id	sid	eid	entity	type
ejpam-4854	1	1	european journal	ORG
ejpam-4854	2	1	16	CARDINAL
ejpam-4854	2	2	4	CARDINAL
ejpam-4854	2	3	2023	CARDINAL
ejpam-4854	2	4	2306-2322	DATE
ejpam-4854	2	5	1307-5543	DATE
ejpam-4854	2	6	new york	GPE
ejpam-4854	2	7	genevieve b. engalan1,∗	PERSON
ejpam-4854	2	8	mary joy r. latayada1 1	PERSON
ejpam-4854	2	9	caraga state university	ORG
ejpam-4854	2	10	butuan city	GPE
ejpam-4854	2	11	philippines	GPE
ejpam-4854	4	1	stirling	GPE
ejpam-4854	4	2	second	ORDINAL
ejpam-4854	6	1	2020	DATE
ejpam-4854	6	2	05	CARDINAL
ejpam-4854	6	3	11	CARDINAL
ejpam-4854	6	4	1	CARDINAL
ejpam-4854	6	5	second	ORDINAL
ejpam-4854	6	6	〈 n k	PERSON
ejpam-4854	7	1	1999	DATE
ejpam-4854	7	2	5	CARDINAL
ejpam-4854	7	3	n∑ k=0	PERSON
ejpam-4854	7	4	〈 n k	PERSON
ejpam-4854	7	5	1	CARDINAL
ejpam-4854	8	1	2	CARDINAL
ejpam-4854	8	2	k	PERSON
ejpam-4854	9	1	k ≤ 0	ORG
ejpam-4854	11	1	corcino	NORP
ejpam-4854	11	2	2002	DATE
ejpam-4854	12	1	6	CARDINAL
ejpam-4854	13	1	corcino	NORP
ejpam-4854	13	2	montero	PERSON
ejpam-4854	13	3	2009	DATE
ejpam-4854	14	1	0	CARDINAL
ejpam-4854	14	2	algebraic combinatorics	ORG
ejpam-4854	16	1	g. engalan	PERSON
ejpam-4854	16	2	mrlatayada@carsu.edu.ph (m.j. layatada	ORG
ejpam-4854	16	3	2306	DATE
ejpam-4854	17	1	2023	CARDINAL
ejpam-4854	18	1	g. engalan	PERSON
ejpam-4854	18	2	m.r. latayada	ORG
ejpam-4854	19	1	j. pure	PERSON
ejpam-4854	19	2	16	CARDINAL
ejpam-4854	19	3	4	CARDINAL
ejpam-4854	19	4	2023	CARDINAL
ejpam-4854	19	5	2306-2322 2307	DATE
ejpam-4854	20	1	two	CARDINAL
ejpam-4854	21	1	2	CARDINAL
ejpam-4854	21	2	2.1	CARDINAL
ejpam-4854	23	1	1	CARDINAL
ejpam-4854	24	1	s(β	PERSON
ejpam-4854	25	1	〈 n k	PERSON
ejpam-4854	25	2	0≤i	CARDINAL
ejpam-4854	25	3	j≤n−1	ORG
ejpam-4854	26	1	1	CARDINAL
ejpam-4854	26	2	s(β	PERSON
ejpam-4854	28	1	1	CARDINAL
ejpam-4854	28	2	0	CARDINAL
ejpam-4854	29	1	1	CARDINAL
ejpam-4854	30	1	3	CARDINAL
ejpam-4854	30	2	n × n	PRODUCT
ejpam-4854	30	3	n × n	ORG
ejpam-4854	30	4	second	ORDINAL
ejpam-4854	30	5	2	CARDINAL
ejpam-4854	30	6	3	CARDINAL
ejpam-4854	32	1	0≤i	CARDINAL
ejpam-4854	32	2	j≤n−1	PERSON
ejpam-4854	34	1	xi−js(i	DATE
ejpam-4854	35	1	0≤i	CARDINAL
ejpam-4854	35	2	j≤n−1	PERSON
ejpam-4854	35	3	s(i, j	ORG
ejpam-4854	35	4	second	ORDINAL
ejpam-4854	36	1	riordan	PERSON
ejpam-4854	36	2	shapiro et al	PERSON
ejpam-4854	37	1	10	CARDINAL
ejpam-4854	38	1	riordan matrices	PERSON
ejpam-4854	40	1	mn	GPE
ejpam-4854	40	2	k]n	GPE
ejpam-4854	40	3	f(0	PERSON
ejpam-4854	40	4	0	CARDINAL
ejpam-4854	41	1	matrixm	PERSON
ejpam-4854	42	1	ifmn	GPE
ejpam-4854	45	1	riordan	PERSON
ejpam-4854	45	2	riordan maxtrix	PERSON
ejpam-4854	45	3	f⟩.	CARDINAL
ejpam-4854	45	4	three	CARDINAL
ejpam-4854	45	5	second	ORDINAL
ejpam-4854	45	6	= 〈 ez	PERSON
ejpam-4854	46	1	1	CARDINAL
ejpam-4854	46	2	1 〉	QUANTITY
ejpam-4854	46	3	s(β	PERSON
ejpam-4854	47	1	g. engalan	PERSON
ejpam-4854	47	2	m.r. latayada	ORG
ejpam-4854	48	1	j. pure	PERSON
ejpam-4854	48	2	16	CARDINAL
ejpam-4854	48	3	4	CARDINAL
ejpam-4854	48	4	2023	CARDINAL
ejpam-4854	48	5	2306-2322 2308	DATE
ejpam-4854	48	6	e-riordan group	ORG
ejpam-4854	48	7	riordan	PERSON
ejpam-4854	48	8	〈 g	PERSON
ejpam-4854	48	9	∗	CARDINAL
ejpam-4854	48	10	l(f	PERSON
ejpam-4854	50	1	s(β	PERSON
ejpam-4854	51	1	s(β	PERSON
ejpam-4854	52	1	〈 e(r−1)z	PERSON
ejpam-4854	53	1	∗ 〈 e(r−1)z	ORG
ejpam-4854	53	2	〈 eze(r−1)z	PERSON
ejpam-4854	55	1	2	CARDINAL
ejpam-4854	55	2	4	CARDINAL
ejpam-4854	56	1	p4s	GPE
ejpam-4854	56	2	r−1)(4	ORG
ejpam-4854	56	3	1	CARDINAL
ejpam-4854	56	4	0	CARDINAL
ejpam-4854	56	5	1	CARDINAL
ejpam-4854	57	1	− 1)2	PERSON
ejpam-4854	59	1	1	CARDINAL
ejpam-4854	60	1	− 1)3 β2 + 3β(r	ORG
ejpam-4854	60	2	1	CARDINAL
ejpam-4854	60	3	1)2	ORDINAL
ejpam-4854	61	1	1	CARDINAL
ejpam-4854	61	2	0	CARDINAL
ejpam-4854	62	1	1	CARDINAL
ejpam-4854	62	2	2	CARDINAL
ejpam-4854	63	1	− s)i−j	PERSON
ejpam-4854	64	1	0≤i	CARDINAL
ejpam-4854	64	2	j≤n−1	PERSON
ejpam-4854	65	1	g. engalan	PERSON
ejpam-4854	65	2	m.r. latayada	ORG
ejpam-4854	66	1	j. pure	PERSON
ejpam-4854	66	2	16	CARDINAL
ejpam-4854	66	3	4	CARDINAL
ejpam-4854	66	4	2023	CARDINAL
ejpam-4854	66	5	2306-2322 2309	DATE
ejpam-4854	66	6	s(β	PERSON
ejpam-4854	66	7	− s]s(β	PERSON
ejpam-4854	66	8	s)(n	ORG
ejpam-4854	66	9	≥ s. proof	PERSON
ejpam-4854	67	1	pn[r −	PERSON
ejpam-4854	67	2	s(β,s)(n	ORG
ejpam-4854	68	1	s)(n	ORG
ejpam-4854	69	1	∗	CARDINAL
ejpam-4854	69	2	〈 e(r−s)zesz	PERSON
ejpam-4854	71	1	3	CARDINAL
ejpam-4854	71	2	4	CARDINAL
ejpam-4854	72	1	1	CARDINAL
ejpam-4854	74	1	1	CARDINAL
ejpam-4854	75	1	2(r	CARDINAL
ejpam-4854	75	2	1 0	CARDINAL
ejpam-4854	76	1	3(r	CARDINAL
ejpam-4854	76	2	3(r	CARDINAL
ejpam-4854	76	3	1	CARDINAL
ejpam-4854	76	4	0	CARDINAL
ejpam-4854	76	5	1	CARDINAL
ejpam-4854	78	1	1	CARDINAL
ejpam-4854	78	2	0	CARDINAL
ejpam-4854	79	1	1	CARDINAL
ejpam-4854	81	1	− 1)2	PERSON
ejpam-4854	81	2	2r	CARDINAL
ejpam-4854	81	3	−2 + 3r + 3	LAW
ejpam-4854	81	4	− 1)2	ORG
ejpam-4854	82	1	− 1)3	ORG
ejpam-4854	82	2	3 + 3b	CARDINAL
ejpam-4854	82	3	1	CARDINAL
ejpam-4854	82	4	1 	CARDINAL
ejpam-4854	82	5	1	CARDINAL
ejpam-4854	82	6	0	CARDINAL
ejpam-4854	83	1	1	CARDINAL
ejpam-4854	83	2	3	CARDINAL
ejpam-4854	83	3	pn[r	PERSON
ejpam-4854	83	4	second	ORDINAL
ejpam-4854	84	1	s(β	PERSON
ejpam-4854	84	2	j = βi−js(i	PERSON
ejpam-4854	84	3	s(i	PERSON
ejpam-4854	84	4	second	ORDINAL
ejpam-4854	85	1	0 ≤	MONEY
ejpam-4854	85	2	1	CARDINAL
ejpam-4854	85	3	g. engalan	PERSON
ejpam-4854	85	4	m.r. latayada	ORG
ejpam-4854	86	1	j. pure	PERSON
ejpam-4854	86	2	16	CARDINAL
ejpam-4854	86	3	4	CARDINAL
ejpam-4854	86	4	2023	CARDINAL
ejpam-4854	86	5	2306-2322	DATE
ejpam-4854	88	1	∗	CARDINAL
ejpam-4854	88	2	1	CARDINAL
ejpam-4854	90	1	4	CARDINAL
ejpam-4854	90	2	4	CARDINAL
ejpam-4854	90	3	1	CARDINAL
ejpam-4854	90	4	0	CARDINAL
ejpam-4854	91	1	1	CARDINAL
ejpam-4854	91	2	2r	CARDINAL
ejpam-4854	91	3	1 	CARDINAL
ejpam-4854	91	4	1	CARDINAL
ejpam-4854	91	5	0	CARDINAL
ejpam-4854	91	6	1	CARDINAL
ejpam-4854	91	7	0	CARDINAL
ejpam-4854	91	8	1	CARDINAL
ejpam-4854	91	9	1	CARDINAL
ejpam-4854	91	10	0	CARDINAL
ejpam-4854	92	1	1	CARDINAL
ejpam-4854	92	2	4	CARDINAL
ejpam-4854	93	1	〈 n k	PERSON
ejpam-4854	93	2	1,r	DATE
ejpam-4854	94	1	s(β	PERSON
ejpam-4854	95	1	〈 e(r−rβ)z	PERSON
ejpam-4854	96	1	g. engalan	PERSON
ejpam-4854	96	2	m.r. latayada	ORG
ejpam-4854	97	1	j. pure	PERSON
ejpam-4854	97	2	16	CARDINAL
ejpam-4854	97	3	4	CARDINAL
ejpam-4854	97	4	2023	CARDINAL
ejpam-4854	97	5	2306-2322 2311	DATE
ejpam-4854	97	6	〈 e(r−rβ)z	PERSON
ejpam-4854	97	7	∗	CARDINAL
ejpam-4854	97	8	〈 e(r−rβ)z+rβz	PERSON
ejpam-4854	98	1	5	CARDINAL
ejpam-4854	98	2	4	CARDINAL
ejpam-4854	98	3	1	CARDINAL
ejpam-4854	99	1	1	CARDINAL
ejpam-4854	100	1	2(r	CARDINAL
ejpam-4854	100	2	1 0	CARDINAL
ejpam-4854	101	1	3(r	CARDINAL
ejpam-4854	102	1	3(r	CARDINAL
ejpam-4854	102	2	1 	DATE
ejpam-4854	103	1	1	CARDINAL
ejpam-4854	104	1	1	CARDINAL
ejpam-4854	106	1	3β	CARDINAL
ejpam-4854	108	1	1	CARDINAL
ejpam-4854	108	2	0	CARDINAL
ejpam-4854	109	1	1	CARDINAL
ejpam-4854	110	1	2.2	CARDINAL
ejpam-4854	110	2	13	CARDINAL
ejpam-4854	111	1	0≤j	CARDINAL
ejpam-4854	111	2	i≤n−1	PRODUCT
ejpam-4854	111	3	1	CARDINAL
ejpam-4854	111	4	1	CARDINAL
ejpam-4854	112	1	1	CARDINAL
ejpam-4854	113	1	1 	DATE
ejpam-4854	114	1	zhang	PERSON
ejpam-4854	114	2	⊕	GPE
ejpam-4854	114	3	1 ≤ k ≤	QUANTITY
ejpam-4854	114	4	1	CARDINAL
ejpam-4854	114	5	g. engalan	PERSON
ejpam-4854	114	6	m.r. latayada	ORG
ejpam-4854	115	1	j. pure	PERSON
ejpam-4854	115	2	16	CARDINAL
ejpam-4854	115	3	4	CARDINAL
ejpam-4854	115	4	2023	CARDINAL
ejpam-4854	115	5	2306-2322 2312	DATE
ejpam-4854	115	6	⊕	GPE
ejpam-4854	116	1	5	CARDINAL
ejpam-4854	117	1	1	CARDINAL
ejpam-4854	117	2	s(β	PERSON
ejpam-4854	120	1	s(β	PERSON
ejpam-4854	121	1	1	CARDINAL
ejpam-4854	121	2	13	CARDINAL
ejpam-4854	122	1	one	CARDINAL
ejpam-4854	122	2	kim	PERSON
ejpam-4854	122	3	3	CARDINAL
ejpam-4854	123	1	s(β	PERSON
ejpam-4854	125	1	2.3	CARDINAL
ejpam-4854	127	1	2	CARDINAL
ejpam-4854	128	1	s(β	PERSON
ejpam-4854	130	1	s(β	PERSON
ejpam-4854	130	2	1	CARDINAL
ejpam-4854	131	1	4	CARDINAL
ejpam-4854	131	2	6	CARDINAL
ejpam-4854	132	1	4	CARDINAL
ejpam-4854	134	1	1	CARDINAL
ejpam-4854	134	2	2	CARDINAL
ejpam-4854	134	3	3	CARDINAL
ejpam-4854	135	1	0	CARDINAL
ejpam-4854	135	2	0	CARDINAL
ejpam-4854	136	1	1	CARDINAL
ejpam-4854	136	2	0	CARDINAL
ejpam-4854	136	3	+ 2r	MONEY
ejpam-4854	136	4	3β + 3r)2	CARDINAL
ejpam-4854	137	1	3	CARDINAL
ejpam-4854	137	2	1	CARDINAL
ejpam-4854	137	3	0	CARDINAL
ejpam-4854	137	4	1	CARDINAL
ejpam-4854	138	1	g. engalan	PERSON
ejpam-4854	138	2	m.r. latayada	ORG
ejpam-4854	139	1	j. pure	PERSON
ejpam-4854	139	2	16	CARDINAL
ejpam-4854	139	3	4	CARDINAL
ejpam-4854	139	4	2023	CARDINAL
ejpam-4854	139	5	2306-2322	DATE
ejpam-4854	139	6	1	CARDINAL
ejpam-4854	141	1	2β	CARDINAL
ejpam-4854	142	1	1)β +	DATE
ejpam-4854	142	2	1 1 1	DATE
ejpam-4854	143	1	1 βt+	PERCENT
ejpam-4854	144	1	2β	CARDINAL
ejpam-4854	145	1	1)β +	DATE
ejpam-4854	146	1	2β	CARDINAL
ejpam-4854	146	2	1)β +	DATE
ejpam-4854	148	1	r)n−1	PERSON
ejpam-4854	148	2	2β	CARDINAL
ejpam-4854	148	3	1)β +	DATE
ejpam-4854	149	1	j i	WORK_OF_ART
ejpam-4854	149	2	0≤i	CARDINAL
ejpam-4854	149	3	j≤n−1	PERSON
ejpam-4854	152	1	5	CARDINAL
ejpam-4854	153	1	1	CARDINAL
ejpam-4854	153	2	n∑ k=0	PERSON
ejpam-4854	153	3	〈n k	PERSON
ejpam-4854	153	4	k.	PERSON
ejpam-4854	153	5	n∑ k=0	PERSON
ejpam-4854	153	6	〈n k	PERSON
ejpam-4854	155	1	n∑ k=0	PERSON
ejpam-4854	155	2	〈n k	PERSON
ejpam-4854	156	1	n∑ k=0	PERSON
ejpam-4854	156	2	〈n k	PERSON
ejpam-4854	157	1	6	CARDINAL
ejpam-4854	157	2	6	CARDINAL
ejpam-4854	157	3	0	CARDINAL
ejpam-4854	157	4	1	DATE
ejpam-4854	157	5	2	CARDINAL
ejpam-4854	159	1	7	CARDINAL
ejpam-4854	160	1	1	CARDINAL
ejpam-4854	162	1	t 1	DATE
ejpam-4854	164	1	βn−1	GPE
ejpam-4854	164	2	1	CARDINAL
ejpam-4854	164	3	g. engalan	PERSON
ejpam-4854	164	4	m.r. latayada	ORG
ejpam-4854	165	1	j. pure	PERSON
ejpam-4854	165	2	16	CARDINAL
ejpam-4854	165	3	4	CARDINAL
ejpam-4854	165	4	2023	CARDINAL
ejpam-4854	165	5	2306	CARDINAL
ejpam-4854	165	6	first	ORDINAL
ejpam-4854	166	1	1	CARDINAL
ejpam-4854	166	2	0	CARDINAL
ejpam-4854	167	1	1	CARDINAL
ejpam-4854	169	1	rn−1 〈 n−	PERSON
ejpam-4854	169	2	1 2	QUANTITY
ejpam-4854	169	3	〈 n−	PERSON
ejpam-4854	169	4	1 3	TIME
ejpam-4854	169	5	2	CARDINAL
ejpam-4854	170	1	1	CARDINAL
ejpam-4854	173	1	βn−1	PERSON
ejpam-4854	174	1	5	CARDINAL
ejpam-4854	176	1	7	CARDINAL
ejpam-4854	176	2	4	CARDINAL
ejpam-4854	179	1	1	CARDINAL
ejpam-4854	179	2	0	CARDINAL
ejpam-4854	180	1	1	CARDINAL
ejpam-4854	180	2	1 1 1 1 βt β(t+ 1	TIME
ejpam-4854	180	3	2	CARDINAL
ejpam-4854	180	4	3	CARDINAL
ejpam-4854	180	5	2	CARDINAL
ejpam-4854	180	6	2	CARDINAL
ejpam-4854	180	7	2	CARDINAL
ejpam-4854	180	8	2	CARDINAL
ejpam-4854	180	9	6	CARDINAL
ejpam-4854	180	10	6	CARDINAL
ejpam-4854	180	11	6	CARDINAL
ejpam-4854	180	12	6	CARDINAL
ejpam-4854	181	1	4	CARDINAL
ejpam-4854	181	2	1	CARDINAL
ejpam-4854	181	3	0	CARDINAL
ejpam-4854	182	1	1	CARDINAL
ejpam-4854	182	2	1 1 1 1 βt β(t+ 1	TIME
ejpam-4854	182	3	2	CARDINAL
ejpam-4854	182	4	3	CARDINAL
ejpam-4854	182	5	2	CARDINAL
ejpam-4854	182	6	2	CARDINAL
ejpam-4854	182	7	2	CARDINAL
ejpam-4854	182	8	2	CARDINAL
ejpam-4854	182	9	6	CARDINAL
ejpam-4854	182	10	6	CARDINAL
ejpam-4854	182	11	6	CARDINAL
ejpam-4854	182	12	6	CARDINAL
ejpam-4854	182	13	1 1 1 1	DATE
ejpam-4854	183	1	2β	CARDINAL
ejpam-4854	184	1	3β	CARDINAL
ejpam-4854	185	1	2β	CARDINAL
ejpam-4854	185	2	3β +	DATE
ejpam-4854	185	3	2β	CARDINAL
ejpam-4854	185	4	3β	CARDINAL
ejpam-4854	185	5		DATE
ejpam-4854	185	6	4	CARDINAL
ejpam-4854	185	7	g. engalan	PERSON
ejpam-4854	185	8	m.r. latayada	ORG
ejpam-4854	186	1	j. pure	PERSON
ejpam-4854	186	2	16	CARDINAL
ejpam-4854	186	3	4	CARDINAL
ejpam-4854	186	4	2023	CARDINAL
ejpam-4854	186	5	2306-2322	DATE
ejpam-4854	186	6	2315	CARDINAL
ejpam-4854	186	7	1	CARDINAL
ejpam-4854	188	1	t i− j	DATE
ejpam-4854	189	1	mi	PERSON
ejpam-4854	189	2	n r−i),∑ i=0	ORG
ejpam-4854	191	1	j i	WORK_OF_ART
ejpam-4854	191	2	0≤i	CARDINAL
ejpam-4854	191	3	j≤n−1	ORG
ejpam-4854	193	1	k=0	PERSON
ejpam-4854	194	1	0≤i	CARDINAL
ejpam-4854	194	2	j≤n−1	ORG
ejpam-4854	195	1	k=0	PERSON
ejpam-4854	195	2	j i	WORK_OF_ART
ejpam-4854	196	1	0≤i	CARDINAL
ejpam-4854	196	2	j≤n−1	PERSON
ejpam-4854	196	3	t i− j	DATE
ejpam-4854	197	1	j i	WORK_OF_ART
ejpam-4854	202	1	1	CARDINAL
ejpam-4854	203	1	8	CARDINAL
ejpam-4854	204	1	1	CARDINAL
ejpam-4854	205	1	4	CARDINAL
ejpam-4854	208	1	1	CARDINAL
ejpam-4854	208	2	0	CARDINAL
ejpam-4854	209	1	1	CARDINAL
ejpam-4854	209	2	+ 3βr + r2	DATE
ejpam-4854	209	3	6β + 6r	CARDINAL
ejpam-4854	210	1	1	CARDINAL
ejpam-4854	210	2	0	CARDINAL
ejpam-4854	210	3	g. engalan	PERSON
ejpam-4854	210	4	m.r. latayada	ORG
ejpam-4854	211	1	j. pure	PERSON
ejpam-4854	211	2	16	CARDINAL
ejpam-4854	211	3	4	CARDINAL
ejpam-4854	211	4	2023	CARDINAL
ejpam-4854	211	5	2306-2322 2316	DATE
ejpam-4854	211	6	4	CARDINAL
ejpam-4854	211	7	1 1 1 1	TIME
ejpam-4854	211	8	0	CARDINAL
ejpam-4854	211	9	0	CARDINAL
ejpam-4854	211	10	0 1 	DATE
ejpam-4854	213	1	1	CARDINAL
ejpam-4854	213	2	0	CARDINAL
ejpam-4854	214	1	1	CARDINAL
ejpam-4854	214	2	+ 3βr + r2	DATE
ejpam-4854	214	3	6β + 6r	CARDINAL
ejpam-4854	214	4	1	CARDINAL
ejpam-4854	214	5	1 1 1	DATE
ejpam-4854	214	6	0	CARDINAL
ejpam-4854	214	7	0	CARDINAL
ejpam-4854	214	8	1	CARDINAL
ejpam-4854	217	1	β(3β	ORG
ejpam-4854	218	1	2β2	CARDINAL
ejpam-4854	219	1	9βr	ORDINAL
ejpam-4854	220	1	6β2(2β +	DATE
ejpam-4854	220	2	6β3	CARDINAL
ejpam-4854	221	1	1 1 1	DATE
ejpam-4854	221	2	0	CARDINAL
ejpam-4854	221	3	0	CARDINAL
ejpam-4854	221	4	2β	CARDINAL
ejpam-4854	221	5	3β	CARDINAL
ejpam-4854	221	6	4β +	DATE
ejpam-4854	221	7	2β +	DATE
ejpam-4854	221	8	3β +	DATE
ejpam-4854	221	9	4β +	DATE
ejpam-4854	221	10	2β	CARDINAL
ejpam-4854	221	11	3β + r)3	DATE
ejpam-4854	221	12	4β +	DATE
ejpam-4854	221	13	4	CARDINAL
ejpam-4854	222	1	2	CARDINAL
ejpam-4854	224	1	n−1∏ k=0 k!βk	PERSON
ejpam-4854	226	1	2β	CARDINAL
ejpam-4854	227	1	1)β +	DATE
ejpam-4854	228	1	11	CARDINAL
ejpam-4854	228	2	det((v	ORG
ejpam-4854	229	1	n−1∏ k=0	PERSON
ejpam-4854	230	1	g. engalan	PERSON
ejpam-4854	230	2	m.r. latayada	ORG
ejpam-4854	231	1	j. pure	PERSON
ejpam-4854	231	2	16	CARDINAL
ejpam-4854	231	3	4	CARDINAL
ejpam-4854	231	4	2023	CARDINAL
ejpam-4854	231	5	2306-2322 2317	DATE
ejpam-4854	231	6	det((v	ORG
ejpam-4854	233	1	1)β +	DATE
ejpam-4854	234	1	1)β +	DATE
ejpam-4854	234	2	2)β +	DATE
ejpam-4854	235	1	2)β +	DATE
ejpam-4854	237	1	2)β +	DATE
ejpam-4854	238	1	3)β +	DATE
ejpam-4854	239	1	3)β +	DATE
ejpam-4854	241	1	3)β +	DATE
ejpam-4854	242	1	4)β +	DATE
ejpam-4854	245	1	1)β	ORDINAL
ejpam-4854	245	2	2)β	CARDINAL
ejpam-4854	245	3	n−	ORG
ejpam-4854	245	4	3)β ·	TIME
ejpam-4854	245	5	2)β	CARDINAL
ejpam-4854	245	6	n−	ORG
ejpam-4854	245	7	3)β ·	TIME
ejpam-4854	245	8	4)β	CARDINAL
ejpam-4854	245	9	3)β ·	TIME
ejpam-4854	245	10	4)β	CARDINAL
ejpam-4854	245	11	5)β	CARDINAL
ejpam-4854	245	12	n−1∏ k=0 k!βk	PERSON
ejpam-4854	245	13	9	CARDINAL
ejpam-4854	246	1	4	CARDINAL
ejpam-4854	247	1	4	CARDINAL
ejpam-4854	247	2	2β	CARDINAL
ejpam-4854	247	3	3β	CARDINAL
ejpam-4854	248	1	4β +	DATE
ejpam-4854	248	2	2β +	DATE
ejpam-4854	248	3	3β +	DATE
ejpam-4854	248	4	4β +	DATE
ejpam-4854	248	5	2β	CARDINAL
ejpam-4854	248	6	3β + r)3	DATE
ejpam-4854	248	7	4β + r)3	DATE
ejpam-4854	248	8	4	CARDINAL
ejpam-4854	249	1	3β	CARDINAL
ejpam-4854	249	2	3β	CARDINAL
ejpam-4854	251	1	3β	CARDINAL
ejpam-4854	252	1	2β	CARDINAL
ejpam-4854	252	2	2β	CARDINAL
ejpam-4854	253	1	2β	CARDINAL
ejpam-4854	256	1	3β	CARDINAL
ejpam-4854	257	1	2β	CARDINAL
ejpam-4854	257	2	3	CARDINAL
ejpam-4854	257	3	2	CARDINAL
ejpam-4854	257	4	1β2)(β	CARDINAL
ejpam-4854	257	5	3!β3)(2!β2)(1!β	CARDINAL
ejpam-4854	258	1	3∏	CARDINAL
ejpam-4854	258	2	k!βk	DATE
ejpam-4854	258	3	1	CARDINAL
ejpam-4854	259	1	ln[β]]1≤i	ORG
ejpam-4854	260	1	the n× n	ORG
ejpam-4854	260	2	s(β	PERSON
ejpam-4854	261	1	g. engalan	PERSON
ejpam-4854	261	2	m.r. latayada	ORG
ejpam-4854	262	1	j. pure	PERSON
ejpam-4854	262	2	16	CARDINAL
ejpam-4854	262	3	4	CARDINAL
ejpam-4854	262	4	2023	CARDINAL
ejpam-4854	262	5	2306	CARDINAL
ejpam-4854	263	1	ln[β]]1≤i	ORG
ejpam-4854	264	1	1≤i	CARDINAL
ejpam-4854	265	1	k=0	PERSON
ejpam-4854	267	1	5	CARDINAL
ejpam-4854	268	1	1)β	ORDINAL
ejpam-4854	270	1	2	CARDINAL
ejpam-4854	271	1	1)]s(β	DATE
ejpam-4854	273	1	1	CARDINAL
ejpam-4854	273	2	1)]s(β	DATE
ejpam-4854	273	3	1)]vβ	DATE
ejpam-4854	273	4	k=0	PERSON
ejpam-4854	275	1	1	CARDINAL
ejpam-4854	275	2	1	CARDINAL
ejpam-4854	276	1	x)]ij	NORP
ejpam-4854	277	1	10	CARDINAL
ejpam-4854	278	1	4	CARDINAL
ejpam-4854	279	1	1	CARDINAL
ejpam-4854	280	1	1	CARDINAL
ejpam-4854	280	2	0	CARDINAL
ejpam-4854	280	3	1	CARDINAL
ejpam-4854	280	4	1	CARDINAL
ejpam-4854	281	1	β(t−	ORG
ejpam-4854	281	2	1 0	CARDINAL
ejpam-4854	284	1	g. engalan	PERSON
ejpam-4854	284	2	m.r. latayada	ORG
ejpam-4854	285	1	j. pure	PERSON
ejpam-4854	285	2	16	CARDINAL
ejpam-4854	285	3	4	CARDINAL
ejpam-4854	285	4	2023	CARDINAL
ejpam-4854	285	5	2306-2322	DATE
ejpam-4854	287	1	1	CARDINAL
ejpam-4854	287	2	0	CARDINAL
ejpam-4854	288	1	1	CARDINAL
ejpam-4854	288	2	+ 3βr + r2	DATE
ejpam-4854	288	3	3β +	CARDINAL
ejpam-4854	288	4	1 1 1 1	TIME
ejpam-4854	288	5	2β	CARDINAL
ejpam-4854	288	6	3β	CARDINAL
ejpam-4854	288	7	2β2 6β2	DATE
ejpam-4854	288	8	12β2	CARDINAL
ejpam-4854	289	1	1	CARDINAL
ejpam-4854	289	2	0	CARDINAL
ejpam-4854	290	1	1	CARDINAL
ejpam-4854	290	2	1	CARDINAL
ejpam-4854	291	1	β(t−	ORG
ejpam-4854	291	2	1 0	CARDINAL
ejpam-4854	293	1	1	CARDINAL
ejpam-4854	293	2	1	CARDINAL
ejpam-4854	293	3	0	CARDINAL
ejpam-4854	293	4	1	CARDINAL
ejpam-4854	293	5	+ 3βr + r2	DATE
ejpam-4854	293	6	3β +	CARDINAL
ejpam-4854	293	7	1 1 1 1	TIME
ejpam-4854	293	8	2β	CARDINAL
ejpam-4854	293	9	3β	CARDINAL
ejpam-4854	293	10	2β2 6β2	DATE
ejpam-4854	293	11	12β2	CARDINAL
ejpam-4854	294	1	1	CARDINAL
ejpam-4854	294	2	0	CARDINAL
ejpam-4854	294	3	1	CARDINAL
ejpam-4854	294	4	1	CARDINAL
ejpam-4854	295	1	β(t−	ORG
ejpam-4854	295	2	1 0	CARDINAL
ejpam-4854	297	1	1	CARDINAL
ejpam-4854	297	2	1 1 1 1	TIME
ejpam-4854	297	3	2β	CARDINAL
ejpam-4854	297	4	0 0	DATE
ejpam-4854	297	5	2β +	DATE
ejpam-4854	297	6	3β +	DATE
ejpam-4854	297	7	4β +	DATE
ejpam-4854	297	8	2β	CARDINAL
ejpam-4854	297	9	3β + r)3	DATE
ejpam-4854	297	10	4β + r)3	DATE
ejpam-4854	297	11	1 1 1 1	DATE
ejpam-4854	298	1	2β	CARDINAL
ejpam-4854	299	1	3β	CARDINAL
ejpam-4854	300	1	2β	CARDINAL
ejpam-4854	300	2	3β +	DATE
ejpam-4854	300	3	2β	CARDINAL
ejpam-4854	300	4	3β	CARDINAL
ejpam-4854	300	5		DATE
ejpam-4854	300	6	4	CARDINAL
ejpam-4854	301	1	2.4	CARDINAL
ejpam-4854	302	1	1	CARDINAL
ejpam-4854	302	2	12	CARDINAL
ejpam-4854	303	1	g. engalan	PERSON
ejpam-4854	303	2	m.r. latayada	ORG
ejpam-4854	304	1	j. pure	PERSON
ejpam-4854	304	2	16	CARDINAL
ejpam-4854	304	3	4	CARDINAL
ejpam-4854	304	4	2023	CARDINAL
ejpam-4854	304	5	2306-2322 2320	DATE
ejpam-4854	304	6	3	CARDINAL
ejpam-4854	305	1	1	CARDINAL
ejpam-4854	305	2	1	CARDINAL
ejpam-4854	305	3	2	DATE
ejpam-4854	306	1	1,β	CARDINAL
ejpam-4854	307	1	1,β	CARDINAL
ejpam-4854	308	1	2β + r)k +	MONEY
ejpam-4854	308	2	j=0	GPE
ejpam-4854	308	3	8) zk	MONEY
ejpam-4854	309	1	2	CARDINAL
ejpam-4854	309	2	3	DATE
ejpam-4854	309	3	4	DATE
ejpam-4854	310	1	9	CARDINAL
ejpam-4854	310	2	1	CARDINAL
ejpam-4854	310	3	first	ORDINAL
ejpam-4854	310	4	1,1,1(l	CARDINAL
ejpam-4854	311	1	1k	CARDINAL
ejpam-4854	312	1	4	CARDINAL
ejpam-4854	313	1	12	CARDINAL
ejpam-4854	313	2	1	CARDINAL
ejpam-4854	313	3	2	DATE
ejpam-4854	316	1	0	CARDINAL
ejpam-4854	318	1	1	CARDINAL
ejpam-4854	320	1	k − 2	ORG
ejpam-4854	320	2	ri	GPE
ejpam-4854	321	1	1	CARDINAL
ejpam-4854	321	2	r(i	PERSON
ejpam-4854	323	1	k−1	GPE
ejpam-4854	323	2	r(i	PERSON
ejpam-4854	323	3	11	CARDINAL
ejpam-4854	323	4	3	CARDINAL
ejpam-4854	323	5	1	CARDINAL
ejpam-4854	323	6	2	DATE
ejpam-4854	323	7	3	DATE
ejpam-4854	325	1	r(k	ORG
ejpam-4854	327	1	βk−1	ORG
ejpam-4854	327	2	n+p−1	PERSON
ejpam-4854	334	1	1	CARDINAL
ejpam-4854	334	2	2	DATE
ejpam-4854	334	3	3	DATE
ejpam-4854	335	1	3.7	CARDINAL
ejpam-4854	335	2	the second row	DATE
ejpam-4854	336	1	2β	CARDINAL
ejpam-4854	336	2	1)β +	DATE
ejpam-4854	336	3	2β	CARDINAL
ejpam-4854	337	1	1)β +	DATE
ejpam-4854	337	2	1,β	CARDINAL
ejpam-4854	338	1	0	CARDINAL
ejpam-4854	338	2	12	CARDINAL
ejpam-4854	341	1	βk−1	ORG
ejpam-4854	341	2	n−1 k−1	ORG
ejpam-4854	344	1	1	CARDINAL
ejpam-4854	344	2	1,β	CARDINAL
ejpam-4854	346	1	k−1 1,β,r(n	ORG
ejpam-4854	347	1	12	CARDINAL
ejpam-4854	347	2	1	CARDINAL
ejpam-4854	348	1	2	CARDINAL
ejpam-4854	349	1	1	CARDINAL
ejpam-4854	350	1	g. engalan	PERSON
ejpam-4854	350	2	m.r. latayada	ORG
ejpam-4854	351	1	j. pure	PERSON
ejpam-4854	351	2	16	CARDINAL
ejpam-4854	351	3	4	CARDINAL
ejpam-4854	351	4	2023	CARDINAL
ejpam-4854	351	5	2306-2322 2321	DATE
ejpam-4854	351	6	10	CARDINAL
ejpam-4854	351	7	11	CARDINAL
ejpam-4854	351	8	1	CARDINAL
ejpam-4854	353	1	1	CARDINAL
ejpam-4854	353	2	2	CARDINAL
ejpam-4854	355	1	1	CARDINAL
ejpam-4854	356	1	12	CARDINAL
ejpam-4854	357	1	11	CARDINAL
ejpam-4854	358	1	12	CARDINAL
ejpam-4854	358	2	3	CARDINAL
ejpam-4854	359	1	1	CARDINAL
ejpam-4854	359	2	3	CARDINAL
ejpam-4854	360	1	1	CARDINAL
ejpam-4854	361	1	0	CARDINAL
ejpam-4854	361	2	1	CARDINAL
ejpam-4854	362	1	+ 3βr + 3r2 6β + 6r	DATE
ejpam-4854	363	1	6βr	ORDINAL
ejpam-4854	363	2	1 4n(βn−	CARDINAL
ejpam-4854	363	3	2r)(β2n2	CARDINAL
ejpam-4854	364	1	2βnr	CARDINAL
ejpam-4854	367	1	1,β	CARDINAL
ejpam-4854	367	2	2 1,β	CARDINAL
ejpam-4854	367	3	3 1,β	CARDINAL
ejpam-4854	368	1	2	CARDINAL
ejpam-4854	368	2	3	CARDINAL
ejpam-4854	368	3	1	CARDINAL
ejpam-4854	368	4	0	CARDINAL
ejpam-4854	369	1	1	CARDINAL
ejpam-4854	370	1	+ 3βr + 3r2 6β + 6r	DATE
ejpam-4854	370	2	2	CARDINAL
ejpam-4854	370	3	4	CARDINAL
ejpam-4854	370	4	1 2 n(n+ 1	QUANTITY
ejpam-4854	370	5	1 12 n(n+ 1)(β2n2	QUANTITY
ejpam-4854	372	1	3β3n2	CARDINAL
ejpam-4854	373	1	2β3n+	CARDINAL
ejpam-4854	377	1	∗	CARDINAL
ejpam-4854	377	2	2 2,β	DATE
ejpam-4854	377	3	3 2,β	DATE
ejpam-4854	379	1	1	CARDINAL
ejpam-4854	379	2	2	DATE
ejpam-4854	379	3	3	DATE
ejpam-4854	379	4	rk+(rk+(β+r)k)+	GPE
ejpam-4854	380	1	jβ+r)k	ORG
ejpam-4854	380	2	3	CARDINAL
ejpam-4854	381	1	1	CARDINAL
ejpam-4854	381	2	2	DATE
ejpam-4854	382	1	np∑ np−1=1	PERSON
ejpam-4854	384	1	〈k	PERSON
ejpam-4854	384	2	1	CARDINAL
ejpam-4854	385	1	2322	CARDINAL
ejpam-4854	385	2	1	CARDINAL
ejpam-4854	385	3	a.	PERSON
ejpam-4854	387	1	25(3):486–489	DATE
ejpam-4854	387	2	2012	DATE
ejpam-4854	388	1	2	CARDINAL
ejpam-4854	388	2	d. velleman	PERSON
ejpam-4854	389	1	pascal	PERSON
ejpam-4854	390	1	american	NORP
ejpam-4854	390	2	monthly	DATE
ejpam-4854	390	3	100(4):372, 1993	DATE
ejpam-4854	391	1	3	CARDINAL
ejpam-4854	391	2	j. kim	PERSON
ejpam-4854	392	1	stirling	PERSON
ejpam-4854	393	1	329(1-3):49–59	CARDINAL
ejpam-4854	394	1	4	CARDINAL
ejpam-4854	394	2	corcino	NORP
ejpam-4854	396	1	128(3):27	CARDINAL
ejpam-4854	397	1	5	CARDINAL
ejpam-4854	399	1	mindanao	GPE
ejpam-4854	399	2	14(2):91–100	DATE
ejpam-4854	399	3	2015	DATE
ejpam-4854	400	1	6	CARDINAL
ejpam-4854	400	2	r. aldema	PERSON
ejpam-4854	402	1	25	CARDINAL
ejpam-4854	402	2	2002	DATE
ejpam-4854	403	1	7	CARDINAL
ejpam-4854	403	2	r. corcino	PERSON
ejpam-4854	403	3	m. montero	PERSON
ejpam-4854	404	1	0 -1 tableau.	ORG
ejpam-4854	405	1	philippines	GPE
ejpam-4854	405	2	32(1):42–52	GPE
ejpam-4854	405	3	2009	DATE
ejpam-4854	406	1	8	CARDINAL
ejpam-4854	406	2	corcino	NORP
ejpam-4854	406	3	c. barrientos	PERSON
ejpam-4854	408	1	malaysian	NORP
ejpam-4854	408	2	34(3):487501, 2011	DATE
ejpam-4854	409	1	9	CARDINAL
ejpam-4854	409	2	corcino	NORP
ejpam-4854	409	3	cb corcino	GPE
ejpam-4854	411	1	81:81–96, 2006	DATE
ejpam-4854	412	1	10	CARDINAL
ejpam-4854	412	2	l. shapiro	PERSON
ejpam-4854	413	1	riordan	PERSON
ejpam-4854	414	1	1991	DATE
ejpam-4854	415	1	11	CARDINAL
ejpam-4854	415	2	d. kalman	PERSON
ejpam-4854	418	1	21, 1984	DATE
ejpam-4854	419	1	12	CARDINAL
ejpam-4854	419	2	i. mező	PERSON
ejpam-4854	419	3	j. ramı́rez	PERSON
ejpam-4854	421	1	26:213–225	CARDINAL
ejpam-4854	421	2	2015	DATE
ejpam-4854	422	1	13	CARDINAL
ejpam-4854	422	2	z. zhang	PERSON
ejpam-4854	424	1	250:49–59, 1997	DATE