id	sid	eid	entity	type
ejpam-3448	1	1	european journal	ORG
ejpam-3448	2	1	12	CARDINAL
ejpam-3448	2	2	3, 2019	DATE
ejpam-3448	2	3	734	CARDINAL
ejpam-3448	2	4	1307-5543	DATE
ejpam-3448	2	5	new york	GPE
ejpam-3448	2	6	s. kaan gürbüzer1	ORG
ejpam-3448	2	7	bedia akyar2,∗	ORG
ejpam-3448	2	8	1	CARDINAL
ejpam-3448	2	9	2	CARDINAL
ejpam-3448	2	10	aalborg university	ORG
ejpam-3448	2	11	aalborg ø	PERSON
ejpam-3448	2	12	denmark	GPE
ejpam-3448	7	1	2010	DATE
ejpam-3448	7	2	51m20	CARDINAL
ejpam-3448	7	3	13p20	CARDINAL
ejpam-3448	7	4	1	CARDINAL
ejpam-3448	8	1	13	CARDINAL
ejpam-3448	8	2	kn	PERSON
ejpam-3448	9	1	the nineties	DATE
ejpam-3448	9	2	sternberg	PERSON
ejpam-3448	9	3	12	CARDINAL
ejpam-3448	9	4	rn+1	GPE
ejpam-3448	9	5	carr	PERSON
ejpam-3448	10	1	1	CARDINAL
ejpam-3448	10	2	kn	PERSON
ejpam-3448	11	1	2	CARDINAL
ejpam-3448	12	1	loday	DATE
ejpam-3448	12	2	6	CARDINAL
ejpam-3448	13	1	loday	DATE
ejpam-3448	13	2	4	CARDINAL
ejpam-3448	14	1	springfield	GPE
ejpam-3448	15	1	3	CARDINAL
ejpam-3448	16	1	∗corresponding	PERSON
ejpam-3448	17	1	s. kaan	PERSON
ejpam-3448	17	2	bedia@math.aau.dk	GPE
ejpam-3448	17	3	bedia akyar	PERSON
ejpam-3448	18	1	734	CARDINAL
ejpam-3448	18	2	2019	CARDINAL
ejpam-3448	19	1	s. k. gürbüzer	PERSON
ejpam-3448	19	2	b. akyar	PERSON
ejpam-3448	20	1	j. pure	PERSON
ejpam-3448	20	2	12	CARDINAL
ejpam-3448	20	3	3	CARDINAL
ejpam-3448	20	4	2019	DATE
ejpam-3448	20	5	734	CARDINAL
ejpam-3448	21	1	one	CARDINAL
ejpam-3448	22	1	10	CARDINAL
ejpam-3448	25	1	8	CARDINAL
ejpam-3448	25	2	9	CARDINAL
ejpam-3448	27	1	section 2	LAW
ejpam-3448	27	2	2	CARDINAL
ejpam-3448	27	3	springfield	GPE
ejpam-3448	28	1	3	CARDINAL
ejpam-3448	30	1	section 3	LAW
ejpam-3448	33	1	comp	NORP
ejpam-3448	35	1	2	CARDINAL
ejpam-3448	35	2	2	CARDINAL
ejpam-3448	36	1	two	CARDINAL
ejpam-3448	36	2	t1 ⊂	ORG
ejpam-3448	36	3	6=	CARDINAL
ejpam-3448	38	1	g1	ORG
ejpam-3448	40	1	gk	PERSON
ejpam-3448	41	1	0 ≤ k ≤ n	QUANTITY
ejpam-3448	44	1	∈	ORG
ejpam-3448	44	2	one	CARDINAL
ejpam-3448	45	1	2	CARDINAL
ejpam-3448	46	1	s. k. gürbüzer	PERSON
ejpam-3448	46	2	b. akyar	PERSON
ejpam-3448	47	1	j. pure	PERSON
ejpam-3448	47	2	12	CARDINAL
ejpam-3448	47	3	3	CARDINAL
ejpam-3448	47	4	2019	DATE
ejpam-3448	47	5	734	CARDINAL
ejpam-3448	47	6	748 736	CARDINAL
ejpam-3448	47	7	1	CARDINAL
ejpam-3448	50	1	affine hyperplanes	ORG
ejpam-3448	51	1	two	CARDINAL
ejpam-3448	52	1	two	CARDINAL
ejpam-3448	52	2	carr	PERSON
ejpam-3448	52	3	1	CARDINAL
ejpam-3448	53	1	•	CARDINAL
ejpam-3448	54	1	•	CARDINAL
ejpam-3448	55	1	1	CARDINAL
ejpam-3448	56	1	1	CARDINAL
ejpam-3448	57	1	1	CARDINAL
ejpam-3448	57	2	kg(t	PERSON
ejpam-3448	58	1	one	CARDINAL
ejpam-3448	58	2	kn−1	ORG
ejpam-3448	59	1	1	CARDINAL
ejpam-3448	59	2	2	DATE
ejpam-3448	62	1	1	CARDINAL
ejpam-3448	64	1	n + 2	PRODUCT
ejpam-3448	65	1	+ 1	DATE
ejpam-3448	69	1	3	CARDINAL
ejpam-3448	69	2	s. k. gürbüzer	PERSON
ejpam-3448	69	3	b. akyar	PERSON
ejpam-3448	70	1	j. pure	PERSON
ejpam-3448	70	2	12	CARDINAL
ejpam-3448	70	3	3	CARDINAL
ejpam-3448	70	4	2019	DATE
ejpam-3448	70	5	734-748 737	QUANTITY
ejpam-3448	70	6	springfield	GPE
ejpam-3448	71	1	loday	DATE
ejpam-3448	71	2	6	CARDINAL
ejpam-3448	72	1	9	CARDINAL
ejpam-3448	73	1	2	CARDINAL
ejpam-3448	74	1	loday	DATE
ejpam-3448	75	1	1	CARDINAL
ejpam-3448	75	2	2	DATE
ejpam-3448	75	3	f(n	ORG
ejpam-3448	77	1	3n	CARDINAL
ejpam-3448	78	1	2	CARDINAL
ejpam-3448	79	1	kp ×kq	PERSON
ejpam-3448	79	2	1	CARDINAL
ejpam-3448	81	1	two	CARDINAL
ejpam-3448	82	1	loday	DATE
ejpam-3448	82	2	1)n−1	CARDINAL
ejpam-3448	84	1	second	ORDINAL
ejpam-3448	84	2	cyclohedron wn	ORG
ejpam-3448	85	1	+ 1	DATE
ejpam-3448	85	2	+ 1	DATE
ejpam-3448	85	3	1	CARDINAL
ejpam-3448	85	4	2	DATE
ejpam-3448	87	1	n + 1	PRODUCT
ejpam-3448	88	1	1	CARDINAL
ejpam-3448	88	2	1	CARDINAL
ejpam-3448	90	1	1	CARDINAL
ejpam-3448	91	1	two	CARDINAL
ejpam-3448	92	1	first	ORDINAL
ejpam-3448	92	2	second	ORDINAL
ejpam-3448	92	3	1	CARDINAL
ejpam-3448	92	4	2	DATE
ejpam-3448	94	1	1 ≤	QUANTITY
ejpam-3448	95	1	second	ORDINAL
ejpam-3448	95	2	9	CARDINAL
ejpam-3448	96	1	1	CARDINAL
ejpam-3448	96	2	kn−1	ORG
ejpam-3448	96	3	kn−1	ORG
ejpam-3448	97	1	loday	DATE
ejpam-3448	98	1	2	CARDINAL
ejpam-3448	103	1	2	CARDINAL
ejpam-3448	103	2	only two	CARDINAL
ejpam-3448	105	1	n∑ k=1	PERSON
ejpam-3448	106	1	1	CARDINAL
ejpam-3448	106	2	1	CARDINAL
ejpam-3448	106	3	1	CARDINAL
ejpam-3448	107	1	s. k. gürbüzer	PERSON
ejpam-3448	107	2	b. akyar	PERSON
ejpam-3448	108	1	j. pure	PERSON
ejpam-3448	108	2	12	CARDINAL
ejpam-3448	108	3	3	CARDINAL
ejpam-3448	108	4	2019	DATE
ejpam-3448	108	5	734	CARDINAL
ejpam-3448	108	6	n∑ k=1	PERSON
ejpam-3448	109	1	1	CARDINAL
ejpam-3448	109	2	1	CARDINAL
ejpam-3448	109	3	1	CARDINAL
ejpam-3448	111	1	1	CARDINAL
ejpam-3448	111	2	k=0	PERSON
ejpam-3448	112	1	1 k	QUANTITY
ejpam-3448	112	2	n−	NORP
ejpam-3448	112	3	1)n−1	CARDINAL
ejpam-3448	112	4	1)n	DATE
ejpam-3448	115	1	1)n−1	CARDINAL
ejpam-3448	115	2	1	CARDINAL
ejpam-3448	115	3	1	CARDINAL
ejpam-3448	116	1	riordan	PERSON
ejpam-3448	117	1	11	CARDINAL
ejpam-3448	118	1	3	CARDINAL
ejpam-3448	118	2	loday	DATE
ejpam-3448	119	1	loday	DATE
ejpam-3448	119	2	4	CARDINAL
ejpam-3448	120	1	two	CARDINAL
ejpam-3448	122	1	loday	DATE
ejpam-3448	123	1	1	CARDINAL
ejpam-3448	125	1	0	CARDINAL
ejpam-3448	125	2	0	CARDINAL
ejpam-3448	128	1	2	CARDINAL
ejpam-3448	128	2	5	CARDINAL
ejpam-3448	128	3	1	CARDINAL
ejpam-3448	134	1		CARDINAL
ejpam-3448	135	1	∈	ORG
ejpam-3448	135	2	+ 1	DATE
ejpam-3448	135	3	1 ≤	QUANTITY
ejpam-3448	136	1	1	CARDINAL
ejpam-3448	141	1	s. k. gürbüzer	PERSON
ejpam-3448	141	2	b. akyar	PERSON
ejpam-3448	142	1	j. pure	PERSON
ejpam-3448	142	2	12	CARDINAL
ejpam-3448	142	3	3	CARDINAL
ejpam-3448	142	4	2019	DATE
ejpam-3448	142	5	734	CARDINAL
ejpam-3448	142	6	2	CARDINAL
ejpam-3448	145	1	two	CARDINAL
ejpam-3448	146	1	t1	ORG
ejpam-3448	146	2	t1 ∨	ORG
ejpam-3448	147	1	+ 1	DATE
ejpam-3448	148	1	0 ∨	QUANTITY
ejpam-3448	148	2	1(a1 + 1	DATE
ejpam-3448	155	1	two	CARDINAL
ejpam-3448	158	1	1	CARDINAL
ejpam-3448	158	2	2341 ∈mp(4	CARDINAL
ejpam-3448	158	3	3	CARDINAL
ejpam-3448	159	1	23413452	DATE
ejpam-3448	160	1	3	CARDINAL
ejpam-3448	160	2	3	CARDINAL
ejpam-3448	162	1	∈	ORG
ejpam-3448	171	1	bm a1	PERSON
ejpam-3448	175	1	2	CARDINAL
ejpam-3448	176	1	231	CARDINAL
ejpam-3448	176	2	4	CARDINAL
ejpam-3448	177	1	4	CARDINAL
ejpam-3448	178	1	4	CARDINAL
ejpam-3448	178	2	s. k. gürbüzer	PERSON
ejpam-3448	178	3	b. akyar	PERSON
ejpam-3448	179	1	j. pure	PERSON
ejpam-3448	179	2	12	CARDINAL
ejpam-3448	179	3	3	CARDINAL
ejpam-3448	179	4	2019	DATE
ejpam-3448	179	5	734	CARDINAL
ejpam-3448	179	6	4	CARDINAL
ejpam-3448	180	1	two	CARDINAL
ejpam-3448	180	2	⋃ t1	PERSON
ejpam-3448	182	1	two	CARDINAL
ejpam-3448	183	1	0	CARDINAL
ejpam-3448	185	1	3	CARDINAL
ejpam-3448	185	2	123	CARDINAL
ejpam-3448	185	3	212	CARDINAL
ejpam-3448	185	4	two	CARDINAL
ejpam-3448	185	5	3	CARDINAL
ejpam-3448	186	1	345212	DATE
ejpam-3448	186	2	245312	DATE
ejpam-3448	186	3	235412	DATE
ejpam-3448	186	4	234512	DATE
ejpam-3448	186	5	134523	DATE
ejpam-3448	186	6	124534	DATE
ejpam-3448	186	7	123545	DATE
ejpam-3448	187	1	5	CARDINAL
ejpam-3448	190	1	⋃	DATE
ejpam-3448	191	1	0	CARDINAL
ejpam-3448	192	1	pp(n	GPE
ejpam-3448	192	2	t̄	GPE
ejpam-3448	197	1	3	CARDINAL
ejpam-3448	198	1	t3	ORG
ejpam-3448	198	2	three	CARDINAL
ejpam-3448	199	1	t3	ORG
ejpam-3448	199	2	t3	ORG
ejpam-3448	200	1	t3	ORG
ejpam-3448	200	2	t1 ∨	ORG
ejpam-3448	200	3	t3	ORG
ejpam-3448	200	4	t1 ∨	ORG
ejpam-3448	200	5	t̄2	EVENT
ejpam-3448	200	6	∨ t̄1	PERSON
ejpam-3448	200	7	+ t̄1	NORP
ejpam-3448	200	8	t1 ∨	ORG
ejpam-3448	207	1	bm	ORG
ejpam-3448	207	2	t3	ORG
ejpam-3448	210	1	first	ORDINAL
ejpam-3448	210	2	three	CARDINAL
ejpam-3448	211	1	three	CARDINAL
ejpam-3448	211	2	t1 ∨	ORG
ejpam-3448	214	1	an1b1	PERSON
ejpam-3448	217	1	t̄2	PERSON
ejpam-3448	217	2	∨ t̄1	PERSON
ejpam-3448	217	3	s. k. gürbüzer	PERSON
ejpam-3448	217	4	b. akyar	PERSON
ejpam-3448	218	1	j. pure	PERSON
ejpam-3448	218	2	12	CARDINAL
ejpam-3448	218	3	3	CARDINAL
ejpam-3448	218	4	2019	DATE
ejpam-3448	218	5	734	CARDINAL
ejpam-3448	239	1	2	CARDINAL
ejpam-3448	239	2	3	CARDINAL
ejpam-3448	239	3	1	CARDINAL
ejpam-3448	240	1	two	CARDINAL
ejpam-3448	241	1	4	CARDINAL
ejpam-3448	242	1	two	CARDINAL
ejpam-3448	242	2	0	CARDINAL
ejpam-3448	243	1	two	CARDINAL
ejpam-3448	243	2	∨	CARDINAL
ejpam-3448	243	3	2 ∪	PERCENT
ejpam-3448	243	4	t l 1	DATE
ejpam-3448	243	5	1	CARDINAL
ejpam-3448	243	6	t l 2	DATE
ejpam-3448	243	7	2	CARDINAL
ejpam-3448	248	1	∈	ORG
ejpam-3448	249	1	two	CARDINAL
ejpam-3448	249	2	1	CARDINAL
ejpam-3448	249	3	1	CARDINAL
ejpam-3448	251	1	t1/t l 2	ORG
ejpam-3448	251	2	∨	CARDINAL
ejpam-3448	251	3	2 ≤	QUANTITY
ejpam-3448	251	4	1 \	QUANTITY
ejpam-3448	253	1	cm+n	PERSON
ejpam-3448	256	1	bm ≤ t ≤ a1	PERSON
ejpam-3448	259	1	4	CARDINAL
ejpam-3448	259	2	t l 1	DATE
ejpam-3448	259	3	2	CARDINAL
ejpam-3448	260	1	two	CARDINAL
ejpam-3448	261	1	l 1	DATE
ejpam-3448	262	1	2	CARDINAL
ejpam-3448	262	2	t l 1	DATE
ejpam-3448	262	3	2	CARDINAL
ejpam-3448	265	1	2	CARDINAL
ejpam-3448	267	1	2	CARDINAL
ejpam-3448	267	2	1	CARDINAL
ejpam-3448	270	1	1	CARDINAL
ejpam-3448	271	1	two	CARDINAL
ejpam-3448	271	2	1 or	CARDINAL
ejpam-3448	271	3	1	CARDINAL
ejpam-3448	272	1	first	ORDINAL
ejpam-3448	272	2	ci = 1	PERSON
ejpam-3448	275	1	an(b1+an	ORG
ejpam-3448	281	1	+ 1	DATE
ejpam-3448	281	2	1	CARDINAL
ejpam-3448	282	1	1	CARDINAL
ejpam-3448	282	2	1	CARDINAL
ejpam-3448	283	1	1)b1	CARDINAL
ejpam-3448	285	1	1	CARDINAL
ejpam-3448	286	1	1	CARDINAL
ejpam-3448	289	1	t l 1	DATE
ejpam-3448	289	2	first	ORDINAL
ejpam-3448	289	3	l 1∨	DATE
ejpam-3448	289	4	1	CARDINAL
ejpam-3448	290	1	first	ORDINAL
ejpam-3448	291	1	s. k. gürbüzer	PERSON
ejpam-3448	291	2	b. akyar	PERSON
ejpam-3448	292	1	j. pure	PERSON
ejpam-3448	292	2	12	CARDINAL
ejpam-3448	292	3	3	CARDINAL
ejpam-3448	292	4	2019	DATE
ejpam-3448	292	5	734-748 742	QUANTITY
ejpam-3448	292	6	second	ORDINAL
ejpam-3448	293	1	t1 \t l 2)∨t	ORG
ejpam-3448	293	2	2	CARDINAL
ejpam-3448	294	1	second	ORDINAL
ejpam-3448	296	1	2 ≤ t ≤	QUANTITY
ejpam-3448	296	2	∨	CARDINAL
ejpam-3448	296	3	2	CARDINAL
ejpam-3448	296	4	∨	CARDINAL
ejpam-3448	296	5	2	CARDINAL
ejpam-3448	296	6	6	CARDINAL
ejpam-3448	297	1	two	CARDINAL
ejpam-3448	299	1	t l 1	DATE
ejpam-3448	299	2	∨	CARDINAL
ejpam-3448	299	3	2	CARDINAL
ejpam-3448	301	1	1	CARDINAL
ejpam-3448	302	1	t3	ORG
ejpam-3448	303	1	t3	ORG
ejpam-3448	303	2	1	CARDINAL
ejpam-3448	303	3	t3	ORG
ejpam-3448	303	4	2	CARDINAL
ejpam-3448	303	5	t3	ORG
ejpam-3448	303	6	t3	ORG
ejpam-3448	303	7	3	CARDINAL
ejpam-3448	303	8	0	CARDINAL
ejpam-3448	305	1	1	CARDINAL
ejpam-3448	305	2	t3	ORG
ejpam-3448	305	3	t1 a t2)l ∨	ORG
ejpam-3448	305	4	t l 1	DATE
ejpam-3448	308	1	t l 1	DATE
ejpam-3448	308	2	t l 1	DATE
ejpam-3448	310	1	2	CARDINAL
ejpam-3448	311	1	t3	ORG
ejpam-3448	311	2	t1 ` t2)l ∨	ORG
ejpam-3448	311	3	∨	CARDINAL
ejpam-3448	311	4	2	CARDINAL
ejpam-3448	311	5	∨	CARDINAL
ejpam-3448	311	6	2	CARDINAL
ejpam-3448	311	7	2 + t3	DATE
ejpam-3448	311	8	t3	ORG
ejpam-3448	312	1	2 + t3	DATE
ejpam-3448	312	2	2 + t3	DATE
ejpam-3448	312	3	2 + t3	DATE
ejpam-3448	312	4	2 + t3	DATE
ejpam-3448	312	5	3	CARDINAL
ejpam-3448	312	6	t3	ORG
ejpam-3448	313	1	3	CARDINAL
ejpam-3448	313	2	3	CARDINAL
ejpam-3448	314	1	3	CARDINAL
ejpam-3448	315	1	3	CARDINAL
ejpam-3448	316	1	t3	ORG
ejpam-3448	316	2	1	CARDINAL
ejpam-3448	317	1	t1 ∈mp(n	ORG
ejpam-3448	317	2	∈mp(m	NORP
ejpam-3448	317	3	two	CARDINAL
ejpam-3448	319	1	7	CARDINAL
ejpam-3448	319	2	1	CARDINAL
ejpam-3448	319	3	∈	ORG
ejpam-3448	319	4	1	CARDINAL
ejpam-3448	319	5	wt	CARDINAL
ejpam-3448	319	6	1	CARDINAL
ejpam-3448	320	1	s. k. gürbüzer	PERSON
ejpam-3448	320	2	b. akyar	PERSON
ejpam-3448	321	1	j. pure	PERSON
ejpam-3448	321	2	12	CARDINAL
ejpam-3448	321	3	3	CARDINAL
ejpam-3448	321	4	2019	DATE
ejpam-3448	321	5	734	CARDINAL
ejpam-3448	321	6	748 743	CARDINAL
ejpam-3448	321	7	4	CARDINAL
ejpam-3448	322	1	2132	CARDINAL
ejpam-3448	322	2	1	CARDINAL
ejpam-3448	322	3	1	CARDINAL
ejpam-3448	322	4	1	CARDINAL
ejpam-3448	323	1	8	CARDINAL
ejpam-3448	324	1	two	CARDINAL
ejpam-3448	327	1	two	CARDINAL
ejpam-3448	328	1	2	CARDINAL
ejpam-3448	329	1	t l 1	DATE
ejpam-3448	329	2	1	CARDINAL
ejpam-3448	330	1	1	CARDINAL
ejpam-3448	331	1	one	CARDINAL
ejpam-3448	331	2	t̄1 × t̄2	PRODUCT
ejpam-3448	331	3	two	CARDINAL
ejpam-3448	333	1	9	CARDINAL
ejpam-3448	334	1	two	CARDINAL
ejpam-3448	334	2	a⊗a→	PERSON
ejpam-3448	335	1	4	CARDINAL
ejpam-3448	335	2	5	CARDINAL
ejpam-3448	335	3	∗	CARDINAL
ejpam-3448	335	4	6	CARDINAL
ejpam-3448	335	5	∈	ORG
ejpam-3448	335	6	∗	CARDINAL
ejpam-3448	336	1	10	CARDINAL
ejpam-3448	338	1	t ∈ mp(n	ORG
ejpam-3448	338	2	n ≥ 1	DATE
ejpam-3448	338	3	1	CARDINAL
ejpam-3448	344	1	two	CARDINAL
ejpam-3448	348	1	2	CARDINAL
ejpam-3448	351	1	two	CARDINAL
ejpam-3448	360	1	1	CARDINAL
ejpam-3448	361	1	4	CARDINAL
ejpam-3448	361	2	9	CARDINAL
ejpam-3448	363	1	first	ORDINAL
ejpam-3448	365	1	∈	ORG
ejpam-3448	367	1	1	CARDINAL
ejpam-3448	367	2	0 ≤	QUANTITY
ejpam-3448	372	1	9	CARDINAL
ejpam-3448	372	2	s. k. gürbüzer	PERSON
ejpam-3448	372	3	b. akyar	PERSON
ejpam-3448	373	1	j. pure	PERSON
ejpam-3448	373	2	12	CARDINAL
ejpam-3448	373	3	3	CARDINAL
ejpam-3448	373	4	2019	DATE
ejpam-3448	373	5	734-748 744	QUANTITY
ejpam-3448	373	6	ãi	ORG
ejpam-3448	373	7	ãi = max(ai	ORG
ejpam-3448	375	1	three	CARDINAL
ejpam-3448	375	2	t3	ORG
ejpam-3448	377	1	0 ≤	MONEY
ejpam-3448	377	2	10	CARDINAL
ejpam-3448	377	3	t3	ORG
ejpam-3448	377	4	t1 ◦j−m t3	ORG
ejpam-3448	377	5	1	CARDINAL
ejpam-3448	378	1	11	CARDINAL
ejpam-3448	378	2	1	CARDINAL
ejpam-3448	380	1	pp(m)}m≥1	ORG
ejpam-3448	380	2	one	CARDINAL
ejpam-3448	381	1	comp	NORP
ejpam-3448	382	1	1	CARDINAL
ejpam-3448	386	1	1	CARDINAL
ejpam-3448	390	1	two	CARDINAL
ejpam-3448	392	1	eik	PERSON
ejpam-3448	392	2	ej1	ORG
ejpam-3448	396	1	eik	PERSON
ejpam-3448	398	1	∈	ORG
ejpam-3448	398	2	ω	ORG
ejpam-3448	398	3	ω	GPE
ejpam-3448	399	1	kn	PERSON
ejpam-3448	401	1	cc∗(k n	ORG
ejpam-3448	402	1	t ′	DATE
ejpam-3448	402	2	12	CARDINAL
ejpam-3448	402	3	p(n + 1	LOC
ejpam-3448	404	1	1	CARDINAL
ejpam-3448	406	1	k + 1	ORG
ejpam-3448	407	1	∂2	ORG
ejpam-3448	407	2	0	CARDINAL
ejpam-3448	409	1	0 ≤	MONEY
ejpam-3448	409	2	pp(n)× pp(m)→ pp(n+m	PERSON
ejpam-3448	409	3	t1	ORG
ejpam-3448	409	4	ω	GPE
ejpam-3448	409	5	ω ′	DATE
ejpam-3448	410	1	ω ∧	ORG
ejpam-3448	410	2	ω′	CARDINAL
ejpam-3448	410	3	m−	NORP
ejpam-3448	410	4	ω ∧	ORG
ejpam-3448	410	5	ω′	CARDINAL
ejpam-3448	413	1	pc(n)×	PERSON
ejpam-3448	413	2	pp(m)→	NORP
ejpam-3448	417	1	+ b̃i)bi+1	PERSON
ejpam-3448	419	1	∈	ORG
ejpam-3448	420	1	1 ≤	QUANTITY
ejpam-3448	421	1	n. s. k. gürbüzer	PERSON
ejpam-3448	421	2	b. akyar	PERSON
ejpam-3448	422	1	j. pure	PERSON
ejpam-3448	422	2	12	CARDINAL
ejpam-3448	422	3	3	CARDINAL
ejpam-3448	422	4	2019	DATE
ejpam-3448	422	5	734-748 745	QUANTITY
ejpam-3448	422	6	3	CARDINAL
ejpam-3448	424	1	pp(m)}m≥1	ORG
ejpam-3448	425	1	9	CARDINAL
ejpam-3448	426	1	5	CARDINAL
ejpam-3448	429	1	11	CARDINAL
ejpam-3448	434	1	only two	CARDINAL
ejpam-3448	434	2	21	CARDINAL
ejpam-3448	434	3	12	DATE
ejpam-3448	434	4	two	CARDINAL
ejpam-3448	434	5	mp(2)× i2	GPE
ejpam-3448	434	6	21	CARDINAL
ejpam-3448	434	7	12	CARDINAL
ejpam-3448	435	1	12	CARDINAL
ejpam-3448	436	1	t1 ⊂	ORG
ejpam-3448	436	2	loday	DATE
ejpam-3448	436	3	5	CARDINAL
ejpam-3448	436	4	t1 ⊂	ORG
ejpam-3448	436	5	⊂	GPE
ejpam-3448	437	1	sn ×	ORG
ejpam-3448	437	2	s1×i1	PERSON
ejpam-3448	438	1	s2× i2 ⊂mp(2)× i2	PERSON
ejpam-3448	439	1	sn×	GPE
ejpam-3448	440	1	21	CARDINAL
ejpam-3448	440	2	12	CARDINAL
ejpam-3448	441	1	sn ×	ORG
ejpam-3448	441	2	f(s	GPE
ejpam-3448	443	1	z2 × i2	ORG
ejpam-3448	445	1	⊕	PERSON
ejpam-3448	447	1	zn × si0 × ·	ORG
ejpam-3448	447	2	0	CARDINAL
ejpam-3448	448	1	zn	ORG
ejpam-3448	450	1	zn × si0 × ·	ORG
ejpam-3448	450	2	ω	ORG
ejpam-3448	451	1	0	CARDINAL
ejpam-3448	452	1	+ 1	DATE
ejpam-3448	452	2	tin s. k. gürbüzer	PERSON
ejpam-3448	452	3	b. akyar	PERSON
ejpam-3448	453	1	j. pure	PERSON
ejpam-3448	453	2	12	CARDINAL
ejpam-3448	453	3	3	CARDINAL
ejpam-3448	453	4	2019	DATE
ejpam-3448	453	5	734	CARDINAL
ejpam-3448	453	6	n∑ k=1	PERSON
ejpam-3448	454	1	−1)kdk	ORG
ejpam-3448	454	2	13	CARDINAL
ejpam-3448	456	1	0	CARDINAL
ejpam-3448	459	1	tk−1	ORG
ejpam-3448	461	1	the k-th	PERSON
ejpam-3448	461	2	zn	DATE
ejpam-3448	462	1	tk−1	ORG
ejpam-3448	462	2	zn	DATE
ejpam-3448	463	1	tk−1	ORG
ejpam-3448	465	1	0	CARDINAL
ejpam-3448	466	1	4	CARDINAL
ejpam-3448	467	1	0	CARDINAL
ejpam-3448	469	1	zn	ORG
ejpam-3448	469	2	t0	PERSON
ejpam-3448	474	1	1	CARDINAL
ejpam-3448	474	2	three	CARDINAL
ejpam-3448	475	1	•	CARDINAL
ejpam-3448	475	2	the k-th	FAC
ejpam-3448	476	1	0	CARDINAL
ejpam-3448	477	1	•	CARDINAL
ejpam-3448	477	2	dj−1dk	CARDINAL
ejpam-3448	477	3	0	CARDINAL
ejpam-3448	478	1	•	CARDINAL
ejpam-3448	478	2	j-th	PERSON
ejpam-3448	478	3	dkdj(zn, t0	GPE
ejpam-3448	487	1	tk−1	ORG
ejpam-3448	493	1	tk−1	ORG
ejpam-3448	500	1	tk−1	ORG
ejpam-3448	503	1	t0	PERSON
ejpam-3448	506	1	dkdk	PERSON
ejpam-3448	508	1	the k-th	FAC
ejpam-3448	509	1	0	CARDINAL
ejpam-3448	511	1	tk−1 ∨	ORG
ejpam-3448	513	1	εk+1(zn	ORG
ejpam-3448	513	2	the k-th	FAC
ejpam-3448	514	1	zn	DATE
ejpam-3448	516	1	0	CARDINAL
ejpam-3448	516	2	13	DATE
ejpam-3448	517	1	ω	ORG
ejpam-3448	517	2	zn	ORG
ejpam-3448	517	3	t0	PERSON
ejpam-3448	518	1	zn	DATE
ejpam-3448	518	2	ω′	CARDINAL
ejpam-3448	520	1	5	CARDINAL
ejpam-3448	520	2	ω	EVENT
ejpam-3448	520	3	k cups	ORG
ejpam-3448	520	4	subcomplex	NORP
ejpam-3448	521	1	∆k−1	DATE
ejpam-3448	521	2	747 proof	PRODUCT
ejpam-3448	524	1	∆k−1	DATE
ejpam-3448	525	1	1)-st	CARDINAL
ejpam-3448	525	2	∆k−1	CARDINAL
ejpam-3448	528	1	dikω	PERSON
ejpam-3448	528	2	the j-th cup of	ORG
ejpam-3448	528	3	zn	DATE
ejpam-3448	529	1	∆k−1	CARDINAL
ejpam-3448	529	2	0	CARDINAL
ejpam-3448	530	1	13	CARDINAL
ejpam-3448	531	1	6	CARDINAL
ejpam-3448	532	1	c∗	ORG
ejpam-3448	532	2	⊕ ω	FAC
ejpam-3448	532	3	ω	ORDINAL
ejpam-3448	534	1	ω ∈ c∗	ORG
ejpam-3448	534	2	ω ∈	ORG
ejpam-3448	535	1	extremal	GPE
ejpam-3448	536	1	1 ≤ j ≤	QUANTITY
ejpam-3448	536	2	ω ∈ cω1	ORG
ejpam-3448	537	1	one	CARDINAL
ejpam-3448	537	2	only one	CARDINAL
ejpam-3448	537	3	cω1	PERSON
ejpam-3448	537	4	ω	CARDINAL
ejpam-3448	538	1	zn	ORG
ejpam-3448	538	2	t0	PERSON
ejpam-3448	540	1	z′n	GPE
ejpam-3448	544	1	0	CARDINAL
ejpam-3448	544	2	z′n	GPE
ejpam-3448	546	1	ω	ORDINAL
ejpam-3448	547	1	ω	ORG
ejpam-3448	552	1	14	CARDINAL
ejpam-3448	552	2	t0	PERSON
ejpam-3448	554	1	14	CARDINAL
ejpam-3448	554	2	ω	CARDINAL
ejpam-3448	555	1	c∗	ORG
ejpam-3448	557	1	h0(c∗	ORG
ejpam-3448	557	2	f. proof	PERSON
ejpam-3448	558	1	5	CARDINAL
ejpam-3448	558	2	6	CARDINAL
ejpam-3448	559	1	only one	CARDINAL
ejpam-3448	560	1	subcomplex	ORDINAL
ejpam-3448	560	2	ω	ORG
ejpam-3448	560	3	0,0	CARDINAL
ejpam-3448	563	1	h0(c∗	ORG
ejpam-3448	563	2	8	CARDINAL
ejpam-3448	564	1	f(z	PRODUCT
ejpam-3448	564	2	f(s	GPE
ejpam-3448	565	1	mp(2)× i2	GPE
ejpam-3448	565	2	f(z	PRODUCT
ejpam-3448	565	3	f(s	GPE
ejpam-3448	567	1	f(z	PRODUCT
ejpam-3448	567	2	f(s	GPE
ejpam-3448	568	1	7, f(z	DATE
ejpam-3448	568	2	f(s	GPE
ejpam-3448	568	3	1	CARDINAL
ejpam-3448	568	4	m. p. carr	PERSON
ejpam-3448	568	5	s. l. devadoss	PERSON
ejpam-3448	568	6	153(12):2155–2168, 2006	DATE
ejpam-3448	569	1	748	CARDINAL
ejpam-3448	569	2	2	CARDINAL
ejpam-3448	569	3	s. l. devadoss	PERSON
ejpam-3448	570	1	309(1):271	CARDINAL
ejpam-3448	570	2	276	CARDINAL
ejpam-3448	570	3	2009	DATE
ejpam-3448	571	1	3	CARDINAL
ejpam-3448	571	2	s. forcey	PERSON
ejpam-3448	571	3	d. springfield	GPE
ejpam-3448	572	1	cyclohedron	ORG
ejpam-3448	573	1	algebraic combinatorics	ORG
ejpam-3448	573	2	32(4):597–627	CARDINAL
ejpam-3448	573	3	2010	DATE
ejpam-3448	574	1	4	CARDINAL
ejpam-3448	574	2	j. l. loday	PERSON
ejpam-3448	575	1	arithmetree	PERSON
ejpam-3448	576	1	258(1):275	CARDINAL
ejpam-3448	576	2	309	CARDINAL
ejpam-3448	576	3	2002	DATE
ejpam-3448	577	1	5	CARDINAL
ejpam-3448	577	2	j. l. loday	PERSON
ejpam-3448	579	1	53:16, 2004	DATE
ejpam-3448	580	1	6	CARDINAL
ejpam-3448	580	2	j. l. loday	PERSON
ejpam-3448	582	1	der mathematik	PERSON
ejpam-3448	582	2	278	CARDINAL
ejpam-3448	582	3	2004	DATE
ejpam-3448	583	1	j. l. loday	PERSON
ejpam-3448	585	1	431	CARDINAL
ejpam-3448	585	2	327–340	CARDINAL
ejpam-3448	586	1	american mathematical society	ORG
ejpam-3448	586	2	ri	GPE
ejpam-3448	586	3	2007	DATE
ejpam-3448	587	1	8	CARDINAL
ejpam-3448	587	2	m. markl	PERSON
ejpam-3448	588	1	24(4):1471–1500, 1996	DATE
ejpam-3448	589	1	9	CARDINAL
ejpam-3448	589	2	m. markl	PERSON
ejpam-3448	590	1	homotopy	ORG
ejpam-3448	590	2	ny	GPE
ejpam-3448	590	3	1996	DATE
ejpam-3448	590	4	227	CARDINAL
ejpam-3448	590	5	235–265	CARDINAL
ejpam-3448	591	1	american mathematical society	ORG
ejpam-3448	591	2	ri	GPE
ejpam-3448	591	3	1999	DATE
ejpam-3448	592	1	10	CARDINAL
ejpam-3448	592	2	m. markl	PERSON
ejpam-3448	592	3	s. shnider	PERSON
ejpam-3448	592	4	j. stasheff	PERSON
ejpam-3448	595	1	american mathematical society	ORG
ejpam-3448	595	2	2007	DATE
ejpam-3448	596	1	11	CARDINAL
ejpam-3448	596	2	j. riordan	PERSON
ejpam-3448	598	1	r. e. krieger pub.	PERSON
ejpam-3448	599	1	1979	DATE
ejpam-3448	600	1	12	CARDINAL
ejpam-3448	600	2	s. shnider	PERSON
ejpam-3448	600	3	s. sternberg	PERSON
ejpam-3448	601	1	quantum	ORG
ejpam-3448	602	1	cambridge	GPE
ejpam-3448	602	2	ma	GPE
ejpam-3448	602	3	1993	DATE
ejpam-3448	603	1	coalgebras	GPE
ejpam-3448	604	1	13	CARDINAL
ejpam-3448	604	2	j. stasheff	PERSON
ejpam-3448	605	1	homotopy	ORG
ejpam-3448	605	2	i. ii	PERSON
ejpam-3448	605	3	american	NORP
ejpam-3448	605	4	108):275–312, 1963	DATE