNCT
ejpam-5016	58	20	and	and	CCONJ
ejpam-5016	58	21	the	the	DET
ejpam-5016	58	22	elements	element	NOUN
ejpam-5016	58	23	(	(	PUNCT
ejpam-5016	58	24	i	i	PROPN
ejpam-5016	58	25	,	,	PUNCT
ejpam-5016	58	26	ℓ	ℓ	PROPN
ejpam-5016	58	27	)	)	PUNCT
ejpam-5016	58	28	and	and	CCONJ
ejpam-5016	58	29	(	(	PUNCT
ejpam-5016	58	30	k	k	X
ejpam-5016	58	31	,	,	PUNCT
ejpam-5016	58	32	j	j	NOUN
ejpam-5016	58	33	)	)	PUNCT
ejpam-5016	58	34	are	be	AUX
ejpam-5016	58	35	called	call	VERB
ejpam-5016	58	36	the	the	DET
ejpam-5016	58	37	antidiagonal	antidiagonal	ADJ
ejpam-5016	58	38	corners	corner	NOUN
ejpam-5016	58	39	of	of	ADP
ejpam-5016	58	40	the	the	DET
ejpam-5016	58	41	interval	interval	NOUN
ejpam-5016	58	42	[	[	X
ejpam-5016	58	43	a	a	X
ejpam-5016	58	44	,	,	PUNCT
ejpam-5016	58	45	b	b	NOUN
ejpam-5016	58	46	]	]	X
ejpam-5016	58	47	.	.	PUNCT
ejpam-5016	59	1	particularly	particularly	ADV
ejpam-5016	59	2	,	,	PUNCT
ejpam-5016	59	3	the	the	DET
ejpam-5016	59	4	elements	element	NOUN
ejpam-5016	59	5	(	(	PUNCT
ejpam-5016	59	6	i	i	PROPN
ejpam-5016	59	7	,	,	PUNCT
ejpam-5016	59	8	j	j	PROPN
ejpam-5016	59	9	)	)	PUNCT
ejpam-5016	59	10	and	and	CCONJ
ejpam-5016	59	11	(	(	PUNCT
ejpam-5016	59	12	k	k	X
ejpam-5016	59	13	,	,	PUNCT
ejpam-5016	59	14	ℓ	ℓ	NUM
ejpam-5016	59	15	)	)	PUNCT
ejpam-5016	59	16	are	be	AUX
ejpam-5016	59	17	called	call	VERB
ejpam-5016	59	18	left	leave	VERB
ejpam-5016	59	19	lower	low	ADJ
ejpam-5016	59	20	corner	corner	NOUN
ejpam-5016	59	21	and	and	CCONJ
ejpam-5016	59	22	the	the	DET
ejpam-5016	59	23	right	right	ADJ
ejpam-5016	59	24	upper	upper	ADJ
ejpam-5016	59	25	corner	corner	NOUN
ejpam-5016	59	26	,	,	PUNCT
ejpam-5016	59	27	respectively	respectively	ADV
ejpam-5016	59	28	,	,	PUNCT
ejpam-5016	59	29	of	of	ADP
ejpam-5016	59	30	the	the	DET
ejpam-5016	59	31	interval	interval	NOUN
ejpam-5016	59	32	[	[	X
ejpam-5016	59	33	a	a	X
ejpam-5016	59	34	,	,	PUNCT
ejpam-5016	59	35	b	b	NOUN
ejpam-5016	59	36	]	]	X
ejpam-5016	59	37	.	.	PUNCT
ejpam-5016	60	1	similarly	similarly	ADV
ejpam-5016	60	2	,	,	PUNCT
ejpam-5016	60	3	the	the	DET
ejpam-5016	60	4	elements	element	NOUN
ejpam-5016	60	5	(	(	PUNCT
ejpam-5016	60	6	i	i	PROPN
ejpam-5016	60	7	,	,	PUNCT
ejpam-5016	60	8	ℓ	ℓ	PROPN
ejpam-5016	60	9	)	)	PUNCT
ejpam-5016	60	10	and	and	CCONJ
ejpam-5016	60	11	(	(	PUNCT
ejpam-5016	60	12	k	k	X
ejpam-5016	60	13	,	,	PUNCT
ejpam-5016	60	14	j	j	NOUN
ejpam-5016	60	15	)	)	PUNCT
ejpam-5016	60	16	are	be	AUX
ejpam-5016	60	17	called	call	VERB
ejpam-5016	60	18	the	the	DET
ejpam-5016	60	19	left	left	ADJ
ejpam-5016	60	20	upper	upper	ADJ
ejpam-5016	60	21	corner	corner	NOUN
ejpam-5016	60	22	and	and	CCONJ
ejpam-5016	60	23	the	the	DET
ejpam-5016	60	24	right	right	ADV
ejpam-5016	60	25	lower	low	ADJ
ejpam-5016	60	26	corner	corner	NOUN
ejpam-5016	60	27	,	,	PUNCT
ejpam-5016	60	28	respectively	respectively	ADV
ejpam-5016	60	29	,	,	PUNCT
ejpam-5016	60	30	of	of	ADP
ejpam-5016	60	31	the	the	DET
ejpam-5016	60	32	interval	interval	NOUN
ejpam-5016	60	33	[	[	X
ejpam-5016	60	34	a	a	X
ejpam-5016	60	35	,	,	PUNCT
ejpam-5016	60	36	b	b	NOUN
ejpam-5016	60	37	]	]	X
ejpam-5016	60	38	.	.	PUNCT
ejpam-5016	61	1	(	(	PUNCT
ejpam-5016	61	2	iii	iii	X
ejpam-5016	61	3	)	)	PUNCT
ejpam-5016	61	4	if	if	SCONJ
ejpam-5016	61	5	b	b	NOUN
ejpam-5016	61	6	=	=	PRON
ejpam-5016	61	7	a+	a+	PUNCT
ejpam-5016	61	8	(	(	PUNCT
ejpam-5016	61	9	1	1	NUM
ejpam-5016	61	10	,	,	PUNCT
ejpam-5016	61	11	1	1	NUM
ejpam-5016	61	12	)	)	PUNCT
ejpam-5016	61	13	then	then	ADV
ejpam-5016	61	14	the	the	DET
ejpam-5016	61	15	interval	interval	NOUN
ejpam-5016	61	16	[	[	X
ejpam-5016	61	17	a	a	X
ejpam-5016	61	18	,	,	PUNCT
ejpam-5016	61	19	b	b	NOUN
ejpam-5016	61	20	]	]	PUNCT
ejpam-5016	61	21	is	be	AUX
ejpam-5016	61	22	called	call	VERB
ejpam-5016	61	23	a	a	DET
ejpam-5016	61	24	cell	cell	NOUN
ejpam-5016	61	25	.	.	PUNCT
ejpam-5016	62	1	(	(	PUNCT
ejpam-5016	62	2	iv	iv	X
ejpam-5016	62	3	)	)	PUNCT
ejpam-5016	62	4	the	the	DET
ejpam-5016	62	5	edges	edge	NOUN
ejpam-5016	62	6	of	of	ADP
ejpam-5016	62	7	a	a	DET
ejpam-5016	62	8	cell	cell	NOUN
ejpam-5016	63	1	[	[	X
ejpam-5016	63	2	a	a	X
ejpam-5016	63	3	,	,	PUNCT
ejpam-5016	63	4	a	a	DET
ejpam-5016	63	5	+	+	X
ejpam-5016	63	6	(	(	PUNCT
ejpam-5016	63	7	1	1	NUM
ejpam-5016	63	8	,	,	PUNCT
ejpam-5016	63	9	1	1	NUM
ejpam-5016	63	10	)	)	PUNCT
ejpam-5016	63	11	]	]	PUNCT
ejpam-5016	63	12	are	be	AUX
ejpam-5016	63	13	the	the	DET
ejpam-5016	63	14	intervals	interval	NOUN
ejpam-5016	63	15	:	:	PUNCT
ejpam-5016	64	1	[	[	X
ejpam-5016	64	2	a	a	X
ejpam-5016	64	3	,	,	PUNCT
ejpam-5016	64	4	a	a	DET
ejpam-5016	64	5	+	+	X
ejpam-5016	64	6	(	(	PUNCT
ejpam-5016	64	7	1	1	NUM
ejpam-5016	64	8	,	,	PUNCT
ejpam-5016	64	9	0	0	NUM
ejpam-5016	64	10	)	)	PUNCT
ejpam-5016	64	11	]	]	PUNCT
ejpam-5016	64	12	,	,	PUNCT
ejpam-5016	64	13	[	[	X
ejpam-5016	64	14	a	a	X
ejpam-5016	64	15	,	,	PUNCT
ejpam-5016	64	16	a	a	DET
ejpam-5016	64	17	+	+	X
ejpam-5016	64	18	(	(	PUNCT
ejpam-5016	64	19	0	0	NUM
ejpam-5016	64	20	,	,	PUNCT
ejpam-5016	64	21	1	1	NUM
ejpam-5016	64	22	)	)	PUNCT
ejpam-5016	64	23	]	]	PUNCT
ejpam-5016	64	24	,	,	PUNCT
ejpam-5016	64	25	[	[	X
ejpam-5016	64	26	a+	a+	X
ejpam-5016	64	27	(	(	PUNCT
ejpam-5016	64	28	0	0	NUM
ejpam-5016	64	29	,	,	PUNCT
ejpam-5016	64	30	1	1	NUM
ejpam-5016	64	31	)	)	PUNCT
ejpam-5016	64	32	,	,	PUNCT
ejpam-5016	64	33	a+	a+	PUNCT
ejpam-5016	64	34	(	(	PUNCT
ejpam-5016	64	35	1	1	NUM
ejpam-5016	64	36	,	,	PUNCT
ejpam-5016	64	37	1	1	NUM
ejpam-5016	64	38	)	)	PUNCT
ejpam-5016	64	39	]	]	PUNCT
ejpam-5016	64	40	,	,	PUNCT
ejpam-5016	64	41	and	and	CCONJ
ejpam-5016	64	42	[	[	X
ejpam-5016	64	43	a+	a+	PUNCT
ejpam-5016	64	44	(	(	PUNCT
ejpam-5016	64	45	1	1	NUM
ejpam-5016	64	46	,	,	PUNCT
ejpam-5016	64	47	0	0	NUM
ejpam-5016	64	48	)	)	PUNCT
ejpam-5016	64	49	,	,	PUNCT
ejpam-5016	64	50	a+	a+	PUNCT
ejpam-5016	64	51	(	(	PUNCT
ejpam-5016	64	52	1	1	NUM
ejpam-5016	64	53	,	,	PUNCT
ejpam-5016	64	54	1	1	NUM
ejpam-5016	64	55	)	)	PUNCT
ejpam-5016	64	56	]	]	PUNCT
ejpam-5016	64	57	.	.	PUNCT
ejpam-5016	65	1	(	(	PUNCT
ejpam-5016	65	2	v	v	NOUN
ejpam-5016	65	3	)	)	PUNCT
ejpam-5016	65	4	let	let	VERB
ejpam-5016	65	5	p	p	PRON
ejpam-5016	65	6	be	be	AUX
ejpam-5016	65	7	a	a	DET
ejpam-5016	65	8	finite	finite	ADJ
ejpam-5016	65	9	collection	collection	NOUN
ejpam-5016	65	10	of	of	ADP
ejpam-5016	65	11	cells	cell	NOUN
ejpam-5016	65	12	in	in	ADP
ejpam-5016	65	13	z2	z2	PROPN
ejpam-5016	65	14	.	.	PUNCT
ejpam-5016	66	1	the	the	DET
ejpam-5016	66	2	collection	collection	NOUN
ejpam-5016	66	3	of	of	ADP
ejpam-5016	66	4	all	all	DET
ejpam-5016	66	5	vertices	vertex	NOUN
ejpam-5016	66	6	of	of	ADP
ejpam-5016	66	7	p	p	NOUN
ejpam-5016	66	8	,	,	PUNCT
ejpam-5016	66	9	denoted	denote	VERB
ejpam-5016	66	10	by	by	ADP
ejpam-5016	66	11	v	v	NOUN
ejpam-5016	66	12	(	(	PUNCT
ejpam-5016	66	13	p	p	NOUN
ejpam-5016	66	14	)	)	PUNCT
ejpam-5016	66	15	is	be	AUX
ejpam-5016	66	16	the	the	DET
ejpam-5016	66	17	union	union	NOUN
ejpam-5016	66	18	of	of	ADP
ejpam-5016	66	19	all	all	DET
ejpam-5016	66	20	corners	corner	NOUN
ejpam-5016	66	21	from	from	ADP
ejpam-5016	66	22	each	each	DET
ejpam-5016	66	23	cells	cell	NOUN
ejpam-5016	66	24	in	in	ADP
ejpam-5016	66	25	p.	p.	PROPN
ejpam-5016	66	26	(	(	PUNCT
ejpam-5016	66	27	vi	vi	X
ejpam-5016	66	28	)	)	PUNCT
ejpam-5016	66	29	let	let	VERB
ejpam-5016	66	30	a	a	PRON
ejpam-5016	66	31	=	=	PUNCT
ejpam-5016	66	32	(	(	PUNCT
ejpam-5016	66	33	i	i	PROPN
ejpam-5016	66	34	,	,	PUNCT
ejpam-5016	66	35	j	j	PROPN
ejpam-5016	66	36	)	)	PUNCT
ejpam-5016	66	37	,	,	PUNCT
ejpam-5016	66	38	b	b	X
ejpam-5016	67	1	=	=	SYM
ejpam-5016	67	2	(	(	PUNCT
ejpam-5016	67	3	k	k	X
ejpam-5016	67	4	,	,	PUNCT
ejpam-5016	67	5	ℓ	ℓ	X
ejpam-5016	67	6	)	)	PUNCT
ejpam-5016	67	7	∈	∈	PROPN
ejpam-5016	67	8	z2	z2	PROPN
ejpam-5016	67	9	.	.	PUNCT
ejpam-5016	68	1	the	the	DET
ejpam-5016	68	2	vertices	vertex	NOUN
ejpam-5016	68	3	a	a	PRON
ejpam-5016	68	4	and	and	CCONJ
ejpam-5016	68	5	b	b	NOUN
ejpam-5016	68	6	are	be	AUX
ejpam-5016	68	7	called	call	VERB
ejpam-5016	68	8	in	in	ADP
ejpam-5016	68	9	horizontal	horizontal	ADJ
ejpam-5016	68	10	position	position	NOUN
ejpam-5016	68	11	if	if	SCONJ
ejpam-5016	68	12	j	j	PROPN
ejpam-5016	68	13	=	=	SYM
ejpam-5016	68	14	ℓ	ℓ	PROPN
ejpam-5016	68	15	and	and	CCONJ
ejpam-5016	68	16	in	in	ADP
ejpam-5016	68	17	vertical	vertical	ADJ
ejpam-5016	68	18	position	position	NOUN
ejpam-5016	68	19	if	if	SCONJ
ejpam-5016	68	20	i	i	PRON
ejpam-5016	68	21	=	=	SYM
ejpam-5016	68	22	k.	k.	PROPN
ejpam-5016	68	23	(	(	PUNCT
ejpam-5016	68	24	vii	vii	PROPN
ejpam-5016	68	25	)	)	PUNCT
ejpam-5016	68	26	let	let	VERB
ejpam-5016	68	27	p	p	PRON
ejpam-5016	68	28	be	be	AUX
ejpam-5016	68	29	a	a	DET
ejpam-5016	68	30	finite	finite	ADJ
ejpam-5016	68	31	collection	collection	NOUN
ejpam-5016	68	32	of	of	ADP
ejpam-5016	68	33	cells	cell	NOUN
ejpam-5016	68	34	in	in	ADP
ejpam-5016	68	35	z2	z2	PROPN
ejpam-5016	68	36	.	.	PUNCT
ejpam-5016	69	1	let	let	VERB
ejpam-5016	70	1	c	c	NOUN
ejpam-5016	71	1	and	and	CCONJ
ejpam-5016	71	2	d	d	NOUN
ejpam-5016	71	3	be	be	AUX
ejpam-5016	71	4	two	two	NUM
ejpam-5016	71	5	cells	cell	NOUN
ejpam-5016	71	6	in	in	ADP
ejpam-5016	71	7	p.	p.	NOUN
ejpam-5016	71	8	the	the	DET
ejpam-5016	71	9	cells	cell	NOUN
ejpam-5016	71	10	c	c	PROPN
ejpam-5016	72	1	and	and	CCONJ
ejpam-5016	72	2	d	d	PROPN
ejpam-5016	72	3	are	be	AUX
ejpam-5016	72	4	called	call	VERB
ejpam-5016	72	5	connected	connect	VERB
ejpam-5016	72	6	if	if	SCONJ
ejpam-5016	72	7	there	there	PRON
ejpam-5016	72	8	exists	exist	VERB
ejpam-5016	72	9	a	a	DET
ejpam-5016	72	10	sequence	sequence	NOUN
ejpam-5016	72	11	of	of	ADP
ejpam-5016	72	12	cells	cell	NOUN
ejpam-5016	72	13	c	c	PUNCT
ejpam-5016	72	14	=	=	PROPN
ejpam-5016	72	15	c1	c1	PROPN
ejpam-5016	72	16	,	,	PUNCT
ejpam-5016	72	17	.	.	PUNCT
ejpam-5016	72	18	.	.	PUNCT
ejpam-5016	73	1	.	.	PUNCT
ejpam-5016	74	1	,	,	PUNCT
ejpam-5016	74	2	cm	cm	NOUN
ejpam-5016	75	1	=	=	SYM
ejpam-5016	75	2	d	d	NOUN
ejpam-5016	75	3	in	in	ADP
ejpam-5016	75	4	p	p	PRON
ejpam-5016	76	1	such	such	ADJ
ejpam-5016	76	2	that	that	DET
ejpam-5016	76	3	ci	ci	PROPN
ejpam-5016	76	4	∩	∩	NOUN
ejpam-5016	76	5	ci+1	ci+1	PROPN
ejpam-5016	76	6	is	be	AUX
ejpam-5016	76	7	an	an	DET
ejpam-5016	76	8	edge	edge	NOUN
ejpam-5016	76	9	of	of	ADP
ejpam-5016	76	10	ci	ci	NOUN
ejpam-5016	76	11	for	for	ADP
ejpam-5016	76	12	all	all	DET
ejpam-5016	76	13	i	i	PRON
ejpam-5016	76	14	=	=	NOUN
ejpam-5016	76	15	1	1	NUM
ejpam-5016	76	16	,	,	PUNCT
ejpam-5016	76	17	2	2	NUM
ejpam-5016	76	18	,	,	PUNCT
ejpam-5016	76	19	.	.	PUNCT
ejpam-5016	76	20	.	.	PUNCT
ejpam-5016	77	1	.	.	PUNCT
ejpam-5016	78	1	,	,	PUNCT
ejpam-5016	78	2	m−	m−	PROPN
ejpam-5016	78	3	1	1	NUM
ejpam-5016	78	4	.	.	PUNCT
ejpam-5016	79	1	(	(	PUNCT
ejpam-5016	79	2	viii	viii	NOUN
ejpam-5016	79	3	)	)	PUNCT
ejpam-5016	79	4	a	a	DET
ejpam-5016	79	5	finite	finite	ADJ
ejpam-5016	79	6	collection	collection	NOUN
ejpam-5016	79	7	of	of	ADP
ejpam-5016	79	8	cells	cell	NOUN
ejpam-5016	79	9	p	p	NOUN
ejpam-5016	79	10	in	in	ADP
ejpam-5016	79	11	z2	z2	PROPN
ejpam-5016	79	12	is	be	AUX
ejpam-5016	79	13	called	call	VERB
ejpam-5016	79	14	a	a	DET
ejpam-5016	79	15	polyomino	polyomino	NOUN
ejpam-5016	79	16	if	if	SCONJ
ejpam-5016	79	17	any	any	DET
ejpam-5016	79	18	two	two	NUM
ejpam-5016	79	19	cells	cell	NOUN
ejpam-5016	79	20	in	in	ADP
ejpam-5016	79	21	p	p	NOUN
ejpam-5016	79	22	are	be	AUX
ejpam-5016	79	23	connected	connect	VERB
ejpam-5016	79	24	.	.	PUNCT
ejpam-5016	80	1	(	(	PUNCT
ejpam-5016	80	2	ix	ix	ADP
ejpam-5016	80	3	)	)	PUNCT
ejpam-5016	80	4	a	a	DET
ejpam-5016	80	5	walk	walk	NOUN
ejpam-5016	80	6	from	from	ADP
ejpam-5016	80	7	cell	cell	NOUN
ejpam-5016	80	8	c	c	NOUN
ejpam-5016	80	9	to	to	PART
ejpam-5016	80	10	cell	cell	VERB
ejpam-5016	80	11	d	d	NOUN
ejpam-5016	80	12	in	in	ADP
ejpam-5016	80	13	z2	z2	PROPN
ejpam-5016	80	14	is	be	AUX
ejpam-5016	80	15	a	a	DET
ejpam-5016	80	16	sequence	sequence	NOUN
ejpam-5016	80	17	of	of	ADP
ejpam-5016	80	18	cells	cell	NOUN
ejpam-5016	80	19	c	c	NOUN
ejpam-5016	80	20	:	:	PUNCT
ejpam-5016	80	21	c	c	X
ejpam-5016	80	22	=	=	SYM
ejpam-5016	80	23	c1	c1	PROPN
ejpam-5016	80	24	,	,	PUNCT
ejpam-5016	80	25	.	.	PUNCT
ejpam-5016	80	26	.	.	PUNCT
ejpam-5016	81	1	.	.	PUNCT
ejpam-5016	82	1	,	,	PUNCT
ejpam-5016	82	2	cm	cm	NOUN
ejpam-5016	82	3	=	=	SYM
ejpam-5016	82	4	d	d	PROPN
ejpam-5016	82	5	in	in	ADP
ejpam-5016	82	6	z2	z2	PROPN
ejpam-5016	82	7	such	such	ADJ
ejpam-5016	82	8	that	that	DET
ejpam-5016	82	9	ci∩ci+1	ci∩ci+1	NOUN
ejpam-5016	82	10	is	be	AUX
ejpam-5016	82	11	an	an	DET
ejpam-5016	82	12	edge	edge	NOUN
ejpam-5016	82	13	of	of	ADP
ejpam-5016	82	14	ci	ci	NOUN
ejpam-5016	82	15	and	and	CCONJ
ejpam-5016	82	16	ci+1	ci+1	PROPN
ejpam-5016	82	17	for	for	ADP
ejpam-5016	82	18	all	all	DET
ejpam-5016	82	19	i	i	PRON
ejpam-5016	82	20	=	=	NOUN
ejpam-5016	82	21	1	1	NUM
ejpam-5016	82	22	,	,	PUNCT
ejpam-5016	82	23	2	2	NUM
ejpam-5016	82	24	,	,	PUNCT
ejpam-5016	82	25	.	.	PUNCT
ejpam-5016	82	26	.	.	PUNCT
ejpam-5016	83	1	.	.	PUNCT
ejpam-5016	84	1	,	,	PUNCT
ejpam-5016	84	2	m−1	m−1	PROPN
ejpam-5016	84	3	.	.	PUNCT
ejpam-5016	85	1	if	if	SCONJ
ejpam-5016	85	2	ci	ci	PROPN
ejpam-5016	85	3	̸=	̸=	PROPN
ejpam-5016	85	4	cj	cj	VERB
ejpam-5016	85	5	for	for	ADP
ejpam-5016	85	6	all	all	PRON
ejpam-5016	85	7	i	i	PRON
ejpam-5016	86	1	̸=	̸=	PROPN
ejpam-5016	86	2	j	j	PROPN
ejpam-5016	86	3	then	then	ADV
ejpam-5016	86	4	c	c	PROPN
ejpam-5016	86	5	is	be	AUX
ejpam-5016	86	6	called	call	VERB
ejpam-5016	86	7	a	a	DET
ejpam-5016	86	8	path	path	NOUN
ejpam-5016	86	9	.	.	PUNCT
ejpam-5016	87	1	a	a	DET
ejpam-5016	87	2	polyomino	polyomino	NOUN
ejpam-5016	87	3	p	p	NOUN
ejpam-5016	87	4	is	be	AUX
ejpam-5016	87	5	called	call	VERB
ejpam-5016	87	6	simple	simple	ADJ
ejpam-5016	87	7	if	if	SCONJ
ejpam-5016	87	8	for	for	ADP
ejpam-5016	87	9	any	any	DET
ejpam-5016	87	10	two	two	NUM
ejpam-5016	87	11	cells	cell	NOUN
ejpam-5016	87	12	c	c	NOUN
ejpam-5016	88	1	and	and	CCONJ
ejpam-5016	88	2	d	d	AUX
ejpam-5016	88	3	not	not	PART
ejpam-5016	88	4	belonging	belong	VERB
ejpam-5016	88	5	to	to	ADP
ejpam-5016	88	6	p	p	NOUN
ejpam-5016	88	7	,	,	PUNCT
ejpam-5016	88	8	there	there	PRON
ejpam-5016	88	9	exist	exist	VERB
ejpam-5016	88	10	a	a	DET
ejpam-5016	88	11	path	path	NOUN
ejpam-5016	89	1	c	c	NOUN
ejpam-5016	89	2	:	:	PUNCT
ejpam-5016	89	3	c	c	X
ejpam-5016	89	4	=	=	SYM
ejpam-5016	89	5	c1	c1	PROPN
ejpam-5016	89	6	,	,	PUNCT
ejpam-5016	89	7	.	.	PUNCT
ejpam-5016	89	8	.	.	PUNCT
ejpam-5016	89	9	.	.	PUNCT
ejpam-5016	90	1	,	,	PUNCT
ejpam-5016	90	2	cm	cm	NOUN
ejpam-5016	90	3	=	=	PUNCT
ejpam-5016	91	1	d	d	PROPN
ejpam-5016	91	2	such	such	ADJ
ejpam-5016	91	3	that	that	DET
ejpam-5016	91	4	ci	ci	NOUN
ejpam-5016	91	5	/∈	/∈	PUNCT
ejpam-5016	92	1	p	p	NOUN
ejpam-5016	92	2	for	for	ADP
ejpam-5016	92	3	all	all	DET
ejpam-5016	92	4	i	i	PRON
ejpam-5016	92	5	=	=	NOUN
ejpam-5016	92	6	1	1	NUM
ejpam-5016	92	7	,	,	PUNCT
ejpam-5016	92	8	.	.	PUNCT
ejpam-5016	92	9	.	.	PUNCT
ejpam-5016	93	1	.	.	PUNCT
ejpam-5016	94	1	,	,	PUNCT
ejpam-5016	94	2	m.	m.	NOUN
ejpam-5016	94	3	(	(	PUNCT
ejpam-5016	94	4	x	x	X
ejpam-5016	94	5	)	)	PUNCT
ejpam-5016	94	6	let	let	VERB
ejpam-5016	94	7	p	p	PRON
ejpam-5016	94	8	be	be	AUX
ejpam-5016	94	9	a	a	DET
ejpam-5016	94	10	polyomino	polyomino	NOUN
ejpam-5016	94	11	and	and	CCONJ
ejpam-5016	94	12	(	(	PUNCT
ejpam-5016	94	13	i	i	PROPN
ejpam-5016	94	14	,	,	PUNCT
ejpam-5016	94	15	j	j	PROPN
ejpam-5016	94	16	)	)	PUNCT
ejpam-5016	94	17	,	,	PUNCT
ejpam-5016	95	1	(	(	PUNCT
ejpam-5016	95	2	k	k	X
ejpam-5016	95	3	,	,	PUNCT
ejpam-5016	95	4	ℓ	ℓ	INTJ
ejpam-5016	95	5	)	)	PUNCT
ejpam-5016	95	6	∈	∈	PROPN
ejpam-5016	95	7	v	v	NOUN
ejpam-5016	95	8	(	(	PUNCT
ejpam-5016	95	9	p	p	NOUN
ejpam-5016	95	10	)	)	PUNCT
ejpam-5016	95	11	such	such	ADJ
ejpam-5016	95	12	that	that	SCONJ
ejpam-5016	95	13	i	i	PRON
ejpam-5016	95	14	<	<	X
ejpam-5016	95	15	k	k	PROPN
ejpam-5016	96	1	and	and	CCONJ
ejpam-5016	96	2	j	j	PROPN
ejpam-5016	96	3	<	<	X
ejpam-5016	96	4	ℓ.	ℓ.	NOUN
ejpam-5016	96	5	the	the	DET
ejpam-5016	96	6	interval	interval	NOUN
ejpam-5016	96	7	[	[	X
ejpam-5016	96	8	(	(	PUNCT
ejpam-5016	96	9	i	i	PROPN
ejpam-5016	96	10	,	,	PUNCT
ejpam-5016	96	11	j	j	PROPN
ejpam-5016	96	12	)	)	PUNCT
ejpam-5016	96	13	,	,	PUNCT
ejpam-5016	96	14	(	(	PUNCT
ejpam-5016	96	15	k	k	X
ejpam-5016	96	16	,	,	PUNCT
ejpam-5016	96	17	ℓ	ℓ	NOUN
ejpam-5016	96	18	)	)	PUNCT
ejpam-5016	96	19	]	]	PUNCT
ejpam-5016	96	20	is	be	AUX
ejpam-5016	96	21	called	call	VERB
ejpam-5016	96	22	an	an	DET
ejpam-5016	96	23	inner	inner	ADJ
ejpam-5016	96	24	interval	interval	NOUN
ejpam-5016	96	25	of	of	ADP
ejpam-5016	96	26	p	p	NOUN
ejpam-5016	96	27	if	if	SCONJ
ejpam-5016	96	28	any	any	DET
ejpam-5016	96	29	cell	cell	NOUN
ejpam-5016	96	30	[	[	X
ejpam-5016	96	31	(	(	PUNCT
ejpam-5016	96	32	r	r	NOUN
ejpam-5016	96	33	,	,	PUNCT
ejpam-5016	96	34	s	s	PART
ejpam-5016	96	35	)	)	PUNCT
ejpam-5016	96	36	,	,	PUNCT
ejpam-5016	96	37	(	(	PUNCT
ejpam-5016	96	38	r	r	NOUN
ejpam-5016	96	39	+	+	NOUN
ejpam-5016	96	40	1	1	NUM
ejpam-5016	96	41	,	,	PUNCT
ejpam-5016	96	42	s+	s+	X
ejpam-5016	96	43	1	1	NUM
ejpam-5016	96	44	)	)	PUNCT
ejpam-5016	96	45	]	]	PUNCT
ejpam-5016	96	46	is	be	AUX
ejpam-5016	96	47	an	an	DET
ejpam-5016	96	48	element	element	NOUN
ejpam-5016	96	49	in	in	ADP
ejpam-5016	96	50	p	p	NOUN
ejpam-5016	96	51	for	for	ADP
ejpam-5016	96	52	all	all	PRON
ejpam-5016	97	1	i	i	PRON
ejpam-5016	97	2	≤	≤	NUM
ejpam-5016	97	3	r	r	NOUN
ejpam-5016	97	4	≤	≤	PUNCT
ejpam-5016	97	5	k	k	NOUN
ejpam-5016	97	6	−	−	PROPN
ejpam-5016	97	7	1	1	NUM
ejpam-5016	97	8	and	and	CCONJ
ejpam-5016	97	9	j	j	PROPN
ejpam-5016	97	10	≤	≤	PROPN
ejpam-5016	97	11	s	s	PART
ejpam-5016	97	12	≤	≤	NOUN
ejpam-5016	97	13	ℓ−	ℓ−	PROPN
ejpam-5016	97	14	1	1	NUM
ejpam-5016	97	15	.	.	PUNCT
ejpam-5016	98	1	(	(	PUNCT
ejpam-5016	98	2	xi	xi	X
ejpam-5016	98	3	)	)	PUNCT
ejpam-5016	98	4	let	let	VERB
ejpam-5016	98	5	p	p	PRON
ejpam-5016	98	6	be	be	AUX
ejpam-5016	98	7	a	a	DET
ejpam-5016	98	8	polyomino	polyomino	NOUN
ejpam-5016	98	9	.	.	PUNCT
ejpam-5016	99	1	the	the	DET
ejpam-5016	99	2	interval	interval	NOUN
ejpam-5016	99	3	[	[	X
ejpam-5016	99	4	(	(	PUNCT
ejpam-5016	99	5	i	i	PROPN
ejpam-5016	99	6	,	,	PUNCT
ejpam-5016	99	7	j	j	PROPN
ejpam-5016	99	8	)	)	PUNCT
ejpam-5016	99	9	,	,	PUNCT
ejpam-5016	99	10	(	(	PUNCT
ejpam-5016	99	11	k	k	X
ejpam-5016	99	12	,	,	PUNCT
ejpam-5016	99	13	j	j	PROPN
ejpam-5016	99	14	)	)	PUNCT
ejpam-5016	99	15	]	]	PUNCT
ejpam-5016	99	16	with	with	ADP
ejpam-5016	99	17	i	i	PRON
ejpam-5016	99	18	<	<	X
ejpam-5016	99	19	k	k	X
ejpam-5016	99	20	is	be	AUX
ejpam-5016	99	21	called	call	VERB
ejpam-5016	99	22	in	in	ADP
ejpam-5016	99	23	a	a	DET
ejpam-5016	99	24	horizontal	horizontal	ADJ
ejpam-5016	99	25	edge	edge	NOUN
ejpam-5016	99	26	interval	interval	NOUN
ejpam-5016	99	27	of	of	ADP
ejpam-5016	99	28	p	p	NOUN
ejpam-5016	99	29	if	if	SCONJ
ejpam-5016	99	30	the	the	DET
ejpam-5016	99	31	interval	interval	NOUN
ejpam-5016	99	32	[	[	X
ejpam-5016	99	33	(	(	PUNCT
ejpam-5016	99	34	ℓ	ℓ	PROPN
ejpam-5016	99	35	,	,	PUNCT
ejpam-5016	99	36	j	j	NOUN
ejpam-5016	99	37	)	)	PUNCT
ejpam-5016	99	38	,	,	PUNCT
ejpam-5016	99	39	(	(	PUNCT
ejpam-5016	99	40	ℓ	ℓ	X
ejpam-5016	99	41	+	+	PROPN
ejpam-5016	99	42	1	1	NUM
ejpam-5016	99	43	,	,	PUNCT
ejpam-5016	99	44	j	j	NOUN
ejpam-5016	99	45	)	)	PUNCT
ejpam-5016	99	46	]	]	PUNCT
ejpam-5016	99	47	are	be	AUX
ejpam-5016	99	48	edges	edge	NOUN
ejpam-5016	99	49	of	of	ADP
ejpam-5016	99	50	cells	cell	NOUN
ejpam-5016	99	51	of	of	ADP
ejpam-5016	99	52	p	p	NOUN
ejpam-5016	99	53	for	for	ADP
ejpam-5016	99	54	all	all	DET
ejpam-5016	99	55	ℓ	ℓ	NOUN
ejpam-5016	99	56	=	=	SYM
ejpam-5016	99	57	i	i	PROPN
ejpam-5016	99	58	,	,	PUNCT
ejpam-5016	99	59	.	.	PUNCT
ejpam-5016	99	60	.	.	PUNCT
ejpam-5016	100	1	.	.	PUNCT
ejpam-5016	101	1	,	,	PUNCT
ejpam-5016	102	1	k	k	PROPN
ejpam-5016	103	1	−	−	PROPN
ejpam-5016	104	1	1	1	X
ejpam-5016	104	2	.	.	PUNCT
ejpam-5016	105	1	if	if	SCONJ
ejpam-5016	105	2	[	[	X
ejpam-5016	105	3	(	(	PUNCT
ejpam-5016	105	4	i−	i−	PROPN
ejpam-5016	105	5	1	1	NUM
ejpam-5016	105	6	,	,	PUNCT
ejpam-5016	105	7	j	j	PROPN
ejpam-5016	105	8	)	)	PUNCT
ejpam-5016	105	9	,	,	PUNCT
ejpam-5016	105	10	(	(	PUNCT
ejpam-5016	105	11	i	i	PROPN
ejpam-5016	105	12	,	,	PUNCT
ejpam-5016	105	13	j	j	PROPN
ejpam-5016	105	14	)	)	PUNCT
ejpam-5016	105	15	]	]	PUNCT
ejpam-5016	105	16	and	and	CCONJ
ejpam-5016	105	17	[	[	X
ejpam-5016	105	18	(	(	PUNCT
ejpam-5016	105	19	k	k	X
ejpam-5016	105	20	,	,	PUNCT
ejpam-5016	105	21	j	j	PROPN
ejpam-5016	105	22	)	)	PUNCT
ejpam-5016	105	23	,	,	PUNCT
ejpam-5016	105	24	(	(	PUNCT
ejpam-5016	105	25	k	k	X
ejpam-5016	105	26	,	,	PUNCT
ejpam-5016	105	27	j	j	PROPN
ejpam-5016	105	28	)	)	PUNCT
ejpam-5016	105	29	]	]	PUNCT
ejpam-5016	105	30	are	be	AUX
ejpam-5016	105	31	not	not	PART
ejpam-5016	105	32	edges	edge	NOUN
ejpam-5016	105	33	af	af	NOUN
ejpam-5016	105	34	cells	cell	NOUN
ejpam-5016	105	35	if	if	SCONJ
ejpam-5016	105	36	p	p	PROPN
ejpam-5016	105	37	then	then	ADV
ejpam-5016	105	38	the	the	DET
ejpam-5016	105	39	interval	interval	NOUN
ejpam-5016	105	40	[	[	X
ejpam-5016	105	41	(	(	PUNCT
ejpam-5016	105	42	i	i	PROPN
ejpam-5016	105	43	,	,	PUNCT
ejpam-5016	105	44	j	j	PROPN
ejpam-5016	105	45	)	)	PUNCT
ejpam-5016	105	46	,	,	PUNCT
ejpam-5016	105	47	(	(	PUNCT
ejpam-5016	105	48	k	k	X
ejpam-5016	105	49	,	,	PUNCT
ejpam-5016	105	50	j	j	PROPN
ejpam-5016	105	51	)	)	PUNCT
ejpam-5016	105	52	]	]	PUNCT
ejpam-5016	105	53	is	be	AUX
ejpam-5016	105	54	called	call	VERB
ejpam-5016	105	55	a	a	DET
ejpam-5016	105	56	maximal	maximal	ADJ
ejpam-5016	105	57	horizontal	horizontal	ADJ
ejpam-5016	105	58	edge	edge	NOUN
ejpam-5016	105	59	interval	interval	NOUN
ejpam-5016	105	60	of	of	ADP
ejpam-5016	105	61	p.	p.	NOUN
ejpam-5016	105	62	we	we	PRON
ejpam-5016	105	63	define	define	VERB
ejpam-5016	105	64	the	the	DET
ejpam-5016	105	65	vertical	vertical	ADJ
ejpam-5016	105	66	edge	edge	NOUN
ejpam-5016	105	67	interval	interval	NOUN
ejpam-5016	105	68	and	and	CCONJ
ejpam-5016	105	69	the	the	DET
ejpam-5016	105	70	maximal	maximal	ADJ
ejpam-5016	105	71	vertical	vertical	ADJ
ejpam-5016	105	72	edge	edge	NOUN
ejpam-5016	105	73	interval	interval	NOUN
ejpam-5016	105	74	similarly	similarly	ADV
ejpam-5016	105	75	.	.	PUNCT
ejpam-5016	106	1	y.	y.	PROPN
ejpam-5016	106	2	y.	y.	PROPN
ejpam-5016	106	3	hamonangan	hamonangan	PROPN
ejpam-5016	106	4	,	,	PUNCT
ejpam-5016	106	5	i.	i.	PROPN
ejpam-5016	106	6	muchtadi	muchtadi	PROPN
ejpam-5016	106	7	-	-	PUNCT
ejpam-5016	106	8	alamsyah	alamsyah	NOUN
ejpam-5016	106	9	/	/	SYM
ejpam-5016	106	10	eur	eur	PROPN
ejpam-5016	106	11	.	.	PUNCT
ejpam-5016	107	1	j.	j.	PROPN
ejpam-5016	107	2	pure	pure	PROPN
ejpam-5016	107	3	appl	appl	PROPN
ejpam-5016	107	4	.	.	PROPN
ejpam-5016	107	5	math	math	PROPN
ejpam-5016	107	6	,	,	PUNCT
ejpam-5016	107	7	17	17	NUM
ejpam-5016	107	8	(	(	PUNCT
ejpam-5016	107	9	4	4	NUM
ejpam-5016	107	10	)	)	PUNCT
ejpam-5016	107	11	(	(	PUNCT
ejpam-5016	107	12	2024	2024	NUM
ejpam-5016	107	13	)	)	PUNCT
ejpam-5016	107	14	,	,	PUNCT
ejpam-5016	107	15	2621	2621	NUM
ejpam-5016	107	16	-	-	SYM
ejpam-5016	107	17	2650	2650	NUM
ejpam-5016	107	18	2624	2624	NUM
ejpam-5016	107	19	(	(	PUNCT
ejpam-5016	107	20	xii	xii	NOUN
ejpam-5016	107	21	)	)	PUNCT
ejpam-5016	107	22	let	let	VERB
ejpam-5016	107	23	p	p	PRON
ejpam-5016	107	24	be	be	AUX
ejpam-5016	107	25	a	a	DET
ejpam-5016	107	26	polyomino	polyomino	NOUN
ejpam-5016	107	27	and	and	CCONJ
ejpam-5016	107	28	k	k	PROPN
ejpam-5016	107	29	be	be	AUX
ejpam-5016	107	30	a	a	DET
ejpam-5016	107	31	field	field	NOUN
ejpam-5016	107	32	.	.	PUNCT
ejpam-5016	108	1	define	define	VERB
ejpam-5016	108	2	the	the	DET
ejpam-5016	108	3	polynomial	polynomial	ADJ
ejpam-5016	108	4	ring	ring	NOUN
ejpam-5016	108	5	s	s	NOUN
ejpam-5016	108	6	over	over	ADP
ejpam-5016	108	7	k	k	PROPN
ejpam-5016	108	8	with	with	ADP
ejpam-5016	108	9	variables	variable	NOUN
ejpam-5016	108	10	xij	xij	PROPN
ejpam-5016	108	11	for	for	ADP
ejpam-5016	108	12	all	all	PRON
ejpam-5016	108	13	(	(	PUNCT
ejpam-5016	108	14	i	i	PROPN
ejpam-5016	108	15	,	,	PUNCT
ejpam-5016	108	16	j	j	PROPN
ejpam-5016	108	17	)	)	PUNCT
ejpam-5016	108	18	∈	∈	PROPN
ejpam-5016	108	19	v	v	NOUN
ejpam-5016	108	20	(	(	PUNCT
ejpam-5016	108	21	p	p	NOUN
ejpam-5016	108	22	)	)	PUNCT
ejpam-5016	108	23	.	.	PUNCT
ejpam-5016	109	1	each	each	DET
ejpam-5016	109	2	inner	inner	ADJ
ejpam-5016	109	3	interval	interval	NOUN
ejpam-5016	109	4	[	[	X
ejpam-5016	109	5	(	(	PUNCT
ejpam-5016	109	6	i	i	PROPN
ejpam-5016	109	7	,	,	PUNCT
ejpam-5016	109	8	j	j	PROPN
ejpam-5016	109	9	)	)	PUNCT
ejpam-5016	109	10	,	,	PUNCT
ejpam-5016	109	11	(	(	PUNCT
ejpam-5016	109	12	k	k	X
ejpam-5016	109	13	,	,	PUNCT
ejpam-5016	109	14	ℓ	ℓ	NOUN
ejpam-5016	109	15	)	)	PUNCT
ejpam-5016	109	16	]	]	PUNCT
ejpam-5016	109	17	in	in	ADP
ejpam-5016	109	18	p	p	PROPN
ejpam-5016	109	19	is	be	AUX
ejpam-5016	109	20	associated	associate	VERB
ejpam-5016	109	21	to	to	ADP
ejpam-5016	109	22	xijxkℓ	xijxkℓ	PROPN
ejpam-5016	109	23	−	−	PROPN
ejpam-5016	109	24	xiℓxkj	xiℓxkj	PROPN
ejpam-5016	109	25	∈	∈	PROPN
ejpam-5016	109	26	s	s	NOUN
ejpam-5016	109	27	,	,	PUNCT
ejpam-5016	109	28	that	that	PRON
ejpam-5016	109	29	is	be	AUX
ejpam-5016	109	30	called	call	VERB
ejpam-5016	109	31	the	the	DET
ejpam-5016	109	32	inner	inner	ADJ
ejpam-5016	109	33	2	2	NUM
ejpam-5016	109	34	-	-	PUNCT
ejpam-5016	109	35	minor	minor	NOUN
ejpam-5016	109	36	of	of	ADP
ejpam-5016	109	37	p.	p.	NOUN
ejpam-5016	109	38	the	the	DET
ejpam-5016	109	39	set	set	NOUN
ejpam-5016	109	40	of	of	ADP
ejpam-5016	109	41	all	all	DET
ejpam-5016	109	42	inner	inner	ADJ
ejpam-5016	109	43	2	2	NUM
ejpam-5016	109	44	-	-	PUNCT
ejpam-5016	109	45	minors	minor	NOUN
ejpam-5016	109	46	of	of	ADP
ejpam-5016	109	47	p	p	NOUN
ejpam-5016	109	48	is	be	AUX
ejpam-5016	109	49	denoted	denote	VERB
ejpam-5016	109	50	by	by	ADP
ejpam-5016	109	51	s2	s2	PROPN
ejpam-5016	109	52	.	.	PUNCT
ejpam-5016	110	1	(	(	PUNCT
ejpam-5016	110	2	xiii	xiii	PROPN
ejpam-5016	110	3	)	)	PUNCT
ejpam-5016	110	4	let	let	VERB
ejpam-5016	110	5	p	p	PRON
ejpam-5016	110	6	be	be	AUX
ejpam-5016	110	7	a	a	DET
ejpam-5016	110	8	polyomino	polyomino	NOUN
ejpam-5016	110	9	.	.	PUNCT
ejpam-5016	111	1	the	the	DET
ejpam-5016	111	2	ideal	ideal	NOUN
ejpam-5016	111	3	ip	ip	VERB
ejpam-5016	111	4	⊆	⊆	NUM
ejpam-5016	111	5	s	s	AUX
ejpam-5016	111	6	generated	generate	VERB
ejpam-5016	111	7	by	by	ADP
ejpam-5016	111	8	s2	s2	PROPN
ejpam-5016	111	9	is	be	AUX
ejpam-5016	111	10	called	call	VERB
ejpam-5016	111	11	the	the	DET
ejpam-5016	111	12	polyomino	polyomino	NOUN
ejpam-5016	111	13	ideal	ideal	NOUN
ejpam-5016	111	14	of	of	ADP
ejpam-5016	111	15	p	p	NOUN
ejpam-5016	111	16	and	and	CCONJ
ejpam-5016	111	17	k[p	k[p	NOUN
ejpam-5016	111	18	]	]	X
ejpam-5016	112	1	=	=	SYM
ejpam-5016	112	2	s	s	X
ejpam-5016	112	3	/	/	SYM
ejpam-5016	112	4	ip	ip	VERB
ejpam-5016	112	5	the	the	DET
ejpam-5016	112	6	coordinate	coordinate	NOUN
ejpam-5016	112	7	ring	ring	NOUN
ejpam-5016	112	8	of	of	ADP
ejpam-5016	112	9	p.	p.	PROPN
ejpam-5016	112	10	(	(	PUNCT
ejpam-5016	112	11	xiv	xiv	PROPN
ejpam-5016	112	12	)	)	PUNCT
ejpam-5016	112	13	let	let	VERB
ejpam-5016	112	14	j	j	PROPN
ejpam-5016	112	15	⊆	⊆	NUM
ejpam-5016	112	16	s	s	AUX
ejpam-5016	112	17	be	be	AUX
ejpam-5016	112	18	a	a	DET
ejpam-5016	112	19	binomial	binomial	ADJ
ejpam-5016	112	20	ideal	ideal	NOUN
ejpam-5016	112	21	and	and	CCONJ
ejpam-5016	112	22	f	f	NOUN
ejpam-5016	112	23	=	=	SYM
ejpam-5016	112	24	f+	f+	PROPN
ejpam-5016	112	25	−	−	PROPN
ejpam-5016	112	26	f−	f−	PROPN
ejpam-5016	112	27	be	be	AUX
ejpam-5016	112	28	a	a	DET
ejpam-5016	112	29	binomial	binomial	NOUN
ejpam-5016	112	30	in	in	ADP
ejpam-5016	112	31	j	j	PROPN
ejpam-5016	112	32	.	.	PUNCT
ejpam-5016	113	1	the	the	DET
ejpam-5016	113	2	binomial	binomial	ADJ
ejpam-5016	113	3	f	f	PROPN
ejpam-5016	113	4	is	be	AUX
ejpam-5016	113	5	called	call	VERB
ejpam-5016	113	6	redundant	redundant	ADJ
ejpam-5016	113	7	if	if	SCONJ
ejpam-5016	113	8	it	it	PRON
ejpam-5016	113	9	can	can	AUX
ejpam-5016	113	10	be	be	AUX
ejpam-5016	113	11	expressed	express	VERB
ejpam-5016	113	12	as	as	ADP
ejpam-5016	113	13	a	a	DET
ejpam-5016	113	14	linear	linear	ADJ
ejpam-5016	113	15	combination	combination	NOUN
ejpam-5016	113	16	of	of	ADP
ejpam-5016	113	17	binomials	binomial	NOUN
ejpam-5016	113	18	in	in	ADP
ejpam-5016	113	19	j	j	PROPN
ejpam-5016	113	20	od	od	PROPN
ejpam-5016	113	21	lower	low	ADJ
ejpam-5016	113	22	degree	degree	NOUN
ejpam-5016	113	23	.	.	PUNCT
ejpam-5016	114	1	the	the	DET
ejpam-5016	114	2	binomal	binomal	PROPN
ejpam-5016	114	3	f	f	PROPN
ejpam-5016	114	4	is	be	AUX
ejpam-5016	114	5	called	call	VERB
ejpam-5016	114	6	irredundant	irredundant	ADJ
ejpam-5016	114	7	if	if	SCONJ
ejpam-5016	114	8	it	it	PRON
ejpam-5016	114	9	is	be	AUX
ejpam-5016	114	10	not	not	PART
ejpam-5016	114	11	redundant	redundant	ADJ
ejpam-5016	114	12	.	.	PUNCT
ejpam-5016	115	1	we	we	PRON
ejpam-5016	115	2	also	also	ADV
ejpam-5016	115	3	denote	denote	VERB
ejpam-5016	115	4	by	by	ADP
ejpam-5016	115	5	v	v	PRON
ejpam-5016	115	6	+	+	CCONJ
ejpam-5016	115	7	f	f	X
ejpam-5016	115	8	the	the	DET
ejpam-5016	115	9	set	set	NOUN
ejpam-5016	115	10	of	of	ADP
ejpam-5016	115	11	vertices	vertex	NOUN
ejpam-5016	115	12	v	v	ADP
ejpam-5016	115	13	such	such	ADJ
ejpam-5016	115	14	that	that	SCONJ
ejpam-5016	115	15	xv	xv	PROPN
ejpam-5016	115	16	divides	divide	VERB
ejpam-5016	115	17	f+	f+	PROPN
ejpam-5016	115	18	and	and	CCONJ
ejpam-5016	115	19	by	by	ADP
ejpam-5016	115	20	v	v	NUM
ejpam-5016	115	21	−	−	PROPN
ejpam-5016	115	22	f	f	PROPN
ejpam-5016	115	23	the	the	DET
ejpam-5016	115	24	set	set	NOUN
ejpam-5016	115	25	of	of	ADP
ejpam-5016	115	26	vertices	vertex	NOUN
ejpam-5016	115	27	v	v	ADP
ejpam-5016	115	28	such	such	ADJ
ejpam-5016	115	29	that	that	SCONJ
ejpam-5016	115	30	xv	xv	PROPN
ejpam-5016	115	31	divides	divide	VERB
ejpam-5016	115	32	f−.	f−.	VERB
ejpam-5016	115	33	3	3	NUM
ejpam-5016	115	34	.	.	PUNCT
ejpam-5016	115	35	buchberger	buchberger	NOUN
ejpam-5016	115	36	algorithm	algorithm	NOUN
ejpam-5016	115	37	in	in	ADP
ejpam-5016	115	38	polyomino	polyomino	PROPN
ejpam-5016	115	39	ideal	ideal	NOUN
ejpam-5016	115	40	let	let	VERB
ejpam-5016	115	41	p	p	PRON
ejpam-5016	115	42	be	be	AUX
ejpam-5016	115	43	a	a	DET
ejpam-5016	115	44	polyomino	polyomino	NOUN
ejpam-5016	115	45	.	.	PUNCT
ejpam-5016	116	1	we	we	PRON
ejpam-5016	116	2	define	define	VERB
ejpam-5016	116	3	an	an	DET
ejpam-5016	116	4	ordering	ordering	NOUN
ejpam-5016	116	5	in	in	ADP
ejpam-5016	116	6	the	the	DET
ejpam-5016	116	7	set	set	NOUN
ejpam-5016	116	8	v	v	NOUN
ejpam-5016	116	9	(	(	PUNCT
ejpam-5016	116	10	p	p	NOUN
ejpam-5016	116	11	)	)	PUNCT
ejpam-5016	116	12	in	in	ADP
ejpam-5016	116	13	the	the	DET
ejpam-5016	116	14	following	following	ADJ
ejpam-5016	116	15	way	way	NOUN
ejpam-5016	116	16	:	:	PUNCT
ejpam-5016	116	17	(	(	PUNCT
ejpam-5016	116	18	i	i	PRON
ejpam-5016	116	19	,	,	PUNCT
ejpam-5016	116	20	j	j	PROPN
ejpam-5016	116	21	)	)	PUNCT
ejpam-5016	117	1	<	<	X
ejpam-5016	117	2	p	p	X
ejpam-5016	117	3	(	(	PUNCT
ejpam-5016	117	4	k	k	X
ejpam-5016	117	5	,	,	PUNCT
ejpam-5016	117	6	ℓ	ℓ	INTJ
ejpam-5016	117	7	)	)	PUNCT
ejpam-5016	118	1	if	if	SCONJ
ejpam-5016	118	2	and	and	CCONJ
ejpam-5016	118	3	only	only	ADV
ejpam-5016	118	4	if	if	SCONJ
ejpam-5016	118	5	•	•	NUM
ejpam-5016	118	6	j	j	PROPN
ejpam-5016	118	7	<	<	X
ejpam-5016	118	8	ℓ	ℓ	PROPN
ejpam-5016	118	9	or	or	CCONJ
ejpam-5016	118	10	•	•	NUM
ejpam-5016	118	11	ȷ	ȷ	NOUN
ejpam-5016	118	12	=	=	SYM
ejpam-5016	118	13	ℓ	ℓ	PROPN
ejpam-5016	118	14	and	and	CCONJ
ejpam-5016	118	15	i	i	PRON
ejpam-5016	118	16	<	<	X
ejpam-5016	118	17	k.	k.	X
ejpam-5016	118	18	by	by	ADP
ejpam-5016	118	19	this	this	DET
ejpam-5016	118	20	ordering	ordering	NOUN
ejpam-5016	118	21	,	,	PUNCT
ejpam-5016	118	22	all	all	DET
ejpam-5016	118	23	the	the	DET
ejpam-5016	118	24	vertices	vertex	NOUN
ejpam-5016	118	25	in	in	ADP
ejpam-5016	118	26	a	a	DET
ejpam-5016	118	27	polyomino	polyomino	NOUN
ejpam-5016	118	28	with	with	ADP
ejpam-5016	118	29	n	n	ADP
ejpam-5016	118	30	vertices	vertex	NOUN
ejpam-5016	118	31	can	can	AUX
ejpam-5016	118	32	be	be	AUX
ejpam-5016	118	33	labelled	label	VERB
ejpam-5016	118	34	with	with	ADP
ejpam-5016	118	35	positive	positive	ADJ
ejpam-5016	118	36	integer	integer	NOUN
ejpam-5016	118	37	1	1	NUM
ejpam-5016	118	38	,	,	PUNCT
ejpam-5016	118	39	2	2	NUM
ejpam-5016	118	40	,	,	PUNCT
ejpam-5016	118	41	.	.	PUNCT
ejpam-5016	119	1	.	.	PUNCT
ejpam-5016	120	1	.	.	PUNCT
ejpam-5016	121	1	,	,	PUNCT
ejpam-5016	121	2	n	n	CCONJ
ejpam-5016	121	3	from	from	ADP
ejpam-5016	121	4	left	left	ADJ
ejpam-5016	121	5	to	to	ADP
ejpam-5016	121	6	right	right	NOUN
ejpam-5016	121	7	,	,	PUNCT
ejpam-5016	121	8	starting	start	VERB
ejpam-5016	121	9	from	from	ADP
ejpam-5016	121	10	the	the	DET
ejpam-5016	121	11	vertices	vertex	NOUN
ejpam-5016	121	12	with	with	ADP
ejpam-5016	121	13	the	the	DET
ejpam-5016	121	14	lowest	low	ADJ
ejpam-5016	121	15	ordinate	ordinate	NOUN
ejpam-5016	121	16	to	to	ADP
ejpam-5016	121	17	the	the	DET
ejpam-5016	121	18	vertices	vertex	NOUN
ejpam-5016	121	19	with	with	ADP
ejpam-5016	121	20	the	the	DET
ejpam-5016	121	21	highest	high	ADJ
ejpam-5016	121	22	ordinate	ordinate	NOUN
ejpam-5016	121	23	.	.	PUNCT
ejpam-5016	122	1	below	below	ADV
ejpam-5016	122	2	is	be	AUX
ejpam-5016	122	3	an	an	DET
ejpam-5016	122	4	example	example	NOUN
ejpam-5016	122	5	of	of	ADP
ejpam-5016	122	6	such	such	ADJ
ejpam-5016	122	7	labelling	labelling	NOUN
ejpam-5016	122	8	.	.	PUNCT
ejpam-5016	123	1	1	1	NUM
ejpam-5016	123	2	2	2	NUM
ejpam-5016	123	3	3	3	NUM
ejpam-5016	123	4	4	4	NUM
ejpam-5016	123	5	5	5	NUM
ejpam-5016	123	6	6	6	NUM
ejpam-5016	123	7	7	7	NUM
ejpam-5016	123	8	8	8	NUM
ejpam-5016	123	9	9	9	NUM
ejpam-5016	123	10	10	10	NUM
ejpam-5016	123	11	11	11	NUM
ejpam-5016	123	12	12	12	NUM
ejpam-5016	123	13	13	13	NUM
ejpam-5016	123	14	14	14	NUM
ejpam-5016	123	15	15	15	NUM
ejpam-5016	123	16	16	16	NUM
ejpam-5016	123	17	17	17	NUM
ejpam-5016	123	18	18	18	NUM
ejpam-5016	123	19	19	19	NUM
ejpam-5016	123	20	20	20	NUM
ejpam-5016	123	21	21	21	NUM
ejpam-5016	123	22	22	22	NUM
ejpam-5016	123	23	23	23	NUM
ejpam-5016	123	24	figure	figure	NOUN
ejpam-5016	123	25	1	1	NUM
ejpam-5016	123	26	:	:	PUNCT
ejpam-5016	123	27	labelling	label	VERB
ejpam-5016	123	28	the	the	DET
ejpam-5016	123	29	set	set	NOUN
ejpam-5016	123	30	v	v	NOUN
ejpam-5016	123	31	(	(	PUNCT
ejpam-5016	123	32	p	p	NOUN
ejpam-5016	123	33	)	)	PUNCT
ejpam-5016	123	34	.	.	PUNCT
ejpam-5016	124	1	by	by	ADP
ejpam-5016	124	2	this	this	DET
ejpam-5016	124	3	labelling	labelling	NOUN
ejpam-5016	124	4	,	,	PUNCT
ejpam-5016	124	5	the	the	DET
ejpam-5016	124	6	polynomial	polynomial	ADJ
ejpam-5016	124	7	ring	ring	NOUN
ejpam-5016	124	8	associated	associate	VERB
ejpam-5016	124	9	to	to	ADP
ejpam-5016	124	10	the	the	DET
ejpam-5016	124	11	polyomino	polyomino	NOUN
ejpam-5016	124	12	ideal	ideal	NOUN
ejpam-5016	124	13	is	be	AUX
ejpam-5016	124	14	s	s	PROPN
ejpam-5016	124	15	=	=	PUNCT
ejpam-5016	124	16	k[x1	k[x1	PROPN
ejpam-5016	124	17	,	,	PUNCT
ejpam-5016	124	18	.	.	PUNCT
ejpam-5016	124	19	.	.	PUNCT
ejpam-5016	125	1	.	.	PUNCT
ejpam-5016	126	1	,	,	PUNCT
ejpam-5016	126	2	xn	xn	PROPN
ejpam-5016	126	3	]	]	X
ejpam-5016	126	4	.	.	PUNCT
ejpam-5016	127	1	we	we	PRON
ejpam-5016	127	2	use	use	VERB
ejpam-5016	127	3	the	the	DET
ejpam-5016	127	4	lexicographic	lexicographic	ADJ
ejpam-5016	127	5	monomial	monomial	ADJ
ejpam-5016	127	6	order	order	NOUN
ejpam-5016	127	7	with	with	ADP
ejpam-5016	127	8	x1	x1	PROPN
ejpam-5016	127	9	>	>	X
ejpam-5016	127	10	x2	x2	PROPN
ejpam-5016	127	11	>	>	X
ejpam-5016	127	12	·	·	PUNCT
ejpam-5016	127	13	·	·	PUNCT
ejpam-5016	127	14	·	·	PUNCT
ejpam-5016	127	15	>	>	PUNCT
ejpam-5016	128	1	xn	xn	X
ejpam-5016	128	2	.	.	PUNCT
ejpam-5016	129	1	for	for	ADP
ejpam-5016	129	2	the	the	DET
ejpam-5016	129	3	sake	sake	NOUN
ejpam-5016	129	4	of	of	ADP
ejpam-5016	129	5	simplicity	simplicity	NOUN
ejpam-5016	129	6	,	,	PUNCT
ejpam-5016	129	7	the	the	DET
ejpam-5016	129	8	elements	element	NOUN
ejpam-5016	129	9	xa	xa	PROPN
ejpam-5016	129	10	∈	∈	PROPN
ejpam-5016	129	11	r	r	NOUN
ejpam-5016	129	12	will	will	AUX
ejpam-5016	129	13	be	be	AUX
ejpam-5016	129	14	written	write	VERB
ejpam-5016	129	15	with	with	ADP
ejpam-5016	129	16	a.	a.	NOUN
ejpam-5016	129	17	we	we	PRON
ejpam-5016	129	18	define	define	VERB
ejpam-5016	129	19	the	the	DET
ejpam-5016	129	20	degree	degree	NOUN
ejpam-5016	129	21	of	of	ADP
ejpam-5016	129	22	monomials	monomial	NOUN
ejpam-5016	129	23	xa11	xa11	PROPN
ejpam-5016	129	24	xa22	xa22	PROPN
ejpam-5016	129	25	.	.	PUNCT
ejpam-5016	129	26	.	.	PUNCT
ejpam-5016	129	27	.	.	PUNCT
ejpam-5016	130	1	xann	xann	PROPN
ejpam-5016	131	1	with	with	ADP
ejpam-5016	131	2	∑n	∑n	PROPN
ejpam-5016	131	3	i=1	i=1	PROPN
ejpam-5016	131	4	ai	ai	VERB
ejpam-5016	131	5	.	.	PUNCT
ejpam-5016	132	1	we	we	PRON
ejpam-5016	132	2	also	also	ADV
ejpam-5016	132	3	define	define	VERB
ejpam-5016	132	4	the	the	DET
ejpam-5016	132	5	interval	interval	NOUN
ejpam-5016	132	6	determined	determine	VERB
ejpam-5016	132	7	by	by	ADP
ejpam-5016	132	8	{	{	PUNCT
ejpam-5016	132	9	a	a	PROPN
ejpam-5016	132	10	,	,	PUNCT
ejpam-5016	132	11	b	b	NOUN
ejpam-5016	132	12	}	}	PUNCT
ejpam-5016	132	13	as	as	ADP
ejpam-5016	132	14	the	the	DET
ejpam-5016	132	15	interval	interval	NOUN
ejpam-5016	132	16	with	with	ADP
ejpam-5016	132	17	diagonal	diagonal	ADJ
ejpam-5016	132	18	corners	corner	NOUN
ejpam-5016	132	19	{	{	PUNCT
ejpam-5016	132	20	a	a	PRON
ejpam-5016	132	21	,	,	PUNCT
ejpam-5016	132	22	b	b	NOUN
ejpam-5016	132	23	}	}	PUNCT
ejpam-5016	132	24	or	or	CCONJ
ejpam-5016	132	25	antidiagonal	antidiagonal	ADJ
ejpam-5016	132	26	corners	corner	NOUN
ejpam-5016	132	27	{	{	PUNCT
ejpam-5016	132	28	a	a	NOUN
ejpam-5016	132	29	,	,	PUNCT
ejpam-5016	132	30	b	b	NOUN
ejpam-5016	132	31	}	}	PUNCT
ejpam-5016	132	32	.	.	PUNCT
ejpam-5016	133	1	now	now	ADV
ejpam-5016	133	2	,	,	PUNCT
ejpam-5016	133	3	we	we	PRON
ejpam-5016	133	4	are	be	AUX
ejpam-5016	133	5	ready	ready	ADJ
ejpam-5016	133	6	to	to	PART
ejpam-5016	133	7	perform	perform	VERB
ejpam-5016	133	8	the	the	DET
ejpam-5016	133	9	buchberger	buchberger	NOUN
ejpam-5016	133	10	algorithm	algorithm	NOUN
ejpam-5016	133	11	.	.	PUNCT
ejpam-5016	134	1	since	since	SCONJ
ejpam-5016	134	2	s2	s2	PROPN
ejpam-5016	134	3	consists	consist	VERB
ejpam-5016	134	4	of	of	ADP
ejpam-5016	134	5	inner	inner	ADJ
ejpam-5016	134	6	2	2	NUM
ejpam-5016	134	7	-	-	PUNCT
ejpam-5016	134	8	minors	minor	NOUN
ejpam-5016	134	9	then	then	ADV
ejpam-5016	134	10	the	the	DET
ejpam-5016	134	11	polynomial	polynomial	NOUN
ejpam-5016	134	12	obtained	obtain	VERB
ejpam-5016	134	13	by	by	ADP
ejpam-5016	134	14	the	the	DET
ejpam-5016	134	15	buchberger	buchberger	NOUN
ejpam-5016	134	16	algorithm	algorithm	NOUN
ejpam-5016	134	17	in	in	ADP
ejpam-5016	134	18	each	each	DET
ejpam-5016	134	19	step	step	NOUN
ejpam-5016	134	20	is	be	AUX
ejpam-5016	134	21	again	again	ADV
ejpam-5016	134	22	a	a	DET
ejpam-5016	134	23	binomial	binomial	NOUN
ejpam-5016	134	24	consisting	consisting	NOUN
ejpam-5016	134	25	of	of	ADP
ejpam-5016	134	26	y.	y.	PROPN
ejpam-5016	134	27	y.	y.	PROPN
ejpam-5016	134	28	hamonangan	hamonangan	PROPN
ejpam-5016	134	29	,	,	PUNCT
ejpam-5016	134	30	i.	i.	PROPN
ejpam-5016	134	31	muchtadi	muchtadi	PROPN
ejpam-5016	134	32	-	-	PUNCT
ejpam-5016	134	33	alamsyah	alamsyah	NOUN
ejpam-5016	134	34	/	/	SYM
ejpam-5016	134	35	eur	eur	PROPN
ejpam-5016	134	36	.	.	PUNCT
ejpam-5016	135	1	j.	j.	PROPN
ejpam-5016	135	2	pure	pure	PROPN
ejpam-5016	135	3	appl	appl	PROPN
ejpam-5016	135	4	.	.	PROPN
ejpam-5016	135	5	math	math	PROPN
ejpam-5016	135	6	,	,	PUNCT
ejpam-5016	135	7	17	17	NUM
ejpam-5016	135	8	(	(	PUNCT
ejpam-5016	135	9	4	4	NUM
ejpam-5016	135	10	)	)	PUNCT
ejpam-5016	135	11	(	(	PUNCT
ejpam-5016	135	12	2024	2024	NUM
ejpam-5016	135	13	)	)	PUNCT
ejpam-5016	135	14	,	,	PUNCT
ejpam-5016	135	15	2621	2621	NUM
ejpam-5016	135	16	-	-	SYM
ejpam-5016	135	17	2650	2650	NUM
ejpam-5016	135	18	2625	2625	NUM
ejpam-5016	135	19	two	two	NUM
ejpam-5016	135	20	monomials	monomial	NOUN
ejpam-5016	135	21	of	of	ADP
ejpam-5016	135	22	the	the	DET
ejpam-5016	135	23	same	same	ADJ
ejpam-5016	135	24	degree	degree	NOUN
ejpam-5016	135	25	.	.	PUNCT
ejpam-5016	136	1	the	the	DET
ejpam-5016	136	2	degree	degree	NOUN
ejpam-5016	136	3	of	of	ADP
ejpam-5016	136	4	this	this	DET
ejpam-5016	136	5	binomial	binomial	NOUN
ejpam-5016	136	6	is	be	AUX
ejpam-5016	136	7	defined	define	VERB
ejpam-5016	136	8	as	as	ADP
ejpam-5016	136	9	the	the	DET
ejpam-5016	136	10	degree	degree	NOUN
ejpam-5016	136	11	of	of	ADP
ejpam-5016	136	12	both	both	DET
ejpam-5016	136	13	monomials	monomial	NOUN
ejpam-5016	136	14	.	.	PUNCT
ejpam-5016	137	1	3.1	3.1	NUM
ejpam-5016	137	2	.	.	PUNCT
ejpam-5016	138	1	binomials	binomial	NOUN
ejpam-5016	138	2	of	of	ADP
ejpam-5016	138	3	degree	degree	NOUN
ejpam-5016	138	4	three	three	NUM
ejpam-5016	138	5	the	the	DET
ejpam-5016	138	6	result	result	NOUN
ejpam-5016	138	7	in	in	ADP
ejpam-5016	138	8	this	this	DET
ejpam-5016	138	9	subsection	subsection	NOUN
ejpam-5016	138	10	can	can	AUX
ejpam-5016	138	11	also	also	ADV
ejpam-5016	138	12	be	be	AUX
ejpam-5016	138	13	derived	derive	VERB
ejpam-5016	138	14	from	from	ADP
ejpam-5016	138	15	[	[	X
ejpam-5016	138	16	34	34	NUM
ejpam-5016	138	17	,	,	PUNCT
ejpam-5016	138	18	theorem	theorem	VERB
ejpam-5016	138	19	4.1	4.1	NUM
ejpam-5016	138	20	]	]	PUNCT
ejpam-5016	138	21	and	and	CCONJ
ejpam-5016	138	22	[	[	X
ejpam-5016	138	23	32	32	NUM
ejpam-5016	138	24	,	,	PUNCT
ejpam-5016	138	25	proposition	proposition	NOUN
ejpam-5016	138	26	3.2	3.2	NUM
ejpam-5016	138	27	]	]	PUNCT
ejpam-5016	138	28	.	.	PUNCT
ejpam-5016	139	1	we	we	PRON
ejpam-5016	139	2	start	start	VERB
ejpam-5016	139	3	the	the	DET
ejpam-5016	139	4	buchberger	buchberger	NOUN
ejpam-5016	139	5	algorithm	algorithm	NOUN
ejpam-5016	139	6	by	by	ADP
ejpam-5016	139	7	computing	compute	VERB
ejpam-5016	139	8	the	the	DET
ejpam-5016	139	9	s	s	ADJ
ejpam-5016	139	10	-	-	ADJ
ejpam-5016	139	11	polynomial	polynomial	ADJ
ejpam-5016	139	12	s(f	s(f	PROPN
ejpam-5016	139	13	,	,	PUNCT
ejpam-5016	139	14	g	g	NOUN
ejpam-5016	139	15	)	)	PUNCT
ejpam-5016	139	16	for	for	ADP
ejpam-5016	139	17	every	every	DET
ejpam-5016	139	18	f	f	PROPN
ejpam-5016	139	19	,	,	PUNCT
ejpam-5016	139	20	g	g	PROPN
ejpam-5016	139	21	∈	∈	PROPN
ejpam-5016	139	22	s2	s2	PROPN
ejpam-5016	139	23	.	.	PUNCT
ejpam-5016	140	1	the	the	DET
ejpam-5016	140	2	s	s	ADJ
ejpam-5016	140	3	-	-	ADJ
ejpam-5016	140	4	polynomial	polynomial	ADJ
ejpam-5016	140	5	s(f	s(f	PROPN
ejpam-5016	140	6	,	,	PUNCT
ejpam-5016	140	7	g	g	NOUN
ejpam-5016	140	8	)	)	PUNCT
ejpam-5016	140	9	is	be	AUX
ejpam-5016	140	10	defined	define	VERB
ejpam-5016	140	11	by	by	ADP
ejpam-5016	140	12	s(f	s(f	PROPN
ejpam-5016	140	13	,	,	PUNCT
ejpam-5016	140	14	g	g	NOUN
ejpam-5016	140	15	)	)	PUNCT
ejpam-5016	140	16	=	=	PUNCT
ejpam-5016	141	1	lcm(in<(f	lcm(in<(f	PROPN
ejpam-5016	141	2	)	)	PUNCT
ejpam-5016	141	3	,	,	PUNCT
ejpam-5016	141	4	in<(g	in<(g	PROPN
ejpam-5016	141	5	)	)	PUNCT
ejpam-5016	141	6	)	)	PUNCT
ejpam-5016	142	1	cf	cf	NOUN
ejpam-5016	142	2	·	·	PUNCT
ejpam-5016	142	3	in<(f	in<(f	NOUN
ejpam-5016	142	4	)	)	PUNCT
ejpam-5016	142	5	−	−	PROPN
ejpam-5016	143	1	lcm(in<(f	lcm(in<(f	PROPN
ejpam-5016	143	2	)	)	PUNCT
ejpam-5016	143	3	,	,	PUNCT
ejpam-5016	143	4	in<(g	in<(g	PROPN
ejpam-5016	143	5	)	)	PUNCT
ejpam-5016	143	6	)	)	PUNCT
ejpam-5016	143	7	cg	cg	NOUN
ejpam-5016	143	8	·	·	PUNCT
ejpam-5016	143	9	in<(g	in<(g	PROPN
ejpam-5016	143	10	)	)	PUNCT
ejpam-5016	143	11	where	where	SCONJ
ejpam-5016	143	12	in<(f	in<(f	NOUN
ejpam-5016	143	13	)	)	PUNCT
ejpam-5016	143	14	(	(	PUNCT
ejpam-5016	143	15	resp	resp	NOUN
ejpam-5016	143	16	.	.	PUNCT
ejpam-5016	144	1	in<(f	in<(f	NOUN
ejpam-5016	144	2	)	)	PUNCT
ejpam-5016	144	3	)	)	PUNCT
ejpam-5016	144	4	denotes	denote	VERB
ejpam-5016	144	5	the	the	DET
ejpam-5016	144	6	initial	initial	ADJ
ejpam-5016	144	7	monomial	monomial	NOUN
ejpam-5016	144	8	of	of	ADP
ejpam-5016	144	9	f	f	PROPN
ejpam-5016	144	10	(	(	PUNCT
ejpam-5016	144	11	resp	resp	NOUN
ejpam-5016	144	12	.	.	PUNCT
ejpam-5016	145	1	g	g	NOUN
ejpam-5016	145	2	)	)	PUNCT
ejpam-5016	146	1	with	with	ADP
ejpam-5016	146	2	respect	respect	NOUN
ejpam-5016	146	3	to	to	ADP
ejpam-5016	146	4	<	<	X
ejpam-5016	146	5	and	and	CCONJ
ejpam-5016	146	6	cf	cf	INTJ
ejpam-5016	146	7	(	(	PUNCT
ejpam-5016	146	8	resp	resp	NOUN
ejpam-5016	146	9	.	.	PUNCT
ejpam-5016	146	10	cg	cg	NOUN
ejpam-5016	146	11	)	)	PUNCT
ejpam-5016	146	12	denotes	denote	VERB
ejpam-5016	146	13	the	the	DET
ejpam-5016	146	14	coefficient	coefficient	NOUN
ejpam-5016	146	15	of	of	ADP
ejpam-5016	146	16	in<(f	in<(f	PROPN
ejpam-5016	146	17	)	)	PUNCT
ejpam-5016	146	18	(	(	PUNCT
ejpam-5016	146	19	resp	resp	NOUN
ejpam-5016	146	20	.	.	PUNCT
ejpam-5016	146	21	in<(g	in<(g	PROPN
ejpam-5016	146	22	)	)	PUNCT
ejpam-5016	146	23	)	)	PUNCT
ejpam-5016	147	1	in	in	ADP
ejpam-5016	147	2	f	f	PROPN
ejpam-5016	147	3	(	(	PUNCT
ejpam-5016	147	4	resp	resp	NOUN
ejpam-5016	147	5	.	.	PUNCT
ejpam-5016	148	1	g	g	NOUN
ejpam-5016	148	2	)	)	PUNCT
ejpam-5016	148	3	.	.	PUNCT
ejpam-5016	149	1	•	•	INTJ
ejpam-5016	149	2	if	if	SCONJ
ejpam-5016	149	3	the	the	DET
ejpam-5016	149	4	initial	initial	ADJ
ejpam-5016	149	5	monomial	monomial	NOUN
ejpam-5016	149	6	of	of	ADP
ejpam-5016	149	7	f	f	PROPN
ejpam-5016	149	8	and	and	CCONJ
ejpam-5016	149	9	g	g	PROPN
ejpam-5016	149	10	are	be	AUX
ejpam-5016	149	11	relatively	relatively	ADV
ejpam-5016	149	12	prime	prime	ADJ
ejpam-5016	149	13	then	then	ADV
ejpam-5016	149	14	s(f	s(f	PROPN
ejpam-5016	149	15	,	,	PUNCT
ejpam-5016	149	16	g	g	NOUN
ejpam-5016	149	17	)	)	PUNCT
ejpam-5016	149	18	is	be	AUX
ejpam-5016	149	19	reduced	reduce	VERB
ejpam-5016	149	20	to	to	ADP
ejpam-5016	149	21	zero	zero	NUM
ejpam-5016	149	22	.	.	PUNCT
ejpam-5016	150	1	•	•	NOUN
ejpam-5016	150	2	if	if	SCONJ
ejpam-5016	150	3	the	the	DET
ejpam-5016	150	4	greatest	great	ADJ
ejpam-5016	150	5	common	common	ADJ
ejpam-5016	150	6	divisor	divisor	NOUN
ejpam-5016	150	7	of	of	ADP
ejpam-5016	150	8	their	their	PRON
ejpam-5016	150	9	initial	initial	ADJ
ejpam-5016	150	10	monomials	monomial	NOUN
ejpam-5016	150	11	is	be	AUX
ejpam-5016	150	12	a	a	DET
ejpam-5016	150	13	monomial	monomial	NOUN
ejpam-5016	150	14	of	of	ADP
ejpam-5016	150	15	degree	degree	NOUN
ejpam-5016	150	16	two	two	NUM
ejpam-5016	151	1	then	then	ADV
ejpam-5016	151	2	f	f	PROPN
ejpam-5016	151	3	=	=	SYM
ejpam-5016	151	4	g	g	PROPN
ejpam-5016	151	5	and	and	CCONJ
ejpam-5016	151	6	s(f	s(f	PROPN
ejpam-5016	151	7	,	,	PUNCT
ejpam-5016	151	8	g	g	NOUN
ejpam-5016	151	9	)	)	PUNCT
ejpam-5016	152	1	=	=	SYM
ejpam-5016	152	2	0	0	X
ejpam-5016	152	3	.	.	NOUN
ejpam-5016	152	4	•	•	NOUN
ejpam-5016	152	5	if	if	SCONJ
ejpam-5016	152	6	the	the	DET
ejpam-5016	152	7	greatest	great	ADJ
ejpam-5016	152	8	common	common	ADJ
ejpam-5016	152	9	divisor	divisor	NOUN
ejpam-5016	152	10	of	of	ADP
ejpam-5016	152	11	their	their	PRON
ejpam-5016	152	12	initial	initial	ADJ
ejpam-5016	152	13	monomials	monomial	NOUN
ejpam-5016	152	14	is	be	AUX
ejpam-5016	152	15	a	a	DET
ejpam-5016	152	16	monomial	monomial	NOUN
ejpam-5016	152	17	of	of	ADP
ejpam-5016	152	18	degree	degree	NOUN
ejpam-5016	152	19	one	one	NUM
ejpam-5016	152	20	then	then	ADV
ejpam-5016	152	21	s(f	s(f	PROPN
ejpam-5016	152	22	,	,	PUNCT
ejpam-5016	152	23	g	g	NOUN
ejpam-5016	152	24	)	)	PUNCT
ejpam-5016	152	25	is	be	AUX
ejpam-5016	152	26	a	a	DET
ejpam-5016	152	27	binomial	binomial	NOUN
ejpam-5016	152	28	of	of	ADP
ejpam-5016	152	29	degree	degree	NOUN
ejpam-5016	152	30	three	three	NUM
ejpam-5016	152	31	.	.	PUNCT
ejpam-5016	153	1	we	we	PRON
ejpam-5016	153	2	will	will	AUX
ejpam-5016	153	3	compute	compute	VERB
ejpam-5016	153	4	s(f	s(f	PROPN
ejpam-5016	153	5	,	,	PUNCT
ejpam-5016	153	6	g	g	NOUN
ejpam-5016	153	7	)	)	PUNCT
ejpam-5016	153	8	in	in	ADP
ejpam-5016	153	9	the	the	DET
ejpam-5016	153	10	last	last	ADJ
ejpam-5016	153	11	possibility	possibility	NOUN
ejpam-5016	153	12	and	and	CCONJ
ejpam-5016	153	13	find	find	VERB
ejpam-5016	153	14	the	the	DET
ejpam-5016	153	15	condition	condition	NOUN
ejpam-5016	153	16	for	for	ADP
ejpam-5016	153	17	the	the	DET
ejpam-5016	153	18	spolynomial	spolynomial	NOUN
ejpam-5016	153	19	to	to	PART
ejpam-5016	153	20	be	be	AUX
ejpam-5016	153	21	not	not	PART
ejpam-5016	153	22	reduced	reduce	VERB
ejpam-5016	153	23	to	to	ADP
ejpam-5016	153	24	zero	zero	NUM
ejpam-5016	153	25	.	.	PUNCT
ejpam-5016	154	1	consider	consider	VERB
ejpam-5016	154	2	the	the	DET
ejpam-5016	154	3	case	case	NOUN
ejpam-5016	154	4	when	when	SCONJ
ejpam-5016	154	5	f	f	PROPN
ejpam-5016	154	6	and	and	CCONJ
ejpam-5016	154	7	g	g	PROPN
ejpam-5016	154	8	have	have	VERB
ejpam-5016	154	9	common	common	ADJ
ejpam-5016	154	10	factor	factor	NOUN
ejpam-5016	154	11	in	in	ADP
ejpam-5016	154	12	their	their	PRON
ejpam-5016	154	13	non	non	ADJ
ejpam-5016	154	14	-	-	ADJ
ejpam-5016	154	15	initial	initial	ADJ
ejpam-5016	154	16	monomials	monomial	NOUN
ejpam-5016	154	17	(	(	PUNCT
ejpam-5016	154	18	reader	reader	NOUN
ejpam-5016	154	19	may	may	AUX
ejpam-5016	154	20	see	see	VERB
ejpam-5016	154	21	[	[	X
ejpam-5016	154	22	6	6	NUM
ejpam-5016	154	23	,	,	PUNCT
ejpam-5016	154	24	remark	remark	NOUN
ejpam-5016	154	25	1	1	NUM
ejpam-5016	154	26	]	]	PUNCT
ejpam-5016	154	27	for	for	ADP
ejpam-5016	154	28	more	more	ADJ
ejpam-5016	154	29	general	general	ADJ
ejpam-5016	154	30	result	result	NOUN
ejpam-5016	154	31	)	)	PUNCT
ejpam-5016	154	32	.	.	PUNCT
ejpam-5016	155	1	so	so	ADV
ejpam-5016	155	2	,	,	PUNCT
ejpam-5016	155	3	let	let	VERB
ejpam-5016	155	4	f	f	PROPN
ejpam-5016	155	5	=	=	SYM
ejpam-5016	156	1	ab−	ab−	PROPN
ejpam-5016	156	2	pq	pq	PROPN
ejpam-5016	156	3	and	and	CCONJ
ejpam-5016	156	4	g	g	PROPN
ejpam-5016	156	5	=	=	SYM
ejpam-5016	156	6	ac−	ac−	PROPN
ejpam-5016	156	7	pr	pr	NOUN
ejpam-5016	156	8	with	with	ADP
ejpam-5016	156	9	initial	initial	ADJ
ejpam-5016	156	10	monomials	monomial	NOUN
ejpam-5016	156	11	ab	ab	PROPN
ejpam-5016	156	12	and	and	CCONJ
ejpam-5016	156	13	ac	ac	PROPN
ejpam-5016	156	14	,	,	PUNCT
ejpam-5016	156	15	respectively	respectively	ADV
ejpam-5016	156	16	.	.	PUNCT
ejpam-5016	157	1	note	note	VERB
ejpam-5016	157	2	that	that	SCONJ
ejpam-5016	157	3	s(f	s(f	PROPN
ejpam-5016	157	4	,	,	PUNCT
ejpam-5016	157	5	g	g	NOUN
ejpam-5016	157	6	)	)	PUNCT
ejpam-5016	157	7	=	=	SYM
ejpam-5016	157	8	p(br	p(br	PROPN
ejpam-5016	157	9	−	−	PROPN
ejpam-5016	157	10	cq	cq	NOUN
ejpam-5016	157	11	)	)	PUNCT
ejpam-5016	157	12	and	and	CCONJ
ejpam-5016	157	13	the	the	DET
ejpam-5016	157	14	interval	interval	NOUN
ejpam-5016	157	15	determined	determine	VERB
ejpam-5016	157	16	by	by	ADP
ejpam-5016	157	17	{	{	PUNCT
ejpam-5016	157	18	b	b	NOUN
ejpam-5016	157	19	,	,	PUNCT
ejpam-5016	157	20	r	r	NOUN
ejpam-5016	157	21	}	}	PUNCT
ejpam-5016	157	22	is	be	AUX
ejpam-5016	157	23	an	an	DET
ejpam-5016	157	24	inner	inner	ADJ
ejpam-5016	157	25	interval	interval	NOUN
ejpam-5016	157	26	.	.	PUNCT
ejpam-5016	158	1	we	we	PRON
ejpam-5016	158	2	conclude	conclude	VERB
ejpam-5016	158	3	that	that	SCONJ
ejpam-5016	158	4	s(f	s(f	PROPN
ejpam-5016	158	5	,	,	PUNCT
ejpam-5016	158	6	g	g	NOUN
ejpam-5016	158	7	)	)	PUNCT
ejpam-5016	158	8	is	be	AUX
ejpam-5016	158	9	reduced	reduce	VERB
ejpam-5016	158	10	to	to	ADP
ejpam-5016	158	11	zero	zero	NUM
ejpam-5016	158	12	.	.	PUNCT
ejpam-5016	159	1	now	now	ADV
ejpam-5016	159	2	we	we	PRON
ejpam-5016	159	3	assume	assume	VERB
ejpam-5016	159	4	that	that	SCONJ
ejpam-5016	159	5	f	f	PROPN
ejpam-5016	159	6	and	and	CCONJ
ejpam-5016	159	7	g	g	PROPN
ejpam-5016	159	8	have	have	VERB
ejpam-5016	159	9	no	no	DET
ejpam-5016	159	10	common	common	ADJ
ejpam-5016	159	11	factor	factor	NOUN
ejpam-5016	159	12	in	in	ADP
ejpam-5016	159	13	their	their	PRON
ejpam-5016	159	14	non	non	ADJ
ejpam-5016	159	15	-	-	ADJ
ejpam-5016	159	16	initial	initial	ADJ
ejpam-5016	159	17	monomial	monomial	NOUN
ejpam-5016	159	18	.	.	PUNCT
ejpam-5016	160	1	let	let	VERB
ejpam-5016	160	2	f	f	PROPN
ejpam-5016	160	3	and	and	CCONJ
ejpam-5016	160	4	g	g	PROPN
ejpam-5016	160	5	be	be	AUX
ejpam-5016	160	6	the	the	DET
ejpam-5016	160	7	inner	inner	ADJ
ejpam-5016	160	8	2	2	NUM
ejpam-5016	160	9	-	-	PUNCT
ejpam-5016	160	10	minors	minor	NOUN
ejpam-5016	160	11	associated	associate	VERB
ejpam-5016	160	12	to	to	ADP
ejpam-5016	160	13	inner	inner	ADJ
ejpam-5016	160	14	intervals	interval	NOUN
ejpam-5016	160	15	[	[	X
ejpam-5016	160	16	a	a	X
ejpam-5016	160	17	,	,	PUNCT
ejpam-5016	160	18	b	b	NOUN
ejpam-5016	160	19	]	]	PUNCT
ejpam-5016	160	20	and	and	CCONJ
ejpam-5016	161	1	[	[	X
ejpam-5016	161	2	c	c	X
ejpam-5016	161	3	,	,	PUNCT
ejpam-5016	161	4	d	d	X
ejpam-5016	161	5	]	]	X
ejpam-5016	161	6	,	,	PUNCT
ejpam-5016	161	7	respectively	respectively	ADV
ejpam-5016	161	8	.	.	PUNCT
ejpam-5016	162	1	without	without	ADP
ejpam-5016	162	2	losing	lose	VERB
ejpam-5016	162	3	of	of	ADP
ejpam-5016	162	4	generality	generality	NOUN
ejpam-5016	162	5	,	,	PUNCT
ejpam-5016	162	6	assume	assume	VERB
ejpam-5016	162	7	that	that	SCONJ
ejpam-5016	162	8	a	a	DET
ejpam-5016	162	9	≤p	≤p	PROPN
ejpam-5016	162	10	c.	c.	NOUN
ejpam-5016	162	11	write	write	PROPN
ejpam-5016	162	12	f	f	PROPN
ejpam-5016	162	13	=	=	SYM
ejpam-5016	162	14	ab	ab	PROPN
ejpam-5016	162	15	−	−	PROPN
ejpam-5016	162	16	pq	pq	PROPN
ejpam-5016	162	17	and	and	CCONJ
ejpam-5016	162	18	g	g	NOUN
ejpam-5016	162	19	=	=	PROPN
ejpam-5016	162	20	cd	cd	PROPN
ejpam-5016	163	1	−	−	NOUN
ejpam-5016	163	2	rs	rs	NOUN
ejpam-5016	163	3	with	with	ADP
ejpam-5016	163	4	p	p	NOUN
ejpam-5016	163	5	<	<	X
ejpam-5016	163	6	p	p	X
ejpam-5016	163	7	q	q	NOUN
ejpam-5016	164	1	and	and	CCONJ
ejpam-5016	164	2	r	r	NOUN
ejpam-5016	164	3	<	<	X
ejpam-5016	164	4	p	p	X
ejpam-5016	164	5	s.	s.	PROPN
ejpam-5016	164	6	we	we	PRON
ejpam-5016	164	7	conclude	conclude	VERB
ejpam-5016	164	8	that	that	SCONJ
ejpam-5016	164	9	a	a	DET
ejpam-5016	164	10	<	<	X
ejpam-5016	164	11	p	p	X
ejpam-5016	164	12	d.	d.	NOUN
ejpam-5016	164	13	we	we	PRON
ejpam-5016	164	14	consider	consider	VERB
ejpam-5016	164	15	three	three	NUM
ejpam-5016	164	16	cases	case	NOUN
ejpam-5016	164	17	.	.	PUNCT
ejpam-5016	165	1	(	(	PUNCT
ejpam-5016	165	2	i	i	NOUN
ejpam-5016	165	3	)	)	PUNCT
ejpam-5016	165	4	if	if	SCONJ
ejpam-5016	165	5	a	a	PRON
ejpam-5016	165	6	=	=	X
ejpam-5016	165	7	c	c	NOUN
ejpam-5016	165	8	then	then	ADV
ejpam-5016	165	9	s(f	s(f	PROPN
ejpam-5016	165	10	,	,	PUNCT
ejpam-5016	165	11	g	g	NOUN
ejpam-5016	165	12	)	)	PUNCT
ejpam-5016	165	13	=	=	SYM
ejpam-5016	166	1	brs−	brs−	PROPN
ejpam-5016	166	2	dpq	dpq	PROPN
ejpam-5016	166	3	.	.	PUNCT
ejpam-5016	167	1	consider	consider	VERB
ejpam-5016	167	2	the	the	DET
ejpam-5016	167	3	location	location	NOUN
ejpam-5016	167	4	of	of	ADP
ejpam-5016	167	5	vertex	vertex	NOUN
ejpam-5016	167	6	d	d	NOUN
ejpam-5016	167	7	,	,	PUNCT
ejpam-5016	167	8	there	there	PRON
ejpam-5016	167	9	are	be	VERB
ejpam-5016	167	10	4	4	NUM
ejpam-5016	167	11	cases	case	NOUN
ejpam-5016	167	12	to	to	PART
ejpam-5016	167	13	discuss	discuss	VERB
ejpam-5016	167	14	(	(	PUNCT
ejpam-5016	167	15	see	see	VERB
ejpam-5016	167	16	the	the	DET
ejpam-5016	167	17	figure	figure	NOUN
ejpam-5016	167	18	below	below	ADP
ejpam-5016	167	19	)	)	PUNCT
ejpam-5016	167	20	.	.	PUNCT
ejpam-5016	168	1	a	a	DET
ejpam-5016	168	2	p	p	NOUN
ejpam-5016	168	3	q	q	NOUN
ejpam-5016	168	4	b	b	NOUN
ejpam-5016	168	5	r	r	NOUN
ejpam-5016	168	6	s	s	PROPN
ejpam-5016	168	7	d	d	NOUN
ejpam-5016	168	8	a	a	DET
ejpam-5016	168	9	pr	pr	NOUN
ejpam-5016	168	10	q	q	PROPN
ejpam-5016	168	11	b	b	PROPN
ejpam-5016	168	12	ds	ds	ADP
ejpam-5016	168	13	a	a	DET
ejpam-5016	168	14	p	p	NOUN
ejpam-5016	168	15	r	r	NOUN
ejpam-5016	168	16	q	q	NOUN
ejpam-5016	168	17	b	b	PROPN
ejpam-5016	168	18	s	s	PROPN
ejpam-5016	168	19	d	d	NOUN
ejpam-5016	168	20	a	a	DET
ejpam-5016	168	21	p	p	X
ejpam-5016	168	22	q	q	PROPN
ejpam-5016	168	23	b	b	PROPN
ejpam-5016	168	24	d	d	NOUN
ejpam-5016	168	25	r	r	NOUN
ejpam-5016	168	26	s	s	NOUN
ejpam-5016	168	27	figure	figure	NOUN
ejpam-5016	168	28	2	2	NUM
ejpam-5016	168	29	:	:	PUNCT
ejpam-5016	168	30	case	case	VERB
ejpam-5016	168	31	a	a	DET
ejpam-5016	168	32	=	=	X
ejpam-5016	168	33	c.	c.	PROPN
ejpam-5016	168	34	y.	y.	PROPN
ejpam-5016	168	35	y.	y.	PROPN
ejpam-5016	168	36	hamonangan	hamonangan	PROPN
ejpam-5016	168	37	,	,	PUNCT
ejpam-5016	168	38	i.	i.	PROPN
ejpam-5016	168	39	muchtadi	muchtadi	PROPN
ejpam-5016	168	40	-	-	PUNCT
ejpam-5016	168	41	alamsyah	alamsyah	NOUN
ejpam-5016	168	42	/	/	SYM
ejpam-5016	168	43	eur	eur	PROPN
ejpam-5016	168	44	.	.	PUNCT
ejpam-5016	169	1	j.	j.	PROPN
ejpam-5016	169	2	pure	pure	PROPN
ejpam-5016	169	3	appl	appl	PROPN
ejpam-5016	169	4	.	.	PROPN
ejpam-5016	169	5	math	math	PROPN
ejpam-5016	169	6	,	,	PUNCT
ejpam-5016	169	7	17	17	NUM
ejpam-5016	169	8	(	(	PUNCT
ejpam-5016	169	9	4	4	NUM
ejpam-5016	169	10	)	)	PUNCT
ejpam-5016	169	11	(	(	PUNCT
ejpam-5016	169	12	2024	2024	NUM
ejpam-5016	169	13	)	)	PUNCT
ejpam-5016	169	14	,	,	PUNCT
ejpam-5016	169	15	2621	2621	NUM
ejpam-5016	169	16	-	-	SYM
ejpam-5016	169	17	2650	2650	NUM
ejpam-5016	169	18	2626	2626	NUM
ejpam-5016	169	19	for	for	ADP
ejpam-5016	169	20	the	the	DET
ejpam-5016	169	21	first	first	ADJ
ejpam-5016	169	22	three	three	NUM
ejpam-5016	169	23	cases	case	NOUN
ejpam-5016	169	24	,	,	PUNCT
ejpam-5016	169	25	the	the	DET
ejpam-5016	169	26	interval	interval	NOUN
ejpam-5016	169	27	determined	determine	VERB
ejpam-5016	169	28	by	by	ADP
ejpam-5016	169	29	{	{	PUNCT
ejpam-5016	169	30	d	d	NOUN
ejpam-5016	169	31	,	,	PUNCT
ejpam-5016	169	32	q	q	ADJ
ejpam-5016	169	33	}	}	PUNCT
ejpam-5016	169	34	is	be	AUX
ejpam-5016	169	35	an	an	DET
ejpam-5016	169	36	inner	inner	ADJ
ejpam-5016	169	37	interval	interval	NOUN
ejpam-5016	169	38	.	.	PUNCT
ejpam-5016	170	1	since	since	SCONJ
ejpam-5016	170	2	s	s	PROPN
ejpam-5016	170	3	,	,	PUNCT
ejpam-5016	170	4	d	d	X
ejpam-5016	170	5	are	be	AUX
ejpam-5016	170	6	in	in	ADP
ejpam-5016	170	7	horizontal	horizontal	ADJ
ejpam-5016	170	8	position	position	NOUN
ejpam-5016	170	9	and	and	CCONJ
ejpam-5016	170	10	s	s	NOUN
ejpam-5016	170	11	,	,	PUNCT
ejpam-5016	170	12	q	q	X
ejpam-5016	170	13	are	be	AUX
ejpam-5016	170	14	in	in	ADP
ejpam-5016	170	15	vertical	vertical	ADJ
ejpam-5016	170	16	position	position	NOUN
ejpam-5016	170	17	,	,	PUNCT
ejpam-5016	170	18	then	then	ADV
ejpam-5016	170	19	there	there	PRON
ejpam-5016	170	20	is	be	VERB
ejpam-5016	170	21	a	a	DET
ejpam-5016	170	22	vertex	vertex	NOUN
ejpam-5016	170	23	y	y	NOUN
ejpam-5016	170	24	such	such	ADJ
ejpam-5016	170	25	that	that	SCONJ
ejpam-5016	170	26	the	the	DET
ejpam-5016	170	27	inner	inner	ADJ
ejpam-5016	170	28	interval	interval	NOUN
ejpam-5016	170	29	determined	determine	VERB
ejpam-5016	170	30	by	by	ADP
ejpam-5016	170	31	{	{	PUNCT
ejpam-5016	170	32	q	q	NOUN
ejpam-5016	170	33	,	,	PUNCT
ejpam-5016	170	34	d	d	NOUN
ejpam-5016	170	35	}	}	PUNCT
ejpam-5016	170	36	is	be	AUX
ejpam-5016	170	37	the	the	DET
ejpam-5016	170	38	inner	inner	ADJ
ejpam-5016	170	39	interval	interval	NOUN
ejpam-5016	170	40	determined	determine	VERB
ejpam-5016	170	41	by	by	ADP
ejpam-5016	170	42	{	{	PUNCT
ejpam-5016	170	43	s	s	PROPN
ejpam-5016	170	44	,	,	PUNCT
ejpam-5016	170	45	y	y	NOUN
ejpam-5016	170	46	}	}	PUNCT
ejpam-5016	170	47	.	.	PUNCT
ejpam-5016	171	1	by	by	ADP
ejpam-5016	171	2	checking	check	VERB
ejpam-5016	171	3	all	all	DET
ejpam-5016	171	4	possible	possible	ADJ
ejpam-5016	171	5	configurations	configuration	NOUN
ejpam-5016	171	6	(	(	PUNCT
ejpam-5016	171	7	see	see	VERB
ejpam-5016	171	8	the	the	DET
ejpam-5016	171	9	figure	figure	NOUN
ejpam-5016	171	10	below	below	ADV
ejpam-5016	171	11	)	)	PUNCT
ejpam-5016	171	12	,	,	PUNCT
ejpam-5016	171	13	we	we	PRON
ejpam-5016	171	14	see	see	VERB
ejpam-5016	171	15	that	that	SCONJ
ejpam-5016	171	16	the	the	DET
ejpam-5016	171	17	inner	inner	ADJ
ejpam-5016	171	18	interval	interval	NOUN
ejpam-5016	171	19	determined	determine	VERB
ejpam-5016	171	20	by	by	ADP
ejpam-5016	171	21	{	{	PUNCT
ejpam-5016	171	22	b	b	NOUN
ejpam-5016	171	23	,	,	PUNCT
ejpam-5016	171	24	r	r	NOUN
ejpam-5016	171	25	}	}	PUNCT
ejpam-5016	171	26	is	be	AUX
ejpam-5016	171	27	the	the	DET
ejpam-5016	171	28	inner	inner	ADJ
ejpam-5016	171	29	interval	interval	NOUN
ejpam-5016	171	30	determined	determine	VERB
ejpam-5016	171	31	by	by	ADP
ejpam-5016	171	32	{	{	PUNCT
ejpam-5016	171	33	p	p	X
ejpam-5016	171	34	,	,	PUNCT
ejpam-5016	171	35	y	y	PROPN
ejpam-5016	171	36	}	}	PUNCT
ejpam-5016	171	37	.	.	PUNCT
ejpam-5016	172	1	a	a	DET
ejpam-5016	172	2	p	p	NOUN
ejpam-5016	172	3	q	q	NOUN
ejpam-5016	172	4	b	b	NOUN
ejpam-5016	172	5	r	r	NOUN
ejpam-5016	172	6	s	s	PROPN
ejpam-5016	172	7	d	d	NOUN
ejpam-5016	172	8	a	a	DET
ejpam-5016	172	9	pr	pr	NOUN
ejpam-5016	172	10	q	q	PROPN
ejpam-5016	172	11	b	b	PROPN
ejpam-5016	172	12	ds	ds	ADP
ejpam-5016	172	13	a	a	DET
ejpam-5016	172	14	p	p	NOUN
ejpam-5016	172	15	r	r	NOUN
ejpam-5016	172	16	q	q	NOUN
ejpam-5016	172	17	b	b	PROPN
ejpam-5016	172	18	s	s	PROPN
ejpam-5016	172	19	d	d	X
ejpam-5016	172	20	y	y	PROPN
ejpam-5016	172	21	y	y	PROPN
ejpam-5016	172	22	y	y	PROPN
ejpam-5016	172	23	figure	figure	VERB
ejpam-5016	172	24	3	3	NUM
ejpam-5016	172	25	:	:	PUNCT
ejpam-5016	172	26	the	the	DET
ejpam-5016	172	27	first	first	ADJ
ejpam-5016	172	28	three	three	NUM
ejpam-5016	172	29	cases	case	NOUN
ejpam-5016	172	30	.	.	PUNCT
ejpam-5016	173	1	note	note	VERB
ejpam-5016	173	2	that	that	SCONJ
ejpam-5016	173	3	s(f	s(f	PROPN
ejpam-5016	173	4	,	,	PUNCT
ejpam-5016	173	5	g	g	NOUN
ejpam-5016	173	6	)	)	PUNCT
ejpam-5016	173	7	=	=	SYM
ejpam-5016	174	1	brs−	brs−	PROPN
ejpam-5016	174	2	dpq	dpq	ADJ
ejpam-5016	174	3	=	=	PUNCT
ejpam-5016	174	4	(	(	PUNCT
ejpam-5016	174	5	br	br	NOUN
ejpam-5016	174	6	−	−	PROPN
ejpam-5016	174	7	py)s+	py)s+	ADV
ejpam-5016	174	8	p(ys−	p(ys−	ADJ
ejpam-5016	174	9	dq	dq	NOUN
ejpam-5016	174	10	)	)	PUNCT
ejpam-5016	174	11	.	.	PUNCT
ejpam-5016	175	1	therefore	therefore	ADV
ejpam-5016	175	2	,	,	PUNCT
ejpam-5016	175	3	s(f	s(f	PROPN
ejpam-5016	175	4	,	,	PUNCT
ejpam-5016	175	5	g	g	NOUN
ejpam-5016	175	6	)	)	PUNCT
ejpam-5016	175	7	is	be	AUX
ejpam-5016	175	8	reduced	reduce	VERB
ejpam-5016	175	9	to	to	ADP
ejpam-5016	175	10	zero	zero	NUM
ejpam-5016	175	11	.	.	PUNCT
ejpam-5016	176	1	a	a	DET
ejpam-5016	176	2	p	p	NOUN
ejpam-5016	176	3	r	r	NOUN
ejpam-5016	176	4	q	q	NOUN
ejpam-5016	176	5	b	b	PROPN
ejpam-5016	176	6	d	d	X
ejpam-5016	176	7	s	s	PART
ejpam-5016	176	8	y	y	NOUN
ejpam-5016	176	9	figure	figure	NOUN
ejpam-5016	176	10	4	4	NUM
ejpam-5016	176	11	:	:	PUNCT
ejpam-5016	176	12	the	the	DET
ejpam-5016	176	13	fourth	fourth	ADJ
ejpam-5016	176	14	case	case	NOUN
ejpam-5016	176	15	.	.	PUNCT
ejpam-5016	177	1	for	for	ADP
ejpam-5016	177	2	the	the	DET
ejpam-5016	177	3	fourth	fourth	ADJ
ejpam-5016	177	4	case	case	NOUN
ejpam-5016	177	5	,	,	PUNCT
ejpam-5016	177	6	the	the	DET
ejpam-5016	177	7	interval	interval	NOUN
ejpam-5016	177	8	determined	determine	VERB
ejpam-5016	177	9	by	by	ADP
ejpam-5016	177	10	{	{	PUNCT
ejpam-5016	177	11	d	d	NOUN
ejpam-5016	177	12	,	,	PUNCT
ejpam-5016	177	13	p	p	PRON
ejpam-5016	177	14	}	}	PUNCT
ejpam-5016	177	15	is	be	AUX
ejpam-5016	177	16	an	an	DET
ejpam-5016	177	17	inner	inner	ADJ
ejpam-5016	177	18	interval	interval	NOUN
ejpam-5016	177	19	(	(	PUNCT
ejpam-5016	177	20	see	see	VERB
ejpam-5016	177	21	the	the	DET
ejpam-5016	177	22	figure	figure	NOUN
ejpam-5016	177	23	above	above	ADP
ejpam-5016	177	24	)	)	PUNCT
ejpam-5016	177	25	.	.	PUNCT
ejpam-5016	178	1	similarly	similarly	ADV
ejpam-5016	178	2	,	,	PUNCT
ejpam-5016	178	3	there	there	PRON
ejpam-5016	178	4	is	be	VERB
ejpam-5016	178	5	a	a	DET
ejpam-5016	178	6	vertex	vertex	NOUN
ejpam-5016	178	7	y	y	NOUN
ejpam-5016	178	8	such	such	ADJ
ejpam-5016	178	9	that	that	SCONJ
ejpam-5016	178	10	the	the	DET
ejpam-5016	178	11	inner	inner	ADJ
ejpam-5016	178	12	interval	interval	NOUN
ejpam-5016	178	13	determined	determine	VERB
ejpam-5016	178	14	by	by	ADP
ejpam-5016	178	15	{	{	PUNCT
ejpam-5016	178	16	p	p	X
ejpam-5016	178	17	,	,	PUNCT
ejpam-5016	178	18	d	d	NOUN
ejpam-5016	178	19	}	}	PUNCT
ejpam-5016	178	20	is	be	AUX
ejpam-5016	178	21	the	the	DET
ejpam-5016	178	22	inner	inner	ADJ
ejpam-5016	178	23	interval	interval	NOUN
ejpam-5016	178	24	determine	determine	NOUN
ejpam-5016	178	25	by	by	ADP
ejpam-5016	178	26	{	{	PUNCT
ejpam-5016	178	27	r	r	NOUN
ejpam-5016	178	28	,	,	PUNCT
ejpam-5016	178	29	y	y	NOUN
ejpam-5016	178	30	}	}	PUNCT
ejpam-5016	178	31	.	.	PUNCT
ejpam-5016	179	1	note	note	VERB
ejpam-5016	179	2	that	that	SCONJ
ejpam-5016	179	3	s(f	s(f	PROPN
ejpam-5016	179	4	,	,	PUNCT
ejpam-5016	179	5	g	g	NOUN
ejpam-5016	179	6	)	)	PUNCT
ejpam-5016	179	7	=	=	SYM
ejpam-5016	180	1	brs−	brs−	PROPN
ejpam-5016	180	2	dpq	dpq	ADJ
ejpam-5016	180	3	=	=	PUNCT
ejpam-5016	180	4	(	(	PUNCT
ejpam-5016	180	5	bs−	bs−	PUNCT
ejpam-5016	180	6	qy)r	qy)r	PROPN
ejpam-5016	180	7	+	+	NUM
ejpam-5016	180	8	q(ry	q(ry	PROPN
ejpam-5016	180	9	−	−	PROPN
ejpam-5016	180	10	dp	dp	NOUN
ejpam-5016	180	11	)	)	PUNCT
ejpam-5016	180	12	.	.	PUNCT
ejpam-5016	181	1	therefore	therefore	ADV
ejpam-5016	181	2	,	,	PUNCT
ejpam-5016	181	3	s(f	s(f	PROPN
ejpam-5016	181	4	,	,	PUNCT
ejpam-5016	181	5	g	g	NOUN
ejpam-5016	181	6	)	)	PUNCT
ejpam-5016	181	7	is	be	AUX
ejpam-5016	181	8	reduced	reduce	VERB
ejpam-5016	181	9	to	to	ADP
ejpam-5016	181	10	zero	zero	NUM
ejpam-5016	181	11	.	.	PUNCT
ejpam-5016	182	1	(	(	PUNCT
ejpam-5016	182	2	ii	ii	NOUN
ejpam-5016	182	3	)	)	PUNCT
ejpam-5016	182	4	if	if	SCONJ
ejpam-5016	182	5	a	a	DET
ejpam-5016	182	6	̸=	̸=	PROPN
ejpam-5016	182	7	c	c	PROPN
ejpam-5016	182	8	and	and	CCONJ
ejpam-5016	182	9	b	b	X
ejpam-5016	182	10	=	=	SYM
ejpam-5016	182	11	d	d	PROPN
ejpam-5016	182	12	then	then	ADV
ejpam-5016	182	13	s(f	s(f	PROPN
ejpam-5016	182	14	,	,	PUNCT
ejpam-5016	182	15	g	g	NOUN
ejpam-5016	182	16	)	)	PUNCT
ejpam-5016	182	17	=	=	SYM
ejpam-5016	182	18	ars−	ars−	PROPN
ejpam-5016	182	19	cpq	cpq	PROPN
ejpam-5016	182	20	a	a	DET
ejpam-5016	182	21	p	p	X
ejpam-5016	182	22	q	q	PROPN
ejpam-5016	182	23	b	b	PROPN
ejpam-5016	182	24	y	y	NOUN
ejpam-5016	182	25	r	r	NOUN
ejpam-5016	182	26	s	s	PROPN
ejpam-5016	182	27	c	c	NOUN
ejpam-5016	182	28	figure	figure	NOUN
ejpam-5016	182	29	5	5	NUM
ejpam-5016	182	30	:	:	PUNCT
ejpam-5016	182	31	case	case	NOUN
ejpam-5016	182	32	a	a	DET
ejpam-5016	182	33	̸=	̸=	PROPN
ejpam-5016	182	34	c	c	PROPN
ejpam-5016	182	35	and	and	CCONJ
ejpam-5016	182	36	b	b	X
ejpam-5016	182	37	=	=	PROPN
ejpam-5016	182	38	d.	d.	PROPN
ejpam-5016	182	39	note	note	VERB
ejpam-5016	182	40	that	that	SCONJ
ejpam-5016	182	41	there	there	PRON
ejpam-5016	182	42	exists	exist	VERB
ejpam-5016	182	43	a	a	DET
ejpam-5016	182	44	vertex	vertex	NOUN
ejpam-5016	182	45	y	y	PRON
ejpam-5016	182	46	such	such	ADJ
ejpam-5016	182	47	that	that	DET
ejpam-5016	182	48	q	q	NOUN
ejpam-5016	182	49	,	,	PUNCT
ejpam-5016	182	50	c	c	PROPN
ejpam-5016	182	51	are	be	AUX
ejpam-5016	182	52	the	the	DET
ejpam-5016	182	53	antidiagonal	antidiagonal	ADJ
ejpam-5016	182	54	corners	corner	NOUN
ejpam-5016	182	55	of	of	ADP
ejpam-5016	182	56	the	the	DET
ejpam-5016	182	57	inner	inner	ADJ
ejpam-5016	182	58	interval	interval	NOUN
ejpam-5016	182	59	determined	determine	VERB
ejpam-5016	182	60	by	by	ADP
ejpam-5016	182	61	{	{	PUNCT
ejpam-5016	182	62	q	q	INTJ
ejpam-5016	182	63	,	,	PUNCT
ejpam-5016	182	64	c	c	NOUN
ejpam-5016	182	65	}	}	PUNCT
ejpam-5016	182	66	.	.	PUNCT
ejpam-5016	183	1	since	since	SCONJ
ejpam-5016	183	2	s(f	s(f	PROPN
ejpam-5016	183	3	,	,	PUNCT
ejpam-5016	183	4	g	g	NOUN
ejpam-5016	183	5	)	)	PUNCT
ejpam-5016	183	6	=	=	SYM
ejpam-5016	183	7	(	(	PUNCT
ejpam-5016	183	8	ar	ar	NOUN
ejpam-5016	183	9	−	−	PROPN
ejpam-5016	183	10	py)s+	py)s+	PROPN
ejpam-5016	183	11	p(ys−	p(ys−	NUM
ejpam-5016	183	12	cq	cq	NOUN
ejpam-5016	183	13	)	)	PUNCT
ejpam-5016	183	14	we	we	PRON
ejpam-5016	183	15	conclude	conclude	VERB
ejpam-5016	183	16	that	that	SCONJ
ejpam-5016	183	17	s(f	s(f	PROPN
ejpam-5016	183	18	,	,	PUNCT
ejpam-5016	183	19	g	g	NOUN
ejpam-5016	183	20	)	)	PUNCT
ejpam-5016	183	21	is	be	AUX
ejpam-5016	183	22	reduced	reduce	VERB
ejpam-5016	183	23	to	to	ADP
ejpam-5016	183	24	zero	zero	NUM
ejpam-5016	183	25	.	.	PUNCT
ejpam-5016	184	1	y.	y.	PROPN
ejpam-5016	184	2	y.	y.	PROPN
ejpam-5016	184	3	hamonangan	hamonangan	PROPN
ejpam-5016	184	4	,	,	PUNCT
ejpam-5016	184	5	i.	i.	PROPN
ejpam-5016	184	6	muchtadi	muchtadi	PROPN
ejpam-5016	184	7	-	-	PUNCT
ejpam-5016	184	8	alamsyah	alamsyah	NOUN
ejpam-5016	184	9	/	/	SYM
ejpam-5016	184	10	eur	eur	PROPN
ejpam-5016	184	11	.	.	PUNCT
ejpam-5016	185	1	j.	j.	PROPN
ejpam-5016	185	2	pure	pure	PROPN
ejpam-5016	185	3	appl	appl	PROPN
ejpam-5016	185	4	.	.	PROPN
ejpam-5016	185	5	math	math	PROPN
ejpam-5016	185	6	,	,	PUNCT
ejpam-5016	185	7	17	17	NUM
ejpam-5016	185	8	(	(	PUNCT
ejpam-5016	185	9	4	4	NUM
ejpam-5016	185	10	)	)	PUNCT
ejpam-5016	185	11	(	(	PUNCT
ejpam-5016	185	12	2024	2024	NUM
ejpam-5016	185	13	)	)	PUNCT
ejpam-5016	185	14	,	,	PUNCT
ejpam-5016	185	15	2621	2621	NUM
ejpam-5016	185	16	-	-	SYM
ejpam-5016	185	17	2650	2650	NUM
ejpam-5016	185	18	2627	2627	NUM
ejpam-5016	185	19	a	a	DET
ejpam-5016	185	20	p	p	X
ejpam-5016	185	21	q	q	NOUN
ejpam-5016	185	22	b	b	NOUN
ejpam-5016	185	23	r	r	NOUN
ejpam-5016	185	24	s	s	PROPN
ejpam-5016	185	25	d	d	X
ejpam-5016	185	26	y	y	PROPN
ejpam-5016	185	27	z	z	NOUN
ejpam-5016	185	28	figure	figure	NOUN
ejpam-5016	185	29	6	6	NUM
ejpam-5016	185	30	:	:	PUNCT
ejpam-5016	185	31	case	case	NOUN
ejpam-5016	185	32	a	a	DET
ejpam-5016	185	33	̸=	̸=	PROPN
ejpam-5016	185	34	c	c	PROPN
ejpam-5016	185	35	and	and	CCONJ
ejpam-5016	185	36	b	b	PROPN
ejpam-5016	185	37	̸=	̸=	PROPN
ejpam-5016	185	38	d.	d.	PROPN
ejpam-5016	185	39	(	(	PUNCT
ejpam-5016	185	40	iii	iii	PROPN
ejpam-5016	185	41	)	)	PUNCT
ejpam-5016	185	42	if	if	SCONJ
ejpam-5016	185	43	a	a	DET
ejpam-5016	185	44	̸=	̸=	PROPN
ejpam-5016	185	45	c	c	PROPN
ejpam-5016	185	46	and	and	CCONJ
ejpam-5016	185	47	b	b	PROPN
ejpam-5016	185	48	̸=	̸=	PROPN
ejpam-5016	185	49	d	d	PROPN
ejpam-5016	185	50	then	then	ADV
ejpam-5016	185	51	b	b	X
ejpam-5016	185	52	=	=	SYM
ejpam-5016	185	53	c	c	PROPN
ejpam-5016	185	54	and	and	CCONJ
ejpam-5016	185	55	s(f	s(f	PROPN
ejpam-5016	185	56	,	,	PUNCT
ejpam-5016	185	57	g	g	NOUN
ejpam-5016	185	58	)	)	PUNCT
ejpam-5016	185	59	=	=	PROPN
ejpam-5016	185	60	ars−	ars−	PROPN
ejpam-5016	185	61	dpq	dpq	PROPN
ejpam-5016	185	62	.	.	PUNCT
ejpam-5016	186	1	note	note	NOUN
ejpam-5016	186	2	that	that	DET
ejpam-5016	186	3	ars	ar	NOUN
ejpam-5016	186	4	is	be	AUX
ejpam-5016	186	5	the	the	DET
ejpam-5016	186	6	initial	initial	ADJ
ejpam-5016	186	7	monomial	monomial	NOUN
ejpam-5016	186	8	of	of	ADP
ejpam-5016	186	9	s(f	s(f	PROPN
ejpam-5016	186	10	,	,	PUNCT
ejpam-5016	186	11	g	g	NOUN
ejpam-5016	186	12	)	)	PUNCT
ejpam-5016	186	13	and	and	CCONJ
ejpam-5016	186	14	this	this	DET
ejpam-5016	186	15	monomial	monomial	NOUN
ejpam-5016	186	16	can	can	AUX
ejpam-5016	186	17	only	only	ADV
ejpam-5016	186	18	be	be	AUX
ejpam-5016	186	19	divided	divide	VERB
ejpam-5016	186	20	by	by	ADP
ejpam-5016	186	21	initial	initial	ADJ
ejpam-5016	186	22	monomials	monomial	NOUN
ejpam-5016	186	23	ar	ar	NOUN
ejpam-5016	186	24	or	or	CCONJ
ejpam-5016	186	25	as	as	ADP
ejpam-5016	186	26	from	from	ADP
ejpam-5016	186	27	an	an	DET
ejpam-5016	186	28	inner	inner	ADJ
ejpam-5016	186	29	2	2	NUM
ejpam-5016	186	30	-	-	PUNCT
ejpam-5016	186	31	minor	minor	ADJ
ejpam-5016	186	32	.	.	PUNCT
ejpam-5016	187	1	this	this	PRON
ejpam-5016	187	2	is	be	AUX
ejpam-5016	187	3	the	the	DET
ejpam-5016	187	4	only	only	ADJ
ejpam-5016	187	5	case	case	NOUN
ejpam-5016	187	6	when	when	SCONJ
ejpam-5016	187	7	[	[	X
ejpam-5016	187	8	a	a	X
ejpam-5016	187	9	,	,	PUNCT
ejpam-5016	187	10	r	r	NOUN
ejpam-5016	187	11	]	]	PUNCT
ejpam-5016	187	12	or	or	CCONJ
ejpam-5016	187	13	[	[	X
ejpam-5016	187	14	a	a	X
ejpam-5016	187	15	,	,	PUNCT
ejpam-5016	187	16	s	s	AUX
ejpam-5016	187	17	]	]	X
ejpam-5016	187	18	is	be	AUX
ejpam-5016	187	19	an	an	DET
ejpam-5016	187	20	inner	inner	ADJ
ejpam-5016	187	21	interval	interval	NOUN
ejpam-5016	187	22	.	.	PUNCT
ejpam-5016	188	1	if	if	SCONJ
ejpam-5016	188	2	[	[	X
ejpam-5016	188	3	a	a	X
ejpam-5016	188	4	,	,	PUNCT
ejpam-5016	188	5	r	r	NOUN
ejpam-5016	188	6	]	]	X
ejpam-5016	188	7	is	be	AUX
ejpam-5016	188	8	an	an	DET
ejpam-5016	188	9	inner	inner	ADJ
ejpam-5016	188	10	interval	interval	NOUN
ejpam-5016	188	11	then	then	ADV
ejpam-5016	188	12	s(f	s(f	PROPN
ejpam-5016	188	13	,	,	PUNCT
ejpam-5016	188	14	g	g	NOUN
ejpam-5016	188	15	)	)	PUNCT
ejpam-5016	188	16	=	=	SYM
ejpam-5016	188	17	(	(	PUNCT
ejpam-5016	188	18	ar	ar	PROPN
ejpam-5016	188	19	−	−	PROPN
ejpam-5016	188	20	qy)s+	qy)s+	PROPN
ejpam-5016	188	21	q(ys−	q(ys−	PROPN
ejpam-5016	188	22	pd	pd	PROPN
ejpam-5016	188	23	)	)	PUNCT
ejpam-5016	188	24	with	with	ADP
ejpam-5016	188	25	y	y	PROPN
ejpam-5016	188	26	is	be	AUX
ejpam-5016	188	27	the	the	DET
ejpam-5016	188	28	antidiagonal	antidiagonal	ADJ
ejpam-5016	188	29	corner	corner	NOUN
ejpam-5016	188	30	other	other	ADJ
ejpam-5016	188	31	than	than	ADP
ejpam-5016	188	32	q	q	PROPN
ejpam-5016	188	33	from	from	ADP
ejpam-5016	188	34	the	the	DET
ejpam-5016	188	35	inner	inner	ADJ
ejpam-5016	188	36	interval	interval	NOUN
ejpam-5016	188	37	[	[	X
ejpam-5016	188	38	a	a	X
ejpam-5016	188	39	,	,	PUNCT
ejpam-5016	188	40	r	r	NOUN
ejpam-5016	188	41	]	]	PUNCT
ejpam-5016	188	42	.	.	PUNCT
ejpam-5016	189	1	if	if	SCONJ
ejpam-5016	189	2	[	[	X
ejpam-5016	189	3	a	a	X
ejpam-5016	189	4	,	,	PUNCT
ejpam-5016	189	5	s	s	AUX
ejpam-5016	189	6	]	]	X
ejpam-5016	189	7	is	be	AUX
ejpam-5016	189	8	an	an	DET
ejpam-5016	189	9	inner	inner	ADJ
ejpam-5016	189	10	interval	interval	NOUN
ejpam-5016	189	11	then	then	ADV
ejpam-5016	189	12	s(f	s(f	PROPN
ejpam-5016	189	13	,	,	PUNCT
ejpam-5016	189	14	g	g	NOUN
ejpam-5016	189	15	)	)	PUNCT
ejpam-5016	189	16	=	=	SYM
ejpam-5016	189	17	(	(	PUNCT
ejpam-5016	189	18	as−	as−	X
ejpam-5016	189	19	pz)r	pz)r	PROPN
ejpam-5016	189	20	+	+	PUNCT
ejpam-5016	189	21	p(zr	p(zr	NUM
ejpam-5016	189	22	−	−	ADP
ejpam-5016	189	23	qd	qd	NOUN
ejpam-5016	189	24	)	)	PUNCT
ejpam-5016	189	25	with	with	ADP
ejpam-5016	189	26	z	z	PROPN
ejpam-5016	189	27	is	be	AUX
ejpam-5016	189	28	the	the	DET
ejpam-5016	189	29	antidiagonal	antidiagonal	ADJ
ejpam-5016	189	30	corner	corner	NOUN
ejpam-5016	189	31	other	other	ADJ
ejpam-5016	189	32	than	than	ADP
ejpam-5016	189	33	p	p	NOUN
ejpam-5016	189	34	from	from	ADP
ejpam-5016	189	35	the	the	DET
ejpam-5016	189	36	inner	inner	ADJ
ejpam-5016	189	37	interval	interval	NOUN
ejpam-5016	189	38	[	[	X
ejpam-5016	189	39	a	a	X
ejpam-5016	189	40	,	,	PUNCT
ejpam-5016	189	41	s	s	PART
ejpam-5016	189	42	]	]	X
ejpam-5016	189	43	.	.	PUNCT
ejpam-5016	190	1	from	from	ADP
ejpam-5016	190	2	the	the	DET
ejpam-5016	190	3	observation	observation	NOUN
ejpam-5016	190	4	above	above	ADV
ejpam-5016	190	5	,	,	PUNCT
ejpam-5016	190	6	we	we	PRON
ejpam-5016	190	7	conclude	conclude	VERB
ejpam-5016	190	8	the	the	DET
ejpam-5016	190	9	following	follow	VERB
ejpam-5016	190	10	theorem	theorem	PROPN
ejpam-5016	190	11	.	.	PUNCT
ejpam-5016	190	12	theorem	theorem	NOUN
ejpam-5016	190	13	1	1	NUM
ejpam-5016	190	14	.	.	PUNCT
ejpam-5016	191	1	let	let	VERB
ejpam-5016	191	2	f	f	PROPN
ejpam-5016	191	3	and	and	CCONJ
ejpam-5016	191	4	g	g	PROPN
ejpam-5016	191	5	be	be	AUX
ejpam-5016	191	6	the	the	DET
ejpam-5016	191	7	inner	inner	ADJ
ejpam-5016	191	8	2	2	NUM
ejpam-5016	191	9	-	-	PUNCT
ejpam-5016	191	10	minors	minor	NOUN
ejpam-5016	191	11	associated	associate	VERB
ejpam-5016	191	12	to	to	ADP
ejpam-5016	191	13	inner	inner	ADJ
ejpam-5016	191	14	interval	interval	NOUN
ejpam-5016	191	15	[	[	X
ejpam-5016	191	16	a	a	X
ejpam-5016	191	17	,	,	PUNCT
ejpam-5016	191	18	b	b	NOUN
ejpam-5016	191	19	]	]	PUNCT
ejpam-5016	191	20	and	and	CCONJ
ejpam-5016	192	1	[	[	X
ejpam-5016	192	2	c	c	X
ejpam-5016	192	3	,	,	PUNCT
ejpam-5016	192	4	d	d	X
ejpam-5016	192	5	]	]	X
ejpam-5016	192	6	,	,	PUNCT
ejpam-5016	192	7	respectively	respectively	ADV
ejpam-5016	192	8	,	,	PUNCT
ejpam-5016	192	9	with	with	ADP
ejpam-5016	192	10	a	a	DET
ejpam-5016	192	11	≤p	≤p	PROPN
ejpam-5016	192	12	c.	c.	NOUN
ejpam-5016	192	13	the	the	DET
ejpam-5016	192	14	binomial	binomial	PROPN
ejpam-5016	192	15	s(f	s(f	PROPN
ejpam-5016	192	16	,	,	PUNCT
ejpam-5016	192	17	g	g	NOUN
ejpam-5016	192	18	)	)	PUNCT
ejpam-5016	192	19	is	be	AUX
ejpam-5016	192	20	not	not	PART
ejpam-5016	192	21	reduced	reduce	VERB
ejpam-5016	192	22	to	to	ADP
ejpam-5016	192	23	zero	zero	NUM
ejpam-5016	192	24	by	by	ADP
ejpam-5016	192	25	all	all	DET
ejpam-5016	192	26	inner	inner	ADJ
ejpam-5016	192	27	2	2	NUM
ejpam-5016	192	28	-	-	PUNCT
ejpam-5016	192	29	minors	minor	NOUN
ejpam-5016	192	30	if	if	SCONJ
ejpam-5016	192	31	and	and	CCONJ
ejpam-5016	192	32	only	only	ADV
ejpam-5016	192	33	if	if	SCONJ
ejpam-5016	192	34	•	•	NUM
ejpam-5016	192	35	b	b	X
ejpam-5016	192	36	=	=	SYM
ejpam-5016	192	37	c	c	PROPN
ejpam-5016	192	38	and	and	CCONJ
ejpam-5016	192	39	•	•	NUM
ejpam-5016	192	40	the	the	DET
ejpam-5016	192	41	interval	interval	NOUN
ejpam-5016	192	42	determined	determine	VERB
ejpam-5016	192	43	by	by	ADP
ejpam-5016	192	44	{	{	PUNCT
ejpam-5016	192	45	a	a	DET
ejpam-5016	192	46	,	,	PUNCT
ejpam-5016	192	47	r	r	NOUN
ejpam-5016	192	48	}	}	PUNCT
ejpam-5016	192	49	for	for	ADP
ejpam-5016	192	50	all	all	DET
ejpam-5016	192	51	r	r	NOUN
ejpam-5016	192	52	that	that	PRON
ejpam-5016	192	53	is	be	AUX
ejpam-5016	192	54	an	an	DET
ejpam-5016	192	55	antidiagonal	antidiagonal	ADJ
ejpam-5016	192	56	corner	corner	NOUN
ejpam-5016	192	57	of	of	ADP
ejpam-5016	192	58	[	[	X
ejpam-5016	192	59	c	c	X
ejpam-5016	192	60	,	,	PUNCT
ejpam-5016	192	61	d	d	X
ejpam-5016	192	62	]	]	X
ejpam-5016	192	63	is	be	AUX
ejpam-5016	192	64	not	not	PART
ejpam-5016	192	65	an	an	DET
ejpam-5016	192	66	inner	inner	ADJ
ejpam-5016	192	67	interval	interval	NOUN
ejpam-5016	192	68	.	.	PUNCT
ejpam-5016	193	1	definition	definition	NOUN
ejpam-5016	193	2	1	1	NUM
ejpam-5016	193	3	.	.	PUNCT
ejpam-5016	194	1	let	let	VERB
ejpam-5016	194	2	p	p	PRON
ejpam-5016	194	3	be	be	AUX
ejpam-5016	194	4	a	a	DET
ejpam-5016	194	5	polyomino	polyomino	NOUN
ejpam-5016	194	6	.	.	PUNCT
ejpam-5016	195	1	define	define	VERB
ejpam-5016	195	2	s3	s3	PROPN
ejpam-5016	195	3	to	to	PART
ejpam-5016	195	4	be	be	AUX
ejpam-5016	195	5	the	the	DET
ejpam-5016	195	6	set	set	NOUN
ejpam-5016	195	7	of	of	ADP
ejpam-5016	195	8	all	all	PRON
ejpam-5016	196	1	binomials	binomial	NOUN
ejpam-5016	196	2	a1a3a5	a1a3a5	NOUN
ejpam-5016	196	3	−	−	NOUN
ejpam-5016	196	4	a2a4a6	a2a4a6	NOUN
ejpam-5016	196	5	such	such	ADJ
ejpam-5016	196	6	that	that	PRON
ejpam-5016	196	7	•	•	NOUN
ejpam-5016	196	8	ai	ai	VERB
ejpam-5016	196	9	,	,	PUNCT
ejpam-5016	196	10	ai+1	ai+1	PRON
ejpam-5016	196	11	are	be	AUX
ejpam-5016	196	12	in	in	ADP
ejpam-5016	196	13	vertical	vertical	ADJ
ejpam-5016	196	14	position	position	NOUN
ejpam-5016	196	15	for	for	ADP
ejpam-5016	196	16	i	i	PRON
ejpam-5016	196	17	=	=	NOUN
ejpam-5016	196	18	1	1	NUM
ejpam-5016	196	19	,	,	PUNCT
ejpam-5016	196	20	3	3	NUM
ejpam-5016	196	21	,	,	PUNCT
ejpam-5016	196	22	5	5	NUM
ejpam-5016	196	23	•	•	NOUN
ejpam-5016	196	24	ai	ai	VERB
ejpam-5016	196	25	,	,	PUNCT
ejpam-5016	196	26	ai+1	ai+1	PRON
ejpam-5016	196	27	are	be	AUX
ejpam-5016	196	28	in	in	ADP
ejpam-5016	196	29	horizontal	horizontal	ADJ
ejpam-5016	196	30	position	position	NOUN
ejpam-5016	196	31	for	for	ADP
ejpam-5016	196	32	i	i	PRON
ejpam-5016	196	33	=	=	NOUN
ejpam-5016	196	34	2	2	NUM
ejpam-5016	196	35	,	,	PUNCT
ejpam-5016	196	36	4	4	NUM
ejpam-5016	196	37	,	,	PUNCT
ejpam-5016	196	38	6	6	NUM
ejpam-5016	196	39	(	(	PUNCT
ejpam-5016	196	40	with	with	ADP
ejpam-5016	196	41	a7	a7	PROPN
ejpam-5016	196	42	=	=	PUNCT
ejpam-5016	196	43	a1	a1	PROPN
ejpam-5016	196	44	)	)	PUNCT
ejpam-5016	196	45	•	•	NUM
ejpam-5016	196	46	a1	a1	NOUN
ejpam-5016	196	47	<	<	X
ejpam-5016	196	48	p	p	X
ejpam-5016	196	49	a2	a2	PROPN
ejpam-5016	196	50	<	<	PROPN
ejpam-5016	196	51	p	p	PROPN
ejpam-5016	196	52	a3	a3	NOUN
ejpam-5016	196	53	<	<	X
ejpam-5016	196	54	p	p	X
ejpam-5016	196	55	a4	a4	NOUN
ejpam-5016	196	56	and	and	CCONJ
ejpam-5016	196	57	a1	a1	VERB
ejpam-5016	196	58	<	<	X
ejpam-5016	196	59	p	p	X
ejpam-5016	196	60	a6	a6	NOUN
ejpam-5016	196	61	<	<	X
ejpam-5016	196	62	p	p	X
ejpam-5016	196	63	a5	a5	PROPN
ejpam-5016	196	64	<	<	X
ejpam-5016	196	65	p	p	X
ejpam-5016	196	66	a4	a4	NOUN
ejpam-5016	196	67	•	•	ADP
ejpam-5016	196	68	both	both	DET
ejpam-5016	196	69	intervals	interval	NOUN
ejpam-5016	196	70	determined	determine	VERB
ejpam-5016	196	71	by	by	ADP
ejpam-5016	196	72	{	{	PUNCT
ejpam-5016	196	73	a1	a1	NOUN
ejpam-5016	196	74	,	,	PUNCT
ejpam-5016	196	75	a3	a3	NOUN
ejpam-5016	196	76	}	}	PUNCT
ejpam-5016	196	77	and	and	CCONJ
ejpam-5016	196	78	{	{	PUNCT
ejpam-5016	196	79	a1	a1	NOUN
ejpam-5016	196	80	,	,	PUNCT
ejpam-5016	196	81	a5	a5	PROPN
ejpam-5016	196	82	}	}	PUNCT
ejpam-5016	196	83	are	be	AUX
ejpam-5016	196	84	not	not	PART
ejpam-5016	196	85	inner	inner	ADJ
ejpam-5016	196	86	intervals	interval	NOUN
ejpam-5016	196	87	•	•	ADP
ejpam-5016	196	88	the	the	DET
ejpam-5016	196	89	interval	interval	NOUN
ejpam-5016	196	90	determined	determine	VERB
ejpam-5016	196	91	by	by	ADP
ejpam-5016	196	92	{	{	PUNCT
ejpam-5016	196	93	a1	a1	PROPN
ejpam-5016	196	94	,	,	PUNCT
ejpam-5016	196	95	b	b	NOUN
ejpam-5016	196	96	}	}	PUNCT
ejpam-5016	196	97	and	and	CCONJ
ejpam-5016	196	98	{	{	PUNCT
ejpam-5016	196	99	b	b	NOUN
ejpam-5016	196	100	,	,	PUNCT
ejpam-5016	196	101	a4	a4	PROPN
ejpam-5016	196	102	}	}	PUNCT
ejpam-5016	196	103	are	be	AUX
ejpam-5016	196	104	inner	inner	ADJ
ejpam-5016	196	105	interval	interval	NOUN
ejpam-5016	196	106	with	with	ADP
ejpam-5016	196	107	b	b	PROPN
ejpam-5016	196	108	is	be	AUX
ejpam-5016	196	109	the	the	DET
ejpam-5016	196	110	intersection	intersection	NOUN
ejpam-5016	196	111	of	of	ADP
ejpam-5016	196	112	the	the	DET
ejpam-5016	196	113	segments	segment	NOUN
ejpam-5016	196	114	a2a3	a2a3	PROPN
ejpam-5016	196	115	and	and	CCONJ
ejpam-5016	196	116	a5a6	a5a6	ADP
ejpam-5016	196	117	.	.	PROPN
ejpam-5016	197	1	note	note	VERB
ejpam-5016	197	2	that	that	SCONJ
ejpam-5016	197	3	there	there	PRON
ejpam-5016	197	4	are	be	VERB
ejpam-5016	197	5	no	no	DET
ejpam-5016	197	6	elements	element	NOUN
ejpam-5016	197	7	in	in	ADP
ejpam-5016	197	8	s3	s3	NOUN
ejpam-5016	197	9	whose	whose	DET
ejpam-5016	197	10	initial	initial	ADJ
ejpam-5016	197	11	monomial	monomial	NOUN
ejpam-5016	197	12	is	be	AUX
ejpam-5016	197	13	divisible	divisible	ADJ
ejpam-5016	197	14	by	by	ADP
ejpam-5016	197	15	the	the	DET
ejpam-5016	197	16	initial	initial	ADJ
ejpam-5016	197	17	monomial	monomial	NOUN
ejpam-5016	197	18	of	of	ADP
ejpam-5016	197	19	an	an	DET
ejpam-5016	197	20	inner	inner	ADJ
ejpam-5016	197	21	2	2	NUM
ejpam-5016	197	22	-	-	PUNCT
ejpam-5016	197	23	minor	minor	ADJ
ejpam-5016	197	24	.	.	PUNCT
ejpam-5016	198	1	therefore	therefore	ADV
ejpam-5016	198	2	,	,	PUNCT
ejpam-5016	198	3	we	we	PRON
ejpam-5016	198	4	conclude	conclude	VERB
ejpam-5016	198	5	that	that	SCONJ
ejpam-5016	198	6	s3	s3	PROPN
ejpam-5016	198	7	is	be	AUX
ejpam-5016	198	8	the	the	DET
ejpam-5016	198	9	set	set	NOUN
ejpam-5016	198	10	of	of	ADP
ejpam-5016	198	11	all	all	DET
ejpam-5016	198	12	binomials	binomial	NOUN
ejpam-5016	198	13	of	of	ADP
ejpam-5016	198	14	degree	degree	NOUN
ejpam-5016	198	15	three	three	NUM
ejpam-5016	198	16	arising	arise	VERB
ejpam-5016	198	17	from	from	ADP
ejpam-5016	198	18	buchberger	buchberger	NOUN
ejpam-5016	198	19	algorithm	algorithm	NOUN
ejpam-5016	198	20	in	in	ADP
ejpam-5016	198	21	the	the	DET
ejpam-5016	198	22	polyomino	polyomino	NOUN
ejpam-5016	198	23	ideal	ideal	NOUN
ejpam-5016	198	24	with	with	ADP
ejpam-5016	198	25	respect	respect	NOUN
ejpam-5016	198	26	to	to	ADP
ejpam-5016	198	27	the	the	DET
ejpam-5016	198	28	given	give	VERB
ejpam-5016	198	29	monomial	monomial	ADJ
ejpam-5016	198	30	order	order	NOUN
ejpam-5016	198	31	<	<	X
ejpam-5016	198	32	p	p	X
ejpam-5016	198	33	.	.	PUNCT
ejpam-5016	199	1	y.	y.	PROPN
ejpam-5016	199	2	y.	y.	PROPN
ejpam-5016	199	3	hamonangan	hamonangan	PROPN
ejpam-5016	199	4	,	,	PUNCT
ejpam-5016	199	5	i.	i.	PROPN
ejpam-5016	199	6	muchtadi	muchtadi	PROPN
ejpam-5016	199	7	-	-	PUNCT
ejpam-5016	199	8	alamsyah	alamsyah	NOUN
ejpam-5016	199	9	/	/	SYM
ejpam-5016	199	10	eur	eur	PROPN
ejpam-5016	199	11	.	.	PUNCT
ejpam-5016	200	1	j.	j.	PROPN
ejpam-5016	200	2	pure	pure	PROPN
ejpam-5016	200	3	appl	appl	PROPN
ejpam-5016	200	4	.	.	PROPN
ejpam-5016	200	5	math	math	PROPN
ejpam-5016	200	6	,	,	PUNCT
ejpam-5016	200	7	17	17	NUM
ejpam-5016	200	8	(	(	PUNCT
ejpam-5016	200	9	4	4	NUM
ejpam-5016	200	10	)	)	PUNCT
ejpam-5016	200	11	(	(	PUNCT
ejpam-5016	200	12	2024	2024	NUM
ejpam-5016	200	13	)	)	PUNCT
ejpam-5016	200	14	,	,	PUNCT
ejpam-5016	200	15	2621	2621	NUM
ejpam-5016	200	16	-	-	SYM
ejpam-5016	200	17	2650	2650	NUM
ejpam-5016	200	18	2628	2628	NUM
ejpam-5016	200	19	a1	a1	NOUN
ejpam-5016	200	20	a2	a2	PROPN
ejpam-5016	200	21	a3	a3	NOUN
ejpam-5016	200	22	a4a5	a4a5	PROPN
ejpam-5016	200	23	a6	a6	PROPN
ejpam-5016	200	24	b	b	PROPN
ejpam-5016	200	25	:	:	PUNCT
ejpam-5016	200	26	every	every	DET
ejpam-5016	200	27	cell	cell	NOUN
ejpam-5016	200	28	is	be	AUX
ejpam-5016	200	29	contained	contain	VERB
ejpam-5016	200	30	in	in	ADP
ejpam-5016	200	31	the	the	DET
ejpam-5016	200	32	polyomino	polyomino	NOUN
ejpam-5016	200	33	:	:	PUNCT
ejpam-5016	200	34	some	some	DET
ejpam-5016	200	35	cells	cell	NOUN
ejpam-5016	200	36	are	be	AUX
ejpam-5016	200	37	not	not	PART
ejpam-5016	200	38	in	in	ADP
ejpam-5016	200	39	the	the	DET
ejpam-5016	200	40	polyomino	polyomino	NOUN
ejpam-5016	200	41	figure	figure	NOUN
ejpam-5016	200	42	7	7	NUM
ejpam-5016	200	43	:	:	PUNCT
ejpam-5016	200	44	binomials	binomial	NOUN
ejpam-5016	200	45	in	in	ADP
ejpam-5016	200	46	s3	s3	PROPN
ejpam-5016	200	47	.	.	PROPN
ejpam-5016	200	48	3.2	3.2	NUM
ejpam-5016	200	49	.	.	PUNCT
ejpam-5016	201	1	binomials	binomial	NOUN
ejpam-5016	201	2	of	of	ADP
ejpam-5016	201	3	degree	degree	NOUN
ejpam-5016	201	4	four	four	NUM
ejpam-5016	201	5	now	now	ADV
ejpam-5016	201	6	,	,	PUNCT
ejpam-5016	201	7	we	we	PRON
ejpam-5016	201	8	have	have	VERB
ejpam-5016	201	9	the	the	DET
ejpam-5016	201	10	set	set	VERB
ejpam-5016	201	11	s2	s2	PROPN
ejpam-5016	201	12	∪	∪	X
ejpam-5016	201	13	s3	s3	PROPN
ejpam-5016	201	14	.	.	PUNCT
ejpam-5016	202	1	we	we	PRON
ejpam-5016	202	2	want	want	VERB
ejpam-5016	202	3	to	to	PART
ejpam-5016	202	4	compute	compute	VERB
ejpam-5016	202	5	s(f	s(f	PROPN
ejpam-5016	202	6	,	,	PUNCT
ejpam-5016	202	7	g	g	NOUN
ejpam-5016	202	8	)	)	PUNCT
ejpam-5016	202	9	for	for	ADP
ejpam-5016	202	10	f	f	PROPN
ejpam-5016	202	11	∈	∈	PROPN
ejpam-5016	202	12	s3	s3	PROPN
ejpam-5016	202	13	,	,	PUNCT
ejpam-5016	202	14	g	g	PROPN
ejpam-5016	202	15	∈	∈	PROPN
ejpam-5016	202	16	s2	s2	NOUN
ejpam-5016	202	17	or	or	CCONJ
ejpam-5016	202	18	f	f	X
ejpam-5016	202	19	,	,	PUNCT
ejpam-5016	202	20	g	g	PROPN
ejpam-5016	202	21	∈	∈	PROPN
ejpam-5016	202	22	s3	s3	PROPN
ejpam-5016	202	23	.	.	PUNCT
ejpam-5016	203	1	for	for	ADP
ejpam-5016	203	2	the	the	DET
ejpam-5016	203	3	case	case	NOUN
ejpam-5016	203	4	f	f	PROPN
ejpam-5016	203	5	∈	∈	PROPN
ejpam-5016	203	6	s3	s3	PROPN
ejpam-5016	203	7	and	and	CCONJ
ejpam-5016	203	8	g	g	PROPN
ejpam-5016	203	9	∈	∈	PROPN
ejpam-5016	203	10	s2	s2	PROPN
ejpam-5016	203	11	,	,	PUNCT
ejpam-5016	203	12	note	note	VERB
ejpam-5016	203	13	that	that	SCONJ
ejpam-5016	203	14	if	if	SCONJ
ejpam-5016	203	15	f	f	PROPN
ejpam-5016	203	16	=	=	VERB
ejpam-5016	203	17	a1a3a5	a1a3a5	NOUN
ejpam-5016	203	18	−	−	ADP
ejpam-5016	203	19	a2a4a5	a2a4a5	PROPN
ejpam-5016	203	20	∈	∈	PROPN
ejpam-5016	203	21	s3	s3	NOUN
ejpam-5016	203	22	then	then	ADV
ejpam-5016	203	23	the	the	DET
ejpam-5016	203	24	pairs	pair	NOUN
ejpam-5016	203	25	(	(	PUNCT
ejpam-5016	203	26	a1	a1	NOUN
ejpam-5016	203	27	,	,	PUNCT
ejpam-5016	203	28	a3	a3	NOUN
ejpam-5016	203	29	)	)	PUNCT
ejpam-5016	203	30	,	,	PUNCT
ejpam-5016	203	31	(	(	PUNCT
ejpam-5016	203	32	a1	a1	NOUN
ejpam-5016	203	33	,	,	PUNCT
ejpam-5016	203	34	a5	a5	PROPN
ejpam-5016	203	35	)	)	PUNCT
ejpam-5016	203	36	,	,	PUNCT
ejpam-5016	203	37	and	and	CCONJ
ejpam-5016	203	38	(	(	PUNCT
ejpam-5016	203	39	a3	a3	NOUN
ejpam-5016	203	40	,	,	PUNCT
ejpam-5016	203	41	a5	a5	PROPN
ejpam-5016	203	42	)	)	PUNCT
ejpam-5016	203	43	are	be	AUX
ejpam-5016	203	44	not	not	PART
ejpam-5016	203	45	pair	pair	NOUN
ejpam-5016	203	46	of	of	ADP
ejpam-5016	203	47	diagonal	diagonal	ADJ
ejpam-5016	203	48	corners	corner	NOUN
ejpam-5016	203	49	of	of	ADP
ejpam-5016	203	50	an	an	DET
ejpam-5016	203	51	inner	inner	ADJ
ejpam-5016	203	52	interval	interval	NOUN
ejpam-5016	203	53	,	,	PUNCT
ejpam-5016	203	54	thus	thus	ADV
ejpam-5016	203	55	we	we	PRON
ejpam-5016	203	56	only	only	ADV
ejpam-5016	203	57	need	need	VERB
ejpam-5016	203	58	to	to	PART
ejpam-5016	203	59	consider	consider	VERB
ejpam-5016	203	60	the	the	DET
ejpam-5016	203	61	case	case	NOUN
ejpam-5016	203	62	when	when	SCONJ
ejpam-5016	203	63	the	the	DET
ejpam-5016	203	64	greatest	great	ADJ
ejpam-5016	203	65	common	common	ADJ
ejpam-5016	203	66	divisor	divisor	NOUN
ejpam-5016	203	67	of	of	ADP
ejpam-5016	203	68	their	their	PRON
ejpam-5016	203	69	initial	initial	ADJ
ejpam-5016	203	70	monomials	monomial	NOUN
ejpam-5016	203	71	has	have	VERB
ejpam-5016	203	72	degree	degree	NOUN
ejpam-5016	203	73	one	one	NUM
ejpam-5016	203	74	.	.	PUNCT
ejpam-5016	204	1	for	for	ADP
ejpam-5016	204	2	the	the	DET
ejpam-5016	204	3	case	case	NOUN
ejpam-5016	204	4	both	both	CCONJ
ejpam-5016	204	5	f	f	X
ejpam-5016	204	6	,	,	PUNCT
ejpam-5016	204	7	g	g	PROPN
ejpam-5016	204	8	∈	∈	PROPN
ejpam-5016	204	9	s3	s3	PROPN
ejpam-5016	204	10	,	,	PUNCT
ejpam-5016	204	11	we	we	PRON
ejpam-5016	204	12	will	will	AUX
ejpam-5016	204	13	consider	consider	VERB
ejpam-5016	204	14	the	the	DET
ejpam-5016	204	15	case	case	NOUN
ejpam-5016	204	16	when	when	SCONJ
ejpam-5016	204	17	the	the	DET
ejpam-5016	204	18	greatest	great	ADJ
ejpam-5016	204	19	common	common	ADJ
ejpam-5016	204	20	divisor	divisor	NOUN
ejpam-5016	204	21	of	of	ADP
ejpam-5016	204	22	their	their	PRON
ejpam-5016	204	23	initial	initial	ADJ
ejpam-5016	204	24	monomials	monomial	NOUN
ejpam-5016	204	25	is	be	AUX
ejpam-5016	204	26	a	a	DET
ejpam-5016	204	27	monomial	monomial	NOUN
ejpam-5016	204	28	of	of	ADP
ejpam-5016	204	29	degree	degree	NOUN
ejpam-5016	204	30	two	two	NUM
ejpam-5016	204	31	.	.	PUNCT
ejpam-5016	205	1	3.2.1	3.2.1	NUM
ejpam-5016	205	2	.	.	PUNCT
ejpam-5016	206	1	the	the	DET
ejpam-5016	206	2	case	case	NOUN
ejpam-5016	206	3	f	f	PROPN
ejpam-5016	206	4	∈	∈	PROPN
ejpam-5016	206	5	s3	s3	PROPN
ejpam-5016	206	6	and	and	CCONJ
ejpam-5016	206	7	g	g	PROPN
ejpam-5016	206	8	∈	∈	PROPN
ejpam-5016	206	9	s2	s2	NOUN
ejpam-5016	206	10	let	let	VERB
ejpam-5016	206	11	f	f	NOUN
ejpam-5016	206	12	=	=	SYM
ejpam-5016	206	13	abc−	abc−	PROPN
ejpam-5016	206	14	def	def	ADJ
ejpam-5016	206	15	and	and	CCONJ
ejpam-5016	206	16	g	g	PROPN
ejpam-5016	206	17	=	=	PROPN
ejpam-5016	206	18	pq	pq	PROPN
ejpam-5016	207	1	−	−	NOUN
ejpam-5016	207	2	rs	rs	NOUN
ejpam-5016	207	3	,	,	PUNCT
ejpam-5016	207	4	with	with	ADP
ejpam-5016	207	5	|{a	|{a	PROPN
ejpam-5016	207	6	,	,	PUNCT
ejpam-5016	207	7	b	b	NOUN
ejpam-5016	207	8	,	,	PUNCT
ejpam-5016	207	9	c	c	NOUN
ejpam-5016	207	10	}	}	PUNCT
ejpam-5016	207	11	∩	∩	NOUN
ejpam-5016	207	12	{	{	PUNCT
ejpam-5016	207	13	p	p	X
ejpam-5016	207	14	,	,	PUNCT
ejpam-5016	207	15	q}|	q}|	ADJ
ejpam-5016	207	16	=	=	SYM
ejpam-5016	207	17	1	1	NUM
ejpam-5016	207	18	as	as	SCONJ
ejpam-5016	207	19	illustrated	illustrate	VERB
ejpam-5016	207	20	below	below	ADV
ejpam-5016	207	21	.	.	PUNCT
ejpam-5016	208	1	a	a	DET
ejpam-5016	208	2	b	b	NOUN
ejpam-5016	208	3	c	c	NOUN
ejpam-5016	208	4	d	d	X
ejpam-5016	208	5	e	e	X
ejpam-5016	208	6	f	f	X
ejpam-5016	208	7	p	p	NOUN
ejpam-5016	208	8	r	r	NOUN
ejpam-5016	208	9	s	s	PART
ejpam-5016	208	10	q	q	NOUN
ejpam-5016	208	11	figure	figure	NOUN
ejpam-5016	208	12	8	8	NUM
ejpam-5016	208	13	:	:	PUNCT
ejpam-5016	208	14	the	the	DET
ejpam-5016	208	15	binomials	binomial	NOUN
ejpam-5016	208	16	f	f	PROPN
ejpam-5016	208	17	and	and	CCONJ
ejpam-5016	208	18	g.	g.	PROPN
ejpam-5016	208	19	recall	recall	VERB
ejpam-5016	208	20	that	that	SCONJ
ejpam-5016	208	21	the	the	DET
ejpam-5016	208	22	intervals	interval	NOUN
ejpam-5016	208	23	determined	determine	VERB
ejpam-5016	208	24	by	by	ADP
ejpam-5016	208	25	{	{	PUNCT
ejpam-5016	208	26	a	a	PROPN
ejpam-5016	208	27	,	,	PUNCT
ejpam-5016	208	28	b	b	NOUN
ejpam-5016	208	29	}	}	PUNCT
ejpam-5016	208	30	and	and	CCONJ
ejpam-5016	208	31	{	{	PUNCT
ejpam-5016	208	32	c	c	X
ejpam-5016	208	33	,	,	PUNCT
ejpam-5016	208	34	d	d	NOUN
ejpam-5016	208	35	}	}	PUNCT
ejpam-5016	208	36	are	be	AUX
ejpam-5016	208	37	not	not	PART
ejpam-5016	208	38	inner	inner	ADJ
ejpam-5016	208	39	intervals	interval	NOUN
ejpam-5016	208	40	.	.	PUNCT
ejpam-5016	209	1	first	first	ADV
ejpam-5016	209	2	,	,	PUNCT
ejpam-5016	209	3	we	we	PRON
ejpam-5016	209	4	observe	observe	VERB
ejpam-5016	209	5	the	the	DET
ejpam-5016	209	6	case	case	NOUN
ejpam-5016	209	7	if	if	SCONJ
ejpam-5016	209	8	f	f	PROPN
ejpam-5016	209	9	and	and	CCONJ
ejpam-5016	209	10	g	g	PROPN
ejpam-5016	209	11	also	also	ADV
ejpam-5016	209	12	have	have	VERB
ejpam-5016	209	13	common	common	ADJ
ejpam-5016	209	14	monomial	monomial	ADJ
ejpam-5016	209	15	divisor	divisor	NOUN
ejpam-5016	209	16	on	on	ADP
ejpam-5016	209	17	their	their	PRON
ejpam-5016	209	18	non	non	ADJ
ejpam-5016	209	19	-	-	ADJ
ejpam-5016	209	20	initial	initial	ADJ
ejpam-5016	209	21	monomials	monomial	NOUN
ejpam-5016	209	22	.	.	PUNCT
ejpam-5016	210	1	we	we	PRON
ejpam-5016	210	2	show	show	VERB
ejpam-5016	210	3	that	that	SCONJ
ejpam-5016	210	4	s(f	s(f	PROPN
ejpam-5016	210	5	,	,	PUNCT
ejpam-5016	210	6	g	g	NOUN
ejpam-5016	210	7	)	)	PUNCT
ejpam-5016	210	8	can	can	AUX
ejpam-5016	210	9	be	be	AUX
ejpam-5016	210	10	reduced	reduce	VERB
ejpam-5016	210	11	to	to	ADP
ejpam-5016	210	12	zero	zero	NUM
ejpam-5016	210	13	.	.	PUNCT
ejpam-5016	211	1	from	from	ADP
ejpam-5016	211	2	the	the	DET
ejpam-5016	211	3	structure	structure	NOUN
ejpam-5016	211	4	of	of	ADP
ejpam-5016	211	5	f	f	PROPN
ejpam-5016	211	6	and	and	CCONJ
ejpam-5016	211	7	g	g	PROPN
ejpam-5016	211	8	,	,	PUNCT
ejpam-5016	211	9	the	the	DET
ejpam-5016	211	10	possible	possible	ADJ
ejpam-5016	211	11	cases	case	NOUN
ejpam-5016	211	12	are	be	AUX
ejpam-5016	211	13	:	:	PUNCT
ejpam-5016	211	14	(	(	PUNCT
ejpam-5016	211	15	i	i	NOUN
ejpam-5016	211	16	)	)	PUNCT
ejpam-5016	211	17	a	a	DET
ejpam-5016	211	18	=	=	PUNCT
ejpam-5016	211	19	p	p	PROPN
ejpam-5016	211	20	and	and	CCONJ
ejpam-5016	211	21	d	d	PROPN
ejpam-5016	211	22	=	=	SYM
ejpam-5016	211	23	s	s	PROPN
ejpam-5016	211	24	;	;	PUNCT
ejpam-5016	211	25	(	(	PUNCT
ejpam-5016	211	26	ii	ii	NOUN
ejpam-5016	211	27	)	)	PUNCT
ejpam-5016	211	28	a	a	DET
ejpam-5016	211	29	=	=	PUNCT
ejpam-5016	211	30	p	p	PROPN
ejpam-5016	211	31	and	and	CCONJ
ejpam-5016	211	32	f	f	NOUN
ejpam-5016	211	33	=	=	SYM
ejpam-5016	211	34	r	r	NOUN
ejpam-5016	211	35	;	;	PUNCT
ejpam-5016	211	36	(	(	PUNCT
ejpam-5016	211	37	iii	iii	X
ejpam-5016	211	38	)	)	PUNCT
ejpam-5016	212	1	b	b	NOUN
ejpam-5016	212	2	=	=	SYM
ejpam-5016	212	3	p	p	PROPN
ejpam-5016	212	4	and	and	CCONJ
ejpam-5016	212	5	e	e	X
ejpam-5016	212	6	=	=	SYM
ejpam-5016	212	7	s	s	PROPN
ejpam-5016	212	8	;	;	PUNCT
ejpam-5016	212	9	(	(	PUNCT
ejpam-5016	212	10	iv	iv	X
ejpam-5016	212	11	)	)	PUNCT
ejpam-5016	212	12	b	b	NOUN
ejpam-5016	212	13	=	=	PUNCT
ejpam-5016	212	14	q	q	PROPN
ejpam-5016	212	15	and	and	CCONJ
ejpam-5016	212	16	d	d	X
ejpam-5016	212	17	=	=	SYM
ejpam-5016	212	18	s	s	PROPN
ejpam-5016	212	19	;	;	PUNCT
ejpam-5016	212	20	y.	y.	PROPN
ejpam-5016	212	21	y.	y.	PROPN
ejpam-5016	212	22	hamonangan	hamonangan	PROPN
ejpam-5016	212	23	,	,	PUNCT
ejpam-5016	212	24	i.	i.	PROPN
ejpam-5016	212	25	muchtadi	muchtadi	PROPN
ejpam-5016	212	26	-	-	PUNCT
ejpam-5016	212	27	alamsyah	alamsyah	NOUN
ejpam-5016	212	28	/	/	SYM
ejpam-5016	212	29	eur	eur	PROPN
ejpam-5016	212	30	.	.	PUNCT
ejpam-5016	213	1	j.	j.	PROPN
ejpam-5016	213	2	pure	pure	PROPN
ejpam-5016	213	3	appl	appl	PROPN
ejpam-5016	213	4	.	.	PROPN
ejpam-5016	213	5	math	math	PROPN
ejpam-5016	213	6	,	,	PUNCT
ejpam-5016	213	7	17	17	NUM
ejpam-5016	213	8	(	(	PUNCT
ejpam-5016	213	9	4	4	NUM
ejpam-5016	213	10	)	)	PUNCT
ejpam-5016	213	11	(	(	PUNCT
ejpam-5016	213	12	2024	2024	NUM
ejpam-5016	213	13	)	)	PUNCT
ejpam-5016	213	14	,	,	PUNCT
ejpam-5016	213	15	2621	2621	NUM
ejpam-5016	213	16	-	-	SYM
ejpam-5016	213	17	2650	2650	NUM
ejpam-5016	213	18	2629	2629	NUM
ejpam-5016	213	19	(	(	PUNCT
ejpam-5016	213	20	v	v	NOUN
ejpam-5016	213	21	)	)	PUNCT
ejpam-5016	213	22	c	c	NOUN
ejpam-5016	214	1	=	=	SYM
ejpam-5016	214	2	p	p	PROPN
ejpam-5016	214	3	and	and	CCONJ
ejpam-5016	214	4	e	e	NOUN
ejpam-5016	214	5	=	=	SYM
ejpam-5016	214	6	r	r	NOUN
ejpam-5016	214	7	;	;	PUNCT
ejpam-5016	214	8	(	(	PUNCT
ejpam-5016	214	9	vi	vi	NOUN
ejpam-5016	214	10	)	)	PUNCT
ejpam-5016	214	11	c	c	NOUN
ejpam-5016	215	1	=	=	PUNCT
ejpam-5016	215	2	q	q	PROPN
ejpam-5016	215	3	and	and	CCONJ
ejpam-5016	215	4	r	r	NOUN
ejpam-5016	215	5	=	=	SYM
ejpam-5016	215	6	f	f	PROPN
ejpam-5016	215	7	.	.	PUNCT
ejpam-5016	216	1	the	the	DET
ejpam-5016	216	2	first	first	ADJ
ejpam-5016	216	3	two	two	NUM
ejpam-5016	216	4	cases	case	NOUN
ejpam-5016	216	5	can	can	AUX
ejpam-5016	216	6	occur	occur	VERB
ejpam-5016	216	7	simultaneously	simultaneously	ADV
ejpam-5016	216	8	.	.	PUNCT
ejpam-5016	217	1	in	in	ADP
ejpam-5016	217	2	that	that	DET
ejpam-5016	217	3	case	case	NOUN
ejpam-5016	217	4	,	,	PUNCT
ejpam-5016	217	5	we	we	PRON
ejpam-5016	217	6	notice	notice	VERB
ejpam-5016	217	7	that	that	SCONJ
ejpam-5016	217	8	q	q	NOUN
ejpam-5016	217	9	is	be	AUX
ejpam-5016	217	10	the	the	DET
ejpam-5016	217	11	intersection	intersection	NOUN
ejpam-5016	217	12	of	of	ADP
ejpam-5016	217	13	the	the	DET
ejpam-5016	217	14	segments	segment	NOUN
ejpam-5016	217	15	cf	cf	INTJ
ejpam-5016	218	1	and	and	CCONJ
ejpam-5016	218	2	bd	bd	PROPN
ejpam-5016	218	3	.	.	PROPN
ejpam-5016	218	4	notice	notice	VERB
ejpam-5016	218	5	that	that	SCONJ
ejpam-5016	218	6	s(f	s(f	PROPN
ejpam-5016	218	7	,	,	PUNCT
ejpam-5016	218	8	g	g	NOUN
ejpam-5016	218	9	)	)	PUNCT
ejpam-5016	218	10	=	=	PUNCT
ejpam-5016	218	11	df(bc	df(bc	VERB
ejpam-5016	218	12	−	−	PROPN
ejpam-5016	218	13	qe	qe	PROPN
ejpam-5016	218	14	)	)	PUNCT
ejpam-5016	218	15	is	be	AUX
ejpam-5016	218	16	reduced	reduce	VERB
ejpam-5016	218	17	to	to	ADP
ejpam-5016	218	18	zero	zero	NUM
ejpam-5016	218	19	since	since	SCONJ
ejpam-5016	218	20	bc−	bc−	PROPN
ejpam-5016	218	21	qe	qe	PROPN
ejpam-5016	218	22	∈	∈	PROPN
ejpam-5016	218	23	s2	s2	PROPN
ejpam-5016	218	24	.	.	PUNCT
ejpam-5016	219	1	now	now	ADV
ejpam-5016	219	2	,	,	PUNCT
ejpam-5016	219	3	we	we	PRON
ejpam-5016	219	4	examine	examine	VERB
ejpam-5016	219	5	all	all	DET
ejpam-5016	219	6	the	the	DET
ejpam-5016	219	7	cases	case	NOUN
ejpam-5016	219	8	separately	separately	ADV
ejpam-5016	219	9	.	.	PUNCT
ejpam-5016	220	1	(	(	PUNCT
ejpam-5016	220	2	i	i	NOUN
ejpam-5016	220	3	)	)	PUNCT
ejpam-5016	220	4	if	if	SCONJ
ejpam-5016	220	5	a	a	DET
ejpam-5016	220	6	=	=	SYM
ejpam-5016	220	7	p	p	NOUN
ejpam-5016	220	8	and	and	CCONJ
ejpam-5016	220	9	d	d	PROPN
ejpam-5016	220	10	=	=	SYM
ejpam-5016	220	11	s	s	PROPN
ejpam-5016	220	12	then	then	ADV
ejpam-5016	220	13	s(f	s(f	PROPN
ejpam-5016	220	14	,	,	PUNCT
ejpam-5016	220	15	g	g	NOUN
ejpam-5016	220	16	)	)	PUNCT
ejpam-5016	220	17	=	=	PUNCT
ejpam-5016	221	1	d(bcr	d(bcr	PROPN
ejpam-5016	221	2	−	−	PROPN
ejpam-5016	221	3	efq	efq	PROPN
ejpam-5016	221	4	)	)	PUNCT
ejpam-5016	221	5	.	.	PUNCT
ejpam-5016	222	1	•	•	INTJ
ejpam-5016	222	2	if	if	SCONJ
ejpam-5016	222	3	a	a	DET
ejpam-5016	222	4	<	<	X
ejpam-5016	222	5	r	r	NOUN
ejpam-5016	222	6	<	<	X
ejpam-5016	222	7	f	f	X
ejpam-5016	222	8	then	then	ADV
ejpam-5016	222	9	consider	consider	VERB
ejpam-5016	222	10	the	the	DET
ejpam-5016	222	11	interval	interval	NOUN
ejpam-5016	222	12	determined	determine	VERB
ejpam-5016	222	13	by	by	ADP
ejpam-5016	222	14	{	{	PUNCT
ejpam-5016	222	15	r	r	NOUN
ejpam-5016	222	16	,	,	PUNCT
ejpam-5016	222	17	c	c	NOUN
ejpam-5016	222	18	}	}	PUNCT
ejpam-5016	222	19	.	.	PUNCT
ejpam-5016	223	1	if	if	SCONJ
ejpam-5016	223	2	it	it	PRON
ejpam-5016	223	3	is	be	AUX
ejpam-5016	223	4	an	an	DET
ejpam-5016	223	5	inner	inner	ADJ
ejpam-5016	223	6	interval	interval	NOUN
ejpam-5016	223	7	then	then	ADV
ejpam-5016	223	8	bcr	bcr	PROPN
ejpam-5016	223	9	−	−	PROPN
ejpam-5016	223	10	efq	efq	PROPN
ejpam-5016	223	11	is	be	AUX
ejpam-5016	223	12	reduced	reduce	VERB
ejpam-5016	223	13	to	to	ADP
ejpam-5016	223	14	zero	zero	NUM
ejpam-5016	223	15	by	by	ADP
ejpam-5016	223	16	similar	similar	ADJ
ejpam-5016	223	17	argument	argument	NOUN
ejpam-5016	223	18	in	in	ADP
ejpam-5016	223	19	section	section	NOUN
ejpam-5016	223	20	3.1	3.1	NUM
ejpam-5016	223	21	(	(	PUNCT
ejpam-5016	223	22	case	case	NOUN
ejpam-5016	223	23	(	(	PUNCT
ejpam-5016	223	24	iii	iii	NOUN
ejpam-5016	223	25	)	)	PUNCT
ejpam-5016	223	26	)	)	PUNCT
ejpam-5016	223	27	.	.	PUNCT
ejpam-5016	224	1	if	if	SCONJ
ejpam-5016	224	2	it	it	PRON
ejpam-5016	224	3	is	be	AUX
ejpam-5016	224	4	not	not	PART
ejpam-5016	224	5	an	an	DET
ejpam-5016	224	6	inner	inner	ADJ
ejpam-5016	224	7	interval	interval	NOUN
ejpam-5016	224	8	,	,	PUNCT
ejpam-5016	224	9	since	since	SCONJ
ejpam-5016	224	10	the	the	DET
ejpam-5016	224	11	interval	interval	NOUN
ejpam-5016	224	12	determined	determine	VERB
ejpam-5016	224	13	by	by	ADP
ejpam-5016	224	14	{	{	PUNCT
ejpam-5016	224	15	r	r	NOUN
ejpam-5016	224	16	,	,	PUNCT
ejpam-5016	224	17	b	b	NOUN
ejpam-5016	224	18	}	}	PUNCT
ejpam-5016	224	19	is	be	AUX
ejpam-5016	224	20	not	not	PART
ejpam-5016	224	21	an	an	DET
ejpam-5016	224	22	inner	inner	ADJ
ejpam-5016	224	23	interval	interval	NOUN
ejpam-5016	224	24	,	,	PUNCT
ejpam-5016	224	25	then	then	ADV
ejpam-5016	224	26	bcr	bcr	PROPN
ejpam-5016	224	27	−	−	PROPN
ejpam-5016	224	28	efq	efq	PROPN
ejpam-5016	224	29	∈	∈	PROPN
ejpam-5016	224	30	s3	s3	PROPN
ejpam-5016	224	31	and	and	CCONJ
ejpam-5016	224	32	it	it	PRON
ejpam-5016	224	33	is	be	AUX
ejpam-5016	224	34	reduced	reduce	VERB
ejpam-5016	224	35	to	to	ADP
ejpam-5016	224	36	zero	zero	NUM
ejpam-5016	224	37	.	.	PUNCT
ejpam-5016	225	1	a	a	DET
ejpam-5016	225	2	b	b	NOUN
ejpam-5016	225	3	c	c	NOUN
ejpam-5016	225	4	d	d	X
ejpam-5016	225	5	e	e	X
ejpam-5016	225	6	fr	fr	PROPN
ejpam-5016	225	7	q	q	NOUN
ejpam-5016	225	8	figure	figure	NOUN
ejpam-5016	225	9	9	9	NUM
ejpam-5016	225	10	:	:	PUNCT
ejpam-5016	225	11	case	case	NOUN
ejpam-5016	225	12	a	a	DET
ejpam-5016	225	13	=	=	SYM
ejpam-5016	225	14	p	p	NOUN
ejpam-5016	225	15	,	,	PUNCT
ejpam-5016	225	16	d	d	PROPN
ejpam-5016	225	17	=	=	SYM
ejpam-5016	225	18	s	s	X
ejpam-5016	225	19	and	and	CCONJ
ejpam-5016	225	20	a	a	DET
ejpam-5016	225	21	<	<	X
ejpam-5016	225	22	r	r	NOUN
ejpam-5016	225	23	<	<	X
ejpam-5016	225	24	f	f	PROPN
ejpam-5016	225	25	.	.	PUNCT
ejpam-5016	226	1	•	•	INTJ
ejpam-5016	226	2	if	if	SCONJ
ejpam-5016	226	3	a	a	DET
ejpam-5016	226	4	<	<	X
ejpam-5016	226	5	f	f	X
ejpam-5016	226	6	<	<	X
ejpam-5016	226	7	r	r	NOUN
ejpam-5016	226	8	,	,	PUNCT
ejpam-5016	226	9	let	let	VERB
ejpam-5016	226	10	z	z	PRON
ejpam-5016	226	11	be	be	AUX
ejpam-5016	226	12	the	the	DET
ejpam-5016	226	13	intersections	intersection	NOUN
ejpam-5016	226	14	of	of	ADP
ejpam-5016	226	15	segments	segment	NOUN
ejpam-5016	226	16	cf	cf	INTJ
ejpam-5016	227	1	and	and	CCONJ
ejpam-5016	227	2	bd	bd	PROPN
ejpam-5016	227	3	,	,	PUNCT
ejpam-5016	227	4	then	then	ADV
ejpam-5016	227	5	bcr	bcr	PROPN
ejpam-5016	227	6	−	−	PROPN
ejpam-5016	227	7	efq	efq	PROPN
ejpam-5016	227	8	=	=	SYM
ejpam-5016	227	9	(	(	PUNCT
ejpam-5016	227	10	−e)(qf	−e)(qf	PROPN
ejpam-5016	227	11	−	−	PROPN
ejpam-5016	227	12	zr	zr	PROPN
ejpam-5016	227	13	)	)	PUNCT
ejpam-5016	228	1	+	+	CCONJ
ejpam-5016	228	2	(	(	PUNCT
ejpam-5016	228	3	−r)(ez	−r)(ez	PROPN
ejpam-5016	228	4	−	−	PROPN
ejpam-5016	228	5	bc	bc	PROPN
ejpam-5016	228	6	)	)	PUNCT
ejpam-5016	228	7	is	be	AUX
ejpam-5016	228	8	reduced	reduce	VERB
ejpam-5016	228	9	to	to	ADP
ejpam-5016	228	10	zero	zero	NUM
ejpam-5016	228	11	.	.	PUNCT
ejpam-5016	229	1	a	a	DET
ejpam-5016	229	2	b	b	NOUN
ejpam-5016	229	3	c	c	NOUN
ejpam-5016	229	4	d	d	X
ejpam-5016	229	5	e	e	X
ejpam-5016	229	6	f	f	PROPN
ejpam-5016	229	7	r	r	NOUN
ejpam-5016	229	8	qz	qz	PROPN
ejpam-5016	229	9	figure	figure	NOUN
ejpam-5016	229	10	10	10	NUM
ejpam-5016	229	11	:	:	PUNCT
ejpam-5016	229	12	case	case	NOUN
ejpam-5016	229	13	a	a	DET
ejpam-5016	229	14	=	=	SYM
ejpam-5016	229	15	p	p	NOUN
ejpam-5016	229	16	,	,	PUNCT
ejpam-5016	229	17	d	d	PROPN
ejpam-5016	229	18	=	=	SYM
ejpam-5016	229	19	s	s	X
ejpam-5016	229	20	and	and	CCONJ
ejpam-5016	229	21	a	a	DET
ejpam-5016	229	22	<	<	X
ejpam-5016	229	23	f	f	X
ejpam-5016	229	24	<	<	X
ejpam-5016	229	25	r.	r.	PROPN
ejpam-5016	229	26	(	(	PUNCT
ejpam-5016	229	27	ii	ii	PROPN
ejpam-5016	229	28	)	)	PUNCT
ejpam-5016	229	29	the	the	DET
ejpam-5016	229	30	case	case	NOUN
ejpam-5016	229	31	a	a	DET
ejpam-5016	229	32	=	=	SYM
ejpam-5016	229	33	p	p	NOUN
ejpam-5016	229	34	and	and	CCONJ
ejpam-5016	229	35	f	f	NOUN
ejpam-5016	230	1	=	=	NOUN
ejpam-5016	230	2	r	r	NOUN
ejpam-5016	230	3	is	be	AUX
ejpam-5016	230	4	similar	similar	ADJ
ejpam-5016	230	5	with	with	ADP
ejpam-5016	230	6	the	the	DET
ejpam-5016	230	7	first	first	ADJ
ejpam-5016	230	8	case	case	NOUN
ejpam-5016	230	9	.	.	PUNCT
ejpam-5016	231	1	(	(	PUNCT
ejpam-5016	231	2	iii	iii	X
ejpam-5016	231	3	)	)	PUNCT
ejpam-5016	231	4	if	if	SCONJ
ejpam-5016	231	5	b	b	NOUN
ejpam-5016	231	6	=	=	SYM
ejpam-5016	232	1	p	p	NOUN
ejpam-5016	232	2	and	and	CCONJ
ejpam-5016	232	3	e	e	X
ejpam-5016	232	4	=	=	SYM
ejpam-5016	232	5	s	s	PROPN
ejpam-5016	232	6	then	then	ADV
ejpam-5016	232	7	s(f	s(f	PROPN
ejpam-5016	232	8	,	,	PUNCT
ejpam-5016	232	9	g	g	NOUN
ejpam-5016	232	10	)	)	PUNCT
ejpam-5016	233	1	=	=	PUNCT
ejpam-5016	233	2	e(acr	e(acr	ADP
ejpam-5016	233	3	−	−	NUM
ejpam-5016	233	4	dfq	dfq	NOUN
ejpam-5016	233	5	)	)	PUNCT
ejpam-5016	233	6	.	.	PUNCT
ejpam-5016	234	1	note	note	VERB
ejpam-5016	234	2	the	the	DET
ejpam-5016	234	3	the	the	DET
ejpam-5016	234	4	interval	interval	NOUN
ejpam-5016	234	5	determined	determine	VERB
ejpam-5016	234	6	by	by	ADP
ejpam-5016	234	7	{	{	PUNCT
ejpam-5016	234	8	a	a	PRON
ejpam-5016	234	9	,	,	PUNCT
ejpam-5016	234	10	r	r	NOUN
ejpam-5016	234	11	}	}	PUNCT
ejpam-5016	234	12	and	and	CCONJ
ejpam-5016	234	13	the	the	DET
ejpam-5016	234	14	interval	interval	NOUN
ejpam-5016	234	15	determined	determine	VERB
ejpam-5016	234	16	by	by	ADP
ejpam-5016	234	17	{	{	PUNCT
ejpam-5016	234	18	a	a	PROPN
ejpam-5016	234	19	,	,	PUNCT
ejpam-5016	234	20	c	c	NOUN
ejpam-5016	234	21	}	}	PUNCT
ejpam-5016	234	22	are	be	AUX
ejpam-5016	234	23	not	not	PART
ejpam-5016	234	24	inner	inner	ADJ
ejpam-5016	234	25	intervals	interval	NOUN
ejpam-5016	234	26	.	.	PUNCT
ejpam-5016	235	1	therefore	therefore	ADV
ejpam-5016	235	2	acr	acr	PROPN
ejpam-5016	235	3	−	−	PROPN
ejpam-5016	235	4	dfq	dfq	PROPN
ejpam-5016	235	5	∈	∈	PROPN
ejpam-5016	235	6	s3	s3	PROPN
ejpam-5016	235	7	and	and	CCONJ
ejpam-5016	235	8	s(f	s(f	PROPN
ejpam-5016	235	9	,	,	PUNCT
ejpam-5016	235	10	g	g	NOUN
ejpam-5016	235	11	)	)	PUNCT
ejpam-5016	235	12	is	be	AUX
ejpam-5016	235	13	reduced	reduce	VERB
ejpam-5016	235	14	to	to	ADP
ejpam-5016	235	15	zero	zero	NUM
ejpam-5016	235	16	.	.	PUNCT
ejpam-5016	236	1	y.	y.	PROPN
ejpam-5016	236	2	y.	y.	PROPN
ejpam-5016	236	3	hamonangan	hamonangan	PROPN
ejpam-5016	236	4	,	,	PUNCT
ejpam-5016	236	5	i.	i.	PROPN
ejpam-5016	236	6	muchtadi	muchtadi	PROPN
ejpam-5016	236	7	-	-	PUNCT
ejpam-5016	236	8	alamsyah	alamsyah	NOUN
ejpam-5016	236	9	/	/	SYM
ejpam-5016	236	10	eur	eur	PROPN
ejpam-5016	236	11	.	.	PUNCT
ejpam-5016	237	1	j.	j.	PROPN
ejpam-5016	237	2	pure	pure	PROPN
ejpam-5016	237	3	appl	appl	PROPN
ejpam-5016	237	4	.	.	PROPN
ejpam-5016	237	5	math	math	PROPN
ejpam-5016	237	6	,	,	PUNCT
ejpam-5016	237	7	17	17	NUM
ejpam-5016	237	8	(	(	PUNCT
ejpam-5016	237	9	4	4	NUM
ejpam-5016	237	10	)	)	PUNCT
ejpam-5016	237	11	(	(	PUNCT
ejpam-5016	237	12	2024	2024	NUM
ejpam-5016	237	13	)	)	PUNCT
ejpam-5016	237	14	,	,	PUNCT
ejpam-5016	237	15	2621	2621	NUM
ejpam-5016	237	16	-	-	SYM
ejpam-5016	237	17	2650	2650	NUM
ejpam-5016	237	18	2630	2630	NUM
ejpam-5016	237	19	(	(	PUNCT
ejpam-5016	237	20	iv	iv	X
ejpam-5016	237	21	)	)	PUNCT
ejpam-5016	237	22	if	if	SCONJ
ejpam-5016	237	23	b	b	X
ejpam-5016	237	24	=	=	SYM
ejpam-5016	237	25	q	q	PROPN
ejpam-5016	237	26	and	and	CCONJ
ejpam-5016	237	27	d	d	PROPN
ejpam-5016	237	28	=	=	SYM
ejpam-5016	237	29	s	s	PROPN
ejpam-5016	237	30	then	then	ADV
ejpam-5016	237	31	s(f	s(f	PROPN
ejpam-5016	237	32	,	,	PUNCT
ejpam-5016	237	33	g	g	NOUN
ejpam-5016	237	34	)	)	PUNCT
ejpam-5016	237	35	=	=	SYM
ejpam-5016	238	1	d(acr	d(acr	NOUN
ejpam-5016	238	2	−	−	PROPN
ejpam-5016	238	3	pef	pef	NOUN
ejpam-5016	238	4	)	)	PUNCT
ejpam-5016	238	5	.	.	PUNCT
ejpam-5016	239	1	since	since	SCONJ
ejpam-5016	239	2	the	the	DET
ejpam-5016	239	3	interval	interval	NOUN
ejpam-5016	239	4	determined	determine	VERB
ejpam-5016	239	5	by	by	ADP
ejpam-5016	239	6	{	{	PUNCT
ejpam-5016	239	7	a	a	PROPN
ejpam-5016	239	8	,	,	PUNCT
ejpam-5016	239	9	b	b	NOUN
ejpam-5016	239	10	}	}	PUNCT
ejpam-5016	239	11	is	be	AUX
ejpam-5016	239	12	not	not	PART
ejpam-5016	239	13	inner	inner	ADJ
ejpam-5016	239	14	interval	interval	NOUN
ejpam-5016	239	15	then	then	ADV
ejpam-5016	239	16	a	a	DET
ejpam-5016	239	17	<	<	X
ejpam-5016	239	18	p	p	X
ejpam-5016	239	19	<	<	X
ejpam-5016	239	20	d	d	NOUN
ejpam-5016	239	21	and	and	CCONJ
ejpam-5016	239	22	the	the	DET
ejpam-5016	239	23	interval	interval	NOUN
ejpam-5016	239	24	determined	determine	VERB
ejpam-5016	239	25	by	by	ADP
ejpam-5016	239	26	{	{	PUNCT
ejpam-5016	239	27	a	a	PRON
ejpam-5016	239	28	,	,	PUNCT
ejpam-5016	239	29	r	r	NOUN
ejpam-5016	239	30	}	}	PUNCT
ejpam-5016	239	31	is	be	AUX
ejpam-5016	239	32	not	not	PART
ejpam-5016	239	33	an	an	DET
ejpam-5016	239	34	inner	inner	ADJ
ejpam-5016	239	35	interval	interval	NOUN
ejpam-5016	239	36	.	.	PUNCT
ejpam-5016	240	1	therefore	therefore	ADV
ejpam-5016	240	2	acr	acr	PROPN
ejpam-5016	240	3	−	−	PROPN
ejpam-5016	240	4	pef	pef	PROPN
ejpam-5016	240	5	∈	∈	PROPN
ejpam-5016	240	6	s3	s3	PROPN
ejpam-5016	240	7	and	and	CCONJ
ejpam-5016	240	8	s(f	s(f	PROPN
ejpam-5016	240	9	,	,	PUNCT
ejpam-5016	240	10	g	g	NOUN
ejpam-5016	240	11	)	)	PUNCT
ejpam-5016	240	12	is	be	AUX
ejpam-5016	240	13	reduced	reduce	VERB
ejpam-5016	240	14	to	to	ADP
ejpam-5016	240	15	zero	zero	NUM
ejpam-5016	240	16	.	.	PUNCT
ejpam-5016	241	1	(	(	PUNCT
ejpam-5016	241	2	v	v	NOUN
ejpam-5016	241	3	)	)	PUNCT
ejpam-5016	241	4	the	the	DET
ejpam-5016	241	5	case	case	NOUN
ejpam-5016	241	6	c	c	X
ejpam-5016	241	7	=	=	SYM
ejpam-5016	241	8	p	p	PROPN
ejpam-5016	241	9	and	and	CCONJ
ejpam-5016	241	10	e	e	NOUN
ejpam-5016	241	11	=	=	NOUN
ejpam-5016	241	12	r	r	NOUN
ejpam-5016	241	13	is	be	AUX
ejpam-5016	241	14	similar	similar	ADJ
ejpam-5016	241	15	with	with	ADP
ejpam-5016	241	16	the	the	DET
ejpam-5016	241	17	case	case	NOUN
ejpam-5016	241	18	(	(	PUNCT
ejpam-5016	241	19	iii	iii	NOUN
ejpam-5016	241	20	)	)	PUNCT
ejpam-5016	241	21	.	.	PUNCT
ejpam-5016	242	1	(	(	PUNCT
ejpam-5016	242	2	vi	vi	X
ejpam-5016	242	3	)	)	PUNCT
ejpam-5016	242	4	the	the	DET
ejpam-5016	242	5	case	case	NOUN
ejpam-5016	242	6	c	c	NOUN
ejpam-5016	242	7	=	=	SYM
ejpam-5016	242	8	q	q	X
ejpam-5016	242	9	and	and	CCONJ
ejpam-5016	242	10	r	r	NOUN
ejpam-5016	242	11	=	=	SYM
ejpam-5016	242	12	f	f	NOUN
ejpam-5016	242	13	is	be	AUX
ejpam-5016	242	14	similar	similar	ADJ
ejpam-5016	242	15	with	with	ADP
ejpam-5016	242	16	the	the	DET
ejpam-5016	242	17	case	case	NOUN
ejpam-5016	242	18	(	(	PUNCT
ejpam-5016	242	19	iv	iv	NUM
ejpam-5016	242	20	)	)	PUNCT
ejpam-5016	242	21	.	.	PUNCT
ejpam-5016	243	1	now	now	ADV
ejpam-5016	243	2	,	,	PUNCT
ejpam-5016	243	3	we	we	PRON
ejpam-5016	243	4	can	can	AUX
ejpam-5016	243	5	assume	assume	VERB
ejpam-5016	243	6	that	that	SCONJ
ejpam-5016	243	7	f	f	PROPN
ejpam-5016	243	8	and	and	CCONJ
ejpam-5016	243	9	g	g	PROPN
ejpam-5016	243	10	have	have	VERB
ejpam-5016	243	11	no	no	DET
ejpam-5016	243	12	common	common	ADJ
ejpam-5016	243	13	monomial	monomial	ADJ
ejpam-5016	243	14	divisor	divisor	NOUN
ejpam-5016	243	15	in	in	ADP
ejpam-5016	243	16	their	their	PRON
ejpam-5016	243	17	noninitial	noninitial	ADJ
ejpam-5016	243	18	monomials	monomial	NOUN
ejpam-5016	243	19	.	.	PUNCT
ejpam-5016	244	1	we	we	PRON
ejpam-5016	244	2	consider	consider	VERB
ejpam-5016	244	3	every	every	DET
ejpam-5016	244	4	possibility	possibility	NOUN
ejpam-5016	244	5	of	of	ADP
ejpam-5016	244	6	{	{	PUNCT
ejpam-5016	244	7	a	a	PROPN
ejpam-5016	244	8	,	,	PUNCT
ejpam-5016	244	9	b	b	NOUN
ejpam-5016	244	10	,	,	PUNCT
ejpam-5016	244	11	c	c	NOUN
ejpam-5016	244	12	}	}	PUNCT
ejpam-5016	244	13	∩	∩	NOUN
ejpam-5016	244	14	{	{	PUNCT
ejpam-5016	244	15	p	p	X
ejpam-5016	244	16	,	,	PUNCT
ejpam-5016	244	17	q	q	NOUN
ejpam-5016	244	18	}	}	PUNCT
ejpam-5016	244	19	.	.	PUNCT
ejpam-5016	245	1	(	(	PUNCT
ejpam-5016	245	2	i	i	NOUN
ejpam-5016	245	3	)	)	PUNCT
ejpam-5016	245	4	if	if	SCONJ
ejpam-5016	245	5	q	q	NOUN
ejpam-5016	245	6	=	=	SYM
ejpam-5016	245	7	c	c	NOUN
ejpam-5016	245	8	then	then	ADV
ejpam-5016	245	9	s(f	s(f	PROPN
ejpam-5016	245	10	,	,	PUNCT
ejpam-5016	245	11	g	g	NOUN
ejpam-5016	245	12	)	)	PUNCT
ejpam-5016	245	13	=	=	VERB
ejpam-5016	245	14	abrs	abr	VERB
ejpam-5016	246	1	−	−	PROPN
ejpam-5016	246	2	pdef	pdef	NOUN
ejpam-5016	246	3	.	.	PUNCT
ejpam-5016	247	1	note	note	VERB
ejpam-5016	247	2	that	that	SCONJ
ejpam-5016	247	3	r	r	NOUN
ejpam-5016	247	4	,	,	PUNCT
ejpam-5016	247	5	c	c	X
ejpam-5016	247	6	,	,	PUNCT
ejpam-5016	247	7	f	f	PROPN
ejpam-5016	247	8	are	be	AUX
ejpam-5016	247	9	in	in	ADP
ejpam-5016	247	10	vertical	vertical	ADJ
ejpam-5016	247	11	position	position	NOUN
ejpam-5016	247	12	.	.	PUNCT
ejpam-5016	248	1	consider	consider	VERB
ejpam-5016	248	2	the	the	DET
ejpam-5016	248	3	vertex	vertex	NOUN
ejpam-5016	248	4	r.	r.	PROPN
ejpam-5016	248	5	if	if	SCONJ
ejpam-5016	248	6	b	b	PROPN
ejpam-5016	248	7	<	<	X
ejpam-5016	248	8	p	p	X
ejpam-5016	248	9	r	r	NOUN
ejpam-5016	248	10	then	then	ADV
ejpam-5016	248	11	the	the	DET
ejpam-5016	248	12	interval	interval	NOUN
ejpam-5016	248	13	determined	determine	VERB
ejpam-5016	248	14	by	by	ADP
ejpam-5016	248	15	{	{	PUNCT
ejpam-5016	248	16	p	p	X
ejpam-5016	248	17	,	,	PUNCT
ejpam-5016	248	18	e	e	NOUN
ejpam-5016	248	19	}	}	PUNCT
ejpam-5016	248	20	is	be	AUX
ejpam-5016	248	21	an	an	DET
ejpam-5016	248	22	inner	inner	ADJ
ejpam-5016	248	23	interval	interval	NOUN
ejpam-5016	248	24	with	with	ADP
ejpam-5016	248	25	s	s	PRON
ejpam-5016	248	26	as	as	ADP
ejpam-5016	248	27	one	one	NUM
ejpam-5016	248	28	of	of	ADP
ejpam-5016	248	29	the	the	DET
ejpam-5016	248	30	antidiagonal	antidiagonal	ADJ
ejpam-5016	248	31	corner	corner	NOUN
ejpam-5016	248	32	.	.	PUNCT
ejpam-5016	249	1	let	let	VERB
ejpam-5016	249	2	y	y	PRON
ejpam-5016	249	3	be	be	AUX
ejpam-5016	249	4	the	the	DET
ejpam-5016	249	5	other	other	ADJ
ejpam-5016	249	6	antidiagonal	antidiagonal	ADJ
ejpam-5016	249	7	corner	corner	NOUN
ejpam-5016	249	8	.	.	PUNCT
ejpam-5016	250	1	it	it	PRON
ejpam-5016	250	2	is	be	AUX
ejpam-5016	250	3	clear	clear	ADJ
ejpam-5016	250	4	that	that	SCONJ
ejpam-5016	250	5	y	y	PROPN
ejpam-5016	250	6	,	,	PUNCT
ejpam-5016	250	7	b	b	PROPN
ejpam-5016	250	8	,	,	PUNCT
ejpam-5016	250	9	e	e	X
ejpam-5016	250	10	are	be	AUX
ejpam-5016	250	11	in	in	ADP
ejpam-5016	250	12	vertical	vertical	ADJ
ejpam-5016	250	13	position	position	NOUN
ejpam-5016	250	14	and	and	CCONJ
ejpam-5016	250	15	b	b	NOUN
ejpam-5016	250	16	<	<	X
ejpam-5016	250	17	p	p	X
ejpam-5016	250	18	y	y	PROPN
ejpam-5016	250	19	<	<	X
ejpam-5016	250	20	p	p	PROPN
ejpam-5016	250	21	e.	e.	PROPN
ejpam-5016	250	22	therefore	therefore	ADV
ejpam-5016	250	23	,	,	PUNCT
ejpam-5016	250	24	s(f	s(f	PROPN
ejpam-5016	250	25	,	,	PUNCT
ejpam-5016	250	26	g	g	NOUN
ejpam-5016	250	27	)	)	PUNCT
ejpam-5016	250	28	=	=	PUNCT
ejpam-5016	251	1	(	(	PUNCT
ejpam-5016	251	2	abr	abr	INTJ
ejpam-5016	251	3	−	−	PROPN
ejpam-5016	251	4	dfy)s+	dfy)s+	NOUN
ejpam-5016	251	5	df(ys−	df(ys−	NOUN
ejpam-5016	251	6	pe	pe	NOUN
ejpam-5016	251	7	)	)	PUNCT
ejpam-5016	251	8	.	.	PUNCT
ejpam-5016	252	1	the	the	DET
ejpam-5016	252	2	binomial	binomial	ADJ
ejpam-5016	252	3	abr−dfy	abr−dfy	NOUN
ejpam-5016	252	4	is	be	AUX
ejpam-5016	252	5	reduced	reduce	VERB
ejpam-5016	252	6	to	to	ADP
ejpam-5016	252	7	zero	zero	NUM
ejpam-5016	252	8	by	by	ADP
ejpam-5016	252	9	s2	s2	PROPN
ejpam-5016	252	10	or	or	CCONJ
ejpam-5016	252	11	an	an	DET
ejpam-5016	252	12	element	element	NOUN
ejpam-5016	252	13	of	of	ADP
ejpam-5016	252	14	s3	s3	PROPN
ejpam-5016	252	15	.	.	PUNCT
ejpam-5016	253	1	hence	hence	ADV
ejpam-5016	253	2	,	,	PUNCT
ejpam-5016	253	3	s(f	s(f	PROPN
ejpam-5016	253	4	,	,	PUNCT
ejpam-5016	253	5	g	g	NOUN
ejpam-5016	253	6	)	)	PUNCT
ejpam-5016	253	7	is	be	AUX
ejpam-5016	253	8	reduced	reduce	VERB
ejpam-5016	253	9	to	to	ADP
ejpam-5016	253	10	zero	zero	NUM
ejpam-5016	253	11	.	.	PUNCT
ejpam-5016	254	1	a	a	DET
ejpam-5016	254	2	b	b	NOUN
ejpam-5016	254	3	c	c	NOUN
ejpam-5016	254	4	d	d	PROPN
ejpam-5016	254	5	e	e	X
ejpam-5016	254	6	f	f	PROPN
ejpam-5016	254	7	s	s	PROPN
ejpam-5016	254	8	p	p	NOUN
ejpam-5016	254	9	r	r	X
ejpam-5016	254	10	y	y	PROPN
ejpam-5016	254	11	a	a	DET
ejpam-5016	254	12	b	b	NOUN
ejpam-5016	254	13	c	c	NOUN
ejpam-5016	254	14	d	d	X
ejpam-5016	254	15	es	es	X
ejpam-5016	254	16	p	p	X
ejpam-5016	254	17	r	r	NOUN
ejpam-5016	254	18	y	y	PROPN
ejpam-5016	254	19	f	f	PROPN
ejpam-5016	254	20	figure	figure	NOUN
ejpam-5016	254	21	11	11	NUM
ejpam-5016	254	22	:	:	PUNCT
ejpam-5016	254	23	case	case	NOUN
ejpam-5016	254	24	q	q	X
ejpam-5016	254	25	=	=	SYM
ejpam-5016	254	26	c	c	NOUN
ejpam-5016	254	27	and	and	CCONJ
ejpam-5016	254	28	b	b	X
ejpam-5016	254	29	<	<	X
ejpam-5016	254	30	p	p	X
ejpam-5016	254	31	r.	r.	PROPN
ejpam-5016	254	32	a	a	DET
ejpam-5016	254	33	b	b	PROPN
ejpam-5016	254	34	c	c	NOUN
ejpam-5016	254	35	d	d	PROPN
ejpam-5016	254	36	e	e	X
ejpam-5016	254	37	f	f	PROPN
ejpam-5016	254	38	s	s	PROPN
ejpam-5016	254	39	p	p	X
ejpam-5016	254	40	y	y	PROPN
ejpam-5016	254	41	r	r	NOUN
ejpam-5016	254	42	a	a	DET
ejpam-5016	254	43	b	b	NOUN
ejpam-5016	254	44	c	c	NOUN
ejpam-5016	254	45	d	d	PROPN
ejpam-5016	254	46	e	e	X
ejpam-5016	254	47	f	f	PROPN
ejpam-5016	254	48	s	s	PROPN
ejpam-5016	254	49	p	p	PROPN
ejpam-5016	254	50	y	y	PROPN
ejpam-5016	254	51	r	r	NOUN
ejpam-5016	254	52	figure	figure	NOUN
ejpam-5016	254	53	12	12	NUM
ejpam-5016	254	54	:	:	PUNCT
ejpam-5016	254	55	case	case	NOUN
ejpam-5016	254	56	q	q	X
ejpam-5016	254	57	=	=	PUNCT
ejpam-5016	254	58	c	c	NOUN
ejpam-5016	254	59	and	and	CCONJ
ejpam-5016	254	60	r	r	NOUN
ejpam-5016	254	61	<	<	X
ejpam-5016	254	62	p	p	X
ejpam-5016	254	63	b.	b.	PROPN
ejpam-5016	254	64	y.	y.	PROPN
ejpam-5016	254	65	y.	y.	PROPN
ejpam-5016	254	66	hamonangan	hamonangan	PROPN
ejpam-5016	254	67	,	,	PUNCT
ejpam-5016	254	68	i.	i.	PROPN
ejpam-5016	254	69	muchtadi	muchtadi	PROPN
ejpam-5016	254	70	-	-	PUNCT
ejpam-5016	254	71	alamsyah	alamsyah	NOUN
ejpam-5016	254	72	/	/	SYM
ejpam-5016	254	73	eur	eur	PROPN
ejpam-5016	254	74	.	.	PUNCT
ejpam-5016	255	1	j.	j.	PROPN
ejpam-5016	255	2	pure	pure	PROPN
ejpam-5016	255	3	appl	appl	PROPN
ejpam-5016	255	4	.	.	PROPN
ejpam-5016	255	5	math	math	PROPN
ejpam-5016	255	6	,	,	PUNCT
ejpam-5016	255	7	17	17	NUM
ejpam-5016	255	8	(	(	PUNCT
ejpam-5016	255	9	4	4	NUM
ejpam-5016	255	10	)	)	PUNCT
ejpam-5016	255	11	(	(	PUNCT
ejpam-5016	255	12	2024	2024	NUM
ejpam-5016	255	13	)	)	PUNCT
ejpam-5016	255	14	,	,	PUNCT
ejpam-5016	255	15	2621	2621	NUM
ejpam-5016	255	16	-	-	SYM
ejpam-5016	255	17	2650	2650	NUM
ejpam-5016	255	18	2631	2631	NUM
ejpam-5016	255	19	if	if	SCONJ
ejpam-5016	255	20	r	r	NOUN
ejpam-5016	255	21	<	<	X
ejpam-5016	255	22	p	p	X
ejpam-5016	255	23	b	b	PROPN
ejpam-5016	256	1	then	then	ADV
ejpam-5016	256	2	the	the	DET
ejpam-5016	256	3	interval	interval	NOUN
ejpam-5016	256	4	determined	determine	VERB
ejpam-5016	256	5	by	by	ADP
ejpam-5016	256	6	{	{	PUNCT
ejpam-5016	256	7	p	p	X
ejpam-5016	256	8	,	,	PUNCT
ejpam-5016	256	9	f	f	X
ejpam-5016	256	10	}	}	PUNCT
ejpam-5016	256	11	is	be	AUX
ejpam-5016	256	12	an	an	DET
ejpam-5016	256	13	inner	inner	ADJ
ejpam-5016	256	14	interval	interval	NOUN
ejpam-5016	256	15	.	.	PUNCT
ejpam-5016	257	1	let	let	VERB
ejpam-5016	257	2	y	y	PRON
ejpam-5016	257	3	be	be	AUX
ejpam-5016	257	4	the	the	DET
ejpam-5016	257	5	vertex	vertex	NOUN
ejpam-5016	257	6	such	such	ADJ
ejpam-5016	257	7	that	that	SCONJ
ejpam-5016	257	8	the	the	DET
ejpam-5016	257	9	interval	interval	NOUN
ejpam-5016	257	10	determined	determine	VERB
ejpam-5016	257	11	by	by	ADP
ejpam-5016	257	12	{	{	PUNCT
ejpam-5016	257	13	y	y	PROPN
ejpam-5016	257	14	,	,	PUNCT
ejpam-5016	257	15	r	r	NOUN
ejpam-5016	257	16	}	}	PUNCT
ejpam-5016	257	17	is	be	AUX
ejpam-5016	257	18	the	the	DET
ejpam-5016	257	19	inner	inner	ADJ
ejpam-5016	257	20	interval	interval	NOUN
ejpam-5016	257	21	determined	determine	VERB
ejpam-5016	257	22	by	by	ADP
ejpam-5016	257	23	{	{	PUNCT
ejpam-5016	257	24	p	p	X
ejpam-5016	257	25	,	,	PUNCT
ejpam-5016	257	26	f	f	NOUN
ejpam-5016	257	27	}	}	PUNCT
ejpam-5016	257	28	.	.	PUNCT
ejpam-5016	258	1	it	it	PRON
ejpam-5016	258	2	is	be	AUX
ejpam-5016	258	3	clear	clear	ADJ
ejpam-5016	258	4	that	that	SCONJ
ejpam-5016	258	5	a	a	X
ejpam-5016	258	6	,	,	PUNCT
ejpam-5016	258	7	y	y	PROPN
ejpam-5016	258	8	,	,	PUNCT
ejpam-5016	258	9	f	f	PROPN
ejpam-5016	258	10	are	be	AUX
ejpam-5016	258	11	in	in	ADP
ejpam-5016	258	12	horizontal	horizontal	ADJ
ejpam-5016	258	13	position	position	NOUN
ejpam-5016	258	14	and	and	CCONJ
ejpam-5016	258	15	a	a	DET
ejpam-5016	258	16	<	<	X
ejpam-5016	258	17	p	p	X
ejpam-5016	258	18	y	y	NOUN
ejpam-5016	258	19	<	<	X
ejpam-5016	258	20	p	p	X
ejpam-5016	258	21	f	f	PROPN
ejpam-5016	258	22	since	since	SCONJ
ejpam-5016	258	23	the	the	DET
ejpam-5016	258	24	interval	interval	NOUN
ejpam-5016	258	25	determined	determine	VERB
ejpam-5016	258	26	by	by	ADP
ejpam-5016	258	27	{	{	PUNCT
ejpam-5016	258	28	a	a	PROPN
ejpam-5016	258	29	,	,	PUNCT
ejpam-5016	258	30	c	c	NOUN
ejpam-5016	258	31	}	}	PUNCT
ejpam-5016	258	32	is	be	AUX
ejpam-5016	258	33	not	not	PART
ejpam-5016	258	34	an	an	DET
ejpam-5016	258	35	inner	inner	ADJ
ejpam-5016	258	36	interval	interval	NOUN
ejpam-5016	258	37	.	.	PUNCT
ejpam-5016	259	1	therefore	therefore	ADV
ejpam-5016	259	2	s(f	s(f	PROPN
ejpam-5016	259	3	,	,	PUNCT
ejpam-5016	259	4	g	g	NOUN
ejpam-5016	259	5	)	)	PUNCT
ejpam-5016	259	6	=	=	PUNCT
ejpam-5016	259	7	(	(	PUNCT
ejpam-5016	259	8	abs−	abs−	PROPN
ejpam-5016	259	9	dey)r	dey)r	PROPN
ejpam-5016	259	10	+	+	CCONJ
ejpam-5016	259	11	de(yr	de(yr	ADJ
ejpam-5016	259	12	−	−	NOUN
ejpam-5016	259	13	pf	pf	NOUN
ejpam-5016	259	14	)	)	PUNCT
ejpam-5016	259	15	and	and	CCONJ
ejpam-5016	259	16	is	be	AUX
ejpam-5016	259	17	reduced	reduce	VERB
ejpam-5016	259	18	to	to	ADP
ejpam-5016	259	19	zero	zero	NUM
ejpam-5016	259	20	of	of	ADP
ejpam-5016	259	21	the	the	DET
ejpam-5016	259	22	previous	previous	ADJ
ejpam-5016	259	23	arguments	argument	NOUN
ejpam-5016	259	24	.	.	PUNCT
ejpam-5016	260	1	(	(	PUNCT
ejpam-5016	260	2	ii	ii	NOUN
ejpam-5016	260	3	)	)	PUNCT
ejpam-5016	261	1	if	if	SCONJ
ejpam-5016	261	2	q	q	NOUN
ejpam-5016	261	3	=	=	SYM
ejpam-5016	261	4	b	b	PROPN
ejpam-5016	261	5	then	then	ADV
ejpam-5016	261	6	s(f	s(f	PROPN
ejpam-5016	261	7	,	,	PUNCT
ejpam-5016	261	8	g	g	NOUN
ejpam-5016	261	9	)	)	PUNCT
ejpam-5016	261	10	=	=	PUNCT
ejpam-5016	261	11	acrs	acr	VERB
ejpam-5016	261	12	−	−	NOUN
ejpam-5016	261	13	pdef	pdef	NOUN
ejpam-5016	261	14	.	.	PUNCT
ejpam-5016	262	1	let	let	VERB
ejpam-5016	262	2	u	u	PRON
ejpam-5016	262	3	be	be	AUX
ejpam-5016	262	4	the	the	DET
ejpam-5016	262	5	intersection	intersection	NOUN
ejpam-5016	262	6	of	of	ADP
ejpam-5016	262	7	the	the	DET
ejpam-5016	262	8	segments	segment	NOUN
ejpam-5016	262	9	cf	cf	VERB
ejpam-5016	262	10	and	and	CCONJ
ejpam-5016	262	11	db	db	AUX
ejpam-5016	262	12	.	.	PROPN
ejpam-5016	262	13	consider	consider	VERB
ejpam-5016	262	14	the	the	DET
ejpam-5016	262	15	vertex	vertex	NOUN
ejpam-5016	262	16	s.	s.	PROPN
ejpam-5016	262	17	if	if	SCONJ
ejpam-5016	262	18	u	u	PROPN
ejpam-5016	262	19	<	<	X
ejpam-5016	262	20	p	p	X
ejpam-5016	262	21	s	s	X
ejpam-5016	262	22	then	then	ADV
ejpam-5016	262	23	[	[	X
ejpam-5016	262	24	p	p	X
ejpam-5016	262	25	,	,	PUNCT
ejpam-5016	262	26	e	e	X
ejpam-5016	262	27	]	]	X
ejpam-5016	262	28	is	be	AUX
ejpam-5016	262	29	an	an	DET
ejpam-5016	262	30	inner	inner	ADJ
ejpam-5016	262	31	interval	interval	NOUN
ejpam-5016	262	32	with	with	ADP
ejpam-5016	262	33	r	r	NOUN
ejpam-5016	262	34	as	as	ADP
ejpam-5016	262	35	one	one	NUM
ejpam-5016	262	36	of	of	ADP
ejpam-5016	262	37	the	the	DET
ejpam-5016	262	38	antidiagonal	antidiagonal	ADJ
ejpam-5016	262	39	corner	corner	NOUN
ejpam-5016	262	40	.	.	PUNCT
ejpam-5016	263	1	let	let	VERB
ejpam-5016	263	2	y	y	PRON
ejpam-5016	263	3	be	be	AUX
ejpam-5016	263	4	the	the	DET
ejpam-5016	263	5	other	other	ADJ
ejpam-5016	263	6	antidiagonal	antidiagonal	ADJ
ejpam-5016	263	7	corner	corner	NOUN
ejpam-5016	263	8	.	.	PUNCT
ejpam-5016	264	1	therefore	therefore	ADV
ejpam-5016	264	2	,	,	PUNCT
ejpam-5016	264	3	s(f	s(f	PROPN
ejpam-5016	264	4	,	,	PUNCT
ejpam-5016	264	5	g	g	NOUN
ejpam-5016	264	6	)	)	PUNCT
ejpam-5016	264	7	=	=	PUNCT
ejpam-5016	265	1	(	(	PUNCT
ejpam-5016	265	2	acs−	acs−	PROPN
ejpam-5016	265	3	dyf)r	dyf)r	PROPN
ejpam-5016	265	4	+	+	CCONJ
ejpam-5016	266	1	df(yr	df(yr	ADJ
ejpam-5016	266	2	−	−	NOUN
ejpam-5016	266	3	pe	pe	NOUN
ejpam-5016	266	4	)	)	PUNCT
ejpam-5016	266	5	and	and	CCONJ
ejpam-5016	266	6	is	be	AUX
ejpam-5016	266	7	reduced	reduce	VERB
ejpam-5016	266	8	to	to	ADP
ejpam-5016	266	9	zero	zero	NUM
ejpam-5016	266	10	.	.	PUNCT
ejpam-5016	267	1	a	a	DET
ejpam-5016	267	2	b	b	NOUN
ejpam-5016	267	3	c	c	NOUN
ejpam-5016	267	4	d	d	PROPN
ejpam-5016	267	5	e	e	X
ejpam-5016	267	6	f	f	PROPN
ejpam-5016	267	7	s	s	PROPN
ejpam-5016	267	8	p	p	X
ejpam-5016	267	9	y	y	PROPN
ejpam-5016	267	10	r	r	NOUN
ejpam-5016	267	11	a	a	DET
ejpam-5016	267	12	b	b	NOUN
ejpam-5016	267	13	c	c	NOUN
ejpam-5016	267	14	d	d	X
ejpam-5016	267	15	e	e	X
ejpam-5016	267	16	s	s	PROPN
ejpam-5016	267	17	p	p	X
ejpam-5016	267	18	y	y	PROPN
ejpam-5016	267	19	r	r	NOUN
ejpam-5016	267	20	f	f	PROPN
ejpam-5016	267	21	figure	figure	NOUN
ejpam-5016	267	22	13	13	NUM
ejpam-5016	267	23	:	:	PUNCT
ejpam-5016	267	24	case	case	NOUN
ejpam-5016	267	25	q	q	X
ejpam-5016	267	26	=	=	SYM
ejpam-5016	267	27	b	b	PROPN
ejpam-5016	267	28	and	and	CCONJ
ejpam-5016	267	29	u	u	NOUN
ejpam-5016	267	30	<	<	X
ejpam-5016	267	31	p	p	X
ejpam-5016	267	32	s.	s.	PROPN
ejpam-5016	267	33	if	if	SCONJ
ejpam-5016	267	34	s	s	VERB
ejpam-5016	267	35	≤p	≤p	ADJ
ejpam-5016	267	36	u	u	NOUN
ejpam-5016	267	37	then	then	ADV
ejpam-5016	267	38	the	the	DET
ejpam-5016	267	39	interval	interval	NOUN
ejpam-5016	267	40	determined	determine	VERB
ejpam-5016	267	41	by	by	ADP
ejpam-5016	267	42	{	{	PUNCT
ejpam-5016	267	43	p	p	X
ejpam-5016	267	44	,	,	PUNCT
ejpam-5016	267	45	d	d	NOUN
ejpam-5016	267	46	}	}	PUNCT
ejpam-5016	267	47	is	be	AUX
ejpam-5016	267	48	an	an	DET
ejpam-5016	267	49	inner	inner	ADJ
ejpam-5016	267	50	interval	interval	NOUN
ejpam-5016	267	51	.	.	PUNCT
ejpam-5016	268	1	a	a	DET
ejpam-5016	268	2	b	b	X
ejpam-5016	268	3	c	c	NOUN
ejpam-5016	268	4	d	d	PROPN
ejpam-5016	268	5	e	e	X
ejpam-5016	268	6	f	f	PROPN
ejpam-5016	268	7	s	s	PROPN
ejpam-5016	268	8	p	p	X
ejpam-5016	268	9	y	y	PROPN
ejpam-5016	268	10	r	r	NOUN
ejpam-5016	268	11	a	a	DET
ejpam-5016	268	12	b	b	NOUN
ejpam-5016	268	13	c	c	NOUN
ejpam-5016	268	14	d	d	X
ejpam-5016	268	15	e	e	X
ejpam-5016	268	16	s	s	PROPN
ejpam-5016	268	17	p	p	X
ejpam-5016	268	18	y	y	PROPN
ejpam-5016	268	19	r	r	NOUN
ejpam-5016	268	20	f	f	PROPN
ejpam-5016	268	21	figure	figure	NOUN
ejpam-5016	268	22	14	14	NUM
ejpam-5016	268	23	:	:	PUNCT
ejpam-5016	268	24	case	case	NOUN
ejpam-5016	268	25	q	q	X
ejpam-5016	269	1	=	=	SYM
ejpam-5016	269	2	b	b	PROPN
ejpam-5016	269	3	and	and	CCONJ
ejpam-5016	269	4	s	s	PROPN
ejpam-5016	269	5	≤p	≤p	PROPN
ejpam-5016	269	6	u.	u.	NOUN
ejpam-5016	269	7	let	let	VERB
ejpam-5016	269	8	y	y	PRON
ejpam-5016	269	9	be	be	AUX
ejpam-5016	269	10	a	a	DET
ejpam-5016	269	11	vertex	vertex	NOUN
ejpam-5016	269	12	such	such	ADJ
ejpam-5016	269	13	that	that	SCONJ
ejpam-5016	269	14	the	the	DET
ejpam-5016	269	15	interval	interval	NOUN
ejpam-5016	269	16	determined	determine	VERB
ejpam-5016	269	17	by	by	ADP
ejpam-5016	269	18	{	{	PUNCT
ejpam-5016	269	19	p	p	X
ejpam-5016	269	20	,	,	PUNCT
ejpam-5016	269	21	d	d	NOUN
ejpam-5016	269	22	}	}	PUNCT
ejpam-5016	269	23	is	be	AUX
ejpam-5016	269	24	the	the	DET
ejpam-5016	269	25	interval	interval	NOUN
ejpam-5016	269	26	determined	determine	VERB
ejpam-5016	269	27	by	by	ADP
ejpam-5016	269	28	{	{	PUNCT
ejpam-5016	269	29	y	y	PROPN
ejpam-5016	269	30	,	,	PUNCT
ejpam-5016	269	31	s	s	PART
ejpam-5016	269	32	}	}	PUNCT
ejpam-5016	269	33	.	.	PUNCT
ejpam-5016	270	1	note	note	VERB
ejpam-5016	270	2	that	that	SCONJ
ejpam-5016	270	3	a	a	X
ejpam-5016	270	4	,	,	PUNCT
ejpam-5016	270	5	y	y	PROPN
ejpam-5016	270	6	,	,	PUNCT
ejpam-5016	270	7	d	d	X
ejpam-5016	270	8	are	be	AUX
ejpam-5016	270	9	in	in	ADP
ejpam-5016	270	10	vertical	vertical	ADJ
ejpam-5016	270	11	position	position	NOUN
ejpam-5016	270	12	and	and	CCONJ
ejpam-5016	270	13	a	a	DET
ejpam-5016	270	14	<	<	X
ejpam-5016	270	15	p	p	X
ejpam-5016	270	16	y	y	NOUN
ejpam-5016	270	17	<	<	X
ejpam-5016	270	18	p	p	X
ejpam-5016	270	19	d	d	PROPN
ejpam-5016	270	20	since	since	SCONJ
ejpam-5016	270	21	the	the	DET
ejpam-5016	270	22	y.	y.	PROPN
ejpam-5016	270	23	y.	y.	PROPN
ejpam-5016	270	24	hamonangan	hamonangan	PROPN
ejpam-5016	270	25	,	,	PUNCT
ejpam-5016	270	26	i.	i.	PROPN
ejpam-5016	270	27	muchtadi	muchtadi	PROPN
ejpam-5016	270	28	-	-	PUNCT
ejpam-5016	270	29	alamsyah	alamsyah	NOUN
ejpam-5016	270	30	/	/	SYM
ejpam-5016	270	31	eur	eur	PROPN
ejpam-5016	270	32	.	.	PUNCT
ejpam-5016	271	1	j.	j.	PROPN
ejpam-5016	271	2	pure	pure	PROPN
ejpam-5016	271	3	appl	appl	PROPN
ejpam-5016	271	4	.	.	PROPN
ejpam-5016	271	5	math	math	PROPN
ejpam-5016	271	6	,	,	PUNCT
ejpam-5016	271	7	17	17	NUM
ejpam-5016	271	8	(	(	PUNCT
ejpam-5016	271	9	4	4	NUM
ejpam-5016	271	10	)	)	PUNCT
ejpam-5016	271	11	(	(	PUNCT
ejpam-5016	271	12	2024	2024	NUM
ejpam-5016	271	13	)	)	PUNCT
ejpam-5016	271	14	,	,	PUNCT
ejpam-5016	271	15	2621	2621	NUM
ejpam-5016	271	16	-	-	SYM
ejpam-5016	271	17	2650	2650	NUM
ejpam-5016	271	18	2632	2632	NUM
ejpam-5016	271	19	interval	interval	NOUN
ejpam-5016	271	20	determined	determine	VERB
ejpam-5016	271	21	by	by	ADP
ejpam-5016	271	22	{	{	PUNCT
ejpam-5016	271	23	a	a	PROPN
ejpam-5016	271	24	,	,	PUNCT
ejpam-5016	271	25	b	b	NOUN
ejpam-5016	271	26	}	}	PUNCT
ejpam-5016	271	27	is	be	AUX
ejpam-5016	271	28	not	not	PART
ejpam-5016	271	29	an	an	DET
ejpam-5016	271	30	inner	inner	ADJ
ejpam-5016	271	31	interval	interval	NOUN
ejpam-5016	271	32	.	.	PUNCT
ejpam-5016	272	1	therefore	therefore	ADV
ejpam-5016	272	2	s(f	s(f	PROPN
ejpam-5016	272	3	,	,	PUNCT
ejpam-5016	272	4	g	g	NOUN
ejpam-5016	272	5	)	)	PUNCT
ejpam-5016	272	6	=	=	SYM
ejpam-5016	273	1	(	(	PUNCT
ejpam-5016	273	2	arc−	arc−	ADJ
ejpam-5016	273	3	yef)s+	yef)s+	NOUN
ejpam-5016	273	4	ef(ys−	ef(ys−	PROPN
ejpam-5016	273	5	pd	pd	PROPN
ejpam-5016	273	6	)	)	PUNCT
ejpam-5016	273	7	and	and	CCONJ
ejpam-5016	273	8	is	be	AUX
ejpam-5016	273	9	reduced	reduce	VERB
ejpam-5016	273	10	to	to	ADP
ejpam-5016	273	11	zero	zero	NUM
ejpam-5016	273	12	.	.	PUNCT
ejpam-5016	274	1	(	(	PUNCT
ejpam-5016	274	2	iii	iii	X
ejpam-5016	274	3	)	)	PUNCT
ejpam-5016	274	4	if	if	SCONJ
ejpam-5016	274	5	q	q	NOUN
ejpam-5016	274	6	=	=	PUNCT
ejpam-5016	274	7	a	a	PRON
ejpam-5016	274	8	then	then	ADV
ejpam-5016	274	9	s(f	s(f	PROPN
ejpam-5016	274	10	,	,	PUNCT
ejpam-5016	274	11	g	g	NOUN
ejpam-5016	274	12	)	)	PUNCT
ejpam-5016	274	13	=	=	NOUN
ejpam-5016	274	14	bcrs	bcrs	NOUN
ejpam-5016	274	15	−	−	PROPN
ejpam-5016	274	16	pdef	pdef	NOUN
ejpam-5016	274	17	.	.	PUNCT
ejpam-5016	275	1	let	let	VERB
ejpam-5016	275	2	u	u	PRON
ejpam-5016	275	3	be	be	AUX
ejpam-5016	275	4	the	the	DET
ejpam-5016	275	5	intersection	intersection	NOUN
ejpam-5016	275	6	of	of	ADP
ejpam-5016	275	7	the	the	DET
ejpam-5016	275	8	segments	segment	NOUN
ejpam-5016	275	9	cf	cf	INTJ
ejpam-5016	276	1	and	and	CCONJ
ejpam-5016	276	2	bd	bd	PROPN
ejpam-5016	276	3	.	.	PROPN
ejpam-5016	276	4	note	note	NOUN
ejpam-5016	277	1	that	that	SCONJ
ejpam-5016	277	2	s(f	s(f	PROPN
ejpam-5016	277	3	,	,	PUNCT
ejpam-5016	277	4	g	g	NOUN
ejpam-5016	277	5	)	)	PUNCT
ejpam-5016	277	6	=	=	PUNCT
ejpam-5016	277	7	(	(	PUNCT
ejpam-5016	277	8	−rs)(ue−	−rs)(ue−	PROPN
ejpam-5016	277	9	bc	bc	PROPN
ejpam-5016	277	10	)	)	PUNCT
ejpam-5016	277	11	+	+	CCONJ
ejpam-5016	277	12	(	(	PUNCT
ejpam-5016	277	13	−e)(pdf	−e)(pdf	PROPN
ejpam-5016	277	14	−	−	PROPN
ejpam-5016	277	15	usr	usr	PROPN
ejpam-5016	277	16	)	)	PUNCT
ejpam-5016	277	17	and	and	CCONJ
ejpam-5016	277	18	therefore	therefore	ADV
ejpam-5016	277	19	is	be	AUX
ejpam-5016	277	20	reduced	reduce	VERB
ejpam-5016	277	21	to	to	ADP
ejpam-5016	277	22	zero	zero	NUM
ejpam-5016	277	23	.	.	PUNCT
ejpam-5016	278	1	a	a	DET
ejpam-5016	278	2	b	b	NOUN
ejpam-5016	278	3	c	c	NOUN
ejpam-5016	278	4	d	d	X
ejpam-5016	278	5	e	e	X
ejpam-5016	278	6	f	f	X
ejpam-5016	278	7	p	p	NOUN
ejpam-5016	278	8	r	r	NOUN
ejpam-5016	278	9	s	s	X
ejpam-5016	278	10	u	u	NOUN
ejpam-5016	278	11	figure	figure	NOUN
ejpam-5016	278	12	15	15	NUM
ejpam-5016	278	13	:	:	PUNCT
ejpam-5016	278	14	case	case	NOUN
ejpam-5016	278	15	q	q	NOUN
ejpam-5016	278	16	=	=	PUNCT
ejpam-5016	278	17	a.	a.	NOUN
ejpam-5016	278	18	(	(	PUNCT
ejpam-5016	278	19	iv	iv	X
ejpam-5016	278	20	)	)	PUNCT
ejpam-5016	278	21	if	if	SCONJ
ejpam-5016	278	22	p	p	NOUN
ejpam-5016	278	23	=	=	NOUN
ejpam-5016	278	24	a	a	PRON
ejpam-5016	278	25	then	then	ADV
ejpam-5016	278	26	s(f	s(f	PROPN
ejpam-5016	278	27	,	,	PUNCT
ejpam-5016	278	28	g	g	NOUN
ejpam-5016	278	29	)	)	PUNCT
ejpam-5016	278	30	=	=	SYM
ejpam-5016	278	31	bcrs	bcrs	NOUN
ejpam-5016	279	1	−	−	NOUN
ejpam-5016	279	2	qdef	qdef	ADJ
ejpam-5016	279	3	.	.	PUNCT
ejpam-5016	280	1	consider	consider	VERB
ejpam-5016	280	2	the	the	DET
ejpam-5016	280	3	vertex	vertex	NOUN
ejpam-5016	280	4	r	r	NOUN
ejpam-5016	280	5	which	which	PRON
ejpam-5016	280	6	is	be	AUX
ejpam-5016	280	7	in	in	ADP
ejpam-5016	280	8	horizontal	horizontal	ADJ
ejpam-5016	280	9	position	position	NOUN
ejpam-5016	280	10	with	with	ADP
ejpam-5016	280	11	a	a	PRON
ejpam-5016	280	12	and	and	CCONJ
ejpam-5016	280	13	f	f	NOUN
ejpam-5016	280	14	.	.	PUNCT
ejpam-5016	281	1	if	if	SCONJ
ejpam-5016	281	2	a	a	DET
ejpam-5016	281	3	<	<	X
ejpam-5016	281	4	p	p	X
ejpam-5016	281	5	r	r	NOUN
ejpam-5016	281	6	<	<	X
ejpam-5016	281	7	p	p	X
ejpam-5016	281	8	f	f	X
ejpam-5016	281	9	then	then	ADV
ejpam-5016	281	10	the	the	DET
ejpam-5016	281	11	interval	interval	NOUN
ejpam-5016	281	12	determined	determine	VERB
ejpam-5016	281	13	by	by	ADP
ejpam-5016	281	14	{	{	PUNCT
ejpam-5016	281	15	q	q	NOUN
ejpam-5016	281	16	,	,	PUNCT
ejpam-5016	281	17	d	d	NOUN
ejpam-5016	281	18	}	}	PUNCT
ejpam-5016	281	19	is	be	AUX
ejpam-5016	281	20	an	an	DET
ejpam-5016	281	21	inner	inner	ADJ
ejpam-5016	281	22	interval	interval	NOUN
ejpam-5016	281	23	and	and	CCONJ
ejpam-5016	281	24	it	it	PRON
ejpam-5016	281	25	is	be	AUX
ejpam-5016	281	26	an	an	DET
ejpam-5016	281	27	interval	interval	NOUN
ejpam-5016	281	28	determined	determine	VERB
ejpam-5016	281	29	by	by	ADP
ejpam-5016	281	30	{	{	PUNCT
ejpam-5016	281	31	s	s	PROPN
ejpam-5016	281	32	,	,	PUNCT
ejpam-5016	281	33	y	y	NOUN
ejpam-5016	281	34	}	}	PUNCT
ejpam-5016	281	35	for	for	ADP
ejpam-5016	281	36	some	some	DET
ejpam-5016	281	37	vertex	vertex	NOUN
ejpam-5016	281	38	y.	y.	PROPN
ejpam-5016	281	39	therefore	therefore	ADV
ejpam-5016	281	40	,	,	PUNCT
ejpam-5016	281	41	s(f	s(f	PROPN
ejpam-5016	281	42	,	,	PUNCT
ejpam-5016	281	43	g	g	NOUN
ejpam-5016	281	44	)	)	PUNCT
ejpam-5016	281	45	=	=	SYM
ejpam-5016	282	1	(	(	PUNCT
ejpam-5016	282	2	bcr	bcr	PROPN
ejpam-5016	282	3	−	−	PROPN
ejpam-5016	282	4	efy)s+	efy)s+	NOUN
ejpam-5016	282	5	ef(ys−	ef(ys−	NOUN
ejpam-5016	282	6	qd	qd	PROPN
ejpam-5016	282	7	)	)	PUNCT
ejpam-5016	282	8	is	be	AUX
ejpam-5016	282	9	reduced	reduce	VERB
ejpam-5016	282	10	to	to	ADP
ejpam-5016	282	11	zero	zero	NUM
ejpam-5016	282	12	.	.	PUNCT
ejpam-5016	283	1	a	a	DET
ejpam-5016	283	2	b	b	NOUN
ejpam-5016	283	3	c	c	NOUN
ejpam-5016	283	4	d	d	X
ejpam-5016	283	5	e	e	X
ejpam-5016	283	6	f	f	X
ejpam-5016	283	7	q	q	NOUN
ejpam-5016	283	8	r	r	NOUN
ejpam-5016	283	9	s	s	PROPN
ejpam-5016	283	10	y	y	PROPN
ejpam-5016	283	11	a	a	DET
ejpam-5016	283	12	b	b	NOUN
ejpam-5016	283	13	c	c	NOUN
ejpam-5016	283	14	d	d	X
ejpam-5016	283	15	e	e	NOUN
ejpam-5016	283	16	r	r	NOUN
ejpam-5016	283	17	qs	qs	PROPN
ejpam-5016	283	18	y	y	PROPN
ejpam-5016	283	19	f	f	PROPN
ejpam-5016	283	20	figure	figure	NOUN
ejpam-5016	283	21	16	16	NUM
ejpam-5016	283	22	:	:	PUNCT
ejpam-5016	283	23	case	case	NOUN
ejpam-5016	283	24	a	a	DET
ejpam-5016	283	25	<	<	X
ejpam-5016	283	26	p	p	X
ejpam-5016	283	27	r	r	NOUN
ejpam-5016	283	28	<	<	X
ejpam-5016	283	29	p	p	X
ejpam-5016	283	30	f	f	X
ejpam-5016	283	31	.	.	PUNCT
ejpam-5016	284	1	if	if	SCONJ
ejpam-5016	284	2	a	a	DET
ejpam-5016	284	3	<	<	X
ejpam-5016	284	4	p	p	X
ejpam-5016	284	5	f	f	X
ejpam-5016	284	6	<	<	X
ejpam-5016	284	7	p	p	X
ejpam-5016	284	8	r	r	NOUN
ejpam-5016	284	9	then	then	ADV
ejpam-5016	284	10	the	the	DET
ejpam-5016	284	11	interval	interval	NOUN
ejpam-5016	284	12	determined	determine	VERB
ejpam-5016	284	13	by	by	ADP
ejpam-5016	284	14	{	{	PUNCT
ejpam-5016	284	15	q	q	INTJ
ejpam-5016	284	16	,	,	PUNCT
ejpam-5016	284	17	f	f	X
ejpam-5016	284	18	}	}	PUNCT
ejpam-5016	284	19	is	be	AUX
ejpam-5016	284	20	an	an	DET
ejpam-5016	284	21	inner	inner	ADJ
ejpam-5016	284	22	interval	interval	NOUN
ejpam-5016	284	23	and	and	CCONJ
ejpam-5016	284	24	it	it	PRON
ejpam-5016	284	25	is	be	AUX
ejpam-5016	284	26	an	an	DET
ejpam-5016	284	27	interval	interval	NOUN
ejpam-5016	284	28	determined	determine	VERB
ejpam-5016	284	29	by	by	ADP
ejpam-5016	284	30	{	{	PUNCT
ejpam-5016	284	31	r	r	NOUN
ejpam-5016	284	32	,	,	PUNCT
ejpam-5016	284	33	y	y	NOUN
ejpam-5016	284	34	}	}	PUNCT
ejpam-5016	284	35	for	for	ADP
ejpam-5016	284	36	some	some	DET
ejpam-5016	284	37	vertex	vertex	NOUN
ejpam-5016	284	38	y.	y.	PROPN
ejpam-5016	284	39	note	note	VERB
ejpam-5016	284	40	that	that	SCONJ
ejpam-5016	284	41	s(f	s(f	PROPN
ejpam-5016	284	42	,	,	PUNCT
ejpam-5016	284	43	g	g	NOUN
ejpam-5016	284	44	)	)	PUNCT
ejpam-5016	284	45	=	=	SYM
ejpam-5016	284	46	(	(	PUNCT
ejpam-5016	284	47	bcs−	bcs−	NOUN
ejpam-5016	284	48	dey)r	dey)r	PROPN
ejpam-5016	284	49	+	+	CCONJ
ejpam-5016	284	50	ed(ry	ed(ry	PROPN
ejpam-5016	284	51	−	−	PROPN
ejpam-5016	284	52	fq	fq	PROPN
ejpam-5016	284	53	)	)	PUNCT
ejpam-5016	284	54	y.	y.	PROPN
ejpam-5016	284	55	y.	y.	PROPN
ejpam-5016	284	56	hamonangan	hamonangan	PROPN
ejpam-5016	284	57	,	,	PUNCT
ejpam-5016	284	58	i.	i.	PROPN
ejpam-5016	284	59	muchtadi	muchtadi	PROPN
ejpam-5016	284	60	-	-	PUNCT
ejpam-5016	284	61	alamsyah	alamsyah	NOUN
ejpam-5016	284	62	/	/	SYM
ejpam-5016	284	63	eur	eur	PROPN
ejpam-5016	284	64	.	.	PUNCT
ejpam-5016	285	1	j.	j.	PROPN
ejpam-5016	285	2	pure	pure	PROPN
ejpam-5016	285	3	appl	appl	PROPN
ejpam-5016	285	4	.	.	PROPN
ejpam-5016	285	5	math	math	PROPN
ejpam-5016	285	6	,	,	PUNCT
ejpam-5016	285	7	17	17	NUM
ejpam-5016	285	8	(	(	PUNCT
ejpam-5016	285	9	4	4	NUM
ejpam-5016	285	10	)	)	PUNCT
ejpam-5016	285	11	(	(	PUNCT
ejpam-5016	285	12	2024	2024	NUM
ejpam-5016	285	13	)	)	PUNCT
ejpam-5016	285	14	,	,	PUNCT
ejpam-5016	285	15	2621	2621	NUM
ejpam-5016	285	16	-	-	SYM
ejpam-5016	285	17	2650	2650	NUM
ejpam-5016	285	18	2633	2633	NUM
ejpam-5016	285	19	is	be	AUX
ejpam-5016	285	20	reduced	reduce	VERB
ejpam-5016	285	21	to	to	ADP
ejpam-5016	285	22	zero	zero	NUM
ejpam-5016	285	23	if	if	SCONJ
ejpam-5016	285	24	a	a	DET
ejpam-5016	285	25	<	<	X
ejpam-5016	285	26	p	p	X
ejpam-5016	285	27	s	s	X
ejpam-5016	285	28	<	<	X
ejpam-5016	285	29	p	p	X
ejpam-5016	285	30	d.	d.	NOUN
ejpam-5016	285	31	if	if	SCONJ
ejpam-5016	285	32	a	a	DET
ejpam-5016	285	33	<	<	X
ejpam-5016	285	34	p	p	X
ejpam-5016	285	35	d	d	X
ejpam-5016	285	36	<	<	X
ejpam-5016	285	37	p	p	X
ejpam-5016	285	38	s	s	PROPN
ejpam-5016	285	39	,	,	PUNCT
ejpam-5016	285	40	note	note	VERB
ejpam-5016	285	41	that	that	SCONJ
ejpam-5016	285	42	y	y	PRON
ejpam-5016	285	43	<	<	X
ejpam-5016	285	44	p	p	X
ejpam-5016	285	45	c	c	PROPN
ejpam-5016	285	46	since	since	SCONJ
ejpam-5016	285	47	[	[	X
ejpam-5016	285	48	a	a	X
ejpam-5016	285	49	,	,	PUNCT
ejpam-5016	285	50	c	c	X
ejpam-5016	285	51	]	]	PUNCT
ejpam-5016	285	52	is	be	AUX
ejpam-5016	285	53	not	not	PART
ejpam-5016	285	54	an	an	DET
ejpam-5016	285	55	inner	inner	ADJ
ejpam-5016	285	56	interval	interval	NOUN
ejpam-5016	285	57	.	.	PUNCT
ejpam-5016	286	1	the	the	DET
ejpam-5016	286	2	binomial	binomial	ADJ
ejpam-5016	286	3	bcs−	bcs−	PROPN
ejpam-5016	286	4	dey	dey	PROPN
ejpam-5016	286	5	is	be	AUX
ejpam-5016	286	6	not	not	PART
ejpam-5016	286	7	in	in	ADP
ejpam-5016	286	8	s3	s3	PROPN
ejpam-5016	286	9	.	.	PUNCT
ejpam-5016	287	1	but	but	CCONJ
ejpam-5016	287	2	bcs−	bcs−	PROPN
ejpam-5016	287	3	dey	dey	PROPN
ejpam-5016	287	4	=	=	SYM
ejpam-5016	287	5	(	(	PUNCT
ejpam-5016	287	6	bc−	bc−	ADJ
ejpam-5016	287	7	ez)s+	ez)s+	NOUN
ejpam-5016	287	8	(	(	PUNCT
ejpam-5016	287	9	−e)(dy	−e)(dy	VERB
ejpam-5016	287	10	−	−	PROPN
ejpam-5016	287	11	sz	sz	NOUN
ejpam-5016	287	12	)	)	PUNCT
ejpam-5016	287	13	with	with	ADP
ejpam-5016	287	14	z	z	PROPN
ejpam-5016	287	15	is	be	AUX
ejpam-5016	287	16	the	the	DET
ejpam-5016	287	17	intersections	intersection	NOUN
ejpam-5016	287	18	of	of	ADP
ejpam-5016	287	19	the	the	DET
ejpam-5016	287	20	segments	segment	NOUN
ejpam-5016	287	21	cf	cf	INTJ
ejpam-5016	288	1	and	and	CCONJ
ejpam-5016	288	2	bd	bd	PROPN
ejpam-5016	288	3	.	.	PUNCT
ejpam-5016	289	1	so	so	ADV
ejpam-5016	289	2	,	,	PUNCT
ejpam-5016	289	3	s(f	s(f	PROPN
ejpam-5016	289	4	,	,	PUNCT
ejpam-5016	289	5	g	g	NOUN
ejpam-5016	289	6	)	)	PUNCT
ejpam-5016	289	7	is	be	AUX
ejpam-5016	289	8	reduced	reduce	VERB
ejpam-5016	289	9	to	to	ADP
ejpam-5016	289	10	zero	zero	NUM
ejpam-5016	289	11	.	.	PUNCT
ejpam-5016	290	1	a	a	DET
ejpam-5016	290	2	b	b	NOUN
ejpam-5016	290	3	c	c	NOUN
ejpam-5016	290	4	d	d	X
ejpam-5016	290	5	e	e	NOUN
ejpam-5016	290	6	r	r	NOUN
ejpam-5016	290	7	qs	qs	PROPN
ejpam-5016	290	8	y	y	PROPN
ejpam-5016	290	9	f	f	PROPN
ejpam-5016	290	10	z	z	PROPN
ejpam-5016	290	11	a	a	PRON
ejpam-5016	290	12	b	b	X
ejpam-5016	290	13	c	c	NOUN
ejpam-5016	290	14	d	d	X
ejpam-5016	290	15	e	e	X
ejpam-5016	290	16	f	f	NOUN
ejpam-5016	290	17	r	r	NOUN
ejpam-5016	290	18	qs	qs	PROPN
ejpam-5016	290	19	y	y	PROPN
ejpam-5016	290	20	figure	figure	NOUN
ejpam-5016	290	21	17	17	NUM
ejpam-5016	290	22	:	:	PUNCT
ejpam-5016	290	23	case	case	NOUN
ejpam-5016	290	24	a	a	DET
ejpam-5016	290	25	<	<	X
ejpam-5016	290	26	p	p	X
ejpam-5016	290	27	f	f	X
ejpam-5016	290	28	<	<	X
ejpam-5016	290	29	p	p	X
ejpam-5016	290	30	r.	r.	PROPN
ejpam-5016	290	31	(	(	PUNCT
ejpam-5016	290	32	v	v	NOUN
ejpam-5016	290	33	)	)	PUNCT
ejpam-5016	291	1	if	if	SCONJ
ejpam-5016	291	2	p	p	NOUN
ejpam-5016	291	3	=	=	SYM
ejpam-5016	291	4	b	b	PROPN
ejpam-5016	291	5	then	then	ADV
ejpam-5016	291	6	s(f	s(f	PROPN
ejpam-5016	291	7	,	,	PUNCT
ejpam-5016	291	8	g	g	NOUN
ejpam-5016	291	9	)	)	PUNCT
ejpam-5016	291	10	=	=	PUNCT
ejpam-5016	291	11	acrs	acr	VERB
ejpam-5016	291	12	−	−	NOUN
ejpam-5016	291	13	qdef	qdef	ADJ
ejpam-5016	291	14	.	.	PUNCT
ejpam-5016	292	1	note	note	VERB
ejpam-5016	292	2	that	that	SCONJ
ejpam-5016	292	3	the	the	DET
ejpam-5016	292	4	vertices	vertex	NOUN
ejpam-5016	292	5	b	b	NUM
ejpam-5016	292	6	,	,	PUNCT
ejpam-5016	292	7	e	e	NOUN
ejpam-5016	292	8	,	,	PUNCT
ejpam-5016	292	9	s	s	VERB
ejpam-5016	292	10	are	be	AUX
ejpam-5016	292	11	in	in	ADP
ejpam-5016	292	12	vertical	vertical	ADJ
ejpam-5016	292	13	position	position	NOUN
ejpam-5016	292	14	.	.	PUNCT
ejpam-5016	293	1	consider	consider	VERB
ejpam-5016	293	2	the	the	DET
ejpam-5016	293	3	vertex	vertex	NOUN
ejpam-5016	293	4	s.	s.	PROPN
ejpam-5016	293	5	if	if	SCONJ
ejpam-5016	293	6	e	e	PROPN
ejpam-5016	293	7	<	<	X
ejpam-5016	293	8	p	p	X
ejpam-5016	293	9	s	s	X
ejpam-5016	293	10	then	then	ADV
ejpam-5016	293	11	there	there	PRON
ejpam-5016	293	12	is	be	VERB
ejpam-5016	293	13	a	a	DET
ejpam-5016	293	14	vertex	vertex	NOUN
ejpam-5016	293	15	y	y	NOUN
ejpam-5016	293	16	such	such	ADJ
ejpam-5016	293	17	that	that	SCONJ
ejpam-5016	293	18	the	the	DET
ejpam-5016	293	19	inner	inner	ADJ
ejpam-5016	293	20	interval	interval	NOUN
ejpam-5016	293	21	[	[	X
ejpam-5016	293	22	e	e	NOUN
ejpam-5016	293	23	,	,	PUNCT
ejpam-5016	293	24	q	q	X
ejpam-5016	293	25	]	]	X
ejpam-5016	293	26	has	have	VERB
ejpam-5016	293	27	s	s	PROPN
ejpam-5016	293	28	,	,	PUNCT
ejpam-5016	293	29	y	y	PROPN
ejpam-5016	293	30	as	as	ADP
ejpam-5016	293	31	the	the	DET
ejpam-5016	293	32	antidiagonal	antidiagonal	ADJ
ejpam-5016	293	33	corners	corner	NOUN
ejpam-5016	293	34	.	.	PUNCT
ejpam-5016	294	1	therefore	therefore	ADV
ejpam-5016	294	2	,	,	PUNCT
ejpam-5016	294	3	s(f	s(f	PROPN
ejpam-5016	294	4	,	,	PUNCT
ejpam-5016	294	5	g	g	NOUN
ejpam-5016	294	6	)	)	PUNCT
ejpam-5016	294	7	=	=	SYM
ejpam-5016	294	8	(	(	PUNCT
ejpam-5016	294	9	arc−	arc−	PROPN
ejpam-5016	294	10	dyf)s+	dyf)s+	NOUN
ejpam-5016	294	11	(	(	PUNCT
ejpam-5016	294	12	−df)(qe−	−df)(qe−	NOUN
ejpam-5016	294	13	ys	ys	NOUN
ejpam-5016	294	14	)	)	PUNCT
ejpam-5016	294	15	is	be	AUX
ejpam-5016	294	16	reduced	reduce	VERB
ejpam-5016	294	17	to	to	ADP
ejpam-5016	294	18	zero	zero	NUM
ejpam-5016	294	19	.	.	PUNCT
ejpam-5016	295	1	a	a	DET
ejpam-5016	295	2	b	b	NOUN
ejpam-5016	295	3	c	c	NOUN
ejpam-5016	295	4	d	d	X
ejpam-5016	295	5	e	e	X
ejpam-5016	295	6	f	f	NOUN
ejpam-5016	295	7	r	r	NOUN
ejpam-5016	295	8	qs	qs	PROPN
ejpam-5016	295	9	y	y	PROPN
ejpam-5016	295	10	figure	figure	NOUN
ejpam-5016	295	11	18	18	NUM
ejpam-5016	295	12	:	:	PUNCT
ejpam-5016	295	13	case	case	NOUN
ejpam-5016	295	14	p	p	X
ejpam-5016	295	15	=	=	PROPN
ejpam-5016	295	16	b	b	PROPN
ejpam-5016	295	17	and	and	CCONJ
ejpam-5016	295	18	e	e	X
ejpam-5016	295	19	<	<	X
ejpam-5016	295	20	p	p	X
ejpam-5016	295	21	s.	s.	PROPN
ejpam-5016	296	1	if	if	SCONJ
ejpam-5016	296	2	s	s	VERB
ejpam-5016	296	3	<	<	X
ejpam-5016	296	4	p	p	X
ejpam-5016	296	5	e	e	NOUN
ejpam-5016	296	6	,	,	PUNCT
ejpam-5016	296	7	note	note	VERB
ejpam-5016	296	8	that	that	SCONJ
ejpam-5016	296	9	there	there	PRON
ejpam-5016	296	10	is	be	VERB
ejpam-5016	296	11	no	no	DET
ejpam-5016	296	12	inner	inner	ADJ
ejpam-5016	296	13	2	2	NUM
ejpam-5016	296	14	-	-	PUNCT
ejpam-5016	296	15	minor	minor	NOUN
ejpam-5016	296	16	whose	whose	DET
ejpam-5016	296	17	initial	initial	ADJ
ejpam-5016	296	18	monomial	monomial	NOUN
ejpam-5016	296	19	divides	divide	VERB
ejpam-5016	296	20	the	the	DET
ejpam-5016	296	21	initial	initial	ADJ
ejpam-5016	296	22	monomial	monomial	NOUN
ejpam-5016	296	23	of	of	ADP
ejpam-5016	296	24	s(f	s(f	PROPN
ejpam-5016	296	25	,	,	PUNCT
ejpam-5016	296	26	g	g	NOUN
ejpam-5016	296	27	)	)	PUNCT
ejpam-5016	296	28	,	,	PUNCT
ejpam-5016	296	29	which	which	PRON
ejpam-5016	296	30	is	be	AUX
ejpam-5016	296	31	acrs	acr	NOUN
ejpam-5016	296	32	.	.	PUNCT
ejpam-5016	297	1	hence	hence	ADV
ejpam-5016	297	2	the	the	DET
ejpam-5016	297	3	binomials	binomial	NOUN
ejpam-5016	297	4	whose	whose	DET
ejpam-5016	297	5	initial	initial	ADJ
ejpam-5016	297	6	monomial	monomial	NOUN
ejpam-5016	297	7	may	may	AUX
ejpam-5016	297	8	divide	divide	VERB
ejpam-5016	297	9	acrs	acr	NOUN
ejpam-5016	297	10	are	be	AUX
ejpam-5016	297	11	the	the	DET
ejpam-5016	297	12	elements	element	NOUN
ejpam-5016	297	13	of	of	ADP
ejpam-5016	297	14	s3	s3	PROPN
ejpam-5016	297	15	.	.	PUNCT
ejpam-5016	298	1	from	from	ADP
ejpam-5016	298	2	theorem	theorem	ADJ
ejpam-5016	298	3	1	1	NUM
ejpam-5016	298	4	,	,	PUNCT
ejpam-5016	298	5	the	the	DET
ejpam-5016	298	6	only	only	ADJ
ejpam-5016	298	7	initial	initial	ADJ
ejpam-5016	298	8	monomials	monomial	NOUN
ejpam-5016	298	9	of	of	ADP
ejpam-5016	298	10	the	the	DET
ejpam-5016	298	11	element	element	NOUN
ejpam-5016	298	12	in	in	ADP
ejpam-5016	298	13	s3	s3	PROPN
ejpam-5016	298	14	that	that	PRON
ejpam-5016	298	15	may	may	AUX
ejpam-5016	298	16	divide	divide	VERB
ejpam-5016	298	17	acrs	acr	NOUN
ejpam-5016	298	18	are	be	AUX
ejpam-5016	298	19	ars	ar	NOUN
ejpam-5016	298	20	,	,	PUNCT
ejpam-5016	298	21	acr	acr	PROPN
ejpam-5016	298	22	,	,	PUNCT
ejpam-5016	298	23	or	or	CCONJ
ejpam-5016	298	24	asc	asc	PROPN
ejpam-5016	298	25	.	.	PUNCT
ejpam-5016	299	1	let	let	VERB
ejpam-5016	299	2	x	x	PRON
ejpam-5016	299	3	,	,	PUNCT
ejpam-5016	299	4	y	y	PROPN
ejpam-5016	299	5	,	,	PUNCT
ejpam-5016	299	6	z	z	X
ejpam-5016	299	7	be	be	AUX
ejpam-5016	299	8	the	the	DET
ejpam-5016	299	9	vertices	vertex	NOUN
ejpam-5016	299	10	such	such	ADJ
ejpam-5016	299	11	that	that	SCONJ
ejpam-5016	299	12	ars−	ars−	PROPN
ejpam-5016	299	13	xdq	xdq	PROPN
ejpam-5016	299	14	,	,	PUNCT
ejpam-5016	299	15	acr−	acr−	PROPN
ejpam-5016	299	16	dyf	dyf	NOUN
ejpam-5016	299	17	,	,	PUNCT
ejpam-5016	299	18	asc−	asc−	PROPN
ejpam-5016	299	19	efz	efz	NOUN
ejpam-5016	299	20	are	be	AUX
ejpam-5016	299	21	the	the	DET
ejpam-5016	299	22	corresponding	corresponding	ADJ
ejpam-5016	299	23	binomials	binomial	NOUN
ejpam-5016	299	24	,	,	PUNCT
ejpam-5016	299	25	respectively	respectively	ADV
ejpam-5016	299	26	.	.	PUNCT
ejpam-5016	300	1	y.	y.	PROPN
ejpam-5016	300	2	y.	y.	PROPN
ejpam-5016	300	3	hamonangan	hamonangan	PROPN
ejpam-5016	300	4	,	,	PUNCT
ejpam-5016	300	5	i.	i.	PROPN
ejpam-5016	300	6	muchtadi	muchtadi	PROPN
ejpam-5016	300	7	-	-	PUNCT
ejpam-5016	300	8	alamsyah	alamsyah	NOUN
ejpam-5016	300	9	/	/	SYM
ejpam-5016	300	10	eur	eur	PROPN
ejpam-5016	300	11	.	.	PUNCT
ejpam-5016	301	1	j.	j.	PROPN
ejpam-5016	301	2	pure	pure	PROPN
ejpam-5016	301	3	appl	appl	PROPN
ejpam-5016	301	4	.	.	PROPN
ejpam-5016	301	5	math	math	PROPN
ejpam-5016	301	6	,	,	PUNCT
ejpam-5016	301	7	17	17	NUM
ejpam-5016	301	8	(	(	PUNCT
ejpam-5016	301	9	4	4	NUM
ejpam-5016	301	10	)	)	PUNCT
ejpam-5016	301	11	(	(	PUNCT
ejpam-5016	301	12	2024	2024	NUM
ejpam-5016	301	13	)	)	PUNCT
ejpam-5016	301	14	,	,	PUNCT
ejpam-5016	301	15	2621	2621	NUM
ejpam-5016	301	16	-	-	SYM
ejpam-5016	301	17	2650	2650	NUM
ejpam-5016	301	18	2634	2634	NUM
ejpam-5016	301	19	a	a	DET
ejpam-5016	301	20	x	x	X
ejpam-5016	301	21	b	b	X
ejpam-5016	301	22	c	c	NOUN
ejpam-5016	301	23	d	d	X
ejpam-5016	301	24	e	e	X
ejpam-5016	301	25	f	f	NOUN
ejpam-5016	301	26	r	r	NOUN
ejpam-5016	301	27	q	q	PROPN
ejpam-5016	301	28	s	s	PROPN
ejpam-5016	301	29	y	y	PROPN
ejpam-5016	301	30	z	z	NOUN
ejpam-5016	301	31	figure	figure	NOUN
ejpam-5016	301	32	19	19	NUM
ejpam-5016	301	33	:	:	PUNCT
ejpam-5016	301	34	case	case	NOUN
ejpam-5016	301	35	p	p	X
ejpam-5016	301	36	=	=	SYM
ejpam-5016	301	37	b	b	PROPN
ejpam-5016	301	38	and	and	CCONJ
ejpam-5016	301	39	s	s	X
ejpam-5016	301	40	<	<	X
ejpam-5016	301	41	p	p	X
ejpam-5016	301	42	e.	e.	PROPN
ejpam-5016	301	43	•	•	PROPN
ejpam-5016	301	44	the	the	DET
ejpam-5016	301	45	binomial	binomial	PROPN
ejpam-5016	301	46	ars−	ars−	PROPN
ejpam-5016	301	47	xdq	xdq	PROPN
ejpam-5016	301	48	is	be	AUX
ejpam-5016	301	49	not	not	PART
ejpam-5016	301	50	in	in	ADP
ejpam-5016	301	51	s3	s3	PROPN
ejpam-5016	301	52	since	since	SCONJ
ejpam-5016	301	53	[	[	X
ejpam-5016	301	54	a	a	X
ejpam-5016	301	55	,	,	PUNCT
ejpam-5016	301	56	b	b	NOUN
ejpam-5016	301	57	]	]	X
ejpam-5016	301	58	is	be	AUX
ejpam-5016	301	59	not	not	PART
ejpam-5016	301	60	an	an	DET
ejpam-5016	301	61	inner	inner	ADJ
ejpam-5016	301	62	interval	interval	NOUN
ejpam-5016	301	63	.	.	PUNCT
ejpam-5016	302	1	•	•	NUM
ejpam-5016	302	2	the	the	DET
ejpam-5016	302	3	binomial	binomial	NOUN
ejpam-5016	302	4	acr−dyf	acr−dyf	VERB
ejpam-5016	302	5	is	be	AUX
ejpam-5016	302	6	contained	contain	VERB
ejpam-5016	302	7	in	in	ADP
ejpam-5016	302	8	s3	s3	PROPN
ejpam-5016	302	9	if	if	SCONJ
ejpam-5016	302	10	and	and	CCONJ
ejpam-5016	302	11	only	only	ADV
ejpam-5016	302	12	if	if	SCONJ
ejpam-5016	302	13	the	the	DET
ejpam-5016	302	14	interval	interval	NOUN
ejpam-5016	302	15	determined	determine	VERB
ejpam-5016	302	16	by	by	ADP
ejpam-5016	302	17	{	{	PUNCT
ejpam-5016	302	18	q	q	NOUN
ejpam-5016	302	19	,	,	PUNCT
ejpam-5016	302	20	e	e	NOUN
ejpam-5016	302	21	}	}	PUNCT
ejpam-5016	302	22	is	be	AUX
ejpam-5016	302	23	an	an	DET
ejpam-5016	302	24	inner	inner	ADJ
ejpam-5016	302	25	interval	interval	NOUN
ejpam-5016	302	26	.	.	PUNCT
ejpam-5016	303	1	if	if	SCONJ
ejpam-5016	303	2	the	the	DET
ejpam-5016	303	3	interval	interval	NOUN
ejpam-5016	303	4	is	be	AUX
ejpam-5016	303	5	an	an	DET
ejpam-5016	303	6	inner	inner	ADJ
ejpam-5016	303	7	interval	interval	NOUN
ejpam-5016	303	8	then	then	ADV
ejpam-5016	303	9	s(f	s(f	PROPN
ejpam-5016	303	10	,	,	PUNCT
ejpam-5016	303	11	g	g	NOUN
ejpam-5016	303	12	)	)	PUNCT
ejpam-5016	303	13	=	=	SYM
ejpam-5016	303	14	(	(	PUNCT
ejpam-5016	303	15	acr	acr	PROPN
ejpam-5016	303	16	−	−	PROPN
ejpam-5016	303	17	dyf)s+	dyf)s+	PROPN
ejpam-5016	303	18	df(ys−	df(ys−	PROPN
ejpam-5016	303	19	qe	qe	PROPN
ejpam-5016	303	20	)	)	PUNCT
ejpam-5016	303	21	is	be	AUX
ejpam-5016	303	22	reduced	reduce	VERB
ejpam-5016	303	23	to	to	ADP
ejpam-5016	303	24	zero	zero	NUM
ejpam-5016	303	25	.	.	PUNCT
ejpam-5016	304	1	•	•	NOUN
ejpam-5016	304	2	the	the	DET
ejpam-5016	304	3	binomial	binomial	ADJ
ejpam-5016	304	4	asc−efz	asc−efz	NOUN
ejpam-5016	304	5	is	be	AUX
ejpam-5016	304	6	contained	contain	VERB
ejpam-5016	304	7	in	in	ADP
ejpam-5016	304	8	s3	s3	PROPN
ejpam-5016	304	9	if	if	SCONJ
ejpam-5016	304	10	and	and	CCONJ
ejpam-5016	304	11	only	only	ADV
ejpam-5016	304	12	if	if	SCONJ
ejpam-5016	304	13	the	the	DET
ejpam-5016	304	14	interval	interval	NOUN
ejpam-5016	304	15	determined	determine	VERB
ejpam-5016	304	16	by	by	ADP
ejpam-5016	304	17	{	{	PUNCT
ejpam-5016	304	18	q	q	NOUN
ejpam-5016	304	19	,	,	PUNCT
ejpam-5016	304	20	d	d	NOUN
ejpam-5016	304	21	}	}	PUNCT
ejpam-5016	304	22	is	be	AUX
ejpam-5016	304	23	an	an	DET
ejpam-5016	304	24	inner	inner	ADJ
ejpam-5016	304	25	interval	interval	NOUN
ejpam-5016	304	26	.	.	PUNCT
ejpam-5016	305	1	if	if	SCONJ
ejpam-5016	305	2	the	the	DET
ejpam-5016	305	3	interval	interval	NOUN
ejpam-5016	305	4	is	be	AUX
ejpam-5016	305	5	an	an	DET
ejpam-5016	305	6	inner	inner	ADJ
ejpam-5016	305	7	interval	interval	NOUN
ejpam-5016	305	8	then	then	ADV
ejpam-5016	305	9	s(f	s(f	PROPN
ejpam-5016	305	10	,	,	PUNCT
ejpam-5016	305	11	g	g	NOUN
ejpam-5016	305	12	)	)	PUNCT
ejpam-5016	305	13	=	=	PUNCT
ejpam-5016	305	14	(	(	PUNCT
ejpam-5016	305	15	asc−	asc−	PROPN
ejpam-5016	305	16	efz)r	efz)r	PROPN
ejpam-5016	305	17	+	+	CCONJ
ejpam-5016	305	18	ef(zr	ef(zr	ADJ
ejpam-5016	305	19	−	−	NUM
ejpam-5016	305	20	qd	qd	NOUN
ejpam-5016	305	21	)	)	PUNCT
ejpam-5016	305	22	.	.	PUNCT
ejpam-5016	306	1	is	be	AUX
ejpam-5016	306	2	reduced	reduce	VERB
ejpam-5016	306	3	to	to	ADP
ejpam-5016	306	4	zero	zero	NUM
ejpam-5016	306	5	.	.	PUNCT
ejpam-5016	307	1	(	(	PUNCT
ejpam-5016	307	2	vi	vi	X
ejpam-5016	307	3	)	)	PUNCT
ejpam-5016	307	4	if	if	SCONJ
ejpam-5016	307	5	p	p	NOUN
ejpam-5016	307	6	=	=	PUNCT
ejpam-5016	307	7	c	c	X
ejpam-5016	307	8	then	then	ADV
ejpam-5016	307	9	s(f	s(f	PROPN
ejpam-5016	307	10	,	,	PUNCT
ejpam-5016	307	11	g	g	NOUN
ejpam-5016	307	12	)	)	PUNCT
ejpam-5016	307	13	=	=	NOUN
ejpam-5016	307	14	abrs−	abrs−	ADV
ejpam-5016	307	15	qdef	qdef	ADJ
ejpam-5016	307	16	.	.	PUNCT
ejpam-5016	308	1	note	note	VERB
ejpam-5016	308	2	that	that	SCONJ
ejpam-5016	308	3	the	the	DET
ejpam-5016	308	4	vertices	vertex	NOUN
ejpam-5016	308	5	e	e	NOUN
ejpam-5016	308	6	,	,	PUNCT
ejpam-5016	308	7	c	c	X
ejpam-5016	308	8	,	,	PUNCT
ejpam-5016	308	9	r	r	NOUN
ejpam-5016	308	10	are	be	AUX
ejpam-5016	308	11	in	in	ADP
ejpam-5016	308	12	horizontal	horizontal	ADJ
ejpam-5016	308	13	position	position	NOUN
ejpam-5016	308	14	.	.	PUNCT
ejpam-5016	309	1	consider	consider	VERB
ejpam-5016	309	2	the	the	DET
ejpam-5016	309	3	vertex	vertex	NOUN
ejpam-5016	309	4	r.	r.	PROPN
ejpam-5016	309	5	if	if	SCONJ
ejpam-5016	309	6	e	e	PROPN
ejpam-5016	309	7	<	<	X
ejpam-5016	309	8	p	p	X
ejpam-5016	309	9	r	r	NOUN
ejpam-5016	309	10	then	then	ADV
ejpam-5016	309	11	there	there	PRON
ejpam-5016	309	12	exists	exist	VERB
ejpam-5016	309	13	a	a	DET
ejpam-5016	309	14	vertex	vertex	NOUN
ejpam-5016	309	15	y	y	PRON
ejpam-5016	309	16	such	such	ADJ
ejpam-5016	309	17	that	that	SCONJ
ejpam-5016	309	18	the	the	DET
ejpam-5016	309	19	inner	inner	ADJ
ejpam-5016	309	20	interval	interval	NOUN
ejpam-5016	309	21	[	[	X
ejpam-5016	309	22	e	e	NOUN
ejpam-5016	309	23	,	,	PUNCT
ejpam-5016	309	24	q	q	X
ejpam-5016	309	25	]	]	X
ejpam-5016	309	26	has	have	VERB
ejpam-5016	309	27	r	r	PROPN
ejpam-5016	309	28	,	,	PUNCT
ejpam-5016	309	29	y	y	PROPN
ejpam-5016	309	30	as	as	ADP
ejpam-5016	309	31	the	the	DET
ejpam-5016	309	32	antidiagonal	antidiagonal	ADJ
ejpam-5016	309	33	corners	corner	NOUN
ejpam-5016	309	34	.	.	PUNCT
ejpam-5016	310	1	therefore	therefore	ADV
ejpam-5016	310	2	,	,	PUNCT
ejpam-5016	310	3	s(f	s(f	PROPN
ejpam-5016	310	4	,	,	PUNCT
ejpam-5016	310	5	g	g	NOUN
ejpam-5016	310	6	)	)	PUNCT
ejpam-5016	310	7	=	=	PUNCT
ejpam-5016	310	8	(	(	PUNCT
ejpam-5016	310	9	abs−	abs−	PROPN
ejpam-5016	310	10	dyf)r	dyf)r	PROPN
ejpam-5016	310	11	+	+	CCONJ
ejpam-5016	310	12	(	(	PUNCT
ejpam-5016	310	13	−df)(qe−	−df)(qe−	NOUN
ejpam-5016	310	14	yr	yr	NOUN
ejpam-5016	310	15	)	)	PUNCT
ejpam-5016	310	16	is	be	AUX
ejpam-5016	310	17	reduced	reduce	VERB
ejpam-5016	310	18	to	to	ADP
ejpam-5016	310	19	zero	zero	NUM
ejpam-5016	310	20	.	.	PUNCT
ejpam-5016	311	1	a	a	DET
ejpam-5016	311	2	b	b	NOUN
ejpam-5016	311	3	c	c	NOUN
ejpam-5016	311	4	d	d	X
ejpam-5016	311	5	e	e	X
ejpam-5016	311	6	f	f	PROPN
ejpam-5016	311	7	s	s	PROPN
ejpam-5016	311	8	qy	qy	PROPN
ejpam-5016	311	9	r	r	NOUN
ejpam-5016	311	10	figure	figure	NOUN
ejpam-5016	311	11	20	20	NUM
ejpam-5016	311	12	:	:	PUNCT
ejpam-5016	311	13	case	case	NOUN
ejpam-5016	311	14	p	p	X
ejpam-5016	311	15	=	=	PUNCT
ejpam-5016	311	16	c	c	PROPN
ejpam-5016	311	17	and	and	CCONJ
ejpam-5016	311	18	e	e	X
ejpam-5016	311	19	<	<	X
ejpam-5016	311	20	p	p	PROPN
ejpam-5016	311	21	r.	r.	PROPN
ejpam-5016	311	22	y.	y.	PROPN
ejpam-5016	311	23	y.	y.	PROPN
ejpam-5016	311	24	hamonangan	hamonangan	PROPN
ejpam-5016	311	25	,	,	PUNCT
ejpam-5016	311	26	i.	i.	PROPN
ejpam-5016	311	27	muchtadi	muchtadi	PROPN
ejpam-5016	311	28	-	-	PUNCT
ejpam-5016	311	29	alamsyah	alamsyah	NOUN
ejpam-5016	311	30	/	/	SYM
ejpam-5016	311	31	eur	eur	PROPN
ejpam-5016	311	32	.	.	PUNCT
ejpam-5016	312	1	j.	j.	PROPN
ejpam-5016	312	2	pure	pure	PROPN
ejpam-5016	312	3	appl	appl	PROPN
ejpam-5016	312	4	.	.	PROPN
ejpam-5016	312	5	math	math	PROPN
ejpam-5016	312	6	,	,	PUNCT
ejpam-5016	312	7	17	17	NUM
ejpam-5016	312	8	(	(	PUNCT
ejpam-5016	312	9	4	4	NUM
ejpam-5016	312	10	)	)	PUNCT
ejpam-5016	312	11	(	(	PUNCT
ejpam-5016	312	12	2024	2024	NUM
ejpam-5016	312	13	)	)	PUNCT
ejpam-5016	312	14	,	,	PUNCT
ejpam-5016	312	15	2621	2621	NUM
ejpam-5016	312	16	-	-	SYM
ejpam-5016	312	17	2650	2650	NUM
ejpam-5016	312	18	2635	2635	NUM
ejpam-5016	312	19	if	if	SCONJ
ejpam-5016	312	20	r	r	NOUN
ejpam-5016	312	21	<	<	X
ejpam-5016	312	22	p	p	X
ejpam-5016	312	23	e	e	NOUN
ejpam-5016	312	24	,	,	PUNCT
ejpam-5016	312	25	note	note	VERB
ejpam-5016	312	26	that	that	SCONJ
ejpam-5016	312	27	there	there	PRON
ejpam-5016	312	28	is	be	VERB
ejpam-5016	312	29	no	no	DET
ejpam-5016	312	30	inner	inner	ADJ
ejpam-5016	312	31	2	2	NUM
ejpam-5016	312	32	-	-	PUNCT
ejpam-5016	312	33	minor	minor	NOUN
ejpam-5016	312	34	whose	whose	DET
ejpam-5016	312	35	initial	initial	ADJ
ejpam-5016	312	36	monomial	monomial	NOUN
ejpam-5016	312	37	divides	divide	VERB
ejpam-5016	312	38	the	the	DET
ejpam-5016	312	39	initial	initial	ADJ
ejpam-5016	312	40	monomial	monomial	NOUN
ejpam-5016	312	41	of	of	ADP
ejpam-5016	312	42	s(f	s(f	PROPN
ejpam-5016	312	43	,	,	PUNCT
ejpam-5016	312	44	g	g	NOUN
ejpam-5016	312	45	)	)	PUNCT
ejpam-5016	312	46	,	,	PUNCT
ejpam-5016	312	47	which	which	PRON
ejpam-5016	312	48	is	be	AUX
ejpam-5016	312	49	abrs	abrs	ADJ
ejpam-5016	312	50	.	.	PUNCT
ejpam-5016	313	1	hence	hence	ADV
ejpam-5016	313	2	the	the	DET
ejpam-5016	313	3	binomials	binomial	NOUN
ejpam-5016	313	4	whose	whose	DET
ejpam-5016	313	5	initial	initial	ADJ
ejpam-5016	313	6	monomial	monomial	NOUN
ejpam-5016	313	7	may	may	AUX
ejpam-5016	313	8	divide	divide	VERB
ejpam-5016	313	9	abrs	abrs	ADJ
ejpam-5016	313	10	are	be	AUX
ejpam-5016	313	11	the	the	DET
ejpam-5016	313	12	elements	element	NOUN
ejpam-5016	313	13	of	of	ADP
ejpam-5016	313	14	s3	s3	PROPN
ejpam-5016	313	15	.	.	PUNCT
ejpam-5016	314	1	from	from	ADP
ejpam-5016	314	2	theorem	theorem	ADJ
ejpam-5016	314	3	1	1	NUM
ejpam-5016	314	4	,	,	PUNCT
ejpam-5016	314	5	the	the	DET
ejpam-5016	314	6	only	only	ADJ
ejpam-5016	314	7	initial	initial	ADJ
ejpam-5016	314	8	monomials	monomial	NOUN
ejpam-5016	314	9	of	of	ADP
ejpam-5016	314	10	the	the	DET
ejpam-5016	314	11	element	element	NOUN
ejpam-5016	314	12	in	in	ADP
ejpam-5016	314	13	s3	s3	PROPN
ejpam-5016	314	14	that	that	PRON
ejpam-5016	314	15	may	may	AUX
ejpam-5016	314	16	divide	divide	VERB
ejpam-5016	314	17	abrs	abrs	ADJ
ejpam-5016	314	18	are	be	AUX
ejpam-5016	314	19	ars	ar	NOUN
ejpam-5016	314	20	,	,	PUNCT
ejpam-5016	314	21	abr	abr	NOUN
ejpam-5016	314	22	,	,	PUNCT
ejpam-5016	314	23	or	or	CCONJ
ejpam-5016	314	24	abs	ab	NOUN
ejpam-5016	314	25	.	.	PUNCT
ejpam-5016	315	1	let	let	VERB
ejpam-5016	315	2	x	x	PRON
ejpam-5016	315	3	,	,	PUNCT
ejpam-5016	315	4	y	y	PROPN
ejpam-5016	315	5	,	,	PUNCT
ejpam-5016	315	6	z	z	X
ejpam-5016	315	7	be	be	AUX
ejpam-5016	315	8	the	the	DET
ejpam-5016	315	9	vertices	vertex	NOUN
ejpam-5016	315	10	such	such	ADJ
ejpam-5016	315	11	that	that	DET
ejpam-5016	315	12	ars	ar	NOUN
ejpam-5016	315	13	−	−	PROPN
ejpam-5016	315	14	qxf	qxf	NOUN
ejpam-5016	315	15	,	,	PUNCT
ejpam-5016	315	16	abr	abr	VERB
ejpam-5016	315	17	−	−	PROPN
ejpam-5016	315	18	dey	dey	PROPN
ejpam-5016	315	19	,	,	PUNCT
ejpam-5016	315	20	abs	ab	VERB
ejpam-5016	315	21	−	−	NOUN
ejpam-5016	316	1	dfz	dfz	ADJ
ejpam-5016	316	2	be	be	AUX
ejpam-5016	316	3	the	the	DET
ejpam-5016	316	4	corresponding	corresponding	ADJ
ejpam-5016	316	5	binomials	binomial	NOUN
ejpam-5016	316	6	,	,	PUNCT
ejpam-5016	316	7	respectively	respectively	ADV
ejpam-5016	316	8	.	.	PUNCT
ejpam-5016	317	1	a	a	DET
ejpam-5016	317	2	x	x	X
ejpam-5016	317	3	b	b	X
ejpam-5016	317	4	c	c	NOUN
ejpam-5016	317	5	d	d	X
ejpam-5016	317	6	e	e	X
ejpam-5016	317	7	f	f	PROPN
ejpam-5016	317	8	s	s	PROPN
ejpam-5016	317	9	q	q	PROPN
ejpam-5016	317	10	z	z	NOUN
ejpam-5016	317	11	r	r	NOUN
ejpam-5016	317	12	y	y	PROPN
ejpam-5016	317	13	figure	figure	NOUN
ejpam-5016	317	14	21	21	NUM
ejpam-5016	317	15	:	:	PUNCT
ejpam-5016	317	16	case	case	NOUN
ejpam-5016	317	17	p	p	X
ejpam-5016	317	18	=	=	PUNCT
ejpam-5016	317	19	c	c	PROPN
ejpam-5016	317	20	and	and	CCONJ
ejpam-5016	317	21	r	r	NOUN
ejpam-5016	317	22	<	<	X
ejpam-5016	317	23	p	p	X
ejpam-5016	317	24	e.	e.	PROPN
ejpam-5016	317	25	•	•	PROPN
ejpam-5016	317	26	the	the	DET
ejpam-5016	317	27	binomial	binomial	PROPN
ejpam-5016	317	28	ars−	ars−	PROPN
ejpam-5016	317	29	qxf	qxf	NOUN
ejpam-5016	317	30	is	be	AUX
ejpam-5016	317	31	not	not	PART
ejpam-5016	317	32	in	in	ADP
ejpam-5016	317	33	s3	s3	PROPN
ejpam-5016	317	34	since	since	SCONJ
ejpam-5016	317	35	[	[	X
ejpam-5016	317	36	a	a	X
ejpam-5016	317	37	,	,	PUNCT
ejpam-5016	317	38	c	c	X
ejpam-5016	317	39	]	]	PUNCT
ejpam-5016	317	40	is	be	AUX
ejpam-5016	317	41	not	not	PART
ejpam-5016	317	42	an	an	DET
ejpam-5016	317	43	inner	inner	ADJ
ejpam-5016	317	44	interval	interval	NOUN
ejpam-5016	317	45	.	.	PUNCT
ejpam-5016	318	1	•	•	NUM
ejpam-5016	318	2	the	the	DET
ejpam-5016	318	3	binomial	binomial	ADJ
ejpam-5016	318	4	abr−dey	abr−dey	PROPN
ejpam-5016	318	5	is	be	AUX
ejpam-5016	318	6	contained	contain	VERB
ejpam-5016	318	7	in	in	ADP
ejpam-5016	318	8	s3	s3	PROPN
ejpam-5016	318	9	if	if	SCONJ
ejpam-5016	318	10	and	and	CCONJ
ejpam-5016	318	11	only	only	ADV
ejpam-5016	318	12	if	if	SCONJ
ejpam-5016	318	13	the	the	DET
ejpam-5016	318	14	interval	interval	NOUN
ejpam-5016	318	15	determined	determine	VERB
ejpam-5016	318	16	by	by	ADP
ejpam-5016	318	17	{	{	PUNCT
ejpam-5016	318	18	q	q	INTJ
ejpam-5016	318	19	,	,	PUNCT
ejpam-5016	318	20	f	f	X
ejpam-5016	318	21	}	}	PUNCT
ejpam-5016	318	22	is	be	AUX
ejpam-5016	318	23	an	an	DET
ejpam-5016	318	24	inner	inner	ADJ
ejpam-5016	318	25	interval	interval	NOUN
ejpam-5016	318	26	.	.	PUNCT
ejpam-5016	319	1	if	if	SCONJ
ejpam-5016	319	2	the	the	DET
ejpam-5016	319	3	interval	interval	NOUN
ejpam-5016	319	4	is	be	AUX
ejpam-5016	319	5	an	an	DET
ejpam-5016	319	6	inner	inner	ADJ
ejpam-5016	319	7	interval	interval	NOUN
ejpam-5016	319	8	then	then	ADV
ejpam-5016	319	9	s(f	s(f	PROPN
ejpam-5016	319	10	,	,	PUNCT
ejpam-5016	319	11	g	g	NOUN
ejpam-5016	319	12	)	)	PUNCT
ejpam-5016	319	13	=	=	PUNCT
ejpam-5016	319	14	(	(	PUNCT
ejpam-5016	319	15	abr	abr	INTJ
ejpam-5016	319	16	−	−	PROPN
ejpam-5016	319	17	dey)s+	dey)s+	NOUN
ejpam-5016	319	18	de(ys−	de(ys−	NOUN
ejpam-5016	319	19	fq	fq	NOUN
ejpam-5016	319	20	)	)	PUNCT
ejpam-5016	319	21	is	be	AUX
ejpam-5016	319	22	reduced	reduce	VERB
ejpam-5016	319	23	to	to	ADP
ejpam-5016	319	24	zero	zero	NUM
ejpam-5016	319	25	.	.	PUNCT
ejpam-5016	320	1	•	•	NOUN
ejpam-5016	320	2	the	the	DET
ejpam-5016	320	3	binomial	binomial	NOUN
ejpam-5016	320	4	abs−dfz	abs−dfz	ADV
ejpam-5016	320	5	is	be	AUX
ejpam-5016	320	6	contained	contain	VERB
ejpam-5016	320	7	in	in	ADP
ejpam-5016	320	8	s3	s3	PROPN
ejpam-5016	320	9	if	if	SCONJ
ejpam-5016	320	10	and	and	CCONJ
ejpam-5016	320	11	only	only	ADV
ejpam-5016	320	12	if	if	SCONJ
ejpam-5016	320	13	the	the	DET
ejpam-5016	320	14	interval	interval	NOUN
ejpam-5016	320	15	determined	determine	VERB
ejpam-5016	320	16	by	by	ADP
ejpam-5016	320	17	{	{	PUNCT
ejpam-5016	320	18	q	q	NOUN
ejpam-5016	320	19	,	,	PUNCT
ejpam-5016	320	20	e	e	NOUN
ejpam-5016	320	21	}	}	PUNCT
ejpam-5016	320	22	is	be	AUX
ejpam-5016	320	23	an	an	DET
ejpam-5016	320	24	inner	inner	ADJ
ejpam-5016	320	25	interval	interval	NOUN
ejpam-5016	320	26	.	.	PUNCT
ejpam-5016	321	1	if	if	SCONJ
ejpam-5016	321	2	the	the	DET
ejpam-5016	321	3	interval	interval	NOUN
ejpam-5016	321	4	is	be	AUX
ejpam-5016	321	5	an	an	DET
ejpam-5016	321	6	inner	inner	ADJ
ejpam-5016	321	7	interval	interval	NOUN
ejpam-5016	321	8	then	then	ADV
ejpam-5016	321	9	s(f	s(f	PROPN
ejpam-5016	321	10	,	,	PUNCT
ejpam-5016	321	11	g	g	NOUN
ejpam-5016	321	12	)	)	PUNCT
ejpam-5016	322	1	=	=	PUNCT
ejpam-5016	322	2	(	(	PUNCT
ejpam-5016	322	3	abs−	abs−	PROPN
ejpam-5016	322	4	dfz)r	dfz)r	PROPN
ejpam-5016	322	5	+	+	NUM
ejpam-5016	322	6	df(zr	df(zr	ADJ
ejpam-5016	322	7	−	−	NOUN
ejpam-5016	322	8	eq	eq	NOUN
ejpam-5016	322	9	)	)	PUNCT
ejpam-5016	322	10	is	be	AUX
ejpam-5016	322	11	reduced	reduce	VERB
ejpam-5016	322	12	to	to	ADP
ejpam-5016	322	13	zero	zero	NUM
ejpam-5016	322	14	.	.	PUNCT
ejpam-5016	323	1	we	we	PRON
ejpam-5016	323	2	summarize	summarize	VERB
ejpam-5016	323	3	our	our	PRON
ejpam-5016	323	4	discussion	discussion	NOUN
ejpam-5016	323	5	above	above	ADP
ejpam-5016	323	6	to	to	ADP
ejpam-5016	323	7	the	the	DET
ejpam-5016	323	8	following	follow	VERB
ejpam-5016	323	9	theorem	theorem	PROPN
ejpam-5016	323	10	.	.	PUNCT
ejpam-5016	323	11	theorem	theorem	NOUN
ejpam-5016	323	12	2	2	NUM
ejpam-5016	323	13	.	.	PUNCT
ejpam-5016	324	1	let	let	VERB
ejpam-5016	324	2	f	f	NOUN
ejpam-5016	324	3	=	=	PUNCT
ejpam-5016	324	4	a1a3a5	a1a3a5	PROPN
ejpam-5016	324	5	−	−	PROPN
ejpam-5016	324	6	a2a4a6	a2a4a6	NOUN
ejpam-5016	324	7	be	be	VERB
ejpam-5016	324	8	the	the	DET
ejpam-5016	324	9	element	element	NOUN
ejpam-5016	324	10	in	in	ADP
ejpam-5016	324	11	s3	s3	PROPN
ejpam-5016	324	12	as	as	ADP
ejpam-5016	324	13	in	in	ADP
ejpam-5016	324	14	definition	definition	NOUN
ejpam-5016	324	15	1	1	NUM
ejpam-5016	324	16	and	and	CCONJ
ejpam-5016	325	1	g	g	PROPN
ejpam-5016	325	2	=	=	SYM
ejpam-5016	325	3	pq	pq	PROPN
ejpam-5016	325	4	−	−	NOUN
ejpam-5016	325	5	rs	rs	NOUN
ejpam-5016	325	6	be	be	AUX
ejpam-5016	325	7	the	the	DET
ejpam-5016	325	8	element	element	NOUN
ejpam-5016	325	9	in	in	ADP
ejpam-5016	325	10	s2	s2	PROPN
ejpam-5016	325	11	associated	associate	VERB
ejpam-5016	325	12	to	to	ADP
ejpam-5016	325	13	the	the	DET
ejpam-5016	325	14	inner	inner	ADJ
ejpam-5016	325	15	interval	interval	NOUN
ejpam-5016	326	1	[	[	X
ejpam-5016	326	2	p	p	X
ejpam-5016	326	3	,	,	PUNCT
ejpam-5016	326	4	q	q	X
ejpam-5016	326	5	]	]	X
ejpam-5016	326	6	with	with	ADP
ejpam-5016	326	7	lower	low	ADJ
ejpam-5016	326	8	-	-	PUNCT
ejpam-5016	326	9	right	right	ADJ
ejpam-5016	326	10	and	and	CCONJ
ejpam-5016	326	11	upper	upper	ADV
ejpam-5016	326	12	-	-	PUNCT
ejpam-5016	326	13	left	leave	VERB
ejpam-5016	326	14	corners	corner	NOUN
ejpam-5016	326	15	r	r	NOUN
ejpam-5016	326	16	and	and	CCONJ
ejpam-5016	326	17	s	s	NOUN
ejpam-5016	326	18	,	,	PUNCT
ejpam-5016	326	19	respectively	respectively	ADV
ejpam-5016	326	20	,	,	PUNCT
ejpam-5016	326	21	then	then	ADV
ejpam-5016	326	22	s(f	s(f	PROPN
ejpam-5016	326	23	,	,	PUNCT
ejpam-5016	326	24	g	g	NOUN
ejpam-5016	326	25	)	)	PUNCT
ejpam-5016	326	26	is	be	AUX
ejpam-5016	326	27	not	not	PART
ejpam-5016	326	28	reduced	reduce	VERB
ejpam-5016	326	29	to	to	ADP
ejpam-5016	326	30	zero	zero	NUM
ejpam-5016	326	31	by	by	ADP
ejpam-5016	326	32	s2	s2	PROPN
ejpam-5016	326	33	∪s3	∪s3	VERB
ejpam-5016	327	1	if	if	SCONJ
ejpam-5016	327	2	and	and	CCONJ
ejpam-5016	327	3	only	only	ADV
ejpam-5016	327	4	if	if	SCONJ
ejpam-5016	327	5	one	one	NUM
ejpam-5016	327	6	of	of	ADP
ejpam-5016	327	7	the	the	DET
ejpam-5016	327	8	following	follow	VERB
ejpam-5016	327	9	statement	statement	NOUN
ejpam-5016	327	10	holds	hold	VERB
ejpam-5016	327	11	:	:	PUNCT
ejpam-5016	327	12	•	•	ADP
ejpam-5016	327	13	p	p	NOUN
ejpam-5016	327	14	=	=	NOUN
ejpam-5016	327	15	a3	a3	NOUN
ejpam-5016	327	16	,	,	PUNCT
ejpam-5016	327	17	a4	a4	X
ejpam-5016	327	18	>	>	X
ejpam-5016	327	19	s	s	NOUN
ejpam-5016	327	20	and	and	CCONJ
ejpam-5016	327	21	both	both	DET
ejpam-5016	327	22	intervals	interval	NOUN
ejpam-5016	327	23	determined	determine	VERB
ejpam-5016	327	24	by	by	ADP
ejpam-5016	327	25	{	{	PUNCT
ejpam-5016	327	26	q	q	PROPN
ejpam-5016	327	27	,	,	PUNCT
ejpam-5016	327	28	a2	a2	PROPN
ejpam-5016	327	29	}	}	PUNCT
ejpam-5016	327	30	and	and	CCONJ
ejpam-5016	327	31	{	{	PUNCT
ejpam-5016	327	32	q	q	ADJ
ejpam-5016	327	33	,	,	PUNCT
ejpam-5016	327	34	a4	a4	NOUN
ejpam-5016	327	35	}	}	PUNCT
ejpam-5016	327	36	are	be	AUX
ejpam-5016	327	37	not	not	PART
ejpam-5016	327	38	inner	inner	ADJ
ejpam-5016	327	39	intervals	interval	NOUN
ejpam-5016	327	40	•	•	NOUN
ejpam-5016	327	41	p	p	X
ejpam-5016	327	42	=	=	SYM
ejpam-5016	327	43	a5	a5	NOUN
ejpam-5016	327	44	,	,	PUNCT
ejpam-5016	327	45	a4	a4	INTJ
ejpam-5016	327	46	>	>	X
ejpam-5016	327	47	r	r	NOUN
ejpam-5016	327	48	and	and	CCONJ
ejpam-5016	327	49	both	both	DET
ejpam-5016	327	50	intervals	interval	NOUN
ejpam-5016	327	51	determined	determine	VERB
ejpam-5016	327	52	by	by	ADP
ejpam-5016	327	53	{	{	PUNCT
ejpam-5016	327	54	q	q	NOUN
ejpam-5016	327	55	,	,	PUNCT
ejpam-5016	327	56	a4	a4	NOUN
ejpam-5016	327	57	}	}	PUNCT
ejpam-5016	327	58	and	and	CCONJ
ejpam-5016	327	59	{	{	PUNCT
ejpam-5016	327	60	q	q	ADJ
ejpam-5016	327	61	,	,	PUNCT
ejpam-5016	327	62	a6	a6	NOUN
ejpam-5016	327	63	}	}	PUNCT
ejpam-5016	327	64	are	be	AUX
ejpam-5016	327	65	not	not	PART
ejpam-5016	327	66	inner	inner	ADJ
ejpam-5016	327	67	intervals	interval	NOUN
ejpam-5016	327	68	.	.	PUNCT
ejpam-5016	328	1	y.	y.	PROPN
ejpam-5016	328	2	y.	y.	PROPN
ejpam-5016	328	3	hamonangan	hamonangan	PROPN
ejpam-5016	328	4	,	,	PUNCT
ejpam-5016	328	5	i.	i.	PROPN
ejpam-5016	328	6	muchtadi	muchtadi	PROPN
ejpam-5016	328	7	-	-	PUNCT
ejpam-5016	328	8	alamsyah	alamsyah	NOUN
ejpam-5016	328	9	/	/	SYM
ejpam-5016	328	10	eur	eur	PROPN
ejpam-5016	328	11	.	.	PUNCT
ejpam-5016	329	1	j.	j.	PROPN
ejpam-5016	329	2	pure	pure	PROPN
ejpam-5016	329	3	appl	appl	PROPN
ejpam-5016	329	4	.	.	PROPN
ejpam-5016	329	5	math	math	PROPN
ejpam-5016	329	6	,	,	PUNCT
ejpam-5016	329	7	17	17	NUM
ejpam-5016	329	8	(	(	PUNCT
ejpam-5016	329	9	4	4	NUM
ejpam-5016	329	10	)	)	PUNCT
ejpam-5016	329	11	(	(	PUNCT
ejpam-5016	329	12	2024	2024	NUM
ejpam-5016	329	13	)	)	PUNCT
ejpam-5016	329	14	,	,	PUNCT
ejpam-5016	329	15	2621	2621	NUM
ejpam-5016	329	16	-	-	SYM
ejpam-5016	329	17	2650	2650	NUM
ejpam-5016	329	18	2636	2636	NUM
ejpam-5016	329	19	a2	a2	PROPN
ejpam-5016	329	20	a1	a1	NOUN
ejpam-5016	329	21	a4a5	a4a5	NOUN
ejpam-5016	329	22	a6	a6	NOUN
ejpam-5016	329	23	p	p	NOUN
ejpam-5016	329	24	=	=	NOUN
ejpam-5016	329	25	a3	a3	NOUN
ejpam-5016	329	26	r	r	NOUN
ejpam-5016	329	27	qs	qs	NOUN
ejpam-5016	329	28	a1	a1	NOUN
ejpam-5016	329	29	a2	a2	PROPN
ejpam-5016	329	30	a3	a3	NOUN
ejpam-5016	329	31	a4	a4	PROPN
ejpam-5016	329	32	a6	a6	NOUN
ejpam-5016	329	33	r	r	NOUN
ejpam-5016	329	34	p	p	NOUN
ejpam-5016	329	35	=	=	X
ejpam-5016	329	36	a5	a5	PROPN
ejpam-5016	329	37	qs	qs	NOUN
ejpam-5016	329	38	:	:	PUNCT
ejpam-5016	329	39	every	every	DET
ejpam-5016	329	40	cell	cell	NOUN
ejpam-5016	329	41	is	be	AUX
ejpam-5016	329	42	contained	contain	VERB
ejpam-5016	329	43	in	in	ADP
ejpam-5016	329	44	the	the	DET
ejpam-5016	329	45	polyomino	polyomino	NOUN
ejpam-5016	329	46	:	:	PUNCT
ejpam-5016	329	47	some	some	DET
ejpam-5016	329	48	cells	cell	NOUN
ejpam-5016	329	49	are	be	AUX
ejpam-5016	329	50	not	not	PART
ejpam-5016	329	51	in	in	ADP
ejpam-5016	329	52	the	the	DET
ejpam-5016	329	53	polyomino	polyomino	NOUN
ejpam-5016	329	54	figure	figure	NOUN
ejpam-5016	329	55	22	22	NUM
ejpam-5016	329	56	:	:	PUNCT
ejpam-5016	329	57	binomial	binomial	ADJ
ejpam-5016	329	58	in	in	ADP
ejpam-5016	329	59	theorem	theorem	NOUN
ejpam-5016	329	60	2	2	NUM
ejpam-5016	329	61	.	.	PUNCT
ejpam-5016	329	62	3.2.2	3.2.2	NUM
ejpam-5016	329	63	.	.	PUNCT
ejpam-5016	330	1	the	the	DET
ejpam-5016	330	2	case	case	NOUN
ejpam-5016	330	3	f	f	PROPN
ejpam-5016	330	4	∈	∈	PROPN
ejpam-5016	330	5	s3	s3	PROPN
ejpam-5016	330	6	and	and	CCONJ
ejpam-5016	330	7	g	g	PROPN
ejpam-5016	330	8	∈	∈	PROPN
ejpam-5016	330	9	s3	s3	PROPN
ejpam-5016	330	10	let	let	VERB
ejpam-5016	330	11	f	f	NOUN
ejpam-5016	330	12	=	=	SYM
ejpam-5016	330	13	a1a2a3	a1a2a3	PROPN
ejpam-5016	330	14	−b1b2b3	−b1b2b3	NOUN
ejpam-5016	330	15	and	and	CCONJ
ejpam-5016	330	16	g	g	NOUN
ejpam-5016	330	17	=	=	PUNCT
ejpam-5016	330	18	a1a2a3	a1a2a3	VERB
ejpam-5016	330	19	−	−	NOUN
ejpam-5016	330	20	b1b2b3	b1b2b3	NOUN
ejpam-5016	330	21	with	with	SCONJ
ejpam-5016	330	22	initial	initial	ADJ
ejpam-5016	330	23	monomials	monomial	NOUN
ejpam-5016	330	24	a1a2a3	a1a2a3	ADJ
ejpam-5016	330	25	and	and	CCONJ
ejpam-5016	330	26	a1a2a3	a1a2a3	ADJ
ejpam-5016	330	27	,	,	PUNCT
ejpam-5016	330	28	respectively	respectively	ADV
ejpam-5016	330	29	.	.	PUNCT
ejpam-5016	331	1	we	we	PRON
ejpam-5016	331	2	assume	assume	VERB
ejpam-5016	331	3	that	that	SCONJ
ejpam-5016	331	4	a1	a1	NOUN
ejpam-5016	331	5	<	<	X
ejpam-5016	331	6	p	p	X
ejpam-5016	331	7	a2	a2	PROPN
ejpam-5016	331	8	<	<	PROPN
ejpam-5016	331	9	p	p	PROPN
ejpam-5016	331	10	a3	a3	NOUN
ejpam-5016	331	11	,	,	PUNCT
ejpam-5016	331	12	b1	b1	NOUN
ejpam-5016	331	13	<	<	NOUN
ejpam-5016	331	14	p	p	NOUN
ejpam-5016	331	15	b2	b2	NOUN
ejpam-5016	331	16	<	<	X
ejpam-5016	331	17	p	p	X
ejpam-5016	331	18	b3	b3	PROPN
ejpam-5016	331	19	,	,	PUNCT
ejpam-5016	331	20	a1	a1	NOUN
ejpam-5016	331	21	<	<	X
ejpam-5016	331	22	p	p	X
ejpam-5016	331	23	a2	a2	PROPN
ejpam-5016	331	24	<	<	PROPN
ejpam-5016	331	25	p	p	PROPN
ejpam-5016	331	26	a3	a3	NOUN
ejpam-5016	331	27	,	,	PUNCT
ejpam-5016	331	28	b1	b1	NOUN
ejpam-5016	331	29	<	<	NOUN
ejpam-5016	331	30	p	p	NOUN
ejpam-5016	331	31	b2	b2	NOUN
ejpam-5016	331	32	<	<	X
ejpam-5016	331	33	p	p	NOUN
ejpam-5016	331	34	b3	b3	PROPN
ejpam-5016	331	35	,	,	PUNCT
ejpam-5016	331	36	and	and	CCONJ
ejpam-5016	331	37	|{a1	|{a1	ADJ
ejpam-5016	331	38	,	,	PUNCT
ejpam-5016	331	39	a2	a2	PROPN
ejpam-5016	331	40	,	,	PUNCT
ejpam-5016	331	41	a3	a3	NOUN
ejpam-5016	331	42	}	}	PUNCT
ejpam-5016	331	43	∩	∩	NOUN
ejpam-5016	331	44	{	{	PUNCT
ejpam-5016	331	45	a1	a1	PROPN
ejpam-5016	331	46	,	,	PUNCT
ejpam-5016	331	47	a2	a2	PROPN
ejpam-5016	331	48	,	,	PUNCT
ejpam-5016	331	49	a3}|	a3}|	PROPN
ejpam-5016	331	50	=	=	SYM
ejpam-5016	331	51	2	2	X
ejpam-5016	331	52	.	.	X
ejpam-5016	331	53	we	we	PRON
ejpam-5016	331	54	consider	consider	VERB
ejpam-5016	331	55	every	every	DET
ejpam-5016	331	56	possibility	possibility	NOUN
ejpam-5016	331	57	of	of	ADP
ejpam-5016	331	58	{	{	PUNCT
ejpam-5016	331	59	a1	a1	PROPN
ejpam-5016	331	60	,	,	PUNCT
ejpam-5016	331	61	a2	a2	PROPN
ejpam-5016	331	62	,	,	PUNCT
ejpam-5016	331	63	a3	a3	NOUN
ejpam-5016	331	64	}	}	PUNCT
ejpam-5016	331	65	∩	∩	NOUN
ejpam-5016	331	66	{	{	PUNCT
ejpam-5016	331	67	a1	a1	PROPN
ejpam-5016	331	68	,	,	PUNCT
ejpam-5016	331	69	a2	a2	PROPN
ejpam-5016	331	70	,	,	PUNCT
ejpam-5016	331	71	a3	a3	NOUN
ejpam-5016	331	72	}	}	PUNCT
ejpam-5016	331	73	(	(	PUNCT
ejpam-5016	331	74	i	i	NOUN
ejpam-5016	331	75	)	)	PUNCT
ejpam-5016	331	76	if	if	SCONJ
ejpam-5016	331	77	{	{	PUNCT
ejpam-5016	331	78	a1	a1	NOUN
ejpam-5016	331	79	,	,	PUNCT
ejpam-5016	331	80	a2	a2	PROPN
ejpam-5016	331	81	,	,	PUNCT
ejpam-5016	331	82	a3	a3	NOUN
ejpam-5016	331	83	}	}	PUNCT
ejpam-5016	331	84	∩	∩	NOUN
ejpam-5016	331	85	{	{	PUNCT
ejpam-5016	331	86	a1	a1	PROPN
ejpam-5016	331	87	,	,	PUNCT
ejpam-5016	331	88	a2	a2	PROPN
ejpam-5016	331	89	,	,	PUNCT
ejpam-5016	331	90	a3	a3	NOUN
ejpam-5016	331	91	}	}	PUNCT
ejpam-5016	331	92	=	=	SYM
ejpam-5016	331	93	{	{	PUNCT
ejpam-5016	331	94	a1	a1	PROPN
ejpam-5016	331	95	,	,	PUNCT
ejpam-5016	331	96	a2	a2	PROPN
ejpam-5016	331	97	}	}	PUNCT
ejpam-5016	331	98	.	.	PUNCT
ejpam-5016	332	1	this	this	DET
ejpam-5016	332	2	case	case	NOUN
ejpam-5016	332	3	is	be	AUX
ejpam-5016	332	4	only	only	ADV
ejpam-5016	332	5	possible	possible	ADJ
ejpam-5016	332	6	if	if	SCONJ
ejpam-5016	332	7	a1	a1	NOUN
ejpam-5016	332	8	=	=	SYM
ejpam-5016	332	9	a1	a1	NOUN
ejpam-5016	332	10	and	and	CCONJ
ejpam-5016	332	11	a2	a2	PROPN
ejpam-5016	332	12	∈	∈	PROPN
ejpam-5016	332	13	{	{	PUNCT
ejpam-5016	332	14	a2	a2	PROPN
ejpam-5016	332	15	,	,	PUNCT
ejpam-5016	332	16	a3	a3	NOUN
ejpam-5016	332	17	}	}	PUNCT
ejpam-5016	332	18	.	.	PUNCT
ejpam-5016	333	1	•	•	INTJ
ejpam-5016	333	2	if	if	SCONJ
ejpam-5016	333	3	a2	a2	PROPN
ejpam-5016	333	4	=	=	SYM
ejpam-5016	333	5	a2	a2	PROPN
ejpam-5016	333	6	then	then	ADV
ejpam-5016	333	7	b2	b2	NOUN
ejpam-5016	333	8	=	=	SYM
ejpam-5016	333	9	b2	b2	NOUN
ejpam-5016	333	10	and	and	CCONJ
ejpam-5016	333	11	s(f	s(f	PROPN
ejpam-5016	333	12	,	,	PUNCT
ejpam-5016	333	13	g	g	NOUN
ejpam-5016	333	14	)	)	PUNCT
ejpam-5016	333	15	=	=	SYM
ejpam-5016	333	16	(	(	PUNCT
ejpam-5016	333	17	−b2)(a3b1b3	−b2)(a3b1b3	NUM
ejpam-5016	333	18	−a3b1b3	−a3b1b3	NUM
ejpam-5016	333	19	)	)	PUNCT
ejpam-5016	333	20	.	.	PUNCT
ejpam-5016	334	1	without	without	ADP
ejpam-5016	334	2	loss	loss	NOUN
ejpam-5016	334	3	of	of	ADP
ejpam-5016	334	4	generality	generality	NOUN
ejpam-5016	334	5	,	,	PUNCT
ejpam-5016	334	6	we	we	PRON
ejpam-5016	334	7	may	may	AUX
ejpam-5016	334	8	assume	assume	VERB
ejpam-5016	334	9	b1	b1	NOUN
ejpam-5016	334	10	<	<	NOUN
ejpam-5016	334	11	p	p	NOUN
ejpam-5016	334	12	b1	b1	NOUN
ejpam-5016	334	13	(	(	PUNCT
ejpam-5016	334	14	for	for	ADP
ejpam-5016	334	15	the	the	DET
ejpam-5016	334	16	possibility	possibility	NOUN
ejpam-5016	334	17	b1	b1	NOUN
ejpam-5016	334	18	=	=	SYM
ejpam-5016	334	19	b1	b1	PROPN
ejpam-5016	334	20	,	,	PUNCT
ejpam-5016	334	21	we	we	PRON
ejpam-5016	334	22	have	have	VERB
ejpam-5016	334	23	the	the	DET
ejpam-5016	334	24	interval	interval	NOUN
ejpam-5016	334	25	determined	determine	VERB
ejpam-5016	334	26	by	by	ADP
ejpam-5016	334	27	{	{	PUNCT
ejpam-5016	334	28	a3	a3	NOUN
ejpam-5016	334	29	,	,	PUNCT
ejpam-5016	334	30	b3	b3	PROPN
ejpam-5016	334	31	}	}	PUNCT
ejpam-5016	334	32	is	be	AUX
ejpam-5016	334	33	an	an	DET
ejpam-5016	334	34	inner	inner	ADJ
ejpam-5016	334	35	interval	interval	NOUN
ejpam-5016	334	36	and	and	CCONJ
ejpam-5016	334	37	hence	hence	ADV
ejpam-5016	334	38	s(f	s(f	PROPN
ejpam-5016	334	39	,	,	PUNCT
ejpam-5016	334	40	g	g	NOUN
ejpam-5016	334	41	)	)	PUNCT
ejpam-5016	334	42	=	=	SYM
ejpam-5016	334	43	b2b1(a3b3	b2b1(a3b3	PROPN
ejpam-5016	334	44	−	−	PROPN
ejpam-5016	334	45	a3b3	a3b3	NOUN
ejpam-5016	334	46	)	)	PUNCT
ejpam-5016	334	47	is	be	AUX
ejpam-5016	334	48	reduced	reduce	VERB
ejpam-5016	334	49	to	to	ADP
ejpam-5016	334	50	zero	zero	NUM
ejpam-5016	334	51	)	)	PUNCT
ejpam-5016	334	52	.	.	PUNCT
ejpam-5016	335	1	–	–	PUNCT
ejpam-5016	335	2	if	if	SCONJ
ejpam-5016	335	3	b3	b3	PROPN
ejpam-5016	335	4	=	=	SYM
ejpam-5016	335	5	b3	b3	PROPN
ejpam-5016	335	6	then	then	ADV
ejpam-5016	335	7	s(f	s(f	PROPN
ejpam-5016	335	8	,	,	PUNCT
ejpam-5016	335	9	g	g	NOUN
ejpam-5016	335	10	)	)	PUNCT
ejpam-5016	335	11	=	=	SYM
ejpam-5016	335	12	(	(	PUNCT
ejpam-5016	335	13	−b2b3)(a3b1	−b2b3)(a3b1	PROPN
ejpam-5016	335	14	−a3b1	−a3b1	PROPN
ejpam-5016	335	15	)	)	PUNCT
ejpam-5016	335	16	is	be	AUX
ejpam-5016	335	17	reduced	reduce	VERB
ejpam-5016	335	18	to	to	ADP
ejpam-5016	335	19	zero	zero	NUM
ejpam-5016	335	20	since	since	SCONJ
ejpam-5016	335	21	a3b3	a3b3	ADP
ejpam-5016	335	22	−	−	NOUN
ejpam-5016	335	23	a3b3	a3b3	NOUN
ejpam-5016	335	24	is	be	AUX
ejpam-5016	335	25	an	an	DET
ejpam-5016	335	26	inner	inner	ADJ
ejpam-5016	335	27	2	2	NUM
ejpam-5016	335	28	-	-	PUNCT
ejpam-5016	335	29	minor	minor	ADJ
ejpam-5016	335	30	.	.	PUNCT
ejpam-5016	336	1	–	–	PUNCT
ejpam-5016	336	2	if	if	SCONJ
ejpam-5016	336	3	b3	b3	PROPN
ejpam-5016	336	4	<	<	X
ejpam-5016	336	5	b3	b3	PROPN
ejpam-5016	336	6	(	(	PUNCT
ejpam-5016	336	7	see	see	VERB
ejpam-5016	336	8	figure	figure	NOUN
ejpam-5016	336	9	23	23	NUM
ejpam-5016	336	10	in	in	ADP
ejpam-5016	336	11	the	the	DET
ejpam-5016	336	12	left	left	ADJ
ejpam-5016	336	13	side	side	NOUN
ejpam-5016	336	14	)	)	PUNCT
ejpam-5016	336	15	then	then	ADV
ejpam-5016	336	16	a3b1b3	a3b1b3	PROPN
ejpam-5016	336	17	−	−	PROPN
ejpam-5016	336	18	a3b1b3	a3b1b3	PROPN
ejpam-5016	336	19	∈	∈	PROPN
ejpam-5016	336	20	s3	s3	PROPN
ejpam-5016	336	21	since	since	SCONJ
ejpam-5016	336	22	the	the	DET
ejpam-5016	336	23	interval	interval	NOUN
ejpam-5016	336	24	determined	determine	VERB
ejpam-5016	336	25	by	by	ADP
ejpam-5016	336	26	{	{	PUNCT
ejpam-5016	336	27	b1	b1	NOUN
ejpam-5016	336	28	,	,	PUNCT
ejpam-5016	336	29	b3	b3	PROPN
ejpam-5016	336	30	}	}	PUNCT
ejpam-5016	336	31	and	and	CCONJ
ejpam-5016	336	32	the	the	DET
ejpam-5016	336	33	interval	interval	NOUN
ejpam-5016	336	34	determined	determine	VERB
ejpam-5016	336	35	by	by	ADP
ejpam-5016	336	36	{	{	PUNCT
ejpam-5016	336	37	a3	a3	NOUN
ejpam-5016	336	38	,	,	PUNCT
ejpam-5016	336	39	a3	a3	NOUN
ejpam-5016	336	40	}	}	PUNCT
ejpam-5016	336	41	,	,	PUNCT
ejpam-5016	336	42	both	both	PRON
ejpam-5016	336	43	are	be	AUX
ejpam-5016	336	44	not	not	PART
ejpam-5016	336	45	inner	inner	ADJ
ejpam-5016	336	46	intervals	interval	NOUN
ejpam-5016	336	47	.	.	PUNCT
ejpam-5016	337	1	therefore	therefore	ADV
ejpam-5016	337	2	s(f	s(f	PROPN
ejpam-5016	337	3	,	,	PUNCT
ejpam-5016	337	4	g	g	NOUN
ejpam-5016	337	5	)	)	PUNCT
ejpam-5016	337	6	is	be	AUX
ejpam-5016	337	7	reduced	reduce	VERB
ejpam-5016	337	8	to	to	ADP
ejpam-5016	337	9	zero	zero	NUM
ejpam-5016	337	10	.	.	PUNCT
ejpam-5016	338	1	–	–	PUNCT
ejpam-5016	338	2	ifb3	ifb3	PROPN
ejpam-5016	338	3	<	<	X
ejpam-5016	338	4	b3	b3	PROPN
ejpam-5016	338	5	(	(	PUNCT
ejpam-5016	338	6	see	see	VERB
ejpam-5016	338	7	figure	figure	NOUN
ejpam-5016	338	8	23	23	NUM
ejpam-5016	338	9	in	in	ADP
ejpam-5016	338	10	the	the	DET
ejpam-5016	338	11	right	right	ADJ
ejpam-5016	338	12	side	side	NOUN
ejpam-5016	338	13	)	)	PUNCT
ejpam-5016	338	14	,	,	PUNCT
ejpam-5016	338	15	note	note	VERB
ejpam-5016	338	16	that	that	SCONJ
ejpam-5016	338	17	the	the	DET
ejpam-5016	338	18	interval	interval	NOUN
ejpam-5016	338	19	determined	determine	VERB
ejpam-5016	338	20	by	by	ADP
ejpam-5016	338	21	{	{	PUNCT
ejpam-5016	338	22	a3	a3	NOUN
ejpam-5016	338	23	,	,	PUNCT
ejpam-5016	338	24	b3	b3	PROPN
ejpam-5016	338	25	}	}	PUNCT
ejpam-5016	338	26	is	be	AUX
ejpam-5016	338	27	an	an	DET
ejpam-5016	338	28	inner	inner	ADJ
ejpam-5016	338	29	interval	interval	NOUN
ejpam-5016	338	30	and	and	CCONJ
ejpam-5016	338	31	is	be	AUX
ejpam-5016	338	32	the	the	DET
ejpam-5016	338	33	same	same	ADJ
ejpam-5016	338	34	with	with	ADP
ejpam-5016	338	35	the	the	DET
ejpam-5016	338	36	interval	interval	NOUN
ejpam-5016	338	37	determined	determine	VERB
ejpam-5016	338	38	by	by	ADP
ejpam-5016	338	39	{	{	PUNCT
ejpam-5016	338	40	b3	b3	PROPN
ejpam-5016	338	41	,	,	PUNCT
ejpam-5016	338	42	y	y	NOUN
ejpam-5016	338	43	}	}	PUNCT
ejpam-5016	338	44	for	for	ADP
ejpam-5016	338	45	some	some	DET
ejpam-5016	338	46	vertex	vertex	NOUN
ejpam-5016	338	47	y.	y.	PROPN
ejpam-5016	338	48	therefore	therefore	ADV
ejpam-5016	338	49	,	,	PUNCT
ejpam-5016	338	50	s(f	s(f	PROPN
ejpam-5016	338	51	,	,	PUNCT
ejpam-5016	338	52	g	g	NOUN
ejpam-5016	338	53	)	)	PUNCT
ejpam-5016	338	54	=	=	PUNCT
ejpam-5016	338	55	(	(	PUNCT
ejpam-5016	338	56	−b2b3)(b1y	−b2b3)(b1y	NUM
ejpam-5016	338	57	−a3b1	−a3b1	PROPN
ejpam-5016	338	58	)	)	PUNCT
ejpam-5016	339	1	+	+	CCONJ
ejpam-5016	339	2	(	(	PUNCT
ejpam-5016	339	3	−b2b1)(a3b3	−b2b1)(a3b3	NOUN
ejpam-5016	339	4	−	−	PROPN
ejpam-5016	339	5	b3y	b3y	NOUN
ejpam-5016	339	6	)	)	PUNCT
ejpam-5016	339	7	is	be	AUX
ejpam-5016	339	8	reduced	reduce	VERB
ejpam-5016	339	9	to	to	ADP
ejpam-5016	339	10	zero	zero	NUM
ejpam-5016	339	11	.	.	PUNCT
ejpam-5016	340	1	y.	y.	PROPN
ejpam-5016	340	2	y.	y.	PROPN
ejpam-5016	340	3	hamonangan	hamonangan	PROPN
ejpam-5016	340	4	,	,	PUNCT
ejpam-5016	340	5	i.	i.	PROPN
ejpam-5016	340	6	muchtadi	muchtadi	PROPN
ejpam-5016	340	7	-	-	PUNCT
ejpam-5016	340	8	alamsyah	alamsyah	NOUN
ejpam-5016	340	9	/	/	SYM
ejpam-5016	340	10	eur	eur	PROPN
ejpam-5016	340	11	.	.	PUNCT
ejpam-5016	341	1	j.	j.	PROPN
ejpam-5016	341	2	pure	pure	PROPN
ejpam-5016	341	3	appl	appl	PROPN
ejpam-5016	341	4	.	.	PROPN
ejpam-5016	341	5	math	math	PROPN
ejpam-5016	341	6	,	,	PUNCT
ejpam-5016	341	7	17	17	NUM
ejpam-5016	341	8	(	(	PUNCT
ejpam-5016	341	9	4	4	NUM
ejpam-5016	341	10	)	)	PUNCT
ejpam-5016	341	11	(	(	PUNCT
ejpam-5016	341	12	2024	2024	NUM
ejpam-5016	341	13	)	)	PUNCT
ejpam-5016	341	14	,	,	PUNCT
ejpam-5016	341	15	2621	2621	NUM
ejpam-5016	341	16	-	-	SYM
ejpam-5016	341	17	2650	2650	NUM
ejpam-5016	341	18	2637	2637	NUM
ejpam-5016	341	19	a1	a1	NOUN
ejpam-5016	341	20	a2	a2	PROPN
ejpam-5016	341	21	a3	a3	PROPN
ejpam-5016	341	22	b1	b1	PROPN
ejpam-5016	341	23	b2	b2	PROPN
ejpam-5016	341	24	b3	b3	PROPN
ejpam-5016	341	25	b1	b1	PROPN
ejpam-5016	341	26	a3	a3	PROPN
ejpam-5016	341	27	b3	b3	PROPN
ejpam-5016	341	28	a1	a1	PROPN
ejpam-5016	341	29	a2	a2	PROPN
ejpam-5016	341	30	a3	a3	PROPN
ejpam-5016	341	31	b1	b1	PROPN
ejpam-5016	341	32	b2	b2	PROPN
ejpam-5016	341	33	b3	b3	PROPN
ejpam-5016	341	34	b1	b1	PROPN
ejpam-5016	341	35	a3	a3	NOUN
ejpam-5016	341	36	b3	b3	PROPN
ejpam-5016	341	37	y	y	PROPN
ejpam-5016	341	38	y	y	PROPN
ejpam-5016	341	39	figure	figure	NOUN
ejpam-5016	341	40	23	23	NUM
ejpam-5016	341	41	:	:	PUNCT
ejpam-5016	341	42	case	case	NOUN
ejpam-5016	341	43	a1	a1	NOUN
ejpam-5016	341	44	=	=	SYM
ejpam-5016	341	45	a1	a1	NOUN
ejpam-5016	341	46	and	and	CCONJ
ejpam-5016	341	47	a2	a2	PROPN
ejpam-5016	341	48	=	=	SYM
ejpam-5016	341	49	a2	a2	PROPN
ejpam-5016	341	50	.	.	PUNCT
ejpam-5016	342	1	•	•	NUM
ejpam-5016	342	2	if	if	SCONJ
ejpam-5016	342	3	a2	a2	PROPN
ejpam-5016	342	4	=	=	SYM
ejpam-5016	342	5	a3	a3	PROPN
ejpam-5016	342	6	then	then	ADV
ejpam-5016	342	7	s(f	s(f	PROPN
ejpam-5016	342	8	,	,	PUNCT
ejpam-5016	342	9	g	g	NOUN
ejpam-5016	342	10	)	)	PUNCT
ejpam-5016	342	11	=	=	PUNCT
ejpam-5016	342	12	a3b1b2b3	a3b1b2b3	NOUN
ejpam-5016	342	13	−	−	NOUN
ejpam-5016	342	14	a2b1b2b3	a2b1b2b3	PROPN
ejpam-5016	342	15	has	have	VERB
ejpam-5016	342	16	initial	initial	ADJ
ejpam-5016	342	17	monomial	monomial	ADJ
ejpam-5016	342	18	a2b1b2b3	a2b1b2b3	PROPN
ejpam-5016	342	19	.	.	PUNCT
ejpam-5016	343	1	a1	a1	NOUN
ejpam-5016	343	2	a2	a2	PROPN
ejpam-5016	343	3	a3	a3	PROPN
ejpam-5016	343	4	b1	b1	PROPN
ejpam-5016	343	5	b2	b2	PROPN
ejpam-5016	343	6	b3	b3	PROPN
ejpam-5016	343	7	a2	a2	PROPN
ejpam-5016	343	8	b2	b2	NOUN
ejpam-5016	343	9	b3	b3	PROPN
ejpam-5016	343	10	z	z	PROPN
ejpam-5016	343	11	y	y	PROPN
ejpam-5016	343	12	b1	b1	PROPN
ejpam-5016	343	13	figure	figure	NOUN
ejpam-5016	343	14	24	24	NUM
ejpam-5016	343	15	:	:	PUNCT
ejpam-5016	343	16	case	case	NOUN
ejpam-5016	343	17	a1	a1	NOUN
ejpam-5016	343	18	=	=	SYM
ejpam-5016	343	19	a1	a1	NOUN
ejpam-5016	343	20	and	and	CCONJ
ejpam-5016	343	21	a2	a2	PROPN
ejpam-5016	343	22	=	=	SYM
ejpam-5016	343	23	a3	a3	PROPN
ejpam-5016	343	24	.	.	PUNCT
ejpam-5016	344	1	note	note	VERB
ejpam-5016	344	2	that	that	SCONJ
ejpam-5016	344	3	there	there	PRON
ejpam-5016	344	4	is	be	VERB
ejpam-5016	344	5	no	no	DET
ejpam-5016	344	6	inner	inner	ADJ
ejpam-5016	344	7	2	2	NUM
ejpam-5016	344	8	-	-	PUNCT
ejpam-5016	344	9	minor	minor	NOUN
ejpam-5016	344	10	whose	whose	DET
ejpam-5016	344	11	initial	initial	ADJ
ejpam-5016	344	12	monomial	monomial	NOUN
ejpam-5016	344	13	divides	divide	VERB
ejpam-5016	344	14	a2b1b2b3	a2b1b2b3	PROPN
ejpam-5016	344	15	.	.	PUNCT
ejpam-5016	345	1	moreover	moreover	ADV
ejpam-5016	345	2	,	,	PUNCT
ejpam-5016	345	3	the	the	DET
ejpam-5016	345	4	binomials	binomial	NOUN
ejpam-5016	345	5	in	in	ADP
ejpam-5016	345	6	s3	s3	PROPN
ejpam-5016	345	7	whose	whose	DET
ejpam-5016	345	8	initial	initial	ADJ
ejpam-5016	345	9	monomial	monomial	NOUN
ejpam-5016	345	10	divides	divide	VERB
ejpam-5016	345	11	a2b1b2b3	a2b1b2b3	PROPN
ejpam-5016	345	12	are	be	AUX
ejpam-5016	345	13	the	the	DET
ejpam-5016	345	14	binomial	binomial	NOUN
ejpam-5016	345	15	with	with	ADP
ejpam-5016	345	16	initial	initial	ADJ
ejpam-5016	345	17	monomial	monomial	ADJ
ejpam-5016	345	18	a2b1b3	a2b1b3	NOUN
ejpam-5016	345	19	.	.	PUNCT
ejpam-5016	346	1	this	this	PRON
ejpam-5016	346	2	can	can	AUX
ejpam-5016	346	3	only	only	ADV
ejpam-5016	346	4	happen	happen	VERB
ejpam-5016	346	5	when	when	SCONJ
ejpam-5016	346	6	the	the	DET
ejpam-5016	346	7	interval	interval	NOUN
ejpam-5016	346	8	determined	determine	VERB
ejpam-5016	346	9	by	by	ADP
ejpam-5016	346	10	{	{	PUNCT
ejpam-5016	346	11	b3	b3	PROPN
ejpam-5016	346	12	,	,	PUNCT
ejpam-5016	346	13	b3	b3	PROPN
ejpam-5016	346	14	}	}	PUNCT
ejpam-5016	346	15	is	be	AUX
ejpam-5016	346	16	an	an	DET
ejpam-5016	346	17	inner	inner	ADJ
ejpam-5016	346	18	interval	interval	NOUN
ejpam-5016	346	19	and	and	CCONJ
ejpam-5016	346	20	the	the	DET
ejpam-5016	346	21	binomial	binomial	NOUN
ejpam-5016	346	22	in	in	ADP
ejpam-5016	346	23	s3	s3	PROPN
ejpam-5016	346	24	that	that	PRON
ejpam-5016	346	25	satisfies	satisfy	VERB
ejpam-5016	346	26	the	the	DET
ejpam-5016	346	27	property	property	NOUN
ejpam-5016	346	28	is	be	AUX
ejpam-5016	346	29	a2b1b3	a2b1b3	NOUN
ejpam-5016	346	30	−	−	NOUN
ejpam-5016	346	31	b1yz	b1yz	X
ejpam-5016	346	32	where	where	SCONJ
ejpam-5016	346	33	z	z	NOUN
ejpam-5016	346	34	is	be	AUX
ejpam-5016	346	35	a	a	DET
ejpam-5016	346	36	vertex	vertex	NOUN
ejpam-5016	346	37	such	such	ADJ
ejpam-5016	346	38	that	that	SCONJ
ejpam-5016	347	1	[	[	X
ejpam-5016	347	2	a1	a1	NOUN
ejpam-5016	347	3	,	,	PUNCT
ejpam-5016	347	4	z	z	X
ejpam-5016	347	5	]	]	X
ejpam-5016	347	6	is	be	AUX
ejpam-5016	347	7	the	the	DET
ejpam-5016	347	8	inner	inner	ADJ
ejpam-5016	347	9	interval	interval	NOUN
ejpam-5016	347	10	determined	determine	VERB
ejpam-5016	347	11	by	by	ADP
ejpam-5016	347	12	{	{	PUNCT
ejpam-5016	347	13	b2	b2	NOUN
ejpam-5016	347	14	,	,	PUNCT
ejpam-5016	347	15	b1	b1	NOUN
ejpam-5016	347	16	}	}	PUNCT
ejpam-5016	347	17	.	.	PUNCT
ejpam-5016	348	1	therefore	therefore	ADV
ejpam-5016	348	2	,	,	PUNCT
ejpam-5016	348	3	s(f	s(f	PROPN
ejpam-5016	348	4	,	,	PUNCT
ejpam-5016	348	5	g	g	NOUN
ejpam-5016	348	6	)	)	PUNCT
ejpam-5016	348	7	is	be	AUX
ejpam-5016	348	8	reduced	reduce	VERB
ejpam-5016	348	9	to	to	ADP
ejpam-5016	348	10	zero	zero	NUM
ejpam-5016	348	11	since	since	SCONJ
ejpam-5016	348	12	s(f	s(f	PROPN
ejpam-5016	348	13	,	,	PUNCT
ejpam-5016	348	14	g	g	NOUN
ejpam-5016	348	15	)	)	PUNCT
ejpam-5016	348	16	=	=	SYM
ejpam-5016	348	17	−b2(a2b1b3	−b2(a2b1b3	NOUN
ejpam-5016	348	18	−	−	NOUN
ejpam-5016	348	19	b1yz	b1yz	NUM
ejpam-5016	348	20	)	)	PUNCT
ejpam-5016	349	1	+	+	CCONJ
ejpam-5016	349	2	b1(a3b2b3	b1(a3b2b3	PROPN
ejpam-5016	349	3	−b2yz	−b2yz	NUM
ejpam-5016	349	4	)	)	PUNCT
ejpam-5016	349	5	and	and	CCONJ
ejpam-5016	349	6	a3b2b3	a3b2b3	PROPN
ejpam-5016	349	7	−b2yz	−b2yz	NUM
ejpam-5016	349	8	is	be	AUX
ejpam-5016	349	9	an	an	DET
ejpam-5016	349	10	element	element	NOUN
ejpam-5016	349	11	in	in	ADP
ejpam-5016	349	12	s3	s3	PROPN
ejpam-5016	349	13	.	.	PUNCT
ejpam-5016	350	1	(	(	PUNCT
ejpam-5016	350	2	ii	ii	NOUN
ejpam-5016	350	3	)	)	PUNCT
ejpam-5016	350	4	if	if	SCONJ
ejpam-5016	350	5	{	{	PUNCT
ejpam-5016	350	6	a1	a1	NOUN
ejpam-5016	350	7	,	,	PUNCT
ejpam-5016	350	8	a2	a2	PROPN
ejpam-5016	350	9	,	,	PUNCT
ejpam-5016	350	10	a3	a3	NOUN
ejpam-5016	350	11	}	}	PUNCT
ejpam-5016	350	12	∩	∩	NOUN
ejpam-5016	350	13	{	{	PUNCT
ejpam-5016	350	14	a1	a1	PROPN
ejpam-5016	350	15	,	,	PUNCT
ejpam-5016	350	16	a2	a2	PROPN
ejpam-5016	350	17	,	,	PUNCT
ejpam-5016	350	18	a3	a3	NOUN
ejpam-5016	350	19	}	}	PUNCT
ejpam-5016	350	20	=	=	SYM
ejpam-5016	350	21	{	{	PUNCT
ejpam-5016	350	22	a1	a1	NOUN
ejpam-5016	350	23	,	,	PUNCT
ejpam-5016	350	24	a3	a3	NOUN
ejpam-5016	350	25	}	}	PUNCT
ejpam-5016	350	26	.	.	PUNCT
ejpam-5016	351	1	this	this	DET
ejpam-5016	351	2	case	case	NOUN
ejpam-5016	351	3	is	be	AUX
ejpam-5016	351	4	only	only	ADV
ejpam-5016	351	5	possible	possible	ADJ
ejpam-5016	351	6	if	if	SCONJ
ejpam-5016	351	7	a1	a1	NOUN
ejpam-5016	351	8	=	=	SYM
ejpam-5016	351	9	a1	a1	NOUN
ejpam-5016	351	10	and	and	CCONJ
ejpam-5016	351	11	a3	a3	NOUN
ejpam-5016	351	12	∈	∈	PROPN
ejpam-5016	351	13	{	{	PUNCT
ejpam-5016	351	14	a2	a2	PROPN
ejpam-5016	351	15	,	,	PUNCT
ejpam-5016	351	16	a3	a3	NOUN
ejpam-5016	351	17	}	}	PUNCT
ejpam-5016	351	18	.	.	PUNCT
ejpam-5016	352	1	for	for	ADP
ejpam-5016	352	2	the	the	DET
ejpam-5016	352	3	case	case	NOUN
ejpam-5016	352	4	a3	a3	NOUN
ejpam-5016	352	5	=	=	SYM
ejpam-5016	352	6	a2	a2	PROPN
ejpam-5016	352	7	,	,	PUNCT
ejpam-5016	352	8	since	since	SCONJ
ejpam-5016	352	9	s(f	s(f	PROPN
ejpam-5016	352	10	,	,	PUNCT
ejpam-5016	352	11	g	g	NOUN
ejpam-5016	352	12	)	)	PUNCT
ejpam-5016	352	13	=	=	SYM
ejpam-5016	352	14	−s(g	−s(g	PROPN
ejpam-5016	352	15	,	,	PUNCT
ejpam-5016	352	16	f	f	PROPN
ejpam-5016	352	17	)	)	PUNCT
ejpam-5016	353	1	then	then	ADV
ejpam-5016	353	2	it	it	PRON
ejpam-5016	353	3	is	be	AUX
ejpam-5016	353	4	similar	similar	ADJ
ejpam-5016	353	5	with	with	ADP
ejpam-5016	353	6	the	the	DET
ejpam-5016	353	7	case	case	NOUN
ejpam-5016	353	8	a1	a1	NOUN
ejpam-5016	353	9	=	=	SYM
ejpam-5016	353	10	a1	a1	NOUN
ejpam-5016	353	11	and	and	CCONJ
ejpam-5016	353	12	a2	a2	PROPN
ejpam-5016	353	13	=	=	SYM
ejpam-5016	353	14	a3	a3	NOUN
ejpam-5016	353	15	.	.	PUNCT
ejpam-5016	354	1	we	we	PRON
ejpam-5016	354	2	conclude	conclude	VERB
ejpam-5016	354	3	that	that	SCONJ
ejpam-5016	354	4	s(f	s(f	PROPN
ejpam-5016	354	5	,	,	PUNCT
ejpam-5016	354	6	g	g	NOUN
ejpam-5016	354	7	)	)	PUNCT
ejpam-5016	354	8	is	be	AUX
ejpam-5016	354	9	reduced	reduce	VERB
ejpam-5016	354	10	to	to	ADP
ejpam-5016	354	11	zero	zero	NUM
ejpam-5016	354	12	if	if	SCONJ
ejpam-5016	354	13	and	and	CCONJ
ejpam-5016	354	14	only	only	ADV
ejpam-5016	354	15	if	if	SCONJ
ejpam-5016	354	16	the	the	DET
ejpam-5016	354	17	interval	interval	NOUN
ejpam-5016	354	18	determined	determine	VERB
ejpam-5016	354	19	by	by	ADP
ejpam-5016	354	20	{	{	PUNCT
ejpam-5016	354	21	b3	b3	PROPN
ejpam-5016	354	22	,	,	PUNCT
ejpam-5016	354	23	b3	b3	PROPN
ejpam-5016	354	24	}	}	PUNCT
ejpam-5016	354	25	is	be	AUX
ejpam-5016	354	26	an	an	DET
ejpam-5016	354	27	inner	inner	ADJ
ejpam-5016	354	28	interval	interval	NOUN
ejpam-5016	354	29	.	.	PUNCT
ejpam-5016	355	1	for	for	ADP
ejpam-5016	355	2	the	the	DET
ejpam-5016	355	3	case	case	NOUN
ejpam-5016	355	4	a3	a3	NOUN
ejpam-5016	355	5	=	=	NOUN
ejpam-5016	355	6	a3	a3	NOUN
ejpam-5016	355	7	,	,	PUNCT
ejpam-5016	355	8	we	we	PRON
ejpam-5016	355	9	have	have	VERB
ejpam-5016	355	10	b1	b1	NOUN
ejpam-5016	355	11	=	=	SYM
ejpam-5016	355	12	b1	b1	PROPN
ejpam-5016	355	13	and	and	CCONJ
ejpam-5016	355	14	s(f	s(f	PROPN
ejpam-5016	355	15	,	,	PUNCT
ejpam-5016	355	16	g	g	NOUN
ejpam-5016	355	17	)	)	PUNCT
ejpam-5016	355	18	=	=	SYM
ejpam-5016	355	19	b1(a2b2b3	b1(a2b2b3	NOUN
ejpam-5016	355	20	−	−	NOUN
ejpam-5016	355	21	a2b2b3	a2b2b3	NOUN
ejpam-5016	355	22	)	)	PUNCT
ejpam-5016	355	23	.	.	PUNCT
ejpam-5016	356	1	y.	y.	PROPN
ejpam-5016	356	2	y.	y.	PROPN
ejpam-5016	356	3	hamonangan	hamonangan	PROPN
ejpam-5016	356	4	,	,	PUNCT
ejpam-5016	356	5	i.	i.	PROPN
ejpam-5016	356	6	muchtadi	muchtadi	PROPN
ejpam-5016	356	7	-	-	PUNCT
ejpam-5016	356	8	alamsyah	alamsyah	NOUN
ejpam-5016	356	9	/	/	SYM
ejpam-5016	356	10	eur	eur	PROPN
ejpam-5016	356	11	.	.	PUNCT
ejpam-5016	357	1	j.	j.	PROPN
ejpam-5016	357	2	pure	pure	PROPN
ejpam-5016	357	3	appl	appl	PROPN
ejpam-5016	357	4	.	.	PROPN
ejpam-5016	357	5	math	math	PROPN
ejpam-5016	357	6	,	,	PUNCT
ejpam-5016	357	7	17	17	NUM
ejpam-5016	357	8	(	(	PUNCT
ejpam-5016	357	9	4	4	NUM
ejpam-5016	357	10	)	)	PUNCT
ejpam-5016	357	11	(	(	PUNCT
ejpam-5016	357	12	2024	2024	NUM
ejpam-5016	357	13	)	)	PUNCT
ejpam-5016	357	14	,	,	PUNCT
ejpam-5016	357	15	2621	2621	NUM
ejpam-5016	357	16	-	-	SYM
ejpam-5016	357	17	2650	2650	NUM
ejpam-5016	357	18	2638	2638	NUM
ejpam-5016	357	19	by	by	ADP
ejpam-5016	357	20	similar	similar	ADJ
ejpam-5016	357	21	argument	argument	NOUN
ejpam-5016	357	22	with	with	ADP
ejpam-5016	357	23	the	the	DET
ejpam-5016	357	24	case	case	NOUN
ejpam-5016	357	25	a1	a1	NOUN
ejpam-5016	357	26	=	=	SYM
ejpam-5016	357	27	a1	a1	NOUN
ejpam-5016	357	28	and	and	CCONJ
ejpam-5016	357	29	a2	a2	PROPN
ejpam-5016	357	30	=	=	SYM
ejpam-5016	357	31	a2	a2	PROPN
ejpam-5016	357	32	,	,	PUNCT
ejpam-5016	357	33	we	we	PRON
ejpam-5016	357	34	may	may	AUX
ejpam-5016	357	35	assume	assume	VERB
ejpam-5016	357	36	b3	b3	PROPN
ejpam-5016	357	37	<	<	PROPN
ejpam-5016	357	38	p	p	X
ejpam-5016	357	39	b3	b3	PROPN
ejpam-5016	357	40	and	and	CCONJ
ejpam-5016	357	41	we	we	PRON
ejpam-5016	357	42	have	have	VERB
ejpam-5016	357	43	three	three	NUM
ejpam-5016	357	44	subcases	subcase	NOUN
ejpam-5016	357	45	•	•	ADP
ejpam-5016	357	46	if	if	SCONJ
ejpam-5016	357	47	b2	b2	NOUN
ejpam-5016	357	48	=	=	SYM
ejpam-5016	357	49	b2	b2	NOUN
ejpam-5016	357	50	then	then	ADV
ejpam-5016	357	51	s(f	s(f	PROPN
ejpam-5016	357	52	,	,	PUNCT
ejpam-5016	357	53	g	g	NOUN
ejpam-5016	357	54	)	)	PUNCT
ejpam-5016	357	55	is	be	AUX
ejpam-5016	357	56	reduced	reduce	VERB
ejpam-5016	357	57	to	to	ADP
ejpam-5016	357	58	zero	zero	NUM
ejpam-5016	357	59	since	since	SCONJ
ejpam-5016	357	60	a2b3−a2b3	a2b3−a2b3	ADJ
ejpam-5016	357	61	is	be	AUX
ejpam-5016	357	62	an	an	DET
ejpam-5016	357	63	inner	inner	ADJ
ejpam-5016	357	64	2	2	NUM
ejpam-5016	357	65	-	-	PUNCT
ejpam-5016	357	66	minor	minor	ADJ
ejpam-5016	357	67	.	.	PUNCT
ejpam-5016	358	1	•	•	NOUN
ejpam-5016	358	2	if	if	SCONJ
ejpam-5016	358	3	b2	b2	NOUN
ejpam-5016	358	4	<	<	X
ejpam-5016	358	5	b2	b2	NOUN
ejpam-5016	358	6	then	then	ADV
ejpam-5016	358	7	s(f	s(f	PROPN
ejpam-5016	358	8	,	,	PUNCT
ejpam-5016	358	9	g	g	NOUN
ejpam-5016	358	10	)	)	PUNCT
ejpam-5016	358	11	is	be	AUX
ejpam-5016	358	12	reduced	reduce	VERB
ejpam-5016	358	13	to	to	ADP
ejpam-5016	358	14	zero	zero	NUM
ejpam-5016	358	15	since	since	SCONJ
ejpam-5016	358	16	a2b2b3	a2b2b3	ADJ
ejpam-5016	358	17	−a2b2b3	−a2b2b3	NOUN
ejpam-5016	358	18	∈	∈	PROPN
ejpam-5016	358	19	s3	s3	PROPN
ejpam-5016	358	20	.	.	PROPN
ejpam-5016	359	1	•	•	NUM
ejpam-5016	359	2	if	if	SCONJ
ejpam-5016	359	3	b2	b2	NOUN
ejpam-5016	359	4	<	<	X
ejpam-5016	359	5	b2	b2	NOUN
ejpam-5016	359	6	,	,	PUNCT
ejpam-5016	359	7	notice	notice	VERB
ejpam-5016	359	8	that	that	SCONJ
ejpam-5016	359	9	the	the	DET
ejpam-5016	359	10	interval	interval	NOUN
ejpam-5016	359	11	determined	determine	VERB
ejpam-5016	359	12	by	by	ADP
ejpam-5016	359	13	{	{	PUNCT
ejpam-5016	359	14	b3	b3	PROPN
ejpam-5016	359	15	,	,	PUNCT
ejpam-5016	359	16	a2	a2	PROPN
ejpam-5016	359	17	}	}	PUNCT
ejpam-5016	359	18	is	be	AUX
ejpam-5016	359	19	an	an	DET
ejpam-5016	359	20	inner	inner	ADJ
ejpam-5016	359	21	interval	interval	NOUN
ejpam-5016	359	22	that	that	PRON
ejpam-5016	359	23	is	be	AUX
ejpam-5016	359	24	the	the	DET
ejpam-5016	359	25	same	same	ADJ
ejpam-5016	359	26	with	with	ADP
ejpam-5016	359	27	[	[	X
ejpam-5016	359	28	y	y	PROPN
ejpam-5016	359	29	,	,	PUNCT
ejpam-5016	359	30	b3	b3	PROPN
ejpam-5016	359	31	]	]	PUNCT
ejpam-5016	359	32	for	for	ADP
ejpam-5016	359	33	some	some	DET
ejpam-5016	359	34	vertex	vertex	NOUN
ejpam-5016	359	35	y.	y.	PROPN
ejpam-5016	359	36	therefore	therefore	ADV
ejpam-5016	359	37	,	,	PUNCT
ejpam-5016	359	38	s(f	s(f	PROPN
ejpam-5016	359	39	,	,	PUNCT
ejpam-5016	359	40	g	g	NOUN
ejpam-5016	359	41	)	)	PUNCT
ejpam-5016	359	42	is	be	AUX
ejpam-5016	359	43	reduced	reduce	VERB
ejpam-5016	359	44	to	to	ADP
ejpam-5016	359	45	zero	zero	NUM
ejpam-5016	359	46	since	since	SCONJ
ejpam-5016	359	47	we	we	PRON
ejpam-5016	359	48	can	can	AUX
ejpam-5016	359	49	write	write	VERB
ejpam-5016	359	50	s(f	s(f	PROPN
ejpam-5016	359	51	,	,	PUNCT
ejpam-5016	359	52	g	g	NOUN
ejpam-5016	359	53	)	)	PUNCT
ejpam-5016	360	1	=	=	PUNCT
ejpam-5016	360	2	b1b3(a2b2	b1b3(a2b2	NOUN
ejpam-5016	360	3	−b2y	−b2y	NUM
ejpam-5016	360	4	)	)	PUNCT
ejpam-5016	361	1	+	+	ADV
ejpam-5016	361	2	b1b2(b3y	b1b2(b3y	X
ejpam-5016	361	3	−	−	NOUN
ejpam-5016	361	4	a2b3	a2b3	NOUN
ejpam-5016	361	5	)	)	PUNCT
ejpam-5016	361	6	.	.	PUNCT
ejpam-5016	362	1	a1	a1	NOUN
ejpam-5016	362	2	a2	a2	PROPN
ejpam-5016	362	3	a3	a3	PROPN
ejpam-5016	362	4	b1	b1	PROPN
ejpam-5016	362	5	b2	b2	PROPN
ejpam-5016	362	6	b3	b3	PROPN
ejpam-5016	362	7	a1	a1	NOUN
ejpam-5016	362	8	a2	a2	PROPN
ejpam-5016	362	9	a3	a3	PROPN
ejpam-5016	362	10	b1	b1	PROPN
ejpam-5016	362	11	b2	b2	PROPN
ejpam-5016	362	12	b3	b3	PROPN
ejpam-5016	362	13	b2	b2	NOUN
ejpam-5016	362	14	a2	a2	PROPN
ejpam-5016	362	15	b3	b3	PROPN
ejpam-5016	362	16	y	y	PROPN
ejpam-5016	362	17	b3	b3	PROPN
ejpam-5016	362	18	a2	a2	PROPN
ejpam-5016	362	19	b2	b2	PROPN
ejpam-5016	362	20	y	y	PROPN
ejpam-5016	362	21	figure	figure	NOUN
ejpam-5016	362	22	25	25	NUM
ejpam-5016	362	23	:	:	PUNCT
ejpam-5016	362	24	case	case	NOUN
ejpam-5016	362	25	a1	a1	NOUN
ejpam-5016	362	26	=	=	SYM
ejpam-5016	362	27	a1	a1	NOUN
ejpam-5016	362	28	and	and	CCONJ
ejpam-5016	362	29	a3	a3	NOUN
ejpam-5016	362	30	=	=	NOUN
ejpam-5016	362	31	a3	a3	NOUN
ejpam-5016	362	32	.	.	PUNCT
ejpam-5016	363	1	(	(	PUNCT
ejpam-5016	363	2	iii	iii	X
ejpam-5016	363	3	)	)	PUNCT
ejpam-5016	363	4	if	if	SCONJ
ejpam-5016	363	5	{	{	PUNCT
ejpam-5016	363	6	a1	a1	NOUN
ejpam-5016	363	7	,	,	PUNCT
ejpam-5016	363	8	a2	a2	PROPN
ejpam-5016	363	9	,	,	PUNCT
ejpam-5016	363	10	a3	a3	NOUN
ejpam-5016	363	11	}	}	PUNCT
ejpam-5016	363	12	∩	∩	NOUN
ejpam-5016	363	13	{	{	PUNCT
ejpam-5016	363	14	a1	a1	PROPN
ejpam-5016	363	15	,	,	PUNCT
ejpam-5016	363	16	a2	a2	PROPN
ejpam-5016	363	17	,	,	PUNCT
ejpam-5016	363	18	a3	a3	NOUN
ejpam-5016	363	19	}	}	PUNCT
ejpam-5016	363	20	=	=	SYM
ejpam-5016	363	21	{	{	PUNCT
ejpam-5016	363	22	a2	a2	PROPN
ejpam-5016	363	23	,	,	PUNCT
ejpam-5016	363	24	a3	a3	NOUN
ejpam-5016	363	25	}	}	PUNCT
ejpam-5016	363	26	then	then	ADV
ejpam-5016	363	27	a2	a2	PROPN
ejpam-5016	363	28	=	=	PROPN
ejpam-5016	363	29	a2	a2	PROPN
ejpam-5016	363	30	and	and	CCONJ
ejpam-5016	363	31	a3	a3	NOUN
ejpam-5016	363	32	=	=	SYM
ejpam-5016	363	33	a3	a3	NOUN
ejpam-5016	363	34	.	.	PUNCT
ejpam-5016	364	1	thus	thus	ADV
ejpam-5016	364	2	,	,	PUNCT
ejpam-5016	364	3	b3	b3	PROPN
ejpam-5016	364	4	=	=	SYM
ejpam-5016	364	5	b3	b3	PROPN
ejpam-5016	364	6	and	and	CCONJ
ejpam-5016	364	7	s(f	s(f	PROPN
ejpam-5016	364	8	,	,	PUNCT
ejpam-5016	364	9	g	g	NOUN
ejpam-5016	364	10	)	)	PUNCT
ejpam-5016	364	11	=	=	SYM
ejpam-5016	364	12	b3(a1b1b2	b3(a1b1b2	PROPN
ejpam-5016	364	13	−	−	PROPN
ejpam-5016	364	14	a1b1b2	a1b1b2	NOUN
ejpam-5016	364	15	)	)	PUNCT
ejpam-5016	364	16	.	.	PUNCT
ejpam-5016	365	1	a1	a1	NOUN
ejpam-5016	365	2	a2	a2	PROPN
ejpam-5016	365	3	a3	a3	PROPN
ejpam-5016	365	4	b1	b1	PROPN
ejpam-5016	365	5	b2	b2	PROPN
ejpam-5016	365	6	b3	b3	PROPN
ejpam-5016	365	7	a1	a1	NOUN
ejpam-5016	365	8	a2	a2	PROPN
ejpam-5016	365	9	a3	a3	PROPN
ejpam-5016	365	10	b1	b1	PROPN
ejpam-5016	365	11	b2	b2	PROPN
ejpam-5016	365	12	b3	b3	PROPN
ejpam-5016	365	13	b2	b2	NOUN
ejpam-5016	365	14	a1	a1	NOUN
ejpam-5016	365	15	b1	b1	NOUN
ejpam-5016	365	16	b2	b2	NOUN
ejpam-5016	365	17	a1	a1	NOUN
ejpam-5016	365	18	b1	b1	NOUN
ejpam-5016	365	19	y	y	PROPN
ejpam-5016	365	20	y	y	PROPN
ejpam-5016	365	21	figure	figure	NOUN
ejpam-5016	365	22	26	26	NUM
ejpam-5016	365	23	:	:	PUNCT
ejpam-5016	365	24	case	case	NOUN
ejpam-5016	365	25	a2	a2	PROPN
ejpam-5016	365	26	=	=	SYM
ejpam-5016	365	27	a2	a2	PROPN
ejpam-5016	365	28	and	and	CCONJ
ejpam-5016	365	29	a3	a3	NOUN
ejpam-5016	365	30	=	=	SYM
ejpam-5016	365	31	a3	a3	NOUN
ejpam-5016	365	32	.	.	PUNCT
ejpam-5016	366	1	similarly	similarly	ADV
ejpam-5016	366	2	,	,	PUNCT
ejpam-5016	366	3	we	we	PRON
ejpam-5016	366	4	may	may	AUX
ejpam-5016	366	5	assume	assume	VERB
ejpam-5016	366	6	b2	b2	NOUN
ejpam-5016	366	7	<	<	NOUN
ejpam-5016	366	8	p	p	NOUN
ejpam-5016	366	9	b2	b2	NOUN
ejpam-5016	366	10	,	,	PUNCT
ejpam-5016	366	11	and	and	CCONJ
ejpam-5016	366	12	this	this	PRON
ejpam-5016	366	13	implies	imply	VERB
ejpam-5016	366	14	that	that	SCONJ
ejpam-5016	366	15	[	[	X
ejpam-5016	366	16	a1	a1	NOUN
ejpam-5016	366	17	,	,	PUNCT
ejpam-5016	366	18	b2	b2	NOUN
ejpam-5016	366	19	]	]	PUNCT
ejpam-5016	366	20	is	be	AUX
ejpam-5016	366	21	an	an	DET
ejpam-5016	366	22	inner	inner	ADJ
ejpam-5016	366	23	interval	interval	NOUN
ejpam-5016	366	24	having	have	VERB
ejpam-5016	366	25	{	{	PUNCT
ejpam-5016	366	26	b2	b2	NOUN
ejpam-5016	366	27	,	,	PUNCT
ejpam-5016	366	28	y	y	NOUN
ejpam-5016	366	29	}	}	PUNCT
ejpam-5016	366	30	as	as	ADP
ejpam-5016	366	31	the	the	DET
ejpam-5016	366	32	antidiagonal	antidiagonal	ADJ
ejpam-5016	366	33	corners	corner	NOUN
ejpam-5016	366	34	for	for	ADP
ejpam-5016	366	35	some	some	DET
ejpam-5016	366	36	vertex	vertex	NOUN
ejpam-5016	366	37	y.	y.	PROPN
ejpam-5016	366	38	therefore	therefore	ADV
ejpam-5016	366	39	,	,	PUNCT
ejpam-5016	366	40	s(f	s(f	PROPN
ejpam-5016	366	41	,	,	PUNCT
ejpam-5016	366	42	g	g	NOUN
ejpam-5016	366	43	)	)	PUNCT
ejpam-5016	366	44	is	be	AUX
ejpam-5016	366	45	reduced	reduce	VERB
ejpam-5016	366	46	to	to	ADP
ejpam-5016	366	47	zero	zero	NUM
ejpam-5016	366	48	since	since	SCONJ
ejpam-5016	366	49	s(f	s(f	PROPN
ejpam-5016	366	50	,	,	PUNCT
ejpam-5016	366	51	g	g	NOUN
ejpam-5016	366	52	)	)	PUNCT
ejpam-5016	366	53	=	=	PUNCT
ejpam-5016	367	1	−b1b3(a1b2	−b1b3(a1b2	NOUN
ejpam-5016	367	2	−	−	PROPN
ejpam-5016	367	3	b2y	b2y	PROPN
ejpam-5016	367	4	)	)	PUNCT
ejpam-5016	368	1	+	+	PROPN
ejpam-5016	368	2	b3b2(a1b1	b3b2(a1b1	PROPN
ejpam-5016	368	3	−b1y	−b1y	NUM
ejpam-5016	368	4	)	)	PUNCT
ejpam-5016	368	5	.	.	PUNCT
ejpam-5016	369	1	we	we	PRON
ejpam-5016	369	2	summarize	summarize	VERB
ejpam-5016	369	3	this	this	DET
ejpam-5016	369	4	discussion	discussion	NOUN
ejpam-5016	369	5	with	with	ADP
ejpam-5016	369	6	the	the	DET
ejpam-5016	369	7	following	follow	VERB
ejpam-5016	369	8	theorem	theorem	NOUN
ejpam-5016	369	9	.	.	PUNCT
ejpam-5016	370	1	y.	y.	PROPN
ejpam-5016	370	2	y.	y.	PROPN
ejpam-5016	370	3	hamonangan	hamonangan	PROPN
ejpam-5016	370	4	,	,	PUNCT
ejpam-5016	370	5	i.	i.	PROPN
ejpam-5016	370	6	muchtadi	muchtadi	PROPN
ejpam-5016	370	7	-	-	PUNCT
ejpam-5016	370	8	alamsyah	alamsyah	NOUN
ejpam-5016	370	9	/	/	SYM
ejpam-5016	370	10	eur	eur	PROPN
ejpam-5016	370	11	.	.	PUNCT
ejpam-5016	371	1	j.	j.	PROPN
ejpam-5016	371	2	pure	pure	PROPN
ejpam-5016	371	3	appl	appl	PROPN
ejpam-5016	371	4	.	.	PROPN
ejpam-5016	371	5	math	math	PROPN
ejpam-5016	371	6	,	,	PUNCT
ejpam-5016	371	7	17	17	NUM
ejpam-5016	371	8	(	(	PUNCT
ejpam-5016	371	9	4	4	NUM
ejpam-5016	371	10	)	)	PUNCT
ejpam-5016	371	11	(	(	PUNCT
ejpam-5016	371	12	2024	2024	NUM
ejpam-5016	371	13	)	)	PUNCT
ejpam-5016	371	14	,	,	PUNCT
ejpam-5016	371	15	2621	2621	NUM
ejpam-5016	371	16	-	-	SYM
ejpam-5016	371	17	2650	2650	NUM
ejpam-5016	371	18	2639	2639	NUM
ejpam-5016	371	19	theorem	theorem	VERB
ejpam-5016	371	20	3	3	X
ejpam-5016	371	21	.	.	PUNCT
ejpam-5016	372	1	let	let	VERB
ejpam-5016	372	2	f	f	NOUN
ejpam-5016	372	3	=	=	SYM
ejpam-5016	372	4	a1a2a3−b1b2b3	a1a2a3−b1b2b3	PRON
ejpam-5016	372	5	and	and	CCONJ
ejpam-5016	372	6	g	g	NOUN
ejpam-5016	372	7	=	=	SYM
ejpam-5016	372	8	a1a2a3−b1b2b3	a1a2a3−b1b2b3	ADJ
ejpam-5016	372	9	with	with	SCONJ
ejpam-5016	372	10	initial	initial	ADJ
ejpam-5016	372	11	monomials	monomial	NOUN
ejpam-5016	372	12	a1a2a3	a1a2a3	ADJ
ejpam-5016	372	13	and	and	CCONJ
ejpam-5016	372	14	a1a2a3	a1a2a3	ADJ
ejpam-5016	372	15	,	,	PUNCT
ejpam-5016	372	16	respectively	respectively	ADV
ejpam-5016	372	17	,	,	PUNCT
ejpam-5016	372	18	in	in	ADP
ejpam-5016	372	19	s3	s3	PROPN
ejpam-5016	372	20	with	with	ADP
ejpam-5016	372	21	a1	a1	NOUN
ejpam-5016	372	22	<	<	PROPN
ejpam-5016	372	23	p	p	X
ejpam-5016	372	24	a2	a2	PROPN
ejpam-5016	372	25	<	<	PROPN
ejpam-5016	372	26	p	p	PROPN
ejpam-5016	372	27	a3	a3	NOUN
ejpam-5016	372	28	,	,	PUNCT
ejpam-5016	372	29	b1	b1	NOUN
ejpam-5016	372	30	<	<	NOUN
ejpam-5016	372	31	p	p	NOUN
ejpam-5016	372	32	b2	b2	NOUN
ejpam-5016	372	33	<	<	X
ejpam-5016	372	34	p	p	X
ejpam-5016	372	35	b3	b3	PROPN
ejpam-5016	372	36	,	,	PUNCT
ejpam-5016	372	37	a1	a1	NOUN
ejpam-5016	372	38	<	<	X
ejpam-5016	372	39	p	p	X
ejpam-5016	372	40	a2	a2	PROPN
ejpam-5016	372	41	<	<	PROPN
ejpam-5016	372	42	p	p	PROPN
ejpam-5016	372	43	a3	a3	NOUN
ejpam-5016	372	44	,	,	PUNCT
ejpam-5016	372	45	b1	b1	NOUN
ejpam-5016	372	46	<	<	NOUN
ejpam-5016	372	47	p	p	NOUN
ejpam-5016	372	48	b2	b2	NOUN
ejpam-5016	372	49	<	<	X
ejpam-5016	372	50	p	p	NOUN
ejpam-5016	372	51	b3	b3	PROPN
ejpam-5016	372	52	,	,	PUNCT
ejpam-5016	372	53	and	and	CCONJ
ejpam-5016	372	54	|{a1	|{a1	ADJ
ejpam-5016	372	55	,	,	PUNCT
ejpam-5016	372	56	a2	a2	PROPN
ejpam-5016	372	57	,	,	PUNCT
ejpam-5016	372	58	a3	a3	NOUN
ejpam-5016	372	59	}	}	PUNCT
ejpam-5016	372	60	∩	∩	NOUN
ejpam-5016	372	61	{	{	PUNCT
ejpam-5016	372	62	a1	a1	PROPN
ejpam-5016	372	63	,	,	PUNCT
ejpam-5016	372	64	a2	a2	PROPN
ejpam-5016	372	65	,	,	PUNCT
ejpam-5016	372	66	a3}|	a3}|	PROPN
ejpam-5016	372	67	=	=	SYM
ejpam-5016	372	68	2	2	NUM
ejpam-5016	372	69	.	.	PUNCT
ejpam-5016	373	1	the	the	DET
ejpam-5016	373	2	binomial	binomial	ADJ
ejpam-5016	373	3	s(f	s(f	PROPN
ejpam-5016	373	4	,	,	PUNCT
ejpam-5016	373	5	g	g	NOUN
ejpam-5016	373	6	)	)	PUNCT
ejpam-5016	373	7	is	be	AUX
ejpam-5016	373	8	not	not	PART
ejpam-5016	373	9	reduced	reduce	VERB
ejpam-5016	373	10	to	to	ADP
ejpam-5016	373	11	zero	zero	NUM
ejpam-5016	373	12	by	by	ADP
ejpam-5016	373	13	s2	s2	PROPN
ejpam-5016	373	14	∪	∪	ADP
ejpam-5016	373	15	s3	s3	PROPN
ejpam-5016	373	16	if	if	SCONJ
ejpam-5016	373	17	and	and	CCONJ
ejpam-5016	373	18	only	only	ADV
ejpam-5016	373	19	if	if	SCONJ
ejpam-5016	373	20	•	•	NUM
ejpam-5016	373	21	a1	a1	NOUN
ejpam-5016	373	22	=	=	SYM
ejpam-5016	373	23	a1	a1	NOUN
ejpam-5016	373	24	,	,	PUNCT
ejpam-5016	373	25	•	•	ADP
ejpam-5016	373	26	the	the	DET
ejpam-5016	373	27	interval	interval	NOUN
ejpam-5016	373	28	determined	determine	VERB
ejpam-5016	373	29	by	by	ADP
ejpam-5016	373	30	{	{	PUNCT
ejpam-5016	373	31	b3	b3	PROPN
ejpam-5016	373	32	,	,	PUNCT
ejpam-5016	373	33	b3	b3	PROPN
ejpam-5016	373	34	}	}	PUNCT
ejpam-5016	373	35	is	be	AUX
ejpam-5016	373	36	not	not	PART
ejpam-5016	373	37	inner	inner	ADJ
ejpam-5016	373	38	interval	interval	NOUN
ejpam-5016	373	39	,	,	PUNCT
ejpam-5016	373	40	and	and	CCONJ
ejpam-5016	373	41	•	•	NUM
ejpam-5016	373	42	a3	a3	NOUN
ejpam-5016	373	43	=	=	SYM
ejpam-5016	373	44	a2	a2	PROPN
ejpam-5016	373	45	or	or	CCONJ
ejpam-5016	373	46	a2	a2	PROPN
ejpam-5016	373	47	=	=	SYM
ejpam-5016	373	48	a3	a3	PROPN
ejpam-5016	373	49	holds	hold	VERB
ejpam-5016	373	50	.	.	PUNCT
ejpam-5016	374	1	a1	a1	NOUN
ejpam-5016	374	2	=	=	SYM
ejpam-5016	374	3	a1	a1	NOUN
ejpam-5016	374	4	b1	b1	NOUN
ejpam-5016	374	5	b1	b1	PROPN
ejpam-5016	374	6	b2	b2	NOUN
ejpam-5016	374	7	a2	a2	PROPN
ejpam-5016	374	8	=	=	SYM
ejpam-5016	374	9	a3	a3	PROPN
ejpam-5016	374	10	b3	b3	PROPN
ejpam-5016	374	11	a3	a3	NOUN
ejpam-5016	374	12	b3	b3	PROPN
ejpam-5016	374	13	a2b2	a2b2	ADP
ejpam-5016	374	14	a1	a1	NOUN
ejpam-5016	374	15	=	=	PUNCT
ejpam-5016	374	16	a1	a1	NOUN
ejpam-5016	374	17	b2	b2	NOUN
ejpam-5016	374	18	a2	a2	PROPN
ejpam-5016	374	19	b3	b3	PROPN
ejpam-5016	374	20	a3	a3	NOUN
ejpam-5016	374	21	=	=	SYM
ejpam-5016	374	22	a2	a2	PROPN
ejpam-5016	374	23	b1	b1	PROPN
ejpam-5016	374	24	b2	b2	NOUN
ejpam-5016	374	25	b3a3	b3a3	PUNCT
ejpam-5016	374	26	b1	b1	NOUN
ejpam-5016	374	27	:	:	PUNCT
ejpam-5016	374	28	every	every	DET
ejpam-5016	374	29	cell	cell	NOUN
ejpam-5016	374	30	is	be	AUX
ejpam-5016	374	31	contained	contain	VERB
ejpam-5016	374	32	in	in	ADP
ejpam-5016	374	33	the	the	DET
ejpam-5016	374	34	polyomino	polyomino	NOUN
ejpam-5016	374	35	:	:	PUNCT
ejpam-5016	374	36	some	some	DET
ejpam-5016	374	37	cells	cell	NOUN
ejpam-5016	374	38	are	be	AUX
ejpam-5016	374	39	not	not	PART
ejpam-5016	374	40	in	in	ADP
ejpam-5016	374	41	the	the	DET
ejpam-5016	374	42	polyomino	polyomino	NOUN
ejpam-5016	374	43	figure	figure	NOUN
ejpam-5016	374	44	27	27	NUM
ejpam-5016	374	45	:	:	PUNCT
ejpam-5016	374	46	binomials	binomial	NOUN
ejpam-5016	374	47	in	in	ADP
ejpam-5016	374	48	theorem	theorem	NOUN
ejpam-5016	374	49	3	3	NUM
ejpam-5016	374	50	.	.	X
ejpam-5016	374	51	note	note	VERB
ejpam-5016	374	52	that	that	SCONJ
ejpam-5016	374	53	there	there	PRON
ejpam-5016	374	54	are	be	VERB
ejpam-5016	374	55	no	no	DET
ejpam-5016	374	56	elements	element	NOUN
ejpam-5016	374	57	in	in	ADP
ejpam-5016	374	58	s2∪s3	s2∪s3	NOUN
ejpam-5016	374	59	whose	whose	DET
ejpam-5016	374	60	initial	initial	ADJ
ejpam-5016	374	61	monomial	monomial	NOUN
ejpam-5016	374	62	divides	divide	VERB
ejpam-5016	374	63	the	the	DET
ejpam-5016	374	64	binomials	binomial	NOUN
ejpam-5016	374	65	s(f	s(f	PROPN
ejpam-5016	374	66	,	,	PUNCT
ejpam-5016	374	67	g	g	NOUN
ejpam-5016	374	68	)	)	PUNCT
ejpam-5016	374	69	discussed	discuss	VERB
ejpam-5016	374	70	in	in	ADP
ejpam-5016	374	71	theorem	theorem	ADJ
ejpam-5016	374	72	2	2	NUM
ejpam-5016	374	73	and	and	CCONJ
ejpam-5016	374	74	3	3	NUM
ejpam-5016	374	75	.	.	X
ejpam-5016	375	1	we	we	PRON
ejpam-5016	375	2	conclude	conclude	VERB
ejpam-5016	375	3	that	that	SCONJ
ejpam-5016	375	4	all	all	DET
ejpam-5016	375	5	binomials	binomial	NOUN
ejpam-5016	375	6	of	of	ADP
ejpam-5016	375	7	degree	degree	NOUN
ejpam-5016	375	8	four	four	NUM
ejpam-5016	375	9	from	from	ADP
ejpam-5016	375	10	the	the	DET
ejpam-5016	375	11	buchberger	buchberger	NOUN
ejpam-5016	375	12	algorithm	algorithm	NOUN
ejpam-5016	375	13	is	be	AUX
ejpam-5016	375	14	of	of	ADP
ejpam-5016	375	15	the	the	DET
ejpam-5016	375	16	form	form	NOUN
ejpam-5016	375	17	a1a2a3a4	a1a2a3a4	PROPN
ejpam-5016	375	18	−	−	NOUN
ejpam-5016	375	19	b1b2b3b4	b1b2b3b4	NOUN
ejpam-5016	375	20	with	with	ADP
ejpam-5016	375	21	a1	a1	NOUN
ejpam-5016	375	22	<	<	PROPN
ejpam-5016	375	23	p	p	X
ejpam-5016	375	24	a2	a2	PROPN
ejpam-5016	375	25	<	<	PROPN
ejpam-5016	375	26	p	p	PROPN
ejpam-5016	375	27	a3	a3	NOUN
ejpam-5016	375	28	<	<	X
ejpam-5016	375	29	p	p	X
ejpam-5016	375	30	a4	a4	PROPN
ejpam-5016	375	31	,	,	PUNCT
ejpam-5016	375	32	b1	b1	NOUN
ejpam-5016	375	33	<	<	NOUN
ejpam-5016	375	34	p	p	NOUN
ejpam-5016	375	35	b2	b2	NOUN
ejpam-5016	375	36	<	<	X
ejpam-5016	375	37	p	p	X
ejpam-5016	375	38	b3	b3	PROPN
ejpam-5016	375	39	<	<	X
ejpam-5016	375	40	p	p	X
ejpam-5016	375	41	b4	b4	NOUN
ejpam-5016	375	42	,	,	PUNCT
ejpam-5016	375	43	and	and	CCONJ
ejpam-5016	375	44	initial	initial	ADJ
ejpam-5016	375	45	monomial	monomial	ADJ
ejpam-5016	375	46	a1a2a3a4	a1a2a3a4	PROPN
ejpam-5016	375	47	,	,	PUNCT
ejpam-5016	375	48	and	and	CCONJ
ejpam-5016	375	49	can	can	AUX
ejpam-5016	375	50	be	be	AUX
ejpam-5016	375	51	illustrated	illustrate	VERB
ejpam-5016	375	52	in	in	ADP
ejpam-5016	375	53	the	the	DET
ejpam-5016	375	54	following	follow	VERB
ejpam-5016	375	55	figure	figure	NOUN
ejpam-5016	375	56	.	.	PUNCT
ejpam-5016	376	1	y.	y.	PROPN
ejpam-5016	376	2	y.	y.	PROPN
ejpam-5016	376	3	hamonangan	hamonangan	PROPN
ejpam-5016	376	4	,	,	PUNCT
ejpam-5016	376	5	i.	i.	PROPN
ejpam-5016	376	6	muchtadi	muchtadi	PROPN
ejpam-5016	376	7	-	-	PUNCT
ejpam-5016	376	8	alamsyah	alamsyah	NOUN
ejpam-5016	376	9	/	/	SYM
ejpam-5016	376	10	eur	eur	PROPN
ejpam-5016	376	11	.	.	PUNCT
ejpam-5016	377	1	j.	j.	PROPN
ejpam-5016	377	2	pure	pure	PROPN
ejpam-5016	377	3	appl	appl	PROPN
ejpam-5016	377	4	.	.	PROPN
ejpam-5016	377	5	math	math	PROPN
ejpam-5016	377	6	,	,	PUNCT
ejpam-5016	377	7	17	17	NUM
ejpam-5016	377	8	(	(	PUNCT
ejpam-5016	377	9	4	4	NUM
ejpam-5016	377	10	)	)	PUNCT
ejpam-5016	377	11	(	(	PUNCT
ejpam-5016	377	12	2024	2024	NUM
ejpam-5016	377	13	)	)	PUNCT
ejpam-5016	377	14	,	,	PUNCT
ejpam-5016	377	15	2621	2621	NUM
ejpam-5016	377	16	-	-	SYM
ejpam-5016	377	17	2650	2650	NUM
ejpam-5016	377	18	2640	2640	NUM
ejpam-5016	377	19	b2	b2	NOUN
ejpam-5016	377	20	a1	a1	NOUN
ejpam-5016	377	21	b4a4	b4a4	NOUN
ejpam-5016	377	22	b1	b1	PROPN
ejpam-5016	377	23	a2	a2	PROPN
ejpam-5016	377	24	b3	b3	PROPN
ejpam-5016	377	25	a3	a3	PROPN
ejpam-5016	377	26	b2	b2	PROPN
ejpam-5016	377	27	a2	a2	PROPN
ejpam-5016	377	28	b3	b3	PROPN
ejpam-5016	377	29	b1	b1	PROPN
ejpam-5016	377	30	a3	a3	PROPN
ejpam-5016	377	31	a4b4	a4b4	X
ejpam-5016	377	32	a1	a1	NOUN
ejpam-5016	377	33	:	:	PUNCT
ejpam-5016	377	34	every	every	DET
ejpam-5016	377	35	cell	cell	NOUN
ejpam-5016	377	36	is	be	AUX
ejpam-5016	377	37	contained	contain	VERB
ejpam-5016	377	38	in	in	ADP
ejpam-5016	377	39	the	the	DET
ejpam-5016	377	40	polyomino	polyomino	NOUN
ejpam-5016	377	41	:	:	PUNCT
ejpam-5016	377	42	some	some	DET
ejpam-5016	377	43	cells	cell	NOUN
ejpam-5016	377	44	are	be	AUX
ejpam-5016	377	45	not	not	PART
ejpam-5016	377	46	in	in	ADP
ejpam-5016	377	47	the	the	DET
ejpam-5016	377	48	polyomino	polyomino	NOUN
ejpam-5016	377	49	figure	figure	NOUN
ejpam-5016	377	50	28	28	NUM
ejpam-5016	377	51	:	:	PUNCT
ejpam-5016	377	52	binomials	binomial	NOUN
ejpam-5016	377	53	in	in	ADP
ejpam-5016	377	54	theorem	theorem	ADJ
ejpam-5016	377	55	2	2	NUM
ejpam-5016	377	56	and	and	CCONJ
ejpam-5016	377	57	theorem	theorem	VERB
ejpam-5016	377	58	3	3	NUM
ejpam-5016	377	59	.	.	NOUN
ejpam-5016	377	60	4	4	NUM
ejpam-5016	377	61	.	.	PUNCT
ejpam-5016	378	1	the	the	DET
ejpam-5016	378	2	socket	socket	NOUN
ejpam-5016	378	3	wrench	wrench	NOUN
ejpam-5016	378	4	polyominoes	polyominoe	NOUN
ejpam-5016	378	5	consider	consider	VERB
ejpam-5016	378	6	the	the	DET
ejpam-5016	378	7	following	follow	VERB
ejpam-5016	378	8	polyomino	polyomino	NOUN
ejpam-5016	378	9	constructed	construct	VERB
ejpam-5016	378	10	from	from	ADP
ejpam-5016	378	11	8	8	NUM
ejpam-5016	378	12	unit	unit	NOUN
ejpam-5016	378	13	squares	square	NOUN
ejpam-5016	378	14	forming	form	VERB
ejpam-5016	378	15	a	a	DET
ejpam-5016	378	16	3	3	NUM
ejpam-5016	378	17	×	×	NOUN
ejpam-5016	378	18	3	3	NUM
ejpam-5016	378	19	square	square	NOUN
ejpam-5016	378	20	without	without	ADP
ejpam-5016	378	21	the	the	DET
ejpam-5016	378	22	unit	unit	NOUN
ejpam-5016	378	23	square	square	NOUN
ejpam-5016	378	24	in	in	ADP
ejpam-5016	378	25	the	the	DET
ejpam-5016	378	26	center	center	NOUN
ejpam-5016	378	27	and	and	CCONJ
ejpam-5016	378	28	continued	continue	VERB
ejpam-5016	378	29	by	by	ADP
ejpam-5016	378	30	adding	add	VERB
ejpam-5016	378	31	n	n	PRON
ejpam-5016	378	32	unit	unit	NOUN
ejpam-5016	378	33	squares	square	NOUN
ejpam-5016	378	34	to	to	ADP
ejpam-5016	378	35	the	the	DET
ejpam-5016	378	36	left	left	NOUN
ejpam-5016	378	37	of	of	ADP
ejpam-5016	378	38	the	the	DET
ejpam-5016	378	39	unit	unit	NOUN
ejpam-5016	378	40	square	square	NOUN
ejpam-5016	378	41	on	on	ADP
ejpam-5016	378	42	the	the	DET
ejpam-5016	378	43	leftmost	leftmost	ADJ
ejpam-5016	378	44	cell	cell	NOUN
ejpam-5016	378	45	on	on	ADP
ejpam-5016	378	46	the	the	DET
ejpam-5016	378	47	middle	middle	PROPN
ejpam-5016	378	48	row	row	NOUN
ejpam-5016	378	49	.	.	PUNCT
ejpam-5016	379	1	we	we	PRON
ejpam-5016	379	2	call	call	VERB
ejpam-5016	379	3	this	this	DET
ejpam-5016	379	4	polyomino	polyomino	NOUN
ejpam-5016	379	5	a	a	DET
ejpam-5016	379	6	socket	socket	NOUN
ejpam-5016	379	7	wrench	wrench	NOUN
ejpam-5016	379	8	polyomino	polyomino	NOUN
ejpam-5016	379	9	,	,	PUNCT
ejpam-5016	379	10	because	because	SCONJ
ejpam-5016	379	11	it	it	PRON
ejpam-5016	379	12	looks	look	VERB
ejpam-5016	379	13	like	like	SCONJ
ejpam-5016	379	14	the	the	DET
ejpam-5016	379	15	socket	socket	NOUN
ejpam-5016	379	16	wrenches	wrench	NOUN
ejpam-5016	379	17	used	use	VERB
ejpam-5016	379	18	by	by	ADP
ejpam-5016	379	19	mechanics	mechanic	NOUN
ejpam-5016	379	20	to	to	PART
ejpam-5016	379	21	tighten	tighten	VERB
ejpam-5016	379	22	or	or	CCONJ
ejpam-5016	379	23	loosen	loosen	VERB
ejpam-5016	379	24	nuts	nut	NOUN
ejpam-5016	379	25	and	and	CCONJ
ejpam-5016	379	26	bolts	bolt	NOUN
ejpam-5016	379	27	.	.	PUNCT
ejpam-5016	380	1	we	we	PRON
ejpam-5016	380	2	use	use	VERB
ejpam-5016	380	3	for	for	ADP
ejpam-5016	380	4	this	this	DET
ejpam-5016	380	5	polyomino	polyomino	NOUN
ejpam-5016	380	6	the	the	DET
ejpam-5016	380	7	same	same	ADJ
ejpam-5016	380	8	labelling	labelling	NOUN
ejpam-5016	380	9	with	with	ADP
ejpam-5016	380	10	reference	reference	NOUN
ejpam-5016	380	11	to	to	ADP
ejpam-5016	380	12	section	section	NOUN
ejpam-5016	380	13	3	3	NUM
ejpam-5016	380	14	.	.	NOUN
ejpam-5016	380	15	1	1	NUM
ejpam-5016	380	16	2	2	NUM
ejpam-5016	380	17	3	3	NUM
ejpam-5016	380	18	4	4	NUM
ejpam-5016	380	19	5	5	NUM
ejpam-5016	380	20	5	5	NUM
ejpam-5016	380	21	+	+	CCONJ
ejpam-5016	380	22	n	n	NUM
ejpam-5016	380	23	6	6	NUM
ejpam-5016	380	24	+	+	CCONJ
ejpam-5016	380	25	n	n	CCONJ
ejpam-5016	380	26	7	7	NUM
ejpam-5016	380	27	+	+	CCONJ
ejpam-5016	380	28	n	n	PRON
ejpam-5016	380	29	8	8	NUM
ejpam-5016	380	30	+	+	CCONJ
ejpam-5016	380	31	n	n	DET
ejpam-5016	380	32	9	9	NUM
ejpam-5016	380	33	+	+	CCONJ
ejpam-5016	380	34	n	n	CCONJ
ejpam-5016	380	35	9	9	NUM
ejpam-5016	380	36	+	+	NUM
ejpam-5016	380	37	2n	2n	NUM
ejpam-5016	380	38	10	10	NUM
ejpam-5016	380	39	+	+	NUM
ejpam-5016	380	40	2n	2n	NUM
ejpam-5016	380	41	11	11	NUM
ejpam-5016	380	42	+	+	NUM
ejpam-5016	380	43	2n	2n	NUM
ejpam-5016	380	44	12	12	NUM
ejpam-5016	380	45	+	+	NUM
ejpam-5016	380	46	2n	2n	NUM
ejpam-5016	380	47	13	13	NUM
ejpam-5016	381	1	+	+	NUM
ejpam-5016	381	2	2n	2n	NUM
ejpam-5016	381	3	14	14	NUM
ejpam-5016	382	1	+	+	NUM
ejpam-5016	382	2	2n	2n	NUM
ejpam-5016	382	3	15	15	NUM
ejpam-5016	382	4	+	+	NUM
ejpam-5016	382	5	2n	2n	NUM
ejpam-5016	383	1	16	16	NUM
ejpam-5016	383	2	+	+	NUM
ejpam-5016	383	3	2n	2n	NUM
ejpam-5016	383	4	figure	figure	NOUN
ejpam-5016	383	5	29	29	NUM
ejpam-5016	383	6	:	:	PUNCT
ejpam-5016	383	7	a	a	DET
ejpam-5016	383	8	socket	socket	NOUN
ejpam-5016	383	9	wrench	wrench	NOUN
ejpam-5016	383	10	polyomino	polyomino	NOUN
ejpam-5016	383	11	with	with	ADP
ejpam-5016	383	12	n	n	CCONJ
ejpam-5016	383	13	additional	additional	ADJ
ejpam-5016	383	14	unit	unit	NOUN
ejpam-5016	383	15	squares	square	NOUN
ejpam-5016	383	16	.	.	PUNCT
ejpam-5016	384	1	theorem	theorem	ADJ
ejpam-5016	384	2	4	4	NUM
ejpam-5016	384	3	.	.	PUNCT
ejpam-5016	385	1	let	let	VERB
ejpam-5016	385	2	p	p	PRON
ejpam-5016	385	3	be	be	AUX
ejpam-5016	385	4	a	a	DET
ejpam-5016	385	5	socket	socket	NOUN
ejpam-5016	385	6	wrench	wrench	NOUN
ejpam-5016	385	7	polyomino	polyomino	NOUN
ejpam-5016	385	8	then	then	ADV
ejpam-5016	385	9	the	the	DET
ejpam-5016	385	10	polyomino	polyomino	PROPN
ejpam-5016	385	11	ideal	ideal	NOUN
ejpam-5016	385	12	ip	ip	VERB
ejpam-5016	385	13	is	be	AUX
ejpam-5016	385	14	a	a	DET
ejpam-5016	385	15	radical	radical	ADJ
ejpam-5016	385	16	.	.	PUNCT
ejpam-5016	386	1	proof	proof	NOUN
ejpam-5016	386	2	.	.	PUNCT
ejpam-5016	387	1	we	we	PRON
ejpam-5016	387	2	claim	claim	VERB
ejpam-5016	387	3	that	that	SCONJ
ejpam-5016	387	4	according	accord	VERB
ejpam-5016	387	5	to	to	ADP
ejpam-5016	387	6	this	this	DET
ejpam-5016	387	7	labelling	labelling	NOUN
ejpam-5016	387	8	and	and	CCONJ
ejpam-5016	387	9	lexicographic	lexicographic	ADJ
ejpam-5016	387	10	order	order	NOUN
ejpam-5016	387	11	,	,	PUNCT
ejpam-5016	387	12	the	the	DET
ejpam-5016	387	13	ideal	ideal	ADJ
ejpam-5016	387	14	ip	ip	NOUN
ejpam-5016	387	15	has	have	VERB
ejpam-5016	387	16	s2	s2	PROPN
ejpam-5016	387	17	∪	∪	NOUN
ejpam-5016	387	18	s3	s3	PROPN
ejpam-5016	387	19	as	as	ADP
ejpam-5016	387	20	the	the	DET
ejpam-5016	387	21	gröbner	gröbner	NOUN
ejpam-5016	387	22	bases	basis	NOUN
ejpam-5016	387	23	.	.	PUNCT
ejpam-5016	388	1	since	since	SCONJ
ejpam-5016	388	2	the	the	DET
ejpam-5016	388	3	initial	initial	ADJ
ejpam-5016	388	4	monomial	monomial	NOUN
ejpam-5016	388	5	of	of	ADP
ejpam-5016	388	6	every	every	DET
ejpam-5016	388	7	element	element	NOUN
ejpam-5016	388	8	in	in	ADP
ejpam-5016	388	9	s2	s2	PROPN
ejpam-5016	388	10	∪	∪	ADP
ejpam-5016	388	11	s3	s3	PROPN
ejpam-5016	388	12	y.	y.	PROPN
ejpam-5016	388	13	y.	y.	PROPN
ejpam-5016	388	14	hamonangan	hamonangan	PROPN
ejpam-5016	388	15	,	,	PUNCT
ejpam-5016	388	16	i.	i.	PROPN
ejpam-5016	388	17	muchtadi	muchtadi	PROPN
ejpam-5016	388	18	-	-	PUNCT
ejpam-5016	388	19	alamsyah	alamsyah	NOUN
ejpam-5016	388	20	/	/	SYM
ejpam-5016	388	21	eur	eur	PROPN
ejpam-5016	388	22	.	.	PUNCT
ejpam-5016	389	1	j.	j.	PROPN
ejpam-5016	389	2	pure	pure	PROPN
ejpam-5016	389	3	appl	appl	PROPN
ejpam-5016	389	4	.	.	PROPN
ejpam-5016	389	5	math	math	PROPN
ejpam-5016	389	6	,	,	PUNCT
ejpam-5016	389	7	17	17	NUM
ejpam-5016	389	8	(	(	PUNCT
ejpam-5016	389	9	4	4	NUM
ejpam-5016	389	10	)	)	PUNCT
ejpam-5016	389	11	(	(	PUNCT
ejpam-5016	389	12	2024	2024	NUM
ejpam-5016	389	13	)	)	PUNCT
ejpam-5016	389	14	,	,	PUNCT
ejpam-5016	389	15	2621	2621	NUM
ejpam-5016	389	16	-	-	SYM
ejpam-5016	389	17	2650	2650	NUM
ejpam-5016	389	18	2641	2641	NUM
ejpam-5016	389	19	is	be	AUX
ejpam-5016	389	20	square	square	ADV
ejpam-5016	389	21	-	-	PUNCT
ejpam-5016	389	22	free	free	ADJ
ejpam-5016	389	23	then	then	ADV
ejpam-5016	389	24	we	we	PRON
ejpam-5016	389	25	have	have	VERB
ejpam-5016	389	26	the	the	DET
ejpam-5016	389	27	result	result	NOUN
ejpam-5016	389	28	.	.	PUNCT
ejpam-5016	390	1	by	by	ADP
ejpam-5016	390	2	theorem	theorem	NOUN
ejpam-5016	390	3	1	1	NUM
ejpam-5016	390	4	,	,	PUNCT
ejpam-5016	390	5	every	every	DET
ejpam-5016	390	6	element	element	NOUN
ejpam-5016	390	7	of	of	ADP
ejpam-5016	390	8	s3	s3	PROPN
ejpam-5016	390	9	is	be	AUX
ejpam-5016	390	10	one	one	NUM
ejpam-5016	390	11	of	of	ADP
ejpam-5016	390	12	the	the	DET
ejpam-5016	390	13	following	follow	VERB
ejpam-5016	390	14	forms	form	NOUN
ejpam-5016	390	15	:	:	PUNCT
ejpam-5016	390	16	•	•	NUM
ejpam-5016	390	17	xix11	xix11	PROPN
ejpam-5016	390	18	+	+	NOUN
ejpam-5016	390	19	2nx14	2nx14	ADJ
ejpam-5016	390	20	+	+	NOUN
ejpam-5016	390	21	2n	2n	NOUN
ejpam-5016	390	22	−	−	ADP
ejpam-5016	390	23	xi+4+nx15	xi+4+nx15	PROPN
ejpam-5016	390	24	+	+	PROPN
ejpam-5016	390	25	2nx6+n	2nx6+n	NUM
ejpam-5016	390	26	,	,	PUNCT
ejpam-5016	390	27	5	5	NUM
ejpam-5016	390	28	≤	≤	NUM
ejpam-5016	390	29	i	i	PRON
ejpam-5016	390	30	≤	≤	NOUN
ejpam-5016	390	31	4	4	NUM
ejpam-5016	390	32	+	+	SYM
ejpam-5016	390	33	n	n	NUM
ejpam-5016	390	34	•	•	ADV
ejpam-5016	390	35	xix12	xix12	PROPN
ejpam-5016	390	36	+	+	PROPN
ejpam-5016	390	37	2nx14	2nx14	ADJ
ejpam-5016	390	38	+	+	NOUN
ejpam-5016	390	39	2n	2n	NOUN
ejpam-5016	390	40	−	−	ADP
ejpam-5016	390	41	xi+4+nx16	xi+4+nx16	PROPN
ejpam-5016	390	42	+	+	PROPN
ejpam-5016	390	43	2nx6+n	2nx6+n	NUM
ejpam-5016	390	44	,	,	PUNCT
ejpam-5016	390	45	5	5	NUM
ejpam-5016	390	46	≤	≤	NUM
ejpam-5016	390	47	i	i	PRON
ejpam-5016	390	48	≤	≤	NOUN
ejpam-5016	390	49	4	4	NUM
ejpam-5016	390	50	+	+	SYM
ejpam-5016	390	51	n	n	NUM
ejpam-5016	390	52	•	•	NOUN
ejpam-5016	390	53	xix11	xix11	PROPN
ejpam-5016	390	54	+	+	PROPN
ejpam-5016	390	55	2nx13	2nx13	PROPN
ejpam-5016	390	56	+	+	ADJ
ejpam-5016	390	57	2n	2n	NUM
ejpam-5016	390	58	−	−	ADP
ejpam-5016	390	59	xi+4+nx15	xi+4+nx15	PROPN
ejpam-5016	390	60	+	+	NOUN
ejpam-5016	390	61	2nx5+n	2nx5+n	NUM
ejpam-5016	390	62	,	,	PUNCT
ejpam-5016	390	63	5	5	NUM
ejpam-5016	390	64	≤	≤	NUM
ejpam-5016	390	65	i	i	PRON
ejpam-5016	390	66	≤	≤	NOUN
ejpam-5016	390	67	4	4	NUM
ejpam-5016	390	68	+	+	SYM
ejpam-5016	390	69	n	n	NUM
ejpam-5016	390	70	•	•	ADV
ejpam-5016	390	71	xix12	xix12	PROPN
ejpam-5016	390	72	+	+	PROPN
ejpam-5016	390	73	2nx13	2nx13	NOUN
ejpam-5016	390	74	+	+	ADJ
ejpam-5016	390	75	2n	2n	NUM
ejpam-5016	390	76	−	−	ADP
ejpam-5016	390	77	xi+4+nx16	xi+4+nx16	PROPN
ejpam-5016	390	78	+	+	NOUN
ejpam-5016	390	79	2nx5+n	2nx5+n	NUM
ejpam-5016	390	80	,	,	PUNCT
ejpam-5016	390	81	5	5	NUM
ejpam-5016	390	82	≤	≤	NUM
ejpam-5016	390	83	i	i	PRON
ejpam-5016	390	84	≤	≤	NOUN
ejpam-5016	390	85	4	4	NUM
ejpam-5016	390	86	+	+	CCONJ
ejpam-5016	390	87	n	n	PART
ejpam-5016	390	88	to	to	PART
ejpam-5016	390	89	complete	complete	VERB
ejpam-5016	390	90	our	our	PRON
ejpam-5016	390	91	claim	claim	NOUN
ejpam-5016	390	92	,	,	PUNCT
ejpam-5016	390	93	we	we	PRON
ejpam-5016	390	94	observe	observe	VERB
ejpam-5016	390	95	the	the	DET
ejpam-5016	390	96	following	following	NOUN
ejpam-5016	390	97	.	.	PUNCT
ejpam-5016	391	1	(	(	PUNCT
ejpam-5016	391	2	i	i	NOUN
ejpam-5016	391	3	)	)	PUNCT
ejpam-5016	391	4	s(f	s(f	PROPN
ejpam-5016	391	5	,	,	PUNCT
ejpam-5016	391	6	g	g	NOUN
ejpam-5016	391	7	)	)	PUNCT
ejpam-5016	391	8	with	with	ADP
ejpam-5016	391	9	f	f	PROPN
ejpam-5016	391	10	,	,	PUNCT
ejpam-5016	391	11	g	g	PROPN
ejpam-5016	391	12	∈	∈	PROPN
ejpam-5016	391	13	s2	s2	NOUN
ejpam-5016	391	14	is	be	AUX
ejpam-5016	391	15	either	either	CCONJ
ejpam-5016	391	16	reduced	reduce	VERB
ejpam-5016	391	17	to	to	ADP
ejpam-5016	391	18	zero	zero	NUM
ejpam-5016	391	19	or	or	CCONJ
ejpam-5016	391	20	contained	contain	VERB
ejpam-5016	391	21	in	in	ADP
ejpam-5016	391	22	s3	s3	PROPN
ejpam-5016	391	23	.	.	PUNCT
ejpam-5016	392	1	(	(	PUNCT
ejpam-5016	392	2	ii	ii	NOUN
ejpam-5016	392	3	)	)	PUNCT
ejpam-5016	392	4	suppose	suppose	VERB
ejpam-5016	392	5	there	there	PRON
ejpam-5016	392	6	are	be	VERB
ejpam-5016	392	7	f	f	PROPN
ejpam-5016	392	8	∈	∈	PROPN
ejpam-5016	392	9	s3	s3	PROPN
ejpam-5016	392	10	and	and	CCONJ
ejpam-5016	392	11	g	g	PROPN
ejpam-5016	392	12	∈	∈	PROPN
ejpam-5016	392	13	s2	s2	NOUN
ejpam-5016	392	14	such	such	ADJ
ejpam-5016	392	15	that	that	SCONJ
ejpam-5016	392	16	s(f	s(f	PROPN
ejpam-5016	392	17	,	,	PUNCT
ejpam-5016	392	18	g	g	NOUN
ejpam-5016	392	19	)	)	PUNCT
ejpam-5016	392	20	is	be	AUX
ejpam-5016	392	21	not	not	PART
ejpam-5016	392	22	reduced	reduce	VERB
ejpam-5016	392	23	to	to	ADP
ejpam-5016	392	24	zero	zero	NUM
ejpam-5016	392	25	.	.	PUNCT
ejpam-5016	393	1	write	write	VERB
ejpam-5016	393	2	f	f	PROPN
ejpam-5016	393	3	=	=	PUNCT
ejpam-5016	393	4	a1a3a5	a1a3a5	PROPN
ejpam-5016	393	5	−	−	PROPN
ejpam-5016	393	6	a2a4a6	a2a4a6	NOUN
ejpam-5016	393	7	as	as	ADP
ejpam-5016	393	8	in	in	ADP
ejpam-5016	393	9	definition	definition	NOUN
ejpam-5016	393	10	1	1	NUM
ejpam-5016	393	11	and	and	CCONJ
ejpam-5016	393	12	g	g	PROPN
ejpam-5016	393	13	=	=	PROPN
ejpam-5016	393	14	pq	pq	PROPN
ejpam-5016	393	15	−	−	NOUN
ejpam-5016	393	16	rs	rs	NOUN
ejpam-5016	393	17	.	.	PUNCT
ejpam-5016	394	1	here	here	ADV
ejpam-5016	394	2	,	,	PUNCT
ejpam-5016	394	3	a1	a1	VERB
ejpam-5016	394	4	<	<	PROPN
ejpam-5016	394	5	p	p	PROPN
ejpam-5016	394	6	a3	a3	NOUN
ejpam-5016	394	7	<	<	X
ejpam-5016	394	8	p	p	X
ejpam-5016	394	9	a5	a5	PROPN
ejpam-5016	394	10	,	,	PUNCT
ejpam-5016	394	11	a6	a6	NOUN
ejpam-5016	394	12	<	<	X
ejpam-5016	394	13	p	p	X
ejpam-5016	394	14	a2	a2	PROPN
ejpam-5016	394	15	<	<	X
ejpam-5016	394	16	p	p	X
ejpam-5016	394	17	a4	a4	PROPN
ejpam-5016	394	18	,	,	PUNCT
ejpam-5016	394	19	p	p	X
ejpam-5016	394	20	<	<	X
ejpam-5016	394	21	p	p	X
ejpam-5016	394	22	q	q	NOUN
ejpam-5016	394	23	,	,	PUNCT
ejpam-5016	394	24	and	and	CCONJ
ejpam-5016	394	25	r	r	NOUN
ejpam-5016	394	26	<	<	X
ejpam-5016	394	27	p	p	X
ejpam-5016	394	28	s.	s.	PROPN
ejpam-5016	394	29	from	from	ADP
ejpam-5016	394	30	the	the	DET
ejpam-5016	394	31	structure	structure	NOUN
ejpam-5016	394	32	of	of	ADP
ejpam-5016	394	33	elements	element	NOUN
ejpam-5016	394	34	in	in	ADP
ejpam-5016	394	35	s3	s3	PROPN
ejpam-5016	394	36	,	,	PUNCT
ejpam-5016	394	37	we	we	PRON
ejpam-5016	394	38	have	have	VERB
ejpam-5016	394	39	a1	a1	NOUN
ejpam-5016	394	40	∈	∈	PROPN
ejpam-5016	395	1	[	[	X
ejpam-5016	395	2	5	5	NUM
ejpam-5016	395	3	,	,	PUNCT
ejpam-5016	395	4	4	4	NUM
ejpam-5016	395	5	+	+	NUM
ejpam-5016	395	6	n	n	CCONJ
ejpam-5016	395	7	]	]	PUNCT
ejpam-5016	395	8	,	,	PUNCT
ejpam-5016	395	9	a3	a3	PROPN
ejpam-5016	395	10	∈	∈	PROPN
ejpam-5016	395	11	{	{	PUNCT
ejpam-5016	395	12	11	11	NUM
ejpam-5016	395	13	+	+	CCONJ
ejpam-5016	395	14	2n	2n	NUM
ejpam-5016	395	15	,	,	PUNCT
ejpam-5016	395	16	12	12	NUM
ejpam-5016	395	17	+	+	NUM
ejpam-5016	395	18	2n	2n	NUM
ejpam-5016	395	19	}	}	PUNCT
ejpam-5016	395	20	,	,	PUNCT
ejpam-5016	395	21	and	and	CCONJ
ejpam-5016	395	22	a5	a5	PROPN
ejpam-5016	395	23	∈	∈	PROPN
ejpam-5016	395	24	{	{	PUNCT
ejpam-5016	395	25	13	13	NUM
ejpam-5016	395	26	+	+	NUM
ejpam-5016	395	27	2n	2n	NUM
ejpam-5016	395	28	,	,	PUNCT
ejpam-5016	395	29	14	14	NUM
ejpam-5016	395	30	+	+	SYM
ejpam-5016	395	31	2n	2n	NUM
ejpam-5016	395	32	}	}	PUNCT
ejpam-5016	395	33	.	.	PUNCT
ejpam-5016	396	1	by	by	ADP
ejpam-5016	396	2	theorem	theorem	NOUN
ejpam-5016	396	3	2	2	NUM
ejpam-5016	396	4	,	,	PUNCT
ejpam-5016	396	5	we	we	PRON
ejpam-5016	396	6	have	have	VERB
ejpam-5016	396	7	p	p	NOUN
ejpam-5016	396	8	=	=	NOUN
ejpam-5016	396	9	a3	a3	NOUN
ejpam-5016	396	10	or	or	CCONJ
ejpam-5016	396	11	p	p	NOUN
ejpam-5016	396	12	=	=	PROPN
ejpam-5016	396	13	a5	a5	PROPN
ejpam-5016	396	14	.	.	PUNCT
ejpam-5016	396	15	suppose	suppose	VERB
ejpam-5016	396	16	p	p	PROPN
ejpam-5016	396	17	=	=	PROPN
ejpam-5016	396	18	a5	a5	PROPN
ejpam-5016	396	19	,	,	PUNCT
ejpam-5016	396	20	then	then	ADV
ejpam-5016	396	21	[	[	X
ejpam-5016	396	22	p	p	X
ejpam-5016	396	23	,	,	PUNCT
ejpam-5016	396	24	q	q	X
ejpam-5016	396	25	]	]	X
ejpam-5016	396	26	can	can	AUX
ejpam-5016	396	27	not	not	PART
ejpam-5016	396	28	be	be	AUX
ejpam-5016	396	29	an	an	DET
ejpam-5016	396	30	inner	inner	ADJ
ejpam-5016	396	31	interval	interval	NOUN
ejpam-5016	396	32	.	.	PUNCT
ejpam-5016	397	1	therefore	therefore	ADV
ejpam-5016	397	2	p	p	PROPN
ejpam-5016	397	3	=	=	PROPN
ejpam-5016	397	4	a3	a3	NOUN
ejpam-5016	397	5	.	.	PUNCT
ejpam-5016	398	1	since	since	SCONJ
ejpam-5016	398	2	[	[	X
ejpam-5016	398	3	p	p	X
ejpam-5016	398	4	,	,	PUNCT
ejpam-5016	398	5	q	q	X
ejpam-5016	398	6	]	]	X
ejpam-5016	398	7	is	be	AUX
ejpam-5016	398	8	an	an	DET
ejpam-5016	398	9	inner	inner	ADJ
ejpam-5016	398	10	interval	interval	NOUN
ejpam-5016	398	11	,	,	PUNCT
ejpam-5016	398	12	then	then	ADV
ejpam-5016	398	13	p	p	NOUN
ejpam-5016	398	14	=	=	NOUN
ejpam-5016	398	15	a3	a3	NOUN
ejpam-5016	398	16	=	=	SYM
ejpam-5016	398	17	11	11	NUM
ejpam-5016	398	18	+	+	NUM
ejpam-5016	398	19	2n	2n	NUM
ejpam-5016	398	20	and	and	CCONJ
ejpam-5016	398	21	q	q	NOUN
ejpam-5016	399	1	=	=	SYM
ejpam-5016	399	2	16	16	NUM
ejpam-5016	399	3	+	+	NUM
ejpam-5016	399	4	2n	2n	NUM
ejpam-5016	399	5	.	.	PUNCT
ejpam-5016	400	1	but	but	CCONJ
ejpam-5016	400	2	then	then	ADV
ejpam-5016	400	3	s	s	PART
ejpam-5016	400	4	=	=	SYM
ejpam-5016	400	5	a4	a4	PROPN
ejpam-5016	400	6	=	=	SYM
ejpam-5016	400	7	15	15	NUM
ejpam-5016	400	8	+	+	NUM
ejpam-5016	400	9	2n	2n	NUM
ejpam-5016	400	10	,	,	PUNCT
ejpam-5016	400	11	contradiction	contradiction	NOUN
ejpam-5016	400	12	with	with	ADP
ejpam-5016	400	13	a4	a4	NOUN
ejpam-5016	400	14	>	>	X
ejpam-5016	400	15	s.	s.	PROPN
ejpam-5016	400	16	(	(	PUNCT
ejpam-5016	400	17	iii	iii	NOUN
ejpam-5016	400	18	)	)	PUNCT
ejpam-5016	400	19	suppose	suppose	VERB
ejpam-5016	400	20	there	there	PRON
ejpam-5016	400	21	are	be	VERB
ejpam-5016	400	22	f	f	X
ejpam-5016	400	23	,	,	PUNCT
ejpam-5016	400	24	g	g	PROPN
ejpam-5016	400	25	∈	∈	PROPN
ejpam-5016	400	26	s3	s3	PROPN
ejpam-5016	400	27	such	such	ADJ
ejpam-5016	400	28	that	that	SCONJ
ejpam-5016	400	29	s(f	s(f	PROPN
ejpam-5016	400	30	,	,	PUNCT
ejpam-5016	400	31	g	g	NOUN
ejpam-5016	400	32	)	)	PUNCT
ejpam-5016	400	33	is	be	AUX
ejpam-5016	400	34	not	not	PART
ejpam-5016	400	35	reduced	reduce	VERB
ejpam-5016	400	36	to	to	ADP
ejpam-5016	400	37	zero	zero	NUM
ejpam-5016	400	38	.	.	PUNCT
ejpam-5016	401	1	by	by	ADP
ejpam-5016	401	2	the	the	DET
ejpam-5016	401	3	definition	definition	NOUN
ejpam-5016	401	4	of	of	ADP
ejpam-5016	401	5	s3	s3	PROPN
ejpam-5016	401	6	,	,	PUNCT
ejpam-5016	401	7	since	since	SCONJ
ejpam-5016	401	8	the	the	DET
ejpam-5016	401	9	non	non	ADJ
ejpam-5016	401	10	-	-	ADJ
ejpam-5016	401	11	initial	initial	ADJ
ejpam-5016	401	12	monomial	monomial	NOUN
ejpam-5016	401	13	of	of	ADP
ejpam-5016	401	14	a	a	DET
ejpam-5016	401	15	binomial	binomial	NOUN
ejpam-5016	401	16	in	in	ADP
ejpam-5016	401	17	s3	s3	PROPN
ejpam-5016	401	18	is	be	AUX
ejpam-5016	401	19	completely	completely	ADV
ejpam-5016	401	20	determined	determine	VERB
ejpam-5016	401	21	by	by	ADP
ejpam-5016	401	22	its	its	PRON
ejpam-5016	401	23	initial	initial	ADJ
ejpam-5016	401	24	monomial	monomial	NOUN
ejpam-5016	401	25	then	then	ADV
ejpam-5016	401	26	we	we	PRON
ejpam-5016	401	27	can	can	AUX
ejpam-5016	401	28	eliminate	eliminate	VERB
ejpam-5016	401	29	the	the	DET
ejpam-5016	401	30	cases	case	NOUN
ejpam-5016	401	31	when	when	SCONJ
ejpam-5016	401	32	the	the	DET
ejpam-5016	401	33	initial	initial	ADJ
ejpam-5016	401	34	monomials	monomial	NOUN
ejpam-5016	401	35	of	of	ADP
ejpam-5016	401	36	f	f	PROPN
ejpam-5016	401	37	,	,	PUNCT
ejpam-5016	401	38	g	g	PROPN
ejpam-5016	401	39	are	be	AUX
ejpam-5016	401	40	relatively	relatively	ADV
ejpam-5016	401	41	prime	prime	ADJ
ejpam-5016	401	42	or	or	CCONJ
ejpam-5016	401	43	equal	equal	ADJ
ejpam-5016	401	44	.	.	PUNCT
ejpam-5016	402	1	(	(	PUNCT
ejpam-5016	402	2	a	a	X
ejpam-5016	402	3	)	)	PUNCT
ejpam-5016	402	4	if	if	SCONJ
ejpam-5016	402	5	the	the	DET
ejpam-5016	402	6	greatest	great	ADJ
ejpam-5016	402	7	common	common	ADJ
ejpam-5016	402	8	divisor	divisor	NOUN
ejpam-5016	402	9	of	of	ADP
ejpam-5016	402	10	their	their	PRON
ejpam-5016	402	11	initial	initial	ADJ
ejpam-5016	402	12	monomial	monomial	NOUN
ejpam-5016	402	13	is	be	AUX
ejpam-5016	402	14	a	a	DET
ejpam-5016	402	15	monomial	monomial	NOUN
ejpam-5016	402	16	of	of	ADP
ejpam-5016	402	17	degree	degree	NOUN
ejpam-5016	402	18	two	two	NUM
ejpam-5016	402	19	,	,	PUNCT
ejpam-5016	402	20	we	we	PRON
ejpam-5016	402	21	will	will	AUX
ejpam-5016	402	22	have	have	VERB
ejpam-5016	402	23	a	a	DET
ejpam-5016	402	24	similar	similar	ADJ
ejpam-5016	402	25	argument	argument	NOUN
ejpam-5016	402	26	as	as	ADP
ejpam-5016	402	27	in	in	ADP
ejpam-5016	402	28	the	the	DET
ejpam-5016	402	29	previous	previous	ADJ
ejpam-5016	402	30	case	case	NOUN
ejpam-5016	402	31	but	but	CCONJ
ejpam-5016	402	32	using	use	VERB
ejpam-5016	402	33	theorem	theorem	NOUN
ejpam-5016	402	34	3	3	NUM
ejpam-5016	402	35	that	that	SCONJ
ejpam-5016	402	36	it	it	PRON
ejpam-5016	402	37	will	will	AUX
ejpam-5016	402	38	come	come	VERB
ejpam-5016	402	39	to	to	ADP
ejpam-5016	402	40	a	a	DET
ejpam-5016	402	41	contradiction	contradiction	NOUN
ejpam-5016	402	42	.	.	PUNCT
ejpam-5016	403	1	(	(	PUNCT
ejpam-5016	403	2	b	b	X
ejpam-5016	403	3	)	)	PUNCT
ejpam-5016	403	4	if	if	SCONJ
ejpam-5016	403	5	the	the	DET
ejpam-5016	403	6	greatest	great	ADJ
ejpam-5016	403	7	common	common	ADJ
ejpam-5016	403	8	divisor	divisor	NOUN
ejpam-5016	403	9	of	of	ADP
ejpam-5016	403	10	their	their	PRON
ejpam-5016	403	11	initial	initial	ADJ
ejpam-5016	403	12	monomial	monomial	NOUN
ejpam-5016	403	13	is	be	AUX
ejpam-5016	403	14	a	a	DET
ejpam-5016	403	15	monomial	monomial	NOUN
ejpam-5016	403	16	of	of	ADP
ejpam-5016	403	17	degree	degree	NOUN
ejpam-5016	403	18	one	one	NUM
ejpam-5016	403	19	,	,	PUNCT
ejpam-5016	403	20	by	by	ADP
ejpam-5016	403	21	our	our	PRON
ejpam-5016	403	22	classifications	classification	NOUN
ejpam-5016	403	23	above	above	ADV
ejpam-5016	403	24	,	,	PUNCT
ejpam-5016	403	25	we	we	PRON
ejpam-5016	403	26	need	need	VERB
ejpam-5016	403	27	to	to	PART
ejpam-5016	403	28	consider	consider	VERB
ejpam-5016	403	29	several	several	ADJ
ejpam-5016	403	30	cases	case	NOUN
ejpam-5016	403	31	of	of	ADP
ejpam-5016	403	32	s(f	s(f	PROPN
ejpam-5016	403	33	,	,	PUNCT
ejpam-5016	403	34	g	g	NOUN
ejpam-5016	403	35	)	)	PUNCT
ejpam-5016	403	36	.	.	PUNCT
ejpam-5016	404	1	•	•	NUM
ejpam-5016	404	2	s(xix11	s(xix11	NOUN
ejpam-5016	404	3	+	+	NOUN
ejpam-5016	404	4	2nx14	2nx14	ADJ
ejpam-5016	404	5	+	+	NOUN
ejpam-5016	404	6	2n−xi+4+nx15	2n−xi+4+nx15	NUM
ejpam-5016	404	7	+	+	NOUN
ejpam-5016	404	8	2nx6+n	2nx6+n	NUM
ejpam-5016	404	9	,	,	PUNCT
ejpam-5016	404	10	xjx12	xjx12	PROPN
ejpam-5016	404	11	+	+	NOUN
ejpam-5016	404	12	2nx14	2nx14	ADJ
ejpam-5016	404	13	+	+	NOUN
ejpam-5016	404	14	2n−xj+4+nx16	2n−xj+4+nx16	NUM
ejpam-5016	404	15	+	+	NOUN
ejpam-5016	404	16	2nx6+n	2nx6+n	NUM
ejpam-5016	404	17	)	)	PUNCT
ejpam-5016	404	18	,	,	PUNCT
ejpam-5016	404	19	5	5	NUM
ejpam-5016	404	20	≤	≤	NUM
ejpam-5016	405	1	i	i	PRON
ejpam-5016	405	2	<	<	X
ejpam-5016	405	3	j	j	PROPN
ejpam-5016	405	4	≤	≤	ADV
ejpam-5016	405	5	4	4	NUM
ejpam-5016	405	6	+	+	CCONJ
ejpam-5016	405	7	n.	n.	NOUN
ejpam-5016	405	8	the	the	DET
ejpam-5016	405	9	above	above	ADJ
ejpam-5016	405	10	expression	expression	NOUN
ejpam-5016	405	11	is	be	AUX
ejpam-5016	405	12	equal	equal	ADJ
ejpam-5016	405	13	to	to	ADP
ejpam-5016	405	14	xix11	xix11	PROPN
ejpam-5016	405	15	+	+	PROPN
ejpam-5016	405	16	2nxj+4+nx16	2nxj+4+nx16	ADJ
ejpam-5016	405	17	+	+	ADJ
ejpam-5016	405	18	2nx6+n	2nx6+n	NUM
ejpam-5016	405	19	−	−	NOUN
ejpam-5016	405	20	xi+4+nx15	xi+4+nx15	PROPN
ejpam-5016	405	21	+	+	PROPN
ejpam-5016	405	22	2nx6+nxjx12	2nx6+nxjx12	NUM
ejpam-5016	405	23	+	+	SYM
ejpam-5016	405	24	2n	2n	ADJ
ejpam-5016	405	25	=	=	SYM
ejpam-5016	405	26	x6+nx11	x6+nx11	SYM
ejpam-5016	405	27	+	+	NOUN
ejpam-5016	405	28	2nx16	2nx16	PROPN
ejpam-5016	405	29	+	+	ADJ
ejpam-5016	405	30	2n(xixj+4+n	2n(xixj+4+n	PROPN
ejpam-5016	405	31	−	−	NOUN
ejpam-5016	405	32	xi+4+nxj	xi+4+nxj	PROPN
ejpam-5016	405	33	)	)	PUNCT
ejpam-5016	406	1	+	+	VERB
ejpam-5016	406	2	x6+nxi+4+nxj(x11	x6+nxi+4+nxj(x11	PROPN
ejpam-5016	406	3	+	+	PROPN
ejpam-5016	406	4	2nx16	2nx16	PROPN
ejpam-5016	406	5	+	+	NOUN
ejpam-5016	406	6	2n	2n	NUM
ejpam-5016	406	7	−	−	ADP
ejpam-5016	406	8	x15	x15	NUM
ejpam-5016	406	9	+	+	NOUN
ejpam-5016	406	10	2nx12	2nx12	NUM
ejpam-5016	406	11	+	+	NOUN
ejpam-5016	406	12	2n	2n	NUM
ejpam-5016	406	13	)	)	PUNCT
ejpam-5016	406	14	and	and	CCONJ
ejpam-5016	406	15	is	be	AUX
ejpam-5016	406	16	reduced	reduce	VERB
ejpam-5016	406	17	to	to	ADP
ejpam-5016	406	18	zero	zero	NUM
ejpam-5016	406	19	.	.	PUNCT
ejpam-5016	406	20	•	•	NUM
ejpam-5016	406	21	s(xix11	s(xix11	NOUN
ejpam-5016	406	22	+	+	NOUN
ejpam-5016	406	23	2nx14	2nx14	ADJ
ejpam-5016	406	24	+	+	NOUN
ejpam-5016	406	25	2n−xi+4+nx15	2n−xi+4+nx15	NUM
ejpam-5016	406	26	+	+	NOUN
ejpam-5016	406	27	2nx6+n	2nx6+n	NUM
ejpam-5016	406	28	,	,	PUNCT
ejpam-5016	406	29	xjx11	xjx11	PROPN
ejpam-5016	406	30	+	+	PROPN
ejpam-5016	406	31	2nx13	2nx13	NOUN
ejpam-5016	406	32	+	+	NOUN
ejpam-5016	406	33	2n−xj+4+nx15	2n−xj+4+nx15	NUM
ejpam-5016	406	34	+	+	NUM
ejpam-5016	406	35	2nx5+n	2nx5+n	NUM
ejpam-5016	406	36	)	)	PUNCT
ejpam-5016	406	37	,	,	PUNCT
ejpam-5016	406	38	5	5	NUM
ejpam-5016	406	39	≤	≤	NUM
ejpam-5016	407	1	i	i	PRON
ejpam-5016	407	2	<	<	X
ejpam-5016	407	3	j	j	PROPN
ejpam-5016	407	4	≤	≤	ADV
ejpam-5016	407	5	4	4	NUM
ejpam-5016	407	6	+	+	CCONJ
ejpam-5016	407	7	n.	n.	NOUN
ejpam-5016	407	8	the	the	DET
ejpam-5016	407	9	above	above	ADJ
ejpam-5016	407	10	expression	expression	NOUN
ejpam-5016	407	11	is	be	AUX
ejpam-5016	407	12	equal	equal	ADJ
ejpam-5016	407	13	to	to	ADP
ejpam-5016	407	14	xix14	xix14	PROPN
ejpam-5016	407	15	+	+	PROPN
ejpam-5016	407	16	2nxj+4+nx15	2nxj+4+nx15	NUM
ejpam-5016	407	17	+	+	NOUN
ejpam-5016	407	18	2nx5+n	2nx5+n	NUM
ejpam-5016	407	19	−	−	NOUN
ejpam-5016	407	20	xjx13	xjx13	NOUN
ejpam-5016	407	21	+	+	NOUN
ejpam-5016	407	22	2nxi+4+nx15	2nxi+4+nx15	NUM
ejpam-5016	407	23	+	+	ADJ
ejpam-5016	407	24	2nx6+n	2nx6+n	NUM
ejpam-5016	407	25	y.	y.	PROPN
ejpam-5016	407	26	y.	y.	PROPN
ejpam-5016	407	27	hamonangan	hamonangan	PROPN
ejpam-5016	407	28	,	,	PUNCT
ejpam-5016	407	29	i.	i.	PROPN
ejpam-5016	407	30	muchtadi	muchtadi	PROPN
ejpam-5016	407	31	-	-	PUNCT
ejpam-5016	407	32	alamsyah	alamsyah	NOUN
ejpam-5016	407	33	/	/	SYM
ejpam-5016	407	34	eur	eur	PROPN
ejpam-5016	407	35	.	.	PUNCT
ejpam-5016	408	1	j.	j.	PROPN
ejpam-5016	408	2	pure	pure	PROPN
ejpam-5016	408	3	appl	appl	PROPN
ejpam-5016	408	4	.	.	PROPN
ejpam-5016	408	5	math	math	PROPN
ejpam-5016	408	6	,	,	PUNCT
ejpam-5016	408	7	17	17	NUM
ejpam-5016	408	8	(	(	PUNCT
ejpam-5016	408	9	4	4	NUM
ejpam-5016	408	10	)	)	PUNCT
ejpam-5016	408	11	(	(	PUNCT
ejpam-5016	408	12	2024	2024	NUM
ejpam-5016	408	13	)	)	PUNCT
ejpam-5016	408	14	,	,	PUNCT
ejpam-5016	408	15	2621	2621	NUM
ejpam-5016	408	16	-	-	SYM
ejpam-5016	408	17	2650	2650	NUM
ejpam-5016	408	18	2642	2642	NUM
ejpam-5016	408	19	=	=	SYM
ejpam-5016	408	20	x15	x15	NUM
ejpam-5016	408	21	+	+	NOUN
ejpam-5016	408	22	2nx14	2nx14	ADJ
ejpam-5016	408	23	+	+	NOUN
ejpam-5016	408	24	2nx5+n(xixj+4+n	2nx5+n(xixj+4+n	NOUN
ejpam-5016	408	25	−	−	PROPN
ejpam-5016	408	26	xjxi+4+n	xjxi+4+n	PRON
ejpam-5016	408	27	)	)	PUNCT
ejpam-5016	409	1	+	+	ADJ
ejpam-5016	409	2	x15	x15	ADJ
ejpam-5016	409	3	+	+	ADJ
ejpam-5016	409	4	2nxjxi+4+n(x14	2nxjxi+4+n(x14	NUM
ejpam-5016	409	5	+	+	NOUN
ejpam-5016	409	6	2nx5+n	2nx5+n	NUM
ejpam-5016	409	7	−	−	NOUN
ejpam-5016	409	8	x6+nx13	x6+nx13	PROPN
ejpam-5016	409	9	+	+	NOUN
ejpam-5016	409	10	2n	2n	NUM
ejpam-5016	409	11	)	)	PUNCT
ejpam-5016	409	12	and	and	CCONJ
ejpam-5016	409	13	is	be	AUX
ejpam-5016	409	14	reduced	reduce	VERB
ejpam-5016	409	15	to	to	ADP
ejpam-5016	409	16	zero	zero	NUM
ejpam-5016	409	17	.	.	PUNCT
ejpam-5016	409	18	•	•	NUM
ejpam-5016	409	19	s(xix11	s(xix11	NOUN
ejpam-5016	409	20	+	+	NOUN
ejpam-5016	409	21	2nx14	2nx14	ADJ
ejpam-5016	409	22	+	+	NOUN
ejpam-5016	409	23	2n−xi+4+nx15	2n−xi+4+nx15	NUM
ejpam-5016	409	24	+	+	NOUN
ejpam-5016	409	25	2nx6+n	2nx6+n	NUM
ejpam-5016	409	26	,	,	PUNCT
ejpam-5016	409	27	xix12	xix12	PROPN
ejpam-5016	409	28	+	+	PROPN
ejpam-5016	409	29	2nx13	2nx13	NOUN
ejpam-5016	409	30	+	+	NOUN
ejpam-5016	409	31	2n−xi+4+nx16	2n−xi+4+nx16	NUM
ejpam-5016	409	32	+	+	NOUN
ejpam-5016	409	33	2nx5+n	2nx5+n	NUM
ejpam-5016	409	34	)	)	PUNCT
ejpam-5016	409	35	,	,	PUNCT
ejpam-5016	409	36	5	5	NUM
ejpam-5016	409	37	≤	≤	NUM
ejpam-5016	409	38	i	i	PRON
ejpam-5016	409	39	≤	≤	NOUN
ejpam-5016	409	40	4	4	NUM
ejpam-5016	409	41	+	+	CCONJ
ejpam-5016	409	42	n.	n.	NOUN
ejpam-5016	409	43	the	the	DET
ejpam-5016	409	44	above	above	ADJ
ejpam-5016	409	45	expression	expression	NOUN
ejpam-5016	409	46	is	be	AUX
ejpam-5016	409	47	equal	equal	ADJ
ejpam-5016	409	48	to	to	ADP
ejpam-5016	409	49	x11	x11	NOUN
ejpam-5016	409	50	+	+	NOUN
ejpam-5016	409	51	2nx14	2nx14	ADJ
ejpam-5016	409	52	+	+	NOUN
ejpam-5016	409	53	2nxi+4+nx16	2nxi+4+nx16	NOUN
ejpam-5016	409	54	+	+	NOUN
ejpam-5016	409	55	2nx5+n	2nx5+n	NUM
ejpam-5016	409	56	−	−	NUM
ejpam-5016	409	57	x12	x12	NUM
ejpam-5016	410	1	+	+	NOUN
ejpam-5016	411	1	2nx13	2nx13	ADJ
ejpam-5016	411	2	+	+	SYM
ejpam-5016	411	3	2nxi+4+nx15	2nxi+4+nx15	NUM
ejpam-5016	411	4	+	+	ADJ
ejpam-5016	411	5	2nx6+n	2nx6+n	NUM
ejpam-5016	411	6	=	=	SYM
ejpam-5016	411	7	xi+4+nx11	xi+4+nx11	PROPN
ejpam-5016	411	8	+	+	NOUN
ejpam-5016	411	9	2nx16	2nx16	PROPN
ejpam-5016	411	10	+	+	NOUN
ejpam-5016	411	11	2n(x5+nx14	2n(x5+nx14	ADJ
ejpam-5016	411	12	+	+	ADJ
ejpam-5016	411	13	2n	2n	NUM
ejpam-5016	411	14	−	−	ADP
ejpam-5016	411	15	x6+nx13	x6+nx13	PROPN
ejpam-5016	411	16	+	+	NOUN
ejpam-5016	411	17	2n	2n	NUM
ejpam-5016	411	18	)	)	PUNCT
ejpam-5016	412	1	+	+	ADJ
ejpam-5016	412	2	xi+4+nx6+nx13	xi+4+nx6+nx13	X
ejpam-5016	412	3	+	+	ADJ
ejpam-5016	412	4	2n(x11	2n(x11	PROPN
ejpam-5016	412	5	+	+	NOUN
ejpam-5016	412	6	2nx16	2nx16	PROPN
ejpam-5016	412	7	+	+	NOUN
ejpam-5016	412	8	2n	2n	NUM
ejpam-5016	412	9	−	−	ADP
ejpam-5016	412	10	x12	x12	NUM
ejpam-5016	412	11	+	+	PROPN
ejpam-5016	412	12	2nx15	2nx15	NUM
ejpam-5016	412	13	+	+	NOUN
ejpam-5016	412	14	2n	2n	NUM
ejpam-5016	412	15	)	)	PUNCT
ejpam-5016	412	16	and	and	CCONJ
ejpam-5016	412	17	is	be	AUX
ejpam-5016	412	18	reduced	reduce	VERB
ejpam-5016	412	19	to	to	ADP
ejpam-5016	412	20	zero	zero	NUM
ejpam-5016	412	21	.	.	PUNCT
ejpam-5016	413	1	•	•	NOUN
ejpam-5016	413	2	s(xix12	s(xix12	NUM
ejpam-5016	413	3	+	+	NOUN
ejpam-5016	413	4	2nx14	2nx14	NOUN
ejpam-5016	413	5	+	+	NOUN
ejpam-5016	413	6	2n−xi+4+nx16	2n−xi+4+nx16	NUM
ejpam-5016	413	7	+	+	NOUN
ejpam-5016	413	8	2nx6+n	2nx6+n	NUM
ejpam-5016	413	9	,	,	PUNCT
ejpam-5016	413	10	xix11	xix11	PROPN
ejpam-5016	413	11	+	+	PROPN
ejpam-5016	413	12	2nx13	2nx13	PROPN
ejpam-5016	413	13	+	+	ADJ
ejpam-5016	413	14	2n−xi+4+nx15	2n−xi+4+nx15	NUM
ejpam-5016	413	15	+	+	NOUN
ejpam-5016	413	16	2nx5+n	2nx5+n	NUM
ejpam-5016	413	17	)	)	PUNCT
ejpam-5016	413	18	,	,	PUNCT
ejpam-5016	413	19	5	5	NUM
ejpam-5016	413	20	≤	≤	NUM
ejpam-5016	413	21	i	i	PRON
ejpam-5016	413	22	≤	≤	NOUN
ejpam-5016	413	23	4	4	NUM
ejpam-5016	414	1	+	+	CCONJ
ejpam-5016	414	2	n.	n.	NOUN
ejpam-5016	414	3	the	the	DET
ejpam-5016	414	4	above	above	ADJ
ejpam-5016	414	5	expression	expression	NOUN
ejpam-5016	414	6	is	be	AUX
ejpam-5016	414	7	equal	equal	ADJ
ejpam-5016	414	8	to	to	ADP
ejpam-5016	414	9	x12	x12	NUM
ejpam-5016	414	10	+	+	NOUN
ejpam-5016	414	11	2nx14	2nx14	NUM
ejpam-5016	414	12	+	+	SYM
ejpam-5016	414	13	2nxi+4+nx15	2nxi+4+nx15	NUM
ejpam-5016	414	14	+	+	SYM
ejpam-5016	414	15	2nx5+n	2nx5+n	NUM
ejpam-5016	414	16	−	−	NOUN
ejpam-5016	414	17	xi+4+nx16	xi+4+nx16	PROPN
ejpam-5016	414	18	+	+	PROPN
ejpam-5016	414	19	2nx6+nx11	2nx6+nx11	PROPN
ejpam-5016	414	20	+	+	ADJ
ejpam-5016	414	21	2nx13	2nx13	NOUN
ejpam-5016	414	22	+	+	ADJ
ejpam-5016	414	23	2n	2n	NUM
ejpam-5016	414	24	=	=	PUNCT
ejpam-5016	414	25	xi+4+nx12	xi+4+nx12	NUM
ejpam-5016	414	26	+	+	PROPN
ejpam-5016	414	27	2nx15	2nx15	ADJ
ejpam-5016	414	28	+	+	ADJ
ejpam-5016	414	29	2n(x5+nx14	2n(x5+nx14	ADJ
ejpam-5016	414	30	+	+	ADJ
ejpam-5016	414	31	2n	2n	NUM
ejpam-5016	414	32	−	−	ADP
ejpam-5016	414	33	x6+nx13	x6+nx13	PROPN
ejpam-5016	414	34	+	+	NOUN
ejpam-5016	414	35	2n	2n	NUM
ejpam-5016	414	36	)	)	PUNCT
ejpam-5016	415	1	+	+	ADJ
ejpam-5016	415	2	xi+4+nx6+nx13	xi+4+nx6+nx13	X
ejpam-5016	415	3	+	+	ADJ
ejpam-5016	415	4	2n(x12	2n(x12	NUM
ejpam-5016	415	5	+	+	ADJ
ejpam-5016	415	6	2nx15	2nx15	NUM
ejpam-5016	415	7	+	+	NOUN
ejpam-5016	415	8	2n	2n	NUM
ejpam-5016	415	9	−	−	ADP
ejpam-5016	415	10	x11	x11	PROPN
ejpam-5016	415	11	+	+	PROPN
ejpam-5016	415	12	2nx16	2nx16	PROPN
ejpam-5016	415	13	+	+	NOUN
ejpam-5016	415	14	2n	2n	NUM
ejpam-5016	415	15	)	)	PUNCT
ejpam-5016	415	16	and	and	CCONJ
ejpam-5016	415	17	is	be	AUX
ejpam-5016	415	18	reduced	reduce	VERB
ejpam-5016	415	19	to	to	ADP
ejpam-5016	415	20	zero	zero	NUM
ejpam-5016	415	21	.	.	PUNCT
ejpam-5016	416	1	•	•	NOUN
ejpam-5016	416	2	s(xix12	s(xix12	NUM
ejpam-5016	416	3	+	+	NOUN
ejpam-5016	416	4	2nx14	2nx14	NOUN
ejpam-5016	416	5	+	+	NOUN
ejpam-5016	416	6	2n−xi+4+nx16	2n−xi+4+nx16	NUM
ejpam-5016	416	7	+	+	NOUN
ejpam-5016	416	8	2nx6+n	2nx6+n	NUM
ejpam-5016	416	9	,	,	PUNCT
ejpam-5016	416	10	xjx12	xjx12	PROPN
ejpam-5016	416	11	+	+	NOUN
ejpam-5016	416	12	2nx13	2nx13	NOUN
ejpam-5016	416	13	+	+	NOUN
ejpam-5016	416	14	2n−xj+4+nx16	2n−xj+4+nx16	NUM
ejpam-5016	416	15	+	+	NOUN
ejpam-5016	416	16	2nx5+n	2nx5+n	NUM
ejpam-5016	416	17	)	)	PUNCT
ejpam-5016	416	18	,	,	PUNCT
ejpam-5016	416	19	5	5	NUM
ejpam-5016	416	20	≤	≤	NUM
ejpam-5016	417	1	i	i	PRON
ejpam-5016	417	2	<	<	X
ejpam-5016	417	3	j	j	PROPN
ejpam-5016	417	4	≤	≤	ADV
ejpam-5016	417	5	4	4	NUM
ejpam-5016	417	6	+	+	CCONJ
ejpam-5016	417	7	n.	n.	NOUN
ejpam-5016	417	8	the	the	DET
ejpam-5016	417	9	above	above	ADJ
ejpam-5016	417	10	expression	expression	NOUN
ejpam-5016	417	11	is	be	AUX
ejpam-5016	417	12	equal	equal	ADJ
ejpam-5016	417	13	to	to	ADP
ejpam-5016	417	14	xix14	xix14	PROPN
ejpam-5016	417	15	+	+	PROPN
ejpam-5016	417	16	2nxj+4+nx16	2nxj+4+nx16	PROPN
ejpam-5016	417	17	+	+	NOUN
ejpam-5016	417	18	2nx5+n	2nx5+n	NUM
ejpam-5016	417	19	−	−	NOUN
ejpam-5016	417	20	xi+4+nx16	xi+4+nx16	PROPN
ejpam-5016	417	21	+	+	PROPN
ejpam-5016	417	22	2nx6+nxjx13	2nx6+nxjx13	PROPN
ejpam-5016	417	23	+	+	ADJ
ejpam-5016	417	24	2n	2n	NUM
ejpam-5016	417	25	=	=	SYM
ejpam-5016	417	26	x16	x16	PROPN
ejpam-5016	417	27	+	+	NOUN
ejpam-5016	417	28	2nx14	2nx14	ADJ
ejpam-5016	417	29	+	+	NOUN
ejpam-5016	417	30	2nx5+n(xixj+4+n	2nx5+n(xixj+4+n	NOUN
ejpam-5016	417	31	−	−	PROPN
ejpam-5016	417	32	xjxi+4+n	xjxi+4+n	PRON
ejpam-5016	417	33	)	)	PUNCT
ejpam-5016	418	1	+	+	NOUN
ejpam-5016	418	2	x16	x16	NOUN
ejpam-5016	418	3	+	+	NOUN
ejpam-5016	418	4	2nxjxi+4+n(x14	2nxjxi+4+n(x14	NUM
ejpam-5016	418	5	+	+	NOUN
ejpam-5016	418	6	2nx5+n	2nx5+n	NUM
ejpam-5016	418	7	−	−	NOUN
ejpam-5016	418	8	x13	x13	NOUN
ejpam-5016	418	9	+	+	NOUN
ejpam-5016	418	10	2nx6+n	2nx6+n	NUM
ejpam-5016	418	11	)	)	PUNCT
ejpam-5016	418	12	and	and	CCONJ
ejpam-5016	418	13	is	be	AUX
ejpam-5016	418	14	reduced	reduce	VERB
ejpam-5016	418	15	to	to	ADP
ejpam-5016	418	16	zero	zero	NUM
ejpam-5016	418	17	.	.	PUNCT
ejpam-5016	418	18	•	•	NUM
ejpam-5016	418	19	s(xix11	s(xix11	NOUN
ejpam-5016	418	20	+	+	NOUN
ejpam-5016	418	21	2nx13	2nx13	NOUN
ejpam-5016	418	22	+	+	SYM
ejpam-5016	418	23	2n−xi+4+nx15	2n−xi+4+nx15	NUM
ejpam-5016	418	24	+	+	NOUN
ejpam-5016	418	25	2nx5+n	2nx5+n	NOUN
ejpam-5016	418	26	,	,	PUNCT
ejpam-5016	418	27	xjx12	xjx12	PROPN
ejpam-5016	418	28	+	+	NOUN
ejpam-5016	418	29	2nx13	2nx13	NOUN
ejpam-5016	418	30	+	+	NOUN
ejpam-5016	418	31	2n−xj+4+nx16	2n−xj+4+nx16	NUM
ejpam-5016	418	32	+	+	NOUN
ejpam-5016	418	33	2nx5+n	2nx5+n	NUM
ejpam-5016	418	34	)	)	PUNCT
ejpam-5016	418	35	,	,	PUNCT
ejpam-5016	418	36	5	5	NUM
ejpam-5016	418	37	≤	≤	NUM
ejpam-5016	419	1	i	i	PRON
ejpam-5016	419	2	<	<	X
ejpam-5016	419	3	j	j	PROPN
ejpam-5016	419	4	≤	≤	ADV
ejpam-5016	419	5	4	4	NUM
ejpam-5016	419	6	+	+	CCONJ
ejpam-5016	419	7	n.	n.	NOUN
ejpam-5016	419	8	the	the	DET
ejpam-5016	419	9	above	above	ADJ
ejpam-5016	419	10	expression	expression	NOUN
ejpam-5016	419	11	is	be	AUX
ejpam-5016	419	12	equal	equal	ADJ
ejpam-5016	419	13	to	to	ADP
ejpam-5016	419	14	xix11	xix11	PROPN
ejpam-5016	419	15	+	+	PROPN
ejpam-5016	419	16	2nxj+4+nx16	2nxj+4+nx16	PROPN
ejpam-5016	419	17	+	+	NOUN
ejpam-5016	419	18	2nx5+n	2nx5+n	NUM
ejpam-5016	419	19	−	−	PROPN
ejpam-5016	419	20	xi+4+nx15	xi+4+nx15	PROPN
ejpam-5016	419	21	+	+	PROPN
ejpam-5016	419	22	2nx5+nxjx12	2nx5+nxjx12	PROPN
ejpam-5016	419	23	+	+	ADJ
ejpam-5016	419	24	2n	2n	ADJ
ejpam-5016	419	25	=	=	PUNCT
ejpam-5016	420	1	x5+nx11	x5+nx11	PROPN
ejpam-5016	420	2	+	+	PROPN
ejpam-5016	420	3	2nx16	2nx16	PROPN
ejpam-5016	420	4	+	+	PROPN
ejpam-5016	420	5	2n(xixj+4+n	2n(xixj+4+n	PROPN
ejpam-5016	420	6	−	−	NOUN
ejpam-5016	420	7	xjxi+4+n	xjxi+4+n	NOUN
ejpam-5016	420	8	)	)	PUNCT
ejpam-5016	421	1	+	+	PROPN
ejpam-5016	421	2	x5+nxjxi+4+n(x11	x5+nxjxi+4+n(x11	PROPN
ejpam-5016	421	3	+	+	PROPN
ejpam-5016	421	4	2nx16	2nx16	PROPN
ejpam-5016	421	5	+	+	NOUN
ejpam-5016	421	6	2n	2n	NUM
ejpam-5016	421	7	−	−	ADP
ejpam-5016	421	8	x12	x12	NUM
ejpam-5016	421	9	+	+	PROPN
ejpam-5016	421	10	2nx15	2nx15	NUM
ejpam-5016	421	11	+	+	NOUN
ejpam-5016	421	12	2n	2n	NUM
ejpam-5016	421	13	)	)	PUNCT
ejpam-5016	421	14	and	and	CCONJ
ejpam-5016	421	15	is	be	AUX
ejpam-5016	421	16	reduced	reduce	VERB
ejpam-5016	421	17	to	to	ADP
ejpam-5016	421	18	zero	zero	NUM
ejpam-5016	421	19	.	.	PUNCT
ejpam-5016	422	1	and	and	CCONJ
ejpam-5016	422	2	we	we	PRON
ejpam-5016	422	3	are	be	AUX
ejpam-5016	422	4	done	do	VERB
ejpam-5016	422	5	with	with	ADP
ejpam-5016	422	6	the	the	DET
ejpam-5016	422	7	proof	proof	NOUN
ejpam-5016	422	8	.	.	PUNCT
ejpam-5016	423	1	y.	y.	PROPN
ejpam-5016	423	2	y.	y.	PROPN
ejpam-5016	423	3	hamonangan	hamonangan	PROPN
ejpam-5016	423	4	,	,	PUNCT
ejpam-5016	423	5	i.	i.	PROPN
ejpam-5016	423	6	muchtadi	muchtadi	PROPN
ejpam-5016	423	7	-	-	PUNCT
ejpam-5016	423	8	alamsyah	alamsyah	NOUN
ejpam-5016	423	9	/	/	SYM
ejpam-5016	423	10	eur	eur	PROPN
ejpam-5016	423	11	.	.	PUNCT
ejpam-5016	424	1	j.	j.	PROPN
ejpam-5016	424	2	pure	pure	PROPN
ejpam-5016	424	3	appl	appl	PROPN
ejpam-5016	424	4	.	.	PROPN
ejpam-5016	424	5	math	math	PROPN
ejpam-5016	424	6	,	,	PUNCT
ejpam-5016	424	7	17	17	NUM
ejpam-5016	424	8	(	(	PUNCT
ejpam-5016	424	9	4	4	NUM
ejpam-5016	424	10	)	)	PUNCT
ejpam-5016	424	11	(	(	PUNCT
ejpam-5016	424	12	2024	2024	NUM
ejpam-5016	424	13	)	)	PUNCT
ejpam-5016	424	14	,	,	PUNCT
ejpam-5016	424	15	2621	2621	NUM
ejpam-5016	424	16	-	-	SYM
ejpam-5016	424	17	2650	2650	NUM
ejpam-5016	424	18	2643	2643	NUM
ejpam-5016	424	19	remark	remark	NOUN
ejpam-5016	424	20	1	1	NUM
ejpam-5016	424	21	.	.	PUNCT
ejpam-5016	424	22	note	note	VERB
ejpam-5016	424	23	that	that	SCONJ
ejpam-5016	424	24	we	we	PRON
ejpam-5016	424	25	can	can	AUX
ejpam-5016	424	26	rotate	rotate	VERB
ejpam-5016	424	27	the	the	DET
ejpam-5016	424	28	socket	socket	NOUN
ejpam-5016	424	29	wrench	wrench	NOUN
ejpam-5016	424	30	polyominoes	polyominoe	NOUN
ejpam-5016	424	31	90	90	NUM
ejpam-5016	424	32	◦	◦	NOUN
ejpam-5016	424	33	,	,	PUNCT
ejpam-5016	424	34	180	180	NUM
ejpam-5016	424	35	◦	◦	NOUN
ejpam-5016	424	36	,	,	PUNCT
ejpam-5016	424	37	and	and	CCONJ
ejpam-5016	424	38	270	270	NUM
ejpam-5016	424	39	◦	◦	NOUN
ejpam-5016	424	40	and	and	CCONJ
ejpam-5016	424	41	get	get	VERB
ejpam-5016	424	42	the	the	DET
ejpam-5016	424	43	same	same	ADJ
ejpam-5016	424	44	conclusion	conclusion	NOUN
ejpam-5016	424	45	since	since	SCONJ
ejpam-5016	424	46	we	we	PRON
ejpam-5016	424	47	also	also	ADV
ejpam-5016	424	48	can	can	AUX
ejpam-5016	424	49	rotate	rotate	VERB
ejpam-5016	424	50	the	the	DET
ejpam-5016	424	51	labelling	labelling	NOUN
ejpam-5016	424	52	and	and	CCONJ
ejpam-5016	424	53	using	use	VERB
ejpam-5016	424	54	the	the	DET
ejpam-5016	424	55	same	same	ADJ
ejpam-5016	424	56	monomial	monomial	ADJ
ejpam-5016	424	57	order	order	NOUN
ejpam-5016	424	58	.	.	PUNCT
ejpam-5016	425	1	we	we	PRON
ejpam-5016	425	2	also	also	ADV
ejpam-5016	425	3	can	can	AUX
ejpam-5016	425	4	prove	prove	VERB
ejpam-5016	425	5	a	a	DET
ejpam-5016	425	6	stronger	strong	ADJ
ejpam-5016	425	7	result	result	NOUN
ejpam-5016	425	8	by	by	ADP
ejpam-5016	425	9	using	use	VERB
ejpam-5016	425	10	the	the	DET
ejpam-5016	425	11	similar	similar	ADJ
ejpam-5016	425	12	argument	argument	NOUN
ejpam-5016	425	13	with	with	ADP
ejpam-5016	425	14	[	[	X
ejpam-5016	425	15	5	5	NUM
ejpam-5016	425	16	,	,	PUNCT
ejpam-5016	425	17	section	section	NOUN
ejpam-5016	425	18	4	4	NUM
ejpam-5016	425	19	]	]	PUNCT
ejpam-5016	425	20	.	.	PUNCT
ejpam-5016	426	1	theorem	theorem	NOUN
ejpam-5016	426	2	5	5	NUM
ejpam-5016	426	3	.	.	PUNCT
ejpam-5016	427	1	let	let	VERB
ejpam-5016	427	2	p	p	PRON
ejpam-5016	427	3	be	be	AUX
ejpam-5016	427	4	a	a	DET
ejpam-5016	427	5	socket	socket	NOUN
ejpam-5016	427	6	wrench	wrench	NOUN
ejpam-5016	427	7	polyomino	polyomino	NOUN
ejpam-5016	427	8	then	then	ADV
ejpam-5016	427	9	the	the	DET
ejpam-5016	427	10	ideal	ideal	ADJ
ejpam-5016	427	11	ip	ip	NOUN
ejpam-5016	427	12	is	be	AUX
ejpam-5016	427	13	prime	prime	ADJ
ejpam-5016	427	14	.	.	PUNCT
ejpam-5016	428	1	proof	proof	NOUN
ejpam-5016	428	2	.	.	PUNCT
ejpam-5016	429	1	we	we	PRON
ejpam-5016	429	2	label	label	VERB
ejpam-5016	429	3	p	p	NOUN
ejpam-5016	429	4	according	accord	VERB
ejpam-5016	429	5	to	to	PART
ejpam-5016	429	6	figure	figure	VERB
ejpam-5016	429	7	29	29	NUM
ejpam-5016	429	8	.	.	PUNCT
ejpam-5016	430	1	let	let	VERB
ejpam-5016	430	2	{	{	PUNCT
ejpam-5016	430	3	vi}i∈i	vi}i∈i	INTJ
ejpam-5016	430	4	be	be	AUX
ejpam-5016	430	5	the	the	DET
ejpam-5016	430	6	set	set	NOUN
ejpam-5016	430	7	of	of	ADP
ejpam-5016	430	8	maximal	maximal	ADJ
ejpam-5016	430	9	vertical	vertical	ADJ
ejpam-5016	430	10	edge	edge	NOUN
ejpam-5016	430	11	intervals	interval	NOUN
ejpam-5016	430	12	of	of	ADP
ejpam-5016	430	13	p	p	NOUN
ejpam-5016	430	14	and	and	CCONJ
ejpam-5016	430	15	{	{	PUNCT
ejpam-5016	430	16	hj}j∈j	hj}j∈j	ADV
ejpam-5016	430	17	be	be	AUX
ejpam-5016	430	18	the	the	DET
ejpam-5016	430	19	set	set	NOUN
ejpam-5016	430	20	of	of	ADP
ejpam-5016	430	21	maximal	maximal	ADJ
ejpam-5016	430	22	horizontal	horizontal	ADJ
ejpam-5016	430	23	edge	edge	NOUN
ejpam-5016	430	24	intervals	interval	NOUN
ejpam-5016	430	25	of	of	ADP
ejpam-5016	430	26	p	p	X
ejpam-5016	430	27	,	,	PUNCT
ejpam-5016	430	28	where	where	SCONJ
ejpam-5016	430	29	i	i	PRON
ejpam-5016	430	30	=	=	PUNCT
ejpam-5016	430	31	{	{	PUNCT
ejpam-5016	430	32	1	1	NUM
ejpam-5016	430	33	,	,	PUNCT
ejpam-5016	430	34	2	2	NUM
ejpam-5016	430	35	,	,	PUNCT
ejpam-5016	430	36	.	.	PUNCT
ejpam-5016	430	37	.	.	PUNCT
ejpam-5016	431	1	.	.	PUNCT
ejpam-5016	432	1	,	,	PUNCT
ejpam-5016	432	2	n	n	PROPN
ejpam-5016	432	3	+	+	CCONJ
ejpam-5016	432	4	4	4	NUM
ejpam-5016	432	5	}	}	PUNCT
ejpam-5016	432	6	and	and	CCONJ
ejpam-5016	432	7	j	j	PROPN
ejpam-5016	433	1	=	=	PUNCT
ejpam-5016	433	2	{	{	PUNCT
ejpam-5016	433	3	1	1	NUM
ejpam-5016	433	4	,	,	PUNCT
ejpam-5016	433	5	2	2	NUM
ejpam-5016	433	6	,	,	PUNCT
ejpam-5016	433	7	3	3	NUM
ejpam-5016	433	8	,	,	PUNCT
ejpam-5016	433	9	4	4	NUM
ejpam-5016	433	10	}	}	PUNCT
ejpam-5016	433	11	.	.	PUNCT
ejpam-5016	434	1	let	let	VERB
ejpam-5016	434	2	{	{	PUNCT
ejpam-5016	434	3	vi}i∈i	vi}i∈i	NOUN
ejpam-5016	434	4	and	and	CCONJ
ejpam-5016	434	5	{	{	PUNCT
ejpam-5016	434	6	hj}j∈j	hj}j∈j	ADV
ejpam-5016	434	7	be	be	AUX
ejpam-5016	434	8	the	the	DET
ejpam-5016	434	9	set	set	NOUN
ejpam-5016	434	10	of	of	ADP
ejpam-5016	434	11	variables	variable	NOUN
ejpam-5016	434	12	associated	associate	VERB
ejpam-5016	434	13	respectively	respectively	ADV
ejpam-5016	434	14	to	to	ADP
ejpam-5016	434	15	{	{	PUNCT
ejpam-5016	434	16	vi}i∈i	vi}i∈i	NOUN
ejpam-5016	434	17	and	and	CCONJ
ejpam-5016	434	18	{	{	PUNCT
ejpam-5016	434	19	hj}j∈j	hj}j∈j	ADV
ejpam-5016	434	20	,	,	PUNCT
ejpam-5016	434	21	respectively	respectively	ADV
ejpam-5016	434	22	.	.	PUNCT
ejpam-5016	435	1	let	let	VERB
ejpam-5016	435	2	w	w	NOUN
ejpam-5016	435	3	be	be	AUX
ejpam-5016	435	4	another	another	DET
ejpam-5016	435	5	variable	variable	NOUN
ejpam-5016	435	6	different	different	ADJ
ejpam-5016	435	7	from	from	ADP
ejpam-5016	435	8	vi	vi	PROPN
ejpam-5016	435	9	and	and	CCONJ
ejpam-5016	435	10	hj	hj	PROPN
ejpam-5016	435	11	.	.	PUNCT
ejpam-5016	436	1	let	let	VERB
ejpam-5016	436	2	a	a	DET
ejpam-5016	436	3	=	=	X
ejpam-5016	436	4	{	{	PUNCT
ejpam-5016	436	5	3	3	NUM
ejpam-5016	436	6	,	,	PUNCT
ejpam-5016	436	7	4	4	NUM
ejpam-5016	436	8	,	,	PUNCT
ejpam-5016	436	9	7	7	NUM
ejpam-5016	436	10	+	+	CCONJ
ejpam-5016	436	11	n	n	CCONJ
ejpam-5016	436	12	,	,	PUNCT
ejpam-5016	436	13	8	8	NUM
ejpam-5016	436	14	+	+	NUM
ejpam-5016	436	15	n	n	CCONJ
ejpam-5016	436	16	}	}	PUNCT
ejpam-5016	436	17	.	.	PUNCT
ejpam-5016	437	1	define	define	VERB
ejpam-5016	437	2	α	α	NOUN
ejpam-5016	437	3	:	:	PUNCT
ejpam-5016	437	4	v	v	NOUN
ejpam-5016	437	5	(	(	PUNCT
ejpam-5016	437	6	p	p	NOUN
ejpam-5016	437	7	)	)	PUNCT
ejpam-5016	437	8	→	→	SYM
ejpam-5016	437	9	k[{vi	k[{vi	PROPN
ejpam-5016	437	10	,	,	PUNCT
ejpam-5016	437	11	hj	hj	PROPN
ejpam-5016	437	12	,	,	PUNCT
ejpam-5016	437	13	w	w	PROPN
ejpam-5016	437	14	}	}	PUNCT
ejpam-5016	437	15	:	:	PUNCT
ejpam-5016	438	1	i	i	PRON
ejpam-5016	438	2	∈	∈	VERB
ejpam-5016	439	1	i	i	PRON
ejpam-5016	439	2	,	,	PUNCT
ejpam-5016	439	3	j	j	PROPN
ejpam-5016	439	4	∈	∈	PROPN
ejpam-5016	439	5	j	j	X
ejpam-5016	439	6	]	]	X
ejpam-5016	439	7	r	r	PROPN
ejpam-5016	439	8	7→	7→	NUM
ejpam-5016	439	9	vihjw	vihjw	NOUN
ejpam-5016	439	10	k	k	NOUN
ejpam-5016	439	11	with	with	ADP
ejpam-5016	439	12	r	r	PROPN
ejpam-5016	439	13	∈	∈	PROPN
ejpam-5016	439	14	vi	vi	NOUN
ejpam-5016	439	15	∩hj	∩hj	NOUN
ejpam-5016	439	16	,	,	PUNCT
ejpam-5016	439	17	k	k	PROPN
ejpam-5016	439	18	=	=	PUNCT
ejpam-5016	439	19	0	0	PUNCT
ejpam-5016	440	1	if	if	SCONJ
ejpam-5016	440	2	r	r	NOUN
ejpam-5016	440	3	/∈	/∈	NOUN
ejpam-5016	440	4	v	v	NOUN
ejpam-5016	440	5	(	(	PUNCT
ejpam-5016	440	6	a	a	NOUN
ejpam-5016	440	7	)	)	PUNCT
ejpam-5016	440	8	,	,	PUNCT
ejpam-5016	440	9	and	and	CCONJ
ejpam-5016	440	10	k	k	X
ejpam-5016	440	11	=	=	NOUN
ejpam-5016	440	12	1	1	NUM
ejpam-5016	440	13	if	if	SCONJ
ejpam-5016	440	14	r	r	NOUN
ejpam-5016	440	15	∈	∈	PROPN
ejpam-5016	440	16	v	v	NOUN
ejpam-5016	440	17	(	(	PUNCT
ejpam-5016	440	18	a	a	NOUN
ejpam-5016	440	19	)	)	PUNCT
ejpam-5016	440	20	.	.	PUNCT
ejpam-5016	441	1	consider	consider	VERB
ejpam-5016	441	2	the	the	DET
ejpam-5016	441	3	following	follow	VERB
ejpam-5016	441	4	surjective	surjective	ADJ
ejpam-5016	441	5	ring	ring	NOUN
ejpam-5016	441	6	homomorphism	homomorphism	PROPN
ejpam-5016	441	7	ϕ	ϕ	X
ejpam-5016	441	8	:	:	PUNCT
ejpam-5016	441	9	k[xr	k[xr	ADJ
ejpam-5016	441	10	:	:	PUNCT
ejpam-5016	441	11	r	r	NOUN
ejpam-5016	441	12	∈	∈	PROPN
ejpam-5016	441	13	v	v	NOUN
ejpam-5016	441	14	(	(	PUNCT
ejpam-5016	441	15	p	p	NOUN
ejpam-5016	441	16	)	)	PUNCT
ejpam-5016	441	17	]	]	PUNCT
ejpam-5016	441	18	→	→	SYM
ejpam-5016	441	19	k[α(v	k[α(v	X
ejpam-5016	441	20	)	)	PUNCT
ejpam-5016	441	21	:	:	PUNCT
ejpam-5016	442	1	v	v	X
ejpam-5016	442	2	∈	∈	PROPN
ejpam-5016	442	3	v	v	NOUN
ejpam-5016	442	4	(	(	PUNCT
ejpam-5016	442	5	p	p	NOUN
ejpam-5016	442	6	)	)	PUNCT
ejpam-5016	442	7	]	]	PUNCT
ejpam-5016	442	8	xr	xr	PROPN
ejpam-5016	442	9	7→	7→	PROPN
ejpam-5016	442	10	α(r	α(r	NOUN
ejpam-5016	442	11	)	)	PUNCT
ejpam-5016	442	12	the	the	DET
ejpam-5016	442	13	toric	toric	ADJ
ejpam-5016	442	14	ideal	ideal	ADJ
ejpam-5016	442	15	jp	jp	NOUN
ejpam-5016	442	16	is	be	AUX
ejpam-5016	442	17	the	the	DET
ejpam-5016	442	18	kernel	kernel	PROPN
ejpam-5016	442	19	of	of	ADP
ejpam-5016	442	20	ϕ.	ϕ.	PROPN
ejpam-5016	442	21	we	we	PRON
ejpam-5016	442	22	will	will	AUX
ejpam-5016	442	23	prove	prove	VERB
ejpam-5016	442	24	that	that	DET
ejpam-5016	442	25	ip	ip	NOUN
ejpam-5016	442	26	=	=	NOUN
ejpam-5016	442	27	jp	jp	NOUN
ejpam-5016	442	28	.	.	PUNCT
ejpam-5016	443	1	we	we	PRON
ejpam-5016	443	2	start	start	VERB
ejpam-5016	443	3	by	by	ADP
ejpam-5016	443	4	proving	prove	VERB
ejpam-5016	443	5	ip	ip	PRON
ejpam-5016	443	6	⊆	⊆	NUM
ejpam-5016	443	7	jp	jp	NOUN
ejpam-5016	443	8	.	.	PUNCT
ejpam-5016	444	1	let	let	VERB
ejpam-5016	444	2	f	f	PROPN
ejpam-5016	444	3	=	=	PRON
ejpam-5016	444	4	xpxq−xrxs	xpxq−xrx	NOUN
ejpam-5016	444	5	be	be	VERB
ejpam-5016	444	6	a	a	DET
ejpam-5016	444	7	generator	generator	NOUN
ejpam-5016	444	8	of	of	ADP
ejpam-5016	444	9	ip	ip	NOUN
ejpam-5016	444	10	that	that	SCONJ
ejpam-5016	444	11	associated	associate	VERB
ejpam-5016	444	12	to	to	ADP
ejpam-5016	444	13	the	the	DET
ejpam-5016	444	14	inner	inner	ADJ
ejpam-5016	444	15	interval	interval	NOUN
ejpam-5016	445	1	[	[	X
ejpam-5016	445	2	p	p	X
ejpam-5016	445	3	,	,	PUNCT
ejpam-5016	445	4	q	q	X
ejpam-5016	445	5	]	]	X
ejpam-5016	445	6	.	.	PUNCT
ejpam-5016	446	1	we	we	PRON
ejpam-5016	446	2	may	may	AUX
ejpam-5016	446	3	assume	assume	VERB
ejpam-5016	446	4	that	that	SCONJ
ejpam-5016	446	5	p	p	X
ejpam-5016	446	6	,	,	PUNCT
ejpam-5016	446	7	r	r	NOUN
ejpam-5016	446	8	and	and	CCONJ
ejpam-5016	446	9	q	q	NOUN
ejpam-5016	446	10	,	,	PUNCT
ejpam-5016	446	11	s	s	NOUN
ejpam-5016	446	12	,	,	PUNCT
ejpam-5016	446	13	respectively	respectively	ADV
ejpam-5016	446	14	,	,	PUNCT
ejpam-5016	446	15	are	be	AUX
ejpam-5016	446	16	on	on	ADP
ejpam-5016	446	17	the	the	DET
ejpam-5016	446	18	same	same	ADJ
ejpam-5016	446	19	maximal	maximal	ADJ
ejpam-5016	446	20	vertical	vertical	ADJ
ejpam-5016	446	21	edge	edge	NOUN
ejpam-5016	446	22	interval	interval	NOUN
ejpam-5016	446	23	.	.	PUNCT
ejpam-5016	447	1	then	then	ADV
ejpam-5016	447	2	,	,	PUNCT
ejpam-5016	447	3	p	p	X
ejpam-5016	447	4	,	,	PUNCT
ejpam-5016	447	5	s	s	X
ejpam-5016	447	6	and	and	CCONJ
ejpam-5016	447	7	q	q	NOUN
ejpam-5016	447	8	,	,	PUNCT
ejpam-5016	447	9	r	r	NOUN
ejpam-5016	447	10	,	,	PUNCT
ejpam-5016	447	11	respectively	respectively	ADV
ejpam-5016	447	12	,	,	PUNCT
ejpam-5016	447	13	are	be	AUX
ejpam-5016	447	14	on	on	ADP
ejpam-5016	447	15	the	the	DET
ejpam-5016	447	16	same	same	ADJ
ejpam-5016	447	17	maximal	maximal	ADJ
ejpam-5016	447	18	horizontal	horizontal	ADJ
ejpam-5016	447	19	edge	edge	NOUN
ejpam-5016	447	20	interval	interval	NOUN
ejpam-5016	447	21	.	.	PUNCT
ejpam-5016	448	1	if	if	SCONJ
ejpam-5016	448	2	[	[	X
ejpam-5016	448	3	p	p	X
ejpam-5016	448	4	,	,	PUNCT
ejpam-5016	448	5	q	q	X
ejpam-5016	448	6	]	]	X
ejpam-5016	448	7	∩	∩	ADJ
ejpam-5016	448	8	a	a	DET
ejpam-5016	448	9	=	=	NOUN
ejpam-5016	448	10	∅	∅	NOUN
ejpam-5016	448	11	then	then	ADV
ejpam-5016	448	12	f	f	PROPN
ejpam-5016	448	13	∈	∈	PROPN
ejpam-5016	448	14	jp	jp	NOUN
ejpam-5016	448	15	.	.	PUNCT
ejpam-5016	449	1	consider	consider	VERB
ejpam-5016	449	2	the	the	DET
ejpam-5016	449	3	case	case	NOUN
ejpam-5016	449	4	[	[	X
ejpam-5016	449	5	p	p	X
ejpam-5016	449	6	,	,	PUNCT
ejpam-5016	449	7	q	q	X
ejpam-5016	449	8	]	]	X
ejpam-5016	449	9	∩	∩	NOUN
ejpam-5016	449	10	a	a	DET
ejpam-5016	449	11	̸=	̸=	PROPN
ejpam-5016	449	12	∅.	∅.	VERB
ejpam-5016	449	13	if	if	SCONJ
ejpam-5016	449	14	[	[	X
ejpam-5016	449	15	p	p	X
ejpam-5016	449	16	,	,	PUNCT
ejpam-5016	449	17	q	q	X
ejpam-5016	449	18	]	]	X
ejpam-5016	449	19	=	=	PUNCT
ejpam-5016	450	1	a	a	DET
ejpam-5016	450	2	then	then	ADV
ejpam-5016	450	3	f	f	PROPN
ejpam-5016	450	4	∈	∈	PROPN
ejpam-5016	450	5	jp	jp	NOUN
ejpam-5016	450	6	.	.	PUNCT
ejpam-5016	451	1	if	if	SCONJ
ejpam-5016	451	2	[	[	X
ejpam-5016	451	3	p	p	X
ejpam-5016	451	4	,	,	PUNCT
ejpam-5016	451	5	q	q	X
ejpam-5016	451	6	]	]	X
ejpam-5016	451	7	̸=	̸=	PROPN
ejpam-5016	451	8	a	a	PART
ejpam-5016	451	9	,	,	PUNCT
ejpam-5016	451	10	by	by	ADP
ejpam-5016	451	11	the	the	DET
ejpam-5016	451	12	construction	construction	NOUN
ejpam-5016	451	13	of	of	ADP
ejpam-5016	451	14	p	p	NOUN
ejpam-5016	451	15	,	,	PUNCT
ejpam-5016	451	16	then	then	ADV
ejpam-5016	451	17	either	either	CCONJ
ejpam-5016	451	18	s	s	PROPN
ejpam-5016	451	19	,	,	PUNCT
ejpam-5016	451	20	q	q	NOUN
ejpam-5016	451	21	or	or	CCONJ
ejpam-5016	451	22	p	p	X
ejpam-5016	451	23	,	,	PUNCT
ejpam-5016	451	24	s	s	VERB
ejpam-5016	451	25	must	must	AUX
ejpam-5016	451	26	be	be	AUX
ejpam-5016	451	27	two	two	NUM
ejpam-5016	451	28	vertices	vertex	NOUN
ejpam-5016	451	29	of	of	ADP
ejpam-5016	451	30	a.	a.	NOUN
ejpam-5016	451	31	in	in	ADP
ejpam-5016	451	32	the	the	DET
ejpam-5016	451	33	first	first	ADJ
ejpam-5016	451	34	case	case	NOUN
ejpam-5016	451	35	,	,	PUNCT
ejpam-5016	451	36	p	p	X
ejpam-5016	451	37	,	,	PUNCT
ejpam-5016	451	38	r	r	NOUN
ejpam-5016	451	39	are	be	AUX
ejpam-5016	451	40	not	not	PART
ejpam-5016	451	41	the	the	DET
ejpam-5016	451	42	vertices	vertex	NOUN
ejpam-5016	451	43	of	of	ADP
ejpam-5016	451	44	a.	a.	NOUN
ejpam-5016	451	45	in	in	ADP
ejpam-5016	451	46	the	the	DET
ejpam-5016	451	47	second	second	ADJ
ejpam-5016	451	48	case	case	NOUN
ejpam-5016	451	49	,	,	PUNCT
ejpam-5016	451	50	r	r	NOUN
ejpam-5016	451	51	,	,	PUNCT
ejpam-5016	451	52	q	q	NOUN
ejpam-5016	451	53	are	be	AUX
ejpam-5016	451	54	not	not	PART
ejpam-5016	451	55	the	the	DET
ejpam-5016	451	56	vertices	vertex	NOUN
ejpam-5016	451	57	of	of	ADP
ejpam-5016	451	58	a.	a.	NOUN
ejpam-5016	451	59	in	in	ADP
ejpam-5016	451	60	both	both	DET
ejpam-5016	451	61	cases	case	NOUN
ejpam-5016	451	62	,	,	PUNCT
ejpam-5016	451	63	we	we	PRON
ejpam-5016	451	64	conclude	conclude	VERB
ejpam-5016	451	65	that	that	SCONJ
ejpam-5016	451	66	f	f	PROPN
ejpam-5016	451	67	∈	∈	PROPN
ejpam-5016	451	68	jp	jp	NOUN
ejpam-5016	451	69	.	.	PUNCT
ejpam-5016	452	1	now	now	ADV
ejpam-5016	452	2	,	,	PUNCT
ejpam-5016	452	3	it	it	PRON
ejpam-5016	452	4	remains	remain	VERB
ejpam-5016	452	5	to	to	PART
ejpam-5016	452	6	prove	prove	VERB
ejpam-5016	452	7	that	that	SCONJ
ejpam-5016	452	8	jp	jp	NOUN
ejpam-5016	453	1	⊆	⊆	NUM
ejpam-5016	453	2	ip	ip	NOUN
ejpam-5016	453	3	.	.	PUNCT
ejpam-5016	454	1	we	we	PRON
ejpam-5016	454	2	will	will	AUX
ejpam-5016	454	3	prove	prove	VERB
ejpam-5016	454	4	this	this	PRON
ejpam-5016	454	5	by	by	ADP
ejpam-5016	454	6	showing	show	VERB
ejpam-5016	454	7	that	that	SCONJ
ejpam-5016	454	8	every	every	DET
ejpam-5016	454	9	binomial	binomial	NOUN
ejpam-5016	454	10	of	of	ADP
ejpam-5016	454	11	degree	degree	NOUN
ejpam-5016	454	12	two	two	NUM
ejpam-5016	454	13	in	in	ADP
ejpam-5016	454	14	jp	jp	NOUN
ejpam-5016	454	15	belongs	belong	VERB
ejpam-5016	454	16	to	to	ADP
ejpam-5016	454	17	ip	ip	NOUN
ejpam-5016	454	18	and	and	CCONJ
ejpam-5016	454	19	every	every	DET
ejpam-5016	454	20	irredundant	irredundant	ADJ
ejpam-5016	454	21	binomial	binomial	NOUN
ejpam-5016	454	22	in	in	ADP
ejpam-5016	454	23	jp	jp	NOUN
ejpam-5016	454	24	is	be	AUX
ejpam-5016	454	25	of	of	ADP
ejpam-5016	454	26	degree	degree	NOUN
ejpam-5016	454	27	two	two	NUM
ejpam-5016	454	28	(	(	PUNCT
ejpam-5016	454	29	or	or	CCONJ
ejpam-5016	454	30	for	for	ADP
ejpam-5016	454	31	some	some	DET
ejpam-5016	454	32	cases	case	NOUN
ejpam-5016	454	33	,	,	PUNCT
ejpam-5016	454	34	it	it	PRON
ejpam-5016	454	35	is	be	AUX
ejpam-5016	454	36	in	in	ADP
ejpam-5016	454	37	ip	ip	NOUN
ejpam-5016	454	38	)	)	PUNCT
ejpam-5016	454	39	.	.	PUNCT
ejpam-5016	455	1	for	for	ADP
ejpam-5016	455	2	the	the	DET
ejpam-5016	455	3	first	first	ADJ
ejpam-5016	455	4	part	part	NOUN
ejpam-5016	455	5	,	,	PUNCT
ejpam-5016	455	6	let	let	VERB
ejpam-5016	455	7	f	f	PROPN
ejpam-5016	455	8	=	=	SYM
ejpam-5016	455	9	xpxq	xpxq	PROPN
ejpam-5016	455	10	−	−	PROPN
ejpam-5016	455	11	xrxs	xrxs	ADJ
ejpam-5016	455	12	be	be	VERB
ejpam-5016	455	13	a	a	DET
ejpam-5016	455	14	binomial	binomial	NOUN
ejpam-5016	455	15	in	in	ADP
ejpam-5016	455	16	jp	jp	NOUN
ejpam-5016	455	17	.	.	PUNCT
ejpam-5016	456	1	if	if	SCONJ
ejpam-5016	456	2	p	p	X
ejpam-5016	456	3	,	,	PUNCT
ejpam-5016	456	4	q	q	X
ejpam-5016	456	5	are	be	AUX
ejpam-5016	456	6	in	in	ADP
ejpam-5016	456	7	horizontal	horizontal	ADJ
ejpam-5016	456	8	or	or	CCONJ
ejpam-5016	456	9	vertical	vertical	ADJ
ejpam-5016	456	10	position	position	NOUN
ejpam-5016	456	11	,	,	PUNCT
ejpam-5016	456	12	since	since	SCONJ
ejpam-5016	456	13	ϕ(f	ϕ(f	PRON
ejpam-5016	456	14	)	)	PUNCT
ejpam-5016	457	1	=	=	SYM
ejpam-5016	457	2	0	0	PUNCT
ejpam-5016	458	1	then	then	ADV
ejpam-5016	458	2	we	we	PRON
ejpam-5016	458	3	can	can	AUX
ejpam-5016	458	4	easily	easily	ADV
ejpam-5016	458	5	argue	argue	VERB
ejpam-5016	458	6	that	that	SCONJ
ejpam-5016	458	7	{	{	PUNCT
ejpam-5016	458	8	p	p	X
ejpam-5016	458	9	,	,	PUNCT
ejpam-5016	458	10	q	q	NOUN
ejpam-5016	458	11	}	}	PUNCT
ejpam-5016	458	12	=	=	SYM
ejpam-5016	458	13	{	{	PUNCT
ejpam-5016	458	14	r	r	NOUN
ejpam-5016	458	15	,	,	PUNCT
ejpam-5016	458	16	s	s	PART
ejpam-5016	458	17	}	}	PUNCT
ejpam-5016	458	18	and	and	CCONJ
ejpam-5016	458	19	f	f	X
ejpam-5016	458	20	=	=	SYM
ejpam-5016	458	21	0	0	NUM
ejpam-5016	458	22	∈	∈	NOUN
ejpam-5016	458	23	ip	ip	NOUN
ejpam-5016	458	24	.	.	PUNCT
ejpam-5016	459	1	we	we	PRON
ejpam-5016	459	2	consider	consider	VERB
ejpam-5016	459	3	the	the	DET
ejpam-5016	459	4	case	case	NOUN
ejpam-5016	459	5	p	p	X
ejpam-5016	459	6	,	,	PUNCT
ejpam-5016	459	7	q	q	X
ejpam-5016	459	8	are	be	AUX
ejpam-5016	459	9	the	the	DET
ejpam-5016	459	10	diagonal	diagonal	ADJ
ejpam-5016	459	11	corners	corner	NOUN
ejpam-5016	459	12	of	of	ADP
ejpam-5016	459	13	an	an	DET
ejpam-5016	459	14	interval	interval	NOUN
ejpam-5016	459	15	(	(	PUNCT
ejpam-5016	459	16	the	the	DET
ejpam-5016	459	17	case	case	NOUN
ejpam-5016	459	18	p	p	X
ejpam-5016	459	19	,	,	PUNCT
ejpam-5016	459	20	q	q	X
ejpam-5016	459	21	are	be	AUX
ejpam-5016	459	22	the	the	DET
ejpam-5016	459	23	antidiagonal	antidiagonal	ADJ
ejpam-5016	459	24	corners	corner	NOUN
ejpam-5016	459	25	can	can	AUX
ejpam-5016	459	26	be	be	AUX
ejpam-5016	459	27	done	do	VERB
ejpam-5016	459	28	similarly	similarly	ADV
ejpam-5016	459	29	)	)	PUNCT
ejpam-5016	459	30	.	.	PUNCT
ejpam-5016	460	1	let	let	VERB
ejpam-5016	460	2	vp	vp	PROPN
ejpam-5016	460	3	and	and	CCONJ
ejpam-5016	460	4	hp	hp	PROPN
ejpam-5016	460	5	be	be	VERB
ejpam-5016	460	6	the	the	DET
ejpam-5016	460	7	variables	variable	NOUN
ejpam-5016	460	8	associated	associate	VERB
ejpam-5016	460	9	to	to	ADP
ejpam-5016	460	10	the	the	DET
ejpam-5016	460	11	maximal	maximal	ADJ
ejpam-5016	460	12	vertical	vertical	ADJ
ejpam-5016	460	13	and	and	CCONJ
ejpam-5016	460	14	horizontal	horizontal	ADJ
ejpam-5016	460	15	edge	edge	NOUN
ejpam-5016	460	16	intervals	interval	NOUN
ejpam-5016	460	17	that	that	PRON
ejpam-5016	460	18	contain	contain	VERB
ejpam-5016	460	19	p	p	PRON
ejpam-5016	460	20	,	,	PUNCT
ejpam-5016	460	21	respectively	respectively	ADV
ejpam-5016	460	22	.	.	PUNCT
ejpam-5016	461	1	we	we	PRON
ejpam-5016	461	2	define	define	VERB
ejpam-5016	461	3	vq	vq	PROPN
ejpam-5016	461	4	,	,	PUNCT
ejpam-5016	461	5	vr	vr	NOUN
ejpam-5016	461	6	,	,	PUNCT
ejpam-5016	461	7	vs	vs	ADP
ejpam-5016	461	8	,	,	PUNCT
ejpam-5016	461	9	hq	hq	NOUN
ejpam-5016	461	10	,	,	PUNCT
ejpam-5016	461	11	hr	hr	PROPN
ejpam-5016	461	12	,	,	PUNCT
ejpam-5016	461	13	hs	hs	X
ejpam-5016	461	14	similarly	similarly	ADV
ejpam-5016	461	15	.	.	PUNCT
ejpam-5016	462	1	we	we	PRON
ejpam-5016	462	2	will	will	AUX
ejpam-5016	462	3	prove	prove	VERB
ejpam-5016	462	4	that	that	SCONJ
ejpam-5016	462	5	r	r	NOUN
ejpam-5016	462	6	,	,	PUNCT
ejpam-5016	462	7	s	s	VERB
ejpam-5016	462	8	are	be	AUX
ejpam-5016	462	9	the	the	DET
ejpam-5016	462	10	antidiagonal	antidiagonal	ADJ
ejpam-5016	462	11	corners	corner	NOUN
ejpam-5016	462	12	of	of	ADP
ejpam-5016	462	13	[	[	X
ejpam-5016	462	14	p	p	X
ejpam-5016	462	15	,	,	PUNCT
ejpam-5016	462	16	q	q	X
ejpam-5016	462	17	]	]	PUNCT
ejpam-5016	462	18	and	and	CCONJ
ejpam-5016	462	19	argue	argue	VERB
ejpam-5016	462	20	that	that	SCONJ
ejpam-5016	462	21	f	f	PROPN
ejpam-5016	462	22	∈	∈	PROPN
ejpam-5016	462	23	ip	ip	VERB
ejpam-5016	462	24	.	.	PUNCT
ejpam-5016	463	1	we	we	PRON
ejpam-5016	463	2	divide	divide	VERB
ejpam-5016	463	3	into	into	ADP
ejpam-5016	463	4	three	three	NUM
ejpam-5016	463	5	cases	case	NOUN
ejpam-5016	463	6	:	:	PUNCT
ejpam-5016	463	7	•	•	ADP
ejpam-5016	463	8	if	if	SCONJ
ejpam-5016	463	9	p	p	X
ejpam-5016	463	10	,	,	PUNCT
ejpam-5016	463	11	q	q	PROPN
ejpam-5016	463	12	∈	∈	PROPN
ejpam-5016	463	13	a.	a.	NOUN
ejpam-5016	463	14	since	since	SCONJ
ejpam-5016	463	15	ϕ(xpxq	ϕ(xpxq	NOUN
ejpam-5016	463	16	)	)	PUNCT
ejpam-5016	464	1	=	=	VERB
ejpam-5016	464	2	vpvqhphqw	vpvqhphqw	NOUN
ejpam-5016	464	3	2	2	NUM
ejpam-5016	464	4	then	then	ADV
ejpam-5016	464	5	w2	w2	NOUN
ejpam-5016	464	6	divides	divide	VERB
ejpam-5016	464	7	ϕ(xrxs	ϕ(xrx	NOUN
ejpam-5016	464	8	)	)	PUNCT
ejpam-5016	464	9	.	.	PUNCT
ejpam-5016	465	1	thus	thus	ADV
ejpam-5016	465	2	,	,	PUNCT
ejpam-5016	465	3	r	r	NOUN
ejpam-5016	465	4	,	,	PUNCT
ejpam-5016	465	5	s	s	NOUN
ejpam-5016	465	6	∈	∈	NOUN
ejpam-5016	465	7	a.	a.	NOUN
ejpam-5016	465	8	if	if	SCONJ
ejpam-5016	465	9	r	r	NOUN
ejpam-5016	465	10	=	=	PUNCT
ejpam-5016	465	11	p	p	NOUN
ejpam-5016	465	12	or	or	CCONJ
ejpam-5016	465	13	r	r	NOUN
ejpam-5016	465	14	=	=	SYM
ejpam-5016	465	15	q	q	NOUN
ejpam-5016	466	1	then	then	ADV
ejpam-5016	466	2	{	{	PUNCT
ejpam-5016	466	3	r	r	NOUN
ejpam-5016	466	4	,	,	PUNCT
ejpam-5016	466	5	s	s	NOUN
ejpam-5016	466	6	}	}	PUNCT
ejpam-5016	466	7	=	=	SYM
ejpam-5016	466	8	{	{	PUNCT
ejpam-5016	466	9	p	p	X
ejpam-5016	466	10	,	,	PUNCT
ejpam-5016	466	11	q	q	NOUN
ejpam-5016	466	12	}	}	PUNCT
ejpam-5016	466	13	and	and	CCONJ
ejpam-5016	466	14	f	f	X
ejpam-5016	466	15	=	=	SYM
ejpam-5016	466	16	0	0	NUM
ejpam-5016	466	17	∈	∈	NOUN
ejpam-5016	466	18	ip	ip	NOUN
ejpam-5016	466	19	.	.	PUNCT
ejpam-5016	467	1	therefore	therefore	ADV
ejpam-5016	467	2	r	r	NOUN
ejpam-5016	467	3	is	be	AUX
ejpam-5016	467	4	an	an	DET
ejpam-5016	467	5	antidiagonal	antidiagonal	ADJ
ejpam-5016	467	6	corner	corner	NOUN
ejpam-5016	467	7	of	of	ADP
ejpam-5016	467	8	[	[	X
ejpam-5016	467	9	p	p	X
ejpam-5016	467	10	,	,	PUNCT
ejpam-5016	467	11	q	q	X
ejpam-5016	467	12	]	]	X
ejpam-5016	467	13	.	.	PUNCT
ejpam-5016	468	1	if	if	SCONJ
ejpam-5016	468	2	ϕ(xr	ϕ(xr	PRON
ejpam-5016	468	3	)	)	PUNCT
ejpam-5016	469	1	=	=	NOUN
ejpam-5016	469	2	vphqw	vphqw	NOUN
ejpam-5016	469	3	then	then	ADV
ejpam-5016	469	4	ϕ(xs	ϕ(x	NOUN
ejpam-5016	469	5	)	)	PUNCT
ejpam-5016	469	6	=	=	SYM
ejpam-5016	469	7	vqhpw	vqhpw	NOUN
ejpam-5016	469	8	and	and	CCONJ
ejpam-5016	469	9	s	s	NOUN
ejpam-5016	469	10	is	be	AUX
ejpam-5016	469	11	also	also	ADV
ejpam-5016	469	12	an	an	DET
ejpam-5016	469	13	antidiagoal	antidiagoal	NOUN
ejpam-5016	469	14	corner	corner	NOUN
ejpam-5016	469	15	of	of	ADP
ejpam-5016	469	16	[	[	X
ejpam-5016	469	17	p	p	X
ejpam-5016	469	18	,	,	PUNCT
ejpam-5016	469	19	q	q	X
ejpam-5016	469	20	]	]	X
ejpam-5016	469	21	.	.	PUNCT
ejpam-5016	470	1	the	the	DET
ejpam-5016	470	2	same	same	ADJ
ejpam-5016	470	3	conclusion	conclusion	NOUN
ejpam-5016	470	4	for	for	ADP
ejpam-5016	470	5	ϕ(xr	ϕ(xr	PRON
ejpam-5016	470	6	)	)	PUNCT
ejpam-5016	471	1	=	=	SYM
ejpam-5016	471	2	vqhpw	vqhpw	NOUN
ejpam-5016	471	3	.	.	PUNCT
ejpam-5016	472	1	clearly	clearly	ADV
ejpam-5016	472	2	,	,	PUNCT
ejpam-5016	472	3	[	[	X
ejpam-5016	472	4	p	p	X
ejpam-5016	472	5	,	,	PUNCT
ejpam-5016	472	6	q	q	X
ejpam-5016	472	7	]	]	X
ejpam-5016	472	8	=	=	PUNCT
ejpam-5016	473	1	[	[	X
ejpam-5016	473	2	3	3	NUM
ejpam-5016	473	3	,	,	PUNCT
ejpam-5016	473	4	n+8	n+8	NUM
ejpam-5016	473	5	]	]	PUNCT
ejpam-5016	473	6	is	be	AUX
ejpam-5016	473	7	an	an	DET
ejpam-5016	473	8	inner	inner	ADJ
ejpam-5016	473	9	interval	interval	NOUN
ejpam-5016	473	10	and	and	CCONJ
ejpam-5016	473	11	thus	thus	ADV
ejpam-5016	473	12	f	f	PROPN
ejpam-5016	473	13	∈	∈	PROPN
ejpam-5016	473	14	ip	ip	VERB
ejpam-5016	473	15	.	.	PUNCT
ejpam-5016	474	1	y.	y.	PROPN
ejpam-5016	474	2	y.	y.	PROPN
ejpam-5016	474	3	hamonangan	hamonangan	PROPN
ejpam-5016	474	4	,	,	PUNCT
ejpam-5016	474	5	i.	i.	PROPN
ejpam-5016	474	6	muchtadi	muchtadi	PROPN
ejpam-5016	474	7	-	-	PUNCT
ejpam-5016	474	8	alamsyah	alamsyah	NOUN
ejpam-5016	474	9	/	/	SYM
ejpam-5016	474	10	eur	eur	PROPN
ejpam-5016	474	11	.	.	PUNCT
ejpam-5016	475	1	j.	j.	PROPN
ejpam-5016	475	2	pure	pure	PROPN
ejpam-5016	475	3	appl	appl	PROPN
ejpam-5016	475	4	.	.	PROPN
ejpam-5016	475	5	math	math	PROPN
ejpam-5016	475	6	,	,	PUNCT
ejpam-5016	475	7	17	17	NUM
ejpam-5016	475	8	(	(	PUNCT
ejpam-5016	475	9	4	4	NUM
ejpam-5016	475	10	)	)	PUNCT
ejpam-5016	475	11	(	(	PUNCT
ejpam-5016	475	12	2024	2024	NUM
ejpam-5016	475	13	)	)	PUNCT
ejpam-5016	475	14	,	,	PUNCT
ejpam-5016	475	15	2621	2621	NUM
ejpam-5016	475	16	-	-	SYM
ejpam-5016	475	17	2650	2650	NUM
ejpam-5016	475	18	2644	2644	NUM
ejpam-5016	475	19	•	•	NOUN
ejpam-5016	475	20	if	if	SCONJ
ejpam-5016	475	21	exactly	exactly	ADV
ejpam-5016	475	22	one	one	NUM
ejpam-5016	475	23	of	of	ADP
ejpam-5016	475	24	p	p	NOUN
ejpam-5016	475	25	,	,	PUNCT
ejpam-5016	475	26	q	q	PROPN
ejpam-5016	475	27	belongs	belong	VERB
ejpam-5016	475	28	to	to	ADP
ejpam-5016	475	29	a.	a.	NOUN
ejpam-5016	475	30	we	we	PRON
ejpam-5016	475	31	consider	consider	VERB
ejpam-5016	475	32	the	the	DET
ejpam-5016	475	33	case	case	NOUN
ejpam-5016	475	34	p	p	X
ejpam-5016	475	35	∈	∈	PROPN
ejpam-5016	475	36	a.	a.	NOUN
ejpam-5016	475	37	by	by	ADP
ejpam-5016	475	38	the	the	DET
ejpam-5016	475	39	construction	construction	NOUN
ejpam-5016	475	40	of	of	ADP
ejpam-5016	475	41	p	p	PRON
ejpam-5016	475	42	,	,	PUNCT
ejpam-5016	475	43	we	we	PRON
ejpam-5016	475	44	have	have	VERB
ejpam-5016	475	45	p	p	NOUN
ejpam-5016	475	46	∈	∈	PROPN
ejpam-5016	475	47	{	{	PUNCT
ejpam-5016	475	48	3	3	NUM
ejpam-5016	475	49	,	,	PUNCT
ejpam-5016	475	50	7	7	NUM
ejpam-5016	475	51	+	+	CCONJ
ejpam-5016	475	52	n	n	CCONJ
ejpam-5016	475	53	}	}	PUNCT
ejpam-5016	475	54	and	and	CCONJ
ejpam-5016	475	55	q	q	PROPN
ejpam-5016	475	56	∈	∈	PROPN
ejpam-5016	475	57	{	{	PUNCT
ejpam-5016	475	58	12	12	NUM
ejpam-5016	475	59	+	+	NUM
ejpam-5016	475	60	2n	2n	NUM
ejpam-5016	475	61	,	,	PUNCT
ejpam-5016	475	62	16	16	NUM
ejpam-5016	475	63	+	+	NUM
ejpam-5016	475	64	2n	2n	NUM
ejpam-5016	475	65	}	}	PUNCT
ejpam-5016	475	66	.	.	PUNCT
ejpam-5016	476	1	since	since	SCONJ
ejpam-5016	476	2	w	w	PROPN
ejpam-5016	476	3	divides	divide	NOUN
ejpam-5016	476	4	ϕ(xp	ϕ(xp	NOUN
ejpam-5016	476	5	)	)	PUNCT
ejpam-5016	476	6	then	then	ADV
ejpam-5016	476	7	r	r	NOUN
ejpam-5016	476	8	∈	∈	PROPN
ejpam-5016	476	9	a	a	DET
ejpam-5016	476	10	or	or	CCONJ
ejpam-5016	476	11	s	s	NOUN
ejpam-5016	476	12	∈	∈	NOUN
ejpam-5016	476	13	a.	a.	NOUN
ejpam-5016	476	14	we	we	PRON
ejpam-5016	476	15	may	may	AUX
ejpam-5016	476	16	assume	assume	VERB
ejpam-5016	476	17	that	that	SCONJ
ejpam-5016	476	18	r	r	NOUN
ejpam-5016	476	19	∈	∈	PROPN
ejpam-5016	476	20	a.	a.	NOUN
ejpam-5016	476	21	if	if	SCONJ
ejpam-5016	476	22	r	r	NOUN
ejpam-5016	476	23	=	=	PUNCT
ejpam-5016	476	24	p	p	X
ejpam-5016	476	25	then	then	ADV
ejpam-5016	476	26	s	s	VERB
ejpam-5016	476	27	=	=	X
ejpam-5016	476	28	q	q	X
ejpam-5016	476	29	and	and	CCONJ
ejpam-5016	476	30	f	f	X
ejpam-5016	477	1	=	=	SYM
ejpam-5016	477	2	0	0	NUM
ejpam-5016	477	3	∈	∈	NOUN
ejpam-5016	477	4	ip	ip	NOUN
ejpam-5016	477	5	.	.	PUNCT
ejpam-5016	478	1	if	if	SCONJ
ejpam-5016	478	2	p	p	X
ejpam-5016	478	3	,	,	PUNCT
ejpam-5016	478	4	r	r	NOUN
ejpam-5016	478	5	are	be	AUX
ejpam-5016	478	6	not	not	PART
ejpam-5016	478	7	in	in	ADP
ejpam-5016	478	8	horizontal	horizontal	ADJ
ejpam-5016	478	9	position	position	NOUN
ejpam-5016	478	10	then	then	ADV
ejpam-5016	478	11	hr	hr	NOUN
ejpam-5016	478	12	contains	contain	VERB
ejpam-5016	478	13	an	an	DET
ejpam-5016	478	14	edge	edge	NOUN
ejpam-5016	478	15	of	of	ADP
ejpam-5016	478	16	a	a	DET
ejpam-5016	478	17	but	but	CCONJ
ejpam-5016	478	18	hp	hp	PROPN
ejpam-5016	478	19	̸=	̸=	PROPN
ejpam-5016	478	20	hr	hr	NOUN
ejpam-5016	478	21	and	and	CCONJ
ejpam-5016	478	22	hq	hq	NOUN
ejpam-5016	478	23	does	do	AUX
ejpam-5016	478	24	not	not	PART
ejpam-5016	478	25	contain	contain	VERB
ejpam-5016	478	26	any	any	DET
ejpam-5016	478	27	edge	edge	NOUN
ejpam-5016	478	28	of	of	ADP
ejpam-5016	478	29	a.	a.	NOUN
ejpam-5016	478	30	therefore	therefore	ADV
ejpam-5016	478	31	hr	hr	NOUN
ejpam-5016	478	32	divides	divide	VERB
ejpam-5016	478	33	ϕ(xrxs	ϕ(xrx	NOUN
ejpam-5016	478	34	)	)	PUNCT
ejpam-5016	478	35	but	but	CCONJ
ejpam-5016	478	36	does	do	AUX
ejpam-5016	478	37	not	not	PART
ejpam-5016	478	38	divide	divide	VERB
ejpam-5016	478	39	ϕ(xpxq	ϕ(xpxq	NOUN
ejpam-5016	478	40	)	)	PUNCT
ejpam-5016	478	41	,	,	PUNCT
ejpam-5016	478	42	a	a	DET
ejpam-5016	478	43	contradiction	contradiction	NOUN
ejpam-5016	478	44	.	.	PUNCT
ejpam-5016	479	1	now	now	ADV
ejpam-5016	479	2	,	,	PUNCT
ejpam-5016	479	3	p	p	X
ejpam-5016	479	4	,	,	PUNCT
ejpam-5016	479	5	r	r	NOUN
ejpam-5016	479	6	are	be	AUX
ejpam-5016	479	7	in	in	ADP
ejpam-5016	479	8	horizontal	horizontal	ADJ
ejpam-5016	479	9	position	position	NOUN
ejpam-5016	479	10	.	.	PUNCT
ejpam-5016	480	1	by	by	ADP
ejpam-5016	480	2	the	the	DET
ejpam-5016	480	3	construction	construction	NOUN
ejpam-5016	480	4	of	of	ADP
ejpam-5016	480	5	p	p	PRON
ejpam-5016	480	6	,	,	PUNCT
ejpam-5016	480	7	we	we	PRON
ejpam-5016	480	8	conclude	conclude	VERB
ejpam-5016	480	9	that	that	SCONJ
ejpam-5016	480	10	r	r	NOUN
ejpam-5016	480	11	,	,	PUNCT
ejpam-5016	480	12	q	q	NOUN
ejpam-5016	480	13	are	be	AUX
ejpam-5016	480	14	in	in	ADP
ejpam-5016	480	15	vertical	vertical	ADJ
ejpam-5016	480	16	position	position	NOUN
ejpam-5016	480	17	.	.	PUNCT
ejpam-5016	481	1	thus	thus	ADV
ejpam-5016	481	2	,	,	PUNCT
ejpam-5016	481	3	ϕ(xs	ϕ(xs	PRON
ejpam-5016	481	4	)	)	PUNCT
ejpam-5016	481	5	=	=	SYM
ejpam-5016	481	6	vphq	vphq	NOUN
ejpam-5016	481	7	and	and	CCONJ
ejpam-5016	481	8	therefore	therefore	ADV
ejpam-5016	481	9	r	r	NOUN
ejpam-5016	481	10	,	,	PUNCT
ejpam-5016	481	11	s	s	VERB
ejpam-5016	481	12	are	be	AUX
ejpam-5016	481	13	the	the	DET
ejpam-5016	481	14	antidiagonal	antidiagonal	ADJ
ejpam-5016	481	15	corners	corner	NOUN
ejpam-5016	481	16	of	of	ADP
ejpam-5016	481	17	[	[	X
ejpam-5016	481	18	p	p	X
ejpam-5016	481	19	,	,	PUNCT
ejpam-5016	481	20	q	q	X
ejpam-5016	481	21	]	]	X
ejpam-5016	481	22	.	.	PUNCT
ejpam-5016	482	1	since	since	SCONJ
ejpam-5016	482	2	p	p	PROPN
ejpam-5016	482	3	∈	∈	PROPN
ejpam-5016	482	4	{	{	PUNCT
ejpam-5016	482	5	3	3	NUM
ejpam-5016	482	6	,	,	PUNCT
ejpam-5016	482	7	7	7	NUM
ejpam-5016	482	8	+	+	CCONJ
ejpam-5016	482	9	n	n	CCONJ
ejpam-5016	482	10	}	}	PUNCT
ejpam-5016	482	11	and	and	CCONJ
ejpam-5016	482	12	q	q	PROPN
ejpam-5016	482	13	∈	∈	PROPN
ejpam-5016	482	14	{	{	PUNCT
ejpam-5016	482	15	12	12	NUM
ejpam-5016	482	16	+	+	NUM
ejpam-5016	482	17	2n	2n	NUM
ejpam-5016	482	18	,	,	PUNCT
ejpam-5016	482	19	16	16	NUM
ejpam-5016	482	20	+	+	SYM
ejpam-5016	482	21	2n	2n	NUM
ejpam-5016	482	22	}	}	PUNCT
ejpam-5016	482	23	then	then	ADV
ejpam-5016	482	24	[	[	X
ejpam-5016	482	25	p	p	X
ejpam-5016	482	26	,	,	PUNCT
ejpam-5016	482	27	q	q	X
ejpam-5016	482	28	]	]	X
ejpam-5016	482	29	is	be	AUX
ejpam-5016	482	30	an	an	DET
ejpam-5016	482	31	inner	inner	ADJ
ejpam-5016	482	32	interval	interval	NOUN
ejpam-5016	482	33	and	and	CCONJ
ejpam-5016	482	34	thus	thus	ADV
ejpam-5016	482	35	f	f	PROPN
ejpam-5016	482	36	∈	∈	PROPN
ejpam-5016	482	37	ip	ip	VERB
ejpam-5016	482	38	.	.	PUNCT
ejpam-5016	483	1	the	the	DET
ejpam-5016	483	2	case	case	NOUN
ejpam-5016	483	3	q	q	X
ejpam-5016	483	4	∈	∈	PROPN
ejpam-5016	483	5	a	a	PRON
ejpam-5016	483	6	is	be	AUX
ejpam-5016	483	7	also	also	ADV
ejpam-5016	483	8	true	true	ADJ
ejpam-5016	483	9	by	by	ADP
ejpam-5016	483	10	symmetry	symmetry	NOUN
ejpam-5016	483	11	.	.	PUNCT
ejpam-5016	484	1	•	•	INTJ
ejpam-5016	484	2	if	if	SCONJ
ejpam-5016	484	3	both	both	PRON
ejpam-5016	484	4	p	p	X
ejpam-5016	484	5	,	,	PUNCT
ejpam-5016	484	6	q	q	X
ejpam-5016	484	7	do	do	AUX
ejpam-5016	484	8	not	not	PART
ejpam-5016	484	9	belong	belong	VERB
ejpam-5016	484	10	to	to	ADP
ejpam-5016	484	11	a.	a.	NOUN
ejpam-5016	484	12	similarly	similarly	ADV
ejpam-5016	484	13	,	,	PUNCT
ejpam-5016	484	14	we	we	PRON
ejpam-5016	484	15	have	have	AUX
ejpam-5016	484	16	that	that	DET
ejpam-5016	484	17	f	f	PROPN
ejpam-5016	484	18	=	=	SYM
ejpam-5016	484	19	0	0	NUM
ejpam-5016	484	20	∈	∈	PROPN
ejpam-5016	484	21	ip	ip	NOUN
ejpam-5016	484	22	or	or	CCONJ
ejpam-5016	484	23	r	r	NOUN
ejpam-5016	484	24	,	,	PUNCT
ejpam-5016	484	25	s	s	VERB
ejpam-5016	484	26	are	be	AUX
ejpam-5016	484	27	the	the	DET
ejpam-5016	484	28	antidiagonal	antidiagonal	ADJ
ejpam-5016	484	29	corners	corner	NOUN
ejpam-5016	484	30	of	of	ADP
ejpam-5016	484	31	[	[	X
ejpam-5016	484	32	p	p	X
ejpam-5016	484	33	,	,	PUNCT
ejpam-5016	484	34	q	q	X
ejpam-5016	484	35	]	]	X
ejpam-5016	484	36	.	.	PUNCT
ejpam-5016	485	1	let	let	VERB
ejpam-5016	485	2	p	p	PRON
ejpam-5016	485	3	′	′	NOUN
ejpam-5016	485	4	be	be	AUX
ejpam-5016	485	5	a	a	DET
ejpam-5016	485	6	polyomino	polyomino	NOUN
ejpam-5016	485	7	obtained	obtain	VERB
ejpam-5016	485	8	by	by	ADP
ejpam-5016	485	9	removing	remove	VERB
ejpam-5016	485	10	the	the	DET
ejpam-5016	485	11	cells	cell	NOUN
ejpam-5016	485	12	that	that	PRON
ejpam-5016	485	13	has	have	VERB
ejpam-5016	485	14	common	common	ADJ
ejpam-5016	485	15	vertices	vertex	NOUN
ejpam-5016	485	16	with	with	ADP
ejpam-5016	485	17	a.	a.	NOUN
ejpam-5016	485	18	note	note	NOUN
ejpam-5016	485	19	that	that	SCONJ
ejpam-5016	485	20	p	p	ADJ
ejpam-5016	485	21	′	′	NOUN
ejpam-5016	485	22	is	be	AUX
ejpam-5016	485	23	a	a	DET
ejpam-5016	485	24	simple	simple	ADJ
ejpam-5016	485	25	polyomino	polyomino	NOUN
ejpam-5016	485	26	.	.	PUNCT
ejpam-5016	486	1	let	let	VERB
ejpam-5016	486	2	ϕ′	ϕ′	NOUN
ejpam-5016	486	3	be	be	AUX
ejpam-5016	486	4	the	the	DET
ejpam-5016	486	5	restriction	restriction	NOUN
ejpam-5016	486	6	of	of	ADP
ejpam-5016	486	7	ϕ	ϕ	NOUN
ejpam-5016	486	8	onk[xa	onk[xa	NOUN
ejpam-5016	486	9	:	:	PUNCT
ejpam-5016	486	10	a	a	DET
ejpam-5016	486	11	∈	∈	PROPN
ejpam-5016	486	12	v	v	NOUN
ejpam-5016	486	13	(	(	PUNCT
ejpam-5016	486	14	p)\a	p)\a	NOUN
ejpam-5016	486	15	]	]	PUNCT
ejpam-5016	486	16	and	and	CCONJ
ejpam-5016	486	17	jp	jp	INTJ
ejpam-5016	486	18	′	′	NUM
ejpam-5016	486	19	be	be	AUX
ejpam-5016	486	20	the	the	DET
ejpam-5016	486	21	kernel	kernel	NOUN
ejpam-5016	486	22	of	of	ADP
ejpam-5016	486	23	ϕ′.	ϕ′.	PROPN
ejpam-5016	486	24	note	note	VERB
ejpam-5016	486	25	that	that	SCONJ
ejpam-5016	486	26	f	f	PROPN
ejpam-5016	486	27	∈	∈	PROPN
ejpam-5016	486	28	jp	jp	NOUN
ejpam-5016	486	29	′	′	NUM
ejpam-5016	486	30	by	by	ADP
ejpam-5016	486	31	[	[	X
ejpam-5016	486	32	36	36	NUM
ejpam-5016	486	33	,	,	PUNCT
ejpam-5016	486	34	theorem	theorem	VERB
ejpam-5016	486	35	2.2	2.2	NUM
ejpam-5016	486	36	]	]	PUNCT
ejpam-5016	486	37	,	,	PUNCT
ejpam-5016	486	38	we	we	PRON
ejpam-5016	486	39	have	have	VERB
ejpam-5016	486	40	that	that	PRON
ejpam-5016	486	41	ip	ip	NOUN
ejpam-5016	486	42	′	′	NOUN
ejpam-5016	486	43	=	=	PUNCT
ejpam-5016	486	44	jp	jp	NOUN
ejpam-5016	487	1	′	′	NUM
ejpam-5016	487	2	.	.	PUNCT
ejpam-5016	488	1	therefore	therefore	ADV
ejpam-5016	488	2	f	f	PROPN
ejpam-5016	488	3	∈	∈	PROPN
ejpam-5016	488	4	jp	jp	NOUN
ejpam-5016	488	5	′	′	NUM
ejpam-5016	489	1	=	=	PUNCT
ejpam-5016	489	2	ip	ip	PROPN
ejpam-5016	489	3	′	′	NUM
ejpam-5016	489	4	⊂	⊂	NOUN
ejpam-5016	489	5	ip	ip	NOUN
ejpam-5016	489	6	.	.	PUNCT
ejpam-5016	490	1	for	for	ADP
ejpam-5016	490	2	the	the	DET
ejpam-5016	490	3	second	second	ADJ
ejpam-5016	490	4	part	part	NOUN
ejpam-5016	490	5	,	,	PUNCT
ejpam-5016	490	6	let	let	VERB
ejpam-5016	490	7	f	f	PRON
ejpam-5016	490	8	be	be	AUX
ejpam-5016	490	9	an	an	DET
ejpam-5016	490	10	irredundant	irredundant	ADJ
ejpam-5016	490	11	binomial	binomial	NOUN
ejpam-5016	490	12	in	in	ADP
ejpam-5016	490	13	jp	jp	NOUN
ejpam-5016	490	14	.	.	PUNCT
ejpam-5016	491	1	clearly	clearly	ADV
ejpam-5016	491	2	,	,	PUNCT
ejpam-5016	491	3	f	f	PROPN
ejpam-5016	491	4	has	have	VERB
ejpam-5016	491	5	degree	degree	NOUN
ejpam-5016	491	6	at	at	ADV
ejpam-5016	491	7	least	least	ADV
ejpam-5016	491	8	two	two	NUM
ejpam-5016	491	9	.	.	PUNCT
ejpam-5016	492	1	suppose	suppose	VERB
ejpam-5016	492	2	that	that	SCONJ
ejpam-5016	492	3	f	f	PROPN
ejpam-5016	492	4	has	have	VERB
ejpam-5016	492	5	degree	degree	NOUN
ejpam-5016	492	6	at	at	ADV
ejpam-5016	492	7	least	least	ADV
ejpam-5016	492	8	three	three	NUM
ejpam-5016	492	9	and	and	CCONJ
ejpam-5016	492	10	choose	choose	VERB
ejpam-5016	492	11	f	f	PROPN
ejpam-5016	492	12	with	with	ADP
ejpam-5016	492	13	the	the	DET
ejpam-5016	492	14	least	least	ADJ
ejpam-5016	492	15	degree	degree	NOUN
ejpam-5016	492	16	.	.	PUNCT
ejpam-5016	493	1	suppose	suppose	VERB
ejpam-5016	493	2	that	that	SCONJ
ejpam-5016	493	3	every	every	DET
ejpam-5016	493	4	variable	variable	NOUN
ejpam-5016	493	5	of	of	ADP
ejpam-5016	493	6	f	f	PROPN
ejpam-5016	493	7	is	be	AUX
ejpam-5016	493	8	in	in	ADP
ejpam-5016	493	9	k[xa	k[xa	NOUN
ejpam-5016	493	10	:	:	PUNCT
ejpam-5016	493	11	a	a	DET
ejpam-5016	493	12	∈	∈	PROPN
ejpam-5016	493	13	v	v	NOUN
ejpam-5016	493	14	(	(	PUNCT
ejpam-5016	493	15	p)\a	p)\a	NOUN
ejpam-5016	493	16	]	]	PUNCT
ejpam-5016	493	17	.	.	PUNCT
ejpam-5016	494	1	define	define	VERB
ejpam-5016	494	2	p	p	NOUN
ejpam-5016	494	3	′	′	NOUN
ejpam-5016	494	4	as	as	ADP
ejpam-5016	494	5	the	the	DET
ejpam-5016	494	6	previous	previous	ADJ
ejpam-5016	494	7	case	case	NOUN
ejpam-5016	494	8	then	then	ADV
ejpam-5016	494	9	f	f	PROPN
ejpam-5016	494	10	is	be	AUX
ejpam-5016	494	11	a	a	DET
ejpam-5016	494	12	binomial	binomial	NOUN
ejpam-5016	494	13	in	in	ADP
ejpam-5016	494	14	jp	jp	NOUN
ejpam-5016	494	15	′	′	NUM
ejpam-5016	495	1	and	and	CCONJ
ejpam-5016	495	2	f	f	PROPN
ejpam-5016	495	3	is	be	AUX
ejpam-5016	495	4	irredundant	irredundant	ADJ
ejpam-5016	495	5	in	in	ADP
ejpam-5016	495	6	jp	jp	NOUN
ejpam-5016	495	7	′	′	NUM
ejpam-5016	495	8	.	.	PUNCT
ejpam-5016	496	1	since	since	SCONJ
ejpam-5016	496	2	ip	ip	NOUN
ejpam-5016	496	3	′	′	NOUN
ejpam-5016	496	4	=	=	PUNCT
ejpam-5016	496	5	jp	jp	NOUN
ejpam-5016	497	1	′	′	INTJ
ejpam-5016	497	2	then	then	ADV
ejpam-5016	497	3	f	f	PROPN
ejpam-5016	497	4	is	be	AUX
ejpam-5016	497	5	an	an	DET
ejpam-5016	497	6	irredundant	irredundant	ADJ
ejpam-5016	497	7	binomial	binomial	NOUN
ejpam-5016	497	8	in	in	ADP
ejpam-5016	497	9	ip	ip	NUM
ejpam-5016	497	10	′	′	NUM
ejpam-5016	497	11	which	which	PRON
ejpam-5016	497	12	means	mean	VERB
ejpam-5016	497	13	that	that	SCONJ
ejpam-5016	497	14	f	f	PROPN
ejpam-5016	497	15	must	must	AUX
ejpam-5016	497	16	be	be	AUX
ejpam-5016	497	17	a	a	DET
ejpam-5016	497	18	binomial	binomial	NOUN
ejpam-5016	497	19	of	of	ADP
ejpam-5016	497	20	degree	degree	NOUN
ejpam-5016	497	21	two	two	NUM
ejpam-5016	497	22	,	,	PUNCT
ejpam-5016	497	23	a	a	DET
ejpam-5016	497	24	contradiction	contradiction	NOUN
ejpam-5016	497	25	.	.	PUNCT
ejpam-5016	498	1	now	now	ADV
ejpam-5016	498	2	,	,	PUNCT
ejpam-5016	498	3	suppose	suppose	VERB
ejpam-5016	498	4	that	that	SCONJ
ejpam-5016	498	5	xv1	xv1	PROPN
ejpam-5016	498	6	is	be	AUX
ejpam-5016	498	7	a	a	DET
ejpam-5016	498	8	variable	variable	NOUN
ejpam-5016	498	9	of	of	ADP
ejpam-5016	498	10	f	f	PROPN
ejpam-5016	498	11	with	with	ADP
ejpam-5016	498	12	v1	v1	PROPN
ejpam-5016	498	13	∈	∈	PROPN
ejpam-5016	498	14	a.	a.	NOUN
ejpam-5016	498	15	write	write	NOUN
ejpam-5016	498	16	f	f	PROPN
ejpam-5016	498	17	=	=	SYM
ejpam-5016	498	18	f+	f+	PROPN
ejpam-5016	498	19	−	−	PROPN
ejpam-5016	498	20	f−.	f−.	NOUN
ejpam-5016	498	21	we	we	PRON
ejpam-5016	498	22	may	may	AUX
ejpam-5016	498	23	assume	assume	VERB
ejpam-5016	498	24	that	that	SCONJ
ejpam-5016	498	25	xv1	xv1	PROPN
ejpam-5016	498	26	divides	divide	VERB
ejpam-5016	498	27	f+	f+	NOUN
ejpam-5016	498	28	.	.	PUNCT
ejpam-5016	499	1	if	if	SCONJ
ejpam-5016	499	2	xv1	xv1	PROPN
ejpam-5016	499	3	divides	divide	VERB
ejpam-5016	499	4	f−	f−	PROPN
ejpam-5016	499	5	then	then	ADV
ejpam-5016	499	6	f	f	PROPN
ejpam-5016	499	7	=	=	SYM
ejpam-5016	499	8	xv1(g	xv1(g	PROPN
ejpam-5016	500	1	+	+	CCONJ
ejpam-5016	500	2	−	−	PROPN
ejpam-5016	500	3	g−	g−	PROPN
ejpam-5016	500	4	)	)	PUNCT
ejpam-5016	500	5	.	.	PUNCT
ejpam-5016	501	1	since	since	SCONJ
ejpam-5016	501	2	jp	jp	NOUN
ejpam-5016	501	3	is	be	AUX
ejpam-5016	501	4	prime	prime	ADJ
ejpam-5016	501	5	then	then	ADV
ejpam-5016	501	6	g	g	PROPN
ejpam-5016	501	7	=	=	PUNCT
ejpam-5016	501	8	g+	g+	PROPN
ejpam-5016	501	9	−	−	NOUN
ejpam-5016	501	10	g−	g−	PROPN
ejpam-5016	501	11	∈	∈	NOUN
ejpam-5016	501	12	jp	jp	NOUN
ejpam-5016	501	13	.	.	PUNCT
ejpam-5016	502	1	if	if	SCONJ
ejpam-5016	502	2	the	the	DET
ejpam-5016	502	3	degree	degree	NOUN
ejpam-5016	502	4	of	of	ADP
ejpam-5016	502	5	g	g	PROPN
ejpam-5016	502	6	is	be	AUX
ejpam-5016	502	7	at	at	ADV
ejpam-5016	502	8	least	least	ADJ
ejpam-5016	502	9	three	three	NUM
ejpam-5016	502	10	then	then	ADV
ejpam-5016	502	11	g	g	PROPN
ejpam-5016	502	12	must	must	AUX
ejpam-5016	502	13	be	be	AUX
ejpam-5016	502	14	irredundant	irredundant	ADJ
ejpam-5016	502	15	.	.	PUNCT
ejpam-5016	503	1	but	but	CCONJ
ejpam-5016	503	2	,	,	PUNCT
ejpam-5016	503	3	this	this	PRON
ejpam-5016	503	4	contradict	contradict	VERB
ejpam-5016	503	5	the	the	DET
ejpam-5016	503	6	choice	choice	NOUN
ejpam-5016	503	7	of	of	ADP
ejpam-5016	503	8	f	f	PROPN
ejpam-5016	503	9	.	.	PUNCT
ejpam-5016	504	1	if	if	SCONJ
ejpam-5016	504	2	the	the	DET
ejpam-5016	504	3	degree	degree	NOUN
ejpam-5016	504	4	of	of	ADP
ejpam-5016	504	5	g	g	PROPN
ejpam-5016	504	6	is	be	AUX
ejpam-5016	504	7	two	two	NUM
ejpam-5016	504	8	then	then	ADV
ejpam-5016	504	9	by	by	ADP
ejpam-5016	504	10	the	the	DET
ejpam-5016	504	11	previous	previous	ADJ
ejpam-5016	504	12	part	part	NOUN
ejpam-5016	504	13	,	,	PUNCT
ejpam-5016	504	14	we	we	PRON
ejpam-5016	504	15	conclude	conclude	VERB
ejpam-5016	504	16	that	that	SCONJ
ejpam-5016	504	17	g	g	PROPN
ejpam-5016	504	18	∈	∈	PROPN
ejpam-5016	504	19	ip	ip	NOUN
ejpam-5016	504	20	and	and	CCONJ
ejpam-5016	504	21	f	f	NOUN
ejpam-5016	504	22	=	=	SYM
ejpam-5016	505	1	xv1	xv1	PROPN
ejpam-5016	505	2	g	g	PROPN
ejpam-5016	505	3	∈	∈	PROPN
ejpam-5016	505	4	ip	ip	NOUN
ejpam-5016	505	5	.	.	PUNCT
ejpam-5016	506	1	now	now	ADV
ejpam-5016	506	2	,	,	PUNCT
ejpam-5016	506	3	suppose	suppose	VERB
ejpam-5016	506	4	that	that	SCONJ
ejpam-5016	506	5	xv1	xv1	PROPN
ejpam-5016	506	6	does	do	AUX
ejpam-5016	506	7	not	not	PART
ejpam-5016	506	8	divide	divide	VERB
ejpam-5016	506	9	f−.	f−.	NOUN
ejpam-5016	506	10	we	we	PRON
ejpam-5016	506	11	may	may	AUX
ejpam-5016	506	12	assume	assume	VERB
ejpam-5016	506	13	that	that	SCONJ
ejpam-5016	506	14	no	no	DET
ejpam-5016	506	15	xv	xv	NOUN
ejpam-5016	506	16	divides	divide	VERB
ejpam-5016	506	17	both	both	DET
ejpam-5016	506	18	f+	f+	NOUN
ejpam-5016	506	19	and	and	CCONJ
ejpam-5016	506	20	f−	f−	PROPN
ejpam-5016	506	21	for	for	ADP
ejpam-5016	506	22	v	v	NOUN
ejpam-5016	506	23	∈	∈	PROPN
ejpam-5016	506	24	a.	a.	NOUN
ejpam-5016	506	25	since	since	SCONJ
ejpam-5016	506	26	w	w	PROPN
ejpam-5016	506	27	divides	divide	NOUN
ejpam-5016	506	28	ϕ(f+	ϕ(f+	ADV
ejpam-5016	506	29	)	)	PUNCT
ejpam-5016	506	30	and	and	CCONJ
ejpam-5016	506	31	ϕ(f+	ϕ(f+	ADV
ejpam-5016	506	32	)	)	PUNCT
ejpam-5016	506	33	=	=	SYM
ejpam-5016	506	34	ϕ(f−	ϕ(f−	NOUN
ejpam-5016	506	35	)	)	PUNCT
ejpam-5016	506	36	then	then	ADV
ejpam-5016	506	37	there	there	PRON
ejpam-5016	506	38	exists	exist	VERB
ejpam-5016	506	39	v′1	v′1	NOUN
ejpam-5016	506	40	∈	∈	PROPN
ejpam-5016	506	41	a	a	DET
ejpam-5016	506	42	such	such	ADJ
ejpam-5016	506	43	that	that	SCONJ
ejpam-5016	506	44	xv′1	xv′1	PROPN
ejpam-5016	506	45	divides	divide	VERB
ejpam-5016	506	46	f−.	f−.	VERB
ejpam-5016	506	47	let	let	VERB
ejpam-5016	506	48	vv1	vv1	NOUN
ejpam-5016	506	49	and	and	CCONJ
ejpam-5016	506	50	hv1	hv1	NOUN
ejpam-5016	506	51	be	be	AUX
ejpam-5016	506	52	the	the	DET
ejpam-5016	506	53	maximal	maximal	ADJ
ejpam-5016	506	54	vertical	vertical	ADJ
ejpam-5016	506	55	and	and	CCONJ
ejpam-5016	506	56	horizontal	horizontal	ADJ
ejpam-5016	506	57	edge	edge	NOUN
ejpam-5016	506	58	intervals	interval	NOUN
ejpam-5016	506	59	,	,	PUNCT
ejpam-5016	506	60	respectively	respectively	ADV
ejpam-5016	506	61	,	,	PUNCT
ejpam-5016	506	62	that	that	PRON
ejpam-5016	506	63	contain	contain	VERB
ejpam-5016	506	64	v1	v1	NOUN
ejpam-5016	506	65	.	.	PUNCT
ejpam-5016	507	1	since	since	SCONJ
ejpam-5016	507	2	vv1	vv1	NOUN
ejpam-5016	507	3	divides	divide	VERB
ejpam-5016	507	4	ϕ(f+	ϕ(f+	ADV
ejpam-5016	507	5	)	)	PUNCT
ejpam-5016	507	6	and	and	CCONJ
ejpam-5016	507	7	ϕ(f+	ϕ(f+	ADV
ejpam-5016	507	8	)	)	PUNCT
ejpam-5016	507	9	=	=	SYM
ejpam-5016	507	10	ϕ(f−	ϕ(f−	NOUN
ejpam-5016	507	11	)	)	PUNCT
ejpam-5016	507	12	then	then	ADV
ejpam-5016	507	13	there	there	PRON
ejpam-5016	507	14	exists	exist	VERB
ejpam-5016	507	15	v′2	v′2	X
ejpam-5016	507	16	∈	∈	PROPN
ejpam-5016	507	17	vv1	vv1	NOUN
ejpam-5016	507	18	such	such	ADJ
ejpam-5016	507	19	that	that	SCONJ
ejpam-5016	507	20	xv′2	xv′2	PROPN
ejpam-5016	507	21	divides	divide	VERB
ejpam-5016	507	22	f−.	f−.	VERB
ejpam-5016	507	23	similarly	similarly	ADV
ejpam-5016	507	24	,	,	PUNCT
ejpam-5016	507	25	there	there	PRON
ejpam-5016	507	26	exists	exist	VERB
ejpam-5016	507	27	v′3	v′3	NOUN
ejpam-5016	507	28	∈	∈	PROPN
ejpam-5016	507	29	hv1	hv1	PROPN
ejpam-5016	507	30	such	such	ADJ
ejpam-5016	507	31	that	that	SCONJ
ejpam-5016	507	32	xv′3	xv′3	PROPN
ejpam-5016	507	33	divides	divide	VERB
ejpam-5016	507	34	f−.	f−.	VERB
ejpam-5016	507	35	define	define	ADJ
ejpam-5016	507	36	vv′1	vv′1	NOUN
ejpam-5016	507	37	and	and	CCONJ
ejpam-5016	507	38	hv′1	hv′1	NOUN
ejpam-5016	507	39	similarly	similarly	ADV
ejpam-5016	507	40	.	.	PUNCT
ejpam-5016	508	1	we	we	PRON
ejpam-5016	508	2	also	also	ADV
ejpam-5016	508	3	get	get	VERB
ejpam-5016	508	4	that	that	SCONJ
ejpam-5016	508	5	there	there	PRON
ejpam-5016	508	6	exists	exist	VERB
ejpam-5016	508	7	v2	v2	PROPN
ejpam-5016	508	8	∈	∈	PROPN
ejpam-5016	508	9	vv′1	vv′1	NOUN
ejpam-5016	508	10	and	and	CCONJ
ejpam-5016	508	11	v3	v3	PROPN
ejpam-5016	508	12	∈	∈	PROPN
ejpam-5016	508	13	hv′1	hv′1	VERB
ejpam-5016	508	14	such	such	ADJ
ejpam-5016	508	15	that	that	SCONJ
ejpam-5016	508	16	both	both	PRON
ejpam-5016	508	17	xv2	xv2	PROPN
ejpam-5016	508	18	and	and	CCONJ
ejpam-5016	508	19	xv3	xv3	PROPN
ejpam-5016	508	20	divide	divide	PROPN
ejpam-5016	508	21	f+	f+	PROPN
ejpam-5016	508	22	.	.	PUNCT
ejpam-5016	509	1	consider	consider	VERB
ejpam-5016	509	2	the	the	DET
ejpam-5016	509	3	following	follow	VERB
ejpam-5016	509	4	cases	case	NOUN
ejpam-5016	509	5	:	:	PUNCT
ejpam-5016	509	6	•	•	NOUN
ejpam-5016	509	7	if	if	SCONJ
ejpam-5016	509	8	v1	v1	NOUN
ejpam-5016	509	9	and	and	CCONJ
ejpam-5016	509	10	v′1	v′1	NOUN
ejpam-5016	509	11	are	be	AUX
ejpam-5016	509	12	on	on	ADP
ejpam-5016	509	13	the	the	DET
ejpam-5016	509	14	same	same	ADJ
ejpam-5016	509	15	horizontal	horizontal	ADJ
ejpam-5016	509	16	edge	edge	NOUN
ejpam-5016	509	17	interval	interval	NOUN
ejpam-5016	509	18	of	of	ADP
ejpam-5016	509	19	p.	p.	NOUN
ejpam-5016	509	20	by	by	ADP
ejpam-5016	509	21	the	the	DET
ejpam-5016	509	22	construction	construction	NOUN
ejpam-5016	509	23	of	of	ADP
ejpam-5016	509	24	p	p	NOUN
ejpam-5016	509	25	then	then	ADV
ejpam-5016	509	26	the	the	DET
ejpam-5016	509	27	interval	interval	NOUN
ejpam-5016	509	28	determined	determine	VERB
ejpam-5016	509	29	by	by	ADP
ejpam-5016	509	30	v1	v1	NOUN
ejpam-5016	509	31	,	,	PUNCT
ejpam-5016	509	32	v2	v2	PROPN
ejpam-5016	509	33	is	be	AUX
ejpam-5016	509	34	an	an	DET
ejpam-5016	509	35	inner	inner	ADJ
ejpam-5016	509	36	interval	interval	NOUN
ejpam-5016	509	37	.	.	PUNCT
ejpam-5016	510	1	by	by	ADP
ejpam-5016	510	2	[	[	X
ejpam-5016	510	3	5	5	NUM
ejpam-5016	510	4	,	,	PUNCT
ejpam-5016	510	5	lemma	lemma	PROPN
ejpam-5016	510	6	2.2	2.2	NUM
ejpam-5016	510	7	]	]	PUNCT
ejpam-5016	510	8	with	with	ADP
ejpam-5016	510	9	three	three	NUM
ejpam-5016	510	10	vertices	vertex	NOUN
ejpam-5016	510	11	v1	v1	NOUN
ejpam-5016	510	12	,	,	PUNCT
ejpam-5016	510	13	v2	v2	PROPN
ejpam-5016	510	14	∈	∈	PROPN
ejpam-5016	510	15	v	v	NOUN
ejpam-5016	510	16	+	+	CCONJ
ejpam-5016	510	17	f	f	PROPN
ejpam-5016	510	18	dan	dan	PROPN
ejpam-5016	510	19	v′1	v′1	PROPN
ejpam-5016	510	20	∈	∈	PROPN
ejpam-5016	510	21	v	v	ADP
ejpam-5016	510	22	−	−	PROPN
ejpam-5016	510	23	f	f	NOUN
ejpam-5016	510	24	,	,	PUNCT
ejpam-5016	510	25	we	we	PRON
ejpam-5016	510	26	get	get	VERB
ejpam-5016	510	27	a	a	DET
ejpam-5016	510	28	contradiction	contradiction	NOUN
ejpam-5016	510	29	.	.	PUNCT
ejpam-5016	511	1	•	•	NOUN
ejpam-5016	511	2	if	if	SCONJ
ejpam-5016	511	3	v1	v1	PROPN
ejpam-5016	511	4	and	and	CCONJ
ejpam-5016	511	5	v′1	v′1	NOUN
ejpam-5016	511	6	are	be	AUX
ejpam-5016	511	7	on	on	ADP
ejpam-5016	511	8	the	the	DET
ejpam-5016	511	9	same	same	ADJ
ejpam-5016	511	10	vertical	vertical	ADJ
ejpam-5016	511	11	edge	edge	NOUN
ejpam-5016	511	12	interval	interval	NOUN
ejpam-5016	511	13	of	of	ADP
ejpam-5016	511	14	p.	p.	NOUN
ejpam-5016	511	15	similarly	similarly	ADV
ejpam-5016	511	16	we	we	PRON
ejpam-5016	511	17	get	get	VERB
ejpam-5016	511	18	a	a	DET
ejpam-5016	511	19	contradiction	contradiction	NOUN
ejpam-5016	511	20	by	by	ADP
ejpam-5016	511	21	[	[	X
ejpam-5016	511	22	5	5	NUM
ejpam-5016	511	23	,	,	PUNCT
ejpam-5016	511	24	lemma	lemma	PROPN
ejpam-5016	511	25	2.2	2.2	NUM
ejpam-5016	511	26	]	]	PUNCT
ejpam-5016	511	27	and	and	CCONJ
ejpam-5016	511	28	three	three	NUM
ejpam-5016	511	29	vertices	vertex	NOUN
ejpam-5016	511	30	v1	v1	NOUN
ejpam-5016	511	31	,	,	PUNCT
ejpam-5016	511	32	v3	v3	PROPN
ejpam-5016	511	33	∈	∈	PROPN
ejpam-5016	511	34	v	v	ADP
ejpam-5016	512	1	+	+	CCONJ
ejpam-5016	512	2	f	f	PROPN
ejpam-5016	512	3	dan	dan	PROPN
ejpam-5016	512	4	v′1	v′1	PROPN
ejpam-5016	512	5	∈	∈	PROPN
ejpam-5016	512	6	v	v	ADP
ejpam-5016	512	7	−	−	PROPN
ejpam-5016	512	8	f	f	PROPN
ejpam-5016	512	9	.	.	PUNCT
ejpam-5016	513	1	•	•	INTJ
ejpam-5016	513	2	if	if	SCONJ
ejpam-5016	513	3	v1	v1	PROPN
ejpam-5016	513	4	and	and	CCONJ
ejpam-5016	513	5	v′1	v′1	NOUN
ejpam-5016	513	6	are	be	AUX
ejpam-5016	513	7	the	the	DET
ejpam-5016	513	8	diagonal	diagonal	ADJ
ejpam-5016	513	9	corners	corner	NOUN
ejpam-5016	513	10	of	of	ADP
ejpam-5016	513	11	[	[	X
ejpam-5016	513	12	3	3	NUM
ejpam-5016	513	13	,	,	PUNCT
ejpam-5016	513	14	8	8	NUM
ejpam-5016	513	15	+	+	CCONJ
ejpam-5016	513	16	n	n	CCONJ
ejpam-5016	513	17	]	]	PUNCT
ejpam-5016	513	18	.	.	PUNCT
ejpam-5016	514	1	we	we	PRON
ejpam-5016	514	2	may	may	AUX
ejpam-5016	514	3	assume	assume	VERB
ejpam-5016	514	4	that	that	SCONJ
ejpam-5016	514	5	v1	v1	NOUN
ejpam-5016	514	6	=	=	SYM
ejpam-5016	514	7	3	3	NUM
ejpam-5016	514	8	and	and	CCONJ
ejpam-5016	514	9	v′1	v′1	X
ejpam-5016	514	10	=	=	SYM
ejpam-5016	514	11	8	8	NUM
ejpam-5016	514	12	+	+	CCONJ
ejpam-5016	514	13	n.	n.	NOUN
ejpam-5016	514	14	consider	consider	VERB
ejpam-5016	514	15	v′3	v′3	NOUN
ejpam-5016	514	16	.	.	PUNCT
ejpam-5016	515	1	if	if	SCONJ
ejpam-5016	515	2	v′3	v′3	NOUN
ejpam-5016	515	3	=	=	NOUN
ejpam-5016	515	4	4	4	NUM
ejpam-5016	515	5	then	then	ADV
ejpam-5016	515	6	v2	v2	PROPN
ejpam-5016	515	7	∈	∈	PROPN
ejpam-5016	515	8	{	{	PUNCT
ejpam-5016	515	9	12	12	NUM
ejpam-5016	515	10	+	+	NUM
ejpam-5016	515	11	2n	2n	NUM
ejpam-5016	515	12	,	,	PUNCT
ejpam-5016	515	13	16	16	NUM
ejpam-5016	515	14	+	+	SYM
ejpam-5016	515	15	2n	2n	NUM
ejpam-5016	515	16	}	}	PUNCT
ejpam-5016	515	17	and	and	CCONJ
ejpam-5016	515	18	we	we	PRON
ejpam-5016	515	19	get	get	VERB
ejpam-5016	515	20	a	a	DET
ejpam-5016	515	21	contradiction	contradiction	NOUN
ejpam-5016	515	22	by	by	ADP
ejpam-5016	515	23	[	[	X
ejpam-5016	515	24	5	5	NUM
ejpam-5016	515	25	,	,	PUNCT
ejpam-5016	515	26	lemma	lemma	PROPN
ejpam-5016	515	27	2.2	2.2	NUM
ejpam-5016	515	28	]	]	PUNCT
ejpam-5016	515	29	and	and	CCONJ
ejpam-5016	515	30	three	three	NUM
ejpam-5016	515	31	vertices	vertex	NOUN
ejpam-5016	515	32	v1	v1	NOUN
ejpam-5016	515	33	,	,	PUNCT
ejpam-5016	515	34	v2	v2	PROPN
ejpam-5016	515	35	∈	∈	PROPN
ejpam-5016	515	36	v	v	NOUN
ejpam-5016	515	37	+	+	CCONJ
ejpam-5016	515	38	f	f	PROPN
ejpam-5016	515	39	dan	dan	PROPN
ejpam-5016	515	40	v′3	v′3	PROPN
ejpam-5016	515	41	∈	∈	PROPN
ejpam-5016	515	42	v	v	ADP
ejpam-5016	515	43	−	−	PROPN
ejpam-5016	515	44	f	f	PROPN
ejpam-5016	515	45	.	.	PUNCT
ejpam-5016	516	1	y.	y.	PROPN
ejpam-5016	516	2	y.	y.	PROPN
ejpam-5016	516	3	hamonangan	hamonangan	PROPN
ejpam-5016	516	4	,	,	PUNCT
ejpam-5016	516	5	i.	i.	PROPN
ejpam-5016	516	6	muchtadi	muchtadi	PROPN
ejpam-5016	516	7	-	-	PUNCT
ejpam-5016	516	8	alamsyah	alamsyah	NOUN
ejpam-5016	516	9	/	/	SYM
ejpam-5016	516	10	eur	eur	PROPN
ejpam-5016	516	11	.	.	PUNCT
ejpam-5016	517	1	j.	j.	PROPN
ejpam-5016	517	2	pure	pure	PROPN
ejpam-5016	517	3	appl	appl	PROPN
ejpam-5016	517	4	.	.	PROPN
ejpam-5016	517	5	math	math	PROPN
ejpam-5016	517	6	,	,	PUNCT
ejpam-5016	517	7	17	17	NUM
ejpam-5016	517	8	(	(	PUNCT
ejpam-5016	517	9	4	4	NUM
ejpam-5016	517	10	)	)	PUNCT
ejpam-5016	517	11	(	(	PUNCT
ejpam-5016	517	12	2024	2024	NUM
ejpam-5016	517	13	)	)	PUNCT
ejpam-5016	517	14	,	,	PUNCT
ejpam-5016	517	15	2621	2621	NUM
ejpam-5016	517	16	-	-	SYM
ejpam-5016	517	17	2650	2650	NUM
ejpam-5016	517	18	2645	2645	NUM
ejpam-5016	517	19	therefore	therefore	ADV
ejpam-5016	517	20	v′3	v′3	NOUN
ejpam-5016	517	21	̸=	̸=	PROPN
ejpam-5016	517	22	4	4	NUM
ejpam-5016	517	23	.	.	PUNCT
ejpam-5016	518	1	in	in	ADP
ejpam-5016	518	2	particular	particular	ADJ
ejpam-5016	518	3	,	,	PUNCT
ejpam-5016	518	4	v′3	v′3	NOUN
ejpam-5016	518	5	is	be	AUX
ejpam-5016	518	6	not	not	PART
ejpam-5016	518	7	the	the	DET
ejpam-5016	518	8	antidiagonal	antidiagonal	ADJ
ejpam-5016	518	9	corner	corner	NOUN
ejpam-5016	518	10	of	of	ADP
ejpam-5016	518	11	[	[	X
ejpam-5016	518	12	3	3	NUM
ejpam-5016	518	13	,	,	PUNCT
ejpam-5016	518	14	8	8	NUM
ejpam-5016	518	15	+	+	CCONJ
ejpam-5016	518	16	n	n	CCONJ
ejpam-5016	518	17	]	]	PUNCT
ejpam-5016	518	18	.	.	PUNCT
ejpam-5016	519	1	with	with	ADP
ejpam-5016	519	2	the	the	DET
ejpam-5016	519	3	similar	similar	ADJ
ejpam-5016	519	4	arguments	argument	NOUN
ejpam-5016	519	5	,	,	PUNCT
ejpam-5016	519	6	we	we	PRON
ejpam-5016	519	7	conclude	conclude	VERB
ejpam-5016	519	8	that	that	PRON
ejpam-5016	519	9	v′2	v′2	NOUN
ejpam-5016	519	10	is	be	AUX
ejpam-5016	519	11	not	not	PART
ejpam-5016	519	12	the	the	DET
ejpam-5016	519	13	antidiagonal	antidiagonal	ADJ
ejpam-5016	519	14	corner	corner	NOUN
ejpam-5016	519	15	of	of	ADP
ejpam-5016	519	16	[	[	X
ejpam-5016	519	17	3	3	NUM
ejpam-5016	519	18	,	,	PUNCT
ejpam-5016	519	19	8+n	8+n	NUM
ejpam-5016	519	20	]	]	PUNCT
ejpam-5016	519	21	.	.	PUNCT
ejpam-5016	520	1	looking	look	VERB
ejpam-5016	520	2	at	at	ADP
ejpam-5016	520	3	the	the	DET
ejpam-5016	520	4	construction	construction	NOUN
ejpam-5016	520	5	of	of	ADP
ejpam-5016	520	6	p	p	PRON
ejpam-5016	520	7	,	,	PUNCT
ejpam-5016	520	8	we	we	PRON
ejpam-5016	520	9	see	see	VERB
ejpam-5016	520	10	that	that	SCONJ
ejpam-5016	520	11	the	the	DET
ejpam-5016	520	12	vertices	vertex	NOUN
ejpam-5016	520	13	v1	v1	NOUN
ejpam-5016	520	14	,	,	PUNCT
ejpam-5016	520	15	v	v	NOUN
ejpam-5016	520	16	′	′	NUM
ejpam-5016	520	17	1	1	NUM
ejpam-5016	520	18	,	,	PUNCT
ejpam-5016	520	19	v	v	NOUN
ejpam-5016	520	20	′	′	NUM
ejpam-5016	520	21	2	2	NUM
ejpam-5016	520	22	,	,	PUNCT
ejpam-5016	520	23	v	v	NOUN
ejpam-5016	520	24	′	′	NUM
ejpam-5016	520	25	3	3	NUM
ejpam-5016	520	26	lie	lie	NOUN
ejpam-5016	520	27	on	on	ADP
ejpam-5016	520	28	p	p	NOUN
ejpam-5016	520	29	as	as	ADP
ejpam-5016	520	30	the	the	DET
ejpam-5016	520	31	following	follow	VERB
ejpam-5016	520	32	figure	figure	NOUN
ejpam-5016	520	33	:	:	PUNCT
ejpam-5016	520	34	v1	v1	NOUN
ejpam-5016	520	35	4	4	NUM
ejpam-5016	520	36	v′1	v′1	PROPN
ejpam-5016	520	37	v′2	v′2	NOUN
ejpam-5016	520	38	v′3	v′3	PROPN
ejpam-5016	520	39	h	h	PROPN
ejpam-5016	520	40	figure	figure	NOUN
ejpam-5016	520	41	30	30	NUM
ejpam-5016	520	42	:	:	PUNCT
ejpam-5016	520	43	illustration	illustration	NOUN
ejpam-5016	520	44	for	for	ADP
ejpam-5016	520	45	v1	v1	NOUN
ejpam-5016	520	46	,	,	PUNCT
ejpam-5016	520	47	v	v	NOUN
ejpam-5016	520	48	′	′	NUM
ejpam-5016	520	49	1	1	NUM
ejpam-5016	520	50	,	,	PUNCT
ejpam-5016	520	51	v	v	NOUN
ejpam-5016	520	52	′	′	NUM
ejpam-5016	520	53	2	2	NUM
ejpam-5016	520	54	,	,	PUNCT
ejpam-5016	520	55	v	v	NOUN
ejpam-5016	520	56	′	′	NUM
ejpam-5016	520	57	3	3	NUM
ejpam-5016	520	58	on	on	ADP
ejpam-5016	520	59	p.	p.	NOUN
ejpam-5016	520	60	note	note	VERB
ejpam-5016	520	61	that	that	SCONJ
ejpam-5016	520	62	[	[	X
ejpam-5016	520	63	v′3	v′3	NOUN
ejpam-5016	520	64	,	,	PUNCT
ejpam-5016	520	65	v	v	ADJ
ejpam-5016	520	66	′	′	NUM
ejpam-5016	520	67	1	1	NUM
ejpam-5016	520	68	]	]	PUNCT
ejpam-5016	520	69	is	be	AUX
ejpam-5016	520	70	an	an	DET
ejpam-5016	520	71	inner	inner	ADJ
ejpam-5016	520	72	interval	interval	NOUN
ejpam-5016	520	73	with	with	ADP
ejpam-5016	520	74	4	4	NUM
ejpam-5016	520	75	as	as	ADP
ejpam-5016	520	76	one	one	NUM
ejpam-5016	520	77	of	of	ADP
ejpam-5016	520	78	the	the	DET
ejpam-5016	520	79	antidiagonal	antidiagonal	ADJ
ejpam-5016	520	80	.	.	PUNCT
ejpam-5016	521	1	let	let	VERB
ejpam-5016	521	2	h	h	NOUN
ejpam-5016	521	3	be	be	AUX
ejpam-5016	521	4	the	the	DET
ejpam-5016	521	5	other	other	ADJ
ejpam-5016	521	6	antidiagonal	antidiagonal	ADJ
ejpam-5016	521	7	.	.	PUNCT
ejpam-5016	522	1	notice	notice	VERB
ejpam-5016	522	2	that	that	SCONJ
ejpam-5016	522	3	f	f	PROPN
ejpam-5016	522	4	=	=	PRON
ejpam-5016	522	5	(	(	PUNCT
ejpam-5016	522	6	f+	f+	PROPN
ejpam-5016	522	7	−	−	PROPN
ejpam-5016	522	8	f−	f−	PROPN
ejpam-5016	522	9	xv′1xv′3	xv′1xv′3	PUNCT
ejpam-5016	522	10	xhx4	xhx4	ADJ
ejpam-5016	522	11	)	)	PUNCT
ejpam-5016	523	1	−	−	PROPN
ejpam-5016	524	1	f−	f−	PROPN
ejpam-5016	524	2	xv′1xv′3	xv′1xv′3	PROPN
ejpam-5016	524	3	(	(	PUNCT
ejpam-5016	524	4	xv′1xv′3	xv′1xv′3	NUM
ejpam-5016	524	5	−	−	PROPN
ejpam-5016	524	6	xhx4	xhx4	ADJ
ejpam-5016	524	7	)	)	PUNCT
ejpam-5016	524	8	.	.	PUNCT
ejpam-5016	525	1	since	since	SCONJ
ejpam-5016	525	2	xv′1xv′3	xv′1xv′3	PROPN
ejpam-5016	525	3	−	−	PROPN
ejpam-5016	525	4	xhx4	xhx4	PROPN
ejpam-5016	525	5	∈	∈	PROPN
ejpam-5016	525	6	ip	ip	VERB
ejpam-5016	525	7	⊆	⊆	NUM
ejpam-5016	525	8	jp	jp	NOUN
ejpam-5016	525	9	then	then	ADV
ejpam-5016	525	10	f+	f+	PROPN
ejpam-5016	525	11	−	−	PROPN
ejpam-5016	526	1	f−	f−	PROPN
ejpam-5016	526	2	xv′1	xv′1	VERB
ejpam-5016	526	3	xv′3	xv′3	PROPN
ejpam-5016	526	4	xhx4	xhx4	PROPN
ejpam-5016	526	5	∈	∈	PROPN
ejpam-5016	526	6	jp	jp	NOUN
ejpam-5016	526	7	.	.	PUNCT
ejpam-5016	527	1	but	but	CCONJ
ejpam-5016	527	2	,	,	PUNCT
ejpam-5016	527	3	both	both	CCONJ
ejpam-5016	527	4	x4	x4	PROPN
ejpam-5016	527	5	and	and	CCONJ
ejpam-5016	527	6	xv′2	xv′2	PROPN
ejpam-5016	527	7	divide	divide	PROPN
ejpam-5016	527	8	f−	f−	PROPN
ejpam-5016	527	9	xv′1	xv′1	VERB
ejpam-5016	527	10	xv′3	xv′3	PROPN
ejpam-5016	527	11	xhx4	xhx4	PROPN
ejpam-5016	527	12	and	and	CCONJ
ejpam-5016	527	13	xv1	xv1	PROPN
ejpam-5016	527	14	divide	divide	PROPN
ejpam-5016	527	15	f+	f+	PROPN
ejpam-5016	527	16	.	.	PUNCT
ejpam-5016	528	1	by	by	ADP
ejpam-5016	528	2	[	[	X
ejpam-5016	528	3	5	5	NUM
ejpam-5016	528	4	,	,	PUNCT
ejpam-5016	528	5	lemma	lemma	PROPN
ejpam-5016	528	6	2.2	2.2	NUM
ejpam-5016	528	7	]	]	PUNCT
ejpam-5016	528	8	and	and	CCONJ
ejpam-5016	528	9	three	three	NUM
ejpam-5016	528	10	vertices	vertex	NOUN
ejpam-5016	528	11	4	4	NUM
ejpam-5016	528	12	,	,	PUNCT
ejpam-5016	528	13	v′2	v′2	ADJ
ejpam-5016	528	14	,	,	PUNCT
ejpam-5016	528	15	v1	v1	VERB
ejpam-5016	528	16	we	we	PRON
ejpam-5016	528	17	get	get	VERB
ejpam-5016	528	18	f+	f+	NOUN
ejpam-5016	528	19	−	−	PROPN
ejpam-5016	528	20	f−	f−	PROPN
ejpam-5016	528	21	xv′1	xv′1	VERB
ejpam-5016	528	22	xv′3	xv′3	PROPN
ejpam-5016	528	23	xhx4	xhx4	PROPN
ejpam-5016	528	24	is	be	AUX
ejpam-5016	528	25	redundant	redundant	ADJ
ejpam-5016	528	26	and	and	CCONJ
ejpam-5016	528	27	f	f	PROPN
ejpam-5016	528	28	is	be	AUX
ejpam-5016	528	29	also	also	ADV
ejpam-5016	528	30	redundant	redundant	ADJ
ejpam-5016	528	31	,	,	PUNCT
ejpam-5016	528	32	a	a	DET
ejpam-5016	528	33	contradiction	contradiction	NOUN
ejpam-5016	528	34	.	.	PUNCT
ejpam-5016	529	1	•	•	INTJ
ejpam-5016	529	2	we	we	PRON
ejpam-5016	529	3	argue	argue	VERB
ejpam-5016	529	4	similarly	similarly	ADV
ejpam-5016	529	5	for	for	ADP
ejpam-5016	529	6	the	the	DET
ejpam-5016	529	7	case	case	NOUN
ejpam-5016	529	8	v1	v1	NOUN
ejpam-5016	529	9	and	and	CCONJ
ejpam-5016	529	10	v′1	v′1	NOUN
ejpam-5016	529	11	are	be	AUX
ejpam-5016	529	12	the	the	DET
ejpam-5016	529	13	antidiagonal	antidiagonal	ADJ
ejpam-5016	529	14	corners	corner	NOUN
ejpam-5016	529	15	of	of	ADP
ejpam-5016	529	16	[	[	X
ejpam-5016	529	17	3	3	NUM
ejpam-5016	529	18	,	,	PUNCT
ejpam-5016	529	19	8	8	NUM
ejpam-5016	529	20	+	+	CCONJ
ejpam-5016	529	21	n	n	CCONJ
ejpam-5016	529	22	]	]	PUNCT
ejpam-5016	529	23	.	.	PUNCT
ejpam-5016	530	1	corollary	corollary	ADJ
ejpam-5016	530	2	1	1	NUM
ejpam-5016	530	3	.	.	PUNCT
ejpam-5016	531	1	let	let	VERB
ejpam-5016	531	2	p	p	PRON
ejpam-5016	531	3	be	be	AUX
ejpam-5016	531	4	a	a	DET
ejpam-5016	531	5	socket	socket	NOUN
ejpam-5016	531	6	wrench	wrench	NOUN
ejpam-5016	531	7	polyomino	polyomino	NOUN
ejpam-5016	531	8	then	then	ADV
ejpam-5016	531	9	k[p	k[p	PROPN
ejpam-5016	531	10	]	]	PUNCT
ejpam-5016	531	11	is	be	AUX
ejpam-5016	531	12	a	a	DET
ejpam-5016	531	13	normal	normal	ADJ
ejpam-5016	531	14	cohen	cohen	NOUN
ejpam-5016	531	15	-	-	PUNCT
ejpam-5016	531	16	macaulay	macaulay	PROPN
ejpam-5016	531	17	domain	domain	NOUN
ejpam-5016	531	18	.	.	PUNCT
ejpam-5016	532	1	proof	proof	NOUN
ejpam-5016	532	2	.	.	PUNCT
ejpam-5016	533	1	by	by	ADP
ejpam-5016	533	2	the	the	DET
ejpam-5016	533	3	previous	previous	ADJ
ejpam-5016	533	4	theorem	theorem	NOUN
ejpam-5016	533	5	,	,	PUNCT
ejpam-5016	533	6	we	we	PRON
ejpam-5016	533	7	have	have	AUX
ejpam-5016	533	8	ip	ip	NOUN
ejpam-5016	533	9	is	be	AUX
ejpam-5016	533	10	a	a	DET
ejpam-5016	533	11	toric	toric	ADJ
ejpam-5016	533	12	ideal	ideal	NOUN
ejpam-5016	533	13	and	and	CCONJ
ejpam-5016	533	14	has	have	VERB
ejpam-5016	533	15	square	square	ADJ
ejpam-5016	533	16	-	-	PUNCT
ejpam-5016	533	17	free	free	ADJ
ejpam-5016	533	18	quadratic	quadratic	ADJ
ejpam-5016	533	19	gröbner	gröbner	NOUN
ejpam-5016	533	20	bases	basis	NOUN
ejpam-5016	533	21	for	for	ADP
ejpam-5016	533	22	the	the	DET
ejpam-5016	533	23	suitable	suitable	ADJ
ejpam-5016	533	24	monomial	monomial	ADJ
ejpam-5016	533	25	order	order	NOUN
ejpam-5016	533	26	.	.	PUNCT
ejpam-5016	534	1	by	by	ADP
ejpam-5016	534	2	a	a	DET
ejpam-5016	534	3	theorem	theorem	NOUN
ejpam-5016	534	4	of	of	ADP
ejpam-5016	534	5	sturmfels	sturmfel	NOUN
ejpam-5016	534	6	[	[	X
ejpam-5016	534	7	23	23	NUM
ejpam-5016	534	8	,	,	PUNCT
ejpam-5016	534	9	corollary	corollary	NOUN
ejpam-5016	534	10	4.26	4.26	NUM
ejpam-5016	534	11	]	]	X
ejpam-5016	534	12	we	we	PRON
ejpam-5016	534	13	conclude	conclude	VERB
ejpam-5016	534	14	thatk[p	thatk[p	PROPN
ejpam-5016	534	15	]	]	PUNCT
ejpam-5016	534	16	is	be	AUX
ejpam-5016	534	17	normal	normal	ADJ
ejpam-5016	534	18	and	and	CCONJ
ejpam-5016	534	19	by	by	ADP
ejpam-5016	534	20	a	a	DET
ejpam-5016	534	21	theorem	theorem	NOUN
ejpam-5016	534	22	of	of	ADP
ejpam-5016	534	23	hochster	hochster	NOUN
ejpam-5016	534	24	[	[	X
ejpam-5016	534	25	4	4	NUM
ejpam-5016	534	26	,	,	PUNCT
ejpam-5016	534	27	theorem	theorem	VERB
ejpam-5016	534	28	6.3.5	6.3.5	NUM
ejpam-5016	534	29	]	]	X
ejpam-5016	534	30	we	we	PRON
ejpam-5016	534	31	have	have	VERB
ejpam-5016	534	32	that	that	DET
ejpam-5016	534	33	k[p	k[p	NOUN
ejpam-5016	534	34	]	]	PUNCT
ejpam-5016	534	35	is	be	AUX
ejpam-5016	534	36	cohen	cohen	NOUN
ejpam-5016	534	37	-	-	PUNCT
ejpam-5016	534	38	macaulay	macaulay	PROPN
ejpam-5016	534	39	.	.	PUNCT
ejpam-5016	535	1	therefore	therefore	ADV
ejpam-5016	535	2	k[p	k[p	PROPN
ejpam-5016	535	3	]	]	X
ejpam-5016	535	4	is	be	AUX
ejpam-5016	535	5	a	a	DET
ejpam-5016	535	6	normal	normal	ADJ
ejpam-5016	535	7	cohen	cohen	NOUN
ejpam-5016	535	8	-	-	PUNCT
ejpam-5016	535	9	macaulay	macaulay	PROPN
ejpam-5016	535	10	domain	domain	NOUN
ejpam-5016	535	11	.	.	PUNCT
ejpam-5016	536	1	next	next	ADV
ejpam-5016	536	2	we	we	PRON
ejpam-5016	536	3	compute	compute	VERB
ejpam-5016	536	4	the	the	DET
ejpam-5016	536	5	h	h	NOUN
ejpam-5016	536	6	-	-	PUNCT
ejpam-5016	536	7	polynomial	polynomial	ADJ
ejpam-5016	536	8	of	of	ADP
ejpam-5016	536	9	socket	socket	NOUN
ejpam-5016	536	10	wrench	wrench	NOUN
ejpam-5016	536	11	polyominoes	polyominoe	NOUN
ejpam-5016	536	12	and	and	CCONJ
ejpam-5016	536	13	prove	prove	VERB
ejpam-5016	536	14	that	that	SCONJ
ejpam-5016	536	15	k[p	k[p	NOUN
ejpam-5016	536	16	]	]	X
ejpam-5016	536	17	is	be	AUX
ejpam-5016	536	18	gorenstein	gorenstein	ADJ
ejpam-5016	536	19	if	if	SCONJ
ejpam-5016	537	1	and	and	CCONJ
ejpam-5016	537	2	only	only	ADV
ejpam-5016	537	3	if	if	SCONJ
ejpam-5016	537	4	there	there	PRON
ejpam-5016	537	5	is	be	VERB
ejpam-5016	537	6	no	no	DET
ejpam-5016	537	7	unit	unit	NOUN
ejpam-5016	537	8	square	square	NOUN
ejpam-5016	537	9	that	that	PRON
ejpam-5016	537	10	we	we	PRON
ejpam-5016	537	11	add	add	VERB
ejpam-5016	537	12	in	in	ADP
ejpam-5016	537	13	the	the	DET
ejpam-5016	537	14	definition	definition	NOUN
ejpam-5016	537	15	of	of	ADP
ejpam-5016	537	16	the	the	DET
ejpam-5016	537	17	socket	socket	NOUN
ejpam-5016	537	18	wrench	wrench	NOUN
ejpam-5016	537	19	polyominoes	polyominoe	NOUN
ejpam-5016	537	20	.	.	PUNCT
ejpam-5016	538	1	we	we	PRON
ejpam-5016	538	2	refer	refer	VERB
ejpam-5016	538	3	the	the	DET
ejpam-5016	538	4	definition	definition	NOUN
ejpam-5016	538	5	of	of	ADP
ejpam-5016	538	6	(	(	PUNCT
ejpam-5016	538	7	l	l	NOUN
ejpam-5016	538	8	,	,	PUNCT
ejpam-5016	538	9	c)-polyomino	c)-polyomino	VERB
ejpam-5016	538	10	in	in	ADP
ejpam-5016	538	11	[	[	X
ejpam-5016	538	12	8	8	NUM
ejpam-5016	538	13	]	]	PUNCT
ejpam-5016	538	14	.	.	PUNCT
ejpam-5016	539	1	the	the	DET
ejpam-5016	539	2	socket	socket	NOUN
ejpam-5016	539	3	wrench	wrench	NOUN
ejpam-5016	539	4	polyominoes	polyominoe	NOUN
ejpam-5016	539	5	are	be	AUX
ejpam-5016	539	6	(	(	PUNCT
ejpam-5016	539	7	l	l	NOUN
ejpam-5016	539	8	,	,	PUNCT
ejpam-5016	539	9	c)-polyominoes	c)-polyominoe	VERB
ejpam-5016	539	10	by	by	ADP
ejpam-5016	539	11	the	the	DET
ejpam-5016	539	12	following	follow	VERB
ejpam-5016	539	13	figure	figure	NOUN
ejpam-5016	539	14	here	here	ADV
ejpam-5016	539	15	,	,	PUNCT
ejpam-5016	539	16	we	we	PRON
ejpam-5016	539	17	take	take	VERB
ejpam-5016	539	18	symmetry	symmetry	NOUN
ejpam-5016	539	19	to	to	ADP
ejpam-5016	539	20	the	the	DET
ejpam-5016	539	21	definition	definition	NOUN
ejpam-5016	539	22	of	of	ADP
ejpam-5016	539	23	(	(	PUNCT
ejpam-5016	539	24	l	l	NOUN
ejpam-5016	539	25	,	,	PUNCT
ejpam-5016	539	26	c)-polyomino	c)-polyomino	PUNCT
ejpam-5016	539	27	so	so	CCONJ
ejpam-5016	539	28	it	it	PRON
ejpam-5016	539	29	is	be	AUX
ejpam-5016	539	30	suitable	suitable	ADJ
ejpam-5016	539	31	to	to	ADP
ejpam-5016	539	32	the	the	DET
ejpam-5016	539	33	socket	socket	NOUN
ejpam-5016	539	34	wrench	wrench	NOUN
ejpam-5016	539	35	.	.	PUNCT
ejpam-5016	540	1	the	the	DET
ejpam-5016	540	2	results	result	NOUN
ejpam-5016	540	3	in	in	ADP
ejpam-5016	540	4	[	[	X
ejpam-5016	540	5	8	8	NUM
ejpam-5016	540	6	]	]	PUNCT
ejpam-5016	540	7	do	do	AUX
ejpam-5016	540	8	not	not	PART
ejpam-5016	540	9	change	change	VERB
ejpam-5016	540	10	.	.	PUNCT
ejpam-5016	541	1	we	we	PRON
ejpam-5016	541	2	also	also	ADV
ejpam-5016	541	3	can	can	AUX
ejpam-5016	541	4	rotate	rotate	VERB
ejpam-5016	541	5	the	the	DET
ejpam-5016	541	6	socket	socket	NOUN
ejpam-5016	541	7	wrench	wrench	NOUN
ejpam-5016	541	8	polyominoes	polyominoe	NOUN
ejpam-5016	541	9	by	by	ADP
ejpam-5016	541	10	180	180	NUM
ejpam-5016	541	11	◦	◦	NOUN
ejpam-5016	541	12	to	to	PART
ejpam-5016	541	13	see	see	VERB
ejpam-5016	541	14	that	that	SCONJ
ejpam-5016	541	15	the	the	DET
ejpam-5016	541	16	socket	socket	NOUN
ejpam-5016	541	17	wrench	wrench	NOUN
ejpam-5016	541	18	polyominoes	polyominoe	NOUN
ejpam-5016	541	19	are	be	AUX
ejpam-5016	541	20	(	(	PUNCT
ejpam-5016	541	21	l	l	NOUN
ejpam-5016	541	22	,	,	PUNCT
ejpam-5016	541	23	c)-polyominoes	c)-polyominoe	VERB
ejpam-5016	541	24	.	.	PUNCT
ejpam-5016	542	1	we	we	PRON
ejpam-5016	542	2	recall	recall	VERB
ejpam-5016	542	3	some	some	DET
ejpam-5016	542	4	terminologies	terminology	NOUN
ejpam-5016	542	5	from	from	ADP
ejpam-5016	542	6	[	[	X
ejpam-5016	542	7	8	8	NUM
ejpam-5016	542	8	]	]	PUNCT
ejpam-5016	542	9	and	and	CCONJ
ejpam-5016	542	10	[	[	X
ejpam-5016	542	11	37	37	NUM
ejpam-5016	542	12	]	]	PUNCT
ejpam-5016	542	13	.	.	PUNCT
ejpam-5016	543	1	(	(	PUNCT
ejpam-5016	543	2	i	i	NOUN
ejpam-5016	543	3	)	)	PUNCT
ejpam-5016	543	4	for	for	ADP
ejpam-5016	543	5	a	a	DET
ejpam-5016	543	6	polyimino	polyimino	NOUN
ejpam-5016	543	7	p	p	NOUN
ejpam-5016	543	8	,	,	PUNCT
ejpam-5016	543	9	the	the	DET
ejpam-5016	543	10	rook	rook	NOUN
ejpam-5016	543	11	number	number	NOUN
ejpam-5016	543	12	r(p	r(p	PROPN
ejpam-5016	543	13	)	)	PUNCT
ejpam-5016	543	14	is	be	AUX
ejpam-5016	543	15	the	the	DET
ejpam-5016	543	16	maximum	maximum	ADJ
ejpam-5016	543	17	number	number	NOUN
ejpam-5016	543	18	of	of	ADP
ejpam-5016	543	19	non	non	ADJ
ejpam-5016	543	20	-	-	ADJ
ejpam-5016	543	21	attacking	attacking	ADJ
ejpam-5016	543	22	rooks	rook	NOUN
ejpam-5016	543	23	that	that	PRON
ejpam-5016	543	24	can	can	AUX
ejpam-5016	543	25	be	be	AUX
ejpam-5016	543	26	placed	place	VERB
ejpam-5016	543	27	in	in	ADP
ejpam-5016	543	28	p.	p.	PROPN
ejpam-5016	543	29	y.	y.	PROPN
ejpam-5016	543	30	y.	y.	PROPN
ejpam-5016	543	31	hamonangan	hamonangan	PROPN
ejpam-5016	543	32	,	,	PUNCT
ejpam-5016	543	33	i.	i.	PROPN
ejpam-5016	543	34	muchtadi	muchtadi	PROPN
ejpam-5016	543	35	-	-	PUNCT
ejpam-5016	543	36	alamsyah	alamsyah	NOUN
ejpam-5016	543	37	/	/	SYM
ejpam-5016	543	38	eur	eur	PROPN
ejpam-5016	543	39	.	.	PUNCT
ejpam-5016	544	1	j.	j.	PROPN
ejpam-5016	544	2	pure	pure	PROPN
ejpam-5016	544	3	appl	appl	PROPN
ejpam-5016	544	4	.	.	PROPN
ejpam-5016	544	5	math	math	PROPN
ejpam-5016	544	6	,	,	PUNCT
ejpam-5016	544	7	17	17	NUM
ejpam-5016	544	8	(	(	PUNCT
ejpam-5016	544	9	4	4	NUM
ejpam-5016	544	10	)	)	PUNCT
ejpam-5016	544	11	(	(	PUNCT
ejpam-5016	544	12	2024	2024	NUM
ejpam-5016	544	13	)	)	PUNCT
ejpam-5016	544	14	,	,	PUNCT
ejpam-5016	544	15	2621	2621	NUM
ejpam-5016	544	16	-	-	SYM
ejpam-5016	544	17	2650	2650	NUM
ejpam-5016	544	18	2646	2646	NUM
ejpam-5016	544	19	a2	a2	PROPN
ejpam-5016	544	20	d2	d2	PROPN
ejpam-5016	544	21	a1	a1	PROPN
ejpam-5016	544	22	d1	d1	PROPN
ejpam-5016	544	23	b2	b2	NOUN
ejpam-5016	544	24	b1	b1	NOUN
ejpam-5016	544	25	b	b	PROPN
ejpam-5016	544	26	d	d	PROPN
ejpam-5016	544	27	c2	c2	PROPN
ejpam-5016	544	28	c1	c1	PROPN
ejpam-5016	544	29	c	c	PROPN
ejpam-5016	545	1	a	a	DET
ejpam-5016	545	2	c	c	PROPN
ejpam-5016	545	3	l	l	NOUN
ejpam-5016	545	4	figure	figure	NOUN
ejpam-5016	545	5	31	31	NUM
ejpam-5016	545	6	:	:	PUNCT
ejpam-5016	545	7	socket	socket	NOUN
ejpam-5016	545	8	wrench	wrench	NOUN
ejpam-5016	545	9	polyominoes	polyominoe	NOUN
ejpam-5016	545	10	are	be	AUX
ejpam-5016	545	11	(	(	PUNCT
ejpam-5016	545	12	l	l	NOUN
ejpam-5016	545	13	,	,	PUNCT
ejpam-5016	545	14	c)-polyominoes	c)-polyominoe	VERB
ejpam-5016	545	15	.	.	PUNCT
ejpam-5016	546	1	(	(	PUNCT
ejpam-5016	546	2	ii	ii	NOUN
ejpam-5016	546	3	)	)	PUNCT
ejpam-5016	546	4	for	for	ADP
ejpam-5016	546	5	a	a	DET
ejpam-5016	546	6	polyomino	polyomino	NOUN
ejpam-5016	546	7	p	p	NOUN
ejpam-5016	546	8	,	,	PUNCT
ejpam-5016	546	9	denote	denote	VERB
ejpam-5016	546	10	by	by	ADP
ejpam-5016	546	11	rk	rk	PRON
ejpam-5016	546	12	the	the	DET
ejpam-5016	546	13	number	number	NOUN
ejpam-5016	546	14	of	of	ADP
ejpam-5016	546	15	ways	way	NOUN
ejpam-5016	546	16	to	to	PART
ejpam-5016	546	17	placed	place	VERB
ejpam-5016	546	18	k	k	PROPN
ejpam-5016	546	19	rook	rook	NOUN
ejpam-5016	546	20	in	in	ADP
ejpam-5016	546	21	p	p	NOUN
ejpam-5016	546	22	in	in	ADP
ejpam-5016	546	23	non	non	ADJ
ejpam-5016	546	24	-	-	ADJ
ejpam-5016	546	25	attacking	attacking	ADJ
ejpam-5016	546	26	position	position	NOUN
ejpam-5016	546	27	,	,	PUNCT
ejpam-5016	546	28	conventionally	conventionally	ADV
ejpam-5016	546	29	r0	r0	VERB
ejpam-5016	546	30	=	=	SYM
ejpam-5016	546	31	1	1	X
ejpam-5016	546	32	.	.	PUNCT
ejpam-5016	546	33	(	(	PUNCT
ejpam-5016	546	34	iii	iii	X
ejpam-5016	546	35	)	)	PUNCT
ejpam-5016	546	36	the	the	DET
ejpam-5016	546	37	polyomino	polyomino	NOUN
ejpam-5016	546	38	p	p	NOUN
ejpam-5016	546	39	is	be	AUX
ejpam-5016	546	40	thin	thin	ADJ
ejpam-5016	546	41	if	if	SCONJ
ejpam-5016	546	42	it	it	PRON
ejpam-5016	546	43	does	do	AUX
ejpam-5016	546	44	not	not	PART
ejpam-5016	546	45	contain	contain	VERB
ejpam-5016	546	46	square	square	ADJ
ejpam-5016	546	47	tetromino	tetromino	NOUN
ejpam-5016	546	48	.	.	PUNCT
ejpam-5016	547	1	(	(	PUNCT
ejpam-5016	547	2	iv	iv	X
ejpam-5016	547	3	)	)	PUNCT
ejpam-5016	547	4	let	let	VERB
ejpam-5016	547	5	p	p	PRON
ejpam-5016	547	6	be	be	AUX
ejpam-5016	547	7	a	a	DET
ejpam-5016	547	8	simple	simple	ADJ
ejpam-5016	547	9	thin	thin	ADJ
ejpam-5016	547	10	polyomino	polyomino	NOUN
ejpam-5016	547	11	.	.	PUNCT
ejpam-5016	548	1	a	a	DET
ejpam-5016	548	2	cell	cell	NOUN
ejpam-5016	548	3	c	c	NOUN
ejpam-5016	548	4	of	of	ADP
ejpam-5016	548	5	p	p	PROPN
ejpam-5016	548	6	is	be	AUX
ejpam-5016	548	7	single	single	ADJ
ejpam-5016	548	8	if	if	SCONJ
ejpam-5016	548	9	there	there	PRON
ejpam-5016	548	10	exists	exist	VERB
ejpam-5016	548	11	a	a	DET
ejpam-5016	548	12	unique	unique	ADJ
ejpam-5016	548	13	maximal	maximal	ADJ
ejpam-5016	548	14	inner	inner	ADJ
ejpam-5016	548	15	interval	interval	NOUN
ejpam-5016	548	16	of	of	ADP
ejpam-5016	548	17	p	p	NOUN
ejpam-5016	548	18	containing	contain	VERB
ejpam-5016	548	19	c.	c.	NOUN
ejpam-5016	548	20	if	if	SCONJ
ejpam-5016	548	21	any	any	DET
ejpam-5016	548	22	maximal	maximal	ADJ
ejpam-5016	548	23	inner	inner	ADJ
ejpam-5016	548	24	interval	interval	NOUN
ejpam-5016	548	25	of	of	ADP
ejpam-5016	548	26	p	p	PROPN
ejpam-5016	548	27	has	have	VERB
ejpam-5016	548	28	exactly	exactly	ADV
ejpam-5016	548	29	one	one	NUM
ejpam-5016	548	30	single	single	ADJ
ejpam-5016	548	31	cell	cell	NOUN
ejpam-5016	548	32	,	,	PUNCT
ejpam-5016	548	33	we	we	PRON
ejpam-5016	548	34	say	say	VERB
ejpam-5016	548	35	that	that	SCONJ
ejpam-5016	548	36	p	p	PROPN
ejpam-5016	548	37	has	have	VERB
ejpam-5016	548	38	the	the	DET
ejpam-5016	548	39	s	s	NOUN
ejpam-5016	548	40	-	-	NOUN
ejpam-5016	548	41	property	property	NOUN
ejpam-5016	548	42	.	.	PUNCT
ejpam-5016	549	1	we	we	PRON
ejpam-5016	549	2	also	also	ADV
ejpam-5016	549	3	use	use	VERB
ejpam-5016	549	4	some	some	DET
ejpam-5016	549	5	terminologies	terminology	NOUN
ejpam-5016	549	6	from	from	ADP
ejpam-5016	549	7	[	[	X
ejpam-5016	549	8	5	5	NUM
ejpam-5016	549	9	]	]	PUNCT
ejpam-5016	549	10	and	and	CCONJ
ejpam-5016	549	11	[	[	X
ejpam-5016	549	12	31	31	NUM
ejpam-5016	549	13	]	]	PUNCT
ejpam-5016	549	14	.	.	PUNCT
ejpam-5016	550	1	(	(	PUNCT
ejpam-5016	550	2	i	i	NOUN
ejpam-5016	550	3	)	)	PUNCT
ejpam-5016	550	4	let	let	VERB
ejpam-5016	550	5	p	p	PRON
ejpam-5016	550	6	be	be	AUX
ejpam-5016	550	7	a	a	DET
ejpam-5016	550	8	polyomino	polyomino	NOUN
ejpam-5016	550	9	.	.	PUNCT
ejpam-5016	551	1	a	a	DET
ejpam-5016	551	2	sequence	sequence	NOUN
ejpam-5016	551	3	of	of	ADP
ejpam-5016	551	4	distinct	distinct	ADJ
ejpam-5016	551	5	inner	inner	ADJ
ejpam-5016	551	6	interval	interval	NOUN
ejpam-5016	551	7	w	w	PROPN
ejpam-5016	551	8	:	:	PUNCT
ejpam-5016	551	9	i1	i1	PROPN
ejpam-5016	551	10	,	,	PUNCT
ejpam-5016	551	11	.	.	PUNCT
ejpam-5016	551	12	.	.	PUNCT
ejpam-5016	551	13	.	.	PUNCT
ejpam-5016	552	1	,	,	PUNCT
ejpam-5016	552	2	iℓ	iℓ	VERB
ejpam-5016	552	3	of	of	ADP
ejpam-5016	552	4	p	p	PRON
ejpam-5016	552	5	such	such	ADJ
ejpam-5016	552	6	that	that	DET
ejpam-5016	552	7	vi	vi	NOUN
ejpam-5016	552	8	,	,	PUNCT
ejpam-5016	552	9	zi	zi	PROPN
ejpam-5016	552	10	are	be	AUX
ejpam-5016	552	11	diagonal	diagonal	ADJ
ejpam-5016	552	12	(	(	PUNCT
ejpam-5016	552	13	resp	resp	NOUN
ejpam-5016	552	14	.	.	PUNCT
ejpam-5016	553	1	antidiagonal	antidiagonal	ADJ
ejpam-5016	553	2	)	)	PUNCT
ejpam-5016	553	3	corners	corner	NOUN
ejpam-5016	553	4	and	and	CCONJ
ejpam-5016	553	5	ui	ui	NOUN
ejpam-5016	553	6	,	,	PUNCT
ejpam-5016	553	7	vi+1	vi+1	X
ejpam-5016	553	8	are	be	AUX
ejpam-5016	553	9	antidiagonal	antidiagonal	ADJ
ejpam-5016	553	10	(	(	PUNCT
ejpam-5016	553	11	resp	resp	NOUN
ejpam-5016	553	12	.	.	PUNCT
ejpam-5016	554	1	diagonal	diagonal	ADJ
ejpam-5016	554	2	)	)	PUNCT
ejpam-5016	554	3	corners	corner	NOUN
ejpam-5016	554	4	of	of	ADP
ejpam-5016	554	5	ii	ii	NOUN
ejpam-5016	554	6	,	,	PUNCT
ejpam-5016	554	7	for	for	ADP
ejpam-5016	554	8	i	i	PROPN
ejpam-5016	554	9	=	=	NOUN
ejpam-5016	554	10	1	1	NUM
ejpam-5016	554	11	,	,	PUNCT
ejpam-5016	554	12	.	.	PUNCT
ejpam-5016	554	13	.	.	PUNCT
ejpam-5016	555	1	.	.	PUNCT
ejpam-5016	556	1	,	,	PUNCT
ejpam-5016	556	2	ℓ	ℓ	X
ejpam-5016	556	3	,	,	PUNCT
ejpam-5016	556	4	is	be	AUX
ejpam-5016	556	5	a	a	DET
ejpam-5016	556	6	zig	zig	VERB
ejpam-5016	556	7	-	-	PUNCT
ejpam-5016	556	8	zag	zag	NOUN
ejpam-5016	556	9	walk	walk	NOUN
ejpam-5016	556	10	of	of	ADP
ejpam-5016	556	11	p	p	X
ejpam-5016	556	12	,	,	PUNCT
ejpam-5016	556	13	if	if	SCONJ
ejpam-5016	556	14	(	(	PUNCT
ejpam-5016	556	15	a	a	X
ejpam-5016	556	16	)	)	PUNCT
ejpam-5016	556	17	i1	i1	PROPN
ejpam-5016	556	18	∩	∩	NOUN
ejpam-5016	556	19	iℓ	iℓ	PROPN
ejpam-5016	556	20	=	=	PUNCT
ejpam-5016	556	21	{	{	PUNCT
ejpam-5016	556	22	v1	v1	NOUN
ejpam-5016	556	23	=	=	SYM
ejpam-5016	556	24	vℓ+1	vℓ+1	X
ejpam-5016	556	25	}	}	PUNCT
ejpam-5016	556	26	and	and	CCONJ
ejpam-5016	556	27	ii	ii	PROPN
ejpam-5016	556	28	∩	∩	NOUN
ejpam-5016	556	29	ii+1	ii+1	NOUN
ejpam-5016	556	30	=	=	SYM
ejpam-5016	556	31	{	{	PUNCT
ejpam-5016	556	32	vi+1	vi+1	NOUN
ejpam-5016	556	33	}	}	PUNCT
ejpam-5016	556	34	for	for	ADP
ejpam-5016	556	35	i	i	PROPN
ejpam-5016	556	36	=	=	NOUN
ejpam-5016	556	37	1	1	NUM
ejpam-5016	556	38	,	,	PUNCT
ejpam-5016	556	39	2	2	NUM
ejpam-5016	556	40	,	,	PUNCT
ejpam-5016	556	41	.	.	PUNCT
ejpam-5016	556	42	.	.	PUNCT
ejpam-5016	557	1	.	.	PUNCT
ejpam-5016	558	1	,	,	PUNCT
ejpam-5016	558	2	ℓ−	ℓ−	PROPN
ejpam-5016	558	3	1	1	NUM
ejpam-5016	558	4	;	;	PUNCT
ejpam-5016	558	5	(	(	PUNCT
ejpam-5016	558	6	b	b	X
ejpam-5016	558	7	)	)	PUNCT
ejpam-5016	558	8	vi	vi	NOUN
ejpam-5016	558	9	and	and	CCONJ
ejpam-5016	558	10	vi+1	vi+1	NOUN
ejpam-5016	558	11	are	be	AUX
ejpam-5016	558	12	on	on	ADP
ejpam-5016	558	13	the	the	DET
ejpam-5016	558	14	same	same	ADJ
ejpam-5016	558	15	edge	edge	NOUN
ejpam-5016	558	16	interval	interval	NOUN
ejpam-5016	558	17	of	of	ADP
ejpam-5016	558	18	p	p	X
ejpam-5016	558	19	,	,	PUNCT
ejpam-5016	558	20	for	for	ADP
ejpam-5016	558	21	i	i	PROPN
ejpam-5016	558	22	=	=	NOUN
ejpam-5016	558	23	1	1	NUM
ejpam-5016	558	24	,	,	PUNCT
ejpam-5016	558	25	.	.	PUNCT
ejpam-5016	558	26	.	.	PUNCT
ejpam-5016	559	1	.	.	PUNCT
ejpam-5016	560	1	,	,	PUNCT
ejpam-5016	560	2	ℓ.	ℓ.	NOUN
ejpam-5016	560	3	(	(	PUNCT
ejpam-5016	560	4	c	c	NOUN
ejpam-5016	560	5	)	)	PUNCT
ejpam-5016	560	6	for	for	ADP
ejpam-5016	560	7	any	any	DET
ejpam-5016	560	8	i	i	PROPN
ejpam-5016	560	9	,	,	PUNCT
ejpam-5016	560	10	j	j	PROPN
ejpam-5016	560	11	∈	∈	PROPN
ejpam-5016	560	12	{	{	PUNCT
ejpam-5016	560	13	1	1	NUM
ejpam-5016	560	14	,	,	PUNCT
ejpam-5016	560	15	.	.	PUNCT
ejpam-5016	560	16	.	.	PUNCT
ejpam-5016	561	1	.	.	PUNCT
ejpam-5016	562	1	,	,	PUNCT
ejpam-5016	562	2	ℓ	ℓ	X
ejpam-5016	562	3	}	}	PUNCT
ejpam-5016	562	4	,	,	PUNCT
ejpam-5016	562	5	with	with	ADP
ejpam-5016	562	6	i	i	PROPN
ejpam-5016	562	7	̸=	̸=	PROPN
ejpam-5016	562	8	j	j	PROPN
ejpam-5016	562	9	,	,	PUNCT
ejpam-5016	562	10	does	do	AUX
ejpam-5016	562	11	not	not	PART
ejpam-5016	562	12	exist	exist	VERB
ejpam-5016	562	13	an	an	DET
ejpam-5016	562	14	inner	inner	ADJ
ejpam-5016	562	15	interval	interval	NOUN
ejpam-5016	562	16	j	j	PROPN
ejpam-5016	562	17	of	of	ADP
ejpam-5016	562	18	p	p	PRON
ejpam-5016	562	19	such	such	ADJ
ejpam-5016	562	20	that	that	DET
ejpam-5016	562	21	zi	zi	NOUN
ejpam-5016	562	22	,	,	PUNCT
ejpam-5016	562	23	zj	zj	PROPN
ejpam-5016	562	24	∈	∈	PROPN
ejpam-5016	562	25	j	j	PROPN
ejpam-5016	562	26	.	.	PUNCT
ejpam-5016	563	1	(	(	PUNCT
ejpam-5016	563	2	ii	ii	NOUN
ejpam-5016	563	3	)	)	PUNCT
ejpam-5016	563	4	a	a	DET
ejpam-5016	563	5	polyomino	polyomino	NOUN
ejpam-5016	563	6	is	be	AUX
ejpam-5016	563	7	called	call	VERB
ejpam-5016	563	8	closed	closed	ADJ
ejpam-5016	563	9	path	path	NOUN
ejpam-5016	563	10	if	if	SCONJ
ejpam-5016	563	11	p	p	NOUN
ejpam-5016	563	12	is	be	AUX
ejpam-5016	563	13	a	a	DET
ejpam-5016	563	14	sequence	sequence	NOUN
ejpam-5016	563	15	of	of	ADP
ejpam-5016	563	16	cells	cell	NOUN
ejpam-5016	563	17	a1	a1	NOUN
ejpam-5016	563	18	,	,	PUNCT
ejpam-5016	563	19	a2	a2	PROPN
ejpam-5016	563	20	,	,	PUNCT
ejpam-5016	563	21	.	.	PUNCT
ejpam-5016	563	22	.	.	PUNCT
ejpam-5016	564	1	.	.	PUNCT
ejpam-5016	565	1	,	,	PUNCT
ejpam-5016	565	2	an	an	DET
ejpam-5016	565	3	,	,	PUNCT
ejpam-5016	565	4	an+1	an+1	NOUN
ejpam-5016	565	5	,	,	PUNCT
ejpam-5016	565	6	n	n	CCONJ
ejpam-5016	565	7	>	>	X
ejpam-5016	565	8	5	5	NUM
ejpam-5016	565	9	such	such	ADJ
ejpam-5016	565	10	that	that	SCONJ
ejpam-5016	565	11	(	(	PUNCT
ejpam-5016	565	12	a	a	X
ejpam-5016	565	13	)	)	PUNCT
ejpam-5016	565	14	a1	a1	NOUN
ejpam-5016	565	15	=	=	PUNCT
ejpam-5016	565	16	an+1	an+1	NOUN
ejpam-5016	565	17	;	;	PUNCT
ejpam-5016	565	18	(	(	PUNCT
ejpam-5016	565	19	b	b	X
ejpam-5016	565	20	)	)	PUNCT
ejpam-5016	565	21	ai	ai	VERB
ejpam-5016	565	22	∩ai+1	∩ai+1	PROPN
ejpam-5016	565	23	is	be	AUX
ejpam-5016	565	24	a	a	DET
ejpam-5016	565	25	common	common	ADJ
ejpam-5016	565	26	edge	edge	NOUN
ejpam-5016	565	27	,	,	PUNCT
ejpam-5016	565	28	for	for	ADP
ejpam-5016	565	29	i	i	PROPN
ejpam-5016	565	30	=	=	SYM
ejpam-5016	565	31	1	1	NUM
ejpam-5016	565	32	,	,	PUNCT
ejpam-5016	565	33	2	2	NUM
ejpam-5016	565	34	,	,	PUNCT
ejpam-5016	565	35	.	.	PUNCT
ejpam-5016	565	36	.	.	PUNCT
ejpam-5016	566	1	.	.	PUNCT
ejpam-5016	567	1	,	,	PUNCT
ejpam-5016	567	2	n	n	CCONJ
ejpam-5016	567	3	;	;	PUNCT
ejpam-5016	567	4	(	(	PUNCT
ejpam-5016	567	5	c	c	X
ejpam-5016	567	6	)	)	PUNCT
ejpam-5016	567	7	ai	ai	VERB
ejpam-5016	567	8	̸=	̸=	PROPN
ejpam-5016	567	9	aj	aj	PROPN
ejpam-5016	567	10	for	for	ADP
ejpam-5016	567	11	all	all	PRON
ejpam-5016	567	12	i	i	PRON
ejpam-5016	567	13	̸=	̸=	PROPN
ejpam-5016	567	14	j	j	PROPN
ejpam-5016	567	15	and	and	CCONJ
ejpam-5016	567	16	i	i	PROPN
ejpam-5016	567	17	,	,	PUNCT
ejpam-5016	567	18	j	j	PROPN
ejpam-5016	567	19	∈	∈	PROPN
ejpam-5016	567	20	{	{	PUNCT
ejpam-5016	567	21	1	1	NUM
ejpam-5016	567	22	,	,	PUNCT
ejpam-5016	567	23	2	2	NUM
ejpam-5016	567	24	,	,	PUNCT
ejpam-5016	567	25	.	.	PUNCT
ejpam-5016	567	26	.	.	PUNCT
ejpam-5016	567	27	.	.	PUNCT
ejpam-5016	567	28	,	,	PUNCT
ejpam-5016	567	29	n	n	CCONJ
ejpam-5016	567	30	}	}	PUNCT
ejpam-5016	567	31	;	;	PUNCT
ejpam-5016	567	32	(	(	PUNCT
ejpam-5016	567	33	d	d	X
ejpam-5016	567	34	)	)	PUNCT
ejpam-5016	567	35	for	for	ADP
ejpam-5016	567	36	all	all	PRON
ejpam-5016	567	37	i	i	PRON
ejpam-5016	567	38	∈	∈	PROPN
ejpam-5016	567	39	{	{	PUNCT
ejpam-5016	567	40	1	1	NUM
ejpam-5016	567	41	,	,	PUNCT
ejpam-5016	567	42	2	2	NUM
ejpam-5016	567	43	,	,	PUNCT
ejpam-5016	567	44	.	.	PUNCT
ejpam-5016	567	45	.	.	PUNCT
ejpam-5016	567	46	.	.	PUNCT
ejpam-5016	567	47	,	,	PUNCT
ejpam-5016	567	48	n	n	CCONJ
ejpam-5016	567	49	}	}	PUNCT
ejpam-5016	567	50	and	and	CCONJ
ejpam-5016	567	51	for	for	ADP
ejpam-5016	567	52	all	all	DET
ejpam-5016	567	53	j	j	PROPN
ejpam-5016	567	54	/∈	/∈	PUNCT
ejpam-5016	567	55	{	{	PUNCT
ejpam-5016	567	56	i−	i−	PROPN
ejpam-5016	567	57	2	2	NUM
ejpam-5016	567	58	,	,	PUNCT
ejpam-5016	567	59	i−	i−	PROPN
ejpam-5016	567	60	1	1	NUM
ejpam-5016	567	61	,	,	PUNCT
ejpam-5016	567	62	i	i	PRON
ejpam-5016	567	63	,	,	PUNCT
ejpam-5016	567	64	i+	i+	NUM
ejpam-5016	567	65	1	1	NUM
ejpam-5016	567	66	,	,	PUNCT
ejpam-5016	567	67	i+	i+	NOUN
ejpam-5016	567	68	2	2	X
ejpam-5016	567	69	}	}	PUNCT
ejpam-5016	567	70	then	then	ADV
ejpam-5016	567	71	v	v	X
ejpam-5016	567	72	(	(	PUNCT
ejpam-5016	567	73	ai	ai	NOUN
ejpam-5016	567	74	)	)	PUNCT
ejpam-5016	567	75	∩	∩	ADJ
ejpam-5016	567	76	v	v	X
ejpam-5016	567	77	(	(	PUNCT
ejpam-5016	567	78	aj	aj	PROPN
ejpam-5016	567	79	)	)	PUNCT
ejpam-5016	567	80	=	=	SYM
ejpam-5016	567	81	∅	∅	NOUN
ejpam-5016	567	82	,	,	PUNCT
ejpam-5016	567	83	where	where	SCONJ
ejpam-5016	567	84	a−1	a−1	PROPN
ejpam-5016	567	85	=	=	PUNCT
ejpam-5016	567	86	an−1	an−1	PROPN
ejpam-5016	567	87	,	,	PUNCT
ejpam-5016	567	88	a0	a0	PROPN
ejpam-5016	567	89	=	=	SYM
ejpam-5016	567	90	an	an	PROPN
ejpam-5016	567	91	,	,	PUNCT
ejpam-5016	567	92	an+1	an+1	NOUN
ejpam-5016	567	93	=	=	SYM
ejpam-5016	567	94	a1	a1	PROPN
ejpam-5016	567	95	,	,	PUNCT
ejpam-5016	567	96	an+2	an+2	PROPN
ejpam-5016	567	97	=	=	PROPN
ejpam-5016	567	98	a2	a2	PROPN
ejpam-5016	567	99	.	.	PUNCT
ejpam-5016	568	1	in	in	ADP
ejpam-5016	568	2	[	[	X
ejpam-5016	568	3	31	31	NUM
ejpam-5016	568	4	,	,	PUNCT
ejpam-5016	568	5	corollary	corollary	ADJ
ejpam-5016	568	6	3.6	3.6	NUM
ejpam-5016	568	7	]	]	PUNCT
ejpam-5016	568	8	,	,	PUNCT
ejpam-5016	568	9	the	the	DET
ejpam-5016	568	10	authors	author	NOUN
ejpam-5016	568	11	prove	prove	VERB
ejpam-5016	568	12	that	that	SCONJ
ejpam-5016	568	13	if	if	SCONJ
ejpam-5016	568	14	there	there	PRON
ejpam-5016	568	15	exists	exist	VERB
ejpam-5016	568	16	a	a	DET
ejpam-5016	568	17	zig	zig	VERB
ejpam-5016	568	18	-	-	PUNCT
ejpam-5016	568	19	zag	zag	NUM
ejpam-5016	568	20	walk	walk	NOUN
ejpam-5016	568	21	in	in	ADP
ejpam-5016	568	22	p	p	NOUN
ejpam-5016	568	23	then	then	ADV
ejpam-5016	568	24	the	the	DET
ejpam-5016	568	25	ideal	ideal	ADJ
ejpam-5016	568	26	ip	ip	NOUN
ejpam-5016	568	27	is	be	AUX
ejpam-5016	568	28	not	not	PART
ejpam-5016	568	29	prime	prime	ADJ
ejpam-5016	568	30	.	.	PUNCT
ejpam-5016	569	1	for	for	ADP
ejpam-5016	569	2	socket	socket	NOUN
ejpam-5016	569	3	wrench	wrench	NOUN
ejpam-5016	569	4	polyominoes	polyominoe	NOUN
ejpam-5016	569	5	,	,	PUNCT
ejpam-5016	569	6	since	since	SCONJ
ejpam-5016	569	7	ip	ip	NOUN
ejpam-5016	569	8	is	be	AUX
ejpam-5016	569	9	prime	prime	ADJ
ejpam-5016	569	10	then	then	ADV
ejpam-5016	569	11	p	p	NOUN
ejpam-5016	569	12	has	have	VERB
ejpam-5016	569	13	no	no	DET
ejpam-5016	569	14	zig	zig	VERB
ejpam-5016	569	15	-	-	PUNCT
ejpam-5016	569	16	zag	zag	NUM
ejpam-5016	569	17	walk	walk	NOUN
ejpam-5016	569	18	.	.	PUNCT
ejpam-5016	570	1	now	now	ADV
ejpam-5016	570	2	,	,	PUNCT
ejpam-5016	570	3	we	we	PRON
ejpam-5016	570	4	are	be	AUX
ejpam-5016	570	5	ready	ready	ADJ
ejpam-5016	570	6	to	to	PART
ejpam-5016	570	7	prove	prove	VERB
ejpam-5016	570	8	the	the	DET
ejpam-5016	570	9	next	next	ADJ
ejpam-5016	570	10	theorem	theorem	PROPN
ejpam-5016	570	11	.	.	PUNCT
ejpam-5016	570	12	theorem	theorem	VERB
ejpam-5016	570	13	6	6	NUM
ejpam-5016	570	14	.	.	PUNCT
ejpam-5016	571	1	let	let	VERB
ejpam-5016	571	2	p	p	PRON
ejpam-5016	571	3	be	be	AUX
ejpam-5016	571	4	a	a	DET
ejpam-5016	571	5	socket	socket	NOUN
ejpam-5016	571	6	wrench	wrench	NOUN
ejpam-5016	571	7	polyomino	polyomino	NOUN
ejpam-5016	571	8	with	with	ADP
ejpam-5016	571	9	n	n	CCONJ
ejpam-5016	571	10	additional	additional	ADJ
ejpam-5016	571	11	unit	unit	NOUN
ejpam-5016	571	12	squares	square	NOUN
ejpam-5016	571	13	.	.	PUNCT
ejpam-5016	572	1	then	then	ADV
ejpam-5016	572	2	:	:	PUNCT
ejpam-5016	572	3	(	(	PUNCT
ejpam-5016	572	4	i	i	NOUN
ejpam-5016	572	5	)	)	PUNCT
ejpam-5016	572	6	the	the	DET
ejpam-5016	572	7	h	h	NOUN
ejpam-5016	572	8	-	-	PUNCT
ejpam-5016	572	9	polynomial	polynomial	ADJ
ejpam-5016	572	10	of	of	ADP
ejpam-5016	572	11	k[p	k[p	NOUN
ejpam-5016	572	12	]	]	PUNCT
ejpam-5016	572	13	is	be	AUX
ejpam-5016	572	14	hk[p](t	hk[p](t	PRON
ejpam-5016	572	15	)	)	PUNCT
ejpam-5016	573	1	=	=	SYM
ejpam-5016	573	2	1	1	NUM
ejpam-5016	573	3	+	+	CCONJ
ejpam-5016	573	4	(	(	PUNCT
ejpam-5016	573	5	n+	n+	NUM
ejpam-5016	573	6	8)t+	8)t+	NUM
ejpam-5016	573	7	(	(	PUNCT
ejpam-5016	573	8	7n+	7n+	NUM
ejpam-5016	573	9	16)t2	16)t2	NUM
ejpam-5016	573	10	+	+	CCONJ
ejpam-5016	573	11	(	(	PUNCT
ejpam-5016	573	12	11n+	11n+	NUM
ejpam-5016	573	13	8)t3	8)t3	NUM
ejpam-5016	573	14	+	+	CCONJ
ejpam-5016	573	15	(	(	PUNCT
ejpam-5016	573	16	3n+	3n+	NUM
ejpam-5016	573	17	1)t4	1)t4	NUM
ejpam-5016	573	18	;	;	PUNCT
ejpam-5016	573	19	y.	y.	PROPN
ejpam-5016	573	20	y.	y.	PROPN
ejpam-5016	573	21	hamonangan	hamonangan	PROPN
ejpam-5016	573	22	,	,	PUNCT
ejpam-5016	573	23	i.	i.	PROPN
ejpam-5016	573	24	muchtadi	muchtadi	PROPN
ejpam-5016	573	25	-	-	PUNCT
ejpam-5016	573	26	alamsyah	alamsyah	NOUN
ejpam-5016	573	27	/	/	SYM
ejpam-5016	573	28	eur	eur	PROPN
ejpam-5016	573	29	.	.	PUNCT
ejpam-5016	574	1	j.	j.	PROPN
ejpam-5016	574	2	pure	pure	PROPN
ejpam-5016	574	3	appl	appl	PROPN
ejpam-5016	574	4	.	.	PROPN
ejpam-5016	574	5	math	math	PROPN
ejpam-5016	574	6	,	,	PUNCT
ejpam-5016	574	7	17	17	NUM
ejpam-5016	574	8	(	(	PUNCT
ejpam-5016	574	9	4	4	NUM
ejpam-5016	574	10	)	)	PUNCT
ejpam-5016	574	11	(	(	PUNCT
ejpam-5016	574	12	2024	2024	NUM
ejpam-5016	574	13	)	)	PUNCT
ejpam-5016	574	14	,	,	PUNCT
ejpam-5016	574	15	2621	2621	NUM
ejpam-5016	574	16	-	-	SYM
ejpam-5016	574	17	2650	2650	NUM
ejpam-5016	574	18	2647	2647	NUM
ejpam-5016	574	19	(	(	PUNCT
ejpam-5016	574	20	ii	ii	NOUN
ejpam-5016	574	21	)	)	PUNCT
ejpam-5016	574	22	reg(k[p	reg(k[p	NOUN
ejpam-5016	574	23	]	]	PUNCT
ejpam-5016	574	24	)	)	PUNCT
ejpam-5016	574	25	=	=	SYM
ejpam-5016	574	26	4	4	NUM
ejpam-5016	574	27	;	;	PUNCT
ejpam-5016	574	28	(	(	PUNCT
ejpam-5016	574	29	iii	iii	X
ejpam-5016	574	30	)	)	PUNCT
ejpam-5016	574	31	k[p	k[p	NOUN
ejpam-5016	574	32	]	]	PUNCT
ejpam-5016	574	33	is	be	AUX
ejpam-5016	574	34	gorenstein	gorenstein	ADJ
ejpam-5016	574	35	if	if	SCONJ
ejpam-5016	575	1	and	and	CCONJ
ejpam-5016	575	2	only	only	ADV
ejpam-5016	575	3	if	if	SCONJ
ejpam-5016	575	4	n	n	PROPN
ejpam-5016	575	5	=	=	SYM
ejpam-5016	575	6	0	0	X
ejpam-5016	575	7	.	.	PUNCT
ejpam-5016	576	1	proof	proof	NOUN
ejpam-5016	576	2	.	.	PUNCT
ejpam-5016	577	1	since	since	SCONJ
ejpam-5016	577	2	p	p	NOUN
ejpam-5016	577	3	is	be	AUX
ejpam-5016	577	4	a	a	DET
ejpam-5016	577	5	(	(	PUNCT
ejpam-5016	577	6	l	l	NOUN
ejpam-5016	577	7	,	,	PUNCT
ejpam-5016	577	8	c)-polyomino	c)-polyomino	PUNCT
ejpam-5016	577	9	and	and	CCONJ
ejpam-5016	577	10	c	c	NOUN
ejpam-5016	577	11	is	be	AUX
ejpam-5016	577	12	a	a	DET
ejpam-5016	577	13	simple	simple	ADJ
ejpam-5016	577	14	and	and	CCONJ
ejpam-5016	577	15	thin	thin	ADJ
ejpam-5016	577	16	polyomino	polyomino	NOUN
ejpam-5016	577	17	then	then	ADV
ejpam-5016	577	18	by	by	ADP
ejpam-5016	577	19	[	[	X
ejpam-5016	577	20	8	8	NUM
ejpam-5016	577	21	,	,	PUNCT
ejpam-5016	577	22	theorem	theorem	VERB
ejpam-5016	577	23	5.2	5.2	NUM
ejpam-5016	577	24	]	]	PUNCT
ejpam-5016	577	25	,	,	PUNCT
ejpam-5016	577	26	we	we	PRON
ejpam-5016	577	27	obtain	obtain	VERB
ejpam-5016	577	28	that	that	DET
ejpam-5016	577	29	hk[p](t	hk[p](t	NOUN
ejpam-5016	577	30	)	)	PUNCT
ejpam-5016	577	31	=	=	NOUN
ejpam-5016	577	32	r(p)∑	r(p)∑	NOUN
ejpam-5016	577	33	k=0	k=0	PROPN
ejpam-5016	577	34	rkt	rkt	PROPN
ejpam-5016	577	35	k	k	PROPN
ejpam-5016	577	36	and	and	CCONJ
ejpam-5016	577	37	reg(k[p	reg(k[p	NOUN
ejpam-5016	577	38	]	]	PUNCT
ejpam-5016	577	39	)	)	PUNCT
ejpam-5016	577	40	=	=	SYM
ejpam-5016	577	41	r(p	r(p	NOUN
ejpam-5016	577	42	)	)	PUNCT
ejpam-5016	577	43	.	.	PUNCT
ejpam-5016	578	1	note	note	VERB
ejpam-5016	578	2	that	that	SCONJ
ejpam-5016	578	3	r(p	r(p	NOUN
ejpam-5016	578	4	)	)	PUNCT
ejpam-5016	578	5	=	=	SYM
ejpam-5016	578	6	4	4	NUM
ejpam-5016	578	7	since	since	SCONJ
ejpam-5016	578	8	the	the	DET
ejpam-5016	578	9	first	first	ADJ
ejpam-5016	578	10	,	,	PUNCT
ejpam-5016	578	11	the	the	DET
ejpam-5016	578	12	second	second	ADJ
ejpam-5016	578	13	and	and	CCONJ
ejpam-5016	578	14	the	the	DET
ejpam-5016	578	15	third	third	ADJ
ejpam-5016	578	16	row	row	NOUN
ejpam-5016	578	17	can	can	AUX
ejpam-5016	578	18	not	not	PART
ejpam-5016	578	19	contain	contain	VERB
ejpam-5016	578	20	more	more	ADJ
ejpam-5016	578	21	than	than	ADP
ejpam-5016	578	22	one	one	NUM
ejpam-5016	578	23	rook	rook	NOUN
ejpam-5016	578	24	,	,	PUNCT
ejpam-5016	578	25	two	two	NUM
ejpam-5016	578	26	rooks	rook	NOUN
ejpam-5016	578	27	,	,	PUNCT
ejpam-5016	578	28	one	one	NUM
ejpam-5016	578	29	rook	rook	NOUN
ejpam-5016	578	30	,	,	PUNCT
ejpam-5016	578	31	respectively	respectively	ADV
ejpam-5016	578	32	,	,	PUNCT
ejpam-5016	578	33	and	and	CCONJ
ejpam-5016	578	34	we	we	PRON
ejpam-5016	578	35	can	can	AUX
ejpam-5016	578	36	place	place	VERB
ejpam-5016	578	37	four	four	NUM
ejpam-5016	578	38	rooks	rook	NOUN
ejpam-5016	578	39	like	like	ADP
ejpam-5016	578	40	illustrated	illustrate	VERB
ejpam-5016	578	41	in	in	ADP
ejpam-5016	578	42	the	the	DET
ejpam-5016	578	43	figure	figure	NOUN
ejpam-5016	578	44	below	below	ADP
ejpam-5016	578	45	r	r	NOUN
ejpam-5016	578	46	r	r	NOUN
ejpam-5016	578	47	r	r	NOUN
ejpam-5016	578	48	r	r	NOUN
ejpam-5016	578	49	figure	figure	NOUN
ejpam-5016	578	50	32	32	NUM
ejpam-5016	578	51	:	:	PUNCT
ejpam-5016	578	52	r(p	r(p	NOUN
ejpam-5016	578	53	)	)	PUNCT
ejpam-5016	578	54	=	=	SYM
ejpam-5016	579	1	4	4	X
ejpam-5016	579	2	.	.	X
ejpam-5016	579	3	we	we	PRON
ejpam-5016	579	4	also	also	ADV
ejpam-5016	579	5	can	can	AUX
ejpam-5016	579	6	easily	easily	ADV
ejpam-5016	579	7	get	get	VERB
ejpam-5016	579	8	r1	r1	PROPN
ejpam-5016	579	9	=	=	SYM
ejpam-5016	579	10	n+8	n+8	PROPN
ejpam-5016	579	11	,	,	PUNCT
ejpam-5016	579	12	r2	r2	PROPN
ejpam-5016	579	13	=	=	PUNCT
ejpam-5016	580	1	7n+16	7n+16	X
ejpam-5016	580	2	,	,	PUNCT
ejpam-5016	580	3	r3	r3	PROPN
ejpam-5016	580	4	=	=	SYM
ejpam-5016	580	5	11n+8	11n+8	NUM
ejpam-5016	580	6	,	,	PUNCT
ejpam-5016	580	7	and	and	CCONJ
ejpam-5016	580	8	r4	r4	NOUN
ejpam-5016	580	9	=	=	SYM
ejpam-5016	580	10	3n+1	3n+1	NOUN
ejpam-5016	580	11	by	by	ADP
ejpam-5016	580	12	some	some	DET
ejpam-5016	580	13	counting	count	VERB
ejpam-5016	580	14	arguments	argument	NOUN
ejpam-5016	580	15	.	.	PUNCT
ejpam-5016	581	1	then	then	ADV
ejpam-5016	581	2	hk[p](t	hk[p](t	INTJ
ejpam-5016	581	3	)	)	PUNCT
ejpam-5016	581	4	=	=	SYM
ejpam-5016	582	1	1	1	NUM
ejpam-5016	582	2	+	+	CCONJ
ejpam-5016	582	3	(	(	PUNCT
ejpam-5016	582	4	n+	n+	NUM
ejpam-5016	582	5	8)t+	8)t+	NUM
ejpam-5016	582	6	(	(	PUNCT
ejpam-5016	582	7	7n+	7n+	NUM
ejpam-5016	582	8	16)t2	16)t2	NUM
ejpam-5016	582	9	+	+	CCONJ
ejpam-5016	582	10	(	(	PUNCT
ejpam-5016	582	11	11n+	11n+	NUM
ejpam-5016	582	12	8)t3	8)t3	NUM
ejpam-5016	582	13	+	+	CCONJ
ejpam-5016	582	14	(	(	PUNCT
ejpam-5016	582	15	3n+	3n+	NUM
ejpam-5016	582	16	1)t4	1)t4	NUM
ejpam-5016	582	17	and	and	CCONJ
ejpam-5016	582	18	reg(k[p	reg(k[p	NOUN
ejpam-5016	582	19	]	]	PUNCT
ejpam-5016	582	20	)	)	PUNCT
ejpam-5016	582	21	=	=	SYM
ejpam-5016	583	1	4	4	NUM
ejpam-5016	583	2	,	,	PUNCT
ejpam-5016	583	3	(	(	PUNCT
ejpam-5016	583	4	i	i	NOUN
ejpam-5016	583	5	)	)	PUNCT
ejpam-5016	583	6	and	and	CCONJ
ejpam-5016	583	7	(	(	PUNCT
ejpam-5016	583	8	ii	ii	NOUN
ejpam-5016	583	9	)	)	PUNCT
ejpam-5016	583	10	are	be	AUX
ejpam-5016	583	11	proven	prove	VERB
ejpam-5016	583	12	.	.	PUNCT
ejpam-5016	584	1	for	for	ADP
ejpam-5016	584	2	(	(	PUNCT
ejpam-5016	584	3	iii	iii	NOUN
ejpam-5016	584	4	)	)	PUNCT
ejpam-5016	584	5	,	,	PUNCT
ejpam-5016	584	6	by	by	ADP
ejpam-5016	584	7	[	[	X
ejpam-5016	584	8	39	39	NUM
ejpam-5016	584	9	,	,	PUNCT
ejpam-5016	584	10	theorem	theorem	VERB
ejpam-5016	584	11	4.2	4.2	NUM
ejpam-5016	584	12	]	]	PUNCT
ejpam-5016	584	13	since	since	SCONJ
ejpam-5016	584	14	1	1	NUM
ejpam-5016	584	15	̸=	̸=	PROPN
ejpam-5016	584	16	3n+1	3n+1	PROPN
ejpam-5016	584	17	for	for	ADP
ejpam-5016	584	18	n	n	X
ejpam-5016	584	19	>	>	X
ejpam-5016	584	20	0	0	PUNCT
ejpam-5016	585	1	then	then	ADV
ejpam-5016	585	2	k[p	k[p	NOUN
ejpam-5016	585	3	]	]	PUNCT
ejpam-5016	585	4	is	be	AUX
ejpam-5016	585	5	not	not	PART
ejpam-5016	585	6	gorenstein	gorenstein	ADJ
ejpam-5016	585	7	.	.	PUNCT
ejpam-5016	586	1	if	if	SCONJ
ejpam-5016	586	2	n	n	NOUN
ejpam-5016	586	3	=	=	SYM
ejpam-5016	586	4	0	0	NUM
ejpam-5016	586	5	,	,	PUNCT
ejpam-5016	586	6	then	then	ADV
ejpam-5016	586	7	p	p	NOUN
ejpam-5016	586	8	is	be	AUX
ejpam-5016	586	9	a	a	DET
ejpam-5016	586	10	closed	closed	ADJ
ejpam-5016	586	11	path	path	NOUN
ejpam-5016	586	12	having	have	VERB
ejpam-5016	586	13	no	no	DET
ejpam-5016	586	14	zig	zig	VERB
ejpam-5016	586	15	-	-	PUNCT
ejpam-5016	586	16	zag	zag	NOUN
ejpam-5016	586	17	walks	walk	NOUN
ejpam-5016	586	18	.	.	PUNCT
ejpam-5016	587	1	we	we	PRON
ejpam-5016	587	2	notice	notice	VERB
ejpam-5016	587	3	that	that	SCONJ
ejpam-5016	587	4	the	the	DET
ejpam-5016	587	5	single	single	ADJ
ejpam-5016	587	6	cells	cell	NOUN
ejpam-5016	587	7	of	of	ADP
ejpam-5016	587	8	p	p	NOUN
ejpam-5016	587	9	are	be	AUX
ejpam-5016	587	10	the	the	DET
ejpam-5016	587	11	four	four	NUM
ejpam-5016	587	12	cells	cell	NOUN
ejpam-5016	587	13	in	in	ADP
ejpam-5016	587	14	the	the	DET
ejpam-5016	587	15	middle	middle	NOUN
ejpam-5016	587	16	of	of	ADP
ejpam-5016	587	17	the	the	DET
ejpam-5016	587	18	first	first	ADJ
ejpam-5016	587	19	row	row	NOUN
ejpam-5016	587	20	,	,	PUNCT
ejpam-5016	587	21	the	the	DET
ejpam-5016	587	22	third	third	ADJ
ejpam-5016	587	23	row	row	NOUN
ejpam-5016	587	24	,	,	PUNCT
ejpam-5016	587	25	the	the	DET
ejpam-5016	587	26	first	first	ADJ
ejpam-5016	587	27	column	column	NOUN
ejpam-5016	587	28	,	,	PUNCT
ejpam-5016	587	29	and	and	CCONJ
ejpam-5016	587	30	the	the	DET
ejpam-5016	587	31	third	third	ADJ
ejpam-5016	587	32	column	column	NOUN
ejpam-5016	587	33	.	.	PUNCT
ejpam-5016	588	1	we	we	PRON
ejpam-5016	588	2	also	also	ADV
ejpam-5016	588	3	notice	notice	VERB
ejpam-5016	588	4	that	that	SCONJ
ejpam-5016	588	5	the	the	DET
ejpam-5016	588	6	maximal	maximal	ADJ
ejpam-5016	588	7	intervals	interval	NOUN
ejpam-5016	588	8	of	of	ADP
ejpam-5016	588	9	p	p	NOUN
ejpam-5016	588	10	are	be	AUX
ejpam-5016	588	11	the	the	DET
ejpam-5016	588	12	four	four	NUM
ejpam-5016	588	13	intervals	interval	NOUN
ejpam-5016	588	14	containing	contain	VERB
ejpam-5016	588	15	three	three	NUM
ejpam-5016	588	16	cells	cell	NOUN
ejpam-5016	588	17	in	in	ADP
ejpam-5016	588	18	the	the	DET
ejpam-5016	588	19	first	first	ADJ
ejpam-5016	588	20	row	row	NOUN
ejpam-5016	588	21	,	,	PUNCT
ejpam-5016	588	22	the	the	DET
ejpam-5016	588	23	third	third	ADJ
ejpam-5016	588	24	row	row	NOUN
ejpam-5016	588	25	,	,	PUNCT
ejpam-5016	588	26	the	the	DET
ejpam-5016	588	27	first	first	ADJ
ejpam-5016	588	28	column	column	NOUN
ejpam-5016	588	29	,	,	PUNCT
ejpam-5016	588	30	and	and	CCONJ
ejpam-5016	588	31	the	the	DET
ejpam-5016	588	32	third	third	ADJ
ejpam-5016	588	33	column	column	NOUN
ejpam-5016	588	34	.	.	PUNCT
ejpam-5016	589	1	each	each	PRON
ejpam-5016	589	2	of	of	ADP
ejpam-5016	589	3	them	they	PRON
ejpam-5016	589	4	only	only	ADV
ejpam-5016	589	5	has	have	VERB
ejpam-5016	589	6	one	one	NUM
ejpam-5016	589	7	single	single	ADJ
ejpam-5016	589	8	cell	cell	NOUN
ejpam-5016	589	9	,	,	PUNCT
ejpam-5016	589	10	and	and	CCONJ
ejpam-5016	589	11	thus	thus	ADV
ejpam-5016	589	12	p	p	X
ejpam-5016	589	13	has	have	VERB
ejpam-5016	589	14	the	the	DET
ejpam-5016	589	15	s	s	NOUN
ejpam-5016	589	16	-	-	NOUN
ejpam-5016	589	17	property	property	NOUN
ejpam-5016	589	18	.	.	PUNCT
ejpam-5016	590	1	by	by	ADP
ejpam-5016	590	2	[	[	X
ejpam-5016	590	3	8	8	NUM
ejpam-5016	590	4	,	,	PUNCT
ejpam-5016	590	5	theorem	theorem	VERB
ejpam-5016	590	6	5.7	5.7	NUM
ejpam-5016	590	7	]	]	PUNCT
ejpam-5016	590	8	,	,	PUNCT
ejpam-5016	590	9	we	we	PRON
ejpam-5016	590	10	conclude	conclude	VERB
ejpam-5016	590	11	that	that	PRON
ejpam-5016	590	12	k[p	k[p	NOUN
ejpam-5016	590	13	]	]	PUNCT
ejpam-5016	590	14	is	be	AUX
ejpam-5016	590	15	gorenstein	gorenstein	ADJ
ejpam-5016	590	16	.	.	PUNCT
ejpam-5016	591	1	5	5	X
ejpam-5016	591	2	.	.	X
ejpam-5016	591	3	conclusion	conclusion	NOUN
ejpam-5016	591	4	in	in	ADP
ejpam-5016	591	5	this	this	DET
ejpam-5016	591	6	paper	paper	NOUN
ejpam-5016	591	7	,	,	PUNCT
ejpam-5016	591	8	we	we	PRON
ejpam-5016	591	9	classify	classify	VERB
ejpam-5016	591	10	some	some	DET
ejpam-5016	591	11	few	few	ADJ
ejpam-5016	591	12	-	-	PUNCT
ejpam-5016	591	13	degree	degree	NOUN
ejpam-5016	591	14	binomials	binomial	NOUN
ejpam-5016	591	15	that	that	PRON
ejpam-5016	591	16	arise	arise	VERB
ejpam-5016	591	17	from	from	ADP
ejpam-5016	591	18	the	the	DET
ejpam-5016	591	19	buchberger	buchberger	NOUN
ejpam-5016	591	20	algorithm	algorithm	NOUN
ejpam-5016	591	21	on	on	ADP
ejpam-5016	591	22	polyomino	polyomino	PROPN
ejpam-5016	591	23	ideal	ideal	NOUN
ejpam-5016	591	24	.	.	PUNCT
ejpam-5016	592	1	based	base	VERB
ejpam-5016	592	2	on	on	ADP
ejpam-5016	592	3	the	the	DET
ejpam-5016	592	4	labelling	labelling	NOUN
ejpam-5016	592	5	and	and	CCONJ
ejpam-5016	592	6	the	the	DET
ejpam-5016	592	7	monomial	monomial	ADJ
ejpam-5016	592	8	order	order	NOUN
ejpam-5016	592	9	that	that	PRON
ejpam-5016	592	10	were	be	AUX
ejpam-5016	592	11	explained	explain	VERB
ejpam-5016	592	12	at	at	ADP
ejpam-5016	592	13	the	the	DET
ejpam-5016	592	14	beginning	beginning	NOUN
ejpam-5016	592	15	of	of	ADP
ejpam-5016	592	16	the	the	DET
ejpam-5016	592	17	third	third	ADJ
ejpam-5016	592	18	section	section	NOUN
ejpam-5016	592	19	,	,	PUNCT
ejpam-5016	592	20	we	we	PRON
ejpam-5016	592	21	obtain	obtain	VERB
ejpam-5016	592	22	that	that	SCONJ
ejpam-5016	592	23	the	the	DET
ejpam-5016	592	24	buchberger	buchberger	NOUN
ejpam-5016	592	25	algorithm	algorithm	NOUN
ejpam-5016	592	26	produces	produce	VERB
ejpam-5016	592	27	binomials	binomial	NOUN
ejpam-5016	592	28	of	of	ADP
ejpam-5016	592	29	degree	degree	NOUN
ejpam-5016	592	30	three	three	NUM
ejpam-5016	592	31	(	(	PUNCT
ejpam-5016	592	32	theorem	theorem	NOUN
ejpam-5016	592	33	1	1	NUM
ejpam-5016	592	34	)	)	PUNCT
ejpam-5016	592	35	and	and	CCONJ
ejpam-5016	592	36	binomials	binomial	NOUN
ejpam-5016	592	37	of	of	ADP
ejpam-5016	592	38	degree	degree	NOUN
ejpam-5016	592	39	four	four	NUM
ejpam-5016	592	40	(	(	PUNCT
ejpam-5016	592	41	theorem	theorem	ADJ
ejpam-5016	592	42	2	2	NUM
ejpam-5016	592	43	and	and	CCONJ
ejpam-5016	592	44	3	3	NUM
ejpam-5016	592	45	)	)	PUNCT
ejpam-5016	592	46	.	.	PUNCT
ejpam-5016	593	1	we	we	PRON
ejpam-5016	593	2	also	also	ADV
ejpam-5016	593	3	give	give	VERB
ejpam-5016	593	4	a	a	DET
ejpam-5016	593	5	class	class	NOUN
ejpam-5016	593	6	of	of	ADP
ejpam-5016	593	7	polyominoes	polyominoe	NOUN
ejpam-5016	593	8	(	(	PUNCT
ejpam-5016	593	9	the	the	DET
ejpam-5016	593	10	socket	socket	NOUN
ejpam-5016	593	11	wrench	wrench	NOUN
ejpam-5016	593	12	polyominoes	polyominoe	NOUN
ejpam-5016	593	13	)	)	PUNCT
ejpam-5016	593	14	that	that	PRON
ejpam-5016	593	15	has	have	VERB
ejpam-5016	593	16	gröbner	gröbner	NOUN
ejpam-5016	593	17	bases	basis	NOUN
ejpam-5016	593	18	of	of	ADP
ejpam-5016	593	19	degree	degree	NOUN
ejpam-5016	593	20	at	at	ADP
ejpam-5016	593	21	most	most	ADV
ejpam-5016	593	22	three	three	NUM
ejpam-5016	593	23	with	with	ADP
ejpam-5016	593	24	respect	respect	NOUN
ejpam-5016	593	25	to	to	ADP
ejpam-5016	593	26	the	the	DET
ejpam-5016	593	27	previous	previous	ADJ
ejpam-5016	593	28	labelling	labelling	NOUN
ejpam-5016	593	29	and	and	CCONJ
ejpam-5016	593	30	monomial	monomial	ADJ
ejpam-5016	593	31	order	order	NOUN
ejpam-5016	593	32	,	,	PUNCT
ejpam-5016	593	33	and	and	CCONJ
ejpam-5016	593	34	hence	hence	ADV
ejpam-5016	593	35	the	the	DET
ejpam-5016	593	36	polyomino	polyomino	NOUN
ejpam-5016	593	37	ideal	ideal	NOUN
ejpam-5016	593	38	is	be	AUX
ejpam-5016	593	39	radical	radical	ADJ
ejpam-5016	593	40	.	.	PUNCT
ejpam-5016	594	1	we	we	PRON
ejpam-5016	594	2	also	also	ADV
ejpam-5016	594	3	study	study	VERB
ejpam-5016	594	4	some	some	DET
ejpam-5016	594	5	properties	property	NOUN
ejpam-5016	594	6	of	of	ADP
ejpam-5016	594	7	the	the	DET
ejpam-5016	594	8	references	reference	NOUN
ejpam-5016	594	9	2648	2648	NUM
ejpam-5016	594	10	polyomino	polyomino	NOUN
ejpam-5016	594	11	ideal	ideal	NOUN
ejpam-5016	594	12	ip	ip	NOUN
ejpam-5016	594	13	of	of	ADP
ejpam-5016	594	14	the	the	DET
ejpam-5016	594	15	socket	socket	NOUN
ejpam-5016	594	16	wrench	wrench	NOUN
ejpam-5016	594	17	polyominoes	polyominoe	NOUN
ejpam-5016	594	18	.	.	PUNCT
ejpam-5016	595	1	the	the	DET
ejpam-5016	595	2	ideal	ideal	ADJ
ejpam-5016	595	3	ip	ip	NOUN
ejpam-5016	595	4	is	be	AUX
ejpam-5016	595	5	prime	prime	ADJ
ejpam-5016	595	6	(	(	PUNCT
ejpam-5016	595	7	theorem	theorem	NOUN
ejpam-5016	595	8	4	4	NUM
ejpam-5016	595	9	)	)	PUNCT
ejpam-5016	595	10	.	.	PUNCT
ejpam-5016	596	1	the	the	DET
ejpam-5016	596	2	quotient	quotient	NOUN
ejpam-5016	596	3	ring	ring	NOUN
ejpam-5016	596	4	kp	kp	PROPN
ejpam-5016	596	5	is	be	AUX
ejpam-5016	596	6	a	a	DET
ejpam-5016	596	7	normal	normal	ADJ
ejpam-5016	596	8	cohen	cohen	NOUN
ejpam-5016	596	9	-	-	PUNCT
ejpam-5016	596	10	macaulay	macaulay	PROPN
ejpam-5016	596	11	domain	domain	NOUN
ejpam-5016	596	12	(	(	PUNCT
ejpam-5016	596	13	corollary	corollary	ADJ
ejpam-5016	596	14	1	1	NUM
ejpam-5016	596	15	)	)	PUNCT
ejpam-5016	596	16	.	.	PUNCT
ejpam-5016	597	1	the	the	DET
ejpam-5016	597	2	hpolynomial	hpolynomial	ADJ
ejpam-5016	597	3	,	,	PUNCT
ejpam-5016	597	4	regularity	regularity	NOUN
ejpam-5016	597	5	,	,	PUNCT
ejpam-5016	597	6	and	and	CCONJ
ejpam-5016	597	7	goreinsteness	goreinsteness	NOUN
ejpam-5016	597	8	are	be	AUX
ejpam-5016	597	9	given	give	VERB
ejpam-5016	597	10	in	in	ADP
ejpam-5016	597	11	theorem	theorem	ADJ
ejpam-5016	597	12	6	6	NUM
ejpam-5016	597	13	.	.	PUNCT
ejpam-5016	598	1	the	the	DET
ejpam-5016	598	2	problem	problem	NOUN
ejpam-5016	598	3	about	about	ADP
ejpam-5016	598	4	gröbner	gröbner	NOUN
ejpam-5016	598	5	bases	basis	NOUN
ejpam-5016	598	6	and	and	CCONJ
ejpam-5016	598	7	radicality	radicality	NOUN
ejpam-5016	598	8	of	of	ADP
ejpam-5016	598	9	polyomino	polyomino	PROPN
ejpam-5016	598	10	ideal	ideal	NOUN
ejpam-5016	598	11	are	be	AUX
ejpam-5016	598	12	still	still	ADV
ejpam-5016	598	13	open	open	ADJ
ejpam-5016	598	14	.	.	PUNCT
ejpam-5016	599	1	acknowledgements	acknowledgement	NOUN
ejpam-5016	599	2	this	this	DET
ejpam-5016	599	3	research	research	NOUN
ejpam-5016	599	4	is	be	AUX
ejpam-5016	599	5	funded	fund	VERB
ejpam-5016	599	6	by	by	ADP
ejpam-5016	599	7	pmdsu	pmdsu	NOUN
ejpam-5016	599	8	program	program	NOUN
ejpam-5016	599	9	2015	2015	NUM
ejpam-5016	599	10	.	.	PUNCT
ejpam-5016	600	1	we	we	PRON
ejpam-5016	600	2	also	also	ADV
ejpam-5016	600	3	thank	thank	VERB
ejpam-5016	600	4	to	to	ADP
ejpam-5016	600	5	ayesha	ayesha	PROPN
ejpam-5016	600	6	qureshi	qureshi	PROPN
ejpam-5016	600	7	for	for	ADP
ejpam-5016	600	8	suggesting	suggest	VERB
ejpam-5016	600	9	the	the	DET
ejpam-5016	600	10	problem	problem	NOUN
ejpam-5016	600	11	,	,	PUNCT
ejpam-5016	600	12	for	for	ADP
ejpam-5016	600	13	the	the	DET
ejpam-5016	600	14	guidance	guidance	NOUN
ejpam-5016	600	15	and	and	CCONJ
ejpam-5016	600	16	for	for	ADP
ejpam-5016	600	17	the	the	DET
ejpam-5016	600	18	useful	useful	ADJ
ejpam-5016	600	19	advice	advice	NOUN
ejpam-5016	600	20	.	.	PUNCT
ejpam-5016	601	1	the	the	DET
ejpam-5016	601	2	authors	author	NOUN
ejpam-5016	601	3	also	also	ADV
ejpam-5016	601	4	thank	thank	VERB
ejpam-5016	601	5	the	the	DET
ejpam-5016	601	6	referees	referee	NOUN
ejpam-5016	601	7	of	of	ADP
ejpam-5016	601	8	european	european	PROPN
ejpam-5016	601	9	journal	journal	PROPN
ejpam-5016	601	10	of	of	ADP
ejpam-5016	601	11	pure	pure	ADJ
ejpam-5016	601	12	and	and	CCONJ
ejpam-5016	601	13	applied	applied	ADJ
ejpam-5016	601	14	mathematics	mathematic	NOUN
ejpam-5016	601	15	,	,	PUNCT
ejpam-5016	601	16	for	for	ADP
ejpam-5016	601	17	their	their	PRON
ejpam-5016	601	18	careful	careful	ADJ
ejpam-5016	601	19	reading	reading	NOUN
ejpam-5016	601	20	and	and	CCONJ
ejpam-5016	601	21	helpful	helpful	ADJ
ejpam-5016	601	22	suggestions	suggestion	NOUN
ejpam-5016	601	23	.	.	PUNCT
ejpam-5016	602	1	references	reference	NOUN
ejpam-5016	602	2	[	[	X
ejpam-5016	602	3	1	1	NUM
ejpam-5016	602	4	]	]	X
ejpam-5016	602	5	c	c	PROPN
ejpam-5016	602	6	andrei	andrei	NOUN
ejpam-5016	602	7	.	.	PUNCT
ejpam-5016	603	1	algebraic	algebraic	ADJ
ejpam-5016	603	2	properties	property	NOUN
ejpam-5016	603	3	of	of	ADP
ejpam-5016	603	4	the	the	DET
ejpam-5016	603	5	coordinate	coordinate	NOUN
ejpam-5016	603	6	ring	ring	NOUN
ejpam-5016	603	7	of	of	ADP
ejpam-5016	603	8	a	a	DET
ejpam-5016	603	9	convex	convex	ADJ
ejpam-5016	603	10	polyomino	polyomino	NOUN
ejpam-5016	603	11	.	.	PUNCT
ejpam-5016	604	1	the	the	DET
ejpam-5016	604	2	electronic	electronic	ADJ
ejpam-5016	604	3	journal	journal	NOUN
ejpam-5016	604	4	of	of	ADP
ejpam-5016	604	5	combinatorics	combinatoric	NOUN
ejpam-5016	604	6	,	,	PUNCT
ejpam-5016	604	7	28:#p1.45	28:#p1.45	NUM
ejpam-5016	604	8	,	,	PUNCT
ejpam-5016	604	9	2021	2021	NUM
ejpam-5016	604	10	.	.	PUNCT
ejpam-5016	605	1	[	[	X
ejpam-5016	605	2	2	2	NUM
ejpam-5016	605	3	]	]	PUNCT
ejpam-5016	605	4	e	e	X
ejpam-5016	605	5	barcucci	barcucci	NOUN
ejpam-5016	605	6	,	,	PUNCT
ejpam-5016	605	7	a	a	DET
ejpam-5016	605	8	del	del	PROPN
ejpam-5016	605	9	lungo	lungo	PROPN
ejpam-5016	605	10	,	,	PUNCT
ejpam-5016	605	11	m	m	VERB
ejpam-5016	605	12	nivat	nivat	ADJ
ejpam-5016	605	13	,	,	PUNCT
ejpam-5016	605	14	and	and	CCONJ
ejpam-5016	605	15	r	r	NOUN
ejpam-5016	605	16	pinzani	pinzani	NOUN
ejpam-5016	605	17	.	.	PUNCT
ejpam-5016	606	1	reconstructing	reconstruct	VERB
ejpam-5016	606	2	convex	convex	NOUN
ejpam-5016	606	3	polyominoes	polyominoe	NOUN
ejpam-5016	606	4	from	from	ADP
ejpam-5016	606	5	horizontal	horizontal	ADJ
ejpam-5016	606	6	and	and	CCONJ
ejpam-5016	606	7	vertical	vertical	ADJ
ejpam-5016	606	8	projections	projection	NOUN
ejpam-5016	606	9	.	.	PUNCT
ejpam-5016	607	1	theoretical	theoretical	ADJ
ejpam-5016	607	2	computer	computer	NOUN
ejpam-5016	607	3	science	science	NOUN
ejpam-5016	607	4	,	,	PUNCT
ejpam-5016	607	5	155(2):321–347	155(2):321–347	NUM
ejpam-5016	607	6	,	,	PUNCT
ejpam-5016	607	7	1996	1996	NUM
ejpam-5016	607	8	.	.	PUNCT
ejpam-5016	608	1	[	[	X
ejpam-5016	608	2	3	3	NUM
ejpam-5016	608	3	]	]	X
ejpam-5016	608	4	c	c	NOUN
ejpam-5016	608	5	berge	berge	NOUN
ejpam-5016	608	6	,	,	PUNCT
ejpam-5016	608	7	c	c	PROPN
ejpam-5016	608	8	c	c	PROPN
ejpam-5016	608	9	chen	chen	PROPN
ejpam-5016	608	10	,	,	PUNCT
ejpam-5016	608	11	v	v	ADP
ejpam-5016	608	12	chvátal	chvátal	NOUN
ejpam-5016	608	13	,	,	PUNCT
ejpam-5016	608	14	and	and	CCONJ
ejpam-5016	608	15	cs	cs	PROPN
ejpam-5016	608	16	seow	seow	PROPN
ejpam-5016	608	17	.	.	PUNCT
ejpam-5016	609	1	combinatorial	combinatorial	ADJ
ejpam-5016	609	2	properties	property	NOUN
ejpam-5016	609	3	of	of	ADP
ejpam-5016	609	4	polyominoes	polyominoe	NOUN
ejpam-5016	609	5	.	.	PUNCT
ejpam-5016	610	1	combinatorica	combinatorica	PROPN
ejpam-5016	610	2	,	,	PUNCT
ejpam-5016	610	3	1(3):217–224	1(3):217–224	NUM
ejpam-5016	610	4	,	,	PUNCT
ejpam-5016	610	5	1981	1981	NUM
ejpam-5016	610	6	.	.	PUNCT
ejpam-5016	611	1	[	[	X
ejpam-5016	611	2	4	4	NUM
ejpam-5016	611	3	]	]	X
ejpam-5016	611	4	winfried	winfrie	VERB
ejpam-5016	611	5	bruns	brun	NOUN
ejpam-5016	611	6	and	and	CCONJ
ejpam-5016	611	7	h	h	NOUN
ejpam-5016	611	8	jürgen	jürgen	PROPN
ejpam-5016	611	9	herzog	herzog	PROPN
ejpam-5016	611	10	.	.	PUNCT
ejpam-5016	612	1	cohen	cohen	PROPN
ejpam-5016	612	2	-	-	PUNCT
ejpam-5016	612	3	macaulay	macaulay	PROPN
ejpam-5016	612	4	rings	ring	NOUN
ejpam-5016	612	5	.	.	PUNCT
ejpam-5016	613	1	number	number	NOUN
ejpam-5016	613	2	39	39	NUM
ejpam-5016	613	3	.	.	PUNCT
ejpam-5016	614	1	cambridge	cambridge	PROPN
ejpam-5016	614	2	university	university	PROPN
ejpam-5016	614	3	press	press	NOUN
ejpam-5016	614	4	,	,	PUNCT
ejpam-5016	614	5	1998	1998	NUM
ejpam-5016	614	6	.	.	PUNCT
ejpam-5016	615	1	[	[	X
ejpam-5016	615	2	5	5	NUM
ejpam-5016	615	3	]	]	SYM
ejpam-5016	615	4	c	c	NOUN
ejpam-5016	615	5	cisto	cisto	NOUN
ejpam-5016	615	6	and	and	CCONJ
ejpam-5016	615	7	f	f	PROPN
ejpam-5016	615	8	navarra	navarra	PROPN
ejpam-5016	615	9	.	.	PUNCT
ejpam-5016	616	1	primality	primality	PROPN
ejpam-5016	616	2	of	of	ADP
ejpam-5016	616	3	closed	closed	ADJ
ejpam-5016	616	4	path	path	NOUN
ejpam-5016	616	5	polyominoes	polyominoe	NOUN
ejpam-5016	616	6	.	.	PUNCT
ejpam-5016	617	1	journal	journal	PROPN
ejpam-5016	617	2	of	of	ADP
ejpam-5016	617	3	algebra	algebra	PROPN
ejpam-5016	617	4	and	and	CCONJ
ejpam-5016	617	5	its	its	PRON
ejpam-5016	617	6	applications	application	NOUN
ejpam-5016	617	7	,	,	PUNCT
ejpam-5016	617	8	22(02):2350055	22(02):2350055	NUM
ejpam-5016	617	9	,	,	PUNCT
ejpam-5016	617	10	2023	2023	NUM
ejpam-5016	617	11	.	.	PUNCT
ejpam-5016	618	1	[	[	X
ejpam-5016	618	2	6	6	NUM
ejpam-5016	618	3	]	]	SYM
ejpam-5016	618	4	c	c	NOUN
ejpam-5016	618	5	cisto	cisto	NOUN
ejpam-5016	618	6	,	,	PUNCT
ejpam-5016	618	7	f	f	PROPN
ejpam-5016	618	8	navarra	navarra	PROPN
ejpam-5016	618	9	,	,	PUNCT
ejpam-5016	618	10	and	and	CCONJ
ejpam-5016	618	11	r	r	NOUN
ejpam-5016	618	12	utano	utano	NOUN
ejpam-5016	618	13	.	.	PUNCT
ejpam-5016	619	1	on	on	ADP
ejpam-5016	619	2	gröbner	gröbner	NOUN
ejpam-5016	619	3	bases	basis	NOUN
ejpam-5016	619	4	and	and	CCONJ
ejpam-5016	619	5	cohen	cohen	NOUN
ejpam-5016	619	6	-	-	PUNCT
ejpam-5016	619	7	macaulay	macaulay	PROPN
ejpam-5016	619	8	property	property	NOUN
ejpam-5016	619	9	of	of	ADP
ejpam-5016	619	10	closed	closed	ADJ
ejpam-5016	619	11	path	path	NOUN
ejpam-5016	619	12	polyominoes	polyominoe	NOUN
ejpam-5016	619	13	.	.	PUNCT
ejpam-5016	620	1	the	the	DET
ejpam-5016	620	2	electric	electric	PROPN
ejpam-5016	620	3	journal	journal	PROPN
ejpam-5016	620	4	of	of	ADP
ejpam-5016	620	5	combinatorics	combinatoric	NOUN
ejpam-5016	620	6	,	,	PUNCT
ejpam-5016	620	7	29:#p3.54	29:#p3.54	NUM
ejpam-5016	620	8	,	,	PUNCT
ejpam-5016	620	9	2022	2022	NUM
ejpam-5016	620	10	.	.	PUNCT
ejpam-5016	621	1	[	[	X
ejpam-5016	621	2	7	7	NUM
ejpam-5016	621	3	]	]	X
ejpam-5016	621	4	c	c	NOUN
ejpam-5016	621	5	cisto	cisto	NOUN
ejpam-5016	621	6	,	,	PUNCT
ejpam-5016	621	7	f	f	PROPN
ejpam-5016	621	8	navarra	navarra	PROPN
ejpam-5016	621	9	,	,	PUNCT
ejpam-5016	621	10	and	and	CCONJ
ejpam-5016	621	11	r	r	NOUN
ejpam-5016	621	12	utano	utano	NOUN
ejpam-5016	621	13	.	.	PUNCT
ejpam-5016	622	1	primality	primality	NOUN
ejpam-5016	622	2	of	of	ADP
ejpam-5016	622	3	weakly	weakly	ADJ
ejpam-5016	622	4	connected	connected	ADJ
ejpam-5016	622	5	collections	collection	NOUN
ejpam-5016	622	6	of	of	ADP
ejpam-5016	622	7	cells	cell	NOUN
ejpam-5016	622	8	and	and	CCONJ
ejpam-5016	622	9	weakly	weakly	ADJ
ejpam-5016	622	10	closed	closed	ADJ
ejpam-5016	622	11	path	path	NOUN
ejpam-5016	622	12	polyominoes	polyominoe	NOUN
ejpam-5016	622	13	.	.	PUNCT
ejpam-5016	623	1	illinois	illinois	PROPN
ejpam-5016	623	2	journal	journal	PROPN
ejpam-5016	623	3	of	of	ADP
ejpam-5016	623	4	mathematics	mathematic	NOUN
ejpam-5016	623	5	,	,	PUNCT
ejpam-5016	623	6	66(4):545–563	66(4):545–563	PROPN
ejpam-5016	623	7	,	,	PUNCT
ejpam-5016	623	8	2022	2022	NUM
ejpam-5016	623	9	.	.	PUNCT
ejpam-5016	624	1	[	[	X
ejpam-5016	624	2	8	8	NUM
ejpam-5016	624	3	]	]	X
ejpam-5016	624	4	c	c	NOUN
ejpam-5016	624	5	cisto	cisto	NOUN
ejpam-5016	624	6	,	,	PUNCT
ejpam-5016	624	7	f	f	PROPN
ejpam-5016	624	8	navarra	navarra	PROPN
ejpam-5016	624	9	,	,	PUNCT
ejpam-5016	624	10	and	and	CCONJ
ejpam-5016	624	11	r	r	NOUN
ejpam-5016	624	12	utano	utano	NOUN
ejpam-5016	624	13	.	.	PUNCT
ejpam-5016	625	1	hilbert	hilbert	PROPN
ejpam-5016	625	2	–	–	PUNCT
ejpam-5016	625	3	poincaré	poincaré	ADJ
ejpam-5016	625	4	series	series	NOUN
ejpam-5016	625	5	and	and	CCONJ
ejpam-5016	625	6	gorenstein	gorenstein	ADJ
ejpam-5016	625	7	property	property	NOUN
ejpam-5016	625	8	for	for	ADP
ejpam-5016	625	9	some	some	DET
ejpam-5016	625	10	non	non	ADJ
ejpam-5016	625	11	-	-	ADJ
ejpam-5016	625	12	simple	simple	ADJ
ejpam-5016	625	13	polyominoes	polyominoe	NOUN
ejpam-5016	625	14	.	.	PUNCT
ejpam-5016	626	1	bulletin	bulletin	NOUN
ejpam-5016	626	2	of	of	ADP
ejpam-5016	626	3	the	the	DET
ejpam-5016	626	4	iranian	iranian	PROPN
ejpam-5016	626	5	mathematical	mathematical	PROPN
ejpam-5016	626	6	society	society	NOUN
ejpam-5016	626	7	,	,	PUNCT
ejpam-5016	626	8	49(3):22	49(3):22	NOUN
ejpam-5016	626	9	,	,	PUNCT
ejpam-5016	626	10	2023	2023	NUM
ejpam-5016	626	11	.	.	PUNCT
ejpam-5016	627	1	[	[	X
ejpam-5016	627	2	9	9	NUM
ejpam-5016	627	3	]	]	SYM
ejpam-5016	627	4	c	c	NOUN
ejpam-5016	627	5	cisto	cisto	NOUN
ejpam-5016	627	6	,	,	PUNCT
ejpam-5016	627	7	f	f	PROPN
ejpam-5016	627	8	navarra	navarra	PROPN
ejpam-5016	627	9	,	,	PUNCT
ejpam-5016	627	10	and	and	CCONJ
ejpam-5016	627	11	d	d	ADP
ejpam-5016	627	12	veer	veer	NOUN
ejpam-5016	627	13	.	.	PUNCT
ejpam-5016	628	1	polyocollection	polyocollection	NOUN
ejpam-5016	628	2	ideals	ideal	NOUN
ejpam-5016	628	3	and	and	CCONJ
ejpam-5016	628	4	primary	primary	ADJ
ejpam-5016	628	5	decomposition	decomposition	NOUN
ejpam-5016	628	6	of	of	ADP
ejpam-5016	628	7	polyomino	polyomino	NOUN
ejpam-5016	628	8	ideals	ideal	NOUN
ejpam-5016	628	9	.	.	PUNCT
ejpam-5016	629	1	journal	journal	NOUN
ejpam-5016	629	2	of	of	ADP
ejpam-5016	629	3	algebra	algebra	PROPN
ejpam-5016	629	4	,	,	PUNCT
ejpam-5016	629	5	641:498–529	641:498–529	NUM
ejpam-5016	629	6	,	,	PUNCT
ejpam-5016	629	7	2024	2024	NUM
ejpam-5016	629	8	.	.	PUNCT
ejpam-5016	630	1	[	[	X
ejpam-5016	630	2	10	10	NUM
ejpam-5016	630	3	]	]	PUNCT
ejpam-5016	630	4	carmelo	carmelo	NOUN
ejpam-5016	630	5	cisto	cisto	NOUN
ejpam-5016	630	6	,	,	PUNCT
ejpam-5016	630	7	rizwan	rizwan	PROPN
ejpam-5016	630	8	jahangir	jahangir	PROPN
ejpam-5016	630	9	,	,	PUNCT
ejpam-5016	630	10	and	and	CCONJ
ejpam-5016	630	11	francesco	francesco	PROPN
ejpam-5016	630	12	navarra	navarra	PROPN
ejpam-5016	630	13	.	.	PUNCT
ejpam-5016	631	1	on	on	ADP
ejpam-5016	631	2	algebraic	algebraic	ADJ
ejpam-5016	631	3	properties	property	NOUN
ejpam-5016	631	4	of	of	ADP
ejpam-5016	631	5	some	some	DET
ejpam-5016	631	6	non	non	ADJ
ejpam-5016	631	7	-	-	ADJ
ejpam-5016	631	8	prime	prime	ADJ
ejpam-5016	631	9	ideals	ideal	NOUN
ejpam-5016	631	10	of	of	ADP
ejpam-5016	631	11	collections	collection	NOUN
ejpam-5016	631	12	of	of	ADP
ejpam-5016	631	13	cells	cell	NOUN
ejpam-5016	631	14	.	.	PUNCT
ejpam-5016	632	1	arxiv	arxiv	PROPN
ejpam-5016	632	2	preprint	preprint	PROPN
ejpam-5016	632	3	arxiv:2401.09152	arxiv:2401.09152	PROPN
ejpam-5016	632	4	,	,	PUNCT
ejpam-5016	632	5	2024	2024	NUM
ejpam-5016	632	6	.	.	PUNCT
ejpam-5016	633	1	references	reference	NOUN
ejpam-5016	633	2	2649	2649	NUM
ejpam-5016	634	1	[	[	X
ejpam-5016	634	2	11	11	NUM
ejpam-5016	634	3	]	]	X
ejpam-5016	634	4	d	d	X
ejpam-5016	634	5	a	a	DET
ejpam-5016	634	6	cox	cox	PROPN
ejpam-5016	634	7	,	,	PUNCT
ejpam-5016	634	8	j	j	PROPN
ejpam-5016	634	9	little	little	ADJ
ejpam-5016	634	10	,	,	PUNCT
ejpam-5016	634	11	and	and	CCONJ
ejpam-5016	634	12	d	d	PROPN
ejpam-5016	634	13	oshea	oshea	PROPN
ejpam-5016	634	14	.	.	PUNCT
ejpam-5016	635	1	ideals	ideal	NOUN
ejpam-5016	635	2	,	,	PUNCT
ejpam-5016	635	3	varieties	variety	NOUN
ejpam-5016	635	4	,	,	PUNCT
ejpam-5016	635	5	and	and	CCONJ
ejpam-5016	635	6	algorithms	algorithm	NOUN
ejpam-5016	635	7	:	:	PUNCT
ejpam-5016	635	8	an	an	DET
ejpam-5016	635	9	introduction	introduction	NOUN
ejpam-5016	635	10	to	to	ADP
ejpam-5016	635	11	computational	computational	ADJ
ejpam-5016	635	12	algebraic	algebraic	ADJ
ejpam-5016	635	13	geometry	geometry	NOUN
ejpam-5016	635	14	and	and	CCONJ
ejpam-5016	635	15	commutative	commutative	ADJ
ejpam-5016	635	16	algebra	algebra	NOUN
ejpam-5016	635	17	.	.	PUNCT
ejpam-5016	636	1	springer	springer	NOUN
ejpam-5016	636	2	science	science	PROPN
ejpam-5016	636	3	&	&	CCONJ
ejpam-5016	636	4	business	business	NOUN
ejpam-5016	636	5	media	medium	NOUN
ejpam-5016	636	6	,	,	PUNCT
ejpam-5016	636	7	2013	2013	NUM
ejpam-5016	636	8	.	.	PUNCT
ejpam-5016	637	1	[	[	X
ejpam-5016	637	2	12	12	NUM
ejpam-5016	637	3	]	]	X
ejpam-5016	637	4	m	m	VERB
ejpam-5016	637	5	delest	del	ADJ
ejpam-5016	637	6	and	and	CCONJ
ejpam-5016	637	7	g	g	ADP
ejpam-5016	637	8	viennot	viennot	NOUN
ejpam-5016	637	9	.	.	PUNCT
ejpam-5016	638	1	algebraic	algebraic	ADJ
ejpam-5016	638	2	languages	language	NOUN
ejpam-5016	638	3	and	and	CCONJ
ejpam-5016	638	4	polyominoes	polyominoe	NOUN
ejpam-5016	638	5	enumeration	enumeration	NOUN
ejpam-5016	638	6	.	.	PUNCT
ejpam-5016	639	1	theoretical	theoretical	ADJ
ejpam-5016	639	2	computer	computer	NOUN
ejpam-5016	639	3	science	science	NOUN
ejpam-5016	639	4	,	,	PUNCT
ejpam-5016	639	5	34(1	34(1	NOUN
ejpam-5016	639	6	-	-	SYM
ejpam-5016	639	7	2):169–206	2):169–206	NUM
ejpam-5016	639	8	,	,	PUNCT
ejpam-5016	639	9	1984	1984	NUM
ejpam-5016	639	10	.	.	PUNCT
ejpam-5016	640	1	[	[	X
ejpam-5016	640	2	13	13	NUM
ejpam-5016	640	3	]	]	SYM
ejpam-5016	640	4	r	r	NOUN
ejpam-5016	640	5	dinu	dinu	NOUN
ejpam-5016	640	6	and	and	CCONJ
ejpam-5016	640	7	f	f	PROPN
ejpam-5016	640	8	navarra	navarra	PROPN
ejpam-5016	640	9	.	.	PUNCT
ejpam-5016	641	1	non	non	ADJ
ejpam-5016	641	2	-	-	ADJ
ejpam-5016	641	3	simple	simple	ADJ
ejpam-5016	641	4	polyominoes	polyominoe	NOUN
ejpam-5016	641	5	of	of	ADP
ejpam-5016	641	6	könig	könig	PROPN
ejpam-5016	641	7	type	type	NOUN
ejpam-5016	641	8	and	and	CCONJ
ejpam-5016	641	9	their	their	PRON
ejpam-5016	641	10	canonical	canonical	ADJ
ejpam-5016	641	11	module	module	NOUN
ejpam-5016	641	12	.	.	PUNCT
ejpam-5016	642	1	page	page	NOUN
ejpam-5016	642	2	arxiv:2210.12665	arxiv:2210.12665	NOUN
ejpam-5016	642	3	.	.	PUNCT
ejpam-5016	643	1	[	[	X
ejpam-5016	643	2	14	14	NUM
ejpam-5016	643	3	]	]	X
ejpam-5016	643	4	r	r	NOUN
ejpam-5016	643	5	dinu	dinu	NOUN
ejpam-5016	643	6	and	and	CCONJ
ejpam-5016	643	7	f	f	PROPN
ejpam-5016	643	8	navarra	navarra	PROPN
ejpam-5016	643	9	.	.	PUNCT
ejpam-5016	644	1	on	on	ADP
ejpam-5016	644	2	the	the	DET
ejpam-5016	644	3	rook	rook	NOUN
ejpam-5016	644	4	polynomial	polynomial	NOUN
ejpam-5016	644	5	of	of	ADP
ejpam-5016	644	6	grid	grid	NOUN
ejpam-5016	644	7	polyominoes	polyominoe	NOUN
ejpam-5016	644	8	.	.	PUNCT
ejpam-5016	645	1	arxiv:2309.01818	arxiv:2309.01818	NOUN
ejpam-5016	645	2	.	.	PUNCT
ejpam-5016	646	1	[	[	X
ejpam-5016	646	2	15	15	NUM
ejpam-5016	646	3	]	]	SYM
ejpam-5016	646	4	v	v	NOUN
ejpam-5016	646	5	ene	ene	PROPN
ejpam-5016	646	6	,	,	PUNCT
ejpam-5016	646	7	j	j	PROPN
ejpam-5016	646	8	herzog	herzog	PROPN
ejpam-5016	646	9	,	,	PUNCT
ejpam-5016	646	10	and	and	CCONJ
ejpam-5016	646	11	t	t	PROPN
ejpam-5016	646	12	hibi	hibi	NOUN
ejpam-5016	646	13	.	.	PUNCT
ejpam-5016	647	1	linearly	linearly	ADV
ejpam-5016	647	2	related	relate	VERB
ejpam-5016	647	3	polyominoes	polyominoe	NOUN
ejpam-5016	647	4	.	.	PUNCT
ejpam-5016	648	1	journal	journal	NOUN
ejpam-5016	648	2	of	of	ADP
ejpam-5016	648	3	algebraic	algebraic	PROPN
ejpam-5016	648	4	combinatorics	combinatoric	NOUN
ejpam-5016	648	5	,	,	PUNCT
ejpam-5016	648	6	41:949–968	41:949–968	PROPN
ejpam-5016	648	7	,	,	PUNCT
ejpam-5016	648	8	2015	2015	NUM
ejpam-5016	648	9	.	.	PUNCT
ejpam-5016	649	1	[	[	X
ejpam-5016	649	2	16	16	NUM
ejpam-5016	649	3	]	]	PUNCT
ejpam-5016	649	4	v	v	NUM
ejpam-5016	649	5	ene	ene	PROPN
ejpam-5016	649	6	,	,	PUNCT
ejpam-5016	649	7	j	j	PROPN
ejpam-5016	649	8	herzog	herzog	PROPN
ejpam-5016	649	9	,	,	PUNCT
ejpam-5016	649	10	a	a	DET
ejpam-5016	649	11	a	a	DET
ejpam-5016	649	12	qureshi	qureshi	PROPN
ejpam-5016	649	13	,	,	PUNCT
ejpam-5016	649	14	and	and	CCONJ
ejpam-5016	649	15	f	f	PROPN
ejpam-5016	649	16	romeo	romeo	PROPN
ejpam-5016	649	17	.	.	PUNCT
ejpam-5016	650	1	regularity	regularity	NOUN
ejpam-5016	650	2	and	and	CCONJ
ejpam-5016	650	3	gorenstein	gorenstein	ADJ
ejpam-5016	650	4	property	property	NOUN
ejpam-5016	650	5	of	of	ADP
ejpam-5016	650	6	the	the	DET
ejpam-5016	650	7	l	l	ADJ
ejpam-5016	650	8	-	-	ADJ
ejpam-5016	650	9	convex	convex	ADJ
ejpam-5016	650	10	polyominoes	polyominoe	NOUN
ejpam-5016	650	11	.	.	PUNCT
ejpam-5016	651	1	the	the	DET
ejpam-5016	651	2	electric	electric	PROPN
ejpam-5016	651	3	journal	journal	PROPN
ejpam-5016	651	4	of	of	ADP
ejpam-5016	651	5	combinatorics	combinatoric	NOUN
ejpam-5016	651	6	,	,	PUNCT
ejpam-5016	651	7	28(1):#p1.50	28(1):#p1.50	NUM
ejpam-5016	651	8	,	,	PUNCT
ejpam-5016	651	9	2021	2021	NUM
ejpam-5016	651	10	.	.	PUNCT
ejpam-5016	652	1	[	[	X
ejpam-5016	652	2	17	17	NUM
ejpam-5016	652	3	]	]	SYM
ejpam-5016	652	4	s	s	PROPN
ejpam-5016	652	5	w	w	NOUN
ejpam-5016	652	6	golomb	golomb	NOUN
ejpam-5016	652	7	.	.	PUNCT
ejpam-5016	653	1	tiling	tile	VERB
ejpam-5016	653	2	with	with	ADP
ejpam-5016	653	3	polyominoes	polyominoe	NOUN
ejpam-5016	653	4	.	.	PUNCT
ejpam-5016	654	1	journal	journal	NOUN
ejpam-5016	654	2	of	of	ADP
ejpam-5016	654	3	combinatorial	combinatorial	ADJ
ejpam-5016	654	4	theory	theory	NOUN
ejpam-5016	654	5	,	,	PUNCT
ejpam-5016	654	6	1(2):280	1(2):280	NUM
ejpam-5016	654	7	–	–	PUNCT
ejpam-5016	654	8	296	296	NUM
ejpam-5016	654	9	,	,	PUNCT
ejpam-5016	654	10	1966	1966	NUM
ejpam-5016	654	11	.	.	PUNCT
ejpam-5016	655	1	[	[	X
ejpam-5016	655	2	18	18	NUM
ejpam-5016	655	3	]	]	SYM
ejpam-5016	655	4	s	s	PROPN
ejpam-5016	655	5	w	w	NOUN
ejpam-5016	655	6	golomb	golomb	NOUN
ejpam-5016	655	7	.	.	PUNCT
ejpam-5016	656	1	tiling	tile	VERB
ejpam-5016	656	2	with	with	ADP
ejpam-5016	656	3	sets	set	NOUN
ejpam-5016	656	4	of	of	ADP
ejpam-5016	656	5	polyominoes	polyominoe	NOUN
ejpam-5016	656	6	.	.	PUNCT
ejpam-5016	657	1	journal	journal	NOUN
ejpam-5016	657	2	of	of	ADP
ejpam-5016	657	3	combinatorial	combinatorial	ADJ
ejpam-5016	657	4	theory	theory	NOUN
ejpam-5016	657	5	,	,	PUNCT
ejpam-5016	657	6	9(1):60–71	9(1):60–71	NUM
ejpam-5016	657	7	,	,	PUNCT
ejpam-5016	657	8	1970	1970	NUM
ejpam-5016	657	9	.	.	PUNCT
ejpam-5016	658	1	[	[	X
ejpam-5016	658	2	19	19	NUM
ejpam-5016	658	3	]	]	SYM
ejpam-5016	658	4	s	s	PROPN
ejpam-5016	658	5	w	w	NOUN
ejpam-5016	658	6	golomb	golomb	NOUN
ejpam-5016	658	7	.	.	PUNCT
ejpam-5016	659	1	polyominoes	polyominoe	NOUN
ejpam-5016	659	2	:	:	PUNCT
ejpam-5016	660	1	puzzles	puzzle	NOUN
ejpam-5016	660	2	,	,	PUNCT
ejpam-5016	660	3	patterns	pattern	NOUN
ejpam-5016	660	4	,	,	PUNCT
ejpam-5016	660	5	problems	problem	NOUN
ejpam-5016	660	6	,	,	PUNCT
ejpam-5016	660	7	and	and	CCONJ
ejpam-5016	660	8	packings	packing	NOUN
ejpam-5016	660	9	.	.	PUNCT
ejpam-5016	661	1	princeton	princeton	PROPN
ejpam-5016	661	2	university	university	PROPN
ejpam-5016	661	3	press	press	NOUN
ejpam-5016	661	4	,	,	PUNCT
ejpam-5016	661	5	1996	1996	NUM
ejpam-5016	661	6	.	.	PUNCT
ejpam-5016	662	1	[	[	X
ejpam-5016	662	2	20	20	NUM
ejpam-5016	662	3	]	]	X
ejpam-5016	662	4	y	y	PROPN
ejpam-5016	662	5	y	y	PROPN
ejpam-5016	662	6	hamonangan	hamonangan	VERB
ejpam-5016	662	7	and	and	CCONJ
ejpam-5016	662	8	i	i	PRON
ejpam-5016	662	9	muchtadi	muchtadi	NOUN
ejpam-5016	662	10	-	-	PUNCT
ejpam-5016	662	11	alamsyah	alamsyah	NOUN
ejpam-5016	662	12	.	.	PUNCT
ejpam-5016	663	1	on	on	ADP
ejpam-5016	663	2	radical	radical	ADJ
ejpam-5016	663	3	property	property	NOUN
ejpam-5016	663	4	of	of	ADP
ejpam-5016	663	5	cross	cross	ADJ
ejpam-5016	663	6	polyomino	polyomino	PROPN
ejpam-5016	663	7	ideal	ideal	NOUN
ejpam-5016	663	8	.	.	PUNCT
ejpam-5016	664	1	journal	journal	PROPN
ejpam-5016	664	2	of	of	ADP
ejpam-5016	664	3	physics	physics	PROPN
ejpam-5016	664	4	:	:	PUNCT
ejpam-5016	664	5	conference	conference	NOUN
ejpam-5016	664	6	series	series	NOUN
ejpam-5016	664	7	,	,	PUNCT
ejpam-5016	664	8	1306(1):012023	1306(1):012023	NUM
ejpam-5016	664	9	,	,	PUNCT
ejpam-5016	664	10	2019	2019	NUM
ejpam-5016	664	11	.	.	PUNCT
ejpam-5016	665	1	[	[	X
ejpam-5016	665	2	21	21	NUM
ejpam-5016	665	3	]	]	X
ejpam-5016	665	4	j	j	PROPN
ejpam-5016	665	5	herzog	herzog	PROPN
ejpam-5016	665	6	and	and	CCONJ
ejpam-5016	665	7	t	t	PROPN
ejpam-5016	665	8	hibi	hibi	PROPN
ejpam-5016	665	9	.	.	PUNCT
ejpam-5016	666	1	finite	finite	VERB
ejpam-5016	666	2	distributive	distributive	ADJ
ejpam-5016	666	3	lattices	lattice	NOUN
ejpam-5016	666	4	,	,	PUNCT
ejpam-5016	666	5	polyominoes	polyominoe	NOUN
ejpam-5016	666	6	and	and	CCONJ
ejpam-5016	666	7	ideals	ideal	NOUN
ejpam-5016	666	8	of	of	ADP
ejpam-5016	666	9	könig	könig	PROPN
ejpam-5016	666	10	type	type	NOUN
ejpam-5016	666	11	.	.	PUNCT
ejpam-5016	667	1	arxiv:2202.09643	arxiv:2202.09643	NOUN
ejpam-5016	667	2	.	.	PUNCT
ejpam-5016	668	1	[	[	X
ejpam-5016	668	2	22	22	NUM
ejpam-5016	668	3	]	]	X
ejpam-5016	668	4	j	j	PROPN
ejpam-5016	668	5	herzog	herzog	PROPN
ejpam-5016	668	6	and	and	CCONJ
ejpam-5016	668	7	t	t	PROPN
ejpam-5016	668	8	hibi	hibi	NOUN
ejpam-5016	668	9	.	.	PUNCT
ejpam-5016	669	1	ideals	ideal	NOUN
ejpam-5016	669	2	generated	generate	VERB
ejpam-5016	669	3	by	by	ADP
ejpam-5016	669	4	adjacent	adjacent	ADJ
ejpam-5016	669	5	2	2	NUM
ejpam-5016	669	6	-	-	PUNCT
ejpam-5016	669	7	minors	minor	NOUN
ejpam-5016	669	8	.	.	PUNCT
ejpam-5016	670	1	journal	journal	PROPN
ejpam-5016	670	2	of	of	ADP
ejpam-5016	670	3	commutative	commutative	ADJ
ejpam-5016	670	4	algebra	algebra	NOUN
ejpam-5016	670	5	,	,	PUNCT
ejpam-5016	670	6	4(4):525–549	4(4):525–549	NUM
ejpam-5016	670	7	,	,	PUNCT
ejpam-5016	670	8	2012	2012	NUM
ejpam-5016	670	9	.	.	PUNCT
ejpam-5016	671	1	[	[	X
ejpam-5016	671	2	23	23	NUM
ejpam-5016	671	3	]	]	X
ejpam-5016	671	4	j	j	PROPN
ejpam-5016	671	5	herzog	herzog	PROPN
ejpam-5016	671	6	,	,	PUNCT
ejpam-5016	671	7	t	t	PROPN
ejpam-5016	671	8	hibi	hibi	NOUN
ejpam-5016	671	9	,	,	PUNCT
ejpam-5016	671	10	and	and	CCONJ
ejpam-5016	671	11	h	h	PROPN
ejpam-5016	671	12	ohsugi	ohsugi	PROPN
ejpam-5016	671	13	.	.	PUNCT
ejpam-5016	672	1	binomial	binomial	ADJ
ejpam-5016	672	2	ideals	ideal	NOUN
ejpam-5016	672	3	,	,	PUNCT
ejpam-5016	672	4	volume	volume	NOUN
ejpam-5016	672	5	279	279	NUM
ejpam-5016	672	6	.	.	PUNCT
ejpam-5016	672	7	springer	springer	NOUN
ejpam-5016	672	8	,	,	PUNCT
ejpam-5016	672	9	2018	2018	NUM
ejpam-5016	672	10	.	.	PUNCT
ejpam-5016	673	1	[	[	X
ejpam-5016	673	2	24	24	NUM
ejpam-5016	673	3	]	]	X
ejpam-5016	673	4	j	j	PROPN
ejpam-5016	673	5	herzog	herzog	PROPN
ejpam-5016	673	6	and	and	CCONJ
ejpam-5016	673	7	s	s	NOUN
ejpam-5016	673	8	s	s	PROPN
ejpam-5016	673	9	madani	madani	PROPN
ejpam-5016	673	10	.	.	PUNCT
ejpam-5016	674	1	the	the	DET
ejpam-5016	674	2	coordinate	coordinate	NOUN
ejpam-5016	674	3	ring	ring	NOUN
ejpam-5016	674	4	of	of	ADP
ejpam-5016	674	5	a	a	DET
ejpam-5016	674	6	simple	simple	ADJ
ejpam-5016	674	7	polyomino	polyomino	NOUN
ejpam-5016	674	8	.	.	PUNCT
ejpam-5016	675	1	illinois	illinois	PROPN
ejpam-5016	675	2	journal	journal	PROPN
ejpam-5016	675	3	of	of	ADP
ejpam-5016	675	4	mathematics	mathematic	NOUN
ejpam-5016	675	5	,	,	PUNCT
ejpam-5016	675	6	58(4):981–995	58(4):981–995	NUM
ejpam-5016	675	7	,	,	PUNCT
ejpam-5016	675	8	2014	2014	NUM
ejpam-5016	675	9	.	.	PUNCT
ejpam-5016	676	1	[	[	X
ejpam-5016	676	2	25	25	NUM
ejpam-5016	676	3	]	]	X
ejpam-5016	676	4	j	j	PROPN
ejpam-5016	676	5	herzog	herzog	PROPN
ejpam-5016	676	6	,	,	PUNCT
ejpam-5016	676	7	ayesha	ayesha	PROPN
ejpam-5016	676	8	a	a	DET
ejpam-5016	676	9	qureshi	qureshi	PROPN
ejpam-5016	676	10	,	,	PUNCT
ejpam-5016	676	11	and	and	CCONJ
ejpam-5016	676	12	a	a	DET
ejpam-5016	676	13	shikama	shikama	NOUN
ejpam-5016	676	14	.	.	PUNCT
ejpam-5016	677	1	gröbner	gröbner	NOUN
ejpam-5016	677	2	bases	basis	NOUN
ejpam-5016	677	3	of	of	ADP
ejpam-5016	677	4	balanced	balanced	ADJ
ejpam-5016	677	5	polyominoes	polyominoe	NOUN
ejpam-5016	677	6	.	.	PUNCT
ejpam-5016	678	1	mathematische	mathematische	PROPN
ejpam-5016	678	2	nachrichten	nachrichten	PROPN
ejpam-5016	678	3	,	,	PUNCT
ejpam-5016	678	4	288(7):775–783	288(7):775–783	NUM
ejpam-5016	678	5	,	,	PUNCT
ejpam-5016	678	6	2015	2015	NUM
ejpam-5016	678	7	.	.	PUNCT
ejpam-5016	679	1	[	[	X
ejpam-5016	679	2	26	26	NUM
ejpam-5016	679	3	]	]	PUNCT
ejpam-5016	679	4	t	t	PROPN
ejpam-5016	679	5	hibi	hibi	PROPN
ejpam-5016	679	6	and	and	CCONJ
ejpam-5016	679	7	a	a	DET
ejpam-5016	679	8	a	a	DET
ejpam-5016	679	9	qureshi	qureshi	PROPN
ejpam-5016	679	10	.	.	PUNCT
ejpam-5016	680	1	nonsimple	nonsimple	ADJ
ejpam-5016	680	2	polyominoes	polyominoe	NOUN
ejpam-5016	680	3	and	and	CCONJ
ejpam-5016	680	4	prime	prime	ADJ
ejpam-5016	680	5	ideals	ideal	NOUN
ejpam-5016	680	6	.	.	PUNCT
ejpam-5016	681	1	illinois	illinois	PROPN
ejpam-5016	681	2	journal	journal	PROPN
ejpam-5016	681	3	of	of	ADP
ejpam-5016	681	4	mathematics	mathematics	PROPN
ejpam-5016	681	5	,	,	PUNCT
ejpam-5016	681	6	59(2):391–398	59(2):391–398	PROPN
ejpam-5016	681	7	,	,	PUNCT
ejpam-5016	681	8	2015	2015	NUM
ejpam-5016	681	9	.	.	PUNCT
ejpam-5016	682	1	references	reference	NOUN
ejpam-5016	682	2	2650	2650	NUM
ejpam-5016	682	3	[	[	X
ejpam-5016	682	4	27	27	NUM
ejpam-5016	682	5	]	]	X
ejpam-5016	682	6	s	s	AUX
ejpam-5016	682	7	hoşten	hoşten	PROPN
ejpam-5016	682	8	and	and	CCONJ
ejpam-5016	682	9	s	s	VERB
ejpam-5016	682	10	sullivant	sullivant	VERB
ejpam-5016	682	11	.	.	PUNCT
ejpam-5016	683	1	ideals	ideal	NOUN
ejpam-5016	683	2	of	of	ADP
ejpam-5016	683	3	adjacent	adjacent	ADJ
ejpam-5016	683	4	minors	minor	NOUN
ejpam-5016	683	5	.	.	PUNCT
ejpam-5016	684	1	journal	journal	PROPN
ejpam-5016	684	2	of	of	ADP
ejpam-5016	684	3	algebra	algebra	PROPN
ejpam-5016	684	4	,	,	PUNCT
ejpam-5016	684	5	277(2):615	277(2):615	NUM
ejpam-5016	684	6	–	–	PUNCT
ejpam-5016	684	7	642	642	NUM
ejpam-5016	684	8	,	,	PUNCT
ejpam-5016	684	9	2004	2004	NUM
ejpam-5016	684	10	.	.	PUNCT
ejpam-5016	685	1	[	[	X
ejpam-5016	685	2	28	28	NUM
ejpam-5016	685	3	]	]	X
ejpam-5016	685	4	r	r	X
ejpam-5016	685	5	jahangir	jahangir	PROPN
ejpam-5016	685	6	and	and	CCONJ
ejpam-5016	685	7	f	f	PROPN
ejpam-5016	685	8	navarra	navarra	PROPN
ejpam-5016	685	9	.	.	PUNCT
ejpam-5016	686	1	shellable	shellable	ADJ
ejpam-5016	686	2	simplicial	simplicial	ADJ
ejpam-5016	686	3	complex	complex	NOUN
ejpam-5016	686	4	and	and	CCONJ
ejpam-5016	686	5	switching	switch	VERB
ejpam-5016	686	6	rook	rook	NOUN
ejpam-5016	686	7	polynomial	polynomial	NOUN
ejpam-5016	686	8	of	of	ADP
ejpam-5016	686	9	frame	frame	NOUN
ejpam-5016	686	10	polyominoes	polyominoe	NOUN
ejpam-5016	686	11	.	.	PUNCT
ejpam-5016	687	1	journal	journal	NOUN
ejpam-5016	687	2	of	of	ADP
ejpam-5016	687	3	pure	pure	ADJ
ejpam-5016	687	4	and	and	CCONJ
ejpam-5016	687	5	applied	applied	ADJ
ejpam-5016	687	6	algebra	algebra	NOUN
ejpam-5016	687	7	,	,	PUNCT
ejpam-5016	687	8	228(6):107576	228(6):107576	PROPN
ejpam-5016	687	9	,	,	PUNCT
ejpam-5016	687	10	2024	2024	NUM
ejpam-5016	687	11	.	.	PUNCT
ejpam-5016	688	1	[	[	X
ejpam-5016	688	2	29	29	NUM
ejpam-5016	688	3	]	]	X
ejpam-5016	688	4	m	m	VERB
ejpam-5016	688	5	kummini	kummini	NOUN
ejpam-5016	688	6	and	and	CCONJ
ejpam-5016	688	7	d	d	ADP
ejpam-5016	688	8	veer	veer	NOUN
ejpam-5016	688	9	.	.	PUNCT
ejpam-5016	689	1	the	the	DET
ejpam-5016	689	2	charney	charney	PROPN
ejpam-5016	689	3	-	-	PUNCT
ejpam-5016	689	4	davis	davis	PROPN
ejpam-5016	689	5	conjecture	conjecture	VERB
ejpam-5016	689	6	for	for	ADP
ejpam-5016	689	7	simple	simple	ADJ
ejpam-5016	689	8	thin	thin	ADJ
ejpam-5016	689	9	polyominoes	polyominoe	NOUN
ejpam-5016	689	10	.	.	PUNCT
ejpam-5016	690	1	communications	communication	NOUN
ejpam-5016	690	2	in	in	ADP
ejpam-5016	690	3	algebra	algebra	NOUN
ejpam-5016	690	4	,	,	PUNCT
ejpam-5016	690	5	51(4):1654–1662	51(4):1654–1662	NUM
ejpam-5016	690	6	,	,	PUNCT
ejpam-5016	690	7	2023	2023	NUM
ejpam-5016	690	8	.	.	PUNCT
ejpam-5016	691	1	[	[	X
ejpam-5016	691	2	30	30	NUM
ejpam-5016	691	3	]	]	X
ejpam-5016	691	4	m	m	VERB
ejpam-5016	691	5	kummini	kummini	NOUN
ejpam-5016	691	6	and	and	CCONJ
ejpam-5016	691	7	d	d	ADP
ejpam-5016	691	8	veer	veer	NOUN
ejpam-5016	691	9	.	.	PUNCT
ejpam-5016	692	1	the	the	DET
ejpam-5016	692	2	h	h	NOUN
ejpam-5016	692	3	-	-	PUNCT
ejpam-5016	692	4	polynomial	polynomial	ADJ
ejpam-5016	692	5	and	and	CCONJ
ejpam-5016	692	6	the	the	DET
ejpam-5016	692	7	rook	rook	NOUN
ejpam-5016	692	8	polynomial	polynomial	NOUN
ejpam-5016	692	9	of	of	ADP
ejpam-5016	692	10	some	some	DET
ejpam-5016	692	11	polyominoes	polyominoe	NOUN
ejpam-5016	692	12	.	.	PUNCT
ejpam-5016	693	1	the	the	DET
ejpam-5016	693	2	electronic	electronic	ADJ
ejpam-5016	693	3	journal	journal	NOUN
ejpam-5016	693	4	of	of	ADP
ejpam-5016	693	5	combinatorics	combinatorics	PROPN
ejpam-5016	693	6	,	,	PUNCT
ejpam-5016	693	7	30(2):p2.6	30(2):p2.6	NUM
ejpam-5016	693	8	,	,	PUNCT
ejpam-5016	693	9	2023	2023	NUM
ejpam-5016	693	10	.	.	PUNCT
ejpam-5016	694	1	[	[	X
ejpam-5016	694	2	31	31	NUM
ejpam-5016	694	3	]	]	X
ejpam-5016	694	4	c	c	PROPN
ejpam-5016	694	5	mascia	mascia	PROPN
ejpam-5016	694	6	,	,	PUNCT
ejpam-5016	694	7	g	g	PROPN
ejpam-5016	694	8	rinaldo	rinaldo	PROPN
ejpam-5016	694	9	,	,	PUNCT
ejpam-5016	694	10	and	and	CCONJ
ejpam-5016	694	11	f	f	PROPN
ejpam-5016	694	12	romeo	romeo	PROPN
ejpam-5016	694	13	.	.	PUNCT
ejpam-5016	695	1	primality	primality	NOUN
ejpam-5016	695	2	of	of	ADP
ejpam-5016	695	3	multiply	multiply	ADV
ejpam-5016	695	4	connected	connected	ADJ
ejpam-5016	695	5	polyominoes	polyominoe	NOUN
ejpam-5016	695	6	.	.	PUNCT
ejpam-5016	696	1	illinois	illinois	PROPN
ejpam-5016	696	2	journal	journal	PROPN
ejpam-5016	696	3	of	of	ADP
ejpam-5016	696	4	mathematics	mathematics	PROPN
ejpam-5016	696	5	,	,	PUNCT
ejpam-5016	696	6	64(7):291–304	64(7):291–304	PROPN
ejpam-5016	696	7	,	,	PUNCT
ejpam-5016	696	8	2020	2020	NUM
ejpam-5016	696	9	.	.	PUNCT
ejpam-5016	697	1	[	[	X
ejpam-5016	697	2	32	32	NUM
ejpam-5016	697	3	]	]	X
ejpam-5016	697	4	c	c	PROPN
ejpam-5016	697	5	mascia	mascia	PROPN
ejpam-5016	697	6	,	,	PUNCT
ejpam-5016	697	7	g	g	PROPN
ejpam-5016	697	8	rinaldo	rinaldo	PROPN
ejpam-5016	697	9	,	,	PUNCT
ejpam-5016	697	10	and	and	CCONJ
ejpam-5016	697	11	f	f	PROPN
ejpam-5016	697	12	romeo	romeo	PROPN
ejpam-5016	697	13	.	.	PUNCT
ejpam-5016	698	1	primality	primality	NOUN
ejpam-5016	698	2	of	of	ADP
ejpam-5016	698	3	polyomino	polyomino	NOUN
ejpam-5016	698	4	ideals	ideal	NOUN
ejpam-5016	698	5	by	by	ADP
ejpam-5016	698	6	quadratic	quadratic	ADJ
ejpam-5016	698	7	gröbner	gröbner	NOUN
ejpam-5016	698	8	basis	basis	NOUN
ejpam-5016	698	9	.	.	PUNCT
ejpam-5016	699	1	mathematische	mathematische	PROPN
ejpam-5016	699	2	nachrichten	nachrichten	PROPN
ejpam-5016	699	3	,	,	PUNCT
ejpam-5016	699	4	295(3):593–606	295(3):593–606	NUM
ejpam-5016	699	5	,	,	PUNCT
ejpam-5016	699	6	2022	2022	NUM
ejpam-5016	699	7	.	.	PUNCT
ejpam-5016	700	1	[	[	X
ejpam-5016	700	2	33	33	NUM
ejpam-5016	700	3	]	]	X
ejpam-5016	700	4	g	g	PROPN
ejpam-5016	700	5	pistone	pistone	PROPN
ejpam-5016	700	6	,	,	PUNCT
ejpam-5016	700	7	e	e	NOUN
ejpam-5016	700	8	riccomagno	riccomagno	NOUN
ejpam-5016	700	9	,	,	PUNCT
ejpam-5016	700	10	and	and	CCONJ
ejpam-5016	700	11	h	h	NOUN
ejpam-5016	700	12	p	p	PROPN
ejpam-5016	700	13	wynn	wynn	PROPN
ejpam-5016	700	14	.	.	PUNCT
ejpam-5016	701	1	algebraic	algebraic	ADJ
ejpam-5016	701	2	statistics	statistic	NOUN
ejpam-5016	701	3	:	:	PUNCT
ejpam-5016	701	4	computational	computational	ADJ
ejpam-5016	701	5	commutative	commutative	ADJ
ejpam-5016	701	6	algebra	algebra	NOUN
ejpam-5016	701	7	in	in	ADP
ejpam-5016	701	8	statistics	statistic	NOUN
ejpam-5016	701	9	.	.	PUNCT
ejpam-5016	702	1	crc	crc	PROPN
ejpam-5016	702	2	press	press	PROPN
ejpam-5016	702	3	,	,	PUNCT
ejpam-5016	702	4	2000	2000	NUM
ejpam-5016	702	5	.	.	PUNCT
ejpam-5016	703	1	[	[	X
ejpam-5016	703	2	34	34	NUM
ejpam-5016	703	3	]	]	X
ejpam-5016	703	4	a	a	DET
ejpam-5016	703	5	a	a	DET
ejpam-5016	703	6	qureshi	qureshi	PROPN
ejpam-5016	703	7	.	.	PUNCT
ejpam-5016	704	1	ideals	ideal	NOUN
ejpam-5016	704	2	generated	generate	VERB
ejpam-5016	704	3	by	by	ADP
ejpam-5016	704	4	2	2	NUM
ejpam-5016	704	5	-	-	PUNCT
ejpam-5016	704	6	minors	minor	NOUN
ejpam-5016	704	7	,	,	PUNCT
ejpam-5016	704	8	collections	collection	NOUN
ejpam-5016	704	9	of	of	ADP
ejpam-5016	704	10	cells	cell	NOUN
ejpam-5016	704	11	and	and	CCONJ
ejpam-5016	704	12	stack	stack	NOUN
ejpam-5016	704	13	polyominoes	polyominoe	NOUN
ejpam-5016	704	14	.	.	PUNCT
ejpam-5016	705	1	journal	journal	PROPN
ejpam-5016	705	2	of	of	ADP
ejpam-5016	705	3	algebra	algebra	PROPN
ejpam-5016	705	4	,	,	PUNCT
ejpam-5016	705	5	357:279–303	357:279–303	NUM
ejpam-5016	705	6	,	,	PUNCT
ejpam-5016	705	7	2012	2012	NUM
ejpam-5016	705	8	.	.	PUNCT
ejpam-5016	706	1	[	[	X
ejpam-5016	706	2	35	35	NUM
ejpam-5016	706	3	]	]	X
ejpam-5016	706	4	a	a	DET
ejpam-5016	706	5	a	a	DET
ejpam-5016	706	6	qureshi	qureshi	PROPN
ejpam-5016	706	7	,	,	PUNCT
ejpam-5016	706	8	g	g	PROPN
ejpam-5016	706	9	rinaldo	rinaldo	PROPN
ejpam-5016	706	10	,	,	PUNCT
ejpam-5016	706	11	and	and	CCONJ
ejpam-5016	706	12	f	f	PROPN
ejpam-5016	706	13	romeo	romeo	PROPN
ejpam-5016	706	14	.	.	PUNCT
ejpam-5016	707	1	hilbert	hilbert	PROPN
ejpam-5016	707	2	series	series	PROPN
ejpam-5016	707	3	of	of	ADP
ejpam-5016	707	4	parallelogram	parallelogram	PROPN
ejpam-5016	707	5	polyominoes	polyominoe	NOUN
ejpam-5016	707	6	.	.	PUNCT
ejpam-5016	708	1	research	research	NOUN
ejpam-5016	708	2	in	in	ADP
ejpam-5016	708	3	the	the	DET
ejpam-5016	708	4	mathematical	mathematical	ADJ
ejpam-5016	708	5	sciences	science	NOUN
ejpam-5016	708	6	,	,	PUNCT
ejpam-5016	708	7	9(2):28	9(2):28	NUM
ejpam-5016	708	8	,	,	PUNCT
ejpam-5016	708	9	2022	2022	NUM
ejpam-5016	708	10	.	.	PUNCT
ejpam-5016	709	1	[	[	X
ejpam-5016	709	2	36	36	NUM
ejpam-5016	709	3	]	]	X
ejpam-5016	709	4	a	a	DET
ejpam-5016	709	5	a	a	DET
ejpam-5016	709	6	qureshi	qureshi	PROPN
ejpam-5016	709	7	,	,	PUNCT
ejpam-5016	709	8	t	t	PROPN
ejpam-5016	709	9	shibuta	shibuta	NOUN
ejpam-5016	709	10	,	,	PUNCT
ejpam-5016	709	11	a	a	DET
ejpam-5016	709	12	shikama	shikama	NOUN
ejpam-5016	709	13	,	,	PUNCT
ejpam-5016	709	14	et	et	PROPN
ejpam-5016	709	15	al	al	PROPN
ejpam-5016	709	16	.	.	PROPN
ejpam-5016	710	1	simple	simple	ADJ
ejpam-5016	710	2	polyominoes	polyominoe	NOUN
ejpam-5016	710	3	are	be	AUX
ejpam-5016	710	4	prime	prime	ADJ
ejpam-5016	710	5	.	.	PUNCT
ejpam-5016	711	1	journal	journal	PROPN
ejpam-5016	711	2	of	of	ADP
ejpam-5016	711	3	commutative	commutative	ADJ
ejpam-5016	711	4	algebra	algebra	NOUN
ejpam-5016	711	5	,	,	PUNCT
ejpam-5016	711	6	9(3):413–422	9(3):413–422	NOUN
ejpam-5016	711	7	,	,	PUNCT
ejpam-5016	711	8	2017	2017	NUM
ejpam-5016	711	9	.	.	PUNCT
ejpam-5016	712	1	[	[	X
ejpam-5016	712	2	37	37	NUM
ejpam-5016	712	3	]	]	X
ejpam-5016	712	4	g	g	PROPN
ejpam-5016	712	5	rinaldo	rinaldo	PROPN
ejpam-5016	712	6	and	and	CCONJ
ejpam-5016	712	7	f	f	PROPN
ejpam-5016	712	8	romeo	romeo	PROPN
ejpam-5016	712	9	.	.	PUNCT
ejpam-5016	713	1	hilbert	hilbert	PROPN
ejpam-5016	713	2	series	series	PROPN
ejpam-5016	713	3	of	of	ADP
ejpam-5016	713	4	simple	simple	ADJ
ejpam-5016	713	5	thin	thin	ADJ
ejpam-5016	713	6	polyominoes	polyominoe	NOUN
ejpam-5016	713	7	.	.	PUNCT
ejpam-5016	714	1	journal	journal	NOUN
ejpam-5016	714	2	of	of	ADP
ejpam-5016	714	3	algebraic	algebraic	PROPN
ejpam-5016	714	4	combinatorics	combinatoric	NOUN
ejpam-5016	714	5	,	,	PUNCT
ejpam-5016	714	6	54(2):607–624	54(2):607–624	NOUN
ejpam-5016	714	7	,	,	PUNCT
ejpam-5016	714	8	2021	2021	NUM
ejpam-5016	714	9	.	.	PUNCT
ejpam-5016	715	1	[	[	X
ejpam-5016	715	2	38	38	NUM
ejpam-5016	715	3	]	]	PUNCT
ejpam-5016	715	4	a	a	DET
ejpam-5016	715	5	shikama	shikama	NOUN
ejpam-5016	715	6	.	.	PUNCT
ejpam-5016	716	1	toric	toric	ADJ
ejpam-5016	716	2	representation	representation	NOUN
ejpam-5016	716	3	of	of	ADP
ejpam-5016	716	4	algebras	algebra	NOUN
ejpam-5016	716	5	defined	define	VERB
ejpam-5016	716	6	by	by	ADP
ejpam-5016	716	7	certain	certain	ADJ
ejpam-5016	716	8	nonsimple	nonsimple	ADJ
ejpam-5016	716	9	polyominoes	polyominoe	NOUN
ejpam-5016	716	10	.	.	PUNCT
ejpam-5016	717	1	j.	j.	PROPN
ejpam-5016	717	2	commut	commut	PROPN
ejpam-5016	717	3	.	.	PUNCT
ejpam-5016	718	1	algebra	algebra	PROPN
ejpam-5016	718	2	,	,	PUNCT
ejpam-5016	718	3	10(2):265–274	10(2):265–274	PROPN
ejpam-5016	718	4	,	,	PUNCT
ejpam-5016	718	5	2018	2018	NUM
ejpam-5016	718	6	.	.	PUNCT
ejpam-5016	719	1	[	[	X
ejpam-5016	719	2	39	39	NUM
ejpam-5016	719	3	]	]	PUNCT
ejpam-5016	719	4	richard	richard	PROPN
ejpam-5016	719	5	p	p	PROPN
ejpam-5016	719	6	stanley	stanley	PROPN
ejpam-5016	719	7	.	.	PUNCT
ejpam-5016	720	1	hilbert	hilbert	NOUN
ejpam-5016	720	2	functions	function	NOUN
ejpam-5016	720	3	of	of	ADP
ejpam-5016	720	4	graded	grade	VERB
ejpam-5016	720	5	algebras	algebra	NOUN
ejpam-5016	720	6	.	.	PUNCT
ejpam-5016	721	1	advances	advance	NOUN
ejpam-5016	721	2	in	in	ADP
ejpam-5016	721	3	mathematics	mathematic	NOUN
ejpam-5016	721	4	,	,	PUNCT
ejpam-5016	721	5	28(1):57–83	28(1):57–83	NUM
ejpam-5016	721	6	,	,	PUNCT
ejpam-5016	721	7	1978	1978	NUM
ejpam-5016	721	8	.	.	PUNCT
ejpam-5016	722	1	[	[	X
ejpam-5016	722	2	40	40	NUM
ejpam-5016	722	3	]	]	SYM
ejpam-5016	722	4	b	b	NOUN
ejpam-5016	722	5	sturmfels	sturmfel	NOUN
ejpam-5016	722	6	.	.	PUNCT
ejpam-5016	723	1	solving	solve	VERB
ejpam-5016	723	2	systems	system	NOUN
ejpam-5016	723	3	of	of	ADP
ejpam-5016	723	4	polynomial	polynomial	ADJ
ejpam-5016	723	5	equations	equation	NOUN
ejpam-5016	723	6	.	.	PUNCT
ejpam-5016	724	1	number	number	NOUN
ejpam-5016	724	2	97	97	NUM
ejpam-5016	724	3	.	.	PUNCT
ejpam-5016	725	1	american	american	PROPN
ejpam-5016	725	2	mathematical	mathematical	PROPN
ejpam-5016	725	3	soc	soc	PROPN
ejpam-5016	725	4	.	.	PUNCT
ejpam-5016	725	5	,	,	PUNCT
ejpam-5016	725	6	2002	2002	NUM
ejpam-5016	725	7	.	.	PUNCT
ejpam-5016	726	1	[	[	X
ejpam-5016	726	2	41	41	NUM
ejpam-5016	726	3	]	]	SYM
ejpam-5016	726	4	s	s	PROPN
ejpam-5016	726	5	g	g	PROPN
ejpam-5016	726	6	whittington	whittington	PROPN
ejpam-5016	726	7	and	and	CCONJ
ejpam-5016	726	8	c	c	NOUN
ejpam-5016	726	9	e	e	NOUN
ejpam-5016	726	10	soteros	soteros	PROPN
ejpam-5016	726	11	.	.	PUNCT
ejpam-5016	727	1	lattice	lattice	ADJ
ejpam-5016	727	2	animals	animal	NOUN
ejpam-5016	727	3	:	:	PUNCT
ejpam-5016	727	4	rigorous	rigorous	ADJ
ejpam-5016	727	5	results	result	NOUN
ejpam-5016	727	6	and	and	CCONJ
ejpam-5016	727	7	wild	wild	ADJ
ejpam-5016	727	8	guesses	guess	NOUN
ejpam-5016	727	9	.	.	PUNCT
ejpam-5016	728	1	disorder	disorder	NOUN
ejpam-5016	728	2	in	in	ADP
ejpam-5016	728	3	physical	physical	ADJ
ejpam-5016	728	4	systems	system	NOUN
ejpam-5016	728	5	,	,	PUNCT
ejpam-5016	728	6	pages	page	NOUN
ejpam-5016	728	7	323–335	323–335	NUM
ejpam-5016	728	8	,	,	PUNCT
ejpam-5016	728	9	1990	1990	NUM
ejpam-5016	728	10	.	.	PUNCT