id	sid	eid	entity	type
ejpam-5658	1	1	european journal	ORG
ejpam-5658	1	2	2025	DATE
ejpam-5658	1	3	18	CARDINAL
ejpam-5658	1	4	1	CARDINAL
ejpam-5658	1	5	5658	CARDINAL
ejpam-5658	1	6	1307-5543	DATE
ejpam-5658	1	7	new york	GPE
ejpam-5658	1	8	jesica m. anoche 1	PERSON
ejpam-5658	1	9	sergio r. canoy	PERSON
ejpam-5658	1	10	1	CARDINAL
ejpam-5658	1	11	msu-iligan institute of technology	ORG
ejpam-5658	1	12	9200	CARDINAL
ejpam-5658	1	13	iligan city	GPE
ejpam-5658	1	14	2	CARDINAL
ejpam-5658	1	15	msu-iligan institute of technology	ORG
ejpam-5658	1	16	9200	CARDINAL
ejpam-5658	1	17	iligan city	GPE
ejpam-5658	1	18	philippines	GPE
ejpam-5658	2	1	⊆	CARDINAL
ejpam-5658	2	2	two	CARDINAL
ejpam-5658	2	3	w ∈ s.	PERSON
ejpam-5658	2	4	two	CARDINAL
ejpam-5658	4	1	np	ORG
ejpam-5658	5	1	2020	DATE
ejpam-5658	5	2	05c69	CARDINAL
ejpam-5658	5	3	1	CARDINAL
ejpam-5658	6	1	natarajan	PERSON
ejpam-5658	8	1	1	CARDINAL
ejpam-5658	8	2	2	CARDINAL
ejpam-5658	8	3	5	CARDINAL
ejpam-5658	8	4	8	CARDINAL
ejpam-5658	8	5	9	CARDINAL
ejpam-5658	8	6	10	CARDINAL
ejpam-5658	9	1	hassan et al	PERSON
ejpam-5658	10	1	4	CARDINAL
ejpam-5658	14	1	cartesian	NORP
ejpam-5658	14	2	two	CARDINAL
ejpam-5658	15	1	jesica.anoche@g.msuiit.edu.ph	PERSON
ejpam-5658	15	2	j. anoche	PERSON
ejpam-5658	15	3	sergio.canoy@g.msuiit.edu.ph	ORG
ejpam-5658	15	4	s. canoy, jr.	PERSON
ejpam-5658	16	1	1	CARDINAL
ejpam-5658	16	2	2025	CARDINAL
ejpam-5658	17	1	j. anoche	PERSON
ejpam-5658	17	2	s. canoy, jr.	PERSON
ejpam-5658	18	1	j. pure	PERSON
ejpam-5658	18	2	18	CARDINAL
ejpam-5658	18	3	1	CARDINAL
ejpam-5658	18	4	2025	CARDINAL
ejpam-5658	18	5	2	CARDINAL
ejpam-5658	18	6	15	CARDINAL
ejpam-5658	19	1	3	CARDINAL
ejpam-5658	20	1	6	CARDINAL
ejpam-5658	20	2	np	ORG
ejpam-5658	21	1	np	ORG
ejpam-5658	22	1	2	CARDINAL
ejpam-5658	22	2	two	CARDINAL
ejpam-5658	23	1	two	CARDINAL
ejpam-5658	23	2	∈	ORG
ejpam-5658	25	1	⊆	CARDINAL
ejpam-5658	25	2	⋃	PERSON
ejpam-5658	26	1	n2 g(u	PRODUCT
ejpam-5658	26	2	∈	ORG
ejpam-5658	26	3	2	CARDINAL
ejpam-5658	28	1	⊆	CARDINAL
ejpam-5658	28	2	n2 g(a	ORG
ejpam-5658	28	3	⋃	DATE
ejpam-5658	28	4	⊆	CARDINAL
ejpam-5658	29	1	⊆	CARDINAL
ejpam-5658	30	1	α(g	PERSON
ejpam-5658	30	2	two	CARDINAL
ejpam-5658	30	3	w	PRODUCT
ejpam-5658	30	4	s. the maximum cardinality	ORG
ejpam-5658	30	5	α(g	PERSON
ejpam-5658	32	1	ω(g	ORG
ejpam-5658	32	2	ω(g	NORP
ejpam-5658	32	3	∈	ORG
ejpam-5658	32	4	one	CARDINAL
ejpam-5658	33	1	∈	ORG
ejpam-5658	34	1	g. letg andh	PERSON
ejpam-5658	35	1	two	CARDINAL
ejpam-5658	35	2	g1	ORG
ejpam-5658	35	3	∈	ORG
ejpam-5658	35	4	g1	ORG
ejpam-5658	35	5	j. anoche	PERSON
ejpam-5658	35	6	s. canoy, jr.	PERSON
ejpam-5658	36	1	j. pure	PERSON
ejpam-5658	36	2	18	CARDINAL
ejpam-5658	36	3	1	CARDINAL
ejpam-5658	36	4	2025	CARDINAL
ejpam-5658	36	5	5658 3	DATE
ejpam-5658	36	6	∈	ORG
ejpam-5658	36	7	g ∨ h	ORG
ejpam-5658	36	8	g ∨ h	ORG
ejpam-5658	37	1	xy ∈	PERSON
ejpam-5658	37	2	pq ∈ e(h	ORG
ejpam-5658	38	1	g ⋄ h of g and h	ORG
ejpam-5658	38	2	one	CARDINAL
ejpam-5658	38	3	two	CARDINAL
ejpam-5658	39	1	∈ e(h	ORG
ejpam-5658	39	2	∈ e(h	ORG
ejpam-5658	40	1	3	CARDINAL
ejpam-5658	40	2	1	CARDINAL
ejpam-5658	40	3	4	CARDINAL
ejpam-5658	44	1	1	CARDINAL
ejpam-5658	44	2	4	CARDINAL
ejpam-5658	48	1	n ≥ 3	DATE
ejpam-5658	48	2	∈	ORG
ejpam-5658	49	1	1	CARDINAL
ejpam-5658	49	2	4	CARDINAL
ejpam-5658	52	1	n ≥ 3	DATE
ejpam-5658	52	2	1	CARDINAL
ejpam-5658	52	3	∈	ORG
ejpam-5658	52	4	kn−1	ORG
ejpam-5658	52	5	1	CARDINAL
ejpam-5658	53	1	i(g	PERSON
ejpam-5658	54	1	i(g	ORG
ejpam-5658	55	1	⊆	CARDINAL
ejpam-5658	55	2	s.	PERSON
ejpam-5658	55	3	2	CARDINAL
ejpam-5658	55	4	gk	PERSON
ejpam-5658	57	1	1	CARDINAL
ejpam-5658	57	2	2	DATE
ejpam-5658	57	3	k}	PERSON
ejpam-5658	60	1	i=1 αh(gj	PERSON
ejpam-5658	61	1	j. anoche	PERSON
ejpam-5658	61	2	s. canoy, jr.	PERSON
ejpam-5658	62	1	j. pure	PERSON
ejpam-5658	62	2	18	CARDINAL
ejpam-5658	62	3	1	CARDINAL
ejpam-5658	62	4	2025	CARDINAL
ejpam-5658	62	5	5658 4	DATE
ejpam-5658	63	1	g1	ORG
ejpam-5658	63	2	sg1 ⊆	PRODUCT
ejpam-5658	63	3	g1	ORG
ejpam-5658	63	4	sg2 ⊆	ORG
ejpam-5658	63	5	a′ ∈	PERSON
ejpam-5658	63	6	∈	ORG
ejpam-5658	63	7	g1	ORG
ejpam-5658	64	1	i(g	PERSON
ejpam-5658	64	2	2	CARDINAL
ejpam-5658	67	1	g1	ORG
ejpam-5658	69	1	⊆	CARDINAL
ejpam-5658	69	2	⊆	CARDINAL
ejpam-5658	70	1	sg1	DATE
ejpam-5658	70	2	sg2	ORG
ejpam-5658	70	3	g1	ORG
ejpam-5658	71	1	sg1 ∩	PERSON
ejpam-5658	71	2	sg1	DATE
ejpam-5658	71	3	g1	ORG
ejpam-5658	75	1	⊆	CARDINAL
ejpam-5658	75	2	g1	ORG
ejpam-5658	76	1	g1	ORG
ejpam-5658	78	1	g1	ORG
ejpam-5658	78	2	g1	ORG
ejpam-5658	78	3	sg1	DATE
ejpam-5658	78	4	g1	ORG
ejpam-5658	82	1	sg1	DATE
ejpam-5658	82	2	sg2 = ∅	ORG
ejpam-5658	83	1	sg1 ̸=	ORG
ejpam-5658	83	2	sg2 ̸=	ORG
ejpam-5658	83	3	sg1 ∩ s′	ORG
ejpam-5658	83	4	∈ sg1 ∩	ORG
ejpam-5658	84	1	∈ s.	PERSON
ejpam-5658	84	2	w ∈ ng1(v	PERSON
ejpam-5658	86	1	1	CARDINAL
ejpam-5658	86	2	dd2(g)(v	PERSON
ejpam-5658	86	3	2	CARDINAL
ejpam-5658	87	1	sg1 ∩	PERSON
ejpam-5658	88	1	sg1	CARDINAL
ejpam-5658	88	2	g1	ORG
ejpam-5658	89	1	sg1	DATE
ejpam-5658	89	2	sg2	ORG
ejpam-5658	89	3	g1	ORG
ejpam-5658	89	4	dd2(g)(x	GPE
ejpam-5658	90	1	2	CARDINAL
ejpam-5658	91	1	dd2(g)(x	GPE
ejpam-5658	92	1	2	CARDINAL
ejpam-5658	93	1	sg1	CARDINAL
ejpam-5658	93	2	g1	ORG
ejpam-5658	94	1	sg2	ORG
ejpam-5658	98	1	sg1 ∪	PERCENT
ejpam-5658	98	2	i1	ORG
ejpam-5658	98	3	sg2 ∪	ORG
ejpam-5658	98	4	g1	ORG
ejpam-5658	100	1	dd2(g)(x	GPE
ejpam-5658	103	1	j. anoche	PERSON
ejpam-5658	103	2	s. canoy, jr.	PERSON
ejpam-5658	104	1	j. pure	PERSON
ejpam-5658	104	2	18	CARDINAL
ejpam-5658	104	3	1	CARDINAL
ejpam-5658	104	4	2025	CARDINAL
ejpam-5658	104	5	5658 5	DATE
ejpam-5658	104	6	15	CARDINAL
ejpam-5658	112	1	g1	ORG
ejpam-5658	114	1	|s∗|	CARDINAL
ejpam-5658	119	1	⊂ q.	PERSON
ejpam-5658	122	1	g1	ORG
ejpam-5658	123	1	g1	ORG
ejpam-5658	125	1	∪qg2 ∪	GPE
ejpam-5658	129	1	5	CARDINAL
ejpam-5658	129	2	two	CARDINAL
ejpam-5658	130	1	3	CARDINAL
ejpam-5658	132	1	g ⋄ h	ORG
ejpam-5658	133	1	huv	ORG
ejpam-5658	136	1	g ⋄ h	ORG
ejpam-5658	136	2	∈	ORG
ejpam-5658	138	1	g ⋄ h	ORG
ejpam-5658	139	1	j. anoche	PERSON
ejpam-5658	139	2	s. canoy, jr.	PERSON
ejpam-5658	140	1	j. pure	PERSON
ejpam-5658	140	2	18	CARDINAL
ejpam-5658	140	3	1	CARDINAL
ejpam-5658	140	4	2025	CARDINAL
ejpam-5658	140	5	6 of 15	DATE
ejpam-5658	140	6	huv	ORG
ejpam-5658	140	7	∈	ORG
ejpam-5658	141	1	2	CARDINAL
ejpam-5658	141	2	g ⋄ h.	ORG
ejpam-5658	142	1	∈	ORG
ejpam-5658	146	1	∈	ORG
ejpam-5658	146	2	∈	ORG
ejpam-5658	146	3	⟨{u	NORP
ejpam-5658	147	1	a.	PERSON
ejpam-5658	147	2	1	CARDINAL
ejpam-5658	149	1	first	ORDINAL
ejpam-5658	149	2	xy	ORG
ejpam-5658	149	3	sxy	ORG
ejpam-5658	151	1	∈	ORG
ejpam-5658	151	2	a. hence	PERSON
ejpam-5658	151	3	∈	ORG
ejpam-5658	151	4	∈	ORG
ejpam-5658	153	1	first	ORDINAL
ejpam-5658	153	2	one	CARDINAL
ejpam-5658	153	3	∈	ORG
ejpam-5658	154	1	y /∈ ng(a	PERSON
ejpam-5658	156	1	∈	ORG
ejpam-5658	156	2	∈	ORG
ejpam-5658	157	1	2	CARDINAL
ejpam-5658	157	2	2	CARDINAL
ejpam-5658	160	1	∈	ORG
ejpam-5658	160	2	∈	ORG
ejpam-5658	160	3	1	CARDINAL
ejpam-5658	160	4	∈	ORG
ejpam-5658	160	5	1 by	CARDINAL
ejpam-5658	162	1	1	CARDINAL
ejpam-5658	163	1	ν(g	GPE
ejpam-5658	163	2	1	CARDINAL
ejpam-5658	163	3	g = k1,n−1	PERSON
ejpam-5658	164	1	1	CARDINAL
ejpam-5658	165	1	2	CARDINAL
ejpam-5658	168	1	1	CARDINAL
ejpam-5658	169	1	3	CARDINAL
ejpam-5658	170	1	n ≥ 4	ORG
ejpam-5658	171	1	ν(g	GPE
ejpam-5658	171	2	1	CARDINAL
ejpam-5658	171	3	xu ∈	PERSON
ejpam-5658	172	1	xu ∈	PERSON
ejpam-5658	176	1	n ≥ 4	DATE
ejpam-5658	178	1	xy	ORG
ejpam-5658	186	1	g = k1,n−1	PERSON
ejpam-5658	188	1	second	ORDINAL
ejpam-5658	188	2	1	CARDINAL
ejpam-5658	189	1	2	CARDINAL
ejpam-5658	189	2	2	CARDINAL
ejpam-5658	189	3	first	ORDINAL
ejpam-5658	190	1	3	CARDINAL
ejpam-5658	193	1	1	CARDINAL
ejpam-5658	193	2	2 + ω(h	DATE
ejpam-5658	194	1	2	CARDINAL
ejpam-5658	194	2	≥ max{αh(g	DATE
ejpam-5658	195	1	j. anoche	PERSON
ejpam-5658	195	2	s. canoy, jr.	PERSON
ejpam-5658	196	1	j. pure	PERSON
ejpam-5658	196	2	18	CARDINAL
ejpam-5658	196	3	1	CARDINAL
ejpam-5658	196	4	2025	CARDINAL
ejpam-5658	196	5	5658 7	DATE
ejpam-5658	196	6	15	CARDINAL
ejpam-5658	198	1	1	CARDINAL
ejpam-5658	200	1	2 + ω(h	DATE
ejpam-5658	201	1	3	CARDINAL
ejpam-5658	202	1	2 + ω(h	DATE
ejpam-5658	203	1	3	CARDINAL
ejpam-5658	203	2	st = pq	PERSON
ejpam-5658	203	3	sst	ORG
ejpam-5658	203	4	hpq	PERSON
ejpam-5658	204	1	∈	ORG
ejpam-5658	205	1	1	CARDINAL
ejpam-5658	205	2	pq	PERSON
ejpam-5658	208	1	w ∈	PERSON
ejpam-5658	209	1	w	GPE
ejpam-5658	210	1	⊆	CARDINAL
ejpam-5658	213	1	∈	ORG
ejpam-5658	215	1	2	CARDINAL
ejpam-5658	216	1	2	CARDINAL
ejpam-5658	216	2	2	CARDINAL
ejpam-5658	216	3	1	CARDINAL
ejpam-5658	219	1	2 + ω(h	DATE
ejpam-5658	220	1	2	CARDINAL
ejpam-5658	221	1	g ⋄ h	ORG
ejpam-5658	221	2	3	CARDINAL
ejpam-5658	223	1	∈	ORG
ejpam-5658	223	2	sxy = ∅	PERSON
ejpam-5658	225	1	3	CARDINAL
ejpam-5658	226	1	≥ max{αh(g	DATE
ejpam-5658	227	1	1	CARDINAL
ejpam-5658	228	1	3	CARDINAL
ejpam-5658	230	1	k5 ⋄ p3	ORG
ejpam-5658	230	2	c4 ⋄ p3	ORG
ejpam-5658	230	3	g ⋄ p3	ORG
ejpam-5658	230	4	3	CARDINAL
ejpam-5658	243	1	3	CARDINAL
ejpam-5658	243	2	5	CARDINAL
ejpam-5658	243	3	αh(c4	ORG
ejpam-5658	243	4	2	CARDINAL
ejpam-5658	243	5	3	CARDINAL
ejpam-5658	244	1	2	CARDINAL
ejpam-5658	244	2	ω(p3	PERSON
ejpam-5658	245	1	2	CARDINAL
ejpam-5658	245	2	5	CARDINAL
ejpam-5658	245	3	4	CARDINAL
ejpam-5658	245	4	αh(c4 ⋄p3	ORG
ejpam-5658	245	5	4	CARDINAL
ejpam-5658	245	6	2	CARDINAL
ejpam-5658	245	7	6	CARDINAL
ejpam-5658	245	8	4	CARDINAL
ejpam-5658	246	1	j. anoche	PERSON
ejpam-5658	246	2	s. canoy, jr.	PERSON
ejpam-5658	247	1	j. pure	PERSON
ejpam-5658	247	2	18	CARDINAL
ejpam-5658	247	3	1	CARDINAL
ejpam-5658	247	4	2025	CARDINAL
ejpam-5658	247	5	5658 8 of 15 6	DATE
ejpam-5658	247	6	4	CARDINAL
ejpam-5658	250	1	g. (ii	PERSON
ejpam-5658	253	1	⊆	CARDINAL
ejpam-5658	253	2	⊆	CARDINAL
ejpam-5658	254	1	∈	ORG
ejpam-5658	255	1	w ̸=	PERSON
ejpam-5658	255	2	vw	GPE
ejpam-5658	256	1	w	GPE
ejpam-5658	256	2	2	CARDINAL
ejpam-5658	257	1	w	ORG
ejpam-5658	259	1	2	CARDINAL
ejpam-5658	264	1	4	CARDINAL
ejpam-5658	268	1	7	CARDINAL
ejpam-5658	268	2	two	CARDINAL
ejpam-5658	268	3	5	CARDINAL
ejpam-5658	270	1	tx	ORG
ejpam-5658	271	1	g. (ii	PERSON
ejpam-5658	271	2	tx	ORG
ejpam-5658	271	3	y ∈ s	PERSON
ejpam-5658	271	4	3	CARDINAL
ejpam-5658	271	5	tx	ORG
ejpam-5658	271	6	∩	PERSON
ejpam-5658	271	7	3	CARDINAL
ejpam-5658	271	8	⊆	CARDINAL
ejpam-5658	271	9	s. proof	PERSON
ejpam-5658	273	1	∈	ORG
ejpam-5658	274	1	2	CARDINAL
ejpam-5658	274	2	w ∈	ORG
ejpam-5658	274	3	∈	ORG
ejpam-5658	274	4	∈	ORG
ejpam-5658	276	1	g ∨ h.	ORG
ejpam-5658	278	1	tx	ORG
ejpam-5658	278	2	g ∨ h	ORG
ejpam-5658	279	1	1 ≤	CARDINAL
ejpam-5658	280	1	1	CARDINAL
ejpam-5658	281	1	pq ∈	PERSON
ejpam-5658	282	1	tx	ORG
ejpam-5658	283	1	j. anoche	PERSON
ejpam-5658	283	2	s. canoy, jr.	PERSON
ejpam-5658	284	1	j. pure	PERSON
ejpam-5658	284	2	18	CARDINAL
ejpam-5658	284	3	1	CARDINAL
ejpam-5658	284	4	2025	CARDINAL
ejpam-5658	284	5	5658 9 of 15	DATE
ejpam-5658	284	6	y ∈ s	PERSON
ejpam-5658	284	7	3	CARDINAL
ejpam-5658	284	8	tx	ORG
ejpam-5658	284	9	̸=	ORG
ejpam-5658	284	10	∈	ORG
ejpam-5658	284	11	tx	ORG
ejpam-5658	287	1	g ∨ h.	ORG
ejpam-5658	287	2	tx	ORG
ejpam-5658	287	3	tx	ORG
ejpam-5658	287	4	∈	ORG
ejpam-5658	288	1	2	CARDINAL
ejpam-5658	288	2	∈	ORG
ejpam-5658	289	1	g ∨ h	ORG
ejpam-5658	291	1	3	CARDINAL
ejpam-5658	293	1	2	CARDINAL
ejpam-5658	293	2	∈	ORG
ejpam-5658	293	3	z	ORG
ejpam-5658	294	1	∈ nh(c)∩nh(d	ORG
ejpam-5658	299	1	1	CARDINAL
ejpam-5658	299	2	w.	PERSON
ejpam-5658	299	3	∈	ORG
ejpam-5658	299	4	1	CARDINAL
ejpam-5658	301	1	1	CARDINAL
ejpam-5658	301	2	2	CARDINAL
ejpam-5658	301	3	first	ORDINAL
ejpam-5658	302	1	1	CARDINAL
ejpam-5658	303	1	1	CARDINAL
ejpam-5658	304	1	1	CARDINAL
ejpam-5658	305	1	w	GPE
ejpam-5658	305	2	3	CARDINAL
ejpam-5658	306	1	1	CARDINAL
ejpam-5658	307	1	1	CARDINAL
ejpam-5658	308	1	3	CARDINAL
ejpam-5658	310	1	3	CARDINAL
ejpam-5658	311	1	qj	CARDINAL
ejpam-5658	311	2	3	CARDINAL
ejpam-5658	312	1	j ∈	PERSON
ejpam-5658	312	2	1	CARDINAL
ejpam-5658	312	3	2	DATE
ejpam-5658	315	1	1	CARDINAL
ejpam-5658	315	2	2	DATE
ejpam-5658	318	1	5	CARDINAL
ejpam-5658	322	1	k=1 qkpk	PERSON
ejpam-5658	326	1	tx	ORG
ejpam-5658	326	2	1 ≤ j ≤	QUANTITY
ejpam-5658	327	1	j. anoche	PERSON
ejpam-5658	327	2	s. canoy, jr.	PERSON
ejpam-5658	328	1	j. pure	PERSON
ejpam-5658	328	2	18	CARDINAL
ejpam-5658	328	3	1	CARDINAL
ejpam-5658	328	4	2025	CARDINAL
ejpam-5658	328	5	10	CARDINAL
ejpam-5658	328	6	5	CARDINAL
ejpam-5658	329	1	k=1 ∑ x∈sqk |tx|	PERSON
ejpam-5658	330	1	k=1 ∑ x∈sqk |dpk	PERSON
ejpam-5658	330	2	k=1 qkpk	PERSON
ejpam-5658	332	1	5	CARDINAL
ejpam-5658	332	2	s0	ORG
ejpam-5658	332	3	∈	ORG
ejpam-5658	333	1	1	CARDINAL
ejpam-5658	333	2	gr1	PERSON
ejpam-5658	333	3	gr2	PERSON
ejpam-5658	333	4	rj	PERSON
ejpam-5658	333	5	1	CARDINAL
ejpam-5658	333	6	2	DATE
ejpam-5658	334	1	5	CARDINAL
ejpam-5658	334	2	gr1	PERSON
ejpam-5658	334	3	gr2	PERSON
ejpam-5658	334	4	⊆	CARDINAL
ejpam-5658	334	5	1	CARDINAL
ejpam-5658	334	6	2	DATE
ejpam-5658	335	1	1 ≤	QUANTITY
ejpam-5658	335	2	j ∈	PERSON
ejpam-5658	335	3	1	CARDINAL
ejpam-5658	335	4	2	DATE
ejpam-5658	337	1	qt2	PERSON
ejpam-5658	337	2	qtn⟩	ORG
ejpam-5658	337	3	h. hence	GPE
ejpam-5658	337	4	qtj ⊆ dpj	PERSON
ejpam-5658	337	5	1	CARDINAL
ejpam-5658	337	6	2	DATE
ejpam-5658	339	1	|rx|	GPE
ejpam-5658	342	1	6	CARDINAL
ejpam-5658	344	1	αh(g∨h	ORG
ejpam-5658	347	1	5	CARDINAL
ejpam-5658	348	1	1	CARDINAL
ejpam-5658	350	1	2ω(h	CARDINAL
ejpam-5658	351	1	8	CARDINAL
ejpam-5658	351	2	two	CARDINAL
ejpam-5658	351	3	6	CARDINAL
ejpam-5658	353	1	⊆	CARDINAL
ejpam-5658	353	2	tx	ORG
ejpam-5658	353	3	⊆	PRODUCT
ejpam-5658	353	4	⊠h	CARDINAL
ejpam-5658	354	1	tx	ORG
ejpam-5658	354	2	tx∪ty	ORG
ejpam-5658	354	3	y ∈ s	PERSON
ejpam-5658	355	1	tx∩ty	CARDINAL
ejpam-5658	355	2	3	CARDINAL
ejpam-5658	355	3	y ∈ s	PERSON
ejpam-5658	355	4	2	CARDINAL
ejpam-5658	355	5	j. anoche	PERSON
ejpam-5658	355	6	s. canoy, jr.	PERSON
ejpam-5658	356	1	j. pure	PERSON
ejpam-5658	356	2	18	CARDINAL
ejpam-5658	356	3	1	CARDINAL
ejpam-5658	356	4	2025	CARDINAL
ejpam-5658	356	5	5658 11	DATE
ejpam-5658	356	6	15	CARDINAL
ejpam-5658	358	1	tx	ORG
ejpam-5658	361	1	⊠h	CARDINAL
ejpam-5658	361	2	dg⊠h((x	PERSON
ejpam-5658	362	1	3	CARDINAL
ejpam-5658	363	1	3	CARDINAL
ejpam-5658	363	2	tx	ORG
ejpam-5658	364	1	y ∈ s	PERSON
ejpam-5658	364	2	tx	ORG
ejpam-5658	364	3	tx	ORG
ejpam-5658	365	1	2	CARDINAL
ejpam-5658	365	2	∈	ORG
ejpam-5658	366	1	first	ORDINAL
ejpam-5658	367	1	1	CARDINAL
ejpam-5658	369	1	2	CARDINAL
ejpam-5658	370	1	p)(z	GPE
ejpam-5658	371	1	dg⊠h((x	PERSON
ejpam-5658	372	1	2	CARDINAL
ejpam-5658	373	1	tx	ORG
ejpam-5658	375	1	2	CARDINAL
ejpam-5658	375	2	∈	ORG
ejpam-5658	376	1	tx	ORG
ejpam-5658	376	2	dg⊠h((x	PERSON
ejpam-5658	377	1	2	CARDINAL
ejpam-5658	378	1	tx	ORG
ejpam-5658	379	1	1	CARDINAL
ejpam-5658	380	1	1	CARDINAL
ejpam-5658	381	1	2	CARDINAL
ejpam-5658	381	2	g ∈ tx	PERSON
ejpam-5658	382	1	2	CARDINAL
ejpam-5658	388	1	1	CARDINAL
ejpam-5658	388	2	w.	PERSON
ejpam-5658	388	3	∈	ORG
ejpam-5658	389	1	dg⊠h((v	ORG
ejpam-5658	390	1	2	CARDINAL
ejpam-5658	390	2	first	ORDINAL
ejpam-5658	390	3	vw	GPE
ejpam-5658	391	1	dg⊠h((v	ORG
ejpam-5658	392	1	1	CARDINAL
ejpam-5658	392	2	pq ∈ e(h	ORG
ejpam-5658	392	3	dg⊠h((v	ORG
ejpam-5658	393	1	1	CARDINAL
ejpam-5658	393	2	pq /∈ e(h	ORG
ejpam-5658	394	1	tw	ORG
ejpam-5658	395	1	3	CARDINAL
ejpam-5658	395	2	dg⊠h((v	ORG
ejpam-5658	396	1	3	CARDINAL
ejpam-5658	397	1	vw	GPE
ejpam-5658	398	1	w	GPE
ejpam-5658	398	2	3	CARDINAL
ejpam-5658	398	3	dg⊠h((v	ORG
ejpam-5658	399	1	3	CARDINAL
ejpam-5658	400	1	2	CARDINAL
ejpam-5658	400	2	∩	PERSON
ejpam-5658	401	1	3	CARDINAL
ejpam-5658	402	1	dg⊠h((v	ORG
ejpam-5658	402	2	3	CARDINAL
ejpam-5658	405	1	αh(g⊠h	ORDINAL
ejpam-5658	408	1	i=1sqi	PERSON
ejpam-5658	409	1	6	CARDINAL
ejpam-5658	410	1	j. anoche	PERSON
ejpam-5658	410	2	s. canoy, jr.	PERSON
ejpam-5658	411	1	j. pure	PERSON
ejpam-5658	411	2	18	CARDINAL
ejpam-5658	411	3	1	CARDINAL
ejpam-5658	411	4	2025	CARDINAL
ejpam-5658	411	5	5658 12	DATE
ejpam-5658	411	6	15	CARDINAL
ejpam-5658	412	1	tx	ORG
ejpam-5658	412	2	αh(g⊠h	ORDINAL
ejpam-5658	412	3	|rx|	GPE
ejpam-5658	412	4	i=1 ∑	PERSON
ejpam-5658	416	1	2	CARDINAL
ejpam-5658	420	1	4	CARDINAL
ejpam-5658	422	1	p6}|+	GPE
ejpam-5658	422	2	p6}| = 16	PERSON
ejpam-5658	423	1	j. anoche	PERSON
ejpam-5658	423	2	s. canoy, jr.	PERSON
ejpam-5658	424	1	j. pure	PERSON
ejpam-5658	424	2	18	CARDINAL
ejpam-5658	424	3	1	CARDINAL
ejpam-5658	424	4	2025	CARDINAL
ejpam-5658	424	5	5658 13	DATE
ejpam-5658	424	6	15	CARDINAL
ejpam-5658	495	1	•	CARDINAL
ejpam-5658	496	1	4	CARDINAL
ejpam-5658	496	2	np	ORG
ejpam-5658	497	1	k ≤	ORG
ejpam-5658	498	1	k ≤	ORG
ejpam-5658	498	2	7	CARDINAL
ejpam-5658	498	3	6	CARDINAL
ejpam-5658	499	1	np	ORG
ejpam-5658	500	1	8	CARDINAL
ejpam-5658	501	1	np	ORG
ejpam-5658	504	1	np	ORG
ejpam-5658	506	1	k ≤	ORG
ejpam-5658	508	1	= k	PERSON
ejpam-5658	510	1	+ 1	DATE
ejpam-5658	510	2	|s∗|	CARDINAL
ejpam-5658	510	3	k+1	TIME
ejpam-5658	510	4	1	CARDINAL
ejpam-5658	510	5	⟨s∗⟩	GPE
ejpam-5658	510	6	at least two	CARDINAL
ejpam-5658	511	1	∈	ORG
ejpam-5658	512	1	j. anoche	PERSON
ejpam-5658	512	2	s. canoy, jr.	PERSON
ejpam-5658	513	1	j. pure	PERSON
ejpam-5658	513	2	18	CARDINAL
ejpam-5658	513	3	1	CARDINAL
ejpam-5658	513	4	2025	CARDINAL
ejpam-5658	513	5	14	CARDINAL
ejpam-5658	513	6	15	CARDINAL
ejpam-5658	513	7	2	CARDINAL
ejpam-5658	514	1	⊆	CARDINAL
ejpam-5658	514	2	∈	ORG
ejpam-5658	520	1	+ 1	DATE
ejpam-5658	520	2	np	ORG
ejpam-5658	521	1	9	CARDINAL
ejpam-5658	521	2	two	CARDINAL
ejpam-5658	522	1	two	CARDINAL
ejpam-5658	522	2	only three	CARDINAL
ejpam-5658	523	1	+ 2	DATE
ejpam-5658	524	1	np	ORG
ejpam-5658	524	2	np	ORG
ejpam-5658	526	1	msu-iligan institute of technology	ORG
ejpam-5658	527	1	1	CARDINAL
ejpam-5658	527	2	s. arriola	PERSON
ejpam-5658	527	3	jr.	PERSON
ejpam-5658	527	4	s. canoy.	PERSON
ejpam-5658	528	1	1	CARDINAL
ejpam-5658	529	1	18(2):179–190	DATE
ejpam-5658	529	2	2017	DATE
ejpam-5658	530	1	2	CARDINAL
ejpam-5658	530	2	b. krishnakumari	PERSON
ejpam-5658	530	3	b. natarjan	PERSON
ejpam-5658	532	1	125(4):449	CARDINAL
ejpam-5658	532	2	455	CARDINAL
ejpam-5658	532	3	2015	DATE
ejpam-5658	533	1	3	CARDINAL
ejpam-5658	533	2	j. hassan1	PERSON
ejpam-5658	533	3	s. canoy.	PERSON
ejpam-5658	536	1	j. pure	PERSON
ejpam-5658	536	2	15(4):1783–1796	CARDINAL
ejpam-5658	536	3	2022	CARDINAL
ejpam-5658	537	1	4	CARDINAL
ejpam-5658	537	2	j. hassan1	PERSON
ejpam-5658	537	3	s. canoy	PERSON
ejpam-5658	537	4	a. aradais	PERSON
ejpam-5658	540	1	j. pure	PERSON
ejpam-5658	540	2	15(2):467–477	DATE
ejpam-5658	540	3	2022	CARDINAL
ejpam-5658	541	1	5	CARDINAL
ejpam-5658	541	2	m. henning	PERSON
ejpam-5658	541	3	n. rad	PERSON
ejpam-5658	542	1	2	CARDINAL
ejpam-5658	543	1	33(4):913–927	DATE
ejpam-5658	543	2	2017	DATE
ejpam-5658	544	1	6	CARDINAL
ejpam-5658	544	2	r. karp	PERSON
ejpam-5658	546	1	new york	GPE
ejpam-5658	546	2	85–103	DATE
ejpam-5658	546	3	1972	DATE
ejpam-5658	547	1	7	CARDINAL
ejpam-5658	547	2	c. natarajan	PERSON
ejpam-5658	547	3	s. ayyaswamy	ORG
ejpam-5658	548	1	versita	PERSON
ejpam-5658	548	2	23(2):187	CARDINAL
ejpam-5658	548	3	199	CARDINAL
ejpam-5658	548	4	2015	DATE
ejpam-5658	549	1	8	CARDINAL
ejpam-5658	549	2	s. canoy	PERSON
ejpam-5658	549	3	r. mollejon	PERSON
ejpam-5658	549	4	j. g. canoy	PERSON
ejpam-5658	552	1	j. pure	PERSON
ejpam-5658	553	1	12(4):1455–1463,	DATE
ejpam-5658	553	2	2019	DATE
ejpam-5658	554	1	j. anoche	PERSON
ejpam-5658	554	2	s. canoy, jr.	PERSON
ejpam-5658	555	1	j. pure	PERSON
ejpam-5658	555	2	18	CARDINAL
ejpam-5658	555	3	1	CARDINAL
ejpam-5658	555	4	2025	CARDINAL
ejpam-5658	555	5	5658 15 of 15	DATE
ejpam-5658	555	6	9	CARDINAL
ejpam-5658	555	7	s. canoy	PERSON
ejpam-5658	555	8	g. salasalan	PERSON
ejpam-5658	557	1	kyungpook mathematical journal	ORG
ejpam-5658	557	2	62:193–204	CARDINAL
ejpam-5658	557	3	2022	CARDINAL
ejpam-5658	558	1	10	CARDINAL
ejpam-5658	558	2	g. salasalan and jr. s. canoy	PERSON
ejpam-5658	561	1	j. pure	PERSON
ejpam-5658	561	2	14(1):112–125	DATE
ejpam-5658	561	3	2021	DATE