id	sid	eid	entity	type
ejpam-4870	1	1	european journal	ORG
ejpam-4870	2	1	16	CARDINAL
ejpam-4870	2	2	4	CARDINAL
ejpam-4870	2	3	2023	CARDINAL
ejpam-4870	2	4	2476	CARDINAL
ejpam-4870	2	5	new york	GPE
ejpam-4870	2	6	cris c. bonifacio1	PERSON
ejpam-4870	2	7	clarence joy m. andaya1	PERSON
ejpam-4870	3	1	daryl m. magpantay1,∗ 1	PERSON
ejpam-4870	3	2	batangas state university	ORG
ejpam-4870	3	3	the national engineering university	ORG
ejpam-4870	3	4	batangas city	GPE
ejpam-4870	3	5	batangas	GPE
ejpam-4870	3	6	philippines	GPE
ejpam-4870	6	1	ec(n	ORG
ejpam-4870	6	2	n ≥ 3	DATE
ejpam-4870	6	3	1 ≤ j ≤ n. two	QUANTITY
ejpam-4870	6	4	one	CARDINAL
ejpam-4870	8	1	j = 1	PERSON
ejpam-4870	8	2	2	CARDINAL
ejpam-4870	8	3	2	CARDINAL
ejpam-4870	8	4	j = 1	PERSON
ejpam-4870	8	5	2	CARDINAL
ejpam-4870	9	1	2 ≤ j ≤	QUANTITY
ejpam-4870	9	2	2	CARDINAL
ejpam-4870	9	3	ec(n	ORG
ejpam-4870	11	1	j = 2	PERSON
ejpam-4870	11	2	2020	DATE
ejpam-4870	11	3	05	CARDINAL
ejpam-4870	11	4	subgraph 1	DATE
ejpam-4870	18	1	daryl.magpantay@g.batstate-u.edu.ph	GPE
ejpam-4870	18	2	d. magpantay	PERSON
ejpam-4870	18	3	2476	CARDINAL
ejpam-4870	18	4	2023	CARDINAL
ejpam-4870	19	1	j.c. bonifacio	PERSON
ejpam-4870	19	2	c.j. andaya	GPE
ejpam-4870	19	3	d. magpantay	PERSON
ejpam-4870	20	1	j. pure	PERSON
ejpam-4870	20	2	16	CARDINAL
ejpam-4870	20	3	4	CARDINAL
ejpam-4870	20	4	2023	CARDINAL
ejpam-4870	20	5	2476	CARDINAL
ejpam-4870	21	1	one	CARDINAL
ejpam-4870	22	1	two	CARDINAL
ejpam-4870	27	1	4	CARDINAL
ejpam-4870	27	2	ept	ORG
ejpam-4870	27	3	two	CARDINAL
ejpam-4870	28	1	ept	ORG
ejpam-4870	29	1	1	CARDINAL
ejpam-4870	32	1	2	CARDINAL
ejpam-4870	33	1	2	CARDINAL
ejpam-4870	36	1	3	CARDINAL
ejpam-4870	36	2	5	CARDINAL
ejpam-4870	36	3	9	CARDINAL
ejpam-4870	36	4	8	CARDINAL
ejpam-4870	37	1	1	CARDINAL
ejpam-4870	39	1	j.c. bonifacio	PERSON
ejpam-4870	39	2	c.j. andaya	GPE
ejpam-4870	39	3	d. magpantay	PERSON
ejpam-4870	40	1	j. pure	PERSON
ejpam-4870	40	2	16	CARDINAL
ejpam-4870	40	3	4	CARDINAL
ejpam-4870	40	4	2023	CARDINAL
ejpam-4870	40	5	2476-2498 2478	QUANTITY
ejpam-4870	41	1	two	CARDINAL
ejpam-4870	47	1	1	CARDINAL
ejpam-4870	47	2	x3	GPE
ejpam-4870	49	1	x4	PERSON
ejpam-4870	51	1	4	CARDINAL
ejpam-4870	51	2	4	CARDINAL
ejpam-4870	52	1	1	CARDINAL
ejpam-4870	54	1	1	CARDINAL
ejpam-4870	55	1	1	CARDINAL
ejpam-4870	55	2	2	CARDINAL
ejpam-4870	59	1	2	CARDINAL
ejpam-4870	59	2	2	CARDINAL
ejpam-4870	64	1	2	CARDINAL
ejpam-4870	64	2	3	CARDINAL
ejpam-4870	65	1	j.c. bonifacio	PERSON
ejpam-4870	65	2	c.j. andaya	GPE
ejpam-4870	65	3	d. magpantay	PERSON
ejpam-4870	66	1	j. pure	PERSON
ejpam-4870	66	2	16	CARDINAL
ejpam-4870	66	3	4	CARDINAL
ejpam-4870	66	4	2023	CARDINAL
ejpam-4870	66	5	2476-2498 2479	DATE
ejpam-4870	66	6	3	CARDINAL
ejpam-4870	69	1	3	CARDINAL
ejpam-4870	69	2	3	CARDINAL
ejpam-4870	71	1	4	CARDINAL
ejpam-4870	73	1	only one	CARDINAL
ejpam-4870	76	1	3	CARDINAL
ejpam-4870	76	2	g1	ORG
ejpam-4870	76	3	g1	ORG
ejpam-4870	77	1	g1	ORG
ejpam-4870	77	2	g1	ORG
ejpam-4870	79	1	x3	GPE
ejpam-4870	81	1	4	CARDINAL
ejpam-4870	83	1	4	CARDINAL
ejpam-4870	83	2	5	CARDINAL
ejpam-4870	84	1	x. j.c.	PERSON
ejpam-4870	84	2	bonifacio	GPE
ejpam-4870	84	3	c.j. andaya	GPE
ejpam-4870	84	4	d. magpantay	PERSON
ejpam-4870	85	1	j. pure	PERSON
ejpam-4870	85	2	16	CARDINAL
ejpam-4870	85	3	4	CARDINAL
ejpam-4870	85	4	2023	CARDINAL
ejpam-4870	85	5	2476-2498 2480	DATE
ejpam-4870	86	1	x.	GPE
ejpam-4870	86	2	4	CARDINAL
ejpam-4870	88	1	x3	GPE
ejpam-4870	88	2	x4	GPE
ejpam-4870	91	1	x4	PERSON
ejpam-4870	91	2	x3, x5]	ORG
ejpam-4870	92	1	5	CARDINAL
ejpam-4870	92	2	3	CARDINAL
ejpam-4870	93	1	3	CARDINAL
ejpam-4870	93	2	1	CARDINAL
ejpam-4870	94	1	5	CARDINAL
ejpam-4870	94	2	5	CARDINAL
ejpam-4870	94	3	5	CARDINAL
ejpam-4870	94	4	1	CARDINAL
ejpam-4870	94	5	5	CARDINAL
ejpam-4870	95	1	1 x2 3	QUANTITY
ejpam-4870	95	2	x3 2	FAC
ejpam-4870	95	3	10	CARDINAL
ejpam-4870	95	4	bonifacio	GPE
ejpam-4870	95	5	c.j. andaya	GPE
ejpam-4870	95	6	d. magpantay	PERSON
ejpam-4870	96	1	j. pure	PERSON
ejpam-4870	96	2	16	CARDINAL
ejpam-4870	96	3	4	CARDINAL
ejpam-4870	96	4	2023	CARDINAL
ejpam-4870	96	5	2476	CARDINAL
ejpam-4870	97	1	1	CARDINAL
ejpam-4870	99	1	2	CARDINAL
ejpam-4870	101	1	6	CARDINAL
ejpam-4870	104	1	1	CARDINAL
ejpam-4870	106	1	2	CARDINAL
ejpam-4870	106	2	1	CARDINAL
ejpam-4870	106	3	2	CARDINAL
ejpam-4870	106	4	2	CARDINAL
ejpam-4870	107	1	one	CARDINAL
ejpam-4870	108	1	7	CARDINAL
ejpam-4870	109	1	xk	PERSON
ejpam-4870	110	1	0	CARDINAL
ejpam-4870	117	1	8	CARDINAL
ejpam-4870	119	1	xn−1	GPE
ejpam-4870	120	1	2	CARDINAL
ejpam-4870	121	1	1	CARDINAL
ejpam-4870	121	2	2	CARDINAL
ejpam-4870	121	3	j.c. bonifacio	PERSON
ejpam-4870	121	4	c.j. andaya	GPE
ejpam-4870	121	5	d. magpantay	PERSON
ejpam-4870	122	1	j. pure	PERSON
ejpam-4870	122	2	16	CARDINAL
ejpam-4870	122	3	4	CARDINAL
ejpam-4870	122	4	2023	CARDINAL
ejpam-4870	122	5	2476	CARDINAL
ejpam-4870	122	6	2	CARDINAL
ejpam-4870	124	1	5	CARDINAL
ejpam-4870	124	2	6	CARDINAL
ejpam-4870	124	3	3	CARDINAL
ejpam-4870	126	1	6	CARDINAL
ejpam-4870	126	2	3	CARDINAL
ejpam-4870	127	1	xn	ORG
ejpam-4870	127	2	vertices 1	DATE
ejpam-4870	127	3	2	DATE
ejpam-4870	128	1	12	CARDINAL
ejpam-4870	129	1	7	CARDINAL
ejpam-4870	129	2	3 1 2	CARDINAL
ejpam-4870	129	3	7	CARDINAL
ejpam-4870	129	4	3	CARDINAL
ejpam-4870	129	5	9	CARDINAL
ejpam-4870	130	1	kn	PERSON
ejpam-4870	131	1	one	CARDINAL
ejpam-4870	133	1	kn	PERSON
ejpam-4870	134	1	1	CARDINAL
ejpam-4870	134	2	2	CARDINAL
ejpam-4870	134	3	1	CARDINAL
ejpam-4870	135	1	2	CARDINAL
ejpam-4870	135	2	1	CARDINAL
ejpam-4870	135	3	2	CARDINAL
ejpam-4870	136	1	2	CARDINAL
ejpam-4870	136	2	bonifacio	GPE
ejpam-4870	136	3	c.j. andaya	GPE
ejpam-4870	136	4	d. magpantay	PERSON
ejpam-4870	137	1	j. pure	PERSON
ejpam-4870	137	2	16	CARDINAL
ejpam-4870	137	3	4	CARDINAL
ejpam-4870	137	4	2023	CARDINAL
ejpam-4870	137	5	2476-2498 2483	DATE
ejpam-4870	138	1	10	CARDINAL
ejpam-4870	139	1	⊆	CARDINAL
ejpam-4870	139	2	⊆	CARDINAL
ejpam-4870	142	1	6	CARDINAL
ejpam-4870	142	2	8	CARDINAL
ejpam-4870	143	1	⊆	CARDINAL
ejpam-4870	144	1	⊆	CARDINAL
ejpam-4870	148	1	8	CARDINAL
ejpam-4870	150	1	11	CARDINAL
ejpam-4870	151	1	7	CARDINAL
ejpam-4870	151	2	9	CARDINAL
ejpam-4870	152	1	⊆	CARDINAL
ejpam-4870	158	1	12	CARDINAL
ejpam-4870	161	1	g. j.c. bonifacio	PERSON
ejpam-4870	161	2	c.j. andaya	GPE
ejpam-4870	161	3	d. magpantay	PERSON
ejpam-4870	162	1	j. pure	PERSON
ejpam-4870	162	2	16	CARDINAL
ejpam-4870	162	3	4	CARDINAL
ejpam-4870	162	4	2023	CARDINAL
ejpam-4870	162	5	2476-2498 2484	DATE
ejpam-4870	165	1	x5 x3	PERSON
ejpam-4870	165	2	9	CARDINAL
ejpam-4870	165	3	3 1 2	CARDINAL
ejpam-4870	165	4	10	CARDINAL
ejpam-4870	165	5	c3	ORG
ejpam-4870	165	6	0	CARDINAL
ejpam-4870	165	7	8	CARDINAL
ejpam-4870	165	8	7	CARDINAL
ejpam-4870	165	9	12	CARDINAL
ejpam-4870	165	10	c3	ORG
ejpam-4870	165	11	3	CARDINAL
ejpam-4870	165	12	c3	ORG
ejpam-4870	166	1	c3	ORG
ejpam-4870	166	2	first	ORDINAL
ejpam-4870	166	3	0	CARDINAL
ejpam-4870	167	1	10	CARDINAL
ejpam-4870	168	1	1	CARDINAL
ejpam-4870	169	1	first	ORDINAL
ejpam-4870	169	2	1	CARDINAL
ejpam-4870	170	1	12	CARDINAL
ejpam-4870	170	2	12	CARDINAL
ejpam-4870	171	1	23	CARDINAL
ejpam-4870	171	2	31	CARDINAL
ejpam-4870	172	1	2	CARDINAL
ejpam-4870	173	1	first	ORDINAL
ejpam-4870	173	2	2	CARDINAL
ejpam-4870	173	3	12	CARDINAL
ejpam-4870	173	4	23	DATE
ejpam-4870	173	5	12	CARDINAL
ejpam-4870	173	6	23	CARDINAL
ejpam-4870	174	1	12	CARDINAL
ejpam-4870	174	2	31	DATE
ejpam-4870	174	3	23	CARDINAL
ejpam-4870	175	1	3	CARDINAL
ejpam-4870	176	1	12	CARDINAL
ejpam-4870	176	2	23	DATE
ejpam-4870	176	3	31	CARDINAL
ejpam-4870	176	4	13	CARDINAL
ejpam-4870	177	1	12	CARDINAL
ejpam-4870	177	2	23	DATE
ejpam-4870	177	3	31	DATE
ejpam-4870	178	1	12	CARDINAL
ejpam-4870	178	2	21	CARDINAL
ejpam-4870	180	1	2	CARDINAL
ejpam-4870	180	2	6	CARDINAL
ejpam-4870	181	1	2	CARDINAL
ejpam-4870	182	1	0 ≤	MONEY
ejpam-4870	182	2	1	CARDINAL
ejpam-4870	182	3	3	CARDINAL
ejpam-4870	183	1	2	CARDINAL
ejpam-4870	183	2	j.c. bonifacio	PERSON
ejpam-4870	183	3	c.j. andaya	GPE
ejpam-4870	183	4	d. magpantay	PERSON
ejpam-4870	184	1	j. pure	PERSON
ejpam-4870	184	2	16	CARDINAL
ejpam-4870	184	3	4	CARDINAL
ejpam-4870	184	4	2023	CARDINAL
ejpam-4870	184	5	2476	CARDINAL
ejpam-4870	184	6	11	CARDINAL
ejpam-4870	184	7	c3	ORG
ejpam-4870	184	8	1	CARDINAL
ejpam-4870	184	9	12	CARDINAL
ejpam-4870	184	10	c3	ORG
ejpam-4870	184	11	2	CARDINAL
ejpam-4870	184	12	1	CARDINAL
ejpam-4870	184	13	c3	ORG
ejpam-4870	184	14	example 8	DATE
ejpam-4870	185	1	j = 2	PERSON
ejpam-4870	185	2	3	CARDINAL
ejpam-4870	185	3	2	CARDINAL
ejpam-4870	186	1	2	CARDINAL
ejpam-4870	187	1	3 2	CARDINAL
ejpam-4870	188	1	3	CARDINAL
ejpam-4870	188	2	two	CARDINAL
ejpam-4870	188	3	g′	PERSON
ejpam-4870	188	4	g′	PERSON
ejpam-4870	191	1	13	DATE
ejpam-4870	192	1	g′	PERSON
ejpam-4870	192	2	g′	PERSON
ejpam-4870	193	1	7−→	CARDINAL
ejpam-4870	193	2	g′	PERSON
ejpam-4870	193	3	one	CARDINAL
ejpam-4870	198	1	one	CARDINAL
ejpam-4870	198	2	one	CARDINAL
ejpam-4870	198	3	g′	PERSON
ejpam-4870	199	1	9	CARDINAL
ejpam-4870	199	2	g′	PERSON
ejpam-4870	199	3	14	CARDINAL
ejpam-4870	200	1	7−→	CARDINAL
ejpam-4870	202	1	one	CARDINAL
ejpam-4870	206	1	j.c. bonifacio	PERSON
ejpam-4870	206	2	c.j. andaya	GPE
ejpam-4870	206	3	d. magpantay	PERSON
ejpam-4870	207	1	j. pure	PERSON
ejpam-4870	207	2	16	CARDINAL
ejpam-4870	207	3	4	CARDINAL
ejpam-4870	207	4	2023	CARDINAL
ejpam-4870	207	5	2476	CARDINAL
ejpam-4870	207	6	3 1 2	QUANTITY
ejpam-4870	207	7	13	CARDINAL
ejpam-4870	207	8	c3	ORG
ejpam-4870	207	9	3	CARDINAL
ejpam-4870	208	1	14	CARDINAL
ejpam-4870	217	1	13	CARDINAL
ejpam-4870	226	1	x3, x4] ∈	ORG
ejpam-4870	234	1	13	CARDINAL
ejpam-4870	236	1	14	DATE
ejpam-4870	238	1	g′	PERSON
ejpam-4870	238	2	7−→	CARDINAL
ejpam-4870	238	3	g′	PERSON
ejpam-4870	240	1	10	CARDINAL
ejpam-4870	241	1	example 9	DATE
ejpam-4870	241	2	7−→	CARDINAL
ejpam-4870	241	3	3	CARDINAL
ejpam-4870	241	4	3	CARDINAL
ejpam-4870	241	5	2	CARDINAL
ejpam-4870	242	1	3	CARDINAL
ejpam-4870	242	2	2	CARDINAL
ejpam-4870	242	3	bonifacio	GPE
ejpam-4870	242	4	c.j. andaya	GPE
ejpam-4870	242	5	d. magpantay	PERSON
ejpam-4870	243	1	j. pure	PERSON
ejpam-4870	243	2	16	CARDINAL
ejpam-4870	243	3	4	CARDINAL
ejpam-4870	243	4	2023	CARDINAL
ejpam-4870	243	5	2476	CARDINAL
ejpam-4870	243	6	3	CARDINAL
ejpam-4870	244	1	c3	PERSON
ejpam-4870	244	2	two	CARDINAL
ejpam-4870	245	1	15	CARDINAL
ejpam-4870	245	2	3 1 2 x3	QUANTITY
ejpam-4870	246	1	15	CARDINAL
ejpam-4870	246	2	1	CARDINAL
ejpam-4870	247	1	c3	PERSON
ejpam-4870	247	2	3	CARDINAL
ejpam-4870	247	3	3	CARDINAL
ejpam-4870	250	1	15	CARDINAL
ejpam-4870	252	1	⊆	CARDINAL
ejpam-4870	254	1	α(g	PERSON
ejpam-4870	254	2	⊆	CARDINAL
ejpam-4870	254	3	α(g	PERSON
ejpam-4870	254	4	16	DATE
ejpam-4870	257	1	nonempty	ORG
ejpam-4870	257	2	i. moreover	ORG
ejpam-4870	257	3	γ(g	NORP
ejpam-4870	259	1	⊆	CARDINAL
ejpam-4870	259	2	γ(g	PERSON
ejpam-4870	260	1	3	CARDINAL
ejpam-4870	260	2	1	CARDINAL
ejpam-4870	260	3	2	CARDINAL
ejpam-4870	260	4	12	CARDINAL
ejpam-4870	261	1	1 ≤ j ≤ n. j.c	QUANTITY
ejpam-4870	261	2	bonifacio	GPE
ejpam-4870	261	3	c.j. andaya	GPE
ejpam-4870	261	4	d. magpantay	PERSON
ejpam-4870	262	1	j. pure	PERSON
ejpam-4870	262	2	16	CARDINAL
ejpam-4870	262	3	4	CARDINAL
ejpam-4870	262	4	2023	CARDINAL
ejpam-4870	262	5	2476	CARDINAL
ejpam-4870	262	6	17	DATE
ejpam-4870	264	1	1 ≤ j ≤ n	QUANTITY
ejpam-4870	265	1	e(cn	LANGUAGE
ejpam-4870	265	2	1 ≤	QUANTITY
ejpam-4870	266	1	two	CARDINAL
ejpam-4870	266	2	∈	ORG
ejpam-4870	266	3	1	CARDINAL
ejpam-4870	267	1	1 ≤ j ≤ n. moreover	QUANTITY
ejpam-4870	268	1	one	CARDINAL
ejpam-4870	269	1	11	CARDINAL
ejpam-4870	270	1	j = 2	PERSON
ejpam-4870	270	2	11	CARDINAL
ejpam-4870	271	1	1	CARDINAL
ejpam-4870	271	2	2	DATE
ejpam-4870	271	3	3	DATE
ejpam-4870	271	4	4	CARDINAL
ejpam-4870	272	1	12	CARDINAL
ejpam-4870	272	2	23	DATE
ejpam-4870	272	3	34	DATE
ejpam-4870	272	4	41	CARDINAL
ejpam-4870	272	5	2	CARDINAL
ejpam-4870	273	1	ec(4,2	PERSON
ejpam-4870	274	1	12	CARDINAL
ejpam-4870	274	2	23	CARDINAL
ejpam-4870	274	3	12	CARDINAL
ejpam-4870	274	4	34	DATE
ejpam-4870	274	5	12	CARDINAL
ejpam-4870	274	6	41	CARDINAL
ejpam-4870	274	7	23	CARDINAL
ejpam-4870	274	8	34	DATE
ejpam-4870	274	9	23	CARDINAL
ejpam-4870	274	10	41	CARDINAL
ejpam-4870	274	11	34	CARDINAL
ejpam-4870	274	12	41	CARDINAL
ejpam-4870	275	1	12	CARDINAL
ejpam-4870	275	2	23	CARDINAL
ejpam-4870	275	3	12	CARDINAL
ejpam-4870	275	4	34	CARDINAL
ejpam-4870	275	5	12	CARDINAL
ejpam-4870	275	6	12	CARDINAL
ejpam-4870	275	7	23	CARDINAL
ejpam-4870	275	8	12	CARDINAL
ejpam-4870	275	9	34	CARDINAL
ejpam-4870	276	1	23	CARDINAL
ejpam-4870	276	2	41	CARDINAL
ejpam-4870	276	3	34	CARDINAL
ejpam-4870	276	4	41	CARDINAL
ejpam-4870	276	5	41	CARDINAL
ejpam-4870	276	6	23	CARDINAL
ejpam-4870	276	7	41	CARDINAL
ejpam-4870	276	8	34	CARDINAL
ejpam-4870	276	9	41	CARDINAL
ejpam-4870	277	1	12	CARDINAL
ejpam-4870	277	2	23	CARDINAL
ejpam-4870	277	3	34	CARDINAL
ejpam-4870	277	4	41	CARDINAL
ejpam-4870	277	5	12	CARDINAL
ejpam-4870	277	6	23	CARDINAL
ejpam-4870	277	7	34	CARDINAL
ejpam-4870	277	8	41	CARDINAL
ejpam-4870	277	9	two	CARDINAL
ejpam-4870	278	1	12	CARDINAL
ejpam-4870	278	2	23	CARDINAL
ejpam-4870	278	3	12	CARDINAL
ejpam-4870	278	4	34	CARDINAL
ejpam-4870	278	5	12	CARDINAL
ejpam-4870	278	6	23	CARDINAL
ejpam-4870	278	7	12	CARDINAL
ejpam-4870	278	8	41	CARDINAL
ejpam-4870	278	9	12	CARDINAL
ejpam-4870	278	10	23	CARDINAL
ejpam-4870	278	11	23	CARDINAL
ejpam-4870	278	12	34	CARDINAL
ejpam-4870	278	13	12	CARDINAL
ejpam-4870	278	14	23	CARDINAL
ejpam-4870	278	15	23	CARDINAL
ejpam-4870	278	16	41	CARDINAL
ejpam-4870	278	17	12	CARDINAL
ejpam-4870	278	18	34	DATE
ejpam-4870	278	19	12	CARDINAL
ejpam-4870	278	20	41	CARDINAL
ejpam-4870	278	21	12	CARDINAL
ejpam-4870	278	22	34	DATE
ejpam-4870	278	23	23	CARDINAL
ejpam-4870	278	24	34	CARDINAL
ejpam-4870	278	25	12	CARDINAL
ejpam-4870	278	26	34	DATE
ejpam-4870	278	27	34	CARDINAL
ejpam-4870	278	28	41	CARDINAL
ejpam-4870	278	29	12	CARDINAL
ejpam-4870	278	30	41	CARDINAL
ejpam-4870	278	31	23	CARDINAL
ejpam-4870	278	32	41	CARDINAL
ejpam-4870	278	33	12	CARDINAL
ejpam-4870	278	34	41	CARDINAL
ejpam-4870	278	35	34	CARDINAL
ejpam-4870	278	36	41	CARDINAL
ejpam-4870	278	37	23	CARDINAL
ejpam-4870	278	38	34	DATE
ejpam-4870	278	39	23	CARDINAL
ejpam-4870	278	40	41	CARDINAL
ejpam-4870	278	41	23	CARDINAL
ejpam-4870	278	42	34	DATE
ejpam-4870	278	43	34	CARDINAL
ejpam-4870	278	44	41	CARDINAL
ejpam-4870	278	45	23	CARDINAL
ejpam-4870	278	46	41	CARDINAL
ejpam-4870	278	47	34	CARDINAL
ejpam-4870	278	48	41	CARDINAL
ejpam-4870	279	1	6	CARDINAL
ejpam-4870	279	2	12	CARDINAL
ejpam-4870	280	1	16	CARDINAL
ejpam-4870	281	1	34	CARDINAL
ejpam-4870	281	2	41	CARDINAL
ejpam-4870	281	3	12	CARDINAL
ejpam-4870	281	4	23	CARDINAL
ejpam-4870	281	5	12	CARDINAL
ejpam-4870	281	6	34	CARDINAL
ejpam-4870	281	7	12	CARDINAL
ejpam-4870	281	8	41	CARDINAL
ejpam-4870	281	9	23	CARDINAL
ejpam-4870	281	10	34}{23	DATE
ejpam-4870	281	11	41	CARDINAL
ejpam-4870	281	12	16	CARDINAL
ejpam-4870	281	13	2	CARDINAL
ejpam-4870	283	1	j.c. bonifacio	PERSON
ejpam-4870	283	2	c.j. andaya	GPE
ejpam-4870	283	3	d. magpantay	PERSON
ejpam-4870	284	1	j. pure	PERSON
ejpam-4870	284	2	16	CARDINAL
ejpam-4870	284	3	4	CARDINAL
ejpam-4870	284	4	2023	CARDINAL
ejpam-4870	284	5	2476-2498 2489	DATE
ejpam-4870	284	6	e(ec(n,j	ORG
ejpam-4870	285	1	2	CARDINAL
ejpam-4870	287	1	first	ORDINAL
ejpam-4870	287	2	ec(n	ORG
ejpam-4870	288	1	3	CARDINAL
ejpam-4870	289	1	n ≥ 3	DATE
ejpam-4870	292	1	17	DATE
ejpam-4870	293	1	2	CARDINAL
ejpam-4870	298	1	n ≥ 3	DATE
ejpam-4870	298	2	2	CARDINAL
ejpam-4870	298	3	ec(4,2	PERSON
ejpam-4870	298	4	16	CARDINAL
ejpam-4870	299	1	6	CARDINAL
ejpam-4870	299	2	3	CARDINAL
ejpam-4870	299	3	j = 2	PERSON
ejpam-4870	300	1	4 2	CARDINAL
ejpam-4870	301	1	6	CARDINAL
ejpam-4870	302	1	one	CARDINAL
ejpam-4870	303	1	j ≥ 1	DATE
ejpam-4870	303	2	3	CARDINAL
ejpam-4870	304	1	1	CARDINAL
ejpam-4870	304	2	j = n. theorem	PERSON
ejpam-4870	304	3	4	CARDINAL
ejpam-4870	304	4	j = n. theorem	PERSON
ejpam-4870	304	5	4	DATE
ejpam-4870	305	1	n ≥ 3	DATE
ejpam-4870	307	1	j = n. proof	PERSON
ejpam-4870	309	1	4	CARDINAL
ejpam-4870	309	2	1	CARDINAL
ejpam-4870	311	1	1	CARDINAL
ejpam-4870	311	2	3	CARDINAL
ejpam-4870	311	3	j = n. if	PERSON
ejpam-4870	311	4	j = n	PERSON
ejpam-4870	313	1	only one	CARDINAL
ejpam-4870	313	2	e(ec(n,n	ORG
ejpam-4870	314	1	2	CARDINAL
ejpam-4870	316	1	e(ec(n,n	ORG
ejpam-4870	319	1	j = 4	PERSON
ejpam-4870	319	2	3	CARDINAL
ejpam-4870	320	1	12	CARDINAL
ejpam-4870	320	2	23	DATE
ejpam-4870	320	3	34	DATE
ejpam-4870	320	4	41	CARDINAL
ejpam-4870	321	1	c4	ORG
ejpam-4870	321	2	4	CARDINAL
ejpam-4870	321	3	4 4	DATE
ejpam-4870	321	4	1	CARDINAL
ejpam-4870	321	5	3	CARDINAL
ejpam-4870	322	1	1	CARDINAL
ejpam-4870	322	2	17	CARDINAL
ejpam-4870	323	1	12	CARDINAL
ejpam-4870	323	2	23	DATE
ejpam-4870	323	3	34	DATE
ejpam-4870	323	4	41	CARDINAL
ejpam-4870	323	5	17	CARDINAL
ejpam-4870	324	1	j = 1	PERSON
ejpam-4870	325	1	j.c. bonifacio	PERSON
ejpam-4870	325	2	c.j. andaya	GPE
ejpam-4870	325	3	d. magpantay	PERSON
ejpam-4870	326	1	j. pure	PERSON
ejpam-4870	326	2	16	CARDINAL
ejpam-4870	326	3	4	CARDINAL
ejpam-4870	326	4	2023	CARDINAL
ejpam-4870	326	5	2476	CARDINAL
ejpam-4870	327	1	n ≥ 3	DATE
ejpam-4870	328	1	j = 1	PERSON
ejpam-4870	329	1	j = 1	PERSON
ejpam-4870	331	1	ec(n,1	GPE
ejpam-4870	333	1	4	CARDINAL
ejpam-4870	333	2	j = 1	PERSON
ejpam-4870	333	3	4	CARDINAL
ejpam-4870	333	4	12	CARDINAL
ejpam-4870	333	5	23	DATE
ejpam-4870	333	6	31	DATE
ejpam-4870	333	7	1	CARDINAL
ejpam-4870	335	1	12	CARDINAL
ejpam-4870	335	2	23	CARDINAL
ejpam-4870	335	3	31	CARDINAL
ejpam-4870	338	1	3	CARDINAL
ejpam-4870	338	2	18	CARDINAL
ejpam-4870	339	1	31	CARDINAL
ejpam-4870	339	2	12	CARDINAL
ejpam-4870	339	3	23	CARDINAL
ejpam-4870	339	4	18	CARDINAL
ejpam-4870	339	5	18	CARDINAL
ejpam-4870	339	6	j = 1	PERSON
ejpam-4870	339	7	zero	CARDINAL
ejpam-4870	340	1	j. lemma	PERSON
ejpam-4870	340	2	1	CARDINAL
ejpam-4870	340	3	two	CARDINAL
ejpam-4870	341	1	1	CARDINAL
ejpam-4870	342	1	1	CARDINAL
ejpam-4870	343	1	1	CARDINAL
ejpam-4870	343	2	0	CARDINAL
ejpam-4870	343	3	1	CARDINAL
ejpam-4870	343	4	two	CARDINAL
ejpam-4870	343	5	1	CARDINAL
ejpam-4870	343	6	∩	PERSON
ejpam-4870	343	7	0	CARDINAL
ejpam-4870	344	1	j =	PERSON
ejpam-4870	344	2	1	CARDINAL
ejpam-4870	345	1	j.	PERSON
ejpam-4870	345	2	2	CARDINAL
ejpam-4870	346	1	j ≤ n. moreover	PERSON
ejpam-4870	346	2	j =	PERSON
ejpam-4870	346	3	+ 1	CARDINAL
ejpam-4870	346	4	2 + 1	DATE
ejpam-4870	346	5	1 2 + 1	CARDINAL
ejpam-4870	347	1	3	CARDINAL
ejpam-4870	348	1	j ≤ n. j.c. bonifacio	PERSON
ejpam-4870	348	2	c.j. andaya	GPE
ejpam-4870	348	3	d. magpantay	PERSON
ejpam-4870	349	1	j. pure	PERSON
ejpam-4870	349	2	16	CARDINAL
ejpam-4870	349	3	4	CARDINAL
ejpam-4870	349	4	2023	CARDINAL
ejpam-4870	349	5	2476-2498 2491	CARDINAL
ejpam-4870	349	6	2	CARDINAL
ejpam-4870	349	7	∩	PERSON
ejpam-4870	349	8	1	CARDINAL
ejpam-4870	349	9	one	CARDINAL
ejpam-4870	350	1	j =	PERSON
ejpam-4870	350	2	1	CARDINAL
ejpam-4870	350	3	2 + 1	DATE
ejpam-4870	350	4	1	CARDINAL
ejpam-4870	351	1	j ≤ n. moreover	PERSON
ejpam-4870	351	2	j =	PERSON
ejpam-4870	351	3	+ 1	CARDINAL
ejpam-4870	351	4	2 + 1	DATE
ejpam-4870	351	5	1 2 + 1− 1	TIME
ejpam-4870	351	6	2	CARDINAL
ejpam-4870	352	1	j ≤ n. therefore	PERSON
ejpam-4870	352	2	1	CARDINAL
ejpam-4870	352	3	5	CARDINAL
ejpam-4870	352	4	two	CARDINAL
ejpam-4870	352	5	j = 3	PERSON
ejpam-4870	352	6	5	CARDINAL
ejpam-4870	352	7	12	CARDINAL
ejpam-4870	352	8	32	DATE
ejpam-4870	352	9	34	DATE
ejpam-4870	352	10	41	CARDINAL
ejpam-4870	352	11	3	CARDINAL
ejpam-4870	354	1	12	CARDINAL
ejpam-4870	354	2	23	DATE
ejpam-4870	354	3	34	CARDINAL
ejpam-4870	354	4	12	CARDINAL
ejpam-4870	354	5	23	DATE
ejpam-4870	354	6	41	CARDINAL
ejpam-4870	354	7	12	CARDINAL
ejpam-4870	354	8	34	DATE
ejpam-4870	354	9	41	CARDINAL
ejpam-4870	354	10	23	CARDINAL
ejpam-4870	354	11	34	DATE
ejpam-4870	354	12	41	CARDINAL
ejpam-4870	355	1	two	CARDINAL
ejpam-4870	355	2	12	CARDINAL
ejpam-4870	355	3	23	DATE
ejpam-4870	355	4	34	CARDINAL
ejpam-4870	355	5	12	CARDINAL
ejpam-4870	355	6	23	DATE
ejpam-4870	355	7	41	CARDINAL
ejpam-4870	355	8	12	CARDINAL
ejpam-4870	355	9	23	DATE
ejpam-4870	355	10	34}∩	DATE
ejpam-4870	355	11	12	CARDINAL
ejpam-4870	355	12	23	DATE
ejpam-4870	355	13	41	CARDINAL
ejpam-4870	355	14	12	CARDINAL
ejpam-4870	355	15	23	CARDINAL
ejpam-4870	355	16	2	CARDINAL
ejpam-4870	356	1	two	CARDINAL
ejpam-4870	356	2	more than 1	CARDINAL
ejpam-4870	356	3	0	CARDINAL
ejpam-4870	356	4	5	CARDINAL
ejpam-4870	356	5	∈	ORG
ejpam-4870	356	6	deg(a	PERSON
ejpam-4870	358	1	lemma 1	ORG
ejpam-4870	358	2	∩	PERSON
ejpam-4870	358	3	1	CARDINAL
ejpam-4870	358	4	17	CARDINAL
ejpam-4870	358	5	two	CARDINAL
ejpam-4870	358	6	one	CARDINAL
ejpam-4870	359	1	∩	PERSON
ejpam-4870	359	2	1	CARDINAL
ejpam-4870	361	1	∈	ORG
ejpam-4870	362	1	deg(a	PERSON
ejpam-4870	362	2	0	CARDINAL
ejpam-4870	362	3	6	CARDINAL
ejpam-4870	362	4	0	CARDINAL
ejpam-4870	362	5	6	CARDINAL
ejpam-4870	363	1	4	CARDINAL
ejpam-4870	364	1	12	CARDINAL
ejpam-4870	364	2	23	DATE
ejpam-4870	364	3	34	DATE
ejpam-4870	364	4	41	CARDINAL
ejpam-4870	365	1	3	CARDINAL
ejpam-4870	366	1	12	CARDINAL
ejpam-4870	366	2	23	DATE
ejpam-4870	366	3	34	CARDINAL
ejpam-4870	366	4	12	CARDINAL
ejpam-4870	366	5	23	DATE
ejpam-4870	366	6	41	CARDINAL
ejpam-4870	366	7	12	CARDINAL
ejpam-4870	366	8	34	DATE
ejpam-4870	366	9	41	CARDINAL
ejpam-4870	366	10	23	CARDINAL
ejpam-4870	366	11	34	DATE
ejpam-4870	366	12	41	CARDINAL
ejpam-4870	366	13	12	CARDINAL
ejpam-4870	366	14	23	DATE
ejpam-4870	366	15	34}∩{12	DATE
ejpam-4870	366	16	23	CARDINAL
ejpam-4870	366	17	41	CARDINAL
ejpam-4870	366	18	12	CARDINAL
ejpam-4870	366	19	23	CARDINAL
ejpam-4870	366	20	2	CARDINAL
ejpam-4870	366	21	17	DATE
ejpam-4870	366	22	12	CARDINAL
ejpam-4870	366	23	23	DATE
ejpam-4870	366	24	34	CARDINAL
ejpam-4870	366	25	12	CARDINAL
ejpam-4870	366	26	23	DATE
ejpam-4870	366	27	41	CARDINAL
ejpam-4870	367	1	12	CARDINAL
ejpam-4870	367	2	34	DATE
ejpam-4870	367	3	41	CARDINAL
ejpam-4870	367	4	23	CARDINAL
ejpam-4870	367	5	34	DATE
ejpam-4870	367	6	41	CARDINAL
ejpam-4870	367	7	|{12	DATE
ejpam-4870	367	8	34	DATE
ejpam-4870	367	9	41	CARDINAL
ejpam-4870	367	10	23	CARDINAL
ejpam-4870	367	11	34	DATE
ejpam-4870	367	12	41}|	CARDINAL
ejpam-4870	367	13	2	CARDINAL
ejpam-4870	368	1	0	CARDINAL
ejpam-4870	369	1	j.c. bonifacio	PERSON
ejpam-4870	369	2	c.j. andaya	GPE
ejpam-4870	369	3	d. magpantay	PERSON
ejpam-4870	370	1	j. pure	PERSON
ejpam-4870	370	2	16	CARDINAL
ejpam-4870	370	3	4	CARDINAL
ejpam-4870	370	4	2023	CARDINAL
ejpam-4870	370	5	2476-2498 2492	DATE
ejpam-4870	370	6	0	CARDINAL
ejpam-4870	372	1	j = 1	PERSON
ejpam-4870	372	2	1	CARDINAL
ejpam-4870	372	3	2 ≤ j ≤	QUANTITY
ejpam-4870	372	4	6	CARDINAL
ejpam-4870	372	5	2 ≤ j ≤	QUANTITY
ejpam-4870	372	6	6	CARDINAL
ejpam-4870	372	7	∈	ORG
ejpam-4870	372	8	2 ≤ j ≤	QUANTITY
ejpam-4870	372	9	deg(a	PERSON
ejpam-4870	374	1	∈	ORG
ejpam-4870	375	1	one	CARDINAL
ejpam-4870	380	1	2 ≤ j ≤	QUANTITY
ejpam-4870	380	2	j = 1	PERSON
ejpam-4870	381	1	7	DATE
ejpam-4870	381	2	2 ≤ j ≤	QUANTITY
ejpam-4870	382	1	3	CARDINAL
ejpam-4870	382	2	7	CARDINAL
ejpam-4870	382	3	12	CARDINAL
ejpam-4870	382	4	23	DATE
ejpam-4870	382	5	34	DATE
ejpam-4870	382	6	45	DATE
ejpam-4870	382	7	51	CARDINAL
ejpam-4870	383	1	j = 3	PERSON
ejpam-4870	385	1	12	CARDINAL
ejpam-4870	385	2	23	DATE
ejpam-4870	385	3	34	CARDINAL
ejpam-4870	385	4	12	CARDINAL
ejpam-4870	385	5	23	DATE
ejpam-4870	385	6	45	DATE
ejpam-4870	385	7	12	CARDINAL
ejpam-4870	385	8	23	DATE
ejpam-4870	385	9	51	DATE
ejpam-4870	385	10	12	CARDINAL
ejpam-4870	385	11	34	DATE
ejpam-4870	385	12	45	CARDINAL
ejpam-4870	385	13	12	CARDINAL
ejpam-4870	385	14	34	DATE
ejpam-4870	385	15	51	CARDINAL
ejpam-4870	385	16	12	CARDINAL
ejpam-4870	385	17	45	DATE
ejpam-4870	385	18	51	DATE
ejpam-4870	385	19	23	CARDINAL
ejpam-4870	385	20	34	DATE
ejpam-4870	385	21	45	CARDINAL
ejpam-4870	385	22	23	CARDINAL
ejpam-4870	385	23	34	DATE
ejpam-4870	385	24	51	CARDINAL
ejpam-4870	385	25	23	CARDINAL
ejpam-4870	385	26	45	DATE
ejpam-4870	385	27	51	DATE
ejpam-4870	385	28	34	CARDINAL
ejpam-4870	385	29	45	DATE
ejpam-4870	385	30	51	CARDINAL
ejpam-4870	385	31	19	CARDINAL
ejpam-4870	386	1	3	CARDINAL
ejpam-4870	387	1	6	CARDINAL
ejpam-4870	387	2	deg(a	PERSON
ejpam-4870	388	1	n−	ORG
ejpam-4870	388	2	j j − 1	WORK_OF_ART
ejpam-4870	388	3	3	CARDINAL
ejpam-4870	388	4	2 2	CARDINAL
ejpam-4870	388	5	3(1	CARDINAL
ejpam-4870	389	1	ec(n	ORG
ejpam-4870	390	1	j.c. bonifacio	PERSON
ejpam-4870	390	2	c.j. andaya	GPE
ejpam-4870	390	3	d. magpantay	PERSON
ejpam-4870	391	1	j. pure	PERSON
ejpam-4870	391	2	16	CARDINAL
ejpam-4870	391	3	4	CARDINAL
ejpam-4870	391	4	2023	CARDINAL
ejpam-4870	391	5	2476-2498 2493	DATE
ejpam-4870	391	6	12	CARDINAL
ejpam-4870	391	7	23	DATE
ejpam-4870	391	8	34	CARDINAL
ejpam-4870	391	9	12	CARDINAL
ejpam-4870	391	10	23	DATE
ejpam-4870	391	11	45	CARDINAL
ejpam-4870	391	12	12	CARDINAL
ejpam-4870	391	13	23	DATE
ejpam-4870	391	14	51	DATE
ejpam-4870	391	15	12	CARDINAL
ejpam-4870	391	16	34	DATE
ejpam-4870	391	17	45	CARDINAL
ejpam-4870	391	18	12	CARDINAL
ejpam-4870	391	19	34	DATE
ejpam-4870	391	20	51	CARDINAL
ejpam-4870	391	21	12	CARDINAL
ejpam-4870	391	22	45	DATE
ejpam-4870	391	23	51	CARDINAL
ejpam-4870	391	24	23	CARDINAL
ejpam-4870	391	25	34	DATE
ejpam-4870	391	26	45	CARDINAL
ejpam-4870	391	27	23	CARDINAL
ejpam-4870	391	28	34	DATE
ejpam-4870	391	29	51	CARDINAL
ejpam-4870	391	30	23	CARDINAL
ejpam-4870	391	31	45	DATE
ejpam-4870	391	32	51	CARDINAL
ejpam-4870	391	33	34	CARDINAL
ejpam-4870	391	34	45	DATE
ejpam-4870	391	35	51	CARDINAL
ejpam-4870	391	36	19	CARDINAL
ejpam-4870	391	37	1	CARDINAL
ejpam-4870	393	1	2 ≤ j ≤	QUANTITY
ejpam-4870	394	1	6	CARDINAL
ejpam-4870	394	2	8	CARDINAL
ejpam-4870	395	1	19	CARDINAL
ejpam-4870	396	1	deg(a	PERSON
ejpam-4870	396	2	3	CARDINAL
ejpam-4870	396	3	∈	ORG
ejpam-4870	396	4	3	CARDINAL
ejpam-4870	398	1	1	CARDINAL
ejpam-4870	398	2	1	CARDINAL
ejpam-4870	398	3	ec(n	ORG
ejpam-4870	401	1	2 ≤ j ≤	QUANTITY
ejpam-4870	401	2	ec(n	ORG
ejpam-4870	401	3	|e(ec(n	PERSON
ejpam-4870	404	1	11	CARDINAL
ejpam-4870	404	2	ec(n	ORG
ejpam-4870	404	3	1	CARDINAL
ejpam-4870	405	1	1	CARDINAL
ejpam-4870	405	2	ec(n	ORG
ejpam-4870	405	3	2	CARDINAL
ejpam-4870	406	1	2 ≤ j ≤	QUANTITY
ejpam-4870	409	1	ec(n	ORG
ejpam-4870	409	2	2 ≤ j ≤	QUANTITY
ejpam-4870	409	3	9	CARDINAL
ejpam-4870	409	4	19	CARDINAL
ejpam-4870	411	1	3	CARDINAL
ejpam-4870	411	2	3	CARDINAL
ejpam-4870	411	3	10	CARDINAL
ejpam-4870	411	4	3	CARDINAL
ejpam-4870	411	5	7	CARDINAL
ejpam-4870	411	6	|e(ec(5,3	PERSON
ejpam-4870	412	1	2	CARDINAL
ejpam-4870	412	2	15	CARDINAL
ejpam-4870	413	1	j.c. bonifacio	PERSON
ejpam-4870	413	2	c.j. andaya	GPE
ejpam-4870	413	3	d. magpantay	PERSON
ejpam-4870	414	1	j. pure	PERSON
ejpam-4870	414	2	16	CARDINAL
ejpam-4870	414	3	4	CARDINAL
ejpam-4870	414	4	2023	CARDINAL
ejpam-4870	414	5	2476	CARDINAL
ejpam-4870	415	1	3	CARDINAL
ejpam-4870	415	2	8	CARDINAL
ejpam-4870	416	1	cn ec(n	PERSON
ejpam-4870	416	2	3	CARDINAL
ejpam-4870	417	1	3	CARDINAL
ejpam-4870	418	1	2	CARDINAL
ejpam-4870	420	1	3	CARDINAL
ejpam-4870	421	1	1 or	CARDINAL
ejpam-4870	421	2	4	CARDINAL
ejpam-4870	422	1	3	CARDINAL
ejpam-4870	423	1	j < 2	LAW
ejpam-4870	423	2	1	CARDINAL
ejpam-4870	424	1	4, ec(n	DATE
ejpam-4870	424	2	3	CARDINAL
ejpam-4870	425	1	j > 2	LAW
ejpam-4870	425	2	1	CARDINAL
ejpam-4870	425	3	4	CARDINAL
ejpam-4870	425	4	3	CARDINAL
ejpam-4870	426	1	2	CARDINAL
ejpam-4870	426	2	2	CARDINAL
ejpam-4870	426	3	2	CARDINAL
ejpam-4870	426	4	6	CARDINAL
ejpam-4870	426	5	2	CARDINAL
ejpam-4870	426	6	3	CARDINAL
ejpam-4870	426	7	3 2	CARDINAL
ejpam-4870	427	1	3	CARDINAL
ejpam-4870	428	1	3	CARDINAL
ejpam-4870	430	1	2	CARDINAL
ejpam-4870	430	2	10	CARDINAL
ejpam-4870	431	1	2	CARDINAL
ejpam-4870	433	1	12	CARDINAL
ejpam-4870	433	2	23	CARDINAL
ejpam-4870	433	3	12	CARDINAL
ejpam-4870	433	4	31	DATE
ejpam-4870	433	5	23	CARDINAL
ejpam-4870	434	1	12	CARDINAL
ejpam-4870	434	2	23	CARDINAL
ejpam-4870	434	3	12	CARDINAL
ejpam-4870	434	4	12	CARDINAL
ejpam-4870	434	5	12	CARDINAL
ejpam-4870	434	6	23	CARDINAL
ejpam-4870	434	7	12	CARDINAL
ejpam-4870	435	1	12	CARDINAL
ejpam-4870	435	2	23	CARDINAL
ejpam-4870	435	3	23	CARDINAL
ejpam-4870	435	4	12	CARDINAL
ejpam-4870	435	5	31	DATE
ejpam-4870	435	6	23	CARDINAL
ejpam-4870	436	1	ec(3,2	PERSON
ejpam-4870	436	2	3	CARDINAL
ejpam-4870	436	3	20	CARDINAL
ejpam-4870	437	1	23	CARDINAL
ejpam-4870	437	2	12	CARDINAL
ejpam-4870	437	3	23	CARDINAL
ejpam-4870	437	4	12	CARDINAL
ejpam-4870	437	5	31	CARDINAL
ejpam-4870	437	6	20	CARDINAL
ejpam-4870	437	7	ec(3,2) 4	ORG
ejpam-4870	438	1	j.c. bonifacio	PERSON
ejpam-4870	438	2	c.j. andaya	GPE
ejpam-4870	438	3	d. magpantay	PERSON
ejpam-4870	439	1	j. pure	PERSON
ejpam-4870	439	2	16	CARDINAL
ejpam-4870	439	3	4	CARDINAL
ejpam-4870	439	4	2023	CARDINAL
ejpam-4870	439	5	2476	CARDINAL
ejpam-4870	440	1	j = 2	PERSON
ejpam-4870	440	2	9	CARDINAL
ejpam-4870	441	1	9	CARDINAL
ejpam-4870	442	1	2	CARDINAL
ejpam-4870	443	1	α(ec(n,2	LANGUAGE
ejpam-4870	446	1	2	CARDINAL
ejpam-4870	446	2	2	CARDINAL
ejpam-4870	447	1	2	CARDINAL
ejpam-4870	448	1	⊆	CARDINAL
ejpam-4870	449	1	two	CARDINAL
ejpam-4870	450	1	α(ec(n,2	LANGUAGE
ejpam-4870	450	2	two	CARDINAL
ejpam-4870	451	1	2	CARDINAL
ejpam-4870	452	1	2	CARDINAL
ejpam-4870	454	1	2	CARDINAL
ejpam-4870	456	1	2	CARDINAL
ejpam-4870	457	1	α(ec(n,2	PERSON
ejpam-4870	458	1	11	CARDINAL
ejpam-4870	458	2	11	CARDINAL
ejpam-4870	459	1	2	CARDINAL
ejpam-4870	461	1	12	CARDINAL
ejpam-4870	461	2	23	CARDINAL
ejpam-4870	461	3	12	CARDINAL
ejpam-4870	461	4	34	DATE
ejpam-4870	461	5	12	CARDINAL
ejpam-4870	461	6	45	DATE
ejpam-4870	461	7	12	CARDINAL
ejpam-4870	461	8	56	DATE
ejpam-4870	461	9	12	CARDINAL
ejpam-4870	461	10	61	DATE
ejpam-4870	461	11	23	CARDINAL
ejpam-4870	461	12	34	DATE
ejpam-4870	461	13	23	CARDINAL
ejpam-4870	461	14	45	DATE
ejpam-4870	461	15	23	CARDINAL
ejpam-4870	461	16	56	DATE
ejpam-4870	461	17	23	CARDINAL
ejpam-4870	461	18	61	DATE
ejpam-4870	461	19	34	CARDINAL
ejpam-4870	461	20	45	DATE
ejpam-4870	461	21	34	CARDINAL
ejpam-4870	461	22	56	DATE
ejpam-4870	461	23	34	CARDINAL
ejpam-4870	461	24	61	DATE
ejpam-4870	461	25	45	CARDINAL
ejpam-4870	461	26	56	DATE
ejpam-4870	461	27	45	CARDINAL
ejpam-4870	461	28	61	DATE
ejpam-4870	461	29	56	CARDINAL
ejpam-4870	461	30	61	CARDINAL
ejpam-4870	462	1	21	CARDINAL
ejpam-4870	463	1	ia ⊆	ORG
ejpam-4870	463	2	1 ≤	QUANTITY
ejpam-4870	464	1	2	CARDINAL
ejpam-4870	465	1	12	CARDINAL
ejpam-4870	465	2	23	CARDINAL
ejpam-4870	465	3	34	CARDINAL
ejpam-4870	465	4	45	CARDINAL
ejpam-4870	465	5	12	CARDINAL
ejpam-4870	465	6	23	CARDINAL
ejpam-4870	465	7	34	CARDINAL
ejpam-4870	465	8	45	CARDINAL
ejpam-4870	465	9	12	CARDINAL
ejpam-4870	465	10	23	CARDINAL
ejpam-4870	465	11	34	CARDINAL
ejpam-4870	465	12	45	DATE
ejpam-4870	466	1	2	CARDINAL
ejpam-4870	467	1	12	CARDINAL
ejpam-4870	467	2	23	CARDINAL
ejpam-4870	467	3	34	CARDINAL
ejpam-4870	467	4	45	DATE
ejpam-4870	467	5	56	CARDINAL
ejpam-4870	467	6	61	CARDINAL
ejpam-4870	469	1	3	CARDINAL
ejpam-4870	469	2	3	CARDINAL
ejpam-4870	470	1	3	CARDINAL
ejpam-4870	471	1	3	CARDINAL
ejpam-4870	471	2	9	CARDINAL
ejpam-4870	471	3	2	CARDINAL
ejpam-4870	472	1	2	CARDINAL
ejpam-4870	473	1	4.2	CARDINAL
ejpam-4870	473	2	j = 2	PERSON
ejpam-4870	473	3	10	CARDINAL
ejpam-4870	474	1	10	CARDINAL
ejpam-4870	475	1	2	CARDINAL
ejpam-4870	477	1	j.c. bonifacio	PERSON
ejpam-4870	477	2	c.j. andaya	GPE
ejpam-4870	477	3	d. magpantay	PERSON
ejpam-4870	478	1	j. pure	PERSON
ejpam-4870	478	2	16	CARDINAL
ejpam-4870	478	3	4	CARDINAL
ejpam-4870	478	4	2023	CARDINAL
ejpam-4870	478	5	2476-2498 2496	QUANTITY
ejpam-4870	478	6	12	CARDINAL
ejpam-4870	478	7	23	CARDINAL
ejpam-4870	478	8	12	CARDINAL
ejpam-4870	478	9	34	CARDINAL
ejpam-4870	478	10	12	CARDINAL
ejpam-4870	478	11	45	DATE
ejpam-4870	478	12	12	CARDINAL
ejpam-4870	478	13	56	CARDINAL
ejpam-4870	478	14	12	CARDINAL
ejpam-4870	478	15	61	DATE
ejpam-4870	478	16	23	CARDINAL
ejpam-4870	478	17	23	CARDINAL
ejpam-4870	478	18	45	DATE
ejpam-4870	478	19	23	CARDINAL
ejpam-4870	478	20	56	CARDINAL
ejpam-4870	478	21	23	CARDINAL
ejpam-4870	478	22	61	DATE
ejpam-4870	478	23	34	CARDINAL
ejpam-4870	478	24	45	CARDINAL
ejpam-4870	478	25	34	CARDINAL
ejpam-4870	478	26	56	CARDINAL
ejpam-4870	478	27	34	CARDINAL
ejpam-4870	478	28	61	DATE
ejpam-4870	478	29	45	CARDINAL
ejpam-4870	478	30	56	CARDINAL
ejpam-4870	478	31	45	CARDINAL
ejpam-4870	478	32	61	DATE
ejpam-4870	478	33	56	CARDINAL
ejpam-4870	478	34	61	CARDINAL
ejpam-4870	478	35	21	CARDINAL
ejpam-4870	479	1	2	CARDINAL
ejpam-4870	479	2	2	CARDINAL
ejpam-4870	480	1	2	CARDINAL
ejpam-4870	481	1	2	CARDINAL
ejpam-4870	482	1	1	CARDINAL
ejpam-4870	482	2	two	CARDINAL
ejpam-4870	485	1	1	CARDINAL
ejpam-4870	491	1	∈	ORG
ejpam-4870	491	2	∩	PERSON
ejpam-4870	491	3	1	CARDINAL
ejpam-4870	492	1	∈	ORG
ejpam-4870	495	1	2	CARDINAL
ejpam-4870	496	1	2	CARDINAL
ejpam-4870	497	1	1 <	QUANTITY
ejpam-4870	501	1	∈	ORG
ejpam-4870	501	2	1	CARDINAL
ejpam-4870	502	1	∈	ORG
ejpam-4870	505	1	12	CARDINAL
ejpam-4870	506	1	12	CARDINAL
ejpam-4870	507	1	21	DATE
ejpam-4870	508	1	12	CARDINAL
ejpam-4870	508	2	23	CARDINAL
ejpam-4870	508	3	34	CARDINAL
ejpam-4870	508	4	45	DATE
ejpam-4870	508	5	56	CARDINAL
ejpam-4870	508	6	61	CARDINAL
ejpam-4870	508	7	⊆	CARDINAL
ejpam-4870	509	1	j.c. bonifacio	GPE
ejpam-4870	509	2	c.j. andaya	GPE
ejpam-4870	509	3	d. magpantay	PERSON
ejpam-4870	510	1	j. pure	PERSON
ejpam-4870	510	2	16	CARDINAL
ejpam-4870	510	3	4	CARDINAL
ejpam-4870	510	4	2023	CARDINAL
ejpam-4870	510	5	2476-2498 2497	QUANTITY
ejpam-4870	512	1	12	CARDINAL
ejpam-4870	512	2	34	DATE
ejpam-4870	512	3	12	CARDINAL
ejpam-4870	512	4	45	DATE
ejpam-4870	512	5	12	CARDINAL
ejpam-4870	512	6	56	DATE
ejpam-4870	512	7	12	CARDINAL
ejpam-4870	512	8	61	DATE
ejpam-4870	512	9	23	CARDINAL
ejpam-4870	512	10	34	DATE
ejpam-4870	512	11	23	CARDINAL
ejpam-4870	512	12	45	DATE
ejpam-4870	512	13	23	CARDINAL
ejpam-4870	512	14	56	DATE
ejpam-4870	512	15	23	CARDINAL
ejpam-4870	512	16	61	DATE
ejpam-4870	512	17	34	CARDINAL
ejpam-4870	512	18	56	DATE
ejpam-4870	512	19	34	CARDINAL
ejpam-4870	512	20	61	DATE
ejpam-4870	512	21	45	CARDINAL
ejpam-4870	512	22	56	DATE
ejpam-4870	512	23	45	CARDINAL
ejpam-4870	512	24	61	DATE
ejpam-4870	513	1	12	CARDINAL
ejpam-4870	513	2	34	CARDINAL
ejpam-4870	513	3	12	CARDINAL
ejpam-4870	513	4	45	DATE
ejpam-4870	513	5	12	CARDINAL
ejpam-4870	513	6	56	DATE
ejpam-4870	513	7	12	CARDINAL
ejpam-4870	513	8	61	DATE
ejpam-4870	513	9	23	CARDINAL
ejpam-4870	513	10	34	DATE
ejpam-4870	513	11	23	CARDINAL
ejpam-4870	513	12	45	DATE
ejpam-4870	513	13	23	CARDINAL
ejpam-4870	513	14	56	DATE
ejpam-4870	513	15	23	CARDINAL
ejpam-4870	513	16	61	DATE
ejpam-4870	513	17	12	CARDINAL
ejpam-4870	513	18	23	CARDINAL
ejpam-4870	514	1	34	CARDINAL
ejpam-4870	514	2	56	DATE
ejpam-4870	514	3	34	CARDINAL
ejpam-4870	514	4	61	DATE
ejpam-4870	514	5	45	CARDINAL
ejpam-4870	514	6	56	DATE
ejpam-4870	514	7	45	CARDINAL
ejpam-4870	514	8	61	DATE
ejpam-4870	514	9	34	CARDINAL
ejpam-4870	514	10	45	DATE
ejpam-4870	515	1	12	CARDINAL
ejpam-4870	515	2	23	CARDINAL
ejpam-4870	515	3	34	CARDINAL
ejpam-4870	515	4	45	DATE
ejpam-4870	516	1	3	CARDINAL
ejpam-4870	517	1	less than 3	CARDINAL
ejpam-4870	518	1	10	CARDINAL
ejpam-4870	518	2	2	CARDINAL
ejpam-4870	519	1	6 2	CARDINAL
ejpam-4870	520	1	5	CARDINAL
ejpam-4870	522	1	two	CARDINAL
ejpam-4870	522	2	one	CARDINAL
ejpam-4870	524	1	e(ec(n,j	ORG
ejpam-4870	527	1	j = n. moreover	PERSON
ejpam-4870	527	2	j = 1	PERSON
ejpam-4870	527	3	0	CARDINAL
ejpam-4870	528	1	2 ≤ j ≤	QUANTITY
ejpam-4870	528	2	∈	ORG
ejpam-4870	528	3	2 ≤ j ≤	QUANTITY
ejpam-4870	528	4	deg(a	PERSON
ejpam-4870	530	1	ec(n	ORG
ejpam-4870	531	1	2	CARDINAL
ejpam-4870	531	2	2 ≤	QUANTITY
ejpam-4870	531	3	3	CARDINAL
ejpam-4870	535	1	j = 2	PERSON
ejpam-4870	535	2	2498	CARDINAL
ejpam-4870	537	1	j.	PERSON
ejpam-4870	540	1	1	CARDINAL
ejpam-4870	540	2	a. asinowski	PERSON
ejpam-4870	540	3	a. suk	PERSON
ejpam-4870	542	1	2009	DATE
ejpam-4870	543	1	2	CARDINAL
ejpam-4870	543	2	m. stern	PERSON
ejpam-4870	546	1	3	CARDINAL
ejpam-4870	549	1	4	CARDINAL
ejpam-4870	549	2	r. jamison	PERSON
ejpam-4870	552	1	1985	DATE
ejpam-4870	553	1	5	CARDINAL
ejpam-4870	554	1	combinatorics	ORG
ejpam-4870	555	1	new york	GPE
ejpam-4870	555	2	ny.2008	ORG
ejpam-4870	556	1	6	CARDINAL
ejpam-4870	556	2	sagan	PERSON
ejpam-4870	556	3	american	NORP
ejpam-4870	557	1	2020	DATE
ejpam-4870	558	1	7	CARDINAL
ejpam-4870	558	2	i. sahul hamid	PERSON
ejpam-4870	558	3	s. balamurgan	PERSON
ejpam-4870	559	1	arab journal of mathematical sciences	ORG
ejpam-4870	560	1	2015	CARDINAL
ejpam-4870	561	1	8	CARDINAL
ejpam-4870	561	2	s. selkow	PERSON
ejpam-4870	563	1	1993	DATE
ejpam-4870	564	1	9	CARDINAL
ejpam-4870	564	2	a. sugumaran	PERSON
ejpam-4870	564	3	e. jayachadran	PERSON
ejpam-4870	567	1	2018	DATE