id	sid	tid	token	lemma	pos
ejpam-3406	1	1	european	european	PROPN
ejpam-3406	1	2	journal	journal	PROPN
ejpam-3406	1	3	of	of	ADP
ejpam-3406	1	4	pure	pure	ADJ
ejpam-3406	1	5	and	and	CCONJ
ejpam-3406	1	6	applied	apply	VERB
ejpam-3406	1	7	mathematics	mathematic	NOUN
ejpam-3406	1	8	vol	vol	NOUN
ejpam-3406	1	9	.	.	PROPN
ejpam-3406	2	1	12	12	NUM
ejpam-3406	2	2	,	,	PUNCT
ejpam-3406	2	3	no	no	INTJ
ejpam-3406	2	4	.	.	NOUN
ejpam-3406	2	5	2	2	NUM
ejpam-3406	2	6	,	,	PUNCT
ejpam-3406	2	7	2019	2019	NUM
ejpam-3406	2	8	,	,	PUNCT
ejpam-3406	2	9	279	279	NUM
ejpam-3406	2	10	-	-	SYM
ejpam-3406	2	11	293	293	NUM
ejpam-3406	2	12	issn	issn	PROPN
ejpam-3406	2	13	1307	1307	NUM
ejpam-3406	2	14	-	-	SYM
ejpam-3406	2	15	5543	5543	NUM
ejpam-3406	2	16	–	–	PUNCT
ejpam-3406	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3406	2	18	published	publish	VERB
ejpam-3406	2	19	by	by	ADP
ejpam-3406	2	20	new	new	PROPN
ejpam-3406	2	21	york	york	PROPN
ejpam-3406	2	22	business	business	PROPN
ejpam-3406	2	23	global	global	ADJ
ejpam-3406	2	24	hankel	hankel	NOUN
ejpam-3406	2	25	transform	transform	NOUN
ejpam-3406	2	26	of	of	ADP
ejpam-3406	2	27	(	(	PUNCT
ejpam-3406	2	28	q	q	ADJ
ejpam-3406	2	29	,	,	PUNCT
ejpam-3406	2	30	r)-dowling	r)-dowle	VERB
ejpam-3406	2	31	numbers	number	NOUN
ejpam-3406	2	32	roberto	roberto	PROPN
ejpam-3406	2	33	b.	b.	PROPN
ejpam-3406	2	34	corcino1	corcino1	PROPN
ejpam-3406	2	35	,	,	PUNCT
ejpam-3406	2	36	mary	mary	PROPN
ejpam-3406	2	37	joy	joy	PROPN
ejpam-3406	2	38	r.	r.	PROPN
ejpam-3406	2	39	latayada2,∗	latayada2,∗	PROPN
ejpam-3406	2	40	,	,	PUNCT
ejpam-3406	3	1	mary	mary	PROPN
ejpam-3406	3	2	ann	ann	PROPN
ejpam-3406	3	3	ritzell	ritzell	PROPN
ejpam-3406	3	4	p.	p.	PROPN
ejpam-3406	3	5	vega3	vega3	PROPN
ejpam-3406	3	6	1	1	NUM
ejpam-3406	3	7	research	research	NOUN
ejpam-3406	3	8	institute	institute	NOUN
ejpam-3406	3	9	for	for	ADP
ejpam-3406	3	10	computational	computational	ADJ
ejpam-3406	3	11	mathematics	mathematic	NOUN
ejpam-3406	3	12	and	and	CCONJ
ejpam-3406	3	13	physics	physics	NOUN
ejpam-3406	3	14	,	,	PUNCT
ejpam-3406	3	15	cebu	cebu	NOUN
ejpam-3406	3	16	normal	normal	ADJ
ejpam-3406	3	17	university	university	NOUN
ejpam-3406	3	18	,	,	PUNCT
ejpam-3406	3	19	6000	6000	NUM
ejpam-3406	3	20	cebu	cebu	NOUN
ejpam-3406	3	21	city	city	NOUN
ejpam-3406	3	22	,	,	PUNCT
ejpam-3406	3	23	philippines	philippines	PROPN
ejpam-3406	3	24	2	2	NUM
ejpam-3406	3	25	department	department	NOUN
ejpam-3406	3	26	of	of	ADP
ejpam-3406	3	27	mathematics	mathematic	NOUN
ejpam-3406	3	28	,	,	PUNCT
ejpam-3406	3	29	caraga	caraga	PROPN
ejpam-3406	3	30	state	state	PROPN
ejpam-3406	3	31	university	university	PROPN
ejpam-3406	3	32	,	,	PUNCT
ejpam-3406	3	33	8600	8600	NUM
ejpam-3406	3	34	butuan	butuan	PROPN
ejpam-3406	3	35	city	city	NOUN
ejpam-3406	3	36	,	,	PUNCT
ejpam-3406	3	37	philippines	philippines	PROPN
ejpam-3406	3	38	3	3	NUM
ejpam-3406	3	39	department	department	NOUN
ejpam-3406	3	40	of	of	ADP
ejpam-3406	3	41	mathematics	mathematic	NOUN
ejpam-3406	3	42	and	and	CCONJ
ejpam-3406	3	43	statistics	statistic	NOUN
ejpam-3406	3	44	,	,	PUNCT
ejpam-3406	3	45	college	college	NOUN
ejpam-3406	3	46	of	of	ADP
ejpam-3406	3	47	science	science	NOUN
ejpam-3406	3	48	and	and	CCONJ
ejpam-3406	3	49	mathematics	mathematic	NOUN
ejpam-3406	3	50	,	,	PUNCT
ejpam-3406	3	51	mindanao	mindanao	PROPN
ejpam-3406	3	52	state	state	PROPN
ejpam-3406	3	53	university	university	PROPN
ejpam-3406	3	54	-	-	PUNCT
ejpam-3406	3	55	iligan	iligan	PROPN
ejpam-3406	3	56	institute	institute	PROPN
ejpam-3406	3	57	of	of	ADP
ejpam-3406	3	58	technology	technology	PROPN
ejpam-3406	3	59	,	,	PUNCT
ejpam-3406	3	60	9200	9200	NUM
ejpam-3406	3	61	iligan	iligan	ADJ
ejpam-3406	3	62	city	city	NOUN
ejpam-3406	3	63	,	,	PUNCT
ejpam-3406	3	64	philippines	philippine	NOUN
ejpam-3406	3	65	abstract	abstract	ADJ
ejpam-3406	3	66	.	.	PUNCT
ejpam-3406	4	1	in	in	ADP
ejpam-3406	4	2	this	this	DET
ejpam-3406	4	3	paper	paper	NOUN
ejpam-3406	4	4	,	,	PUNCT
ejpam-3406	4	5	the	the	DET
ejpam-3406	4	6	authors	author	NOUN
ejpam-3406	4	7	establish	establish	VERB
ejpam-3406	4	8	certain	certain	ADJ
ejpam-3406	4	9	combinatorial	combinatorial	ADJ
ejpam-3406	4	10	interpretation	interpretation	NOUN
ejpam-3406	4	11	for	for	ADP
ejpam-3406	4	12	q	q	NOUN
ejpam-3406	4	13	-	-	PUNCT
ejpam-3406	4	14	analogue	analogue	NOUN
ejpam-3406	4	15	of	of	ADP
ejpam-3406	4	16	r	r	NOUN
ejpam-3406	4	17	-	-	PUNCT
ejpam-3406	4	18	whitney	whitney	NOUN
ejpam-3406	4	19	numbers	number	NOUN
ejpam-3406	4	20	of	of	ADP
ejpam-3406	4	21	the	the	DET
ejpam-3406	4	22	second	second	ADJ
ejpam-3406	4	23	kind	kind	NOUN
ejpam-3406	4	24	defined	define	VERB
ejpam-3406	4	25	by	by	ADP
ejpam-3406	4	26	corcino	corcino	NOUN
ejpam-3406	4	27	and	and	CCONJ
ejpam-3406	4	28	cañete	cañete	NOUN
ejpam-3406	4	29	in	in	ADP
ejpam-3406	4	30	the	the	DET
ejpam-3406	4	31	context	context	NOUN
ejpam-3406	4	32	of	of	ADP
ejpam-3406	4	33	atableaux	atableaux	PROPN
ejpam-3406	4	34	.	.	PUNCT
ejpam-3406	5	1	they	they	PRON
ejpam-3406	5	2	derive	derive	VERB
ejpam-3406	5	3	convolution	convolution	NOUN
ejpam-3406	5	4	-	-	PUNCT
ejpam-3406	5	5	type	type	NOUN
ejpam-3406	5	6	identities	identity	NOUN
ejpam-3406	5	7	by	by	ADP
ejpam-3406	5	8	making	make	VERB
ejpam-3406	5	9	use	use	NOUN
ejpam-3406	5	10	of	of	ADP
ejpam-3406	5	11	the	the	DET
ejpam-3406	5	12	combinatorics	combinatoric	NOUN
ejpam-3406	5	13	of	of	ADP
ejpam-3406	5	14	atableaux	atableaux	PROPN
ejpam-3406	5	15	.	.	PUNCT
ejpam-3406	6	1	finally	finally	ADV
ejpam-3406	6	2	,	,	PUNCT
ejpam-3406	6	3	they	they	PRON
ejpam-3406	6	4	define	define	VERB
ejpam-3406	6	5	a	a	DET
ejpam-3406	6	6	q	q	NOUN
ejpam-3406	6	7	-	-	PUNCT
ejpam-3406	6	8	analogue	analogue	NOUN
ejpam-3406	6	9	of	of	ADP
ejpam-3406	6	10	r	r	NOUN
ejpam-3406	6	11	-	-	PUNCT
ejpam-3406	6	12	dowling	dowle	VERB
ejpam-3406	6	13	numbers	number	NOUN
ejpam-3406	6	14	and	and	CCONJ
ejpam-3406	6	15	obtain	obtain	VERB
ejpam-3406	6	16	some	some	DET
ejpam-3406	6	17	necessary	necessary	ADJ
ejpam-3406	6	18	properties	property	NOUN
ejpam-3406	6	19	including	include	VERB
ejpam-3406	6	20	its	its	PRON
ejpam-3406	6	21	hankel	hankel	NOUN
ejpam-3406	6	22	transform	transform	NOUN
ejpam-3406	6	23	.	.	PUNCT
ejpam-3406	7	1	key	key	ADJ
ejpam-3406	7	2	words	word	NOUN
ejpam-3406	7	3	and	and	CCONJ
ejpam-3406	7	4	phrases	phrase	NOUN
ejpam-3406	7	5	:	:	PUNCT
ejpam-3406	7	6	whitney	whitney	NOUN
ejpam-3406	7	7	numbers	number	NOUN
ejpam-3406	7	8	,	,	PUNCT
ejpam-3406	7	9	dowling	dowling	NOUN
ejpam-3406	7	10	numbers	number	NOUN
ejpam-3406	7	11	,	,	PUNCT
ejpam-3406	7	12	generating	generate	VERB
ejpam-3406	7	13	function	function	NOUN
ejpam-3406	7	14	,	,	PUNCT
ejpam-3406	7	15	q	q	NOUN
ejpam-3406	7	16	-	-	PUNCT
ejpam-3406	7	17	analogue	analogue	NOUN
ejpam-3406	7	18	,	,	PUNCT
ejpam-3406	7	19	q	q	ADJ
ejpam-3406	7	20	-	-	ADJ
ejpam-3406	7	21	exponential	exponential	ADJ
ejpam-3406	7	22	function	function	NOUN
ejpam-3406	7	23	,	,	PUNCT
ejpam-3406	7	24	a	a	DET
ejpam-3406	7	25	-	-	PUNCT
ejpam-3406	7	26	tableau	tableau	NOUN
ejpam-3406	7	27	,	,	PUNCT
ejpam-3406	7	28	convolution	convolution	NOUN
ejpam-3406	7	29	formula	formula	NOUN
ejpam-3406	7	30	,	,	PUNCT
ejpam-3406	7	31	hankel	hankel	NOUN
ejpam-3406	7	32	transform	transform	NOUN
ejpam-3406	7	33	,	,	PUNCT
ejpam-3406	7	34	hankel	hankel	NOUN
ejpam-3406	7	35	matrix	matrix	NOUN
ejpam-3406	7	36	,	,	PUNCT
ejpam-3406	7	37	binomial	binomial	ADJ
ejpam-3406	7	38	transform	transform	NOUN
ejpam-3406	7	39	.	.	PUNCT
ejpam-3406	8	1	1	1	X
ejpam-3406	8	2	.	.	X
ejpam-3406	8	3	introduction	introduction	NOUN
ejpam-3406	8	4	the	the	DET
ejpam-3406	8	5	binomial	binomial	ADJ
ejpam-3406	8	6	transform	transform	NOUN
ejpam-3406	8	7	b	b	PROPN
ejpam-3406	8	8	of	of	ADP
ejpam-3406	8	9	a	a	DET
ejpam-3406	8	10	sequence	sequence	NOUN
ejpam-3406	8	11	a	a	PRON
ejpam-3406	8	12	=	=	X
ejpam-3406	8	13	{	{	PUNCT
ejpam-3406	8	14	an	an	PRON
ejpam-3406	8	15	}	}	PUNCT
ejpam-3406	8	16	is	be	AUX
ejpam-3406	8	17	the	the	DET
ejpam-3406	8	18	sequence	sequence	NOUN
ejpam-3406	8	19	{	{	PUNCT
ejpam-3406	8	20	bn	bn	NOUN
ejpam-3406	8	21	}	}	PUNCT
ejpam-3406	8	22	defined	define	VERB
ejpam-3406	8	23	by	by	ADP
ejpam-3406	8	24	bn	bn	PROPN
ejpam-3406	8	25	=	=	SYM
ejpam-3406	8	26	n∑	n∑	PROPN
ejpam-3406	8	27	k=0	k=0	PROPN
ejpam-3406	8	28	(	(	PUNCT
ejpam-3406	8	29	−1)k	−1)k	PROPN
ejpam-3406	8	30	(	(	PUNCT
ejpam-3406	8	31	n	n	X
ejpam-3406	8	32	k	k	PROPN
ejpam-3406	8	33	)	)	PUNCT
ejpam-3406	8	34	ak	ak	PROPN
ejpam-3406	8	35	.	.	PROPN
ejpam-3406	9	1	that	that	PRON
ejpam-3406	9	2	is	be	AUX
ejpam-3406	9	3	,	,	PUNCT
ejpam-3406	9	4	b(a	b(a	X
ejpam-3406	9	5	)	)	PUNCT
ejpam-3406	10	1	=	=	SYM
ejpam-3406	10	2	bn	bn	X
ejpam-3406	10	3	.	.	PUNCT
ejpam-3406	11	1	it	it	PRON
ejpam-3406	11	2	is	be	AUX
ejpam-3406	11	3	one	one	NUM
ejpam-3406	11	4	of	of	ADP
ejpam-3406	11	5	the	the	DET
ejpam-3406	11	6	common	common	ADJ
ejpam-3406	11	7	and	and	CCONJ
ejpam-3406	11	8	useful	useful	ADJ
ejpam-3406	11	9	transforms	transform	NOUN
ejpam-3406	11	10	that	that	PRON
ejpam-3406	11	11	frequently	frequently	ADV
ejpam-3406	11	12	appeared	appear	VERB
ejpam-3406	11	13	in	in	ADP
ejpam-3406	11	14	the	the	DET
ejpam-3406	11	15	literature	literature	NOUN
ejpam-3406	11	16	of	of	ADP
ejpam-3406	11	17	integer	integer	NOUN
ejpam-3406	11	18	sequences	sequence	NOUN
ejpam-3406	11	19	(	(	PUNCT
ejpam-3406	11	20	see	see	VERB
ejpam-3406	11	21	[	[	X
ejpam-3406	11	22	16	16	NUM
ejpam-3406	11	23	]	]	SYM
ejpam-3406	11	24	)	)	PUNCT
ejpam-3406	11	25	.	.	PUNCT
ejpam-3406	12	1	the	the	DET
ejpam-3406	12	2	inverse	inverse	ADJ
ejpam-3406	12	3	binomial	binomial	NOUN
ejpam-3406	12	4	transform	transform	NOUN
ejpam-3406	12	5	(	(	PUNCT
ejpam-3406	12	6	or	or	CCONJ
ejpam-3406	12	7	inverse	inverse	NOUN
ejpam-3406	12	8	transform	transform	NOUN
ejpam-3406	12	9	)	)	PUNCT
ejpam-3406	12	10	c	c	NOUN
ejpam-3406	12	11	of	of	ADP
ejpam-3406	12	12	a	a	DET
ejpam-3406	12	13	sequence	sequence	NOUN
ejpam-3406	12	14	a	a	PRON
ejpam-3406	12	15	is	be	AUX
ejpam-3406	12	16	the	the	DET
ejpam-3406	12	17	sequence	sequence	NOUN
ejpam-3406	12	18	{	{	PUNCT
ejpam-3406	12	19	cn	cn	PROPN
ejpam-3406	12	20	}	}	PUNCT
ejpam-3406	12	21	defined	define	VERB
ejpam-3406	12	22	by	by	ADP
ejpam-3406	12	23	cn	cn	PROPN
ejpam-3406	12	24	=	=	PROPN
ejpam-3406	12	25	n∑	n∑	PROPN
ejpam-3406	12	26	k=0	k=0	PROPN
ejpam-3406	12	27	(	(	PUNCT
ejpam-3406	12	28	n	n	X
ejpam-3406	12	29	k	k	PROPN
ejpam-3406	12	30	)	)	PUNCT
ejpam-3406	12	31	ak	ak	PROPN
ejpam-3406	12	32	.	.	PROPN
ejpam-3406	13	1	that	that	PRON
ejpam-3406	13	2	is	be	AUX
ejpam-3406	13	3	,	,	PUNCT
ejpam-3406	13	4	c(a	c(a	ADV
ejpam-3406	13	5	)	)	PUNCT
ejpam-3406	13	6	=	=	SYM
ejpam-3406	14	1	cn	cn	PROPN
ejpam-3406	14	2	.	.	PUNCT
ejpam-3406	14	3	∗corresponding	∗corresponde	VERB
ejpam-3406	14	4	author	author	NOUN
ejpam-3406	14	5	.	.	PUNCT
ejpam-3406	15	1	doi	doi	NOUN
ejpam-3406	15	2	:	:	PUNCT
ejpam-3406	15	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3406	https://doi.org/10.29020/nybg.ejpam.v12i2.3406	ADJ
ejpam-3406	15	4	email	email	NOUN
ejpam-3406	15	5	addresses	address	NOUN
ejpam-3406	15	6	:	:	PUNCT
ejpam-3406	15	7	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-3406	15	8	(	(	PUNCT
ejpam-3406	15	9	r.	r.	PROPN
ejpam-3406	15	10	corcino	corcino	PROPN
ejpam-3406	15	11	)	)	PUNCT
ejpam-3406	15	12	,	,	PUNCT
ejpam-3406	15	13	mrlatayada@gmail.com	mrlatayada@gmail.com	X
ejpam-3406	15	14	(	(	PUNCT
ejpam-3406	15	15	mj	mj	PROPN
ejpam-3406	15	16	.	.	PUNCT
ejpam-3406	15	17	latayada	latayada	PROPN
ejpam-3406	15	18	)	)	PUNCT
ejpam-3406	15	19	,	,	PUNCT
ejpam-3406	15	20	maryannritzel.vega@g.msuiit.edu.ph	maryannritzel.vega@g.msuiit.edu.ph	PROPN
ejpam-3406	15	21	(	(	PUNCT
ejpam-3406	15	22	mar	mar	PROPN
ejpam-3406	15	23	.	.	PROPN
ejpam-3406	15	24	vega	vega	PROPN
ejpam-3406	15	25	)	)	PUNCT
ejpam-3406	15	26	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3406	16	1	279	279	NUM
ejpam-3406	16	2	c	c	X
ejpam-3406	16	3	©	©	PROPN
ejpam-3406	16	4	2019	2019	NUM
ejpam-3406	16	5	ejpam	ejpam	NOUN
ejpam-3406	16	6	all	all	DET
ejpam-3406	16	7	rights	right	NOUN
ejpam-3406	16	8	reserved	reserve	VERB
ejpam-3406	16	9	.	.	PUNCT
ejpam-3406	17	1	r.	r.	PROPN
ejpam-3406	17	2	corcino	corcino	PROPN
ejpam-3406	17	3	,	,	PUNCT
ejpam-3406	17	4	mj	mj	PROPN
ejpam-3406	17	5	.	.	PUNCT
ejpam-3406	17	6	latayada	latayada	PROPN
ejpam-3406	17	7	,	,	PUNCT
ejpam-3406	17	8	mar	mar	PROPN
ejpam-3406	17	9	.	.	PROPN
ejpam-3406	17	10	vega	vega	PROPN
ejpam-3406	17	11	/	/	SYM
ejpam-3406	17	12	eur	eur	PROPN
ejpam-3406	17	13	.	.	PUNCT
ejpam-3406	18	1	j.	j.	PROPN
ejpam-3406	18	2	pure	pure	PROPN
ejpam-3406	18	3	appl	appl	PROPN
ejpam-3406	18	4	.	.	PROPN
ejpam-3406	18	5	math	math	PROPN
ejpam-3406	18	6	,	,	PUNCT
ejpam-3406	18	7	12	12	NUM
ejpam-3406	18	8	(	(	PUNCT
ejpam-3406	18	9	2	2	NUM
ejpam-3406	18	10	)	)	PUNCT
ejpam-3406	18	11	(	(	PUNCT
ejpam-3406	18	12	2019	2019	NUM
ejpam-3406	18	13	)	)	PUNCT
ejpam-3406	18	14	,	,	PUNCT
ejpam-3406	18	15	279	279	NUM
ejpam-3406	18	16	-	-	SYM
ejpam-3406	18	17	293	293	NUM
ejpam-3406	18	18	280	280	NUM
ejpam-3406	18	19	the	the	DET
ejpam-3406	18	20	hankel	hankel	NOUN
ejpam-3406	18	21	matrix	matrix	NOUN
ejpam-3406	18	22	hn	hn	NOUN
ejpam-3406	18	23	of	of	ADP
ejpam-3406	18	24	order	order	NOUN
ejpam-3406	18	25	n	n	PROPN
ejpam-3406	18	26	of	of	ADP
ejpam-3406	18	27	a	a	DET
ejpam-3406	18	28	sequence	sequence	NOUN
ejpam-3406	18	29	a	a	PRON
ejpam-3406	18	30	=	=	SYM
ejpam-3406	18	31	{	{	PUNCT
ejpam-3406	18	32	a0	a0	PROPN
ejpam-3406	18	33	,	,	PUNCT
ejpam-3406	18	34	a1	a1	NOUN
ejpam-3406	18	35	,	,	PUNCT
ejpam-3406	18	36	.	.	PUNCT
ejpam-3406	18	37	.	.	PUNCT
ejpam-3406	19	1	.	.	PUNCT
ejpam-3406	20	1	,	,	PUNCT
ejpam-3406	20	2	an	an	PRON
ejpam-3406	20	3	}	}	PUNCT
ejpam-3406	20	4	is	be	AUX
ejpam-3406	20	5	given	give	VERB
ejpam-3406	20	6	by	by	ADP
ejpam-3406	20	7	hn	hn	PROPN
ejpam-3406	20	8	=	=	PUNCT
ejpam-3406	20	9	(	(	PUNCT
ejpam-3406	20	10	ai+j)0≤i	ai+j)0≤i	NOUN
ejpam-3406	20	11	,	,	PUNCT
ejpam-3406	20	12	j≤n	j≤n	PROPN
ejpam-3406	20	13	.	.	PUNCT
ejpam-3406	21	1	the	the	DET
ejpam-3406	21	2	hankel	hankel	NOUN
ejpam-3406	21	3	determinant	determinant	VERB
ejpam-3406	21	4	hn	hn	NOUN
ejpam-3406	21	5	of	of	ADP
ejpam-3406	21	6	order	order	NOUN
ejpam-3406	21	7	of	of	ADP
ejpam-3406	21	8	n	n	PROPN
ejpam-3406	21	9	of	of	ADP
ejpam-3406	21	10	a	a	PRON
ejpam-3406	21	11	is	be	AUX
ejpam-3406	21	12	the	the	DET
ejpam-3406	21	13	determinant	determinant	NOUN
ejpam-3406	21	14	of	of	ADP
ejpam-3406	21	15	the	the	DET
ejpam-3406	21	16	corresponding	correspond	VERB
ejpam-3406	21	17	hankel	hankel	NOUN
ejpam-3406	21	18	matrix	matrix	NOUN
ejpam-3406	21	19	of	of	ADP
ejpam-3406	21	20	order	order	NOUN
ejpam-3406	21	21	n.	n.	NOUN
ejpam-3406	21	22	that	that	PRON
ejpam-3406	21	23	is	be	AUX
ejpam-3406	21	24	,	,	PUNCT
ejpam-3406	21	25	hn	hn	PROPN
ejpam-3406	21	26	=	=	NOUN
ejpam-3406	21	27	det(hn	det(hn	PROPN
ejpam-3406	21	28	)	)	PUNCT
ejpam-3406	21	29	.	.	PUNCT
ejpam-3406	22	1	the	the	DET
ejpam-3406	22	2	hankel	hankel	NOUN
ejpam-3406	22	3	transform	transform	NOUN
ejpam-3406	22	4	of	of	ADP
ejpam-3406	22	5	the	the	DET
ejpam-3406	22	6	sequence	sequence	NOUN
ejpam-3406	22	7	a	a	NOUN
ejpam-3406	22	8	,	,	PUNCT
ejpam-3406	22	9	denoted	denote	VERB
ejpam-3406	22	10	by	by	ADP
ejpam-3406	22	11	h(a	h(a	PROPN
ejpam-3406	22	12	)	)	PUNCT
ejpam-3406	22	13	,	,	PUNCT
ejpam-3406	22	14	is	be	AUX
ejpam-3406	22	15	the	the	DET
ejpam-3406	22	16	sequence	sequence	NOUN
ejpam-3406	22	17	{	{	PUNCT
ejpam-3406	22	18	hn	hn	NOUN
ejpam-3406	22	19	}	}	PUNCT
ejpam-3406	22	20	of	of	ADP
ejpam-3406	22	21	hankel	hankel	NOUN
ejpam-3406	22	22	determinants	determinant	NOUN
ejpam-3406	22	23	of	of	ADP
ejpam-3406	22	24	a.	a.	NOUN
ejpam-3406	22	25	for	for	ADP
ejpam-3406	22	26	instance	instance	NOUN
ejpam-3406	22	27	,	,	PUNCT
ejpam-3406	22	28	the	the	DET
ejpam-3406	22	29	hankel	hankel	NOUN
ejpam-3406	22	30	transform	transform	NOUN
ejpam-3406	22	31	of	of	ADP
ejpam-3406	22	32	the	the	DET
ejpam-3406	22	33	sequence	sequence	NOUN
ejpam-3406	22	34	of	of	ADP
ejpam-3406	22	35	catalan	catalan	NOUN
ejpam-3406	22	36	numbers	number	NOUN
ejpam-3406	22	37	c	c	NOUN
ejpam-3406	22	38	=	=	SYM
ejpam-3406	22	39	{	{	PUNCT
ejpam-3406	22	40	1	1	NUM
ejpam-3406	22	41	n+1	n+1	PROPN
ejpam-3406	22	42	(	(	PUNCT
ejpam-3406	22	43	2n	2n	NUM
ejpam-3406	22	44	n	n	NOUN
ejpam-3406	22	45	)	)	PUNCT
ejpam-3406	22	46	}	}	PUNCT
ejpam-3406	22	47	∞n=1	∞n=1	PROPN
ejpam-3406	22	48	,	,	PUNCT
ejpam-3406	22	49	is	be	AUX
ejpam-3406	22	50	given	give	VERB
ejpam-3406	22	51	by	by	ADP
ejpam-3406	22	52	h(c	h(c	PROPN
ejpam-3406	22	53	)	)	PUNCT
ejpam-3406	22	54	=	=	PUNCT
ejpam-3406	22	55	{	{	PUNCT
ejpam-3406	22	56	1	1	NUM
ejpam-3406	22	57	,	,	PUNCT
ejpam-3406	22	58	1	1	NUM
ejpam-3406	22	59	,	,	PUNCT
ejpam-3406	22	60	1	1	NUM
ejpam-3406	22	61	,	,	PUNCT
ejpam-3406	22	62	.	.	PUNCT
ejpam-3406	22	63	.	.	PUNCT
ejpam-3406	22	64	.	.	PUNCT
ejpam-3406	23	1	,	,	PUNCT
ejpam-3406	23	2	}	}	PUNCT
ejpam-3406	23	3	and	and	CCONJ
ejpam-3406	23	4	the	the	DET
ejpam-3406	23	5	sequence	sequence	NOUN
ejpam-3406	23	6	of	of	ADP
ejpam-3406	23	7	the	the	DET
ejpam-3406	23	8	sum	sum	NOUN
ejpam-3406	23	9	of	of	ADP
ejpam-3406	23	10	two	two	NUM
ejpam-3406	23	11	consecutive	consecutive	ADJ
ejpam-3406	23	12	catalan	catalan	NOUN
ejpam-3406	23	13	numbers	number	NOUN
ejpam-3406	23	14	,	,	PUNCT
ejpam-3406	23	15	an	an	DET
ejpam-3406	23	16	=	=	X
ejpam-3406	23	17	cn	cn	PROPN
ejpam-3406	23	18	+	+	NOUN
ejpam-3406	23	19	cn+1	cn+1	NUM
ejpam-3406	23	20	,	,	PUNCT
ejpam-3406	23	21	with	with	ADP
ejpam-3406	23	22	cn	cn	PROPN
ejpam-3406	23	23	the	the	DET
ejpam-3406	23	24	nth	nth	PROPN
ejpam-3406	23	25	catalan	catalan	NOUN
ejpam-3406	23	26	numbers	number	NOUN
ejpam-3406	23	27	,	,	PUNCT
ejpam-3406	23	28	has	have	AUX
ejpam-3406	23	29	the	the	DET
ejpam-3406	23	30	hankel	hankel	NOUN
ejpam-3406	23	31	transform	transform	VERB
ejpam-3406	23	32	h(an	h(an	PRON
ejpam-3406	23	33	)	)	PUNCT
ejpam-3406	23	34	=	=	PRON
ejpam-3406	23	35	{	{	PUNCT
ejpam-3406	24	1	f2n+1}∞n=0	f2n+1}∞n=0	ADJ
ejpam-3406	24	2	where	where	SCONJ
ejpam-3406	24	3	fn	fn	NOUN
ejpam-3406	24	4	is	be	AUX
ejpam-3406	24	5	the	the	DET
ejpam-3406	24	6	nth	nth	PROPN
ejpam-3406	24	7	fibonacci	fibonacci	NOUN
ejpam-3406	24	8	numbers	number	NOUN
ejpam-3406	24	9	[	[	X
ejpam-3406	24	10	12	12	NUM
ejpam-3406	24	11	]	]	PUNCT
ejpam-3406	24	12	.	.	PUNCT
ejpam-3406	25	1	one	one	NUM
ejpam-3406	25	2	remarkable	remarkable	ADJ
ejpam-3406	25	3	property	property	NOUN
ejpam-3406	25	4	of	of	ADP
ejpam-3406	25	5	hankel	hankel	NOUN
ejpam-3406	25	6	transform	transform	NOUN
ejpam-3406	25	7	is	be	AUX
ejpam-3406	25	8	established	establish	VERB
ejpam-3406	25	9	by	by	ADP
ejpam-3406	25	10	layman	layman	NOUN
ejpam-3406	25	11	[	[	X
ejpam-3406	25	12	12	12	NUM
ejpam-3406	25	13	]	]	PUNCT
ejpam-3406	25	14	,	,	PUNCT
ejpam-3406	25	15	which	which	PRON
ejpam-3406	25	16	states	state	VERB
ejpam-3406	25	17	that	that	SCONJ
ejpam-3406	25	18	the	the	DET
ejpam-3406	25	19	hankel	hankel	NOUN
ejpam-3406	25	20	transform	transform	NOUN
ejpam-3406	25	21	of	of	ADP
ejpam-3406	25	22	an	an	DET
ejpam-3406	25	23	integer	integer	NOUN
ejpam-3406	25	24	sequence	sequence	NOUN
ejpam-3406	25	25	is	be	AUX
ejpam-3406	25	26	invariant	invariant	ADJ
ejpam-3406	25	27	under	under	ADP
ejpam-3406	25	28	binomial	binomial	ADJ
ejpam-3406	25	29	and	and	CCONJ
ejpam-3406	25	30	inverse	inverse	NOUN
ejpam-3406	25	31	transforms	transform	VERB
ejpam-3406	25	32	.	.	PUNCT
ejpam-3406	26	1	that	that	PRON
ejpam-3406	26	2	is	be	AUX
ejpam-3406	26	3	,	,	PUNCT
ejpam-3406	26	4	if	if	SCONJ
ejpam-3406	26	5	a	a	PRON
ejpam-3406	26	6	is	be	AUX
ejpam-3406	26	7	an	an	DET
ejpam-3406	26	8	integer	integer	NOUN
ejpam-3406	26	9	sequence	sequence	NOUN
ejpam-3406	26	10	,	,	PUNCT
ejpam-3406	26	11	b	b	NOUN
ejpam-3406	26	12	is	be	AUX
ejpam-3406	26	13	binomial	binomial	ADJ
ejpam-3406	26	14	transform	transform	NOUN
ejpam-3406	26	15	of	of	ADP
ejpam-3406	26	16	a	a	PRON
ejpam-3406	26	17	and	and	CCONJ
ejpam-3406	26	18	c	c	NOUN
ejpam-3406	26	19	is	be	AUX
ejpam-3406	26	20	the	the	DET
ejpam-3406	26	21	inverse	inverse	NOUN
ejpam-3406	26	22	transform	transform	NOUN
ejpam-3406	26	23	of	of	ADP
ejpam-3406	26	24	a	a	DET
ejpam-3406	26	25	,	,	PUNCT
ejpam-3406	26	26	then	then	ADV
ejpam-3406	26	27	h(b(a	h(b(a	PROPN
ejpam-3406	26	28	)	)	PUNCT
ejpam-3406	26	29	)	)	PUNCT
ejpam-3406	27	1	=	=	SYM
ejpam-3406	27	2	h(a	h(a	PROPN
ejpam-3406	27	3	)	)	PUNCT
ejpam-3406	27	4	and	and	CCONJ
ejpam-3406	27	5	h(c(a	h(c(a	PROPN
ejpam-3406	27	6	)	)	PUNCT
ejpam-3406	27	7	)	)	PUNCT
ejpam-3406	28	1	=	=	PUNCT
ejpam-3406	28	2	h(a	h(a	PROPN
ejpam-3406	28	3	)	)	PUNCT
ejpam-3406	28	4	.	.	PUNCT
ejpam-3406	29	1	this	this	DET
ejpam-3406	29	2	property	property	NOUN
ejpam-3406	29	3	played	play	VERB
ejpam-3406	29	4	an	an	DET
ejpam-3406	29	5	important	important	ADJ
ejpam-3406	29	6	role	role	NOUN
ejpam-3406	29	7	in	in	ADP
ejpam-3406	29	8	proving	prove	VERB
ejpam-3406	29	9	that	that	SCONJ
ejpam-3406	29	10	the	the	DET
ejpam-3406	29	11	hankel	hankel	NOUN
ejpam-3406	29	12	transform	transform	NOUN
ejpam-3406	29	13	of	of	ADP
ejpam-3406	29	14	the	the	DET
ejpam-3406	29	15	sequence	sequence	NOUN
ejpam-3406	29	16	of	of	ADP
ejpam-3406	29	17	bell	bell	NOUN
ejpam-3406	29	18	number	number	NOUN
ejpam-3406	29	19	{	{	PUNCT
ejpam-3406	29	20	bn	bn	NOUN
ejpam-3406	29	21	)	)	PUNCT
ejpam-3406	29	22	}	}	PUNCT
ejpam-3406	30	1	[	[	X
ejpam-3406	30	2	1	1	X
ejpam-3406	30	3	]	]	PUNCT
ejpam-3406	30	4	and	and	CCONJ
ejpam-3406	30	5	that	that	PRON
ejpam-3406	30	6	of	of	ADP
ejpam-3406	30	7	r	r	NOUN
ejpam-3406	30	8	-	-	PUNCT
ejpam-3406	30	9	bell	bell	NOUN
ejpam-3406	30	10	numbers	number	NOUN
ejpam-3406	30	11	{	{	PUNCT
ejpam-3406	30	12	bn	bn	INTJ
ejpam-3406	30	13	,	,	PUNCT
ejpam-3406	30	14	r	r	NOUN
ejpam-3406	30	15	}	}	PUNCT
ejpam-3406	30	16	[	[	X
ejpam-3406	30	17	14	14	NUM
ejpam-3406	30	18	]	]	PUNCT
ejpam-3406	30	19	are	be	AUX
ejpam-3406	30	20	equal	equal	ADJ
ejpam-3406	30	21	.	.	PUNCT
ejpam-3406	31	1	recently	recently	ADV
ejpam-3406	31	2	,	,	PUNCT
ejpam-3406	31	3	in	in	ADP
ejpam-3406	31	4	the	the	DET
ejpam-3406	31	5	paper	paper	NOUN
ejpam-3406	31	6	by	by	ADP
ejpam-3406	31	7	r.	r.	PROPN
ejpam-3406	31	8	corcino	corcino	PROPN
ejpam-3406	31	9	and	and	CCONJ
ejpam-3406	31	10	c.	c.	PROPN
ejpam-3406	31	11	corcino	corcino	PROPN
ejpam-3406	32	1	[	[	X
ejpam-3406	32	2	7	7	NUM
ejpam-3406	32	3	]	]	PUNCT
ejpam-3406	32	4	,	,	PUNCT
ejpam-3406	32	5	this	this	DET
ejpam-3406	32	6	property	property	NOUN
ejpam-3406	32	7	has	have	AUX
ejpam-3406	32	8	also	also	ADV
ejpam-3406	32	9	been	be	AUX
ejpam-3406	32	10	used	use	VERB
ejpam-3406	32	11	in	in	ADP
ejpam-3406	32	12	proving	prove	VERB
ejpam-3406	32	13	that	that	SCONJ
ejpam-3406	32	14	the	the	DET
ejpam-3406	32	15	hankel	hankel	NOUN
ejpam-3406	32	16	transform	transform	NOUN
ejpam-3406	32	17	of	of	ADP
ejpam-3406	32	18	the	the	DET
ejpam-3406	32	19	sequence	sequence	NOUN
ejpam-3406	32	20	of	of	ADP
ejpam-3406	32	21	generalized	generalized	ADJ
ejpam-3406	32	22	bell	bell	NOUN
ejpam-3406	32	23	numbers	number	NOUN
ejpam-3406	32	24	{	{	PUNCT
ejpam-3406	32	25	gn	gn	INTJ
ejpam-3406	32	26	,	,	PUNCT
ejpam-3406	32	27	r	r	PROPN
ejpam-3406	32	28	,	,	PUNCT
ejpam-3406	32	29	β	β	NOUN
ejpam-3406	32	30	}	}	PUNCT
ejpam-3406	32	31	is	be	AUX
ejpam-3406	32	32	given	give	VERB
ejpam-3406	32	33	by	by	ADP
ejpam-3406	32	34	h(gn	h(gn	NOUN
ejpam-3406	32	35	,	,	PUNCT
ejpam-3406	32	36	r	r	NOUN
ejpam-3406	32	37	,	,	PUNCT
ejpam-3406	32	38	β	β	NOUN
ejpam-3406	32	39	)	)	PUNCT
ejpam-3406	32	40	=	=	SYM
ejpam-3406	32	41	n∏	n∏	PROPN
ejpam-3406	32	42	j=0	j=0	PROPN
ejpam-3406	32	43	βjj	βjj	PUNCT
ejpam-3406	32	44	!	!	PUNCT
ejpam-3406	33	1	where	where	SCONJ
ejpam-3406	33	2	gn	gn	PROPN
ejpam-3406	33	3	,	,	PUNCT
ejpam-3406	33	4	r	r	PROPN
ejpam-3406	33	5	,	,	PUNCT
ejpam-3406	33	6	β	β	X
ejpam-3406	33	7	is	be	AUX
ejpam-3406	33	8	the	the	DET
ejpam-3406	33	9	sum	sum	NOUN
ejpam-3406	33	10	of	of	ADP
ejpam-3406	33	11	(	(	PUNCT
ejpam-3406	33	12	r	r	NOUN
ejpam-3406	33	13	,	,	PUNCT
ejpam-3406	33	14	β)-stirling	β)-stirle	VERB
ejpam-3406	33	15	numbers	number	NOUN
ejpam-3406	33	16	{	{	PUNCT
ejpam-3406	33	17	n	n	NOUN
ejpam-3406	33	18	k	k	NOUN
ejpam-3406	33	19	}	}	PUNCT
ejpam-3406	33	20	r	r	PROPN
ejpam-3406	33	21	,	,	PUNCT
ejpam-3406	33	22	β	β	X
ejpam-3406	33	23	gn	gn	PROPN
ejpam-3406	33	24	,	,	PUNCT
ejpam-3406	33	25	r	r	PROPN
ejpam-3406	33	26	,	,	PUNCT
ejpam-3406	33	27	β	β	X
ejpam-3406	33	28	=	=	SYM
ejpam-3406	33	29	n∑	n∑	PROPN
ejpam-3406	33	30	k=0	k=0	PROPN
ejpam-3406	33	31	{	{	PUNCT
ejpam-3406	33	32	n	n	NOUN
ejpam-3406	33	33	k	k	NOUN
ejpam-3406	33	34	}	}	PUNCT
ejpam-3406	33	35	r	r	NOUN
ejpam-3406	33	36	,	,	PUNCT
ejpam-3406	33	37	β	β	X
ejpam-3406	33	38	(	(	PUNCT
ejpam-3406	33	39	see	see	VERB
ejpam-3406	33	40	[	[	X
ejpam-3406	33	41	5	5	NUM
ejpam-3406	33	42	,	,	PUNCT
ejpam-3406	33	43	8	8	NUM
ejpam-3406	33	44	]	]	NUM
ejpam-3406	33	45	)	)	PUNCT
ejpam-3406	33	46	,	,	PUNCT
ejpam-3406	33	47	which	which	PRON
ejpam-3406	33	48	are	be	AUX
ejpam-3406	33	49	also	also	ADV
ejpam-3406	33	50	known	know	VERB
ejpam-3406	33	51	as	as	ADP
ejpam-3406	33	52	(	(	PUNCT
ejpam-3406	33	53	r	r	NOUN
ejpam-3406	33	54	,	,	PUNCT
ejpam-3406	33	55	β)-bell	β)-bell	NOUN
ejpam-3406	33	56	numbers	number	NOUN
ejpam-3406	33	57	.	.	PUNCT
ejpam-3406	34	1	in	in	ADP
ejpam-3406	34	2	the	the	DET
ejpam-3406	34	3	same	same	ADJ
ejpam-3406	34	4	paper	paper	NOUN
ejpam-3406	34	5	,	,	PUNCT
ejpam-3406	34	6	the	the	DET
ejpam-3406	34	7	authors	author	NOUN
ejpam-3406	34	8	have	have	AUX
ejpam-3406	34	9	made	make	VERB
ejpam-3406	34	10	an	an	DET
ejpam-3406	34	11	attempt	attempt	NOUN
ejpam-3406	34	12	to	to	PART
ejpam-3406	34	13	establish	establish	VERB
ejpam-3406	34	14	the	the	DET
ejpam-3406	34	15	hankel	hankel	NOUN
ejpam-3406	34	16	transform	transform	NOUN
ejpam-3406	34	17	for	for	ADP
ejpam-3406	34	18	the	the	DET
ejpam-3406	34	19	q	q	NOUN
ejpam-3406	34	20	-	-	PUNCT
ejpam-3406	34	21	analogue	analogue	NOUN
ejpam-3406	34	22	of	of	ADP
ejpam-3406	34	23	(	(	PUNCT
ejpam-3406	34	24	r	r	NOUN
ejpam-3406	34	25	,	,	PUNCT
ejpam-3406	34	26	β)-bell	β)-bell	NOUN
ejpam-3406	34	27	numbers	number	NOUN
ejpam-3406	34	28	.	.	PUNCT
ejpam-3406	35	1	however	however	ADV
ejpam-3406	35	2	,	,	PUNCT
ejpam-3406	35	3	they	they	PRON
ejpam-3406	35	4	are	be	AUX
ejpam-3406	35	5	not	not	PART
ejpam-3406	35	6	successful	successful	ADJ
ejpam-3406	35	7	with	with	ADP
ejpam-3406	35	8	their	their	PRON
ejpam-3406	35	9	attempt	attempt	NOUN
ejpam-3406	35	10	and	and	CCONJ
ejpam-3406	35	11	have	have	AUX
ejpam-3406	35	12	conjectured	conjecture	VERB
ejpam-3406	35	13	that	that	SCONJ
ejpam-3406	35	14	the	the	DET
ejpam-3406	35	15	hankel	hankel	NOUN
ejpam-3406	35	16	transform	transform	VERB
ejpam-3406	35	17	for	for	ADP
ejpam-3406	35	18	the	the	DET
ejpam-3406	35	19	q	q	NOUN
ejpam-3406	35	20	-	-	PUNCT
ejpam-3406	35	21	analogue	analogue	NOUN
ejpam-3406	35	22	of	of	ADP
ejpam-3406	35	23	(	(	PUNCT
ejpam-3406	35	24	r	r	NOUN
ejpam-3406	35	25	,	,	PUNCT
ejpam-3406	35	26	β)-bell	β)-bell	PUNCT
ejpam-3406	35	27	numbers	number	NOUN
ejpam-3406	35	28	when	when	SCONJ
ejpam-3406	35	29	r	r	NOUN
ejpam-3406	35	30	=	=	SYM
ejpam-3406	35	31	0	0	NUM
ejpam-3406	35	32	is	be	AUX
ejpam-3406	35	33	equal	equal	ADJ
ejpam-3406	35	34	to	to	ADP
ejpam-3406	35	35	h	h	PROPN
ejpam-3406	35	36	(	(	PUNCT
ejpam-3406	35	37	gqn	gqn	NOUN
ejpam-3406	35	38	,	,	PUNCT
ejpam-3406	35	39	β,0	β,0	NUM
ejpam-3406	35	40	)	)	PUNCT
ejpam-3406	36	1	=	=	PUNCT
ejpam-3406	36	2	n∏	n∏	PROPN
ejpam-3406	36	3	k=0	k=0	PROPN
ejpam-3406	36	4	qf(n	qf(n	PROPN
ejpam-3406	36	5	,	,	PUNCT
ejpam-3406	36	6	k)[β]kq	k)[β]kq	PROPN
ejpam-3406	37	1	[	[	X
ejpam-3406	37	2	k]qβ	k]qβ	NOUN
ejpam-3406	37	3	!	!	PUNCT
ejpam-3406	38	1	(	(	PUNCT
ejpam-3406	38	2	1	1	X
ejpam-3406	38	3	)	)	PUNCT
ejpam-3406	38	4	for	for	ADP
ejpam-3406	38	5	some	some	DET
ejpam-3406	38	6	number	number	NOUN
ejpam-3406	38	7	f(n	f(n	PROPN
ejpam-3406	38	8	,	,	PUNCT
ejpam-3406	38	9	k	k	NOUN
ejpam-3406	38	10	)	)	PUNCT
ejpam-3406	38	11	,	,	PUNCT
ejpam-3406	38	12	which	which	PRON
ejpam-3406	38	13	is	be	AUX
ejpam-3406	38	14	a	a	DET
ejpam-3406	38	15	function	function	NOUN
ejpam-3406	38	16	of	of	ADP
ejpam-3406	38	17	n	n	PROPN
ejpam-3406	38	18	and	and	CCONJ
ejpam-3406	38	19	k.	k.	NOUN
ejpam-3406	38	20	with	with	ADP
ejpam-3406	38	21	this	this	PRON
ejpam-3406	38	22	,	,	PUNCT
ejpam-3406	38	23	the	the	DET
ejpam-3406	38	24	present	present	ADJ
ejpam-3406	38	25	authors	author	NOUN
ejpam-3406	38	26	have	have	AUX
ejpam-3406	38	27	decided	decide	VERB
ejpam-3406	38	28	to	to	PART
ejpam-3406	38	29	use	use	VERB
ejpam-3406	38	30	other	other	ADJ
ejpam-3406	38	31	method	method	NOUN
ejpam-3406	38	32	.	.	PUNCT
ejpam-3406	39	1	recently	recently	ADV
ejpam-3406	39	2	,	,	PUNCT
ejpam-3406	39	3	r.	r.	PROPN
ejpam-3406	39	4	corcino	corcino	PROPN
ejpam-3406	39	5	et	et	PROPN
ejpam-3406	39	6	al.[9	al.[9	PROPN
ejpam-3406	39	7	]	]	PUNCT
ejpam-3406	39	8	have	have	AUX
ejpam-3406	39	9	successfully	successfully	ADV
ejpam-3406	39	10	r.	r.	PROPN
ejpam-3406	39	11	corcino	corcino	PROPN
ejpam-3406	39	12	,	,	PUNCT
ejpam-3406	39	13	mj	mj	PROPN
ejpam-3406	39	14	.	.	PUNCT
ejpam-3406	39	15	latayada	latayada	PROPN
ejpam-3406	39	16	,	,	PUNCT
ejpam-3406	39	17	mar	mar	PROPN
ejpam-3406	39	18	.	.	PROPN
ejpam-3406	39	19	vega	vega	PROPN
ejpam-3406	39	20	/	/	SYM
ejpam-3406	39	21	eur	eur	PROPN
ejpam-3406	39	22	.	.	PUNCT
ejpam-3406	40	1	j.	j.	PROPN
ejpam-3406	40	2	pure	pure	PROPN
ejpam-3406	40	3	appl	appl	PROPN
ejpam-3406	40	4	.	.	PROPN
ejpam-3406	40	5	math	math	PROPN
ejpam-3406	40	6	,	,	PUNCT
ejpam-3406	40	7	12	12	NUM
ejpam-3406	40	8	(	(	PUNCT
ejpam-3406	40	9	2	2	NUM
ejpam-3406	40	10	)	)	PUNCT
ejpam-3406	40	11	(	(	PUNCT
ejpam-3406	40	12	2019	2019	NUM
ejpam-3406	40	13	)	)	PUNCT
ejpam-3406	40	14	,	,	PUNCT
ejpam-3406	40	15	279	279	NUM
ejpam-3406	40	16	-	-	SYM
ejpam-3406	40	17	293	293	NUM
ejpam-3406	40	18	281	281	NUM
ejpam-3406	40	19	established	establish	VERB
ejpam-3406	40	20	the	the	DET
ejpam-3406	40	21	hankel	hankel	NOUN
ejpam-3406	40	22	transform	transform	NOUN
ejpam-3406	40	23	for	for	ADP
ejpam-3406	40	24	the	the	DET
ejpam-3406	40	25	q	q	NOUN
ejpam-3406	40	26	-	-	PUNCT
ejpam-3406	40	27	analogue	analogue	NOUN
ejpam-3406	40	28	of	of	ADP
ejpam-3406	40	29	noncentral	noncentral	ADJ
ejpam-3406	40	30	bell	bell	NOUN
ejpam-3406	40	31	numbers	number	NOUN
ejpam-3406	40	32	.	.	PUNCT
ejpam-3406	41	1	this	this	PRON
ejpam-3406	41	2	motivates	motivate	VERB
ejpam-3406	41	3	the	the	DET
ejpam-3406	41	4	present	present	ADJ
ejpam-3406	41	5	authors	author	NOUN
ejpam-3406	41	6	to	to	PART
ejpam-3406	41	7	use	use	VERB
ejpam-3406	41	8	this	this	DET
ejpam-3406	41	9	method	method	NOUN
ejpam-3406	41	10	to	to	PART
ejpam-3406	41	11	establish	establish	VERB
ejpam-3406	41	12	the	the	DET
ejpam-3406	41	13	hankel	hankel	NOUN
ejpam-3406	41	14	transform	transform	NOUN
ejpam-3406	41	15	for	for	ADP
ejpam-3406	41	16	the	the	DET
ejpam-3406	41	17	q	q	NOUN
ejpam-3406	41	18	-	-	PUNCT
ejpam-3406	41	19	analogue	analogue	NOUN
ejpam-3406	41	20	of	of	ADP
ejpam-3406	41	21	(	(	PUNCT
ejpam-3406	41	22	r	r	NOUN
ejpam-3406	41	23	,	,	PUNCT
ejpam-3406	41	24	β)-bell	β)-bell	PUNCT
ejpam-3406	41	25	numbers	number	NOUN
ejpam-3406	41	26	gn	gn	PROPN
ejpam-3406	41	27	,	,	PUNCT
ejpam-3406	41	28	r	r	PROPN
ejpam-3406	41	29	,	,	PUNCT
ejpam-3406	41	30	β	β	NOUN
ejpam-3406	41	31	.	.	PUNCT
ejpam-3406	42	1	it	it	PRON
ejpam-3406	42	2	is	be	AUX
ejpam-3406	42	3	important	important	ADJ
ejpam-3406	42	4	to	to	PART
ejpam-3406	42	5	note	note	VERB
ejpam-3406	42	6	that	that	SCONJ
ejpam-3406	42	7	the	the	DET
ejpam-3406	42	8	numbers	number	NOUN
ejpam-3406	42	9	gn	gn	PROPN
ejpam-3406	42	10	,	,	PUNCT
ejpam-3406	42	11	r	r	PROPN
ejpam-3406	42	12	,	,	PUNCT
ejpam-3406	42	13	β	β	X
ejpam-3406	42	14	are	be	AUX
ejpam-3406	42	15	equivalent	equivalent	ADJ
ejpam-3406	42	16	to	to	ADP
ejpam-3406	42	17	the	the	DET
ejpam-3406	42	18	r	r	NOUN
ejpam-3406	42	19	-	-	PUNCT
ejpam-3406	42	20	dowling	dowle	VERB
ejpam-3406	42	21	numbers	number	NOUN
ejpam-3406	42	22	dm	dm	NOUN
ejpam-3406	42	23	,	,	PUNCT
ejpam-3406	42	24	r(n	r(n	PROPN
ejpam-3406	42	25	)	)	PUNCT
ejpam-3406	42	26	,	,	PUNCT
ejpam-3406	42	27	which	which	PRON
ejpam-3406	42	28	are	be	AUX
ejpam-3406	42	29	defined	define	VERB
ejpam-3406	42	30	as	as	ADP
ejpam-3406	42	31	the	the	DET
ejpam-3406	42	32	sum	sum	NOUN
ejpam-3406	42	33	of	of	ADP
ejpam-3406	42	34	r	r	NOUN
ejpam-3406	42	35	-	-	PUNCT
ejpam-3406	42	36	whitney	whitney	NOUN
ejpam-3406	42	37	numbers	number	NOUN
ejpam-3406	42	38	of	of	ADP
ejpam-3406	42	39	the	the	DET
ejpam-3406	42	40	second	second	ADJ
ejpam-3406	42	41	kind	kind	NOUN
ejpam-3406	42	42	,	,	PUNCT
ejpam-3406	42	43	denoted	denote	VERB
ejpam-3406	42	44	by	by	ADP
ejpam-3406	42	45	wm	wm	PROPN
ejpam-3406	42	46	,	,	PUNCT
ejpam-3406	42	47	r(n	r(n	PROPN
ejpam-3406	42	48	,	,	PUNCT
ejpam-3406	42	49	k	k	NOUN
ejpam-3406	42	50	)	)	PUNCT
ejpam-3406	42	51	.	.	PUNCT
ejpam-3406	43	1	that	that	PRON
ejpam-3406	43	2	is	is	ADV
ejpam-3406	43	3	,	,	PUNCT
ejpam-3406	43	4	dm	dm	INTJ
ejpam-3406	43	5	,	,	PUNCT
ejpam-3406	43	6	r(n	r(n	PROPN
ejpam-3406	43	7	)	)	PUNCT
ejpam-3406	43	8	=	=	SYM
ejpam-3406	43	9	n∑	n∑	PROPN
ejpam-3406	43	10	k=0	k=0	PROPN
ejpam-3406	43	11	wm	wm	PROPN
ejpam-3406	43	12	,	,	PUNCT
ejpam-3406	43	13	r(n	r(n	PROPN
ejpam-3406	43	14	,	,	PUNCT
ejpam-3406	43	15	k	k	NOUN
ejpam-3406	43	16	)	)	PUNCT
ejpam-3406	43	17	.	.	PUNCT
ejpam-3406	44	1	the	the	DET
ejpam-3406	44	2	term	term	NOUN
ejpam-3406	44	3	“	"	PUNCT
ejpam-3406	44	4	r	r	NOUN
ejpam-3406	44	5	-	-	PUNCT
ejpam-3406	44	6	dowling	dowle	VERB
ejpam-3406	44	7	numbers	number	NOUN
ejpam-3406	44	8	”	"	PUNCT
ejpam-3406	44	9	was	be	AUX
ejpam-3406	44	10	introduced	introduce	VERB
ejpam-3406	44	11	by	by	ADP
ejpam-3406	44	12	cheon	cheon	PROPN
ejpam-3406	44	13	and	and	CCONJ
ejpam-3406	44	14	jung	jung	PROPN
ejpam-3406	45	1	[	[	X
ejpam-3406	45	2	3	3	NUM
ejpam-3406	45	3	]	]	PUNCT
ejpam-3406	45	4	.	.	PUNCT
ejpam-3406	46	1	2	2	X
ejpam-3406	46	2	.	.	X
ejpam-3406	46	3	a	a	DET
ejpam-3406	46	4	q	q	NOUN
ejpam-3406	46	5	-	-	PUNCT
ejpam-3406	46	6	analogue	analogue	NOUN
ejpam-3406	46	7	of	of	ADP
ejpam-3406	46	8	wm	wm	PROPN
ejpam-3406	46	9	,	,	PUNCT
ejpam-3406	46	10	r(n	r(n	PROPN
ejpam-3406	46	11	,	,	PUNCT
ejpam-3406	46	12	k	k	NOUN
ejpam-3406	46	13	):	):	PUNCT
ejpam-3406	46	14	second	second	ADJ
ejpam-3406	46	15	form	form	NOUN
ejpam-3406	46	16	a	a	DET
ejpam-3406	46	17	q	q	NOUN
ejpam-3406	46	18	-	-	PUNCT
ejpam-3406	46	19	analogue	analogue	NOUN
ejpam-3406	46	20	of	of	ADP
ejpam-3406	46	21	both	both	DET
ejpam-3406	46	22	kinds	kind	NOUN
ejpam-3406	46	23	of	of	ADP
ejpam-3406	46	24	stirling	stirling	NOUN
ejpam-3406	46	25	numbers	number	NOUN
ejpam-3406	46	26	was	be	AUX
ejpam-3406	46	27	first	first	ADV
ejpam-3406	46	28	defined	define	VERB
ejpam-3406	46	29	by	by	ADP
ejpam-3406	46	30	carlitz	carlitz	NOUN
ejpam-3406	46	31	in	in	ADP
ejpam-3406	46	32	[	[	X
ejpam-3406	46	33	2	2	NUM
ejpam-3406	46	34	]	]	PUNCT
ejpam-3406	46	35	.	.	PUNCT
ejpam-3406	47	1	the	the	DET
ejpam-3406	47	2	second	second	ADJ
ejpam-3406	47	3	kind	kind	NOUN
ejpam-3406	47	4	of	of	ADP
ejpam-3406	47	5	which	which	PRON
ejpam-3406	47	6	,	,	PUNCT
ejpam-3406	47	7	known	know	VERB
ejpam-3406	47	8	as	as	ADP
ejpam-3406	47	9	q	q	ADJ
ejpam-3406	47	10	-	-	PUNCT
ejpam-3406	47	11	stirling	stirling	ADJ
ejpam-3406	47	12	numbers	number	NOUN
ejpam-3406	47	13	of	of	ADP
ejpam-3406	47	14	the	the	DET
ejpam-3406	47	15	second	second	ADJ
ejpam-3406	47	16	kind	kind	NOUN
ejpam-3406	47	17	,	,	PUNCT
ejpam-3406	47	18	is	be	AUX
ejpam-3406	47	19	defined	define	VERB
ejpam-3406	47	20	in	in	ADP
ejpam-3406	47	21	terms	term	NOUN
ejpam-3406	47	22	of	of	ADP
ejpam-3406	47	23	the	the	DET
ejpam-3406	47	24	following	follow	VERB
ejpam-3406	47	25	recurrence	recurrence	PROPN
ejpam-3406	47	26	relation	relation	PROPN
ejpam-3406	47	27	sq[n	sq[n	PROPN
ejpam-3406	47	28	,	,	PUNCT
ejpam-3406	47	29	k	k	X
ejpam-3406	48	1	]	]	X
ejpam-3406	48	2	=	=	PUNCT
ejpam-3406	48	3	sq[n−	sq[n−	NOUN
ejpam-3406	48	4	1	1	NUM
ejpam-3406	48	5	,	,	PUNCT
ejpam-3406	48	6	k	k	PROPN
ejpam-3406	48	7	−	−	PROPN
ejpam-3406	48	8	1	1	NUM
ejpam-3406	48	9	]	]	PUNCT
ejpam-3406	48	10	+	+	CCONJ
ejpam-3406	48	11	[	[	X
ejpam-3406	48	12	k]qsq[n−	k]qsq[n−	NOUN
ejpam-3406	48	13	1	1	NUM
ejpam-3406	48	14	,	,	PUNCT
ejpam-3406	48	15	k	k	X
ejpam-3406	48	16	]	]	X
ejpam-3406	48	17	(	(	PUNCT
ejpam-3406	48	18	2	2	NUM
ejpam-3406	48	19	)	)	PUNCT
ejpam-3406	48	20	in	in	ADP
ejpam-3406	48	21	connection	connection	NOUN
ejpam-3406	48	22	with	with	ADP
ejpam-3406	48	23	a	a	DET
ejpam-3406	48	24	problem	problem	NOUN
ejpam-3406	48	25	in	in	ADP
ejpam-3406	48	26	abelian	abelian	ADJ
ejpam-3406	48	27	groups	group	NOUN
ejpam-3406	48	28	,	,	PUNCT
ejpam-3406	48	29	such	such	ADJ
ejpam-3406	48	30	that	that	SCONJ
ejpam-3406	48	31	when	when	SCONJ
ejpam-3406	48	32	q	q	X
ejpam-3406	48	33	→	→	SYM
ejpam-3406	48	34	1	1	NUM
ejpam-3406	48	35	,	,	PUNCT
ejpam-3406	48	36	this	this	PRON
ejpam-3406	48	37	gives	give	VERB
ejpam-3406	48	38	the	the	DET
ejpam-3406	48	39	triangular	triangular	NOUN
ejpam-3406	48	40	recurrence	recurrence	NOUN
ejpam-3406	48	41	relation	relation	NOUN
ejpam-3406	48	42	for	for	ADP
ejpam-3406	48	43	the	the	DET
ejpam-3406	48	44	classical	classical	ADJ
ejpam-3406	48	45	stirling	stirling	NOUN
ejpam-3406	48	46	numbers	number	NOUN
ejpam-3406	48	47	of	of	ADP
ejpam-3406	48	48	the	the	DET
ejpam-3406	48	49	second	second	ADJ
ejpam-3406	48	50	kind	kind	NOUN
ejpam-3406	48	51	s(n	s(n	PROPN
ejpam-3406	48	52	,	,	PUNCT
ejpam-3406	48	53	k	k	NOUN
ejpam-3406	48	54	)	)	PUNCT
ejpam-3406	48	55	s(n	s(n	PROPN
ejpam-3406	48	56	,	,	PUNCT
ejpam-3406	48	57	k	k	NOUN
ejpam-3406	48	58	)	)	PUNCT
ejpam-3406	48	59	=	=	SYM
ejpam-3406	48	60	s(n−	s(n−	PROPN
ejpam-3406	48	61	1	1	NUM
ejpam-3406	48	62	,	,	PUNCT
ejpam-3406	48	63	k	k	PROPN
ejpam-3406	48	64	−	−	PROPN
ejpam-3406	48	65	1	1	NUM
ejpam-3406	48	66	)	)	PUNCT
ejpam-3406	49	1	+	+	CCONJ
ejpam-3406	49	2	ks(n−	ks(n−	PROPN
ejpam-3406	49	3	1	1	NUM
ejpam-3406	49	4	,	,	PUNCT
ejpam-3406	49	5	k	k	NOUN
ejpam-3406	49	6	)	)	PUNCT
ejpam-3406	49	7	.	.	PUNCT
ejpam-3406	50	1	(	(	PUNCT
ejpam-3406	50	2	3	3	X
ejpam-3406	50	3	)	)	PUNCT
ejpam-3406	50	4	a	a	DET
ejpam-3406	50	5	different	different	ADJ
ejpam-3406	50	6	way	way	NOUN
ejpam-3406	50	7	of	of	ADP
ejpam-3406	50	8	defining	define	VERB
ejpam-3406	50	9	q	q	NOUN
ejpam-3406	50	10	-	-	PUNCT
ejpam-3406	50	11	analogue	analogue	NOUN
ejpam-3406	50	12	of	of	ADP
ejpam-3406	50	13	stirling	stirling	NOUN
ejpam-3406	50	14	numbers	number	NOUN
ejpam-3406	50	15	of	of	ADP
ejpam-3406	50	16	the	the	DET
ejpam-3406	50	17	second	second	ADJ
ejpam-3406	50	18	kind	kind	NOUN
ejpam-3406	50	19	has	have	AUX
ejpam-3406	50	20	been	be	AUX
ejpam-3406	50	21	adapted	adapt	VERB
ejpam-3406	50	22	in	in	ADP
ejpam-3406	50	23	the	the	DET
ejpam-3406	50	24	paper	paper	NOUN
ejpam-3406	50	25	by	by	ADP
ejpam-3406	50	26	[	[	X
ejpam-3406	50	27	10	10	NUM
ejpam-3406	50	28	]	]	PUNCT
ejpam-3406	50	29	which	which	PRON
ejpam-3406	50	30	is	be	AUX
ejpam-3406	50	31	given	give	VERB
ejpam-3406	50	32	as	as	SCONJ
ejpam-3406	50	33	follows	follow	VERB
ejpam-3406	50	34	sq[n	sq[n	PROPN
ejpam-3406	50	35	,	,	PUNCT
ejpam-3406	50	36	k	k	X
ejpam-3406	50	37	]	]	X
ejpam-3406	50	38	=	=	SYM
ejpam-3406	50	39	qk−1sq[n−	qk−1sq[n−	NOUN
ejpam-3406	50	40	1	1	NUM
ejpam-3406	50	41	,	,	PUNCT
ejpam-3406	50	42	k	k	PROPN
ejpam-3406	50	43	−	−	PROPN
ejpam-3406	51	1	1	1	NUM
ejpam-3406	51	2	]	]	PUNCT
ejpam-3406	51	3	+	+	CCONJ
ejpam-3406	52	1	[	[	X
ejpam-3406	52	2	k]qsq[n−	k]qsq[n−	NOUN
ejpam-3406	52	3	1	1	NUM
ejpam-3406	52	4	,	,	PUNCT
ejpam-3406	52	5	k	k	NOUN
ejpam-3406	52	6	]	]	X
ejpam-3406	52	7	.	.	PUNCT
ejpam-3406	53	1	(	(	PUNCT
ejpam-3406	53	2	4	4	X
ejpam-3406	53	3	)	)	PUNCT
ejpam-3406	53	4	this	this	DET
ejpam-3406	53	5	type	type	NOUN
ejpam-3406	53	6	of	of	ADP
ejpam-3406	53	7	q	q	NOUN
ejpam-3406	53	8	-	-	PUNCT
ejpam-3406	53	9	analogue	analogue	NOUN
ejpam-3406	53	10	gives	give	VERB
ejpam-3406	53	11	the	the	DET
ejpam-3406	53	12	hankel	hankel	NOUN
ejpam-3406	53	13	transform	transform	NOUN
ejpam-3406	53	14	of	of	ADP
ejpam-3406	53	15	q	q	ADJ
ejpam-3406	53	16	-	-	ADJ
ejpam-3406	53	17	exponential	exponential	ADJ
ejpam-3406	53	18	polynomials	polynomial	NOUN
ejpam-3406	53	19	and	and	CCONJ
ejpam-3406	53	20	numbers	number	NOUN
ejpam-3406	53	21	which	which	PRON
ejpam-3406	53	22	are	be	AUX
ejpam-3406	53	23	certain	certain	ADJ
ejpam-3406	53	24	q	q	ADJ
ejpam-3406	53	25	-	-	PUNCT
ejpam-3406	53	26	analogue	analogue	NOUN
ejpam-3406	53	27	of	of	ADP
ejpam-3406	53	28	bell	bell	NOUN
ejpam-3406	53	29	polynomials	polynomial	NOUN
ejpam-3406	53	30	and	and	CCONJ
ejpam-3406	53	31	numbers	number	NOUN
ejpam-3406	53	32	.	.	PUNCT
ejpam-3406	54	1	recently	recently	ADV
ejpam-3406	54	2	,	,	PUNCT
ejpam-3406	54	3	a	a	DET
ejpam-3406	54	4	qanalogue	qanalogue	NOUN
ejpam-3406	54	5	of	of	ADP
ejpam-3406	54	6	r	r	NOUN
ejpam-3406	54	7	-	-	PUNCT
ejpam-3406	54	8	whitney	whitney	NOUN
ejpam-3406	54	9	numbers	number	NOUN
ejpam-3406	54	10	of	of	ADP
ejpam-3406	54	11	the	the	DET
ejpam-3406	54	12	second	second	ADJ
ejpam-3406	54	13	kind	kind	NOUN
ejpam-3406	54	14	was	be	AUX
ejpam-3406	54	15	defined	define	VERB
ejpam-3406	54	16	by	by	ADP
ejpam-3406	54	17	corcino	corcino	NOUN
ejpam-3406	54	18	and	and	CCONJ
ejpam-3406	54	19	cañete	cañete	NOUN
ejpam-3406	54	20	[	[	X
ejpam-3406	54	21	6	6	NUM
ejpam-3406	54	22	]	]	PUNCT
ejpam-3406	54	23	parallel	parallel	NOUN
ejpam-3406	54	24	to	to	ADP
ejpam-3406	54	25	the	the	DET
ejpam-3406	54	26	definition	definition	NOUN
ejpam-3406	54	27	for	for	ADP
ejpam-3406	54	28	q	q	NOUN
ejpam-3406	54	29	-	-	PUNCT
ejpam-3406	54	30	analogue	analogue	NOUN
ejpam-3406	54	31	of	of	ADP
ejpam-3406	54	32	noncentral	noncentral	ADJ
ejpam-3406	54	33	stirling	stirling	NOUN
ejpam-3406	54	34	numbers	number	NOUN
ejpam-3406	54	35	of	of	ADP
ejpam-3406	54	36	the	the	DET
ejpam-3406	54	37	second	second	ADJ
ejpam-3406	54	38	kind	kind	NOUN
ejpam-3406	54	39	as	as	SCONJ
ejpam-3406	54	40	follows	follow	VERB
ejpam-3406	54	41	:	:	PUNCT
ejpam-3406	54	42	definition	definition	NOUN
ejpam-3406	54	43	1	1	NUM
ejpam-3406	54	44	.	.	PUNCT
ejpam-3406	55	1	for	for	ADP
ejpam-3406	55	2	non	non	ADJ
ejpam-3406	55	3	-	-	ADJ
ejpam-3406	55	4	negative	negative	ADJ
ejpam-3406	55	5	integers	integer	NOUN
ejpam-3406	55	6	n	n	PRON
ejpam-3406	55	7	and	and	CCONJ
ejpam-3406	55	8	k	k	NOUN
ejpam-3406	55	9	,	,	PUNCT
ejpam-3406	55	10	and	and	CCONJ
ejpam-3406	55	11	real	real	ADJ
ejpam-3406	55	12	number	number	NOUN
ejpam-3406	55	13	a	a	NOUN
ejpam-3406	55	14	,	,	PUNCT
ejpam-3406	55	15	a	a	DET
ejpam-3406	55	16	q	q	ADJ
ejpam-3406	55	17	-	-	PUNCT
ejpam-3406	55	18	analogue	analogue	NOUN
ejpam-3406	55	19	wm	wm	PROPN
ejpam-3406	55	20	,	,	PUNCT
ejpam-3406	55	21	r[n	r[n	NOUN
ejpam-3406	55	22	,	,	PUNCT
ejpam-3406	55	23	k]q	k]q	NOUN
ejpam-3406	55	24	of	of	ADP
ejpam-3406	55	25	wm	wm	PROPN
ejpam-3406	55	26	,	,	PUNCT
ejpam-3406	55	27	r(n	r(n	PROPN
ejpam-3406	55	28	,	,	PUNCT
ejpam-3406	55	29	k	k	NOUN
ejpam-3406	55	30	)	)	PUNCT
ejpam-3406	55	31	is	be	AUX
ejpam-3406	55	32	defined	define	VERB
ejpam-3406	55	33	by	by	ADP
ejpam-3406	55	34	wm	wm	PROPN
ejpam-3406	55	35	,	,	PUNCT
ejpam-3406	55	36	r[n	r[n	NOUN
ejpam-3406	55	37	,	,	PUNCT
ejpam-3406	55	38	k]q	k]q	NOUN
ejpam-3406	56	1	=	=	SYM
ejpam-3406	56	2	qm(k−1)+rwm	qm(k−1)+rwm	PROPN
ejpam-3406	56	3	,	,	PUNCT
ejpam-3406	56	4	r[n−	r[n−	PROPN
ejpam-3406	56	5	1	1	NUM
ejpam-3406	56	6	,	,	PUNCT
ejpam-3406	56	7	k	k	PROPN
ejpam-3406	56	8	−	−	PROPN
ejpam-3406	57	1	1]q	1]q	PROPN
ejpam-3406	58	1	+	+	NUM
ejpam-3406	58	2	[	[	X
ejpam-3406	58	3	mk	mk	X
ejpam-3406	58	4	+	+	CCONJ
ejpam-3406	58	5	r]qwm	r]qwm	NOUN
ejpam-3406	58	6	,	,	PUNCT
ejpam-3406	58	7	r[n−	r[n−	PROPN
ejpam-3406	58	8	1	1	NUM
ejpam-3406	58	9	,	,	PUNCT
ejpam-3406	58	10	k]q	k]q	PROPN
ejpam-3406	58	11	.	.	PUNCT
ejpam-3406	59	1	(	(	PUNCT
ejpam-3406	59	2	5	5	NUM
ejpam-3406	59	3	)	)	PUNCT
ejpam-3406	59	4	where	where	SCONJ
ejpam-3406	59	5	wm	wm	PROPN
ejpam-3406	59	6	,	,	PUNCT
ejpam-3406	59	7	r[0	r[0	PROPN
ejpam-3406	59	8	,	,	PUNCT
ejpam-3406	59	9	0]q	0]q	NOUN
ejpam-3406	59	10	=	=	SYM
ejpam-3406	60	1	1	1	NUM
ejpam-3406	60	2	,	,	PUNCT
ejpam-3406	60	3	wm	wm	PROPN
ejpam-3406	60	4	,	,	PUNCT
ejpam-3406	60	5	r[n	r[n	NOUN
ejpam-3406	60	6	,	,	PUNCT
ejpam-3406	60	7	k]q	k]q	NOUN
ejpam-3406	60	8	=	=	NOUN
ejpam-3406	60	9	0	0	NUM
ejpam-3406	60	10	for	for	ADP
ejpam-3406	60	11	n	n	X
ejpam-3406	60	12	<	<	X
ejpam-3406	60	13	k	k	PROPN
ejpam-3406	60	14	or	or	CCONJ
ejpam-3406	60	15	n	n	CCONJ
ejpam-3406	60	16	,	,	PUNCT
ejpam-3406	61	1	k	k	X
ejpam-3406	61	2	<	<	X
ejpam-3406	61	3	0	0	PUNCT
ejpam-3406	62	1	and	and	CCONJ
ejpam-3406	63	1	[	[	X
ejpam-3406	63	2	t−	t−	PROPN
ejpam-3406	63	3	k]q	k]q	NOUN
ejpam-3406	63	4	=	=	SYM
ejpam-3406	63	5	1	1	NUM
ejpam-3406	63	6	qk	qk	NOUN
ejpam-3406	63	7	(	(	PUNCT
ejpam-3406	63	8	[	[	X
ejpam-3406	63	9	t]q	t]q	NOUN
ejpam-3406	63	10	−	−	NOUN
ejpam-3406	64	1	[	[	X
ejpam-3406	64	2	k]q	k]q	NOUN
ejpam-3406	64	3	)	)	PUNCT
ejpam-3406	64	4	.	.	PUNCT
ejpam-3406	65	1	remark	remark	PROPN
ejpam-3406	65	2	1	1	NUM
ejpam-3406	65	3	.	.	PUNCT
ejpam-3406	66	1	when	when	SCONJ
ejpam-3406	66	2	m	m	VERB
ejpam-3406	66	3	=	=	SYM
ejpam-3406	66	4	1	1	NUM
ejpam-3406	66	5	and	and	CCONJ
ejpam-3406	66	6	r	r	NOUN
ejpam-3406	66	7	=	=	SYM
ejpam-3406	66	8	0	0	NUM
ejpam-3406	66	9	,	,	PUNCT
ejpam-3406	66	10	the	the	DET
ejpam-3406	66	11	relation	relation	NOUN
ejpam-3406	66	12	(	(	PUNCT
ejpam-3406	66	13	5	5	NUM
ejpam-3406	66	14	)	)	PUNCT
ejpam-3406	66	15	reduces	reduce	VERB
ejpam-3406	66	16	to	to	ADP
ejpam-3406	66	17	(	(	PUNCT
ejpam-3406	66	18	4	4	NUM
ejpam-3406	66	19	)	)	PUNCT
ejpam-3406	66	20	.	.	PUNCT
ejpam-3406	67	1	this	this	PRON
ejpam-3406	67	2	implies	imply	VERB
ejpam-3406	67	3	that	that	SCONJ
ejpam-3406	67	4	w1,0[n	w1,0[n	VERB
ejpam-3406	67	5	,	,	PUNCT
ejpam-3406	67	6	k]q	k]q	NOUN
ejpam-3406	67	7	=	=	SYM
ejpam-3406	67	8	sq[n	sq[n	PROPN
ejpam-3406	67	9	,	,	PUNCT
ejpam-3406	67	10	k	k	X
ejpam-3406	67	11	]	]	X
ejpam-3406	67	12	.	.	PUNCT
ejpam-3406	68	1	(	(	PUNCT
ejpam-3406	68	2	6	6	NUM
ejpam-3406	68	3	)	)	PUNCT
ejpam-3406	68	4	r.	r.	NOUN
ejpam-3406	68	5	corcino	corcino	PROPN
ejpam-3406	68	6	,	,	PUNCT
ejpam-3406	68	7	mj	mj	PROPN
ejpam-3406	68	8	.	.	PUNCT
ejpam-3406	68	9	latayada	latayada	PROPN
ejpam-3406	68	10	,	,	PUNCT
ejpam-3406	68	11	mar	mar	PROPN
ejpam-3406	68	12	.	.	PROPN
ejpam-3406	68	13	vega	vega	PROPN
ejpam-3406	68	14	/	/	SYM
ejpam-3406	68	15	eur	eur	PROPN
ejpam-3406	68	16	.	.	PUNCT
ejpam-3406	69	1	j.	j.	PROPN
ejpam-3406	69	2	pure	pure	PROPN
ejpam-3406	69	3	appl	appl	PROPN
ejpam-3406	69	4	.	.	PROPN
ejpam-3406	69	5	math	math	PROPN
ejpam-3406	69	6	,	,	PUNCT
ejpam-3406	69	7	12	12	NUM
ejpam-3406	69	8	(	(	PUNCT
ejpam-3406	69	9	2	2	NUM
ejpam-3406	69	10	)	)	PUNCT
ejpam-3406	69	11	(	(	PUNCT
ejpam-3406	69	12	2019	2019	NUM
ejpam-3406	69	13	)	)	PUNCT
ejpam-3406	69	14	,	,	PUNCT
ejpam-3406	69	15	279	279	NUM
ejpam-3406	69	16	-	-	SYM
ejpam-3406	69	17	293	293	NUM
ejpam-3406	69	18	282	282	NUM
ejpam-3406	69	19	the	the	DET
ejpam-3406	69	20	q	q	ADJ
ejpam-3406	69	21	-	-	PUNCT
ejpam-3406	69	22	analogue	analogue	NOUN
ejpam-3406	69	23	wm	wm	PROPN
ejpam-3406	69	24	,	,	PUNCT
ejpam-3406	69	25	r[n	r[n	PROPN
ejpam-3406	69	26	,	,	PUNCT
ejpam-3406	69	27	k]q	k]q	AUX
ejpam-3406	69	28	satisfies	satisfy	VERB
ejpam-3406	69	29	the	the	DET
ejpam-3406	69	30	following	follow	VERB
ejpam-3406	69	31	properties	property	NOUN
ejpam-3406	69	32	:	:	PUNCT
ejpam-3406	69	33	vertical	vertical	ADJ
ejpam-3406	69	34	and	and	CCONJ
ejpam-3406	69	35	horizontal	horizontal	ADJ
ejpam-3406	69	36	recurrence	recurrence	NOUN
ejpam-3406	69	37	relations	relations	PROPN
ejpam-3406	69	38	wm	wm	PROPN
ejpam-3406	69	39	,	,	PUNCT
ejpam-3406	69	40	r[n+	r[n+	NOUN
ejpam-3406	69	41	1	1	NUM
ejpam-3406	69	42	,	,	PUNCT
ejpam-3406	69	43	k	k	PROPN
ejpam-3406	70	1	+	+	PROPN
ejpam-3406	70	2	1]q	1]q	NUM
ejpam-3406	70	3	=	=	SYM
ejpam-3406	70	4	qmk+r	qmk+r	PROPN
ejpam-3406	70	5	n∑	n∑	PROPN
ejpam-3406	70	6	j	j	PROPN
ejpam-3406	71	1	=	=	PROPN
ejpam-3406	71	2	k	k	PROPN
ejpam-3406	72	1	[	[	X
ejpam-3406	72	2	m(k	m(k	PROPN
ejpam-3406	72	3	+	+	CCONJ
ejpam-3406	72	4	1	1	NUM
ejpam-3406	72	5	)	)	PUNCT
ejpam-3406	72	6	+	+	NUM
ejpam-3406	72	7	r]n−jq	r]n−jq	VERB
ejpam-3406	72	8	wm	wm	PROPN
ejpam-3406	72	9	,	,	PUNCT
ejpam-3406	72	10	r[j	r[j	NOUN
ejpam-3406	72	11	,	,	PUNCT
ejpam-3406	72	12	k]q	k]q	PROPN
ejpam-3406	72	13	;	;	PUNCT
ejpam-3406	72	14	(	(	PUNCT
ejpam-3406	72	15	7	7	X
ejpam-3406	72	16	)	)	PUNCT
ejpam-3406	72	17	wm	wm	PROPN
ejpam-3406	72	18	,	,	PUNCT
ejpam-3406	72	19	r[n	r[n	NOUN
ejpam-3406	72	20	,	,	PUNCT
ejpam-3406	72	21	k]q	k]q	PROPN
ejpam-3406	72	22	=	=	PUNCT
ejpam-3406	72	23	n−k∑	n−k∑	NOUN
ejpam-3406	72	24	j=0	j=0	PROPN
ejpam-3406	72	25	(	(	PUNCT
ejpam-3406	72	26	−1)jq−r−m(k+j	−1)jq−r−m(k+j	PROPN
ejpam-3406	72	27	)	)	PUNCT
ejpam-3406	72	28	rk+j+1,q	rk+j+1,q	PROPN
ejpam-3406	72	29	rk+1,q	rk+1,q	PROPN
ejpam-3406	72	30	wm	wm	PROPN
ejpam-3406	72	31	,	,	PUNCT
ejpam-3406	72	32	r[n+	r[n+	NOUN
ejpam-3406	72	33	1	1	NUM
ejpam-3406	72	34	,	,	PUNCT
ejpam-3406	72	35	k	k	PROPN
ejpam-3406	72	36	+	+	NUM
ejpam-3406	72	37	j	j	PROPN
ejpam-3406	73	1	+	+	PROPN
ejpam-3406	73	2	1]q	1]q	NUM
ejpam-3406	73	3	;	;	PUNCT
ejpam-3406	73	4	(	(	PUNCT
ejpam-3406	73	5	8)	8)	NUM
ejpam-3406	73	6	horizontal	horizontal	ADJ
ejpam-3406	73	7	generating	generating	NOUN
ejpam-3406	73	8	function	function	NOUN
ejpam-3406	73	9	n∑	n∑	PROPN
ejpam-3406	73	10	k=0	k=0	PROPN
ejpam-3406	73	11	wm	wm	PROPN
ejpam-3406	73	12	,	,	PUNCT
ejpam-3406	73	13	r[n	r[n	NOUN
ejpam-3406	73	14	,	,	PUNCT
ejpam-3406	73	15	k]q[t−	k]q[t−	NOUN
ejpam-3406	73	16	r|m]k	r|m]k	NUM
ejpam-3406	73	17	,	,	PUNCT
ejpam-3406	73	18	q	q	NOUN
ejpam-3406	74	1	=	=	PUNCT
ejpam-3406	75	1	[	[	X
ejpam-3406	75	2	t]nq	t]nq	NOUN
ejpam-3406	75	3	.	.	PUNCT
ejpam-3406	76	1	(	(	PUNCT
ejpam-3406	76	2	9	9	X
ejpam-3406	76	3	)	)	PUNCT
ejpam-3406	76	4	explicit	explicit	ADJ
ejpam-3406	76	5	formula	formula	NOUN
ejpam-3406	76	6	wm	wm	PROPN
ejpam-3406	76	7	,	,	PUNCT
ejpam-3406	76	8	r[n	r[n	NOUN
ejpam-3406	76	9	,	,	PUNCT
ejpam-3406	76	10	k]q	k]q	NOUN
ejpam-3406	76	11	=	=	SYM
ejpam-3406	76	12	1	1	NUM
ejpam-3406	77	1	[	[	X
ejpam-3406	77	2	k]qm	k]qm	X
ejpam-3406	77	3	!	!	PUNCT
ejpam-3406	78	1	[	[	X
ejpam-3406	78	2	m]kq	m]kq	PROPN
ejpam-3406	78	3	k∑	k∑	VERB
ejpam-3406	78	4	j=0	j=0	PROPN
ejpam-3406	78	5	(	(	PUNCT
ejpam-3406	78	6	−1)k−jqm(k−j2	−1)k−jqm(k−j2	NOUN
ejpam-3406	78	7	)	)	PUNCT
ejpam-3406	79	1	[	[	PUNCT
ejpam-3406	79	2	k	k	X
ejpam-3406	79	3	j	j	X
ejpam-3406	79	4	]	]	PUNCT
ejpam-3406	79	5	qm	qm	PROPN
ejpam-3406	80	1	[	[	X
ejpam-3406	80	2	jm+	jm+	NOUN
ejpam-3406	80	3	r]nq	r]nq	X
ejpam-3406	80	4	(	(	PUNCT
ejpam-3406	80	5	10	10	NUM
ejpam-3406	80	6	)	)	PUNCT
ejpam-3406	80	7	=	=	SYM
ejpam-3406	80	8	1	1	NUM
ejpam-3406	81	1	[	[	X
ejpam-3406	81	2	k]qm	k]qm	X
ejpam-3406	81	3	!	!	PUNCT
ejpam-3406	82	1	[	[	X
ejpam-3406	82	2	m]kq	m]kq	X
ejpam-3406	82	3	[	[	PUNCT
ejpam-3406	82	4	∆k	∆k	PROPN
ejpam-3406	82	5	qm	qm	PROPN
ejpam-3406	82	6	,	,	PUNCT
ejpam-3406	82	7	m[x+	m[x+	VERB
ejpam-3406	82	8	r]nq	r]nq	NOUN
ejpam-3406	82	9	]	]	X
ejpam-3406	82	10	x=0	x=0	PROPN
ejpam-3406	83	1	(	(	PUNCT
ejpam-3406	83	2	11	11	NUM
ejpam-3406	83	3	)	)	PUNCT
ejpam-3406	83	4	exponential	exponential	NOUN
ejpam-3406	83	5	generating	generating	NOUN
ejpam-3406	83	6	function	function	NOUN
ejpam-3406	83	7	∑	∑	PROPN
ejpam-3406	83	8	n≥0	n≥0	PROPN
ejpam-3406	83	9	wm	wm	PROPN
ejpam-3406	83	10	,	,	PUNCT
ejpam-3406	83	11	r[n	r[n	NOUN
ejpam-3406	83	12	,	,	PUNCT
ejpam-3406	83	13	k]q	k]q	VERB
ejpam-3406	84	1	[	[	X
ejpam-3406	84	2	t]nq	t]nq	NOUN
ejpam-3406	84	3	[	[	X
ejpam-3406	84	4	n]q	n]q	X
ejpam-3406	84	5	!	!	PUNCT
ejpam-3406	85	1	=	=	SYM
ejpam-3406	85	2	1	1	NUM
ejpam-3406	86	1	[	[	X
ejpam-3406	86	2	k]qm![m]kq	k]qm![m]kq	X
ejpam-3406	86	3	[	[	PUNCT
ejpam-3406	86	4	∆qm	∆qm	PROPN
ejpam-3406	86	5	,	,	PUNCT
ejpam-3406	86	6	mkeq	mkeq	NOUN
ejpam-3406	86	7	(	(	PUNCT
ejpam-3406	86	8	[	[	X
ejpam-3406	86	9	x+	x+	ADJ
ejpam-3406	86	10	jm+	jm+	NOUN
ejpam-3406	86	11	r]q[t]q	r]q[t]q	NUM
ejpam-3406	86	12	)	)	PUNCT
ejpam-3406	86	13	]	]	PUNCT
ejpam-3406	87	1	x=0	x=0	PUNCT
ejpam-3406	87	2	.	.	PUNCT
ejpam-3406	88	1	(	(	PUNCT
ejpam-3406	88	2	12	12	NUM
ejpam-3406	88	3	)	)	PUNCT
ejpam-3406	88	4	rational	rational	ADJ
ejpam-3406	88	5	generating	generating	NOUN
ejpam-3406	88	6	function	function	NOUN
ejpam-3406	88	7	ψk(t	ψk(t	NOUN
ejpam-3406	88	8	)	)	PUNCT
ejpam-3406	89	1	=	=	PUNCT
ejpam-3406	89	2	∑	∑	PROPN
ejpam-3406	89	3	n≥k	n≥k	PROPN
ejpam-3406	89	4	wm	wm	PROPN
ejpam-3406	89	5	,	,	PUNCT
ejpam-3406	89	6	r[n	r[n	NOUN
ejpam-3406	89	7	,	,	PUNCT
ejpam-3406	89	8	k]q[t	k]q[t	X
ejpam-3406	89	9	]	]	X
ejpam-3406	89	10	n	n	PRON
ejpam-3406	89	11	q	q	NOUN
ejpam-3406	89	12	=	=	SYM
ejpam-3406	89	13	qm(k2)+kr[t]kq∏k	qm(k2)+kr[t]kq∏k	PROPN
ejpam-3406	89	14	j=0(1−	j=0(1−	PROPN
ejpam-3406	89	15	[	[	X
ejpam-3406	89	16	mj	mj	X
ejpam-3406	89	17	+	+	NUM
ejpam-3406	89	18	r]q[t]q	r]q[t]q	NUM
ejpam-3406	89	19	)	)	PUNCT
ejpam-3406	89	20	.	.	PUNCT
ejpam-3406	90	1	explicit	explicit	ADJ
ejpam-3406	90	2	formula	formula	NOUN
ejpam-3406	90	3	in	in	ADP
ejpam-3406	90	4	symmetric	symmetric	ADJ
ejpam-3406	90	5	function	function	NOUN
ejpam-3406	90	6	form	form	NOUN
ejpam-3406	90	7	wm	wm	PROPN
ejpam-3406	90	8	,	,	PUNCT
ejpam-3406	90	9	r[n	r[n	NOUN
ejpam-3406	90	10	,	,	PUNCT
ejpam-3406	90	11	k]q	k]q	NOUN
ejpam-3406	90	12	=	=	SYM
ejpam-3406	90	13	qm(k2)+kr	qm(k2)+kr	PROPN
ejpam-3406	90	14	∑	∑	ADV
ejpam-3406	90	15	s1+s2+···sk	s1+s2+···sk	NOUN
ejpam-3406	90	16	=	=	NOUN
ejpam-3406	90	17	n−k	n−k	NOUN
ejpam-3406	90	18	k∏	k∏	PROPN
ejpam-3406	90	19	j=0	j=0	PROPN
ejpam-3406	91	1	[	[	X
ejpam-3406	91	2	mj	mj	X
ejpam-3406	91	3	+	+	X
ejpam-3406	91	4	r	r	X
ejpam-3406	91	5	]	]	X
ejpam-3406	91	6	sj	sj	NOUN
ejpam-3406	91	7	q	q	NOUN
ejpam-3406	91	8	=	=	PUNCT
ejpam-3406	91	9	∑	∑	PROPN
ejpam-3406	91	10	0≤j1≤j2≤···jn−k≤k	0≤j1≤j2≤···jn−k≤k	NUM
ejpam-3406	91	11	qm(k2)+kr	qm(k2)+kr	PROPN
ejpam-3406	91	12	n−k∏	n−k∏	PROPN
ejpam-3406	91	13	i=1	i=1	PUNCT
ejpam-3406	92	1	[	[	X
ejpam-3406	92	2	mj	mj	NOUN
ejpam-3406	92	3	+	+	NUM
ejpam-3406	92	4	r]q	r]q	NOUN
ejpam-3406	92	5	.	.	PUNCT
ejpam-3406	93	1	r.	r.	PROPN
ejpam-3406	93	2	corcino	corcino	PROPN
ejpam-3406	93	3	,	,	PUNCT
ejpam-3406	93	4	mj	mj	PROPN
ejpam-3406	93	5	.	.	PUNCT
ejpam-3406	93	6	latayada	latayada	PROPN
ejpam-3406	93	7	,	,	PUNCT
ejpam-3406	93	8	mar	mar	PROPN
ejpam-3406	93	9	.	.	PROPN
ejpam-3406	93	10	vega	vega	PROPN
ejpam-3406	93	11	/	/	SYM
ejpam-3406	93	12	eur	eur	PROPN
ejpam-3406	93	13	.	.	PUNCT
ejpam-3406	94	1	j.	j.	PROPN
ejpam-3406	94	2	pure	pure	PROPN
ejpam-3406	94	3	appl	appl	PROPN
ejpam-3406	94	4	.	.	PROPN
ejpam-3406	94	5	math	math	PROPN
ejpam-3406	94	6	,	,	PUNCT
ejpam-3406	94	7	12	12	NUM
ejpam-3406	94	8	(	(	PUNCT
ejpam-3406	94	9	2	2	NUM
ejpam-3406	94	10	)	)	PUNCT
ejpam-3406	94	11	(	(	PUNCT
ejpam-3406	94	12	2019	2019	NUM
ejpam-3406	94	13	)	)	PUNCT
ejpam-3406	94	14	,	,	PUNCT
ejpam-3406	94	15	279	279	NUM
ejpam-3406	94	16	-	-	SYM
ejpam-3406	94	17	293	293	NUM
ejpam-3406	94	18	283	283	NUM
ejpam-3406	94	19	we	we	PRON
ejpam-3406	94	20	now	now	ADV
ejpam-3406	94	21	define	define	VERB
ejpam-3406	94	22	another	another	DET
ejpam-3406	94	23	form	form	NOUN
ejpam-3406	94	24	of	of	ADP
ejpam-3406	94	25	q	q	NOUN
ejpam-3406	94	26	-	-	PUNCT
ejpam-3406	94	27	analogue	analogue	NOUN
ejpam-3406	94	28	of	of	ADP
ejpam-3406	94	29	r	r	NOUN
ejpam-3406	94	30	-	-	PUNCT
ejpam-3406	94	31	whitney	whitney	NOUN
ejpam-3406	94	32	numbers	number	NOUN
ejpam-3406	94	33	of	of	ADP
ejpam-3406	94	34	the	the	DET
ejpam-3406	94	35	second	second	ADJ
ejpam-3406	94	36	,	,	PUNCT
ejpam-3406	94	37	denoted	denote	VERB
ejpam-3406	94	38	by	by	ADP
ejpam-3406	94	39	w	w	PROPN
ejpam-3406	94	40	∗m	∗m	PROPN
ejpam-3406	94	41	,	,	PUNCT
ejpam-3406	94	42	r[n	r[n	NOUN
ejpam-3406	94	43	,	,	PUNCT
ejpam-3406	94	44	k]q	k]q	PROPN
ejpam-3406	94	45	,	,	PUNCT
ejpam-3406	94	46	as	as	SCONJ
ejpam-3406	94	47	follows	follow	VERB
ejpam-3406	94	48	w	w	ADP
ejpam-3406	94	49	∗m	∗m	NOUN
ejpam-3406	94	50	,	,	PUNCT
ejpam-3406	94	51	r[n	r[n	NOUN
ejpam-3406	94	52	,	,	PUNCT
ejpam-3406	94	53	k]q	k]q	ADV
ejpam-3406	94	54	:	:	PUNCT
ejpam-3406	94	55	=	=	SYM
ejpam-3406	94	56	q−kr−m(k2)wm	q−kr−m(k2)wm	NOUN
ejpam-3406	94	57	,	,	PUNCT
ejpam-3406	94	58	r[n	r[n	NOUN
ejpam-3406	94	59	,	,	PUNCT
ejpam-3406	94	60	k]q	k]q	PROPN
ejpam-3406	94	61	.	.	PUNCT
ejpam-3406	95	1	hence	hence	ADV
ejpam-3406	95	2	,	,	PUNCT
ejpam-3406	95	3	w	w	PROPN
ejpam-3406	95	4	∗m	∗m	NOUN
ejpam-3406	95	5	,	,	PUNCT
ejpam-3406	95	6	r[n	r[n	NOUN
ejpam-3406	95	7	,	,	PUNCT
ejpam-3406	95	8	k	k	X
ejpam-3406	95	9	]	]	X
ejpam-3406	95	10	=	=	PUNCT
ejpam-3406	95	11	∑	∑	PUNCT
ejpam-3406	95	12	0≤j1≤j2≤	0≤j1≤j2≤	NUM
ejpam-3406	95	13	...	...	PUNCT
ejpam-3406	95	14	≤jn−k≤k	≤jn−k≤k	NUM
ejpam-3406	95	15	n−k∏	n−k∏	PROPN
ejpam-3406	95	16	i=1	i=1	X
ejpam-3406	96	1	[	[	X
ejpam-3406	96	2	mji	mji	ADJ
ejpam-3406	96	3	+	+	X
ejpam-3406	96	4	r]q	r]q	NOUN
ejpam-3406	96	5	.	.	PUNCT
ejpam-3406	97	1	(	(	PUNCT
ejpam-3406	97	2	13	13	NUM
ejpam-3406	97	3	)	)	PUNCT
ejpam-3406	97	4	all	all	DET
ejpam-3406	97	5	other	other	ADJ
ejpam-3406	97	6	properties	property	NOUN
ejpam-3406	97	7	parallel	parallel	ADJ
ejpam-3406	97	8	to	to	ADP
ejpam-3406	97	9	those	those	PRON
ejpam-3406	97	10	of	of	ADP
ejpam-3406	97	11	wm	wm	PROPN
ejpam-3406	97	12	,	,	PUNCT
ejpam-3406	97	13	r[n	r[n	PROPN
ejpam-3406	97	14	,	,	PUNCT
ejpam-3406	97	15	k]q	k]q	NOUN
ejpam-3406	97	16	can	can	AUX
ejpam-3406	97	17	easily	easily	ADV
ejpam-3406	97	18	be	be	AUX
ejpam-3406	97	19	established	establish	VERB
ejpam-3406	97	20	by	by	ADP
ejpam-3406	97	21	imbedding	imbed	VERB
ejpam-3406	97	22	the	the	DET
ejpam-3406	97	23	factor	factor	NOUN
ejpam-3406	97	24	q−kr−m(k2	q−kr−m(k2	NOUN
ejpam-3406	97	25	)	)	PUNCT
ejpam-3406	97	26	in	in	ADP
ejpam-3406	97	27	the	the	DET
ejpam-3406	97	28	derivations	derivation	NOUN
ejpam-3406	97	29	or	or	CCONJ
ejpam-3406	97	30	multiply	multiply	VERB
ejpam-3406	97	31	directly	directly	ADV
ejpam-3406	97	32	to	to	ADP
ejpam-3406	97	33	the	the	DET
ejpam-3406	97	34	resulting	result	VERB
ejpam-3406	97	35	identities	identity	NOUN
ejpam-3406	97	36	/	/	SYM
ejpam-3406	97	37	formula	formula	NOUN
ejpam-3406	97	38	.	.	PUNCT
ejpam-3406	98	1	definition	definition	NOUN
ejpam-3406	98	2	2	2	NUM
ejpam-3406	98	3	.	.	PUNCT
ejpam-3406	99	1	[	[	X
ejpam-3406	99	2	13	13	NUM
ejpam-3406	99	3	]	]	X
ejpam-3406	99	4	an	an	DET
ejpam-3406	99	5	a	a	PRON
ejpam-3406	99	6	-	-	PUNCT
ejpam-3406	99	7	tableau	tableau	NOUN
ejpam-3406	99	8	is	be	AUX
ejpam-3406	99	9	a	a	DET
ejpam-3406	99	10	list	list	NOUN
ejpam-3406	99	11	φ	φ	NOUN
ejpam-3406	99	12	of	of	ADP
ejpam-3406	99	13	column	column	PROPN
ejpam-3406	99	14	c	c	PROPN
ejpam-3406	99	15	of	of	ADP
ejpam-3406	99	16	a	a	DET
ejpam-3406	99	17	ferrer	ferrer	PROPN
ejpam-3406	99	18	’s	’s	PART
ejpam-3406	99	19	diagram	diagram	NOUN
ejpam-3406	99	20	of	of	ADP
ejpam-3406	99	21	a	a	DET
ejpam-3406	99	22	partition	partition	NOUN
ejpam-3406	99	23	λ(by	λ(by	NOUN
ejpam-3406	99	24	decreasing	decrease	VERB
ejpam-3406	99	25	order	order	NOUN
ejpam-3406	99	26	of	of	ADP
ejpam-3406	99	27	length	length	NOUN
ejpam-3406	99	28	)	)	PUNCT
ejpam-3406	99	29	such	such	ADJ
ejpam-3406	99	30	that	that	SCONJ
ejpam-3406	99	31	the	the	DET
ejpam-3406	99	32	lengths	length	NOUN
ejpam-3406	99	33	|c|	|c|	PROPN
ejpam-3406	99	34	are	be	AUX
ejpam-3406	99	35	part	part	NOUN
ejpam-3406	99	36	of	of	ADP
ejpam-3406	99	37	the	the	DET
ejpam-3406	99	38	sequence	sequence	NOUN
ejpam-3406	99	39	a	a	PRON
ejpam-3406	99	40	=	=	SYM
ejpam-3406	99	41	(	(	PUNCT
ejpam-3406	99	42	ri)i≥0	ri)i≥0	PROPN
ejpam-3406	99	43	,	,	PUNCT
ejpam-3406	99	44	a	a	DET
ejpam-3406	99	45	strictly	strictly	ADV
ejpam-3406	99	46	increasing	increase	VERB
ejpam-3406	99	47	sequence	sequence	NOUN
ejpam-3406	99	48	of	of	ADP
ejpam-3406	99	49	nonnegative	nonnegative	ADJ
ejpam-3406	99	50	integers	integer	NOUN
ejpam-3406	99	51	.	.	PUNCT
ejpam-3406	100	1	let	let	VERB
ejpam-3406	100	2	ω	ω	PRON
ejpam-3406	100	3	be	be	AUX
ejpam-3406	100	4	a	a	DET
ejpam-3406	100	5	function	function	NOUN
ejpam-3406	100	6	from	from	ADP
ejpam-3406	100	7	the	the	DET
ejpam-3406	100	8	set	set	NOUN
ejpam-3406	100	9	of	of	ADP
ejpam-3406	100	10	nonnegative	nonnegative	ADJ
ejpam-3406	100	11	integers	integer	NOUN
ejpam-3406	100	12	n	n	X
ejpam-3406	100	13	to	to	ADP
ejpam-3406	100	14	a	a	DET
ejpam-3406	100	15	ring	ring	NOUN
ejpam-3406	100	16	k.	k.	PROPN
ejpam-3406	100	17	suppose	suppose	VERB
ejpam-3406	100	18	φ	φ	PROPN
ejpam-3406	100	19	is	be	AUX
ejpam-3406	100	20	an	an	DET
ejpam-3406	100	21	a	a	DET
ejpam-3406	100	22	-	-	PUNCT
ejpam-3406	100	23	tableau	tableau	NOUN
ejpam-3406	100	24	with	with	ADP
ejpam-3406	100	25	l	l	NOUN
ejpam-3406	100	26	columns	column	NOUN
ejpam-3406	100	27	of	of	ADP
ejpam-3406	100	28	lengths	length	NOUN
ejpam-3406	100	29	|c|	|c|	PROPN
ejpam-3406	100	30	≤	≤	ADJ
ejpam-3406	100	31	h.	h.	NOUN
ejpam-3406	100	32	we	we	PRON
ejpam-3406	100	33	use	use	VERB
ejpam-3406	100	34	tar	tar	NOUN
ejpam-3406	100	35	(	(	PUNCT
ejpam-3406	100	36	h	h	NOUN
ejpam-3406	100	37	,	,	PUNCT
ejpam-3406	100	38	l	l	NOUN
ejpam-3406	100	39	)	)	PUNCT
ejpam-3406	100	40	to	to	PART
ejpam-3406	100	41	denote	denote	VERB
ejpam-3406	100	42	the	the	DET
ejpam-3406	100	43	set	set	NOUN
ejpam-3406	100	44	of	of	ADP
ejpam-3406	100	45	such	such	DET
ejpam-3406	100	46	a	a	DET
ejpam-3406	100	47	-	-	PUNCT
ejpam-3406	100	48	tableaux	tableaux	NOUN
ejpam-3406	100	49	.	.	PUNCT
ejpam-3406	101	1	then	then	ADV
ejpam-3406	101	2	,	,	PUNCT
ejpam-3406	101	3	we	we	PRON
ejpam-3406	101	4	set	set	VERB
ejpam-3406	101	5	ωa(φ	ωa(φ	NOUN
ejpam-3406	101	6	)	)	PUNCT
ejpam-3406	101	7	=	=	SYM
ejpam-3406	101	8	∏	∏	PROPN
ejpam-3406	101	9	c∈φ	c∈φ	NOUN
ejpam-3406	101	10	ω(|c|	ω(|c|	NUM
ejpam-3406	101	11	)	)	PUNCT
ejpam-3406	101	12	.	.	PUNCT
ejpam-3406	102	1	note	note	VERB
ejpam-3406	102	2	that	that	SCONJ
ejpam-3406	102	3	φ	φ	PROPN
ejpam-3406	102	4	might	might	AUX
ejpam-3406	102	5	contain	contain	VERB
ejpam-3406	102	6	a	a	DET
ejpam-3406	102	7	finite	finite	ADJ
ejpam-3406	102	8	number	number	NOUN
ejpam-3406	102	9	of	of	ADP
ejpam-3406	102	10	columns	column	NOUN
ejpam-3406	102	11	whose	whose	DET
ejpam-3406	102	12	lengths	length	NOUN
ejpam-3406	102	13	are	be	AUX
ejpam-3406	102	14	zero	zero	NUM
ejpam-3406	102	15	since	since	SCONJ
ejpam-3406	102	16	0	0	NUM
ejpam-3406	102	17	∈	∈	PROPN
ejpam-3406	102	18	a	a	X
ejpam-3406	102	19	=	=	X
ejpam-3406	102	20	{	{	PUNCT
ejpam-3406	102	21	0	0	NUM
ejpam-3406	102	22	,	,	PUNCT
ejpam-3406	102	23	1	1	NUM
ejpam-3406	102	24	,	,	PUNCT
ejpam-3406	102	25	2	2	NUM
ejpam-3406	102	26	,	,	PUNCT
ejpam-3406	102	27	.	.	PUNCT
ejpam-3406	102	28	.	.	PUNCT
ejpam-3406	102	29	.	.	PUNCT
ejpam-3406	103	1	,	,	PUNCT
ejpam-3406	103	2	k	k	X
ejpam-3406	103	3	}	}	PUNCT
ejpam-3406	103	4	and	and	CCONJ
ejpam-3406	103	5	if	if	SCONJ
ejpam-3406	103	6	ω(0	ω(0	NOUN
ejpam-3406	103	7	)	)	PUNCT
ejpam-3406	103	8	6=	6=	ADP
ejpam-3406	103	9	0	0	NUM
ejpam-3406	103	10	.	.	PUNCT
ejpam-3406	104	1	from	from	ADP
ejpam-3406	104	2	this	this	DET
ejpam-3406	104	3	point	point	NOUN
ejpam-3406	104	4	onward	onward	ADV
ejpam-3406	104	5	,	,	PUNCT
ejpam-3406	104	6	whenever	whenever	SCONJ
ejpam-3406	104	7	an	an	DET
ejpam-3406	104	8	a	a	PRON
ejpam-3406	104	9	-	-	PUNCT
ejpam-3406	104	10	tableau	tableau	NOUN
ejpam-3406	104	11	is	be	AUX
ejpam-3406	104	12	mentioned	mention	VERB
ejpam-3406	104	13	,	,	PUNCT
ejpam-3406	104	14	it	it	PRON
ejpam-3406	104	15	is	be	AUX
ejpam-3406	104	16	always	always	ADV
ejpam-3406	104	17	associated	associate	VERB
ejpam-3406	104	18	with	with	ADP
ejpam-3406	104	19	the	the	DET
ejpam-3406	104	20	sequence	sequence	NOUN
ejpam-3406	104	21	a	a	PRON
ejpam-3406	104	22	=	=	SYM
ejpam-3406	104	23	{	{	PUNCT
ejpam-3406	104	24	0	0	NUM
ejpam-3406	104	25	,	,	PUNCT
ejpam-3406	104	26	1	1	NUM
ejpam-3406	104	27	,	,	PUNCT
ejpam-3406	104	28	2	2	NUM
ejpam-3406	104	29	,	,	PUNCT
ejpam-3406	104	30	.	.	PUNCT
ejpam-3406	104	31	.	.	PUNCT
ejpam-3406	105	1	.	.	PUNCT
ejpam-3406	106	1	,	,	PUNCT
ejpam-3406	106	2	k	k	X
ejpam-3406	106	3	}	}	PUNCT
ejpam-3406	106	4	.	.	PUNCT
ejpam-3406	107	1	we	we	PRON
ejpam-3406	107	2	are	be	AUX
ejpam-3406	107	3	now	now	ADV
ejpam-3406	107	4	ready	ready	ADJ
ejpam-3406	107	5	to	to	PART
ejpam-3406	107	6	mention	mention	VERB
ejpam-3406	107	7	the	the	DET
ejpam-3406	107	8	following	follow	VERB
ejpam-3406	107	9	theorem	theorem	NOUN
ejpam-3406	107	10	.	.	PUNCT
ejpam-3406	107	11	theorem	theorem	NOUN
ejpam-3406	107	12	1	1	NUM
ejpam-3406	107	13	.	.	PUNCT
ejpam-3406	108	1	let	let	VERB
ejpam-3406	108	2	ω	ω	NOUN
ejpam-3406	108	3	:	:	PUNCT
ejpam-3406	108	4	n	n	PROPN
ejpam-3406	108	5	→	→	SYM
ejpam-3406	108	6	k	k	X
ejpam-3406	108	7	denote	denote	VERB
ejpam-3406	108	8	a	a	DET
ejpam-3406	108	9	function	function	NOUN
ejpam-3406	108	10	from	from	ADP
ejpam-3406	108	11	n	n	PRON
ejpam-3406	108	12	to	to	ADP
ejpam-3406	108	13	a	a	DET
ejpam-3406	108	14	ring	ring	NOUN
ejpam-3406	108	15	k	k	X
ejpam-3406	108	16	(	(	PUNCT
ejpam-3406	108	17	column	column	NOUN
ejpam-3406	108	18	weights	weight	VERB
ejpam-3406	108	19	according	accord	VERB
ejpam-3406	108	20	to	to	ADP
ejpam-3406	108	21	length	length	NOUN
ejpam-3406	108	22	)	)	PUNCT
ejpam-3406	108	23	which	which	PRON
ejpam-3406	108	24	is	be	AUX
ejpam-3406	108	25	defined	define	VERB
ejpam-3406	108	26	by	by	ADP
ejpam-3406	108	27	ω(|c|	ω(|c|	NOUN
ejpam-3406	108	28	)	)	PUNCT
ejpam-3406	108	29	=	=	NOUN
ejpam-3406	109	1	[	[	X
ejpam-3406	109	2	m|c|+	m|c|+	NOUN
ejpam-3406	109	3	r]q	r]q	VERB
ejpam-3406	109	4	where	where	SCONJ
ejpam-3406	109	5	r	r	NOUN
ejpam-3406	109	6	is	be	AUX
ejpam-3406	109	7	a	a	DET
ejpam-3406	109	8	complex	complex	ADJ
ejpam-3406	109	9	number	number	NOUN
ejpam-3406	109	10	,	,	PUNCT
ejpam-3406	109	11	and	and	CCONJ
ejpam-3406	109	12	|c|	|c|	PROPN
ejpam-3406	109	13	is	be	AUX
ejpam-3406	109	14	the	the	DET
ejpam-3406	109	15	length	length	NOUN
ejpam-3406	109	16	of	of	ADP
ejpam-3406	109	17	column	column	NOUN
ejpam-3406	109	18	l	l	NOUN
ejpam-3406	109	19	of	of	ADP
ejpam-3406	109	20	an	an	DET
ejpam-3406	109	21	a	a	PRON
ejpam-3406	109	22	-	-	PUNCT
ejpam-3406	109	23	tableau	tableau	NOUN
ejpam-3406	109	24	in	in	ADP
ejpam-3406	109	25	tar	tar	NOUN
ejpam-3406	109	26	(	(	PUNCT
ejpam-3406	109	27	k	k	NOUN
ejpam-3406	109	28	,	,	PUNCT
ejpam-3406	109	29	n−	n−	PROPN
ejpam-3406	109	30	k	k	NOUN
ejpam-3406	109	31	)	)	PUNCT
ejpam-3406	109	32	.	.	PUNCT
ejpam-3406	110	1	then	then	ADV
ejpam-3406	110	2	w	w	PROPN
ejpam-3406	110	3	∗m	∗m	PROPN
ejpam-3406	110	4	,	,	PUNCT
ejpam-3406	110	5	r[n	r[n	NOUN
ejpam-3406	110	6	,	,	PUNCT
ejpam-3406	110	7	k	k	X
ejpam-3406	110	8	]	]	X
ejpam-3406	110	9	=	=	PUNCT
ejpam-3406	110	10	∑	∑	PUNCT
ejpam-3406	110	11	φ∈tar	φ∈tar	PROPN
ejpam-3406	110	12	(	(	PUNCT
ejpam-3406	110	13	k	k	NOUN
ejpam-3406	110	14	,	,	PUNCT
ejpam-3406	110	15	n−k	n−k	NOUN
ejpam-3406	110	16	)	)	PUNCT
ejpam-3406	110	17	∏	∏	PROPN
ejpam-3406	110	18	c∈φ	c∈φ	PROPN
ejpam-3406	110	19	ω(|c|	ω(|c|	NUM
ejpam-3406	110	20	)	)	PUNCT
ejpam-3406	110	21	.	.	PUNCT
ejpam-3406	111	1	proof	proof	NOUN
ejpam-3406	111	2	.	.	PUNCT
ejpam-3406	112	1	let	let	VERB
ejpam-3406	112	2	φ	φ	PROPN
ejpam-3406	112	3	∈	∈	PROPN
ejpam-3406	112	4	tar	tar	NOUN
ejpam-3406	112	5	(	(	PUNCT
ejpam-3406	112	6	k	k	NOUN
ejpam-3406	112	7	,	,	PUNCT
ejpam-3406	112	8	n	n	PROPN
ejpam-3406	112	9	−	−	PROPN
ejpam-3406	112	10	k	k	NOUN
ejpam-3406	112	11	)	)	PUNCT
ejpam-3406	112	12	.	.	PUNCT
ejpam-3406	113	1	this	this	PRON
ejpam-3406	113	2	means	mean	VERB
ejpam-3406	113	3	that	that	SCONJ
ejpam-3406	113	4	φ	φ	PROPN
ejpam-3406	113	5	has	have	VERB
ejpam-3406	113	6	exactly	exactly	ADV
ejpam-3406	114	1	n	n	PRON
ejpam-3406	114	2	−	−	NOUN
ejpam-3406	114	3	k	k	X
ejpam-3406	114	4	columns	column	NOUN
ejpam-3406	114	5	say	say	VERB
ejpam-3406	114	6	c1	c1	PROPN
ejpam-3406	114	7	,	,	PUNCT
ejpam-3406	114	8	c2	c2	PROPN
ejpam-3406	114	9	,	,	PUNCT
ejpam-3406	114	10	·	·	PUNCT
ejpam-3406	114	11	·	·	PUNCT
ejpam-3406	114	12	·	·	PUNCT
ejpam-3406	114	13	,	,	PUNCT
ejpam-3406	114	14	cn−k	cn−k	VERB
ejpam-3406	114	15	whose	whose	DET
ejpam-3406	114	16	lengths	length	NOUN
ejpam-3406	114	17	are	be	AUX
ejpam-3406	114	18	j1	j1	PROPN
ejpam-3406	114	19	,	,	PUNCT
ejpam-3406	114	20	j2	j2	PROPN
ejpam-3406	114	21	,	,	PUNCT
ejpam-3406	114	22	·	·	PUNCT
ejpam-3406	114	23	·	·	PUNCT
ejpam-3406	114	24	·	·	PUNCT
ejpam-3406	114	25	,	,	PUNCT
ejpam-3406	114	26	jn−k	jn−k	PROPN
ejpam-3406	114	27	,	,	PUNCT
ejpam-3406	114	28	respectively	respectively	ADV
ejpam-3406	114	29	.	.	PUNCT
ejpam-3406	115	1	now	now	ADV
ejpam-3406	115	2	,	,	PUNCT
ejpam-3406	115	3	for	for	ADP
ejpam-3406	115	4	each	each	DET
ejpam-3406	115	5	column	column	NOUN
ejpam-3406	115	6	ci	ci	PROPN
ejpam-3406	115	7	∈	∈	PROPN
ejpam-3406	115	8	φ	φ	PROPN
ejpam-3406	115	9	,	,	PUNCT
ejpam-3406	115	10	i	i	NOUN
ejpam-3406	115	11	=	=	NOUN
ejpam-3406	115	12	1	1	NUM
ejpam-3406	115	13	,	,	PUNCT
ejpam-3406	115	14	2	2	NUM
ejpam-3406	115	15	,	,	PUNCT
ejpam-3406	115	16	3	3	NUM
ejpam-3406	115	17	,	,	PUNCT
ejpam-3406	115	18	·	·	PUNCT
ejpam-3406	115	19	·	·	PUNCT
ejpam-3406	115	20	·	·	PUNCT
ejpam-3406	115	21	,	,	PUNCT
ejpam-3406	115	22	n−	n−	NOUN
ejpam-3406	115	23	k	k	PROPN
ejpam-3406	115	24	,	,	PUNCT
ejpam-3406	115	25	we	we	PRON
ejpam-3406	115	26	have	have	VERB
ejpam-3406	115	27	|ci|	|ci|	PROPN
ejpam-3406	115	28	=	=	PUNCT
ejpam-3406	115	29	ji	ji	PROPN
ejpam-3406	115	30	and	and	CCONJ
ejpam-3406	115	31	ω(|ci|	ω(|ci|	NUM
ejpam-3406	115	32	)	)	PUNCT
ejpam-3406	116	1	=	=	NOUN
ejpam-3406	117	1	[	[	X
ejpam-3406	117	2	m|ji|+	m|ji|+	NOUN
ejpam-3406	117	3	r]q	r]q	NOUN
ejpam-3406	117	4	.	.	PUNCT
ejpam-3406	118	1	r.	r.	PROPN
ejpam-3406	118	2	corcino	corcino	PROPN
ejpam-3406	118	3	,	,	PUNCT
ejpam-3406	118	4	mj	mj	PROPN
ejpam-3406	118	5	.	.	PUNCT
ejpam-3406	118	6	latayada	latayada	PROPN
ejpam-3406	118	7	,	,	PUNCT
ejpam-3406	118	8	mar	mar	PROPN
ejpam-3406	118	9	.	.	PROPN
ejpam-3406	118	10	vega	vega	PROPN
ejpam-3406	118	11	/	/	SYM
ejpam-3406	118	12	eur	eur	PROPN
ejpam-3406	118	13	.	.	PUNCT
ejpam-3406	119	1	j.	j.	PROPN
ejpam-3406	119	2	pure	pure	PROPN
ejpam-3406	119	3	appl	appl	PROPN
ejpam-3406	119	4	.	.	PROPN
ejpam-3406	119	5	math	math	PROPN
ejpam-3406	119	6	,	,	PUNCT
ejpam-3406	119	7	12	12	NUM
ejpam-3406	119	8	(	(	PUNCT
ejpam-3406	119	9	2	2	NUM
ejpam-3406	119	10	)	)	PUNCT
ejpam-3406	119	11	(	(	PUNCT
ejpam-3406	119	12	2019	2019	NUM
ejpam-3406	119	13	)	)	PUNCT
ejpam-3406	119	14	,	,	PUNCT
ejpam-3406	119	15	279	279	NUM
ejpam-3406	119	16	-	-	SYM
ejpam-3406	119	17	293	293	NUM
ejpam-3406	119	18	284	284	NUM
ejpam-3406	119	19	then	then	ADV
ejpam-3406	119	20	∏	∏	PROPN
ejpam-3406	119	21	c∈φ	c∈φ	PROPN
ejpam-3406	119	22	ω(|c|	ω(|c|	NOUN
ejpam-3406	119	23	)	)	PUNCT
ejpam-3406	119	24	=	=	SYM
ejpam-3406	119	25	n−k∏	n−k∏	PROPN
ejpam-3406	119	26	i=1	i=1	PROPN
ejpam-3406	119	27	ω(|ci|	ω(|ci|	NOUN
ejpam-3406	119	28	)	)	PUNCT
ejpam-3406	120	1	=	=	SYM
ejpam-3406	120	2	n−k∏	n−k∏	PROPN
ejpam-3406	120	3	i=1	i=1	X
ejpam-3406	121	1	[	[	X
ejpam-3406	121	2	m|ji|+	m|ji|+	NOUN
ejpam-3406	121	3	r]q	r]q	NOUN
ejpam-3406	121	4	.	.	PUNCT
ejpam-3406	122	1	since	since	SCONJ
ejpam-3406	122	2	φ	φ	PROPN
ejpam-3406	122	3	∈	∈	PROPN
ejpam-3406	122	4	tar	tar	NOUN
ejpam-3406	122	5	(	(	PUNCT
ejpam-3406	122	6	k	k	NOUN
ejpam-3406	122	7	,	,	PUNCT
ejpam-3406	122	8	n−	n−	PROPN
ejpam-3406	122	9	k	k	NOUN
ejpam-3406	122	10	)	)	PUNCT
ejpam-3406	122	11	,	,	PUNCT
ejpam-3406	122	12	then∑	then∑	VERB
ejpam-3406	122	13	φ∈tar	φ∈tar	PROPN
ejpam-3406	122	14	(	(	PUNCT
ejpam-3406	122	15	k	k	NOUN
ejpam-3406	122	16	,	,	PUNCT
ejpam-3406	122	17	n−k	n−k	NOUN
ejpam-3406	122	18	)	)	PUNCT
ejpam-3406	122	19	∏	∏	PROPN
ejpam-3406	122	20	c∈φ	c∈φ	NOUN
ejpam-3406	122	21	ω(|c|	ω(|c|	NOUN
ejpam-3406	122	22	)	)	PUNCT
ejpam-3406	122	23	=	=	PUNCT
ejpam-3406	123	1	∑	∑	PROPN
ejpam-3406	123	2	0≤j1≤j2≤	0≤j1≤j2≤	NUM
ejpam-3406	123	3	...	...	PUNCT
ejpam-3406	123	4	≤jn−k≤k	≤jn−k≤k	PUNCT
ejpam-3406	123	5	∏	∏	PROPN
ejpam-3406	123	6	c∈φ	c∈φ	PROPN
ejpam-3406	123	7	ω(|c|	ω(|c|	NOUN
ejpam-3406	123	8	)	)	PUNCT
ejpam-3406	123	9	=	=	PUNCT
ejpam-3406	123	10	∑	∑	PROPN
ejpam-3406	123	11	0≤j1≤j2≤	0≤j1≤j2≤	NUM
ejpam-3406	123	12	...	...	PUNCT
ejpam-3406	123	13	≤jn−k≤k	≤jn−k≤k	NUM
ejpam-3406	123	14	n−k∏	n−k∏	PROPN
ejpam-3406	123	15	i=1	i=1	PUNCT
ejpam-3406	124	1	[	[	X
ejpam-3406	124	2	m|ji|+	m|ji|+	NOUN
ejpam-3406	124	3	r]q	r]q	NOUN
ejpam-3406	124	4	=	=	SYM
ejpam-3406	124	5	w	w	PROPN
ejpam-3406	124	6	∗m	∗m	NOUN
ejpam-3406	124	7	,	,	PUNCT
ejpam-3406	124	8	r[n	r[n	NOUN
ejpam-3406	124	9	,	,	PUNCT
ejpam-3406	124	10	k	k	X
ejpam-3406	124	11	]	]	X
ejpam-3406	124	12	.	.	PUNCT
ejpam-3406	125	1	�	�	PROPN
ejpam-3406	125	2	suppose	suppose	VERB
ejpam-3406	125	3	that	that	SCONJ
ejpam-3406	125	4	for	for	ADP
ejpam-3406	125	5	some	some	DET
ejpam-3406	125	6	numbers	number	NOUN
ejpam-3406	125	7	r1	r1	NOUN
ejpam-3406	125	8	and	and	CCONJ
ejpam-3406	125	9	r2	r2	PROPN
ejpam-3406	125	10	,	,	PUNCT
ejpam-3406	125	11	we	we	PRON
ejpam-3406	125	12	have	have	VERB
ejpam-3406	125	13	r	r	NOUN
ejpam-3406	125	14	=	=	SYM
ejpam-3406	125	15	r1	r1	NOUN
ejpam-3406	125	16	+	+	CCONJ
ejpam-3406	125	17	r2	r2	NOUN
ejpam-3406	125	18	.	.	PUNCT
ejpam-3406	126	1	then	then	ADV
ejpam-3406	126	2	,	,	PUNCT
ejpam-3406	126	3	equation	equation	NOUN
ejpam-3406	126	4	(	(	PUNCT
ejpam-3406	126	5	13	13	NUM
ejpam-3406	126	6	)	)	PUNCT
ejpam-3406	126	7	yields	yield	NOUN
ejpam-3406	126	8	w	w	ADP
ejpam-3406	126	9	∗m	∗m	NOUN
ejpam-3406	126	10	,	,	PUNCT
ejpam-3406	126	11	r[n	r[n	NOUN
ejpam-3406	126	12	,	,	PUNCT
ejpam-3406	126	13	k]q	k]q	NOUN
ejpam-3406	126	14	=	=	SYM
ejpam-3406	126	15	∑	∑	PROPN
ejpam-3406	126	16	0≤j1≤j2≤	0≤j1≤j2≤	NUM
ejpam-3406	126	17	...	...	PUNCT
ejpam-3406	126	18	≤jn−k≤k	≤jn−k≤k	NUM
ejpam-3406	126	19	n−k∏	n−k∏	PROPN
ejpam-3406	126	20	i=1	i=1	X
ejpam-3406	127	1	[	[	X
ejpam-3406	127	2	(	(	PUNCT
ejpam-3406	127	3	mji	mji	ADJ
ejpam-3406	127	4	+	+	CCONJ
ejpam-3406	127	5	r1	r1	NOUN
ejpam-3406	127	6	)	)	PUNCT
ejpam-3406	128	1	+	+	PUNCT
ejpam-3406	129	1	r2]q	r2]q	X
ejpam-3406	129	2	.	.	PUNCT
ejpam-3406	130	1	that	that	PRON
ejpam-3406	130	2	is	be	AUX
ejpam-3406	130	3	,	,	PUNCT
ejpam-3406	130	4	for	for	ADP
ejpam-3406	130	5	any	any	DET
ejpam-3406	130	6	φ	φ	PROPN
ejpam-3406	130	7	∈	∈	PROPN
ejpam-3406	130	8	tar	tar	NOUN
ejpam-3406	130	9	(	(	PUNCT
ejpam-3406	130	10	k	k	NOUN
ejpam-3406	130	11	,	,	PUNCT
ejpam-3406	130	12	n−	n−	PROPN
ejpam-3406	130	13	k	k	NOUN
ejpam-3406	130	14	)	)	PUNCT
ejpam-3406	130	15	,	,	PUNCT
ejpam-3406	130	16	ωa(φ	ωa(φ	NUM
ejpam-3406	130	17	)	)	PUNCT
ejpam-3406	130	18	=	=	SYM
ejpam-3406	130	19	∏	∏	PROPN
ejpam-3406	130	20	c∈φ	c∈φ	NOUN
ejpam-3406	130	21	[	[	X
ejpam-3406	130	22	(	(	PUNCT
ejpam-3406	130	23	mji	mji	ADJ
ejpam-3406	130	24	+	+	CCONJ
ejpam-3406	130	25	r1	r1	NOUN
ejpam-3406	130	26	)	)	PUNCT
ejpam-3406	130	27	+	+	PUNCT
ejpam-3406	130	28	r2]q	r2]q	SYM
ejpam-3406	130	29	,	,	PUNCT
ejpam-3406	130	30	where	where	SCONJ
ejpam-3406	130	31	|c|	|c|	PROPN
ejpam-3406	130	32	∈	∈	PROPN
ejpam-3406	130	33	{	{	PUNCT
ejpam-3406	130	34	0	0	NUM
ejpam-3406	130	35	,	,	PUNCT
ejpam-3406	130	36	1	1	NUM
ejpam-3406	130	37	,	,	PUNCT
ejpam-3406	130	38	2	2	NUM
ejpam-3406	130	39	,	,	PUNCT
ejpam-3406	130	40	.	.	PUNCT
ejpam-3406	130	41	.	.	PUNCT
ejpam-3406	130	42	.	.	PUNCT
ejpam-3406	131	1	,	,	PUNCT
ejpam-3406	131	2	k	k	X
ejpam-3406	131	3	}	}	PUNCT
ejpam-3406	131	4	.	.	PUNCT
ejpam-3406	132	1	note	note	VERB
ejpam-3406	132	2	that	that	SCONJ
ejpam-3406	132	3	the	the	DET
ejpam-3406	132	4	weight	weight	NOUN
ejpam-3406	132	5	of	of	ADP
ejpam-3406	132	6	each	each	DET
ejpam-3406	132	7	column	column	NOUN
ejpam-3406	132	8	of	of	ADP
ejpam-3406	132	9	φ	φ	PROPN
ejpam-3406	132	10	can	can	AUX
ejpam-3406	132	11	be	be	AUX
ejpam-3406	132	12	considered	consider	VERB
ejpam-3406	132	13	as	as	ADP
ejpam-3406	132	14	a	a	DET
ejpam-3406	132	15	finite	finite	ADJ
ejpam-3406	132	16	sum	sum	NOUN
ejpam-3406	132	17	with	with	ADP
ejpam-3406	132	18	additive	additive	ADJ
ejpam-3406	132	19	constant	constant	ADJ
ejpam-3406	132	20	r2	r2	NOUN
ejpam-3406	132	21	,	,	PUNCT
ejpam-3406	132	22	that	that	ADV
ejpam-3406	132	23	is	is	ADV
ejpam-3406	132	24	,	,	PUNCT
ejpam-3406	132	25	for	for	ADP
ejpam-3406	132	26	each	each	DET
ejpam-3406	132	27	c	c	PROPN
ejpam-3406	132	28	∈	∈	PROPN
ejpam-3406	132	29	φ	φ	PROPN
ejpam-3406	132	30	,	,	PUNCT
ejpam-3406	132	31	we	we	PRON
ejpam-3406	132	32	can	can	AUX
ejpam-3406	132	33	write	write	VERB
ejpam-3406	132	34	ω(|c|	ω(|c|	PRON
ejpam-3406	132	35	)	)	PUNCT
ejpam-3406	132	36	=	=	SYM
ejpam-3406	132	37	1	1	NUM
ejpam-3406	132	38	qr2	qr2	PROPN
ejpam-3406	132	39	(	(	PUNCT
ejpam-3406	132	40	ω∗(|c|	ω∗(|c|	ADV
ejpam-3406	132	41	)	)	PUNCT
ejpam-3406	132	42	+	+	CCONJ
ejpam-3406	133	1	[	[	X
ejpam-3406	133	2	r2]q	r2]q	X
ejpam-3406	133	3	)	)	PUNCT
ejpam-3406	133	4	,	,	PUNCT
ejpam-3406	133	5	(	(	PUNCT
ejpam-3406	133	6	14	14	NUM
ejpam-3406	133	7	)	)	PUNCT
ejpam-3406	133	8	where	where	SCONJ
ejpam-3406	133	9	ω∗(|c|	ω∗(|c|	ADV
ejpam-3406	133	10	)	)	PUNCT
ejpam-3406	133	11	=	=	PUNCT
ejpam-3406	134	1	[	[	X
ejpam-3406	134	2	m|c|+	m|c|+	PROPN
ejpam-3406	134	3	r1]q	r1]q	PROPN
ejpam-3406	134	4	.	.	PUNCT
ejpam-3406	135	1	the	the	DET
ejpam-3406	135	2	following	follow	VERB
ejpam-3406	135	3	theorem	theorem	VERB
ejpam-3406	135	4	determines	determine	NOUN
ejpam-3406	135	5	how	how	SCONJ
ejpam-3406	135	6	an	an	DET
ejpam-3406	135	7	additive	additive	ADJ
ejpam-3406	135	8	constant	constant	ADJ
ejpam-3406	135	9	affects	affect	VERB
ejpam-3406	135	10	the	the	DET
ejpam-3406	135	11	recurrence	recurrence	NOUN
ejpam-3406	135	12	formula	formula	NOUN
ejpam-3406	135	13	for	for	ADP
ejpam-3406	135	14	wm	wm	PROPN
ejpam-3406	135	15	,	,	PUNCT
ejpam-3406	135	16	r[n	r[n	NOUN
ejpam-3406	135	17	,	,	PUNCT
ejpam-3406	135	18	k]q	k]q	PROPN
ejpam-3406	135	19	.	.	PUNCT
ejpam-3406	136	1	from	from	ADP
ejpam-3406	136	2	theorem	theorem	ADJ
ejpam-3406	136	3	1	1	NUM
ejpam-3406	136	4	,	,	PUNCT
ejpam-3406	136	5	w	w	NOUN
ejpam-3406	136	6	∗m	∗m	NOUN
ejpam-3406	136	7	,	,	PUNCT
ejpam-3406	136	8	r[n	r[n	NOUN
ejpam-3406	136	9	,	,	PUNCT
ejpam-3406	136	10	k]q	k]q	NOUN
ejpam-3406	136	11	=	=	PUNCT
ejpam-3406	136	12	∑	∑	PROPN
ejpam-3406	136	13	φ∈tar	φ∈tar	PROPN
ejpam-3406	136	14	(	(	PUNCT
ejpam-3406	136	15	k	k	NOUN
ejpam-3406	136	16	,	,	PUNCT
ejpam-3406	136	17	n−k	n−k	NOUN
ejpam-3406	136	18	)	)	PUNCT
ejpam-3406	136	19	ωa(φ	ωa(φ	NUM
ejpam-3406	136	20	)	)	PUNCT
ejpam-3406	136	21	=	=	PUNCT
ejpam-3406	136	22	∑	∑	PUNCT
ejpam-3406	136	23	φ∈tar	φ∈tar	PROPN
ejpam-3406	136	24	(	(	PUNCT
ejpam-3406	136	25	k	k	NOUN
ejpam-3406	136	26	,	,	PUNCT
ejpam-3406	136	27	n−k	n−k	NOUN
ejpam-3406	136	28	)	)	PUNCT
ejpam-3406	136	29	∏	∏	PROPN
ejpam-3406	136	30	c∈φ	c∈φ	PROPN
ejpam-3406	136	31	ω(|c|	ω(|c|	PROPN
ejpam-3406	136	32	)	)	PUNCT
ejpam-3406	136	33	where	where	SCONJ
ejpam-3406	136	34	ωa(φ	ωa(φ	NOUN
ejpam-3406	136	35	)	)	PUNCT
ejpam-3406	136	36	=	=	SYM
ejpam-3406	136	37	∏	∏	PROPN
ejpam-3406	136	38	c∈φ	c∈φ	NOUN
ejpam-3406	136	39	[	[	X
ejpam-3406	136	40	m|c|+	m|c|+	NOUN
ejpam-3406	136	41	r]q	r]q	VERB
ejpam-3406	136	42	,	,	PUNCT
ejpam-3406	136	43	where	where	SCONJ
ejpam-3406	136	44	|c|	|c|	PROPN
ejpam-3406	136	45	∈	∈	PROPN
ejpam-3406	136	46	{	{	PUNCT
ejpam-3406	136	47	0	0	NUM
ejpam-3406	136	48	,	,	PUNCT
ejpam-3406	136	49	1	1	NUM
ejpam-3406	136	50	,	,	PUNCT
ejpam-3406	136	51	.	.	PUNCT
ejpam-3406	136	52	.	.	PUNCT
ejpam-3406	136	53	.	.	PUNCT
ejpam-3406	137	1	,	,	PUNCT
ejpam-3406	137	2	k	k	X
ejpam-3406	137	3	}	}	PUNCT
ejpam-3406	137	4	=	=	SYM
ejpam-3406	137	5	n−k∏	n−k∏	PROPN
ejpam-3406	137	6	i=1	i=1	X
ejpam-3406	138	1	[	[	X
ejpam-3406	138	2	mji	mji	ADJ
ejpam-3406	138	3	+	+	X
ejpam-3406	138	4	r]q	r]q	NOUN
ejpam-3406	138	5	,	,	PUNCT
ejpam-3406	138	6	where	where	SCONJ
ejpam-3406	138	7	ji	ji	PROPN
ejpam-3406	138	8	∈	∈	PROPN
ejpam-3406	138	9	{	{	PUNCT
ejpam-3406	138	10	0	0	NUM
ejpam-3406	138	11	,	,	PUNCT
ejpam-3406	138	12	1	1	NUM
ejpam-3406	138	13	,	,	PUNCT
ejpam-3406	138	14	.	.	PUNCT
ejpam-3406	138	15	.	.	PUNCT
ejpam-3406	138	16	.	.	PUNCT
ejpam-3406	138	17	,	,	PUNCT
ejpam-3406	138	18	k	k	X
ejpam-3406	138	19	}	}	PUNCT
ejpam-3406	138	20	.	.	PUNCT
ejpam-3406	139	1	r.	r.	PROPN
ejpam-3406	139	2	corcino	corcino	PROPN
ejpam-3406	139	3	,	,	PUNCT
ejpam-3406	139	4	mj	mj	PROPN
ejpam-3406	139	5	.	.	PUNCT
ejpam-3406	139	6	latayada	latayada	PROPN
ejpam-3406	139	7	,	,	PUNCT
ejpam-3406	139	8	mar	mar	PROPN
ejpam-3406	139	9	.	.	PROPN
ejpam-3406	139	10	vega	vega	PROPN
ejpam-3406	139	11	/	/	SYM
ejpam-3406	139	12	eur	eur	PROPN
ejpam-3406	139	13	.	.	PUNCT
ejpam-3406	140	1	j.	j.	PROPN
ejpam-3406	140	2	pure	pure	PROPN
ejpam-3406	140	3	appl	appl	PROPN
ejpam-3406	140	4	.	.	PROPN
ejpam-3406	140	5	math	math	PROPN
ejpam-3406	140	6	,	,	PUNCT
ejpam-3406	140	7	12	12	NUM
ejpam-3406	140	8	(	(	PUNCT
ejpam-3406	140	9	2	2	NUM
ejpam-3406	140	10	)	)	PUNCT
ejpam-3406	140	11	(	(	PUNCT
ejpam-3406	140	12	2019	2019	NUM
ejpam-3406	140	13	)	)	PUNCT
ejpam-3406	140	14	,	,	PUNCT
ejpam-3406	140	15	279	279	NUM
ejpam-3406	140	16	-	-	SYM
ejpam-3406	140	17	293	293	NUM
ejpam-3406	140	18	285	285	NUM
ejpam-3406	140	19	if	if	SCONJ
ejpam-3406	140	20	r	r	NOUN
ejpam-3406	140	21	=	=	SYM
ejpam-3406	140	22	r1	r1	PROPN
ejpam-3406	140	23	+	+	CCONJ
ejpam-3406	140	24	r2	r2	PROPN
ejpam-3406	140	25	for	for	ADP
ejpam-3406	140	26	some	some	DET
ejpam-3406	140	27	r1	r1	NOUN
ejpam-3406	140	28	and	and	CCONJ
ejpam-3406	140	29	r2	r2	PROPN
ejpam-3406	140	30	,	,	PUNCT
ejpam-3406	140	31	then	then	ADV
ejpam-3406	140	32	by	by	ADP
ejpam-3406	140	33	(	(	PUNCT
ejpam-3406	140	34	14	14	NUM
ejpam-3406	140	35	)	)	PUNCT
ejpam-3406	140	36	,	,	PUNCT
ejpam-3406	140	37	ωa(φ	ωa(φ	NUM
ejpam-3406	140	38	)	)	PUNCT
ejpam-3406	140	39	=	=	SYM
ejpam-3406	140	40	n−k∏	n−k∏	PROPN
ejpam-3406	140	41	i=1	i=1	PROPN
ejpam-3406	140	42	1	1	NUM
ejpam-3406	140	43	qr2	qr2	PROPN
ejpam-3406	140	44	(	(	PUNCT
ejpam-3406	140	45	ω∗(ji	ω∗(ji	PROPN
ejpam-3406	140	46	)	)	PUNCT
ejpam-3406	140	47	+	+	CCONJ
ejpam-3406	141	1	[	[	X
ejpam-3406	141	2	r2]q	r2]q	X
ejpam-3406	141	3	)	)	PUNCT
ejpam-3406	141	4	,	,	PUNCT
ejpam-3406	141	5	where	where	SCONJ
ejpam-3406	141	6	ω∗(ji	ω∗(ji	NOUN
ejpam-3406	141	7	)	)	PUNCT
ejpam-3406	141	8	=	=	PUNCT
ejpam-3406	142	1	[	[	X
ejpam-3406	142	2	mji	mji	X
ejpam-3406	142	3	+	+	CCONJ
ejpam-3406	142	4	r1]q	r1]q	X
ejpam-3406	142	5	=	=	SYM
ejpam-3406	142	6	q−(n−k)r2	q−(n−k)r2	NOUN
ejpam-3406	142	7	(	(	PUNCT
ejpam-3406	142	8	ω∗(j1	ω∗(j1	ADJ
ejpam-3406	142	9	)	)	PUNCT
ejpam-3406	142	10	+	+	CCONJ
ejpam-3406	143	1	[	[	X
ejpam-3406	143	2	r2]q	r2]q	X
ejpam-3406	143	3	)	)	PUNCT
ejpam-3406	143	4	(	(	PUNCT
ejpam-3406	143	5	ω∗(j2	ω∗(j2	NOUN
ejpam-3406	143	6	)	)	PUNCT
ejpam-3406	143	7	+	+	CCONJ
ejpam-3406	144	1	[	[	X
ejpam-3406	144	2	r2]q	r2]q	X
ejpam-3406	144	3	)	)	PUNCT
ejpam-3406	144	4	·	·	PUNCT
ejpam-3406	144	5	·	·	PUNCT
ejpam-3406	144	6	·	·	PUNCT
ejpam-3406	144	7	(	(	PUNCT
ejpam-3406	144	8	ω∗(jn−k	ω∗(jn−k	ADP
ejpam-3406	144	9	)	)	PUNCT
ejpam-3406	144	10	+	+	CCONJ
ejpam-3406	145	1	[	[	X
ejpam-3406	145	2	r2]q	r2]q	X
ejpam-3406	145	3	)	)	PUNCT
ejpam-3406	145	4	)	)	PUNCT
ejpam-3406	146	1	=	=	PUNCT
ejpam-3406	146	2	q−(n−k)r2	q−(n−k)r2	NOUN
ejpam-3406	146	3	n−k∑	n−k∑	NOUN
ejpam-3406	146	4	l=0	l=0	PROPN
ejpam-3406	146	5	(	(	PUNCT
ejpam-3406	146	6	[	[	X
ejpam-3406	146	7	r2]q	r2]q	X
ejpam-3406	146	8	)	)	PUNCT
ejpam-3406	146	9	n−k−l	n−k−l	ADV
ejpam-3406	146	10	∑	∑	PROPN
ejpam-3406	146	11	j1≤j1≤j2≤	j1≤j1≤j2≤	PROPN
ejpam-3406	146	12	...	...	PUNCT
ejpam-3406	146	13	≤jl≤jn−k	≤jl≤jn−k	PROPN
ejpam-3406	146	14	l∏	l∏	PROPN
ejpam-3406	146	15	i=1	i=1	PROPN
ejpam-3406	146	16	ω∗(ji	ω∗(ji	PROPN
ejpam-3406	146	17	)	)	PUNCT
ejpam-3406	146	18	.	.	PUNCT
ejpam-3406	147	1	suppose	suppose	VERB
ejpam-3406	147	2	bφ	bφ	NOUN
ejpam-3406	147	3	is	be	AUX
ejpam-3406	147	4	the	the	DET
ejpam-3406	147	5	set	set	NOUN
ejpam-3406	147	6	of	of	ADP
ejpam-3406	147	7	all	all	DET
ejpam-3406	147	8	a	a	DET
ejpam-3406	147	9	-	-	PUNCT
ejpam-3406	147	10	tableaux	tableaux	NOUN
ejpam-3406	147	11	corresponding	corresponding	NOUN
ejpam-3406	147	12	to	to	ADP
ejpam-3406	147	13	φ	φ	NUM
ejpam-3406	147	14	such	such	ADJ
ejpam-3406	147	15	that	that	SCONJ
ejpam-3406	147	16	for	for	ADP
ejpam-3406	147	17	each	each	DET
ejpam-3406	147	18	ψ	ψ	X
ejpam-3406	147	19	∈	∈	PROPN
ejpam-3406	147	20	bφ	bφ	NOUN
ejpam-3406	147	21	,	,	PUNCT
ejpam-3406	147	22	either	either	CCONJ
ejpam-3406	147	23	ψ	ψ	ADP
ejpam-3406	147	24	has	have	VERB
ejpam-3406	147	25	no	no	DET
ejpam-3406	147	26	column	column	NOUN
ejpam-3406	147	27	whose	whose	DET
ejpam-3406	147	28	weight	weight	NOUN
ejpam-3406	147	29	is	be	AUX
ejpam-3406	147	30	[	[	X
ejpam-3406	147	31	r2]q	r2]q	X
ejpam-3406	147	32	,	,	PUNCT
ejpam-3406	147	33	or	or	CCONJ
ejpam-3406	147	34	ψ	ψ	NOUN
ejpam-3406	147	35	has	have	VERB
ejpam-3406	147	36	one	one	NUM
ejpam-3406	147	37	column	column	NOUN
ejpam-3406	147	38	whose	whose	DET
ejpam-3406	147	39	weight	weight	NOUN
ejpam-3406	147	40	is	be	AUX
ejpam-3406	147	41	[	[	X
ejpam-3406	147	42	r2]q	r2]q	X
ejpam-3406	147	43	,	,	PUNCT
ejpam-3406	147	44	or	or	CCONJ
ejpam-3406	147	45	ψ	ψ	NOUN
ejpam-3406	147	46	has	have	VERB
ejpam-3406	147	47	two	two	NUM
ejpam-3406	147	48	columns	column	NOUN
ejpam-3406	147	49	whose	whose	DET
ejpam-3406	147	50	weights	weight	NOUN
ejpam-3406	147	51	are	be	AUX
ejpam-3406	147	52	[	[	X
ejpam-3406	147	53	r2]q	r2]q	X
ejpam-3406	147	54	,	,	PUNCT
ejpam-3406	147	55	or	or	CCONJ
ejpam-3406	147	56	...	...	PUNCT
ejpam-3406	148	1	ψ	ψ	X
ejpam-3406	148	2	has	have	VERB
ejpam-3406	148	3	(	(	PUNCT
ejpam-3406	148	4	n−	n−	NOUN
ejpam-3406	148	5	k	k	X
ejpam-3406	148	6	)	)	PUNCT
ejpam-3406	148	7	columns	column	NOUN
ejpam-3406	148	8	whose	whose	DET
ejpam-3406	148	9	weights	weight	NOUN
ejpam-3406	148	10	are	be	AUX
ejpam-3406	148	11	[	[	X
ejpam-3406	148	12	r2]q	r2]q	X
ejpam-3406	148	13	.	.	PUNCT
ejpam-3406	149	1	then	then	ADV
ejpam-3406	149	2	,	,	PUNCT
ejpam-3406	149	3	we	we	PRON
ejpam-3406	149	4	may	may	AUX
ejpam-3406	149	5	write	write	VERB
ejpam-3406	149	6	ωa(φ	ωa(φ	NOUN
ejpam-3406	149	7	)	)	PUNCT
ejpam-3406	149	8	=	=	PUNCT
ejpam-3406	149	9	∑	∑	PUNCT
ejpam-3406	149	10	ψ∈bφ	ψ∈bφ	NOUN
ejpam-3406	149	11	ωa(ψ	ωa(ψ	NUM
ejpam-3406	149	12	)	)	PUNCT
ejpam-3406	149	13	.	.	PUNCT
ejpam-3406	150	1	now	now	ADV
ejpam-3406	150	2	,	,	PUNCT
ejpam-3406	150	3	if	if	SCONJ
ejpam-3406	150	4	l	l	NOUN
ejpam-3406	150	5	columns	column	NOUN
ejpam-3406	150	6	in	in	ADP
ejpam-3406	150	7	ψ	ψ	X
ejpam-3406	150	8	have	have	VERB
ejpam-3406	150	9	weights	weight	NOUN
ejpam-3406	150	10	other	other	ADJ
ejpam-3406	150	11	than	than	ADP
ejpam-3406	150	12	[	[	X
ejpam-3406	150	13	r2]q	r2]q	X
ejpam-3406	150	14	,	,	PUNCT
ejpam-3406	150	15	then	then	ADV
ejpam-3406	150	16	ωa(ψ	ωa(ψ	PUNCT
ejpam-3406	150	17	)	)	PUNCT
ejpam-3406	151	1	=	=	SYM
ejpam-3406	151	2	∏	∏	PROPN
ejpam-3406	151	3	c∈ψ	c∈ψ	NOUN
ejpam-3406	151	4	ω∗(|c|	ω∗(|c|	NOUN
ejpam-3406	151	5	)	)	PUNCT
ejpam-3406	151	6	=	=	SYM
ejpam-3406	151	7	q−(n−k)r2([r2]q	q−(n−k)r2([r2]q	NOUN
ejpam-3406	151	8	)	)	PUNCT
ejpam-3406	151	9	n−k−r	n−k−r	PROPN
ejpam-3406	152	1	r∏	r∏	NOUN
ejpam-3406	152	2	i=1	i=1	PUNCT
ejpam-3406	153	1	ω∗(qi	ω∗(qi	ADJ
ejpam-3406	153	2	)	)	PUNCT
ejpam-3406	154	1	where	where	SCONJ
ejpam-3406	154	2	q1	q1	PROPN
ejpam-3406	154	3	,	,	PUNCT
ejpam-3406	154	4	q2	q2	NOUN
ejpam-3406	154	5	,	,	PUNCT
ejpam-3406	154	6	.	.	PUNCT
ejpam-3406	154	7	.	.	PUNCT
ejpam-3406	155	1	.	.	PUNCT
ejpam-3406	156	1	,	,	PUNCT
ejpam-3406	156	2	qr	qr	PROPN
ejpam-3406	156	3	∈	∈	PROPN
ejpam-3406	156	4	{	{	PUNCT
ejpam-3406	156	5	j1	j1	PROPN
ejpam-3406	156	6	,	,	PUNCT
ejpam-3406	156	7	j2	j2	PROPN
ejpam-3406	156	8	,	,	PUNCT
ejpam-3406	156	9	.	.	PUNCT
ejpam-3406	156	10	.	.	PUNCT
ejpam-3406	156	11	.	.	PUNCT
ejpam-3406	157	1	,	,	PUNCT
ejpam-3406	157	2	jn−k	jn−k	PROPN
ejpam-3406	157	3	}	}	PUNCT
ejpam-3406	157	4	.	.	PUNCT
ejpam-3406	158	1	note	note	VERB
ejpam-3406	158	2	that	that	SCONJ
ejpam-3406	158	3	for	for	ADP
ejpam-3406	158	4	each	each	DET
ejpam-3406	158	5	l	l	NOUN
ejpam-3406	158	6	,	,	PUNCT
ejpam-3406	158	7	there	there	PRON
ejpam-3406	158	8	corresponds	correspond	VERB
ejpam-3406	158	9	(	(	PUNCT
ejpam-3406	158	10	n−	n−	NOUN
ejpam-3406	158	11	k	k	X
ejpam-3406	158	12	l	l	NOUN
ejpam-3406	158	13	)	)	PUNCT
ejpam-3406	158	14	tableaux	tableaux	ADV
ejpam-3406	158	15	with	with	ADP
ejpam-3406	158	16	l	l	NOUN
ejpam-3406	158	17	columns	column	NOUN
ejpam-3406	158	18	having	have	VERB
ejpam-3406	158	19	weights	weight	NOUN
ejpam-3406	158	20	ω∗(ji	ω∗(ji	PROPN
ejpam-3406	158	21	)	)	PUNCT
ejpam-3406	158	22	=	=	PUNCT
ejpam-3406	159	1	[	[	X
ejpam-3406	159	2	mji+r1]q	mji+r1]q	NOUN
ejpam-3406	159	3	.	.	PUNCT
ejpam-3406	160	1	it	it	PRON
ejpam-3406	160	2	can	can	AUX
ejpam-3406	160	3	be	be	AUX
ejpam-3406	160	4	easily	easily	ADV
ejpam-3406	160	5	verified	verify	VERB
ejpam-3406	160	6	that	that	SCONJ
ejpam-3406	160	7	,	,	PUNCT
ejpam-3406	160	8	|tar	|tar	NOUN
ejpam-3406	160	9	(	(	PUNCT
ejpam-3406	160	10	k	k	X
ejpam-3406	160	11	,	,	PUNCT
ejpam-3406	160	12	n−	n−	NOUN
ejpam-3406	160	13	k)|	k)|	NOUN
ejpam-3406	160	14	=	=	PUNCT
ejpam-3406	160	15	(	(	PUNCT
ejpam-3406	160	16	(	(	PUNCT
ejpam-3406	160	17	n−	n−	NOUN
ejpam-3406	160	18	k	k	NOUN
ejpam-3406	160	19	)	)	PUNCT
ejpam-3406	161	1	+	+	CCONJ
ejpam-3406	161	2	k	k	PROPN
ejpam-3406	161	3	n−	n−	NOUN
ejpam-3406	161	4	k	k	PROPN
ejpam-3406	161	5	)	)	PUNCT
ejpam-3406	162	1	=	=	PUNCT
ejpam-3406	162	2	(	(	PUNCT
ejpam-3406	162	3	n	n	NUM
ejpam-3406	162	4	n−	n−	PROPN
ejpam-3406	162	5	k	k	PROPN
ejpam-3406	162	6	)	)	PUNCT
ejpam-3406	163	1	=	=	PUNCT
ejpam-3406	163	2	(	(	PUNCT
ejpam-3406	163	3	n	n	X
ejpam-3406	163	4	k	k	NOUN
ejpam-3406	163	5	)	)	PUNCT
ejpam-3406	163	6	.	.	PUNCT
ejpam-3406	164	1	thus	thus	ADV
ejpam-3406	164	2	,	,	PUNCT
ejpam-3406	164	3	∀φ	∀φ	PROPN
ejpam-3406	164	4	∈	∈	NOUN
ejpam-3406	164	5	tar	tar	NOUN
ejpam-3406	164	6	(	(	PUNCT
ejpam-3406	164	7	k	k	NOUN
ejpam-3406	164	8	,	,	PUNCT
ejpam-3406	164	9	n−	n−	PROPN
ejpam-3406	164	10	k	k	PROPN
ejpam-3406	164	11	)	)	PUNCT
ejpam-3406	164	12	,	,	PUNCT
ejpam-3406	164	13	bφ	bφ	NOUN
ejpam-3406	164	14	contains	contain	VERB
ejpam-3406	164	15	a	a	DET
ejpam-3406	164	16	total	total	NOUN
ejpam-3406	164	17	of	of	ADP
ejpam-3406	164	18	(	(	PUNCT
ejpam-3406	164	19	n	n	X
ejpam-3406	164	20	k	k	NOUN
ejpam-3406	164	21	)	)	PUNCT
ejpam-3406	164	22	(	(	PUNCT
ejpam-3406	164	23	n−	n−	NOUN
ejpam-3406	164	24	k	k	X
ejpam-3406	164	25	l	l	PROPN
ejpam-3406	164	26	)	)	PUNCT
ejpam-3406	164	27	r.	r.	PROPN
ejpam-3406	164	28	corcino	corcino	PROPN
ejpam-3406	164	29	,	,	PUNCT
ejpam-3406	164	30	mj	mj	PROPN
ejpam-3406	164	31	.	.	PUNCT
ejpam-3406	164	32	latayada	latayada	PROPN
ejpam-3406	164	33	,	,	PUNCT
ejpam-3406	164	34	mar	mar	PROPN
ejpam-3406	164	35	.	.	PROPN
ejpam-3406	164	36	vega	vega	PROPN
ejpam-3406	164	37	/	/	SYM
ejpam-3406	164	38	eur	eur	PROPN
ejpam-3406	164	39	.	.	PUNCT
ejpam-3406	165	1	j.	j.	PROPN
ejpam-3406	165	2	pure	pure	PROPN
ejpam-3406	165	3	appl	appl	PROPN
ejpam-3406	165	4	.	.	PROPN
ejpam-3406	165	5	math	math	PROPN
ejpam-3406	165	6	,	,	PUNCT
ejpam-3406	165	7	12	12	NUM
ejpam-3406	165	8	(	(	PUNCT
ejpam-3406	165	9	2	2	NUM
ejpam-3406	165	10	)	)	PUNCT
ejpam-3406	165	11	(	(	PUNCT
ejpam-3406	165	12	2019	2019	NUM
ejpam-3406	165	13	)	)	PUNCT
ejpam-3406	165	14	,	,	PUNCT
ejpam-3406	165	15	279	279	NUM
ejpam-3406	165	16	-	-	SYM
ejpam-3406	165	17	293	293	NUM
ejpam-3406	165	18	286	286	NUM
ejpam-3406	165	19	tableaux	tableau	NOUN
ejpam-3406	165	20	with	with	ADP
ejpam-3406	165	21	l	l	NOUN
ejpam-3406	165	22	columns	column	NOUN
ejpam-3406	165	23	of	of	ADP
ejpam-3406	165	24	weights	weight	NOUN
ejpam-3406	165	25	ω∗(ji	ω∗(ji	PROPN
ejpam-3406	165	26	)	)	PUNCT
ejpam-3406	165	27	.	.	PUNCT
ejpam-3406	166	1	however	however	ADV
ejpam-3406	166	2	,	,	PUNCT
ejpam-3406	166	3	only	only	ADV
ejpam-3406	166	4	(	(	PUNCT
ejpam-3406	166	5	l+k	l+k	PROPN
ejpam-3406	166	6	l	l	NOUN
ejpam-3406	166	7	)	)	PUNCT
ejpam-3406	166	8	tableaux	tableaux	ADV
ejpam-3406	166	9	with	with	ADP
ejpam-3406	166	10	l	l	NOUN
ejpam-3406	166	11	columns	column	NOUN
ejpam-3406	166	12	in	in	ADP
ejpam-3406	166	13	bφ	bφ	NOUN
ejpam-3406	166	14	are	be	AUX
ejpam-3406	166	15	distinct	distinct	ADJ
ejpam-3406	166	16	.	.	PUNCT
ejpam-3406	167	1	hence	hence	ADV
ejpam-3406	167	2	,	,	PUNCT
ejpam-3406	167	3	every	every	DET
ejpam-3406	167	4	distinct	distinct	ADJ
ejpam-3406	167	5	tableaux	tableaux	NOUN
ejpam-3406	167	6	ψ	ψ	NOUN
ejpam-3406	167	7	with	with	ADP
ejpam-3406	167	8	l	l	NOUN
ejpam-3406	167	9	columns	column	NOUN
ejpam-3406	167	10	of	of	ADP
ejpam-3406	167	11	weights	weight	NOUN
ejpam-3406	167	12	other	other	ADJ
ejpam-3406	167	13	than	than	ADP
ejpam-3406	167	14	[	[	PUNCT
ejpam-3406	167	15	r2]q	r2]q	PRON
ejpam-3406	167	16	appears	appear	VERB
ejpam-3406	167	17	(	(	PUNCT
ejpam-3406	167	18	n	n	X
ejpam-3406	167	19	k	k	NOUN
ejpam-3406	167	20	)	)	PUNCT
ejpam-3406	167	21	(	(	PUNCT
ejpam-3406	167	22	n−k	n−k	NOUN
ejpam-3406	167	23	l	l	NOUN
ejpam-3406	167	24	)	)	PUNCT
ejpam-3406	167	25	(	(	PUNCT
ejpam-3406	167	26	l+k	l+k	PROPN
ejpam-3406	167	27	l	l	NOUN
ejpam-3406	167	28	)	)	PUNCT
ejpam-3406	167	29	=	=	PUNCT
ejpam-3406	167	30	(	(	PUNCT
ejpam-3406	167	31	n	n	X
ejpam-3406	167	32	l	l	NOUN
ejpam-3406	167	33	+	+	CCONJ
ejpam-3406	167	34	k	k	X
ejpam-3406	167	35	)	)	PUNCT
ejpam-3406	167	36	times	time	NOUN
ejpam-3406	167	37	in	in	ADP
ejpam-3406	167	38	the	the	DET
ejpam-3406	167	39	collection	collection	NOUN
ejpam-3406	167	40	.	.	PUNCT
ejpam-3406	168	1	thus	thus	ADV
ejpam-3406	168	2	,	,	PUNCT
ejpam-3406	168	3	∑	∑	PROPN
ejpam-3406	168	4	φ∈tar	φ∈tar	PROPN
ejpam-3406	168	5	(	(	PUNCT
ejpam-3406	168	6	k	k	NOUN
ejpam-3406	168	7	,	,	PUNCT
ejpam-3406	168	8	n−k	n−k	NOUN
ejpam-3406	168	9	)	)	PUNCT
ejpam-3406	168	10	ωa(φ	ωa(φ	NUM
ejpam-3406	168	11	)	)	PUNCT
ejpam-3406	168	12	=	=	PUNCT
ejpam-3406	168	13	n−k∑	n−k∑	NUM
ejpam-3406	168	14	l=0	l=0	PROPN
ejpam-3406	168	15	(	(	PUNCT
ejpam-3406	168	16	n	n	NOUN
ejpam-3406	168	17	l	l	NOUN
ejpam-3406	168	18	+	+	CCONJ
ejpam-3406	168	19	k	k	X
ejpam-3406	168	20	)	)	PUNCT
ejpam-3406	168	21	q−(n−k)r2([r2]q	q−(n−k)r2([r2]q	NOUN
ejpam-3406	168	22	)	)	PUNCT
ejpam-3406	168	23	n−k−l	n−k−l	ADV
ejpam-3406	168	24	∑	∑	PROPN
ejpam-3406	168	25	ϕ∈b̄l	ϕ∈b̄l	NUM
ejpam-3406	168	26	∏	∏	PROPN
ejpam-3406	168	27	c∈ϕ	c∈ϕ	PROPN
ejpam-3406	168	28	ω∗(|c|	ω∗(|c|	PROPN
ejpam-3406	168	29	)	)	PUNCT
ejpam-3406	168	30	where	where	SCONJ
ejpam-3406	168	31	b̄l	b̄l	PROPN
ejpam-3406	168	32	denotes	denote	VERB
ejpam-3406	168	33	the	the	DET
ejpam-3406	168	34	set	set	NOUN
ejpam-3406	168	35	of	of	ADP
ejpam-3406	168	36	all	all	DET
ejpam-3406	168	37	tableaux	tableaux	NOUN
ejpam-3406	168	38	ϕ	ϕ	NOUN
ejpam-3406	168	39	having	have	VERB
ejpam-3406	168	40	l	l	NOUN
ejpam-3406	168	41	columns	column	NOUN
ejpam-3406	168	42	of	of	ADP
ejpam-3406	168	43	weights	weight	NOUN
ejpam-3406	168	44	ω∗(ji	ω∗(ji	PROPN
ejpam-3406	168	45	)	)	PUNCT
ejpam-3406	168	46	=	=	PUNCT
ejpam-3406	169	1	[	[	X
ejpam-3406	169	2	mji+r1]q	mji+r1]q	NOUN
ejpam-3406	169	3	.	.	PUNCT
ejpam-3406	170	1	reindexing	reindexe	VERB
ejpam-3406	170	2	the	the	DET
ejpam-3406	170	3	double	double	ADJ
ejpam-3406	170	4	sum	sum	NOUN
ejpam-3406	170	5	,	,	PUNCT
ejpam-3406	170	6	we	we	PRON
ejpam-3406	170	7	get	get	VERB
ejpam-3406	170	8	∑	∑	ADV
ejpam-3406	170	9	φ∈tar	φ∈tar	PROPN
ejpam-3406	170	10	(	(	PUNCT
ejpam-3406	170	11	k	k	NOUN
ejpam-3406	170	12	,	,	PUNCT
ejpam-3406	170	13	n−k	n−k	NOUN
ejpam-3406	170	14	)	)	PUNCT
ejpam-3406	170	15	ωa(φ	ωa(φ	NUM
ejpam-3406	170	16	)	)	PUNCT
ejpam-3406	170	17	=	=	SYM
ejpam-3406	171	1	n∑	n∑	PROPN
ejpam-3406	171	2	j	j	PROPN
ejpam-3406	172	1	=	=	PROPN
ejpam-3406	172	2	k	k	PROPN
ejpam-3406	172	3	(	(	PUNCT
ejpam-3406	172	4	n	n	X
ejpam-3406	172	5	j	j	PROPN
ejpam-3406	172	6	)	)	PUNCT
ejpam-3406	172	7	q−nr2([r2]q	q−nr2([r2]q	NUM
ejpam-3406	172	8	)	)	PUNCT
ejpam-3406	172	9	n−j	n−j	ADV
ejpam-3406	172	10	∑	∑	ADP
ejpam-3406	172	11	ϕ∈b̄j−k	ϕ∈b̄j−k	PROPN
ejpam-3406	172	12	∏	∏	PROPN
ejpam-3406	172	13	c∈ϕ	c∈ϕ	PROPN
ejpam-3406	172	14	ω∗(|c|	ω∗(|c|	PROPN
ejpam-3406	172	15	)	)	PUNCT
ejpam-3406	172	16	where	where	SCONJ
ejpam-3406	172	17	b̄j−k	b̄j−k	NOUN
ejpam-3406	172	18	is	be	AUX
ejpam-3406	172	19	the	the	DET
ejpam-3406	172	20	set	set	NOUN
ejpam-3406	172	21	of	of	ADP
ejpam-3406	172	22	all	all	DET
ejpam-3406	172	23	tableaux	tableaux	ADJ
ejpam-3406	172	24	ϕ	ϕ	NOUN
ejpam-3406	172	25	with	with	ADP
ejpam-3406	172	26	j	j	PROPN
ejpam-3406	172	27	−	−	PROPN
ejpam-3406	172	28	k	k	PROPN
ejpam-3406	172	29	columns	column	NOUN
ejpam-3406	172	30	of	of	ADP
ejpam-3406	172	31	weights	weight	NOUN
ejpam-3406	172	32	ω∗(ji	ω∗(ji	PROPN
ejpam-3406	172	33	)	)	PUNCT
ejpam-3406	172	34	=	=	PUNCT
ejpam-3406	173	1	[	[	X
ejpam-3406	173	2	mji	mji	X
ejpam-3406	173	3	+	+	X
ejpam-3406	173	4	r1]q	r1]q	X
ejpam-3406	173	5	for	for	ADP
ejpam-3406	173	6	each	each	DET
ejpam-3406	173	7	i	i	NOUN
ejpam-3406	173	8	=	=	NOUN
ejpam-3406	173	9	1	1	NUM
ejpam-3406	173	10	,	,	PUNCT
ejpam-3406	173	11	2	2	NUM
ejpam-3406	173	12	,	,	PUNCT
ejpam-3406	173	13	.	.	PUNCT
ejpam-3406	173	14	.	.	PUNCT
ejpam-3406	173	15	.	.	PUNCT
ejpam-3406	174	1	,	,	PUNCT
ejpam-3406	174	2	j	j	PROPN
ejpam-3406	174	3	−	−	PROPN
ejpam-3406	174	4	k.	k.	PROPN
ejpam-3406	174	5	clearly	clearly	ADV
ejpam-3406	174	6	b̄j−k	b̄j−k	VERB
ejpam-3406	174	7	=	=	SYM
ejpam-3406	174	8	tar1(k	tar1(k	NUM
ejpam-3406	174	9	,	,	PUNCT
ejpam-3406	174	10	j	j	PROPN
ejpam-3406	174	11	−	−	PROPN
ejpam-3406	174	12	k	k	PROPN
ejpam-3406	174	13	)	)	PUNCT
ejpam-3406	174	14	.	.	PUNCT
ejpam-3406	175	1	hence	hence	ADV
ejpam-3406	175	2	,	,	PUNCT
ejpam-3406	175	3	∑	∑	PROPN
ejpam-3406	175	4	φ∈tar	φ∈tar	PROPN
ejpam-3406	175	5	(	(	PUNCT
ejpam-3406	175	6	k	k	NOUN
ejpam-3406	175	7	,	,	PUNCT
ejpam-3406	175	8	n−k	n−k	NOUN
ejpam-3406	175	9	)	)	PUNCT
ejpam-3406	175	10	ωa(φ	ωa(φ	NUM
ejpam-3406	175	11	)	)	PUNCT
ejpam-3406	175	12	=	=	SYM
ejpam-3406	175	13	n∑	n∑	PROPN
ejpam-3406	175	14	j	j	PROPN
ejpam-3406	176	1	=	=	PROPN
ejpam-3406	176	2	k	k	PROPN
ejpam-3406	176	3	(	(	PUNCT
ejpam-3406	176	4	n	n	X
ejpam-3406	176	5	j	j	PROPN
ejpam-3406	176	6	)	)	PUNCT
ejpam-3406	176	7	q−nr2([r2]q	q−nr2([r2]q	NUM
ejpam-3406	176	8	)	)	PUNCT
ejpam-3406	176	9	n−j	n−j	ADV
ejpam-3406	176	10	∑	∑	PUNCT
ejpam-3406	176	11	ϕ∈tar1	ϕ∈tar1	PROPN
ejpam-3406	176	12	(	(	PUNCT
ejpam-3406	176	13	k	k	NOUN
ejpam-3406	176	14	,	,	PUNCT
ejpam-3406	176	15	j−k	j−k	NOUN
ejpam-3406	176	16	)	)	PUNCT
ejpam-3406	176	17	ωa(ϕ	ωa(ϕ	NUM
ejpam-3406	176	18	)	)	PUNCT
ejpam-3406	176	19	.	.	PUNCT
ejpam-3406	177	1	applying	apply	VERB
ejpam-3406	177	2	theorem	theorem	NOUN
ejpam-3406	177	3	1	1	NUM
ejpam-3406	177	4	,	,	PUNCT
ejpam-3406	177	5	we	we	PRON
ejpam-3406	177	6	obtain	obtain	VERB
ejpam-3406	177	7	the	the	DET
ejpam-3406	177	8	following	follow	VERB
ejpam-3406	177	9	theorem	theorem	VERB
ejpam-3406	177	10	.	.	PUNCT
ejpam-3406	177	11	theorem	theorem	NOUN
ejpam-3406	177	12	2	2	NUM
ejpam-3406	177	13	.	.	PUNCT
ejpam-3406	178	1	the	the	DET
ejpam-3406	178	2	q	q	NOUN
ejpam-3406	178	3	-	-	PUNCT
ejpam-3406	178	4	analogue	analogue	NOUN
ejpam-3406	178	5	w	w	PROPN
ejpam-3406	178	6	∗m	∗m	NOUN
ejpam-3406	178	7	,	,	PUNCT
ejpam-3406	178	8	r[n	r[n	NOUN
ejpam-3406	178	9	,	,	PUNCT
ejpam-3406	178	10	k]q	k]q	VERB
ejpam-3406	178	11	satisfies	satisfy	VERB
ejpam-3406	178	12	the	the	DET
ejpam-3406	178	13	following	follow	VERB
ejpam-3406	178	14	identity	identity	NOUN
ejpam-3406	178	15	w	w	ADP
ejpam-3406	178	16	∗m	∗m	NOUN
ejpam-3406	178	17	,	,	PUNCT
ejpam-3406	178	18	r[n	r[n	NOUN
ejpam-3406	178	19	,	,	PUNCT
ejpam-3406	178	20	k]q	k]q	NOUN
ejpam-3406	178	21	=	=	SYM
ejpam-3406	179	1	n∑	n∑	PROPN
ejpam-3406	179	2	j	j	PROPN
ejpam-3406	180	1	=	=	PROPN
ejpam-3406	180	2	k	k	PROPN
ejpam-3406	180	3	(	(	PUNCT
ejpam-3406	180	4	−1)n−j	−1)n−j	X
ejpam-3406	180	5	(	(	PUNCT
ejpam-3406	180	6	n	n	X
ejpam-3406	180	7	j	j	NOUN
ejpam-3406	180	8	)	)	PUNCT
ejpam-3406	180	9	q−nr2	q−nr2	INTJ
ejpam-3406	181	1	[	[	X
ejpam-3406	181	2	r2]n−jq	r2]n−jq	X
ejpam-3406	181	3	w	w	PROPN
ejpam-3406	181	4	∗m	∗m	NOUN
ejpam-3406	181	5	,	,	PUNCT
ejpam-3406	181	6	r1	r1	PROPN
ejpam-3406	182	1	[	[	X
ejpam-3406	182	2	j	j	X
ejpam-3406	182	3	,	,	PUNCT
ejpam-3406	182	4	k]q	k]q	VERB
ejpam-3406	182	5	where	where	SCONJ
ejpam-3406	182	6	r	r	NOUN
ejpam-3406	182	7	=	=	SYM
ejpam-3406	182	8	r1	r1	PROPN
ejpam-3406	182	9	+	+	CCONJ
ejpam-3406	182	10	r2	r2	PROPN
ejpam-3406	182	11	for	for	ADP
ejpam-3406	182	12	some	some	DET
ejpam-3406	182	13	numbers	number	NOUN
ejpam-3406	182	14	r1	r1	NOUN
ejpam-3406	182	15	and	and	CCONJ
ejpam-3406	182	16	r2	r2	PROPN
ejpam-3406	182	17	.	.	PUNCT
ejpam-3406	183	1	suppose	suppose	VERB
ejpam-3406	183	2	φ1	φ1	PROPN
ejpam-3406	183	3	is	be	AUX
ejpam-3406	183	4	a	a	DET
ejpam-3406	183	5	tableau	tableau	NOUN
ejpam-3406	183	6	with	with	ADP
ejpam-3406	183	7	k	k	PROPN
ejpam-3406	184	1	−	−	PROPN
ejpam-3406	184	2	s	s	PART
ejpam-3406	184	3	columns	column	NOUN
ejpam-3406	184	4	whose	whose	DET
ejpam-3406	184	5	lengths	length	NOUN
ejpam-3406	184	6	are	be	AUX
ejpam-3406	184	7	in	in	ADP
ejpam-3406	184	8	the	the	DET
ejpam-3406	184	9	set	set	NOUN
ejpam-3406	184	10	{	{	PUNCT
ejpam-3406	184	11	0	0	NUM
ejpam-3406	184	12	,	,	PUNCT
ejpam-3406	184	13	1	1	NUM
ejpam-3406	184	14	,	,	PUNCT
ejpam-3406	184	15	.	.	PUNCT
ejpam-3406	184	16	.	.	PUNCT
ejpam-3406	184	17	.	.	PUNCT
ejpam-3406	185	1	,	,	PUNCT
ejpam-3406	185	2	s	s	X
ejpam-3406	185	3	}	}	PUNCT
ejpam-3406	185	4	,	,	PUNCT
ejpam-3406	185	5	and	and	CCONJ
ejpam-3406	185	6	φ2	φ2	PROPN
ejpam-3406	185	7	be	be	VERB
ejpam-3406	185	8	a	a	DET
ejpam-3406	185	9	tableau	tableau	NOUN
ejpam-3406	185	10	with	with	ADP
ejpam-3406	185	11	n−	n−	PROPN
ejpam-3406	186	1	k	k	PROPN
ejpam-3406	186	2	−	−	PUNCT
ejpam-3406	186	3	j	j	PROPN
ejpam-3406	186	4	columns	column	NOUN
ejpam-3406	186	5	whose	whose	DET
ejpam-3406	186	6	lengths	length	NOUN
ejpam-3406	186	7	are	be	AUX
ejpam-3406	186	8	in	in	ADP
ejpam-3406	186	9	the	the	DET
ejpam-3406	186	10	set	set	NOUN
ejpam-3406	186	11	{	{	PUNCT
ejpam-3406	186	12	s+	s+	NUM
ejpam-3406	186	13	1	1	NUM
ejpam-3406	186	14	,	,	PUNCT
ejpam-3406	186	15	s+	s+	X
ejpam-3406	186	16	2	2	NUM
ejpam-3406	186	17	,	,	PUNCT
ejpam-3406	186	18	.	.	PUNCT
ejpam-3406	186	19	.	.	PUNCT
ejpam-3406	186	20	.	.	PUNCT
ejpam-3406	187	1	,	,	PUNCT
ejpam-3406	187	2	s+	s+	ADV
ejpam-3406	187	3	j	j	PROPN
ejpam-3406	187	4	+	+	CCONJ
ejpam-3406	187	5	1	1	X
ejpam-3406	187	6	}	}	PUNCT
ejpam-3406	187	7	then	then	ADV
ejpam-3406	187	8	φ1	φ1	PROPN
ejpam-3406	187	9	∈	∈	PROPN
ejpam-3406	187	10	ta1(s	ta1(s	PROPN
ejpam-3406	187	11	,	,	PUNCT
ejpam-3406	187	12	k	k	PROPN
ejpam-3406	187	13	−	−	PROPN
ejpam-3406	187	14	s	s	PART
ejpam-3406	187	15	)	)	PUNCT
ejpam-3406	187	16	and	and	CCONJ
ejpam-3406	187	17	φ2	φ2	PROPN
ejpam-3406	187	18	∈	∈	PROPN
ejpam-3406	187	19	ta2(j	ta2(j	PROPN
ejpam-3406	187	20	,	,	PUNCT
ejpam-3406	187	21	n−	n−	PROPN
ejpam-3406	187	22	k	k	NOUN
ejpam-3406	187	23	−	−	PROPN
ejpam-3406	187	24	j	j	PROPN
ejpam-3406	187	25	)	)	PUNCT
ejpam-3406	187	26	r.	r.	PROPN
ejpam-3406	187	27	corcino	corcino	PROPN
ejpam-3406	187	28	,	,	PUNCT
ejpam-3406	187	29	mj	mj	PROPN
ejpam-3406	187	30	.	.	PUNCT
ejpam-3406	187	31	latayada	latayada	PROPN
ejpam-3406	187	32	,	,	PUNCT
ejpam-3406	187	33	mar	mar	PROPN
ejpam-3406	187	34	.	.	PROPN
ejpam-3406	187	35	vega	vega	PROPN
ejpam-3406	187	36	/	/	SYM
ejpam-3406	187	37	eur	eur	PROPN
ejpam-3406	187	38	.	.	PUNCT
ejpam-3406	188	1	j.	j.	PROPN
ejpam-3406	188	2	pure	pure	PROPN
ejpam-3406	188	3	appl	appl	PROPN
ejpam-3406	188	4	.	.	PROPN
ejpam-3406	188	5	math	math	PROPN
ejpam-3406	188	6	,	,	PUNCT
ejpam-3406	188	7	12	12	NUM
ejpam-3406	188	8	(	(	PUNCT
ejpam-3406	188	9	2	2	NUM
ejpam-3406	188	10	)	)	PUNCT
ejpam-3406	188	11	(	(	PUNCT
ejpam-3406	188	12	2019	2019	NUM
ejpam-3406	188	13	)	)	PUNCT
ejpam-3406	188	14	,	,	PUNCT
ejpam-3406	188	15	279	279	NUM
ejpam-3406	188	16	-	-	SYM
ejpam-3406	188	17	293	293	NUM
ejpam-3406	188	18	287	287	NUM
ejpam-3406	188	19	where	where	SCONJ
ejpam-3406	188	20	a1	a1	NOUN
ejpam-3406	188	21	=	=	SYM
ejpam-3406	188	22	{	{	PUNCT
ejpam-3406	188	23	0	0	NUM
ejpam-3406	188	24	,	,	PUNCT
ejpam-3406	188	25	1	1	NUM
ejpam-3406	188	26	,	,	PUNCT
ejpam-3406	188	27	.	.	PUNCT
ejpam-3406	188	28	.	.	PUNCT
ejpam-3406	189	1	.	.	PUNCT
ejpam-3406	190	1	,	,	PUNCT
ejpam-3406	190	2	s	s	X
ejpam-3406	190	3	}	}	PUNCT
ejpam-3406	190	4	and	and	CCONJ
ejpam-3406	190	5	a2	a2	PROPN
ejpam-3406	190	6	=	=	PUNCT
ejpam-3406	190	7	{	{	PUNCT
ejpam-3406	190	8	s+	s+	NOUN
ejpam-3406	190	9	1	1	NUM
ejpam-3406	190	10	,	,	PUNCT
ejpam-3406	190	11	s+	s+	X
ejpam-3406	190	12	2	2	NUM
ejpam-3406	190	13	,	,	PUNCT
ejpam-3406	190	14	.	.	PUNCT
ejpam-3406	190	15	.	.	PUNCT
ejpam-3406	191	1	.	.	PUNCT
ejpam-3406	192	1	,	,	PUNCT
ejpam-3406	192	2	s+	s+	ADV
ejpam-3406	192	3	j	j	PROPN
ejpam-3406	192	4	+	+	PROPN
ejpam-3406	192	5	1	1	NUM
ejpam-3406	192	6	}	}	PUNCT
ejpam-3406	192	7	.	.	PUNCT
ejpam-3406	193	1	notice	notice	VERB
ejpam-3406	193	2	that	that	SCONJ
ejpam-3406	193	3	by	by	ADP
ejpam-3406	193	4	joining	join	VERB
ejpam-3406	193	5	the	the	DET
ejpam-3406	193	6	columns	column	NOUN
ejpam-3406	193	7	of	of	ADP
ejpam-3406	193	8	φ1	φ1	PROPN
ejpam-3406	193	9	and	and	CCONJ
ejpam-3406	193	10	φ2	φ2	PROPN
ejpam-3406	193	11	,	,	PUNCT
ejpam-3406	193	12	we	we	PRON
ejpam-3406	193	13	obtain	obtain	VERB
ejpam-3406	193	14	an	an	DET
ejpam-3406	193	15	a	a	DET
ejpam-3406	193	16	-	-	PUNCT
ejpam-3406	193	17	tableau	tableau	NOUN
ejpam-3406	193	18	φ	φ	PROPN
ejpam-3406	193	19	with	with	ADP
ejpam-3406	193	20	n−	n−	PROPN
ejpam-3406	193	21	s−	s−	PROPN
ejpam-3406	193	22	j	j	PROPN
ejpam-3406	193	23	columns	column	NOUN
ejpam-3406	193	24	whose	whose	DET
ejpam-3406	193	25	lengths	length	NOUN
ejpam-3406	193	26	are	be	AUX
ejpam-3406	193	27	in	in	ADP
ejpam-3406	193	28	the	the	DET
ejpam-3406	193	29	set	set	NOUN
ejpam-3406	193	30	a	a	DET
ejpam-3406	193	31	=	=	NOUN
ejpam-3406	193	32	a1	a1	NOUN
ejpam-3406	193	33	∪a2	∪a2	NOUN
ejpam-3406	193	34	=	=	SYM
ejpam-3406	193	35	{	{	PUNCT
ejpam-3406	193	36	0	0	NUM
ejpam-3406	193	37	,	,	PUNCT
ejpam-3406	193	38	1	1	NUM
ejpam-3406	193	39	,	,	PUNCT
ejpam-3406	193	40	.	.	PUNCT
ejpam-3406	193	41	.	.	PUNCT
ejpam-3406	193	42	.	.	PUNCT
ejpam-3406	194	1	,	,	PUNCT
ejpam-3406	194	2	s+	s+	ADV
ejpam-3406	194	3	j+	j+	NUM
ejpam-3406	194	4	1	1	NUM
ejpam-3406	194	5	}	}	PUNCT
ejpam-3406	194	6	.	.	PUNCT
ejpam-3406	195	1	that	that	PRON
ejpam-3406	195	2	is	is	ADV
ejpam-3406	195	3	,	,	PUNCT
ejpam-3406	195	4	φ	φ	PROPN
ejpam-3406	195	5	∈	∈	PROPN
ejpam-3406	195	6	ta(s+	ta(s+	CCONJ
ejpam-3406	195	7	j+	j+	NUM
ejpam-3406	195	8	1	1	NUM
ejpam-3406	195	9	,	,	PUNCT
ejpam-3406	195	10	n−	n−	PROPN
ejpam-3406	195	11	s−	s−	PROPN
ejpam-3406	195	12	j	j	PROPN
ejpam-3406	195	13	)	)	PUNCT
ejpam-3406	195	14	.	.	PUNCT
ejpam-3406	196	1	then	then	ADV
ejpam-3406	196	2	,	,	PUNCT
ejpam-3406	196	3	∑	∑	ADV
ejpam-3406	196	4	φ∈ta(s+j+1,n−s−j	φ∈ta(s+j+1,n−s−j	NUM
ejpam-3406	196	5	)	)	PUNCT
ejpam-3406	196	6	ωa(φ	ωa(φ	NUM
ejpam-3406	196	7	)	)	PUNCT
ejpam-3406	196	8	=	=	SYM
ejpam-3406	196	9	n−j∑	n−j∑	PRON
ejpam-3406	196	10	k	k	X
ejpam-3406	196	11	=	=	NOUN
ejpam-3406	196	12	s	s	NOUN
ejpam-3406	196	13			PUNCT
ejpam-3406	196	14	∑	∑	ADV
ejpam-3406	196	15	φ1∈ta1	φ1∈ta1	NOUN
ejpam-3406	196	16	(	(	PUNCT
ejpam-3406	196	17	s	s	PROPN
ejpam-3406	196	18	,	,	PUNCT
ejpam-3406	196	19	k−s	k−s	NOUN
ejpam-3406	196	20	)	)	PUNCT
ejpam-3406	196	21	ωa1(φ1	ωa1(φ1	NOUN
ejpam-3406	196	22	)	)	PUNCT
ejpam-3406	197	1			NOUN
ejpam-3406	197	2			PUNCT
ejpam-3406	197	3	∑	∑	PROPN
ejpam-3406	197	4	φ2∈ta2	φ2∈ta2	PROPN
ejpam-3406	197	5	(	(	PUNCT
ejpam-3406	197	6	j	j	PROPN
ejpam-3406	197	7	,	,	PUNCT
ejpam-3406	197	8	n−k−j	n−k−j	NOUN
ejpam-3406	197	9	)	)	PUNCT
ejpam-3406	197	10	ωa2(φ2	ωa2(φ2	NOUN
ejpam-3406	197	11	)	)	PUNCT
ejpam-3406	197	12			NOUN
ejpam-3406	197	13	.	.	PUNCT
ejpam-3406	198	1	note	note	VERB
ejpam-3406	198	2	that	that	SCONJ
ejpam-3406	198	3	∑	∑	PROPN
ejpam-3406	198	4	φ2∈ta2	φ2∈ta2	PROPN
ejpam-3406	198	5	(	(	PUNCT
ejpam-3406	198	6	j	j	PROPN
ejpam-3406	198	7	,	,	PUNCT
ejpam-3406	198	8	n−k−j	n−k−j	NOUN
ejpam-3406	198	9	)	)	PUNCT
ejpam-3406	198	10	ωa2(φ2	ωa2(φ2	NOUN
ejpam-3406	198	11	)	)	PUNCT
ejpam-3406	198	12	=	=	PUNCT
ejpam-3406	198	13	∑	∑	PROPN
ejpam-3406	198	14	φ2∈ta2	φ2∈ta2	PROPN
ejpam-3406	198	15	(	(	PUNCT
ejpam-3406	198	16	j	j	PROPN
ejpam-3406	198	17	,	,	PUNCT
ejpam-3406	198	18	n−k−j	n−k−j	PROPN
ejpam-3406	198	19	)	)	PUNCT
ejpam-3406	198	20	∏	∏	NOUN
ejpam-3406	198	21	c∈φ2	c∈φ2	NOUN
ejpam-3406	198	22	[	[	X
ejpam-3406	198	23	m|c|+	m|c|+	NOUN
ejpam-3406	198	24	r]q	r]q	NOUN
ejpam-3406	198	25	=	=	NOUN
ejpam-3406	198	26	∑	∑	NOUN
ejpam-3406	198	27	s+1≤g1≤	s+1≤g1≤	PROPN
ejpam-3406	198	28	...	...	PUNCT
ejpam-3406	199	1	≤g	≤g	NOUN
ejpam-3406	199	2	n−k−j≤	n−k−j≤	ADP
ejpam-3406	199	3	s+j+1	s+j+1	PROPN
ejpam-3406	199	4	n−k−j∏	n−k−j∏	PROPN
ejpam-3406	199	5	i=1	i=1	PROPN
ejpam-3406	200	1	[	[	X
ejpam-3406	200	2	mgi	mgi	NOUN
ejpam-3406	200	3	+	+	NUM
ejpam-3406	200	4	r]q	r]q	NOUN
ejpam-3406	200	5	=	=	PUNCT
ejpam-3406	200	6	∑	∑	NOUN
ejpam-3406	200	7	0≤g1≤	0≤g1≤	NUM
ejpam-3406	200	8	...	...	PUNCT
ejpam-3406	201	1	≤g	≤g	PROPN
ejpam-3406	201	2	n−k−j≤j	n−k−j≤j	PROPN
ejpam-3406	202	1	n−k−j∏	n−k−j∏	PROPN
ejpam-3406	202	2	i=1	i=1	PROPN
ejpam-3406	203	1	[	[	X
ejpam-3406	203	2	mgi	mgi	NOUN
ejpam-3406	203	3	+	+	ADJ
ejpam-3406	203	4	m(s+	m(s+	ADJ
ejpam-3406	203	5	1	1	NUM
ejpam-3406	203	6	)	)	PUNCT
ejpam-3406	203	7	+	+	NUM
ejpam-3406	203	8	r]q	r]q	NOUN
ejpam-3406	203	9	.	.	PUNCT
ejpam-3406	204	1	thus	thus	ADV
ejpam-3406	204	2	,	,	PUNCT
ejpam-3406	204	3	∑	∑	PROPN
ejpam-3406	204	4	0≤g1≤	0≤g1≤	NUM
ejpam-3406	204	5	...	...	PUNCT
ejpam-3406	204	6	≤gn−s−j≤s+j+1	≤gn−s−j≤s+j+1	PROPN
ejpam-3406	204	7	n−s−j∏	n−s−j∏	PROPN
ejpam-3406	204	8	i=1	i=1	PROPN
ejpam-3406	205	1	[	[	X
ejpam-3406	205	2	mgi	mgi	NOUN
ejpam-3406	205	3	+	+	CCONJ
ejpam-3406	205	4	r]q	r]q	NOUN
ejpam-3406	205	5	=	=	PUNCT
ejpam-3406	205	6	n−j∑	n−j∑	PRON
ejpam-3406	205	7	k	k	NOUN
ejpam-3406	205	8	=	=	NOUN
ejpam-3406	205	9	s	s	NOUN
ejpam-3406	205	10			PUNCT
ejpam-3406	205	11	∑	∑	PROPN
ejpam-3406	205	12	0≤g1≤	0≤g1≤	NUM
ejpam-3406	205	13	...	...	PUNCT
ejpam-3406	206	1	≤gk−s≤s	≤gk−s≤s	NUM
ejpam-3406	206	2	k−s∏	k−s∏	ADJ
ejpam-3406	206	3	i=1	i=1	PROPN
ejpam-3406	207	1	[	[	X
ejpam-3406	207	2	mgi	mgi	NOUN
ejpam-3406	207	3	+	+	CCONJ
ejpam-3406	207	4	r]q	r]q	ADJ
ejpam-3406	207	5			NOUN
ejpam-3406	207	6			PUNCT
ejpam-3406	207	7	∑	∑	PROPN
ejpam-3406	207	8	0≤g1≤	0≤g1≤	NUM
ejpam-3406	207	9	...	...	PUNCT
ejpam-3406	207	10	≤gn−k−j≤j	≤gn−k−j≤j	PROPN
ejpam-3406	207	11	n−k−j∏	n−k−j∏	PROPN
ejpam-3406	207	12	i=1	i=1	PROPN
ejpam-3406	208	1	[	[	X
ejpam-3406	208	2	mgi	mgi	NOUN
ejpam-3406	208	3	+	+	ADJ
ejpam-3406	208	4	m(s+	m(s+	ADJ
ejpam-3406	208	5	1	1	NUM
ejpam-3406	208	6	)	)	PUNCT
ejpam-3406	209	1	+	+	CCONJ
ejpam-3406	209	2	r]q	r]q	NOUN
ejpam-3406	209	3	.	.	INTJ
ejpam-3406	209	4	by	by	ADP
ejpam-3406	209	5	(	(	PUNCT
ejpam-3406	209	6	13	13	NUM
ejpam-3406	209	7	)	)	PUNCT
ejpam-3406	209	8	,	,	PUNCT
ejpam-3406	209	9	we	we	PRON
ejpam-3406	209	10	obtain	obtain	VERB
ejpam-3406	209	11	the	the	DET
ejpam-3406	209	12	following	follow	VERB
ejpam-3406	209	13	theorem	theorem	VERB
ejpam-3406	209	14	.	.	PUNCT
ejpam-3406	210	1	theorem	theorem	NOUN
ejpam-3406	210	2	3	3	NUM
ejpam-3406	210	3	.	.	PUNCT
ejpam-3406	211	1	the	the	DET
ejpam-3406	211	2	q	q	ADJ
ejpam-3406	211	3	-	-	PUNCT
ejpam-3406	211	4	analogue	analogue	NOUN
ejpam-3406	211	5	w	w	PROPN
ejpam-3406	211	6	∗m	∗m	NOUN
ejpam-3406	211	7	,	,	PUNCT
ejpam-3406	211	8	r[n	r[n	NOUN
ejpam-3406	211	9	,	,	PUNCT
ejpam-3406	211	10	k	k	X
ejpam-3406	211	11	]	]	X
ejpam-3406	211	12	satisfies	satisfy	VERB
ejpam-3406	211	13	the	the	DET
ejpam-3406	211	14	following	follow	VERB
ejpam-3406	211	15	convolution	convolution	NOUN
ejpam-3406	211	16	-	-	PUNCT
ejpam-3406	211	17	type	type	NOUN
ejpam-3406	211	18	identity	identity	NOUN
ejpam-3406	211	19	w	w	ADP
ejpam-3406	211	20	∗m	∗m	NOUN
ejpam-3406	211	21	,	,	PUNCT
ejpam-3406	211	22	r[n+	r[n+	NOUN
ejpam-3406	211	23	1	1	NUM
ejpam-3406	211	24	,	,	PUNCT
ejpam-3406	211	25	s+	s+	PUNCT
ejpam-3406	211	26	j	j	PROPN
ejpam-3406	211	27	+	+	PROPN
ejpam-3406	211	28	1]q	1]q	NUM
ejpam-3406	212	1	=	=	SYM
ejpam-3406	212	2	n∑	n∑	PROPN
ejpam-3406	212	3	k=0	k=0	PROPN
ejpam-3406	212	4	w	w	PROPN
ejpam-3406	212	5	∗m	∗m	PROPN
ejpam-3406	212	6	,	,	PUNCT
ejpam-3406	212	7	r[k	r[k	PROPN
ejpam-3406	212	8	,	,	PUNCT
ejpam-3406	212	9	s]qw	s]qw	PROPN
ejpam-3406	212	10	∗	∗	NOUN
ejpam-3406	212	11	m	m	NOUN
ejpam-3406	212	12	,	,	PUNCT
ejpam-3406	212	13	r+m(s+1)[n−	r+m(s+1)[n−	CCONJ
ejpam-3406	212	14	k	k	NOUN
ejpam-3406	212	15	,	,	PUNCT
ejpam-3406	212	16	j]q	j]q	PROPN
ejpam-3406	212	17	.	.	PUNCT
ejpam-3406	213	1	the	the	DET
ejpam-3406	213	2	next	next	ADJ
ejpam-3406	213	3	theorem	theorem	NOUN
ejpam-3406	213	4	provides	provide	VERB
ejpam-3406	213	5	another	another	DET
ejpam-3406	213	6	form	form	NOUN
ejpam-3406	213	7	of	of	ADP
ejpam-3406	213	8	convolution	convolution	NOUN
ejpam-3406	213	9	-	-	PUNCT
ejpam-3406	213	10	type	type	NOUN
ejpam-3406	213	11	identity	identity	NOUN
ejpam-3406	213	12	.	.	PUNCT
ejpam-3406	214	1	theorem	theorem	VERB
ejpam-3406	214	2	4	4	NUM
ejpam-3406	214	3	.	.	PUNCT
ejpam-3406	215	1	the	the	DET
ejpam-3406	215	2	q	q	NOUN
ejpam-3406	215	3	-	-	PUNCT
ejpam-3406	215	4	analogue	analogue	NOUN
ejpam-3406	215	5	w	w	PROPN
ejpam-3406	215	6	∗m	∗m	NOUN
ejpam-3406	215	7	,	,	PUNCT
ejpam-3406	215	8	r[n	r[n	NOUN
ejpam-3406	215	9	,	,	PUNCT
ejpam-3406	215	10	k]q	k]q	VERB
ejpam-3406	215	11	satisfies	satisfy	VERB
ejpam-3406	215	12	the	the	DET
ejpam-3406	215	13	following	follow	VERB
ejpam-3406	215	14	second	second	ADJ
ejpam-3406	215	15	form	form	NOUN
ejpam-3406	215	16	of	of	ADP
ejpam-3406	215	17	convolution	convolution	NOUN
ejpam-3406	215	18	formula	formula	NOUN
ejpam-3406	215	19	w	w	ADP
ejpam-3406	215	20	∗m	∗m	NOUN
ejpam-3406	215	21	,	,	PUNCT
ejpam-3406	215	22	r[s+	r[s+	PROPN
ejpam-3406	215	23	j	j	PROPN
ejpam-3406	215	24	,	,	PUNCT
ejpam-3406	215	25	n]q	n]q	PROPN
ejpam-3406	215	26	=	=	SYM
ejpam-3406	215	27	n−j∑	n−j∑	PRON
ejpam-3406	215	28	k	k	NOUN
ejpam-3406	215	29	=	=	NOUN
ejpam-3406	215	30	s	s	NOUN
ejpam-3406	215	31	w	w	NOUN
ejpam-3406	215	32	∗m	∗m	NOUN
ejpam-3406	215	33	,	,	PUNCT
ejpam-3406	215	34	r[s	r[s	PROPN
ejpam-3406	215	35	,	,	PUNCT
ejpam-3406	215	36	k]qw	k]qw	PROPN
ejpam-3406	215	37	∗	∗	NOUN
ejpam-3406	215	38	m	m	PROPN
ejpam-3406	215	39	,	,	PUNCT
ejpam-3406	215	40	r+mk[j	r+mk[j	PROPN
ejpam-3406	215	41	,	,	PUNCT
ejpam-3406	215	42	n−	n−	PROPN
ejpam-3406	215	43	k]q	k]q	PROPN
ejpam-3406	215	44	.	.	PUNCT
ejpam-3406	216	1	r.	r.	PROPN
ejpam-3406	216	2	corcino	corcino	PROPN
ejpam-3406	216	3	,	,	PUNCT
ejpam-3406	216	4	mj	mj	PROPN
ejpam-3406	216	5	.	.	PUNCT
ejpam-3406	216	6	latayada	latayada	PROPN
ejpam-3406	216	7	,	,	PUNCT
ejpam-3406	216	8	mar	mar	PROPN
ejpam-3406	216	9	.	.	PROPN
ejpam-3406	216	10	vega	vega	PROPN
ejpam-3406	216	11	/	/	SYM
ejpam-3406	216	12	eur	eur	PROPN
ejpam-3406	216	13	.	.	PUNCT
ejpam-3406	217	1	j.	j.	PROPN
ejpam-3406	217	2	pure	pure	PROPN
ejpam-3406	217	3	appl	appl	PROPN
ejpam-3406	217	4	.	.	PROPN
ejpam-3406	217	5	math	math	PROPN
ejpam-3406	217	6	,	,	PUNCT
ejpam-3406	217	7	12	12	NUM
ejpam-3406	217	8	(	(	PUNCT
ejpam-3406	217	9	2	2	NUM
ejpam-3406	217	10	)	)	PUNCT
ejpam-3406	217	11	(	(	PUNCT
ejpam-3406	217	12	2019	2019	NUM
ejpam-3406	217	13	)	)	PUNCT
ejpam-3406	217	14	,	,	PUNCT
ejpam-3406	217	15	279	279	NUM
ejpam-3406	217	16	-	-	SYM
ejpam-3406	217	17	293	293	NUM
ejpam-3406	217	18	288	288	NUM
ejpam-3406	217	19	proof	proof	NOUN
ejpam-3406	217	20	.	.	PUNCT
ejpam-3406	218	1	let	let	VERB
ejpam-3406	218	2	φ1	φ1	PROPN
ejpam-3406	218	3	be	be	AUX
ejpam-3406	218	4	a	a	DET
ejpam-3406	218	5	tableau	tableau	NOUN
ejpam-3406	218	6	with	with	ADP
ejpam-3406	218	7	s−	s−	PROPN
ejpam-3406	218	8	k	k	PROPN
ejpam-3406	218	9	columns	column	NOUN
ejpam-3406	218	10	whose	whose	DET
ejpam-3406	218	11	lengths	length	NOUN
ejpam-3406	218	12	are	be	AUX
ejpam-3406	218	13	in	in	ADP
ejpam-3406	218	14	a1	a1	NOUN
ejpam-3406	218	15	=	=	PUNCT
ejpam-3406	218	16	{	{	PUNCT
ejpam-3406	218	17	0	0	NUM
ejpam-3406	218	18	,	,	PUNCT
ejpam-3406	218	19	1	1	NUM
ejpam-3406	218	20	,	,	PUNCT
ejpam-3406	218	21	.	.	PUNCT
ejpam-3406	218	22	.	.	PUNCT
ejpam-3406	219	1	.	.	PUNCT
ejpam-3406	220	1	,	,	PUNCT
ejpam-3406	220	2	k	k	X
ejpam-3406	220	3	}	}	PUNCT
ejpam-3406	220	4	,	,	PUNCT
ejpam-3406	220	5	and	and	CCONJ
ejpam-3406	220	6	φ2	φ2	PROPN
ejpam-3406	220	7	be	be	VERB
ejpam-3406	220	8	a	a	DET
ejpam-3406	220	9	tableau	tableau	NOUN
ejpam-3406	220	10	with	with	ADP
ejpam-3406	220	11	j	j	PROPN
ejpam-3406	221	1	−	−	PROPN
ejpam-3406	221	2	n+	n+	ADP
ejpam-3406	222	1	k	k	PROPN
ejpam-3406	222	2	columns	column	NOUN
ejpam-3406	222	3	whose	whose	DET
ejpam-3406	222	4	lengths	length	NOUN
ejpam-3406	222	5	are	be	AUX
ejpam-3406	222	6	in	in	ADP
ejpam-3406	222	7	a2	a2	PROPN
ejpam-3406	222	8	=	=	PUNCT
ejpam-3406	222	9	{	{	PUNCT
ejpam-3406	222	10	k	k	NOUN
ejpam-3406	222	11	,	,	PUNCT
ejpam-3406	222	12	k	k	PROPN
ejpam-3406	222	13	+	+	PROPN
ejpam-3406	222	14	1	1	NUM
ejpam-3406	222	15	,	,	PUNCT
ejpam-3406	222	16	.	.	PUNCT
ejpam-3406	222	17	.	.	PUNCT
ejpam-3406	222	18	.	.	PUNCT
ejpam-3406	222	19	,	,	PUNCT
ejpam-3406	222	20	n	n	CCONJ
ejpam-3406	222	21	}	}	PUNCT
ejpam-3406	222	22	.	.	PUNCT
ejpam-3406	223	1	then	then	ADV
ejpam-3406	223	2	φ1	φ1	PROPN
ejpam-3406	223	3	∈	∈	PROPN
ejpam-3406	223	4	ta1(k	ta1(k	PROPN
ejpam-3406	223	5	,	,	PUNCT
ejpam-3406	223	6	s−	s−	PROPN
ejpam-3406	223	7	k	k	NOUN
ejpam-3406	223	8	)	)	PUNCT
ejpam-3406	223	9	and	and	CCONJ
ejpam-3406	223	10	φ2	φ2	PROPN
ejpam-3406	223	11	∈	∈	PROPN
ejpam-3406	223	12	ta2(n−	ta2(n−	PROPN
ejpam-3406	224	1	k	k	PROPN
ejpam-3406	224	2	,	,	PUNCT
ejpam-3406	224	3	j−n+	j−n+	PROPN
ejpam-3406	224	4	k	k	NOUN
ejpam-3406	224	5	)	)	PUNCT
ejpam-3406	224	6	.	.	PUNCT
ejpam-3406	225	1	using	use	VERB
ejpam-3406	225	2	the	the	DET
ejpam-3406	225	3	same	same	ADJ
ejpam-3406	225	4	argument	argument	NOUN
ejpam-3406	225	5	above	above	ADV
ejpam-3406	225	6	,	,	PUNCT
ejpam-3406	225	7	we	we	PRON
ejpam-3406	225	8	can	can	AUX
ejpam-3406	225	9	easily	easily	ADV
ejpam-3406	225	10	obtain	obtain	VERB
ejpam-3406	225	11	the	the	DET
ejpam-3406	225	12	convolution	convolution	NOUN
ejpam-3406	225	13	formula	formula	NOUN
ejpam-3406	225	14	.	.	PUNCT
ejpam-3406	226	1	�	�	PROPN
ejpam-3406	226	2	3	3	NUM
ejpam-3406	226	3	.	.	PUNCT
ejpam-3406	227	1	(	(	PUNCT
ejpam-3406	227	2	q	q	ADJ
ejpam-3406	227	3	,	,	PUNCT
ejpam-3406	227	4	r)−dowling	r)−dowle	VERB
ejpam-3406	227	5	number	number	NOUN
ejpam-3406	227	6	and	and	CCONJ
ejpam-3406	227	7	its	its	PRON
ejpam-3406	227	8	hankel	hankel	NOUN
ejpam-3406	227	9	transform	transform	NOUN
ejpam-3406	227	10	in	in	ADP
ejpam-3406	227	11	this	this	DET
ejpam-3406	227	12	section	section	NOUN
ejpam-3406	227	13	,	,	PUNCT
ejpam-3406	227	14	we	we	PRON
ejpam-3406	227	15	define	define	VERB
ejpam-3406	227	16	a	a	DET
ejpam-3406	227	17	q	q	NOUN
ejpam-3406	227	18	-	-	PUNCT
ejpam-3406	227	19	analogue	analogue	NOUN
ejpam-3406	227	20	of	of	ADP
ejpam-3406	227	21	the	the	DET
ejpam-3406	227	22	r	r	NOUN
ejpam-3406	227	23	-	-	PUNCT
ejpam-3406	227	24	dowling	dowle	VERB
ejpam-3406	227	25	numbers	number	NOUN
ejpam-3406	227	26	and	and	CCONJ
ejpam-3406	227	27	obtain	obtain	VERB
ejpam-3406	227	28	some	some	DET
ejpam-3406	227	29	combinatorial	combinatorial	ADJ
ejpam-3406	227	30	properties	property	NOUN
ejpam-3406	227	31	that	that	PRON
ejpam-3406	227	32	will	will	AUX
ejpam-3406	227	33	be	be	AUX
ejpam-3406	227	34	used	use	VERB
ejpam-3406	227	35	to	to	PART
ejpam-3406	227	36	establish	establish	VERB
ejpam-3406	227	37	its	its	PRON
ejpam-3406	227	38	hankel	hankel	NOUN
ejpam-3406	227	39	transform	transform	NOUN
ejpam-3406	227	40	.	.	PUNCT
ejpam-3406	228	1	a	a	DET
ejpam-3406	228	2	q	q	NOUN
ejpam-3406	228	3	-	-	PUNCT
ejpam-3406	228	4	analogue	analogue	NOUN
ejpam-3406	228	5	of	of	ADP
ejpam-3406	228	6	the	the	DET
ejpam-3406	228	7	r	r	NOUN
ejpam-3406	228	8	-	-	PUNCT
ejpam-3406	228	9	dowling	dowle	VERB
ejpam-3406	228	10	numbers	number	NOUN
ejpam-3406	228	11	,	,	PUNCT
ejpam-3406	228	12	denoted	denote	VERB
ejpam-3406	228	13	by	by	ADP
ejpam-3406	228	14	d̃m	d̃m	PROPN
ejpam-3406	228	15	,	,	PUNCT
ejpam-3406	228	16	r[n]q	r[n]q	NOUN
ejpam-3406	228	17	,	,	PUNCT
ejpam-3406	228	18	is	be	AUX
ejpam-3406	228	19	defined	define	VERB
ejpam-3406	228	20	by	by	ADP
ejpam-3406	228	21	d̃m	d̃m	PROPN
ejpam-3406	228	22	,	,	PUNCT
ejpam-3406	228	23	r[n]q	r[n]q	PROPN
ejpam-3406	228	24	=	=	SYM
ejpam-3406	228	25	n∑	n∑	PROPN
ejpam-3406	228	26	k=0	k=0	PROPN
ejpam-3406	228	27	w̃m	w̃m	PROPN
ejpam-3406	228	28	,	,	PUNCT
ejpam-3406	228	29	r[n	r[n	NOUN
ejpam-3406	228	30	,	,	PUNCT
ejpam-3406	228	31	k]q	k]q	VERB
ejpam-3406	228	32	where	where	SCONJ
ejpam-3406	228	33	w̃m	w̃m	PROPN
ejpam-3406	228	34	,	,	PUNCT
ejpam-3406	228	35	r[n	r[n	NOUN
ejpam-3406	228	36	,	,	PUNCT
ejpam-3406	228	37	k]q	k]q	NOUN
ejpam-3406	228	38	=	=	SYM
ejpam-3406	228	39	qkrw	qkrw	ADJ
ejpam-3406	228	40	∗m	∗m	NOUN
ejpam-3406	228	41	,	,	PUNCT
ejpam-3406	228	42	r[n	r[n	NOUN
ejpam-3406	228	43	,	,	PUNCT
ejpam-3406	228	44	k]q	k]q	NOUN
ejpam-3406	228	45	=	=	SYM
ejpam-3406	228	46	q−m(k2)wm	q−m(k2)wm	NOUN
ejpam-3406	228	47	,	,	PUNCT
ejpam-3406	228	48	r[n	r[n	NOUN
ejpam-3406	228	49	,	,	PUNCT
ejpam-3406	228	50	k	k	X
ejpam-3406	228	51	]	]	X
ejpam-3406	228	52	.	.	PUNCT
ejpam-3406	229	1	for	for	ADP
ejpam-3406	229	2	brevity	brevity	NOUN
ejpam-3406	229	3	,	,	PUNCT
ejpam-3406	229	4	we	we	PRON
ejpam-3406	229	5	use	use	VERB
ejpam-3406	229	6	the	the	DET
ejpam-3406	229	7	term	term	NOUN
ejpam-3406	229	8	(	(	PUNCT
ejpam-3406	229	9	q	q	ADJ
ejpam-3406	229	10	,	,	PUNCT
ejpam-3406	229	11	r)-dowling	r)-dowle	VERB
ejpam-3406	229	12	numbers	number	NOUN
ejpam-3406	229	13	for	for	ADP
ejpam-3406	229	14	d̃m	d̃m	PROPN
ejpam-3406	229	15	,	,	PUNCT
ejpam-3406	229	16	r[n]q	r[n]q	NOUN
ejpam-3406	229	17	.	.	PUNCT
ejpam-3406	230	1	remark	remark	PROPN
ejpam-3406	230	2	2	2	NUM
ejpam-3406	230	3	.	.	PUNCT
ejpam-3406	231	1	when	when	SCONJ
ejpam-3406	231	2	m	m	VERB
ejpam-3406	231	3	=	=	SYM
ejpam-3406	231	4	1	1	NUM
ejpam-3406	231	5	and	and	CCONJ
ejpam-3406	231	6	r	r	NOUN
ejpam-3406	231	7	=	=	SYM
ejpam-3406	231	8	0	0	NUM
ejpam-3406	231	9	,	,	PUNCT
ejpam-3406	231	10	(	(	PUNCT
ejpam-3406	231	11	6	6	X
ejpam-3406	231	12	)	)	PUNCT
ejpam-3406	231	13	yields	yield	NOUN
ejpam-3406	231	14	w̃1,0[n	w̃1,0[n	VERB
ejpam-3406	231	15	,	,	PUNCT
ejpam-3406	231	16	k]q	k]q	X
ejpam-3406	231	17	=	=	SYM
ejpam-3406	231	18	q−(k2)w1,0[n	q−(k2)w1,0[n	PROPN
ejpam-3406	231	19	,	,	PUNCT
ejpam-3406	231	20	k	k	X
ejpam-3406	231	21	]	]	X
ejpam-3406	231	22	=	=	SYM
ejpam-3406	231	23	q−(k2)sq[n	q−(k2)sq[n	PROPN
ejpam-3406	231	24	,	,	PUNCT
ejpam-3406	231	25	k	k	X
ejpam-3406	231	26	]	]	X
ejpam-3406	231	27	=	=	SYM
ejpam-3406	231	28	s̃q[n	s̃q[n	PROPN
ejpam-3406	231	29	,	,	PUNCT
ejpam-3406	231	30	k	k	X
ejpam-3406	231	31	]	]	X
ejpam-3406	231	32	.	.	PUNCT
ejpam-3406	232	1	(	(	PUNCT
ejpam-3406	232	2	15	15	X
ejpam-3406	232	3	)	)	PUNCT
ejpam-3406	232	4	it	it	PRON
ejpam-3406	232	5	follows	follow	VERB
ejpam-3406	232	6	that	that	SCONJ
ejpam-3406	232	7	the	the	PRON
ejpam-3406	232	8	(	(	PUNCT
ejpam-3406	232	9	q	q	ADJ
ejpam-3406	232	10	,	,	PUNCT
ejpam-3406	232	11	r)-dowling	r)-dowle	VERB
ejpam-3406	232	12	numbers	number	NOUN
ejpam-3406	232	13	reduces	reduce	VERB
ejpam-3406	232	14	to	to	ADP
ejpam-3406	232	15	d̃1,0[n]q	d̃1,0[n]q	NOUN
ejpam-3406	232	16	=	=	SYM
ejpam-3406	232	17	ẽq	ẽq	PROPN
ejpam-3406	232	18	,	,	PUNCT
ejpam-3406	232	19	n[1	n[1	PROPN
ejpam-3406	232	20	]	]	X
ejpam-3406	232	21	(	(	PUNCT
ejpam-3406	232	22	16	16	NUM
ejpam-3406	232	23	)	)	PUNCT
ejpam-3406	232	24	where	where	SCONJ
ejpam-3406	232	25	ẽq	ẽq	PROPN
ejpam-3406	232	26	,	,	PUNCT
ejpam-3406	232	27	n[z	n[z	NOUN
ejpam-3406	232	28	]	]	PUNCT
ejpam-3406	232	29	is	be	AUX
ejpam-3406	232	30	the	the	DET
ejpam-3406	232	31	q	q	ADJ
ejpam-3406	232	32	-	-	ADJ
ejpam-3406	232	33	exponential	exponential	ADJ
ejpam-3406	232	34	polynomial	polynomial	NOUN
ejpam-3406	232	35	in	in	ADP
ejpam-3406	232	36	[	[	X
ejpam-3406	232	37	11	11	NUM
ejpam-3406	232	38	]	]	PUNCT
ejpam-3406	232	39	defined	define	VERB
ejpam-3406	232	40	by	by	ADP
ejpam-3406	232	41	ẽq	ẽq	PROPN
ejpam-3406	232	42	,	,	PUNCT
ejpam-3406	232	43	n[z	n[z	X
ejpam-3406	232	44	]	]	X
ejpam-3406	232	45	=	=	SYM
ejpam-3406	232	46	n∑	n∑	PROPN
ejpam-3406	232	47	k=0	k=0	PROPN
ejpam-3406	232	48	s̃q[n	s̃q[n	PROPN
ejpam-3406	232	49	,	,	PUNCT
ejpam-3406	232	50	k]zk	k]zk	PROPN
ejpam-3406	232	51	.	.	PUNCT
ejpam-3406	233	1	(	(	PUNCT
ejpam-3406	233	2	17	17	NUM
ejpam-3406	233	3	)	)	PUNCT
ejpam-3406	233	4	remark	remark	NOUN
ejpam-3406	233	5	3	3	NUM
ejpam-3406	233	6	.	.	PUNCT
ejpam-3406	234	1	we	we	PRON
ejpam-3406	234	2	recall	recall	VERB
ejpam-3406	234	3	that	that	SCONJ
ejpam-3406	234	4	the	the	DET
ejpam-3406	234	5	hankel	hankel	NOUN
ejpam-3406	234	6	transform	transform	NOUN
ejpam-3406	234	7	of	of	ADP
ejpam-3406	234	8	the	the	DET
ejpam-3406	234	9	q	q	ADJ
ejpam-3406	234	10	-	-	ADJ
ejpam-3406	234	11	exponential	exponential	ADJ
ejpam-3406	234	12	polynomial	polynomial	ADJ
ejpam-3406	234	13	ẽq	ẽq	PROPN
ejpam-3406	234	14	,	,	PUNCT
ejpam-3406	234	15	n[z	n[z	NOUN
ejpam-3406	234	16	]	]	PUNCT
ejpam-3406	234	17	is	be	AUX
ejpam-3406	234	18	given	give	VERB
ejpam-3406	234	19	by	by	ADP
ejpam-3406	234	20	h	h	PROPN
ejpam-3406	234	21	(	(	PUNCT
ejpam-3406	234	22	ẽq	ẽq	PROPN
ejpam-3406	234	23	,	,	PUNCT
ejpam-3406	234	24	n(z	n(z	NOUN
ejpam-3406	234	25	)	)	PUNCT
ejpam-3406	234	26	)	)	PUNCT
ejpam-3406	235	1	=	=	PUNCT
ejpam-3406	236	1	q	q	X
ejpam-3406	236	2	(	(	PUNCT
ejpam-3406	236	3	n+1	n+1	PROPN
ejpam-3406	236	4	3	3	NUM
ejpam-3406	236	5	)	)	PUNCT
ejpam-3406	237	1	[	[	X
ejpam-3406	237	2	0]![1	0]![1	X
ejpam-3406	237	3	]	]	X
ejpam-3406	237	4	!	!	PUNCT
ejpam-3406	237	5	.	.	PUNCT
ejpam-3406	237	6	.	.	PUNCT
ejpam-3406	237	7	.	.	PUNCT
ejpam-3406	238	1	[	[	X
ejpam-3406	238	2	n]!(z	n]!(z	NOUN
ejpam-3406	238	3	)	)	PUNCT
ejpam-3406	238	4	(	(	PUNCT
ejpam-3406	238	5	n+1	n+1	PROPN
ejpam-3406	238	6	2	2	NUM
ejpam-3406	238	7	)	)	PUNCT
ejpam-3406	238	8	.	.	PUNCT
ejpam-3406	239	1	it	it	PRON
ejpam-3406	239	2	can	can	AUX
ejpam-3406	239	3	easily	easily	ADV
ejpam-3406	239	4	be	be	AUX
ejpam-3406	239	5	verified	verify	VERB
ejpam-3406	239	6	that	that	SCONJ
ejpam-3406	239	7	the	the	DET
ejpam-3406	239	8	hankel	hankel	NOUN
ejpam-3406	239	9	transform	transform	NOUN
ejpam-3406	239	10	of	of	ADP
ejpam-3406	239	11	ēq	ēq	NOUN
ejpam-3406	239	12	,	,	PUNCT
ejpam-3406	239	13	n[z	n[z	PART
ejpam-3406	239	14	]	]	X
ejpam-3406	239	15	=	=	SYM
ejpam-3406	239	16	n∑	n∑	PROPN
ejpam-3406	239	17	k=0	k=0	PROPN
ejpam-3406	239	18	s̃q[n	s̃q[n	PROPN
ejpam-3406	239	19	,	,	PUNCT
ejpam-3406	239	20	k]zn−k	k]zn−k	NOUN
ejpam-3406	239	21	(	(	PUNCT
ejpam-3406	239	22	18	18	NUM
ejpam-3406	239	23	)	)	PUNCT
ejpam-3406	239	24	is	be	AUX
ejpam-3406	239	25	equal	equal	ADJ
ejpam-3406	239	26	to	to	ADP
ejpam-3406	239	27	that	that	PRON
ejpam-3406	239	28	of	of	ADP
ejpam-3406	239	29	ẽq	ẽq	PROPN
ejpam-3406	239	30	,	,	PUNCT
ejpam-3406	239	31	n[z	n[z	NOUN
ejpam-3406	239	32	]	]	PUNCT
ejpam-3406	239	33	.	.	PUNCT
ejpam-3406	240	1	r.	r.	PROPN
ejpam-3406	240	2	corcino	corcino	PROPN
ejpam-3406	240	3	,	,	PUNCT
ejpam-3406	240	4	mj	mj	PROPN
ejpam-3406	240	5	.	.	PUNCT
ejpam-3406	240	6	latayada	latayada	PROPN
ejpam-3406	240	7	,	,	PUNCT
ejpam-3406	240	8	mar	mar	PROPN
ejpam-3406	240	9	.	.	PROPN
ejpam-3406	240	10	vega	vega	PROPN
ejpam-3406	240	11	/	/	SYM
ejpam-3406	240	12	eur	eur	PROPN
ejpam-3406	240	13	.	.	PUNCT
ejpam-3406	241	1	j.	j.	PROPN
ejpam-3406	241	2	pure	pure	PROPN
ejpam-3406	241	3	appl	appl	PROPN
ejpam-3406	241	4	.	.	PROPN
ejpam-3406	241	5	math	math	PROPN
ejpam-3406	241	6	,	,	PUNCT
ejpam-3406	241	7	12	12	NUM
ejpam-3406	241	8	(	(	PUNCT
ejpam-3406	241	9	2	2	NUM
ejpam-3406	241	10	)	)	PUNCT
ejpam-3406	241	11	(	(	PUNCT
ejpam-3406	241	12	2019	2019	NUM
ejpam-3406	241	13	)	)	PUNCT
ejpam-3406	241	14	,	,	PUNCT
ejpam-3406	241	15	279	279	NUM
ejpam-3406	241	16	-	-	SYM
ejpam-3406	241	17	293	293	NUM
ejpam-3406	241	18	289	289	NUM
ejpam-3406	241	19	remark	remark	NOUN
ejpam-3406	241	20	4	4	NUM
ejpam-3406	241	21	.	.	PUNCT
ejpam-3406	242	1	since	since	SCONJ
ejpam-3406	242	2	wm,0[n	wm,0[n	NOUN
ejpam-3406	242	3	,	,	PUNCT
ejpam-3406	242	4	k]q	k]q	VERB
ejpam-3406	242	5	=	=	PUNCT
ejpam-3406	243	1	[	[	X
ejpam-3406	243	2	m]n−kq	m]n−kq	X
ejpam-3406	243	3			NUM
ejpam-3406	243	4	1	1	NUM
ejpam-3406	243	5	[	[	X
ejpam-3406	243	6	k]qm	k]qm	X
ejpam-3406	243	7	!	!	PUNCT
ejpam-3406	244	1	k∑	k∑	PROPN
ejpam-3406	245	1	j=0	j=0	PROPN
ejpam-3406	245	2	(	(	PUNCT
ejpam-3406	245	3	−1)k−jqm(k−j2	−1)k−jqm(k−j2	NOUN
ejpam-3406	245	4	)	)	PUNCT
ejpam-3406	246	1	[	[	PUNCT
ejpam-3406	246	2	k	k	X
ejpam-3406	246	3	j	j	X
ejpam-3406	246	4	]	]	PUNCT
ejpam-3406	246	5	qm	qm	PROPN
ejpam-3406	247	1	[	[	X
ejpam-3406	247	2	j]nqm	j]nqm	X
ejpam-3406	247	3			NOUN
ejpam-3406	247	4	=	=	PUNCT
ejpam-3406	248	1	[	[	X
ejpam-3406	248	2	m]n−kq	m]n−kq	X
ejpam-3406	248	3	sqm	sqm	NUM
ejpam-3406	248	4	[	[	X
ejpam-3406	248	5	n	n	CCONJ
ejpam-3406	248	6	,	,	PUNCT
ejpam-3406	248	7	k	k	X
ejpam-3406	248	8	]	]	X
ejpam-3406	248	9	,	,	PUNCT
ejpam-3406	248	10	we	we	PRON
ejpam-3406	248	11	have	have	VERB
ejpam-3406	248	12	w̃m,0[n	w̃m,0[n	NOUN
ejpam-3406	248	13	,	,	PUNCT
ejpam-3406	248	14	k]q	k]q	NOUN
ejpam-3406	248	15	=	=	SYM
ejpam-3406	248	16	q−m(k2)wm,0[n	q−m(k2)wm,0[n	NUM
ejpam-3406	248	17	,	,	PUNCT
ejpam-3406	248	18	k	k	X
ejpam-3406	248	19	]	]	X
ejpam-3406	248	20	=	=	PUNCT
ejpam-3406	249	1	[	[	X
ejpam-3406	249	2	m]n−kq	m]n−kq	X
ejpam-3406	249	3	(	(	PUNCT
ejpam-3406	249	4	qm)−(k2	qm)−(k2	NUM
ejpam-3406	249	5	)	)	PUNCT
ejpam-3406	249	6	sqm	sqm	NOUN
ejpam-3406	249	7	[	[	X
ejpam-3406	249	8	n	n	CCONJ
ejpam-3406	249	9	,	,	PUNCT
ejpam-3406	249	10	k	k	X
ejpam-3406	249	11	]	]	X
ejpam-3406	249	12	=	=	PUNCT
ejpam-3406	250	1	[	[	X
ejpam-3406	250	2	m]n−kq	m]n−kq	X
ejpam-3406	250	3	s̃qm	s̃qm	X
ejpam-3406	250	4	[	[	X
ejpam-3406	250	5	n	n	CCONJ
ejpam-3406	250	6	,	,	PUNCT
ejpam-3406	250	7	k	k	X
ejpam-3406	250	8	]	]	X
ejpam-3406	250	9	.	.	PUNCT
ejpam-3406	251	1	this	this	PRON
ejpam-3406	251	2	implies	imply	VERB
ejpam-3406	251	3	that	that	SCONJ
ejpam-3406	251	4	d̃m,0[n]q	d̃m,0[n]q	PRON
ejpam-3406	251	5	=	=	SYM
ejpam-3406	251	6	n∑	n∑	PROPN
ejpam-3406	251	7	k=0	k=0	PROPN
ejpam-3406	251	8	w̃m,0[n	w̃m,0[n	NOUN
ejpam-3406	251	9	,	,	PUNCT
ejpam-3406	251	10	k]q	k]q	NOUN
ejpam-3406	251	11	=	=	SYM
ejpam-3406	251	12	n∑	n∑	PROPN
ejpam-3406	251	13	k=0	k=0	PROPN
ejpam-3406	251	14	s̃qm	s̃qm	ADP
ejpam-3406	251	15	[	[	X
ejpam-3406	251	16	n	n	CCONJ
ejpam-3406	251	17	,	,	PUNCT
ejpam-3406	251	18	k][m]n−kq	k][m]n−kq	PROPN
ejpam-3406	251	19	.	.	PUNCT
ejpam-3406	252	1	(	(	PUNCT
ejpam-3406	252	2	19	19	NUM
ejpam-3406	252	3	)	)	PUNCT
ejpam-3406	252	4	thus	thus	ADV
ejpam-3406	252	5	,	,	PUNCT
ejpam-3406	252	6	using	use	VERB
ejpam-3406	252	7	remark	remark	NOUN
ejpam-3406	252	8	3	3	NUM
ejpam-3406	252	9	,	,	PUNCT
ejpam-3406	252	10	the	the	DET
ejpam-3406	252	11	hankel	hankel	NOUN
ejpam-3406	252	12	transform	transform	NOUN
ejpam-3406	252	13	of	of	ADP
ejpam-3406	252	14	d̃m,0[n]q	d̃m,0[n]q	PRON
ejpam-3406	252	15	is	be	AUX
ejpam-3406	252	16	given	give	VERB
ejpam-3406	252	17	by	by	ADP
ejpam-3406	252	18	h	h	PROPN
ejpam-3406	252	19	(	(	PUNCT
ejpam-3406	252	20	d̃m,0[n]q	d̃m,0[n]q	NOUN
ejpam-3406	252	21	)	)	PUNCT
ejpam-3406	252	22	)	)	PUNCT
ejpam-3406	253	1	=	=	SYM
ejpam-3406	253	2	h	h	NOUN
ejpam-3406	253	3	(	(	PUNCT
ejpam-3406	253	4	ēqm	ēqm	PROPN
ejpam-3406	253	5	,	,	PUNCT
ejpam-3406	253	6	n([m]q	n([m]q	PROPN
ejpam-3406	253	7	)	)	PUNCT
ejpam-3406	253	8	)	)	PUNCT
ejpam-3406	254	1	=	=	PUNCT
ejpam-3406	254	2	qm(n+1	qm(n+1	PROPN
ejpam-3406	254	3	3	3	NUM
ejpam-3406	254	4	)	)	PUNCT
ejpam-3406	255	1	[	[	X
ejpam-3406	255	2	0]qm	0]qm	NUM
ejpam-3406	255	3	!	!	PUNCT
ejpam-3406	256	1	[	[	X
ejpam-3406	256	2	1]qm	1]qm	NUM
ejpam-3406	256	3	!	!	PUNCT
ejpam-3406	256	4	.	.	PUNCT
ejpam-3406	256	5	.	.	PUNCT
ejpam-3406	256	6	.	.	PUNCT
ejpam-3406	257	1	[	[	X
ejpam-3406	257	2	n]qm	n]qm	NOUN
ejpam-3406	257	3	!	!	PUNCT
ejpam-3406	258	1	[	[	X
ejpam-3406	258	2	m	m	X
ejpam-3406	258	3	]	]	X
ejpam-3406	258	4	(	(	PUNCT
ejpam-3406	258	5	n+1	n+1	PROPN
ejpam-3406	258	6	2	2	X
ejpam-3406	258	7	)	)	PUNCT
ejpam-3406	258	8	q	q	NOUN
ejpam-3406	258	9	(	(	PUNCT
ejpam-3406	258	10	20	20	NUM
ejpam-3406	258	11	)	)	PUNCT
ejpam-3406	258	12	clearly	clearly	ADV
ejpam-3406	258	13	,	,	PUNCT
ejpam-3406	258	14	when	when	SCONJ
ejpam-3406	258	15	q	q	X
ejpam-3406	258	16	→	→	SYM
ejpam-3406	258	17	1	1	NUM
ejpam-3406	258	18	,	,	PUNCT
ejpam-3406	258	19	d̃m	d̃m	PROPN
ejpam-3406	258	20	,	,	PUNCT
ejpam-3406	258	21	r[n]q	r[n]q	PROPN
ejpam-3406	258	22	→	→	SYM
ejpam-3406	258	23	d̃m	d̃m	PROPN
ejpam-3406	258	24	,	,	PUNCT
ejpam-3406	258	25	r(n	r(n	PROPN
ejpam-3406	258	26	)	)	PUNCT
ejpam-3406	258	27	,	,	PUNCT
ejpam-3406	258	28	the	the	DET
ejpam-3406	258	29	r	r	NOUN
ejpam-3406	258	30	-	-	PUNCT
ejpam-3406	258	31	dowling	dowle	VERB
ejpam-3406	258	32	numbers	number	NOUN
ejpam-3406	258	33	.	.	PUNCT
ejpam-3406	259	1	by	by	ADP
ejpam-3406	259	2	making	make	VERB
ejpam-3406	259	3	use	use	NOUN
ejpam-3406	259	4	of	of	ADP
ejpam-3406	259	5	theorem	theorem	NOUN
ejpam-3406	259	6	2	2	NUM
ejpam-3406	259	7	,	,	PUNCT
ejpam-3406	259	8	with	with	ADP
ejpam-3406	259	9	r1	r1	NOUN
ejpam-3406	259	10	=	=	PUNCT
ejpam-3406	259	11	r	r	NOUN
ejpam-3406	259	12	−	−	NOUN
ejpam-3406	259	13	1	1	NUM
ejpam-3406	259	14	and	and	CCONJ
ejpam-3406	259	15	r2	r2	PROPN
ejpam-3406	259	16	=	=	SYM
ejpam-3406	259	17	1	1	NUM
ejpam-3406	259	18	and	and	CCONJ
ejpam-3406	259	19	multiplying	multiply	VERB
ejpam-3406	259	20	both	both	DET
ejpam-3406	259	21	sides	side	NOUN
ejpam-3406	259	22	by	by	ADP
ejpam-3406	259	23	q−kr	q−kr	NOUN
ejpam-3406	259	24	,	,	PUNCT
ejpam-3406	259	25	we	we	PRON
ejpam-3406	259	26	have	have	VERB
ejpam-3406	259	27	w̃m	w̃m	PROPN
ejpam-3406	259	28	,	,	PUNCT
ejpam-3406	259	29	r[n	r[n	NOUN
ejpam-3406	259	30	,	,	PUNCT
ejpam-3406	259	31	k]q	k]q	NOUN
ejpam-3406	259	32	=	=	SYM
ejpam-3406	259	33	n∑	n∑	PROPN
ejpam-3406	259	34	j	j	PROPN
ejpam-3406	260	1	=	=	PROPN
ejpam-3406	260	2	k	k	PROPN
ejpam-3406	260	3	(	(	PUNCT
ejpam-3406	260	4	−1)n−j	−1)n−j	X
ejpam-3406	260	5	(	(	PUNCT
ejpam-3406	260	6	n	n	X
ejpam-3406	260	7	j	j	NOUN
ejpam-3406	260	8	)	)	PUNCT
ejpam-3406	260	9	q−nw̃m	q−nw̃m	NOUN
ejpam-3406	260	10	,	,	PUNCT
ejpam-3406	260	11	r−1[j	r−1[j	VERB
ejpam-3406	260	12	,	,	PUNCT
ejpam-3406	260	13	k]q	k]q	PROPN
ejpam-3406	260	14	.	.	PUNCT
ejpam-3406	261	1	(	(	PUNCT
ejpam-3406	261	2	21	21	NUM
ejpam-3406	261	3	)	)	PUNCT
ejpam-3406	261	4	summing	sum	VERB
ejpam-3406	261	5	up	up	ADP
ejpam-3406	261	6	both	both	DET
ejpam-3406	261	7	sides	side	NOUN
ejpam-3406	261	8	of	of	ADP
ejpam-3406	261	9	(	(	PUNCT
ejpam-3406	261	10	21	21	NUM
ejpam-3406	261	11	)	)	PUNCT
ejpam-3406	261	12	,	,	PUNCT
ejpam-3406	261	13	we	we	PRON
ejpam-3406	261	14	have	have	VERB
ejpam-3406	261	15	d̃m	d̃m	PROPN
ejpam-3406	261	16	,	,	PUNCT
ejpam-3406	261	17	r[n]q	r[n]q	PROPN
ejpam-3406	261	18	=	=	SYM
ejpam-3406	262	1	n∑	n∑	PROPN
ejpam-3406	262	2	k=0	k=0	PROPN
ejpam-3406	262	3	n∑	n∑	PROPN
ejpam-3406	263	1	j	j	PROPN
ejpam-3406	264	1	=	=	PROPN
ejpam-3406	264	2	k	k	PROPN
ejpam-3406	264	3	(	(	PUNCT
ejpam-3406	264	4	−1)n−j	−1)n−j	X
ejpam-3406	264	5	(	(	PUNCT
ejpam-3406	264	6	n	n	X
ejpam-3406	264	7	j	j	NOUN
ejpam-3406	264	8	)	)	PUNCT
ejpam-3406	264	9	q−nw̃m	q−nw̃m	NOUN
ejpam-3406	264	10	,	,	PUNCT
ejpam-3406	264	11	r−1[j	r−1[j	VERB
ejpam-3406	264	12	,	,	PUNCT
ejpam-3406	264	13	k]q	k]q	NOUN
ejpam-3406	264	14	=	=	SYM
ejpam-3406	264	15	n∑	n∑	PROPN
ejpam-3406	264	16	j=0	j=0	PROPN
ejpam-3406	264	17	j∑	j∑	PROPN
ejpam-3406	264	18	k=0	k=0	PROPN
ejpam-3406	264	19	(	(	PUNCT
ejpam-3406	264	20	−1)n−j	−1)n−j	X
ejpam-3406	264	21	(	(	PUNCT
ejpam-3406	264	22	n	n	X
ejpam-3406	264	23	j	j	NOUN
ejpam-3406	264	24	)	)	PUNCT
ejpam-3406	264	25	q−nw̃m	q−nw̃m	NOUN
ejpam-3406	264	26	,	,	PUNCT
ejpam-3406	264	27	r−1[j	r−1[j	VERB
ejpam-3406	264	28	,	,	PUNCT
ejpam-3406	264	29	k]q	k]q	NOUN
ejpam-3406	264	30	=	=	SYM
ejpam-3406	264	31	n∑	n∑	X
ejpam-3406	264	32	j=0	j=0	PROPN
ejpam-3406	264	33	(	(	PUNCT
ejpam-3406	264	34	−1)n−j	−1)n−j	X
ejpam-3406	264	35	(	(	PUNCT
ejpam-3406	264	36	n	n	X
ejpam-3406	264	37	j	j	PROPN
ejpam-3406	264	38	)	)	PUNCT
ejpam-3406	264	39	q−n	q−n	PROPN
ejpam-3406	264	40	j∑	j∑	PROPN
ejpam-3406	264	41	k=0	k=0	PROPN
ejpam-3406	264	42	w̃m	w̃m	PROPN
ejpam-3406	264	43	,	,	PUNCT
ejpam-3406	264	44	r−1[j	r−1[j	ADJ
ejpam-3406	264	45	,	,	PUNCT
ejpam-3406	264	46	k]q	k]q	NOUN
ejpam-3406	264	47	=	=	SYM
ejpam-3406	264	48	n∑	n∑	X
ejpam-3406	264	49	j=0	j=0	PROPN
ejpam-3406	264	50	(	(	PUNCT
ejpam-3406	264	51	−1)n−j	−1)n−j	X
ejpam-3406	264	52	(	(	PUNCT
ejpam-3406	264	53	n	n	X
ejpam-3406	264	54	j	j	PROPN
ejpam-3406	264	55	)	)	PUNCT
ejpam-3406	264	56	q−nd̃m	q−nd̃m	PROPN
ejpam-3406	264	57	,	,	PUNCT
ejpam-3406	264	58	r−1[j]q	r−1[j]q	PROPN
ejpam-3406	264	59	.	.	PUNCT
ejpam-3406	265	1	the	the	DET
ejpam-3406	265	2	following	follow	VERB
ejpam-3406	265	3	theorem	theorem	ADJ
ejpam-3406	265	4	states	state	NOUN
ejpam-3406	265	5	formally	formally	ADV
ejpam-3406	265	6	the	the	DET
ejpam-3406	265	7	above	above	ADJ
ejpam-3406	265	8	recurrence	recurrence	NOUN
ejpam-3406	265	9	relation	relation	NOUN
ejpam-3406	265	10	for	for	ADP
ejpam-3406	265	11	d̃m	d̃m	PROPN
ejpam-3406	265	12	,	,	PUNCT
ejpam-3406	265	13	r[n]q	r[n]q	NOUN
ejpam-3406	265	14	.	.	PUNCT
ejpam-3406	266	1	theorem	theorem	VERB
ejpam-3406	266	2	5	5	NUM
ejpam-3406	266	3	.	.	PUNCT
ejpam-3406	267	1	the	the	PRON
ejpam-3406	267	2	(	(	PUNCT
ejpam-3406	267	3	q	q	ADJ
ejpam-3406	267	4	,	,	PUNCT
ejpam-3406	267	5	r)-dowling	r)-dowle	VERB
ejpam-3406	267	6	numbers	number	NOUN
ejpam-3406	267	7	satisfy	satisfy	VERB
ejpam-3406	267	8	the	the	DET
ejpam-3406	267	9	following	follow	VERB
ejpam-3406	267	10	relation	relation	NOUN
ejpam-3406	267	11	qnd̃m	qnd̃m	PROPN
ejpam-3406	267	12	,	,	PUNCT
ejpam-3406	267	13	r[n]q	r[n]q	X
ejpam-3406	267	14	=	=	SYM
ejpam-3406	267	15	n∑	n∑	X
ejpam-3406	267	16	j=0	j=0	PROPN
ejpam-3406	267	17	(	(	PUNCT
ejpam-3406	267	18	−1)n−j	−1)n−j	X
ejpam-3406	267	19	(	(	PUNCT
ejpam-3406	267	20	n	n	X
ejpam-3406	267	21	j	j	PROPN
ejpam-3406	267	22	)	)	PUNCT
ejpam-3406	267	23	d̃m	d̃m	PROPN
ejpam-3406	267	24	,	,	PUNCT
ejpam-3406	267	25	r−1[j]q	r−1[j]q	PROPN
ejpam-3406	267	26	.	.	PUNCT
ejpam-3406	268	1	(	(	PUNCT
ejpam-3406	268	2	22	22	NUM
ejpam-3406	268	3	)	)	PUNCT
ejpam-3406	268	4	r.	r.	PROPN
ejpam-3406	268	5	corcino	corcino	PROPN
ejpam-3406	268	6	,	,	PUNCT
ejpam-3406	268	7	mj	mj	PROPN
ejpam-3406	268	8	.	.	PUNCT
ejpam-3406	268	9	latayada	latayada	PROPN
ejpam-3406	268	10	,	,	PUNCT
ejpam-3406	268	11	mar	mar	PROPN
ejpam-3406	268	12	.	.	PROPN
ejpam-3406	268	13	vega	vega	PROPN
ejpam-3406	268	14	/	/	SYM
ejpam-3406	268	15	eur	eur	PROPN
ejpam-3406	268	16	.	.	PUNCT
ejpam-3406	269	1	j.	j.	PROPN
ejpam-3406	269	2	pure	pure	PROPN
ejpam-3406	269	3	appl	appl	PROPN
ejpam-3406	269	4	.	.	PROPN
ejpam-3406	269	5	math	math	PROPN
ejpam-3406	269	6	,	,	PUNCT
ejpam-3406	269	7	12	12	NUM
ejpam-3406	269	8	(	(	PUNCT
ejpam-3406	269	9	2	2	NUM
ejpam-3406	269	10	)	)	PUNCT
ejpam-3406	269	11	(	(	PUNCT
ejpam-3406	269	12	2019	2019	NUM
ejpam-3406	269	13	)	)	PUNCT
ejpam-3406	269	14	,	,	PUNCT
ejpam-3406	269	15	279	279	NUM
ejpam-3406	269	16	-	-	SYM
ejpam-3406	269	17	293	293	NUM
ejpam-3406	269	18	290	290	NUM
ejpam-3406	269	19	the	the	DET
ejpam-3406	269	20	following	follow	VERB
ejpam-3406	269	21	corollary	corollary	NOUN
ejpam-3406	269	22	is	be	AUX
ejpam-3406	269	23	a	a	DET
ejpam-3406	269	24	direct	direct	ADJ
ejpam-3406	269	25	consequence	consequence	NOUN
ejpam-3406	269	26	of	of	ADP
ejpam-3406	269	27	theorem	theorem	NOUN
ejpam-3406	269	28	5	5	NUM
ejpam-3406	269	29	which	which	PRON
ejpam-3406	269	30	can	can	AUX
ejpam-3406	269	31	be	be	AUX
ejpam-3406	269	32	proved	prove	VERB
ejpam-3406	269	33	using	use	VERB
ejpam-3406	269	34	the	the	DET
ejpam-3406	269	35	inversion	inversion	NOUN
ejpam-3406	269	36	formula	formula	NOUN
ejpam-3406	269	37	by	by	ADP
ejpam-3406	269	38	riordan	riordan	PROPN
ejpam-3406	270	1	[	[	X
ejpam-3406	270	2	4	4	NUM
ejpam-3406	270	3	,	,	PUNCT
ejpam-3406	270	4	15	15	NUM
ejpam-3406	270	5	]	]	PUNCT
ejpam-3406	270	6	.	.	PUNCT
ejpam-3406	271	1	corollary	corollary	ADJ
ejpam-3406	271	2	1	1	NUM
ejpam-3406	271	3	.	.	PUNCT
ejpam-3406	272	1	the	the	PRON
ejpam-3406	272	2	(	(	PUNCT
ejpam-3406	272	3	q	q	ADJ
ejpam-3406	272	4	,	,	PUNCT
ejpam-3406	272	5	r)-dowling	r)-dowle	VERB
ejpam-3406	272	6	numbers	number	NOUN
ejpam-3406	272	7	satisfy	satisfy	VERB
ejpam-3406	272	8	the	the	DET
ejpam-3406	272	9	following	follow	VERB
ejpam-3406	272	10	relations	relation	NOUN
ejpam-3406	272	11	d̃m	d̃m	PROPN
ejpam-3406	272	12	,	,	PUNCT
ejpam-3406	272	13	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	272	14	=	=	SYM
ejpam-3406	272	15	n∑	n∑	X
ejpam-3406	272	16	j=0	j=0	PROPN
ejpam-3406	272	17	(	(	PUNCT
ejpam-3406	272	18	n	n	X
ejpam-3406	272	19	j	j	PROPN
ejpam-3406	272	20	)	)	PUNCT
ejpam-3406	272	21	qjd̃m	qjd̃m	PROPN
ejpam-3406	272	22	,	,	PUNCT
ejpam-3406	272	23	r[j]q	r[j]q	PROPN
ejpam-3406	272	24	.	.	PUNCT
ejpam-3406	273	1	(	(	PUNCT
ejpam-3406	273	2	23	23	NUM
ejpam-3406	273	3	)	)	PUNCT
ejpam-3406	273	4	to	to	PART
ejpam-3406	273	5	establish	establish	VERB
ejpam-3406	273	6	the	the	DET
ejpam-3406	273	7	hankel	hankel	NOUN
ejpam-3406	273	8	transform	transform	NOUN
ejpam-3406	273	9	of	of	ADP
ejpam-3406	273	10	d̃m	d̃m	PROPN
ejpam-3406	273	11	,	,	PUNCT
ejpam-3406	273	12	r[n]q	r[n]q	NOUN
ejpam-3406	273	13	,	,	PUNCT
ejpam-3406	273	14	we	we	PRON
ejpam-3406	273	15	need	need	VERB
ejpam-3406	273	16	the	the	DET
ejpam-3406	273	17	concept	concept	NOUN
ejpam-3406	273	18	of	of	ADP
ejpam-3406	273	19	rising	rise	VERB
ejpam-3406	273	20	k	k	ADJ
ejpam-3406	273	21	-	-	ADJ
ejpam-3406	273	22	binomial	binomial	ADJ
ejpam-3406	273	23	transform	transform	NOUN
ejpam-3406	273	24	by	by	ADP
ejpam-3406	273	25	spivey	spivey	PROPN
ejpam-3406	273	26	and	and	CCONJ
ejpam-3406	273	27	steil	steil	PROPN
ejpam-3406	274	1	[	[	X
ejpam-3406	274	2	17	17	NUM
ejpam-3406	274	3	]	]	PUNCT
ejpam-3406	274	4	as	as	ADV
ejpam-3406	274	5	well	well	ADV
ejpam-3406	274	6	as	as	ADP
ejpam-3406	274	7	its	its	PRON
ejpam-3406	274	8	property	property	NOUN
ejpam-3406	274	9	in	in	ADP
ejpam-3406	274	10	relation	relation	NOUN
ejpam-3406	274	11	to	to	PART
ejpam-3406	274	12	hankel	hankel	NOUN
ejpam-3406	274	13	transform	transform	VERB
ejpam-3406	274	14	.	.	PUNCT
ejpam-3406	275	1	definition	definition	NOUN
ejpam-3406	275	2	3	3	NUM
ejpam-3406	275	3	.	.	PUNCT
ejpam-3406	276	1	(	(	PUNCT
ejpam-3406	276	2	spivey	spivey	PROPN
ejpam-3406	276	3	-	-	PUNCT
ejpam-3406	276	4	steil	steil	PROPN
ejpam-3406	277	1	[	[	X
ejpam-3406	277	2	17	17	NUM
ejpam-3406	277	3	]	]	PUNCT
ejpam-3406	277	4	)	)	PUNCT
ejpam-3406	277	5	the	the	DET
ejpam-3406	277	6	rising	rise	VERB
ejpam-3406	277	7	k	k	ADJ
ejpam-3406	277	8	-	-	ADJ
ejpam-3406	277	9	binomial	binomial	ADJ
ejpam-3406	277	10	transform	transform	NOUN
ejpam-3406	277	11	r	r	NOUN
ejpam-3406	277	12	of	of	ADP
ejpam-3406	277	13	a	a	DET
ejpam-3406	277	14	sequence	sequence	NOUN
ejpam-3406	277	15	a	a	PRON
ejpam-3406	277	16	=	=	X
ejpam-3406	277	17	{	{	PUNCT
ejpam-3406	277	18	an	an	PRON
ejpam-3406	277	19	}	}	PUNCT
ejpam-3406	277	20	is	be	AUX
ejpam-3406	277	21	the	the	DET
ejpam-3406	277	22	sequence	sequence	NOUN
ejpam-3406	277	23	r(a	r(a	NOUN
ejpam-3406	277	24	;	;	PUNCT
ejpam-3406	277	25	k	k	X
ejpam-3406	277	26	)	)	PUNCT
ejpam-3406	277	27	=	=	SYM
ejpam-3406	277	28	{	{	PUNCT
ejpam-3406	277	29	rn	rn	PROPN
ejpam-3406	277	30	}	}	PUNCT
ejpam-3406	277	31	,	,	PUNCT
ejpam-3406	277	32	where	where	SCONJ
ejpam-3406	277	33	rn	rn	PROPN
ejpam-3406	277	34	is	be	AUX
ejpam-3406	277	35	given	give	VERB
ejpam-3406	277	36	by	by	ADP
ejpam-3406	277	37	rn	rn	PROPN
ejpam-3406	277	38	=	=	PROPN
ejpam-3406	277	39	n∑	n∑	PROPN
ejpam-3406	277	40	j=0	j=0	PROPN
ejpam-3406	277	41	(	(	PUNCT
ejpam-3406	277	42	n	n	CCONJ
ejpam-3406	277	43	j	j	PROPN
ejpam-3406	277	44	)	)	PUNCT
ejpam-3406	277	45	kjaj	kjaj	PROPN
ejpam-3406	277	46	,	,	PUNCT
ejpam-3406	277	47	k	k	PROPN
ejpam-3406	277	48	6=	6=	PROPN
ejpam-3406	277	49	0	0	NUM
ejpam-3406	277	50	.	.	PUNCT
ejpam-3406	278	1	(	(	PUNCT
ejpam-3406	278	2	24	24	NUM
ejpam-3406	278	3	)	)	PUNCT
ejpam-3406	278	4	we	we	PRON
ejpam-3406	278	5	use	use	VERB
ejpam-3406	278	6	r(a	r(a	PROPN
ejpam-3406	278	7	,	,	PUNCT
ejpam-3406	278	8	k	k	NOUN
ejpam-3406	278	9	)	)	PUNCT
ejpam-3406	278	10	to	to	PART
ejpam-3406	278	11	denote	denote	VERB
ejpam-3406	278	12	the	the	DET
ejpam-3406	278	13	set	set	NOUN
ejpam-3406	278	14	of	of	ADP
ejpam-3406	278	15	rising	rise	VERB
ejpam-3406	278	16	k	k	ADJ
ejpam-3406	278	17	-	-	ADJ
ejpam-3406	278	18	binomial	binomial	ADJ
ejpam-3406	278	19	transform	transform	NOUN
ejpam-3406	278	20	of	of	ADP
ejpam-3406	278	21	a.	a.	NOUN
ejpam-3406	278	22	that	that	PRON
ejpam-3406	278	23	is	be	AUX
ejpam-3406	278	24	,	,	PUNCT
ejpam-3406	278	25	r(a	r(a	PROPN
ejpam-3406	278	26	,	,	PUNCT
ejpam-3406	278	27	k	k	NOUN
ejpam-3406	278	28	)	)	PUNCT
ejpam-3406	278	29	=	=	SYM
ejpam-3406	278	30	{	{	PUNCT
ejpam-3406	278	31	rn	rn	NOUN
ejpam-3406	278	32	}	}	PUNCT
ejpam-3406	278	33	.	.	PUNCT
ejpam-3406	279	1	then	then	ADV
ejpam-3406	279	2	we	we	PRON
ejpam-3406	279	3	have	have	VERB
ejpam-3406	279	4	the	the	DET
ejpam-3406	279	5	following	follow	VERB
ejpam-3406	279	6	theorem	theorem	VERB
ejpam-3406	279	7	by	by	ADP
ejpam-3406	279	8	spivey	spivey	PROPN
ejpam-3406	279	9	and	and	CCONJ
ejpam-3406	279	10	steil	steil	PROPN
ejpam-3406	279	11	.	.	PUNCT
ejpam-3406	280	1	theorem	theorem	VERB
ejpam-3406	280	2	6	6	NUM
ejpam-3406	280	3	.	.	PUNCT
ejpam-3406	281	1	(	(	PUNCT
ejpam-3406	281	2	spivey	spivey	PROPN
ejpam-3406	281	3	-	-	PUNCT
ejpam-3406	281	4	steil	steil	PROPN
ejpam-3406	282	1	[	[	X
ejpam-3406	282	2	17	17	NUM
ejpam-3406	282	3	]	]	PUNCT
ejpam-3406	282	4	)	)	PUNCT
ejpam-3406	282	5	given	give	VERB
ejpam-3406	282	6	a	a	DET
ejpam-3406	282	7	sequence	sequence	NOUN
ejpam-3406	282	8	a	a	PRON
ejpam-3406	282	9	=	=	SYM
ejpam-3406	282	10	{	{	PUNCT
ejpam-3406	282	11	a0	a0	PROPN
ejpam-3406	282	12	,	,	PUNCT
ejpam-3406	282	13	a1	a1	NOUN
ejpam-3406	282	14	,	,	PUNCT
ejpam-3406	282	15	.	.	PUNCT
ejpam-3406	282	16	.	.	PUNCT
ejpam-3406	282	17	.	.	PUNCT
ejpam-3406	283	1	,	,	PUNCT
ejpam-3406	283	2	}	}	PUNCT
ejpam-3406	283	3	.	.	PUNCT
ejpam-3406	284	1	let	let	VERB
ejpam-3406	284	2	h(a	h(a	PROPN
ejpam-3406	284	3	)	)	PUNCT
ejpam-3406	285	1	=	=	PRON
ejpam-3406	285	2	{	{	PUNCT
ejpam-3406	285	3	hn	hn	NOUN
ejpam-3406	285	4	}	}	PUNCT
ejpam-3406	285	5	.	.	PUNCT
ejpam-3406	286	1	then	then	ADV
ejpam-3406	286	2	h(r(a	h(r(a	PROPN
ejpam-3406	286	3	,	,	PUNCT
ejpam-3406	286	4	k	k	NOUN
ejpam-3406	286	5	)	)	PUNCT
ejpam-3406	286	6	)	)	PUNCT
ejpam-3406	287	1	=	=	PRON
ejpam-3406	287	2	{	{	PUNCT
ejpam-3406	287	3	a0	a0	PROPN
ejpam-3406	287	4	,	,	PUNCT
ejpam-3406	287	5	0	0	NUM
ejpam-3406	287	6	,	,	PUNCT
ejpam-3406	287	7	0	0	NUM
ejpam-3406	287	8	,	,	PUNCT
ejpam-3406	287	9	.	.	PUNCT
ejpam-3406	287	10	.	.	PUNCT
ejpam-3406	287	11	.	.	PUNCT
ejpam-3406	288	1	,	,	PUNCT
ejpam-3406	288	2	}	}	PUNCT
ejpam-3406	288	3	.	.	PUNCT
ejpam-3406	289	1	if	if	SCONJ
ejpam-3406	289	2	k	k	PROPN
ejpam-3406	289	3	6=	6=	PROPN
ejpam-3406	289	4	0	0	NUM
ejpam-3406	289	5	,	,	PUNCT
ejpam-3406	289	6	h(r(a	h(r(a	PROPN
ejpam-3406	289	7	,	,	PUNCT
ejpam-3406	289	8	k	k	NOUN
ejpam-3406	289	9	)	)	PUNCT
ejpam-3406	289	10	)	)	PUNCT
ejpam-3406	290	1	=	=	PRON
ejpam-3406	290	2	{	{	PUNCT
ejpam-3406	290	3	kn(n+1)hn	kn(n+1)hn	PROPN
ejpam-3406	290	4	}	}	PUNCT
ejpam-3406	290	5	.	.	PUNCT
ejpam-3406	291	1	now	now	ADV
ejpam-3406	291	2	,	,	PUNCT
ejpam-3406	291	3	we	we	PRON
ejpam-3406	291	4	are	be	AUX
ejpam-3406	291	5	ready	ready	ADJ
ejpam-3406	291	6	to	to	PART
ejpam-3406	291	7	state	state	VERB
ejpam-3406	291	8	the	the	DET
ejpam-3406	291	9	main	main	ADJ
ejpam-3406	291	10	result	result	NOUN
ejpam-3406	291	11	of	of	ADP
ejpam-3406	291	12	the	the	DET
ejpam-3406	291	13	paper	paper	NOUN
ejpam-3406	291	14	.	.	PUNCT
ejpam-3406	292	1	theorem	theorem	VERB
ejpam-3406	292	2	7	7	NUM
ejpam-3406	292	3	.	.	PUNCT
ejpam-3406	293	1	the	the	DET
ejpam-3406	293	2	hankel	hankel	NOUN
ejpam-3406	293	3	transform	transform	NOUN
ejpam-3406	293	4	of	of	ADP
ejpam-3406	293	5	the	the	DET
ejpam-3406	293	6	sequence	sequence	NOUN
ejpam-3406	293	7	of	of	ADP
ejpam-3406	293	8	(	(	PUNCT
ejpam-3406	293	9	q	q	ADJ
ejpam-3406	293	10	,	,	PUNCT
ejpam-3406	293	11	r)-dowling	r)-dowle	VERB
ejpam-3406	293	12	numbers	number	NOUN
ejpam-3406	293	13	{	{	PUNCT
ejpam-3406	293	14	d̃m	d̃m	PROPN
ejpam-3406	293	15	,	,	PUNCT
ejpam-3406	293	16	r[n]q	r[n]q	PROPN
ejpam-3406	293	17	}	}	PUNCT
ejpam-3406	293	18	is	be	AUX
ejpam-3406	293	19	given	give	VERB
ejpam-3406	293	20	by	by	ADP
ejpam-3406	293	21	h(d̃m	h(d̃m	PROPN
ejpam-3406	293	22	,	,	PUNCT
ejpam-3406	293	23	r[n]q	r[n]q	NOUN
ejpam-3406	293	24	)	)	PUNCT
ejpam-3406	293	25	=	=	PUNCT
ejpam-3406	294	1	qm(n+1	qm(n+1	PROPN
ejpam-3406	294	2	3	3	NUM
ejpam-3406	294	3	)	)	PUNCT
ejpam-3406	294	4	−rn(n+1)[0]qm	−rn(n+1)[0]qm	NOUN
ejpam-3406	294	5	!	!	PUNCT
ejpam-3406	295	1	[	[	X
ejpam-3406	295	2	1]qm	1]qm	NUM
ejpam-3406	295	3	!	!	PUNCT
ejpam-3406	295	4	.	.	PUNCT
ejpam-3406	295	5	.	.	PUNCT
ejpam-3406	295	6	.	.	PUNCT
ejpam-3406	296	1	[	[	X
ejpam-3406	296	2	n]qm	n]qm	NOUN
ejpam-3406	296	3	!	!	PUNCT
ejpam-3406	297	1	[	[	X
ejpam-3406	297	2	m	m	X
ejpam-3406	297	3	]	]	X
ejpam-3406	297	4	(	(	PUNCT
ejpam-3406	297	5	n+1	n+1	PROPN
ejpam-3406	297	6	2	2	X
ejpam-3406	297	7	)	)	PUNCT
ejpam-3406	297	8	q	q	NOUN
ejpam-3406	297	9	.	.	PUNCT
ejpam-3406	298	1	(	(	PUNCT
ejpam-3406	298	2	25	25	NUM
ejpam-3406	298	3	)	)	PUNCT
ejpam-3406	298	4	proof	proof	NOUN
ejpam-3406	298	5	.	.	PUNCT
ejpam-3406	299	1	using	use	VERB
ejpam-3406	299	2	equation	equation	NOUN
ejpam-3406	299	3	(	(	PUNCT
ejpam-3406	299	4	18	18	NUM
ejpam-3406	299	5	)	)	PUNCT
ejpam-3406	299	6	in	in	ADP
ejpam-3406	299	7	remark	remark	NOUN
ejpam-3406	299	8	4	4	NUM
ejpam-3406	299	9	,	,	PUNCT
ejpam-3406	299	10	we	we	PRON
ejpam-3406	299	11	have	have	VERB
ejpam-3406	299	12	h(d̃m,0[n]q	h(d̃m,0[n]q	PRON
ejpam-3406	299	13	)	)	PUNCT
ejpam-3406	300	1	=	=	PUNCT
ejpam-3406	300	2	qm(n+1	qm(n+1	PROPN
ejpam-3406	300	3	3	3	NUM
ejpam-3406	300	4	)	)	PUNCT
ejpam-3406	301	1	[	[	X
ejpam-3406	301	2	0]qm	0]qm	NUM
ejpam-3406	301	3	!	!	PUNCT
ejpam-3406	302	1	[	[	X
ejpam-3406	302	2	1]qm	1]qm	NUM
ejpam-3406	302	3	!	!	PUNCT
ejpam-3406	302	4	.	.	PUNCT
ejpam-3406	302	5	.	.	PUNCT
ejpam-3406	302	6	.	.	PUNCT
ejpam-3406	303	1	[	[	X
ejpam-3406	303	2	n]qm	n]qm	NOUN
ejpam-3406	303	3	!	!	PUNCT
ejpam-3406	304	1	[	[	X
ejpam-3406	304	2	m	m	X
ejpam-3406	304	3	]	]	X
ejpam-3406	304	4	(	(	PUNCT
ejpam-3406	304	5	n+1	n+1	PROPN
ejpam-3406	304	6	2	2	X
ejpam-3406	304	7	)	)	PUNCT
ejpam-3406	304	8	q	q	NOUN
ejpam-3406	304	9	.	.	PUNCT
ejpam-3406	305	1	(	(	PUNCT
ejpam-3406	305	2	26	26	NUM
ejpam-3406	305	3	)	)	PUNCT
ejpam-3406	305	4	from	from	ADP
ejpam-3406	305	5	corollary	corollary	ADJ
ejpam-3406	305	6	1	1	NUM
ejpam-3406	305	7	,	,	PUNCT
ejpam-3406	305	8	we	we	PRON
ejpam-3406	305	9	say	say	VERB
ejpam-3406	305	10	that	that	PRON
ejpam-3406	305	11	d̃m	d̃m	PROPN
ejpam-3406	305	12	,	,	PUNCT
ejpam-3406	305	13	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	305	14	is	be	AUX
ejpam-3406	305	15	the	the	DET
ejpam-3406	305	16	binomial	binomial	ADJ
ejpam-3406	305	17	transform	transform	NOUN
ejpam-3406	305	18	of	of	ADP
ejpam-3406	305	19	qnd̃m	qnd̃m	PROPN
ejpam-3406	305	20	,	,	PUNCT
ejpam-3406	305	21	r[n]q	r[n]q	NOUN
ejpam-3406	305	22	.	.	PUNCT
ejpam-3406	306	1	this	this	PRON
ejpam-3406	306	2	means	mean	VERB
ejpam-3406	306	3	that	that	SCONJ
ejpam-3406	306	4	b(qnd̃m	b(qnd̃m	PROPN
ejpam-3406	306	5	,	,	PUNCT
ejpam-3406	306	6	r[n]q	r[n]q	NOUN
ejpam-3406	306	7	)	)	PUNCT
ejpam-3406	306	8	=	=	SYM
ejpam-3406	306	9	d̃m	d̃m	PROPN
ejpam-3406	306	10	,	,	PUNCT
ejpam-3406	306	11	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	306	12	.	.	PUNCT
ejpam-3406	307	1	hence	hence	ADV
ejpam-3406	307	2	,	,	PUNCT
ejpam-3406	307	3	by	by	ADP
ejpam-3406	307	4	layman	layman	PROPN
ejpam-3406	307	5	’s	’s	PART
ejpam-3406	307	6	theorem	theorem	NOUN
ejpam-3406	307	7	[	[	X
ejpam-3406	307	8	12	12	NUM
ejpam-3406	307	9	]	]	PUNCT
ejpam-3406	307	10	,	,	PUNCT
ejpam-3406	307	11	h(b(qnd̃m	h(b(qnd̃m	NOUN
ejpam-3406	307	12	,	,	PUNCT
ejpam-3406	307	13	r[n]q	r[n]q	NOUN
ejpam-3406	307	14	)	)	PUNCT
ejpam-3406	307	15	)	)	PUNCT
ejpam-3406	308	1	=	=	SYM
ejpam-3406	308	2	h(qnd̃m	h(qnd̃m	PROPN
ejpam-3406	308	3	,	,	PUNCT
ejpam-3406	308	4	r[n]q	r[n]q	NOUN
ejpam-3406	308	5	)	)	PUNCT
ejpam-3406	308	6	.	.	PUNCT
ejpam-3406	309	1	r.	r.	PROPN
ejpam-3406	309	2	corcino	corcino	PROPN
ejpam-3406	309	3	,	,	PUNCT
ejpam-3406	309	4	mj	mj	PROPN
ejpam-3406	309	5	.	.	PUNCT
ejpam-3406	309	6	latayada	latayada	PROPN
ejpam-3406	309	7	,	,	PUNCT
ejpam-3406	309	8	mar	mar	PROPN
ejpam-3406	309	9	.	.	PROPN
ejpam-3406	309	10	vega	vega	PROPN
ejpam-3406	309	11	/	/	SYM
ejpam-3406	309	12	eur	eur	PROPN
ejpam-3406	309	13	.	.	PUNCT
ejpam-3406	310	1	j.	j.	PROPN
ejpam-3406	310	2	pure	pure	PROPN
ejpam-3406	310	3	appl	appl	PROPN
ejpam-3406	310	4	.	.	PROPN
ejpam-3406	310	5	math	math	PROPN
ejpam-3406	310	6	,	,	PUNCT
ejpam-3406	310	7	12	12	NUM
ejpam-3406	310	8	(	(	PUNCT
ejpam-3406	310	9	2	2	NUM
ejpam-3406	310	10	)	)	PUNCT
ejpam-3406	310	11	(	(	PUNCT
ejpam-3406	310	12	2019	2019	NUM
ejpam-3406	310	13	)	)	PUNCT
ejpam-3406	310	14	,	,	PUNCT
ejpam-3406	310	15	279	279	NUM
ejpam-3406	310	16	-	-	SYM
ejpam-3406	310	17	293	293	NUM
ejpam-3406	310	18	291	291	NUM
ejpam-3406	310	19	that	that	PRON
ejpam-3406	310	20	is	be	AUX
ejpam-3406	310	21	,	,	PUNCT
ejpam-3406	310	22	h(d̃m	h(d̃m	ADJ
ejpam-3406	310	23	,	,	PUNCT
ejpam-3406	310	24	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	310	25	)	)	PUNCT
ejpam-3406	310	26	=	=	SYM
ejpam-3406	311	1	h(qnd̃m	h(qnd̃m	PROPN
ejpam-3406	311	2	,	,	PUNCT
ejpam-3406	311	3	r[n]q	r[n]q	NOUN
ejpam-3406	311	4	)	)	PUNCT
ejpam-3406	311	5	.	.	PUNCT
ejpam-3406	312	1	now	now	ADV
ejpam-3406	312	2	,	,	PUNCT
ejpam-3406	312	3	corollary	corollary	ADJ
ejpam-3406	312	4	1	1	NUM
ejpam-3406	312	5	can	can	AUX
ejpam-3406	312	6	also	also	ADV
ejpam-3406	312	7	be	be	AUX
ejpam-3406	312	8	stated	state	VERB
ejpam-3406	312	9	as	as	ADP
ejpam-3406	312	10	d̃m	d̃m	PROPN
ejpam-3406	312	11	,	,	PUNCT
ejpam-3406	312	12	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	312	13	is	be	AUX
ejpam-3406	312	14	the	the	DET
ejpam-3406	312	15	rising	rise	VERB
ejpam-3406	312	16	q	q	ADJ
ejpam-3406	312	17	-	-	PUNCT
ejpam-3406	312	18	binomial	binomial	ADJ
ejpam-3406	312	19	transform	transform	NOUN
ejpam-3406	312	20	of	of	ADP
ejpam-3406	312	21	d̃m	d̃m	PROPN
ejpam-3406	312	22	,	,	PUNCT
ejpam-3406	312	23	r[n]q	r[n]q	NOUN
ejpam-3406	312	24	.	.	PUNCT
ejpam-3406	313	1	using	use	VERB
ejpam-3406	313	2	spivey	spivey	PROPN
ejpam-3406	313	3	-	-	PUNCT
ejpam-3406	313	4	steil	steil	PROPN
ejpam-3406	313	5	theorem	theorem	PROPN
ejpam-3406	313	6	,	,	PUNCT
ejpam-3406	313	7	with	with	ADP
ejpam-3406	313	8	a	a	DET
ejpam-3406	313	9	=	=	X
ejpam-3406	313	10	{	{	PUNCT
ejpam-3406	313	11	d̃m	d̃m	PROPN
ejpam-3406	313	12	,	,	PUNCT
ejpam-3406	313	13	r[n]q	r[n]q	PROPN
ejpam-3406	313	14	}	}	PUNCT
ejpam-3406	313	15	,	,	PUNCT
ejpam-3406	313	16	hn	hn	PROPN
ejpam-3406	313	17	=	=	SYM
ejpam-3406	313	18	h(d̃m	h(d̃m	PROPN
ejpam-3406	313	19	,	,	PUNCT
ejpam-3406	313	20	r[n]q	r[n]q	NOUN
ejpam-3406	313	21	)	)	PUNCT
ejpam-3406	313	22	and	and	CCONJ
ejpam-3406	313	23	rn	rn	PROPN
ejpam-3406	313	24	=	=	PROPN
ejpam-3406	313	25	d̃m	d̃m	PROPN
ejpam-3406	313	26	,	,	PUNCT
ejpam-3406	313	27	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	313	28	,	,	PUNCT
ejpam-3406	313	29	we	we	PRON
ejpam-3406	313	30	have	have	VERB
ejpam-3406	313	31	h(d̃m	h(d̃m	PROPN
ejpam-3406	313	32	,	,	PUNCT
ejpam-3406	313	33	r−1[n]q	r−1[n]q	PROPN
ejpam-3406	313	34	)	)	PUNCT
ejpam-3406	314	1	=	=	SYM
ejpam-3406	314	2	qn(n+1)h(d̃m	qn(n+1)h(d̃m	PROPN
ejpam-3406	314	3	,	,	PUNCT
ejpam-3406	314	4	r[n]q	r[n]q	NOUN
ejpam-3406	314	5	)	)	PUNCT
ejpam-3406	314	6	.	.	PUNCT
ejpam-3406	315	1	we	we	PRON
ejpam-3406	315	2	observe	observe	VERB
ejpam-3406	315	3	that	that	SCONJ
ejpam-3406	315	4	,	,	PUNCT
ejpam-3406	315	5	when	when	SCONJ
ejpam-3406	315	6	r	r	NOUN
ejpam-3406	315	7	=	=	SYM
ejpam-3406	315	8	1	1	NUM
ejpam-3406	315	9	and	and	CCONJ
ejpam-3406	315	10	using	use	VERB
ejpam-3406	315	11	(	(	PUNCT
ejpam-3406	315	12	26	26	NUM
ejpam-3406	315	13	)	)	PUNCT
ejpam-3406	315	14	,	,	PUNCT
ejpam-3406	315	15	we	we	PRON
ejpam-3406	315	16	have	have	VERB
ejpam-3406	315	17	h(d̃m,1[n]q	h(d̃m,1[n]q	NOUN
ejpam-3406	315	18	)	)	PUNCT
ejpam-3406	315	19	=	=	PUNCT
ejpam-3406	316	1	q−n(n+1)h(d̃m,0[n]q	q−n(n+1)h(d̃m,0[n]q	X
ejpam-3406	316	2	)	)	PUNCT
ejpam-3406	317	1	=	=	SYM
ejpam-3406	317	2	q−n(n+1)qm(n+1	q−n(n+1)qm(n+1	PROPN
ejpam-3406	317	3	3	3	X
ejpam-3406	317	4	)	)	PUNCT
ejpam-3406	318	1	[	[	X
ejpam-3406	318	2	0]qm	0]qm	NUM
ejpam-3406	318	3	!	!	PUNCT
ejpam-3406	319	1	[	[	X
ejpam-3406	319	2	1]qm	1]qm	NUM
ejpam-3406	319	3	!	!	PUNCT
ejpam-3406	319	4	.	.	PUNCT
ejpam-3406	319	5	.	.	PUNCT
ejpam-3406	319	6	.	.	PUNCT
ejpam-3406	320	1	[	[	X
ejpam-3406	320	2	n]qm	n]qm	NOUN
ejpam-3406	320	3	!	!	PUNCT
ejpam-3406	321	1	[	[	X
ejpam-3406	321	2	m	m	X
ejpam-3406	321	3	]	]	X
ejpam-3406	321	4	(	(	PUNCT
ejpam-3406	321	5	n+1	n+1	PROPN
ejpam-3406	321	6	2	2	X
ejpam-3406	321	7	)	)	PUNCT
ejpam-3406	321	8	q	q	NOUN
ejpam-3406	322	1	=	=	PUNCT
ejpam-3406	322	2	qm(n+1	qm(n+1	PROPN
ejpam-3406	322	3	3	3	NUM
ejpam-3406	322	4	)	)	PUNCT
ejpam-3406	322	5	−n(n+1)[0]qm	−n(n+1)[0]qm	X
ejpam-3406	322	6	!	!	PUNCT
ejpam-3406	323	1	[	[	X
ejpam-3406	323	2	1]qm	1]qm	NUM
ejpam-3406	323	3	!	!	PUNCT
ejpam-3406	323	4	.	.	PUNCT
ejpam-3406	323	5	.	.	PUNCT
ejpam-3406	323	6	.	.	PUNCT
ejpam-3406	324	1	[	[	X
ejpam-3406	324	2	n]qm	n]qm	NOUN
ejpam-3406	324	3	!	!	PUNCT
ejpam-3406	325	1	[	[	X
ejpam-3406	325	2	m	m	X
ejpam-3406	325	3	]	]	X
ejpam-3406	325	4	(	(	PUNCT
ejpam-3406	325	5	n+1	n+1	PROPN
ejpam-3406	325	6	2	2	X
ejpam-3406	325	7	)	)	PUNCT
ejpam-3406	325	8	q	q	NOUN
ejpam-3406	326	1	also	also	ADV
ejpam-3406	326	2	,	,	PUNCT
ejpam-3406	326	3	when	when	SCONJ
ejpam-3406	326	4	r	r	NOUN
ejpam-3406	326	5	=	=	SYM
ejpam-3406	326	6	2	2	NUM
ejpam-3406	326	7	,	,	PUNCT
ejpam-3406	326	8	h(d̃m,2[n]q	h(d̃m,2[n]q	NOUN
ejpam-3406	326	9	)	)	PUNCT
ejpam-3406	326	10	=	=	PUNCT
ejpam-3406	326	11	qm(n+1	qm(n+1	PROPN
ejpam-3406	326	12	3	3	NUM
ejpam-3406	326	13	)	)	PUNCT
ejpam-3406	326	14	−2n(n+1)[0]qm	−2n(n+1)[0]qm	PROPN
ejpam-3406	326	15	!	!	PUNCT
ejpam-3406	327	1	[	[	X
ejpam-3406	327	2	1]qm	1]qm	NUM
ejpam-3406	327	3	!	!	PUNCT
ejpam-3406	327	4	.	.	PUNCT
ejpam-3406	327	5	.	.	PUNCT
ejpam-3406	327	6	.	.	PUNCT
ejpam-3406	328	1	[	[	X
ejpam-3406	328	2	n]qm	n]qm	NOUN
ejpam-3406	328	3	!	!	PUNCT
ejpam-3406	329	1	[	[	X
ejpam-3406	329	2	m	m	X
ejpam-3406	329	3	]	]	X
ejpam-3406	329	4	(	(	PUNCT
ejpam-3406	329	5	n+1	n+1	PROPN
ejpam-3406	329	6	2	2	X
ejpam-3406	329	7	)	)	PUNCT
ejpam-3406	329	8	q	q	NOUN
ejpam-3406	329	9	.	.	PUNCT
ejpam-3406	330	1	continuing	continue	VERB
ejpam-3406	330	2	this	this	DET
ejpam-3406	330	3	argument	argument	NOUN
ejpam-3406	330	4	,	,	PUNCT
ejpam-3406	330	5	we	we	PRON
ejpam-3406	330	6	obtain	obtain	VERB
ejpam-3406	330	7	h(d̃m	h(d̃m	PROPN
ejpam-3406	330	8	,	,	PUNCT
ejpam-3406	330	9	r[n]q	r[n]q	NOUN
ejpam-3406	330	10	)	)	PUNCT
ejpam-3406	330	11	=	=	PUNCT
ejpam-3406	331	1	qm(n+1	qm(n+1	PROPN
ejpam-3406	331	2	3	3	NUM
ejpam-3406	331	3	)	)	PUNCT
ejpam-3406	331	4	−rn(n+1)[0]qm	−rn(n+1)[0]qm	NOUN
ejpam-3406	331	5	!	!	PUNCT
ejpam-3406	332	1	[	[	X
ejpam-3406	332	2	1]qm	1]qm	NUM
ejpam-3406	332	3	!	!	PUNCT
ejpam-3406	332	4	.	.	PUNCT
ejpam-3406	332	5	.	.	PUNCT
ejpam-3406	332	6	.	.	PUNCT
ejpam-3406	333	1	[	[	X
ejpam-3406	333	2	n]qm	n]qm	NOUN
ejpam-3406	333	3	!	!	PUNCT
ejpam-3406	334	1	[	[	X
ejpam-3406	334	2	m	m	X
ejpam-3406	334	3	]	]	X
ejpam-3406	334	4	(	(	PUNCT
ejpam-3406	334	5	n+1	n+1	PROPN
ejpam-3406	334	6	2	2	X
ejpam-3406	334	7	)	)	PUNCT
ejpam-3406	334	8	q	q	PROPN
ejpam-3406	334	9	�	�	PROPN
ejpam-3406	334	10	remark	remark	NOUN
ejpam-3406	334	11	5	5	NUM
ejpam-3406	334	12	.	.	PUNCT
ejpam-3406	335	1	when	when	SCONJ
ejpam-3406	335	2	m	m	VERB
ejpam-3406	335	3	=	=	SYM
ejpam-3406	335	4	1	1	NUM
ejpam-3406	335	5	,	,	PUNCT
ejpam-3406	335	6	the	the	DET
ejpam-3406	335	7	hankel	hankel	NOUN
ejpam-3406	335	8	transform	transform	VERB
ejpam-3406	335	9	in	in	ADP
ejpam-3406	335	10	(	(	PUNCT
ejpam-3406	335	11	25	25	NUM
ejpam-3406	335	12	)	)	PUNCT
ejpam-3406	335	13	reduces	reduce	VERB
ejpam-3406	335	14	to	to	ADP
ejpam-3406	335	15	h(d̃1,r[n]q	h(d̃1,r[n]q	PROPN
ejpam-3406	335	16	)	)	PUNCT
ejpam-3406	336	1	=	=	SYM
ejpam-3406	337	1	q	q	X
ejpam-3406	337	2	(	(	PUNCT
ejpam-3406	337	3	n+1	n+1	PROPN
ejpam-3406	337	4	3	3	NUM
ejpam-3406	337	5	)	)	PUNCT
ejpam-3406	337	6	−rn(n+1)[0]![1	−rn(n+1)[0]![1	NOUN
ejpam-3406	337	7	]	]	PUNCT
ejpam-3406	337	8	!	!	PUNCT
ejpam-3406	337	9	.	.	PUNCT
ejpam-3406	337	10	.	.	PUNCT
ejpam-3406	337	11	.	.	PUNCT
ejpam-3406	338	1	[	[	X
ejpam-3406	338	2	n	n	X
ejpam-3406	338	3	]	]	PUNCT
ejpam-3406	338	4	!	!	PUNCT
ejpam-3406	338	5	,	,	PUNCT
ejpam-3406	338	6	which	which	PRON
ejpam-3406	338	7	is	be	AUX
ejpam-3406	338	8	exactly	exactly	ADV
ejpam-3406	338	9	the	the	DET
ejpam-3406	338	10	hankel	hankel	NOUN
ejpam-3406	338	11	transform	transform	VERB
ejpam-3406	338	12	for	for	ADP
ejpam-3406	338	13	the	the	DET
ejpam-3406	338	14	q	q	ADJ
ejpam-3406	338	15	-	-	ADJ
ejpam-3406	338	16	noncentral	noncentral	ADJ
ejpam-3406	338	17	bell	bell	NOUN
ejpam-3406	338	18	numbers	number	NOUN
ejpam-3406	338	19	in	in	ADP
ejpam-3406	338	20	[	[	X
ejpam-3406	338	21	9	9	NUM
ejpam-3406	338	22	]	]	PUNCT
ejpam-3406	338	23	.	.	PUNCT
ejpam-3406	339	1	remark	remark	PROPN
ejpam-3406	339	2	6	6	NUM
ejpam-3406	339	3	.	.	PUNCT
ejpam-3406	340	1	when	when	SCONJ
ejpam-3406	340	2	q	q	X
ejpam-3406	340	3	→	→	SYM
ejpam-3406	340	4	1	1	NUM
ejpam-3406	340	5	,	,	PUNCT
ejpam-3406	340	6	the	the	DET
ejpam-3406	340	7	hankel	hankel	NOUN
ejpam-3406	340	8	transform	transform	VERB
ejpam-3406	340	9	in	in	ADP
ejpam-3406	340	10	(	(	PUNCT
ejpam-3406	340	11	25	25	NUM
ejpam-3406	340	12	)	)	PUNCT
ejpam-3406	340	13	yields	yield	NOUN
ejpam-3406	340	14	h(d̃m	h(d̃m	PROPN
ejpam-3406	340	15	,	,	PUNCT
ejpam-3406	340	16	r[n]q	r[n]q	NOUN
ejpam-3406	340	17	)	)	PUNCT
ejpam-3406	340	18	=	=	PUNCT
ejpam-3406	341	1	[	[	X
ejpam-3406	341	2	0]![1	0]![1	X
ejpam-3406	341	3	]	]	X
ejpam-3406	341	4	!	!	PUNCT
ejpam-3406	341	5	.	.	PUNCT
ejpam-3406	341	6	.	.	PUNCT
ejpam-3406	341	7	.	.	PUNCT
ejpam-3406	342	1	[	[	X
ejpam-3406	342	2	n]!m(n+1	n]!m(n+1	NOUN
ejpam-3406	342	3	2	2	NUM
ejpam-3406	342	4	)	)	PUNCT
ejpam-3406	342	5	,	,	PUNCT
ejpam-3406	342	6	which	which	PRON
ejpam-3406	342	7	is	be	AUX
ejpam-3406	342	8	exactly	exactly	ADV
ejpam-3406	342	9	the	the	DET
ejpam-3406	342	10	hankel	hankel	NOUN
ejpam-3406	342	11	transform	transform	VERB
ejpam-3406	342	12	for	for	ADP
ejpam-3406	342	13	the	the	DET
ejpam-3406	342	14	q	q	NOUN
ejpam-3406	342	15	-	-	PUNCT
ejpam-3406	342	16	analogue	analogue	NOUN
ejpam-3406	342	17	of	of	ADP
ejpam-3406	342	18	(	(	PUNCT
ejpam-3406	342	19	r	r	NOUN
ejpam-3406	342	20	,	,	PUNCT
ejpam-3406	342	21	β)-bell	β)-bell	PUNCT
ejpam-3406	342	22	numbers	number	NOUN
ejpam-3406	342	23	in	in	ADP
ejpam-3406	342	24	[	[	X
ejpam-3406	342	25	9	9	NUM
ejpam-3406	342	26	]	]	PUNCT
ejpam-3406	342	27	.	.	PUNCT
ejpam-3406	343	1	remark	remark	PROPN
ejpam-3406	343	2	7	7	NUM
ejpam-3406	343	3	.	.	PUNCT
ejpam-3406	344	1	the	the	DET
ejpam-3406	344	2	hankel	hankel	NOUN
ejpam-3406	344	3	transform	transform	VERB
ejpam-3406	344	4	in	in	ADP
ejpam-3406	344	5	(	(	PUNCT
ejpam-3406	344	6	25	25	NUM
ejpam-3406	344	7	)	)	PUNCT
ejpam-3406	344	8	can	can	AUX
ejpam-3406	344	9	also	also	ADV
ejpam-3406	344	10	be	be	AUX
ejpam-3406	344	11	written	write	VERB
ejpam-3406	344	12	as	as	ADP
ejpam-3406	344	13	h(d̃m	h(d̃m	PROPN
ejpam-3406	344	14	,	,	PUNCT
ejpam-3406	344	15	r[n]q	r[n]q	NOUN
ejpam-3406	344	16	)	)	PUNCT
ejpam-3406	344	17	=	=	PUNCT
ejpam-3406	345	1	qm(n+1	qm(n+1	PROPN
ejpam-3406	345	2	3	3	NUM
ejpam-3406	345	3	)	)	PUNCT
ejpam-3406	345	4	n∏	n∏	NOUN
ejpam-3406	345	5	k=0	k=0	PROPN
ejpam-3406	346	1	q−2rk[m]kq	q−2rk[m]kq	PROPN
ejpam-3406	347	1	[	[	X
ejpam-3406	347	2	k]qm	k]qm	X
ejpam-3406	347	3	!	!	PUNCT
ejpam-3406	348	1	such	such	ADJ
ejpam-3406	348	2	that	that	PRON
ejpam-3406	348	3	,	,	PUNCT
ejpam-3406	348	4	when	when	SCONJ
ejpam-3406	348	5	r	r	NOUN
ejpam-3406	348	6	=	=	SYM
ejpam-3406	348	7	0	0	NUM
ejpam-3406	348	8	,	,	PUNCT
ejpam-3406	348	9	we	we	PRON
ejpam-3406	348	10	have	have	VERB
ejpam-3406	348	11	h(d̃m,0[n]q	h(d̃m,0[n]q	PRON
ejpam-3406	348	12	)	)	PUNCT
ejpam-3406	349	1	=	=	SYM
ejpam-3406	349	2	qm(n+1	qm(n+1	PROPN
ejpam-3406	349	3	3	3	NUM
ejpam-3406	349	4	)	)	PUNCT
ejpam-3406	349	5	n∏	n∏	NOUN
ejpam-3406	349	6	k=0	k=0	PROPN
ejpam-3406	350	1	[	[	X
ejpam-3406	350	2	m]kq	m]kq	X
ejpam-3406	350	3	[	[	X
ejpam-3406	350	4	k]qm	k]qm	PROPN
ejpam-3406	350	5	!	!	PUNCT
ejpam-3406	350	6	,	,	PUNCT
ejpam-3406	350	7	which	which	PRON
ejpam-3406	350	8	is	be	AUX
ejpam-3406	350	9	exactly	exactly	ADV
ejpam-3406	350	10	the	the	DET
ejpam-3406	350	11	conjectured	conjecture	VERB
ejpam-3406	350	12	hankel	hankel	NOUN
ejpam-3406	350	13	transform	transform	NOUN
ejpam-3406	350	14	in	in	ADP
ejpam-3406	350	15	(	(	PUNCT
ejpam-3406	350	16	1	1	NUM
ejpam-3406	350	17	)	)	PUNCT
ejpam-3406	350	18	with	with	ADP
ejpam-3406	350	19	m	m	PROPN
ejpam-3406	350	20	=	=	SYM
ejpam-3406	350	21	β	β	X
ejpam-3406	350	22	and	and	CCONJ
ejpam-3406	350	23	n∏	n∏	PROPN
ejpam-3406	350	24	k=0	k=0	PROPN
ejpam-3406	350	25	f(n	f(n	PROPN
ejpam-3406	350	26	,	,	PUNCT
ejpam-3406	350	27	k	k	NOUN
ejpam-3406	350	28	)	)	PUNCT
ejpam-3406	350	29	=	=	SYM
ejpam-3406	350	30	qm(n+1	qm(n+1	PROPN
ejpam-3406	350	31	3	3	NUM
ejpam-3406	350	32	)	)	PUNCT
ejpam-3406	350	33	.	.	PUNCT
ejpam-3406	351	1	references	reference	NOUN
ejpam-3406	351	2	292	292	NUM
ejpam-3406	351	3	acknowledgements	acknowledgement	NOUN
ejpam-3406	351	4	the	the	DET
ejpam-3406	351	5	first	first	ADJ
ejpam-3406	351	6	author	author	NOUN
ejpam-3406	351	7	would	would	AUX
ejpam-3406	351	8	like	like	VERB
ejpam-3406	351	9	to	to	PART
ejpam-3406	351	10	thank	thank	VERB
ejpam-3406	351	11	cebu	cebu	NOUN
ejpam-3406	351	12	normal	normal	ADJ
ejpam-3406	351	13	university	university	NOUN
ejpam-3406	351	14	(	(	PUNCT
ejpam-3406	351	15	cnu	cnu	PROPN
ejpam-3406	351	16	)	)	PUNCT
ejpam-3406	351	17	and	and	CCONJ
ejpam-3406	351	18	the	the	DET
ejpam-3406	351	19	commission	commission	NOUN
ejpam-3406	351	20	on	on	ADP
ejpam-3406	351	21	higher	high	ADJ
ejpam-3406	351	22	education	education	NOUN
ejpam-3406	351	23	-	-	PUNCT
ejpam-3406	351	24	grants	grant	NOUN
ejpam-3406	351	25	-	-	PUNCT
ejpam-3406	351	26	in	in	ADP
ejpam-3406	351	27	-	-	PUNCT
ejpam-3406	351	28	aid	aid	NOUN
ejpam-3406	351	29	for	for	ADP
ejpam-3406	351	30	research	research	NOUN
ejpam-3406	351	31	(	(	PUNCT
ejpam-3406	351	32	ched	che	VERB
ejpam-3406	351	33	-	-	PUNCT
ejpam-3406	351	34	gia	gia	NOUN
ejpam-3406	351	35	)	)	PUNCT
ejpam-3406	351	36	for	for	ADP
ejpam-3406	351	37	the	the	DET
ejpam-3406	351	38	financial	financial	ADJ
ejpam-3406	351	39	support	support	NOUN
ejpam-3406	351	40	extended	extend	VERB
ejpam-3406	351	41	to	to	ADP
ejpam-3406	351	42	this	this	DET
ejpam-3406	351	43	project	project	NOUN
ejpam-3406	351	44	.	.	PUNCT
ejpam-3406	352	1	the	the	DET
ejpam-3406	352	2	second	second	ADJ
ejpam-3406	352	3	author	author	NOUN
ejpam-3406	352	4	would	would	AUX
ejpam-3406	352	5	also	also	ADV
ejpam-3406	352	6	like	like	VERB
ejpam-3406	352	7	to	to	PART
ejpam-3406	352	8	thank	thank	VERB
ejpam-3406	352	9	the	the	DET
ejpam-3406	352	10	commission	commission	NOUN
ejpam-3406	352	11	on	on	ADP
ejpam-3406	352	12	higher	high	ADJ
ejpam-3406	352	13	education	education	NOUN
ejpam-3406	352	14	-	-	PUNCT
ejpam-3406	352	15	faculty	faculty	NOUN
ejpam-3406	352	16	development	development	NOUN
ejpam-3406	352	17	program	program	NOUN
ejpam-3406	352	18	(	(	PUNCT
ejpam-3406	352	19	ched	che	VERB
ejpam-3406	352	20	-	-	PUNCT
ejpam-3406	352	21	fdp	fdp	NOUN
ejpam-3406	352	22	)	)	PUNCT
ejpam-3406	352	23	for	for	ADP
ejpam-3406	352	24	providing	provide	VERB
ejpam-3406	352	25	her	her	PRON
ejpam-3406	352	26	financial	financial	ADJ
ejpam-3406	352	27	support	support	NOUN
ejpam-3406	352	28	in	in	ADP
ejpam-3406	352	29	pursuing	pursue	VERB
ejpam-3406	352	30	ph.d	ph.d	PROPN
ejpam-3406	352	31	.	.	PUNCT
ejpam-3406	353	1	math	math	PROPN
ejpam-3406	353	2	program	program	NOUN
ejpam-3406	353	3	at	at	ADP
ejpam-3406	353	4	the	the	DET
ejpam-3406	353	5	mathematics	mathematics	PROPN
ejpam-3406	353	6	department	department	PROPN
ejpam-3406	353	7	of	of	ADP
ejpam-3406	353	8	msu	msu	PROPN
ejpam-3406	353	9	iligan	iligan	PROPN
ejpam-3406	353	10	institute	institute	PROPN
ejpam-3406	353	11	of	of	ADP
ejpam-3406	353	12	technology	technology	PROPN
ejpam-3406	353	13	.	.	PUNCT
ejpam-3406	354	1	lastly	lastly	ADV
ejpam-3406	354	2	,	,	PUNCT
ejpam-3406	354	3	the	the	DET
ejpam-3406	354	4	authors	author	NOUN
ejpam-3406	354	5	would	would	AUX
ejpam-3406	354	6	like	like	VERB
ejpam-3406	354	7	to	to	PART
ejpam-3406	354	8	thank	thank	VERB
ejpam-3406	354	9	the	the	DET
ejpam-3406	354	10	two	two	NUM
ejpam-3406	354	11	anonymous	anonymous	ADJ
ejpam-3406	354	12	referees	referee	NOUN
ejpam-3406	354	13	for	for	ADP
ejpam-3406	354	14	spending	spend	VERB
ejpam-3406	354	15	their	their	PRON
ejpam-3406	354	16	free	free	ADJ
ejpam-3406	354	17	time	time	NOUN
ejpam-3406	354	18	in	in	ADP
ejpam-3406	354	19	reviewing	review	VERB
ejpam-3406	354	20	our	our	PRON
ejpam-3406	354	21	paper	paper	NOUN
ejpam-3406	354	22	.	.	PUNCT
ejpam-3406	355	1	their	their	PRON
ejpam-3406	355	2	comments	comment	NOUN
ejpam-3406	355	3	and	and	CCONJ
ejpam-3406	355	4	suggestions	suggestion	NOUN
ejpam-3406	355	5	have	have	AUX
ejpam-3406	355	6	helped	help	VERB
ejpam-3406	355	7	a	a	DET
ejpam-3406	355	8	lot	lot	NOUN
ejpam-3406	355	9	in	in	ADP
ejpam-3406	355	10	improving	improve	VERB
ejpam-3406	355	11	the	the	DET
ejpam-3406	355	12	paper	paper	NOUN
ejpam-3406	355	13	.	.	PUNCT
ejpam-3406	356	1	references	reference	NOUN
ejpam-3406	356	2	[	[	X
ejpam-3406	356	3	1	1	NUM
ejpam-3406	356	4	]	]	PUNCT
ejpam-3406	356	5	aigner	aigner	NOUN
ejpam-3406	356	6	,	,	PUNCT
ejpam-3406	356	7	m.	m.	NOUN
ejpam-3406	356	8	,	,	PUNCT
ejpam-3406	356	9	a	a	DET
ejpam-3406	356	10	characterization	characterization	NOUN
ejpam-3406	356	11	of	of	ADP
ejpam-3406	356	12	the	the	DET
ejpam-3406	356	13	bell	bell	NOUN
ejpam-3406	356	14	numbers	number	NOUN
ejpam-3406	356	15	,	,	PUNCT
ejpam-3406	356	16	discrete	discrete	ADJ
ejpam-3406	356	17	math	math	NOUN
ejpam-3406	356	18	.	.	PUNCT
ejpam-3406	357	1	205	205	NUM
ejpam-3406	357	2	(	(	PUNCT
ejpam-3406	357	3	1999	1999	NUM
ejpam-3406	357	4	)	)	PUNCT
ejpam-3406	357	5	,	,	PUNCT
ejpam-3406	357	6	207	207	NUM
ejpam-3406	357	7	-	-	SYM
ejpam-3406	357	8	210	210	NUM
ejpam-3406	357	9	.	.	PUNCT
ejpam-3406	358	1	[	[	X
ejpam-3406	358	2	2	2	NUM
ejpam-3406	358	3	]	]	PUNCT
ejpam-3406	358	4	carlitz	carlitz	PROPN
ejpam-3406	358	5	,	,	PUNCT
ejpam-3406	358	6	l.	l.	PROPN
ejpam-3406	358	7	,	,	PUNCT
ejpam-3406	358	8	q	q	ADJ
ejpam-3406	358	9	-	-	PUNCT
ejpam-3406	358	10	bernoulli	bernoulli	NOUN
ejpam-3406	358	11	numbers	number	NOUN
ejpam-3406	358	12	and	and	CCONJ
ejpam-3406	358	13	polynomials	polynomial	NOUN
ejpam-3406	358	14	.	.	PUNCT
ejpam-3406	359	1	duke	duke	PROPN
ejpam-3406	359	2	math	math	PROPN
ejpam-3406	359	3	.	.	PUNCT
ejpam-3406	360	1	j.	j.	PROPN
ejpam-3406	360	2	15	15	NUM
ejpam-3406	360	3	(	(	PUNCT
ejpam-3406	360	4	1948	1948	NUM
ejpam-3406	360	5	)	)	PUNCT
ejpam-3406	360	6	987	987	NUM
ejpam-3406	360	7	-	-	SYM
ejpam-3406	360	8	1000	1000	NUM
ejpam-3406	360	9	.	.	PUNCT
ejpam-3406	361	1	[	[	X
ejpam-3406	361	2	3	3	NUM
ejpam-3406	361	3	]	]	X
ejpam-3406	361	4	cheon	cheon	X
ejpam-3406	361	5	,	,	PUNCT
ejpam-3406	361	6	g.s	g.s	PROPN
ejpam-3406	361	7	.	.	PROPN
ejpam-3406	361	8	and	and	CCONJ
ejpam-3406	361	9	jung	jung	PROPN
ejpam-3406	361	10	,	,	PUNCT
ejpam-3406	361	11	j.h	j.h	PROPN
ejpam-3406	361	12	.	.	PROPN
ejpam-3406	361	13	,	,	PUNCT
ejpam-3406	361	14	r	r	X
ejpam-3406	361	15	-	-	PUNCT
ejpam-3406	361	16	whitney	whitney	NOUN
ejpam-3406	361	17	number	number	NOUN
ejpam-3406	361	18	of	of	ADP
ejpam-3406	361	19	dowling	dowling	NOUN
ejpam-3406	361	20	lattices	lattice	NOUN
ejpam-3406	361	21	,	,	PUNCT
ejpam-3406	361	22	discrete	discrete	ADJ
ejpam-3406	361	23	math	math	NOUN
ejpam-3406	361	24	.	.	PUNCT
ejpam-3406	362	1	312(2012	312(2012	NUM
ejpam-3406	362	2	)	)	PUNCT
ejpam-3406	362	3	,	,	PUNCT
ejpam-3406	362	4	2337–2348	2337–2348	NUM
ejpam-3406	362	5	.	.	PUNCT
ejpam-3406	363	1	[	[	X
ejpam-3406	363	2	4	4	NUM
ejpam-3406	363	3	]	]	X
ejpam-3406	363	4	comtet	comtet	NOUN
ejpam-3406	363	5	,	,	PUNCT
ejpam-3406	363	6	l.	l.	PROPN
ejpam-3406	363	7	,	,	PUNCT
ejpam-3406	363	8	advanced	advanced	ADJ
ejpam-3406	363	9	combinatorics	combinatoric	NOUN
ejpam-3406	363	10	,	,	PUNCT
ejpam-3406	363	11	reidel	reidel	PROPN
ejpam-3406	363	12	,	,	PUNCT
ejpam-3406	363	13	dordrecht	dordrecht	PROPN
ejpam-3406	363	14	,	,	PUNCT
ejpam-3406	363	15	the	the	DET
ejpam-3406	363	16	netherlands	netherlands	PROPN
ejpam-3406	363	17	,	,	PUNCT
ejpam-3406	363	18	1974	1974	NUM
ejpam-3406	363	19	.	.	PUNCT
ejpam-3406	364	1	[	[	X
ejpam-3406	364	2	5	5	NUM
ejpam-3406	364	3	]	]	X
ejpam-3406	364	4	corcino	corcino	NOUN
ejpam-3406	364	5	,	,	PUNCT
ejpam-3406	364	6	r.b	r.b	PROPN
ejpam-3406	364	7	.	.	PROPN
ejpam-3406	364	8	,	,	PUNCT
ejpam-3406	364	9	the	the	DET
ejpam-3406	364	10	(	(	PUNCT
ejpam-3406	364	11	r	r	NOUN
ejpam-3406	364	12	,	,	PUNCT
ejpam-3406	364	13	β)-stirling	β)-stirle	VERB
ejpam-3406	364	14	numbers	number	NOUN
ejpam-3406	364	15	.	.	PUNCT
ejpam-3406	365	1	mindanao	mindanao	PROPN
ejpam-3406	365	2	forum	forum	PROPN
ejpam-3406	365	3	.	.	PUNCT
ejpam-3406	366	1	14(2	14(2	NUM
ejpam-3406	366	2	)	)	PUNCT
ejpam-3406	366	3	(	(	PUNCT
ejpam-3406	366	4	1999	1999	NUM
ejpam-3406	366	5	)	)	PUNCT
ejpam-3406	366	6	.	.	PUNCT
ejpam-3406	367	1	[	[	X
ejpam-3406	367	2	6	6	NUM
ejpam-3406	367	3	]	]	X
ejpam-3406	367	4	corcino	corcino	NOUN
ejpam-3406	367	5	,	,	PUNCT
ejpam-3406	367	6	r.b	r.b	PROPN
ejpam-3406	367	7	.	.	PROPN
ejpam-3406	367	8	and	and	CCONJ
ejpam-3406	367	9	cañete	cañete	PROPN
ejpam-3406	367	10	,	,	PUNCT
ejpam-3406	367	11	j.t	j.t	PROPN
ejpam-3406	367	12	.	.	PROPN
ejpam-3406	367	13	,	,	PUNCT
ejpam-3406	367	14	a	a	DET
ejpam-3406	367	15	q	q	NOUN
ejpam-3406	367	16	-	-	PUNCT
ejpam-3406	367	17	analogue	analogue	NOUN
ejpam-3406	367	18	of	of	ADP
ejpam-3406	367	19	r	r	NOUN
ejpam-3406	367	20	-	-	PUNCT
ejpam-3406	367	21	whitney	whitney	NOUN
ejpam-3406	367	22	numbers	number	NOUN
ejpam-3406	367	23	of	of	ADP
ejpam-3406	367	24	the	the	DET
ejpam-3406	367	25	second	second	ADJ
ejpam-3406	367	26	kind	kind	NOUN
ejpam-3406	367	27	,	,	PUNCT
ejpam-3406	367	28	preprint	preprint	NOUN
ejpam-3406	367	29	.	.	PUNCT
ejpam-3406	368	1	[	[	X
ejpam-3406	368	2	7	7	NUM
ejpam-3406	368	3	]	]	X
ejpam-3406	368	4	corcino	corcino	NOUN
ejpam-3406	368	5	,	,	PUNCT
ejpam-3406	368	6	r.b	r.b	PROPN
ejpam-3406	368	7	.	.	PROPN
ejpam-3406	368	8	and	and	CCONJ
ejpam-3406	368	9	corcino	corcino	PROPN
ejpam-3406	368	10	,	,	PUNCT
ejpam-3406	368	11	c.b	c.b	PROPN
ejpam-3406	368	12	.	.	PROPN
ejpam-3406	368	13	,	,	PUNCT
ejpam-3406	368	14	the	the	DET
ejpam-3406	368	15	hankel	hankel	NOUN
ejpam-3406	368	16	transform	transform	NOUN
ejpam-3406	368	17	of	of	ADP
ejpam-3406	368	18	generalized	generalized	ADJ
ejpam-3406	368	19	bell	bell	NOUN
ejpam-3406	368	20	numbers	number	NOUN
ejpam-3406	368	21	and	and	CCONJ
ejpam-3406	368	22	its	its	PRON
ejpam-3406	368	23	q	q	NOUN
ejpam-3406	368	24	-	-	PUNCT
ejpam-3406	368	25	analogue	analogue	NOUN
ejpam-3406	368	26	,	,	PUNCT
ejpam-3406	368	27	utilitas	utilitas	PROPN
ejpam-3406	368	28	mathematica	mathematica	PROPN
ejpam-3406	368	29	,	,	PUNCT
ejpam-3406	368	30	89	89	NUM
ejpam-3406	368	31	(	(	PUNCT
ejpam-3406	368	32	2012	2012	NUM
ejpam-3406	368	33	)	)	PUNCT
ejpam-3406	368	34	,	,	PUNCT
ejpam-3406	368	35	297	297	NUM
ejpam-3406	368	36	-	-	SYM
ejpam-3406	368	37	309	309	NUM
ejpam-3406	368	38	.	.	PUNCT
ejpam-3406	369	1	[	[	X
ejpam-3406	369	2	8	8	NUM
ejpam-3406	369	3	]	]	X
ejpam-3406	369	4	corcino	corcino	NOUN
ejpam-3406	369	5	,	,	PUNCT
ejpam-3406	369	6	r.b	r.b	PROPN
ejpam-3406	369	7	.	.	PROPN
ejpam-3406	369	8	and	and	CCONJ
ejpam-3406	369	9	corcino	corcino	PROPN
ejpam-3406	369	10	,	,	PUNCT
ejpam-3406	369	11	c.b	c.b	PROPN
ejpam-3406	369	12	.	.	PROPN
ejpam-3406	369	13	,	,	PUNCT
ejpam-3406	369	14	and	and	CCONJ
ejpam-3406	369	15	aldema	aldema	PROPN
ejpam-3406	369	16	,	,	PUNCT
ejpam-3406	369	17	r.	r.	PROPN
ejpam-3406	369	18	,	,	PUNCT
ejpam-3406	369	19	asymptotic	asymptotic	ADJ
ejpam-3406	369	20	normality	normality	NOUN
ejpam-3406	369	21	of	of	ADP
ejpam-3406	369	22	the	the	DET
ejpam-3406	369	23	(	(	PUNCT
ejpam-3406	369	24	r	r	NOUN
ejpam-3406	369	25	,	,	PUNCT
ejpam-3406	369	26	β)stirling	β)stirle	VERB
ejpam-3406	369	27	numbers	number	NOUN
ejpam-3406	369	28	,	,	PUNCT
ejpam-3406	369	29	ars	ar	VERB
ejpam-3406	369	30	combinatorics	combinatoric	NOUN
ejpam-3406	369	31	,	,	PUNCT
ejpam-3406	369	32	81	81	NUM
ejpam-3406	369	33	(	(	PUNCT
ejpam-3406	369	34	2006	2006	NUM
ejpam-3406	369	35	)	)	PUNCT
ejpam-3406	369	36	,	,	PUNCT
ejpam-3406	369	37	81	81	NUM
ejpam-3406	369	38	-	-	SYM
ejpam-3406	369	39	96	96	NUM
ejpam-3406	369	40	.	.	PUNCT
ejpam-3406	370	1	[	[	X
ejpam-3406	370	2	9	9	NUM
ejpam-3406	370	3	]	]	SYM
ejpam-3406	370	4	corcino	corcino	NOUN
ejpam-3406	370	5	,	,	PUNCT
ejpam-3406	370	6	c.b	c.b	PROPN
ejpam-3406	370	7	.	.	PROPN
ejpam-3406	370	8	,	,	PUNCT
ejpam-3406	370	9	corcino	corcino	PROPN
ejpam-3406	370	10	,	,	PUNCT
ejpam-3406	370	11	r.b	r.b	PROPN
ejpam-3406	370	12	.	.	PROPN
ejpam-3406	370	13	,	,	PUNCT
ejpam-3406	370	14	ontolan	ontolan	ADJ
ejpam-3406	370	15	,	,	PUNCT
ejpam-3406	370	16	j.m	j.m	PROPN
ejpam-3406	370	17	.	.	PROPN
ejpam-3406	370	18	,	,	PUNCT
ejpam-3406	370	19	perez	perez	PROPN
ejpam-3406	370	20	-	-	PUNCT
ejpam-3406	370	21	fernandez	fernandez	PROPN
ejpam-3406	370	22	,	,	PUNCT
ejpam-3406	370	23	c.m	c.m	PROPN
ejpam-3406	370	24	.	.	PROPN
ejpam-3406	370	25	,	,	PUNCT
ejpam-3406	370	26	and	and	CCONJ
ejpam-3406	370	27	cantallopez	cantallopez	PROPN
ejpam-3406	370	28	,	,	PUNCT
ejpam-3406	370	29	e.r	e.r	PROPN
ejpam-3406	370	30	.	.	PROPN
ejpam-3406	370	31	,	,	PUNCT
ejpam-3406	370	32	the	the	DET
ejpam-3406	370	33	hankel	hankel	NOUN
ejpam-3406	370	34	transform	transform	NOUN
ejpam-3406	370	35	of	of	ADP
ejpam-3406	370	36	q	q	ADJ
ejpam-3406	370	37	-	-	ADJ
ejpam-3406	370	38	noncentral	noncentral	ADJ
ejpam-3406	370	39	bell	bell	NOUN
ejpam-3406	370	40	numbers	number	NOUN
ejpam-3406	370	41	,	,	PUNCT
ejpam-3406	370	42	international	international	ADJ
ejpam-3406	370	43	journal	journal	NOUN
ejpam-3406	370	44	of	of	ADP
ejpam-3406	370	45	mathematics	mathematics	PROPN
ejpam-3406	370	46	and	and	CCONJ
ejpam-3406	370	47	mathematical	mathematical	ADJ
ejpam-3406	370	48	analysis	analysis	NOUN
ejpam-3406	370	49	,	,	PUNCT
ejpam-3406	370	50	volume	volume	NOUN
ejpam-3406	370	51	2015	2015	NUM
ejpam-3406	370	52	,	,	PUNCT
ejpam-3406	370	53	article	article	NOUN
ejpam-3406	370	54	i	i	PROPN
ejpam-3406	370	55	d	d	PROPN
ejpam-3406	370	56	417327	417327	NUM
ejpam-3406	370	57	,	,	PUNCT
ejpam-3406	370	58	10	10	NUM
ejpam-3406	370	59	pages	page	NOUN
ejpam-3406	370	60	.	.	PUNCT
ejpam-3406	371	1	[	[	X
ejpam-3406	371	2	10	10	NUM
ejpam-3406	371	3	]	]	X
ejpam-3406	371	4	ehrenborg	ehrenborg	ADJ
ejpam-3406	371	5	,	,	PUNCT
ejpam-3406	371	6	r.	r.	PROPN
ejpam-3406	371	7	,	,	PUNCT
ejpam-3406	371	8	the	the	DET
ejpam-3406	371	9	hankel	hankel	NOUN
ejpam-3406	371	10	determinant	determinant	ADJ
ejpam-3406	371	11	of	of	ADP
ejpam-3406	371	12	exponential	exponential	ADJ
ejpam-3406	371	13	polynomials	polynomial	NOUN
ejpam-3406	371	14	,	,	PUNCT
ejpam-3406	371	15	amer	amer	PROPN
ejpam-3406	371	16	.	.	PROPN
ejpam-3406	371	17	math	math	PROPN
ejpam-3406	371	18	.	.	PUNCT
ejpam-3406	372	1	monthly	monthly	ADJ
ejpam-3406	372	2	,	,	PUNCT
ejpam-3406	372	3	107(2000	107(2000	NUM
ejpam-3406	372	4	)	)	PUNCT
ejpam-3406	372	5	,	,	PUNCT
ejpam-3406	372	6	557	557	NUM
ejpam-3406	372	7	-	-	SYM
ejpam-3406	372	8	560	560	NUM
ejpam-3406	372	9	.	.	PUNCT
ejpam-3406	373	1	[	[	X
ejpam-3406	373	2	11	11	NUM
ejpam-3406	373	3	]	]	X
ejpam-3406	373	4	ehrenborg	ehrenborg	ADJ
ejpam-3406	373	5	,	,	PUNCT
ejpam-3406	373	6	r.	r.	PROPN
ejpam-3406	373	7	,	,	PUNCT
ejpam-3406	373	8	determinants	determinant	NOUN
ejpam-3406	373	9	of	of	ADP
ejpam-3406	373	10	involving	involve	VERB
ejpam-3406	373	11	q	q	ADJ
ejpam-3406	373	12	-	-	PUNCT
ejpam-3406	373	13	stirling	stirling	NOUN
ejpam-3406	373	14	numbers	number	NOUN
ejpam-3406	373	15	,	,	PUNCT
ejpam-3406	373	16	advances	advance	NOUN
ejpam-3406	373	17	in	in	ADP
ejpam-3406	373	18	applied	apply	VERB
ejpam-3406	373	19	mathematics	mathematic	NOUN
ejpam-3406	373	20	,	,	PUNCT
ejpam-3406	373	21	31(2003	31(2003	NUM
ejpam-3406	373	22	)	)	PUNCT
ejpam-3406	373	23	,	,	PUNCT
ejpam-3406	373	24	630	630	NUM
ejpam-3406	373	25	-	-	SYM
ejpam-3406	373	26	642	642	NUM
ejpam-3406	373	27	.	.	PUNCT
ejpam-3406	374	1	[	[	X
ejpam-3406	374	2	12	12	NUM
ejpam-3406	374	3	]	]	X
ejpam-3406	374	4	layman	layman	NOUN
ejpam-3406	374	5	,	,	PUNCT
ejpam-3406	374	6	j.w	j.w	PROPN
ejpam-3406	374	7	.	.	PROPN
ejpam-3406	374	8	,	,	PUNCT
ejpam-3406	374	9	the	the	DET
ejpam-3406	374	10	hankel	hankel	NOUN
ejpam-3406	374	11	transform	transform	NOUN
ejpam-3406	374	12	and	and	CCONJ
ejpam-3406	374	13	some	some	PRON
ejpam-3406	374	14	of	of	ADP
ejpam-3406	374	15	its	its	PRON
ejpam-3406	374	16	properties	property	NOUN
ejpam-3406	374	17	,	,	PUNCT
ejpam-3406	374	18	journal	journal	NOUN
ejpam-3406	374	19	of	of	ADP
ejpam-3406	374	20	integer	integer	PROPN
ejpam-3406	374	21	sequences	sequence	NOUN
ejpam-3406	374	22	4	4	NUM
ejpam-3406	374	23	(	(	PUNCT
ejpam-3406	374	24	2001	2001	NUM
ejpam-3406	374	25	)	)	PUNCT
ejpam-3406	374	26	,	,	PUNCT
ejpam-3406	374	27	article	article	NOUN
ejpam-3406	374	28	01.1.5	01.1.5	PUNCT
ejpam-3406	374	29	.	.	PUNCT
ejpam-3406	375	1	references	reference	NOUN
ejpam-3406	375	2	293	293	NUM
ejpam-3406	375	3	[	[	SYM
ejpam-3406	375	4	13	13	NUM
ejpam-3406	375	5	]	]	X
ejpam-3406	375	6	medicis	medicis	PROPN
ejpam-3406	375	7	,	,	PUNCT
ejpam-3406	375	8	a.	a.	PROPN
ejpam-3406	375	9	de	de	PROPN
ejpam-3406	375	10	and	and	CCONJ
ejpam-3406	375	11	leroux	leroux	PROPN
ejpam-3406	375	12	,	,	PUNCT
ejpam-3406	375	13	p.	p.	NOUN
ejpam-3406	375	14	,	,	PUNCT
ejpam-3406	375	15	generalized	generalize	VERB
ejpam-3406	375	16	stirling	stirling	NOUN
ejpam-3406	375	17	numbers	number	NOUN
ejpam-3406	375	18	,	,	PUNCT
ejpam-3406	375	19	convolution	convolution	NOUN
ejpam-3406	375	20	formulae	formulae	NOUN
ejpam-3406	375	21	and	and	CCONJ
ejpam-3406	375	22	p	p	X
ejpam-3406	375	23	,	,	PUNCT
ejpam-3406	375	24	q	q	NOUN
ejpam-3406	375	25	-	-	PUNCT
ejpam-3406	375	26	analogues	analogue	NOUN
ejpam-3406	375	27	,	,	PUNCT
ejpam-3406	375	28	can	can	AUX
ejpam-3406	375	29	.	.	PUNCT
ejpam-3406	376	1	j.	j.	PROPN
ejpam-3406	376	2	math	math	PROPN
ejpam-3406	376	3	47(3	47(3	PROPN
ejpam-3406	376	4	)	)	PUNCT
ejpam-3406	376	5	(	(	PUNCT
ejpam-3406	376	6	1995	1995	NUM
ejpam-3406	376	7	)	)	PUNCT
ejpam-3406	376	8	,	,	PUNCT
ejpam-3406	376	9	474	474	NUM
ejpam-3406	376	10	-	-	SYM
ejpam-3406	376	11	499	499	NUM
ejpam-3406	376	12	.	.	PUNCT
ejpam-3406	377	1	[	[	X
ejpam-3406	377	2	14	14	NUM
ejpam-3406	377	3	]	]	X
ejpam-3406	377	4	mező	mező	PROPN
ejpam-3406	377	5	,	,	PUNCT
ejpam-3406	377	6	i.	i.	NOUN
ejpam-3406	377	7	,	,	PUNCT
ejpam-3406	377	8	the	the	DET
ejpam-3406	377	9	r	r	NOUN
ejpam-3406	377	10	-	-	PUNCT
ejpam-3406	377	11	bell	bell	NOUN
ejpam-3406	377	12	numbers	number	NOUN
ejpam-3406	377	13	,	,	PUNCT
ejpam-3406	377	14	journal	journal	NOUN
ejpam-3406	377	15	of	of	ADP
ejpam-3406	377	16	integer	integer	PROPN
ejpam-3406	377	17	sequences	sequence	NOUN
ejpam-3406	377	18	14	14	NUM
ejpam-3406	377	19	(	(	PUNCT
ejpam-3406	377	20	2011	2011	NUM
ejpam-3406	377	21	)	)	PUNCT
ejpam-3406	377	22	,	,	PUNCT
ejpam-3406	377	23	article	article	NOUN
ejpam-3406	377	24	11.1.1	11.1.1	NUM
ejpam-3406	377	25	.	.	PUNCT
ejpam-3406	378	1	[	[	X
ejpam-3406	378	2	15	15	NUM
ejpam-3406	378	3	]	]	X
ejpam-3406	378	4	riordan	riordan	PROPN
ejpam-3406	378	5	,	,	PUNCT
ejpam-3406	378	6	j.	j.	PROPN
ejpam-3406	378	7	,	,	PUNCT
ejpam-3406	378	8	combinatorial	combinatorial	ADJ
ejpam-3406	378	9	identities	identity	NOUN
ejpam-3406	378	10	,	,	PUNCT
ejpam-3406	378	11	wiley	wiley	PROPN
ejpam-3406	378	12	,	,	PUNCT
ejpam-3406	378	13	new	new	PROPN
ejpam-3406	378	14	york	york	PROPN
ejpam-3406	378	15	,	,	PUNCT
ejpam-3406	378	16	1968	1968	NUM
ejpam-3406	378	17	[	[	X
ejpam-3406	378	18	16	16	NUM
ejpam-3406	378	19	]	]	X
ejpam-3406	378	20	sloane	sloane	NOUN
ejpam-3406	378	21	,	,	PUNCT
ejpam-3406	378	22	n.	n.	PROPN
ejpam-3406	378	23	j.	j.	PROPN
ejpam-3406	378	24	a.	a.	PROPN
ejpam-3406	378	25	and	and	CCONJ
ejpam-3406	378	26	plouffe	plouffe	PROPN
ejpam-3406	378	27	,	,	PUNCT
ejpam-3406	378	28	s.	s.	PROPN
ejpam-3406	378	29	,	,	PUNCT
ejpam-3406	378	30	the	the	DET
ejpam-3406	378	31	encyclopedia	encyclopedia	NOUN
ejpam-3406	378	32	of	of	ADP
ejpam-3406	378	33	integer	integer	PROPN
ejpam-3406	378	34	sequences	sequence	NOUN
ejpam-3406	378	35	,	,	PUNCT
ejpam-3406	378	36	san	san	PROPN
ejpam-3406	378	37	diego	diego	PROPN
ejpam-3406	378	38	,	,	PUNCT
ejpam-3406	378	39	ca	ca	NOUN
ejpam-3406	378	40	,	,	PUNCT
ejpam-3406	378	41	academic	academic	ADJ
ejpam-3406	378	42	press	press	NOUN
ejpam-3406	378	43	,	,	PUNCT
ejpam-3406	378	44	1995	1995	NUM
ejpam-3406	378	45	.	.	PUNCT
ejpam-3406	379	1	[	[	X
ejpam-3406	379	2	17	17	NUM
ejpam-3406	379	3	]	]	X
ejpam-3406	379	4	spivey	spivey	PROPN
ejpam-3406	379	5	,	,	PUNCT
ejpam-3406	379	6	m.z	m.z	PROPN
ejpam-3406	379	7	.	.	PROPN
ejpam-3406	379	8	and	and	CCONJ
ejpam-3406	379	9	steil	steil	PROPN
ejpam-3406	379	10	,	,	PUNCT
ejpam-3406	379	11	l.	l.	PROPN
ejpam-3406	379	12	l.	l.	PROPN
ejpam-3406	379	13	,	,	PUNCT
ejpam-3406	379	14	the	the	DET
ejpam-3406	379	15	k	k	ADJ
ejpam-3406	379	16	-	-	ADJ
ejpam-3406	379	17	binomial	binomial	ADJ
ejpam-3406	379	18	transform	transform	NOUN
ejpam-3406	379	19	and	and	CCONJ
ejpam-3406	379	20	the	the	DET
ejpam-3406	379	21	hankel	hankel	NOUN
ejpam-3406	379	22	transform	transform	NOUN
ejpam-3406	379	23	,	,	PUNCT
ejpam-3406	379	24	journal	journal	NOUN
ejpam-3406	379	25	of	of	ADP
ejpam-3406	379	26	integer	integer	NOUN
ejpam-3406	379	27	sequences	sequence	NOUN
ejpam-3406	379	28	9(2006	9(2006	NUM
ejpam-3406	379	29	)	)	PUNCT
ejpam-3406	379	30	,	,	PUNCT
ejpam-3406	379	31	article	article	NOUN
ejpam-3406	379	32	06.1.1	06.1.1	NOUN