id	sid	eid	entity	type
ejpam-5305	1	1	european journal	ORG
ejpam-5305	1	2	2025	DATE
ejpam-5305	1	3	18	CARDINAL
ejpam-5305	1	4	2	CARDINAL
ejpam-5305	1	5	5305	CARDINAL
ejpam-5305	1	6	1307-5543	DATE
ejpam-5305	1	7	new york	GPE
ejpam-5305	1	8	saengsura1,∗	GPE
ejpam-5305	1	9	tiang poomsa	PERSON
ejpam-5305	1	10	1	CARDINAL
ejpam-5305	1	11	kantarawichai	GPE
ejpam-5305	1	12	mahasarakham	GPE
ejpam-5305	1	13	thailand 2	ORG
ejpam-5305	1	14	science	ORG
ejpam-5305	1	15	khonkaen university	ORG
ejpam-5305	1	16	khonkaen	GPE
ejpam-5305	1	17	thailand	GPE
ejpam-5305	2	1	0	CARDINAL
ejpam-5305	2	2	1	DATE
ejpam-5305	2	3	2	CARDINAL
ejpam-5305	3	1	∈	ORG
ejpam-5305	3	2	1	CARDINAL
ejpam-5305	3	3	2	DATE
ejpam-5305	3	4	3	DATE
ejpam-5305	4	1	one	CARDINAL
ejpam-5305	4	2	at least 3	CARDINAL
ejpam-5305	4	3	2	CARDINAL
ejpam-5305	6	1	2020	DATE
ejpam-5305	6	2	05c05	CARDINAL
ejpam-5305	6	3	05c15	CARDINAL
ejpam-5305	6	4	1	CARDINAL
ejpam-5305	7	1	1	CARDINAL
ejpam-5305	8	1	2	CARDINAL
ejpam-5305	9	1	0	CARDINAL
ejpam-5305	9	2	1	DATE
ejpam-5305	9	3	2	CARDINAL
ejpam-5305	11	1	xy	ORG
ejpam-5305	14	1	3	CARDINAL
ejpam-5305	14	2	4	CARDINAL
ejpam-5305	16	1	1964	DATE
ejpam-5305	16	2	rangel	PERSON
ejpam-5305	16	3	rosa	PERSON
ejpam-5305	16	4	5	CARDINAL
ejpam-5305	17	1	6	CARDINAL
ejpam-5305	20	1	one	CARDINAL
ejpam-5305	20	2	at least 3	CARDINAL
ejpam-5305	20	3	2	CARDINAL
ejpam-5305	20	4	gillian	PERSON
ejpam-5305	23	1	kittisak.s@msu.ac.th	PERSON
ejpam-5305	23	2	k. saengsura	PERSON
ejpam-5305	23	3	t. poomsa-ard	GPE
ejpam-5305	23	4	1	CARDINAL
ejpam-5305	24	1	2025	CARDINAL
ejpam-5305	25	1	k. saengsura	PERSON
ejpam-5305	25	2	t. poomsa-	GPE
ejpam-5305	26	1	j. pure	PERSON
ejpam-5305	26	2	18	CARDINAL
ejpam-5305	26	3	2	CARDINAL
ejpam-5305	26	4	2025	CARDINAL
ejpam-5305	26	5	5305 2	CARDINAL
ejpam-5305	26	6	8	CARDINAL
ejpam-5305	27	1	huang et al	PERSON
ejpam-5305	28	1	three or	CARDINAL
ejpam-5305	28	2	four	CARDINAL
ejpam-5305	29	1	bahls et al	PERSON
ejpam-5305	30	1	8	CARDINAL
ejpam-5305	30	2	two	CARDINAL
ejpam-5305	32	1	9	CARDINAL
ejpam-5305	32	2	10	CARDINAL
ejpam-5305	32	3	section 2.	LAW
ejpam-5305	33	1	11	CARDINAL
ejpam-5305	33	2	four	CARDINAL
ejpam-5305	36	1	0	CARDINAL
ejpam-5305	36	2	1	DATE
ejpam-5305	36	3	2	CARDINAL
ejpam-5305	39	1	xy	ORG
ejpam-5305	40	1	1	CARDINAL
ejpam-5305	40	2	2	DATE
ejpam-5305	40	3	3	DATE
ejpam-5305	43	1	12	CARDINAL
ejpam-5305	43	2	1	CARDINAL
ejpam-5305	43	3	10	CARDINAL
ejpam-5305	43	4	2	CARDINAL
ejpam-5305	43	5	3	CARDINAL
ejpam-5305	44	1	1	CARDINAL
ejpam-5305	46	1	0	CARDINAL
ejpam-5305	46	2	1	DATE
ejpam-5305	46	3	2	CARDINAL
ejpam-5305	48	1	2	CARDINAL
ejpam-5305	51	1	a+2	GPE
ejpam-5305	53	1	a+n	GPE
ejpam-5305	57	1	∈	ORG
ejpam-5305	57	2	m−	NORP
ejpam-5305	57	3	2	CARDINAL
ejpam-5305	58	1	m+	CARDINAL
ejpam-5305	58	2	1	CARDINAL
ejpam-5305	59	1	3	CARDINAL
ejpam-5305	62	1	+ 2	DATE
ejpam-5305	65	1	∈	ORG
ejpam-5305	65	2	1	CARDINAL
ejpam-5305	65	3	2	DATE
ejpam-5305	65	4	3	DATE
ejpam-5305	66	1	1	CARDINAL
ejpam-5305	70	1	un	ORG
ejpam-5305	72	1	un	ORG
ejpam-5305	73	1	un−1un	DATE
ejpam-5305	74	1	13	CARDINAL
ejpam-5305	74	2	4	CARDINAL
ejpam-5305	75	1	4	CARDINAL
ejpam-5305	77	1	0	CARDINAL
ejpam-5305	78	1	un	ORG
ejpam-5305	78	2	n ≥ 1	DATE
ejpam-5305	78	3	one	CARDINAL
ejpam-5305	85	1	1	CARDINAL
ejpam-5305	85	2	2	DATE
ejpam-5305	86	1	k.	PERSON
ejpam-5305	86	2	11	CARDINAL
ejpam-5305	86	3	5	CARDINAL
ejpam-5305	86	4	6	CARDINAL
ejpam-5305	87	1	5	CARDINAL
ejpam-5305	88	1	sk(m1,m2	DATE
ejpam-5305	96	1	0	CARDINAL
ejpam-5305	97	1	6	CARDINAL
ejpam-5305	98	1	sk(m1,m2	DATE
ejpam-5305	102	1	0	CARDINAL
ejpam-5305	104	1	k. saengsura	PERSON
ejpam-5305	104	2	t. poomsa-	GPE
ejpam-5305	105	1	j. pure	PERSON
ejpam-5305	105	2	18	CARDINAL
ejpam-5305	105	3	2	CARDINAL
ejpam-5305	105	4	2025	CARDINAL
ejpam-5305	105	5	5305 3	CARDINAL
ejpam-5305	105	6	two	CARDINAL
ejpam-5305	107	1	2	CARDINAL
ejpam-5305	107	2	1	CARDINAL
ejpam-5305	107	3	2	DATE
ejpam-5305	109	1	1	CARDINAL
ejpam-5305	111	1	+ 1	DATE
ejpam-5305	119	1	j j j jj � �	PERSON
ejpam-5305	120	1	v(n−2)mn−2	PERSON
ejpam-5305	121	1	1	CARDINAL
ejpam-5305	121	2	vv31, vv41	ORG
ejpam-5305	125	1	v(n−2)m(n−2	PERSON
ejpam-5305	130	1	2p + 1	CARDINAL
ejpam-5305	138	1	2p′.	CARDINAL
ejpam-5305	143	1	two	CARDINAL
ejpam-5305	144	1	two	CARDINAL
ejpam-5305	145	1	first	ORDINAL
ejpam-5305	145	2	second	ORDINAL
ejpam-5305	146	1	2	CARDINAL
ejpam-5305	147	1	first	ORDINAL
ejpam-5305	147	2	n − 2	PRODUCT
ejpam-5305	147	3	1	CARDINAL
ejpam-5305	150	1	mn	GPE
ejpam-5305	151	1	2	CARDINAL
ejpam-5305	151	2	3	DATE
ejpam-5305	152	1	1	CARDINAL
ejpam-5305	154	1	1	CARDINAL
ejpam-5305	154	2	k. saengsura	PERSON
ejpam-5305	154	3	t. poomsa-	GPE
ejpam-5305	155	1	j. pure	PERSON
ejpam-5305	155	2	18	CARDINAL
ejpam-5305	155	3	2	CARDINAL
ejpam-5305	155	4	2025	CARDINAL
ejpam-5305	155	5	5305 4	DATE
ejpam-5305	155	6	8	CARDINAL
ejpam-5305	155	7	1	CARDINAL
ejpam-5305	156	1	i.	PERSON
ejpam-5305	157	1	2m2	CARDINAL
ejpam-5305	160	1	m3	PERSON
ejpam-5305	160	2	lemma 2	ORG
ejpam-5305	163	1	4 ≤	QUANTITY
ejpam-5305	164	1	2mi−1	CARDINAL
ejpam-5305	164	2	′′	ORG
ejpam-5305	168	1	lemma 2	ORG
ejpam-5305	170	1	′′	ORG
ejpam-5305	171	1	′′	ORG
ejpam-5305	171	2	′′	ORG
ejpam-5305	171	3	′′	ORG
ejpam-5305	172	1	t amit	PERSON
ejpam-5305	173	1	2	CARDINAL
ejpam-5305	174	1	1	CARDINAL
ejpam-5305	175	1	second	ORDINAL
ejpam-5305	175	2	2	CARDINAL
ejpam-5305	178	1	mn	GPE
ejpam-5305	181	1	+ 1	DATE
ejpam-5305	181	2	2	CARDINAL
ejpam-5305	181	3	3	DATE
ejpam-5305	182	1	1	CARDINAL
ejpam-5305	184	1	1	CARDINAL
ejpam-5305	184	2	1	CARDINAL
ejpam-5305	185	1	i.	PERSON
ejpam-5305	186	1	m3 = m2 + 1	PERSON
ejpam-5305	190	1	|f ′(v31)− f(v)| =	ORG
ejpam-5305	191	1	4 ≤	QUANTITY
ejpam-5305	191	2	1	CARDINAL
ejpam-5305	193	1	mi = m2 + m3 +	PERSON
ejpam-5305	194	1	+ 1	DATE
ejpam-5305	194	2	|f(vi1)−f(v(i− 1)mi−1)|	ORG
ejpam-5305	197	1	′′	ORG
ejpam-5305	198	1	′′	ORG
ejpam-5305	199	1	t amit	PERSON
ejpam-5305	200	1	2	CARDINAL
ejpam-5305	201	1	1	CARDINAL
ejpam-5305	202	1	1	CARDINAL
ejpam-5305	203	1	3	CARDINAL
ejpam-5305	206	1	mn	GPE
ejpam-5305	207	1	m3,m4	PERSON
ejpam-5305	209	1	mn	ORG
ejpam-5305	209	2	2	CARDINAL
ejpam-5305	209	3	3	DATE
ejpam-5305	211	1	n − 1	ORG
ejpam-5305	213	1	1	CARDINAL
ejpam-5305	213	2	1	CARDINAL
ejpam-5305	214	1	i.	PERSON
ejpam-5305	215	1	2m2	CARDINAL
ejpam-5305	216	1	m3	PERSON
ejpam-5305	216	2	lemma 2	ORG
ejpam-5305	218	1	|f ′(v31)− f(v)| =	ORG
ejpam-5305	218	2	k. saengsura	PERSON
ejpam-5305	218	3	t. poomsa-	GPE
ejpam-5305	219	1	j. pure	PERSON
ejpam-5305	219	2	18	CARDINAL
ejpam-5305	219	3	2	CARDINAL
ejpam-5305	219	4	2025	CARDINAL
ejpam-5305	219	5	5305 5	DATE
ejpam-5305	220	1	4 ≤	QUANTITY
ejpam-5305	223	1	2mi−1	CARDINAL
ejpam-5305	225	1	lemma 2	ORG
ejpam-5305	227	1	′′	ORG
ejpam-5305	228	1	′′	ORG
ejpam-5305	228	2	′′	ORG
ejpam-5305	228	3	′′	ORG
ejpam-5305	229	1	t amit	PERSON
ejpam-5305	230	1	2	CARDINAL
ejpam-5305	231	1	1	CARDINAL
ejpam-5305	232	1	fourth	ORDINAL
ejpam-5305	232	2	4	CARDINAL
ejpam-5305	235	1	mn	GPE
ejpam-5305	237	1	3	CARDINAL
ejpam-5305	237	2	4	DATE
ejpam-5305	238	1	2	CARDINAL
ejpam-5305	240	1	1	CARDINAL
ejpam-5305	240	2	1	CARDINAL
ejpam-5305	241	1	i.	PERSON
ejpam-5305	242	1	m3 = m2	PERSON
ejpam-5305	243	1	4 ≤	QUANTITY
ejpam-5305	243	2	|f(vi1)−f(v(i−1)mi−1	PERSON
ejpam-5305	244	1	mi = m2 + m3 +	PERSON
ejpam-5305	248	1	f(v(n−1)mn−1	ORDINAL
ejpam-5305	256	1	t amit	PERSON
ejpam-5305	257	1	2	CARDINAL
ejpam-5305	258	1	1	CARDINAL
ejpam-5305	259	1	2	CARDINAL
ejpam-5305	260	1	5	CARDINAL
ejpam-5305	263	1	mn	GPE
ejpam-5305	264	1	m3,m4	PERSON
ejpam-5305	266	1	mn	ORG
ejpam-5305	267	1	2	CARDINAL
ejpam-5305	267	2	3	DATE
ejpam-5305	269	1	n − 1	ORG
ejpam-5305	271	1	1	CARDINAL
ejpam-5305	271	2	1	CARDINAL
ejpam-5305	272	1	i.	PERSON
ejpam-5305	273	1	m3 ≥ m2 + 1	FAC
ejpam-5305	274	1	m3 = m2 + 1	PERSON
ejpam-5305	278	1	+ 1	DATE
ejpam-5305	278	2	m3	PERSON
ejpam-5305	278	3	lemma 2	ORG
ejpam-5305	280	1	′′	ORG
ejpam-5305	281	1	′′	ORG
ejpam-5305	281	2	′′	ORG
ejpam-5305	281	3	k. saengsura	PERSON
ejpam-5305	281	4	t. poomsa-	GPE
ejpam-5305	282	1	j. pure	PERSON
ejpam-5305	282	2	18	CARDINAL
ejpam-5305	282	3	2	CARDINAL
ejpam-5305	282	4	2025	CARDINAL
ejpam-5305	282	5	5305 6	CARDINAL
ejpam-5305	282	6	′′	ORG
ejpam-5305	283	1	4 ≤	QUANTITY
ejpam-5305	287	1	mi ≥ m′	PERSON
ejpam-5305	287	2	+ 1	DATE
ejpam-5305	289	1	mi = m′	PERSON
ejpam-5305	289	2	+ 1	DATE
ejpam-5305	295	1	lemma 2	ORG
ejpam-5305	298	1	t amit	PERSON
ejpam-5305	299	1	2	CARDINAL
ejpam-5305	300	1	1	CARDINAL
ejpam-5305	301	1	2	CARDINAL
ejpam-5305	301	2	5	CARDINAL
ejpam-5305	301	3	6	CARDINAL
ejpam-5305	304	1	mn	GPE
ejpam-5305	307	1	+ 1	DATE
ejpam-5305	309	1	+ 1	DATE
ejpam-5305	309	2	3	CARDINAL
ejpam-5305	309	3	4	DATE
ejpam-5305	313	1	1	CARDINAL
ejpam-5305	313	2	1	CARDINAL
ejpam-5305	314	1	i.	PERSON
ejpam-5305	314	2	3	CARDINAL
ejpam-5305	314	3	4	DATE
ejpam-5305	320	1	mi ≥	PERSON
ejpam-5305	320	2	m′+1	LANGUAGE
ejpam-5305	322	1	mi	PERSON
ejpam-5305	329	1	mi = m′	PERSON
ejpam-5305	330	1	+ 1	DATE
ejpam-5305	332	1	′′	ORG
ejpam-5305	333	1	′′	ORG
ejpam-5305	335	1	lemma 2	ORG
ejpam-5305	338	1	t amit	PERSON
ejpam-5305	339	1	2	CARDINAL
ejpam-5305	340	1	1	CARDINAL
ejpam-5305	342	1	7	CARDINAL
ejpam-5305	345	1	mn	GPE
ejpam-5305	349	1	1	CARDINAL
ejpam-5305	349	2	k. saengsura	PERSON
ejpam-5305	349	3	t. poomsa-	GPE
ejpam-5305	350	1	j. pure	PERSON
ejpam-5305	350	2	18	CARDINAL
ejpam-5305	350	3	2	CARDINAL
ejpam-5305	350	4	2025	CARDINAL
ejpam-5305	350	5	5305 7	DATE
ejpam-5305	350	6	8	CARDINAL
ejpam-5305	350	7	1	CARDINAL
ejpam-5305	351	1	i.	PERSON
ejpam-5305	356	1	|f(v3m3)−f(v)| = |f(vn1)−f(v(n−1)mn−1	PERSON
ejpam-5305	357	1	3	CARDINAL
ejpam-5305	357	2	5	DATE
ejpam-5305	365	1	|f(v(n−1)mn−1	PERSON
ejpam-5305	365	2	f(v)|	DATE
ejpam-5305	367	1	|f(v3m3)−f(v)| = |f(vn1)−f(v(n−1)mn−1	PERSON
ejpam-5305	368	1	3	CARDINAL
ejpam-5305	368	2	5	DATE
ejpam-5305	369	1	n−1	ORG
ejpam-5305	372	1	2	CARDINAL
ejpam-5305	373	1	1	CARDINAL
ejpam-5305	374	1	3	CARDINAL
ejpam-5305	374	2	1	CARDINAL
ejpam-5305	374	3	7	CARDINAL
ejpam-5305	378	1	1	CARDINAL
ejpam-5305	378	2	j. a. gillian	PERSON
ejpam-5305	380	1	combinatorics	ORG
ejpam-5305	380	2	16	CARDINAL
ejpam-5305	380	3	ds6	ORG
ejpam-5305	380	4	2015	DATE
ejpam-5305	381	1	2	CARDINAL
ejpam-5305	381	2	g. s.	PERSON
ejpam-5305	381	3	s. w. golomb	PERSON
ejpam-5305	383	1	65(4):562–570, 1977	DATE
ejpam-5305	384	1	3	CARDINAL
ejpam-5305	384	2	b. j. septory	PERSON
ejpam-5305	384	3	l. susilowati	PERSON
ejpam-5305	386	1	european journal	ORG
ejpam-5305	386	2	16(1):271–285	GPE
ejpam-5305	386	3	2023	CARDINAL
ejpam-5305	387	1	4	CARDINAL
ejpam-5305	387	2	b. j. septory	PERSON
ejpam-5305	387	3	l. susilowati	PERSON
ejpam-5305	389	1	2023	CARDINAL
ejpam-5305	390	1	k. saengsura	PERSON
ejpam-5305	390	2	t. poomsa-	GPE
ejpam-5305	391	1	j. pure	PERSON
ejpam-5305	391	2	18	CARDINAL
ejpam-5305	391	3	2	CARDINAL
ejpam-5305	391	4	2025	CARDINAL
ejpam-5305	391	5	5305 8 of 8	DATE
ejpam-5305	391	6	5	CARDINAL
ejpam-5305	393	1	162	CARDINAL
ejpam-5305	393	2	prague	GPE
ejpam-5305	393	3	1964	DATE
ejpam-5305	394	1	czechoslovak academy of sciences	ORG
ejpam-5305	395	1	6	CARDINAL
ejpam-5305	395	2	a. rosa	PERSON
ejpam-5305	397	1	rome	GPE
ejpam-5305	397	2	july 1966	DATE
ejpam-5305	397	3	349–355	CARDINAL
ejpam-5305	397	4	new york	GPE
ejpam-5305	397	5	1966	DATE
ejpam-5305	398	1	gordon	PERSON
ejpam-5305	399	1	7	CARDINAL
ejpam-5305	399	2	c. huang	PERSON
ejpam-5305	399	3	a. kotzig	PERSON
ejpam-5305	399	4	a. rosa	PERSON
ejpam-5305	401	1	utilitas mathematica	PERSON
ejpam-5305	401	2	21:31–48, 1982	DATE
ejpam-5305	402	1	8	CARDINAL
ejpam-5305	402	2	s. lake	GPE
ejpam-5305	402	3	a. wertheim	PERSON
ejpam-5305	404	1	3(3):241–247	CARDINAL
ejpam-5305	404	2	2010	DATE
ejpam-5305	405	1	9	CARDINAL
ejpam-5305	405	2	k. nakprasit	PERSON
ejpam-5305	405	3	t. poomsa-ard	GPE
ejpam-5305	405	4	three	CARDINAL
ejpam-5305	406	1	thai journal of mathematics	ORG
ejpam-5305	406	2	12(3):621–630	CARDINAL
ejpam-5305	406	3	2014	DATE
ejpam-5305	407	1	10	CARDINAL
ejpam-5305	407	2	t. poomsa-ard	GPE
ejpam-5305	408	1	three	CARDINAL
ejpam-5305	409	1	far east journal of mathematical sciences	ORG
ejpam-5305	409	2	100(1):51–64	CARDINAL
ejpam-5305	409	3	2016	DATE
ejpam-5305	410	1	11	CARDINAL
ejpam-5305	410	2	t. poomsa-ard	GPE
ejpam-5305	411	1	four	CARDINAL
ejpam-5305	412	1	2016:5327026	CARDINAL
ejpam-5305	412	2	2016	DATE
ejpam-5305	413	1	12	CARDINAL
ejpam-5305	413	2	a. haviar	PERSON
ejpam-5305	414	1	five	CARDINAL
ejpam-5305	415	1	233(1-3):133–150	CARDINAL
ejpam-5305	415	2	2001	DATE
ejpam-5305	416	1	13	CARDINAL
ejpam-5305	416	2	k. saengsura	PERSON
ejpam-5305	416	3	t. poomsa-ard	GPE
ejpam-5305	416	4	four	CARDINAL
ejpam-5305	416	5	2	CARDINAL
ejpam-5305	417	1	far east journal of mathematical sciences	ORG
ejpam-5305	417	2	100(2):255–269	DATE
ejpam-5305	417	3	2016	DATE