id	sid	eid	entity	type
ejpam-1773	1	1	9_yildiz.dvi	CARDINAL
ejpam-1773	1	2	european	NORP
ejpam-1773	2	1	6	CARDINAL
ejpam-1773	2	2	1, 2013	DATE
ejpam-1773	2	3	89	CARDINAL
ejpam-1773	2	4	1307-5543	CARDINAL
ejpam-1773	2	5	steven dougherty1	PERSON
ejpam-1773	2	6	bahattin yıldız2,∗	ORG
ejpam-1773	2	7	karadeniz2 1	ORG
ejpam-1773	2	8	scranton university	ORG
ejpam-1773	2	9	scranton	GPE
ejpam-1773	2	10	pa, usa 2	ORG
ejpam-1773	2	11	istanbul	GPE
ejpam-1773	2	12	turkey	GPE
ejpam-1773	4	1	k ≥ 2	ORG
ejpam-1773	5	1	2k	CARDINAL
ejpam-1773	6	1	2010	DATE
ejpam-1773	6	2	94b05	CARDINAL
ejpam-1773	6	3	extremal	ORG
ejpam-1773	6	4	1	CARDINAL
ejpam-1773	7	1	selfdual	DATE
ejpam-1773	8	1	4	CARDINAL
ejpam-1773	8	2	9	CARDINAL
ejpam-1773	8	3	5	CARDINAL
ejpam-1773	10	1	6	CARDINAL
ejpam-1773	12	1	2	CARDINAL
ejpam-1773	12	2	quaternionic	NORP
ejpam-1773	13	1	rk	ORG
ejpam-1773	13	2	quaternionic	NORP
ejpam-1773	14	1	first	ORDINAL
ejpam-1773	15	1	2	CARDINAL
ejpam-1773	15	2	2k	CARDINAL
ejpam-1773	17	1	doughertys1	ORG
ejpam-1773	17	2	s. dougherty	ORG
ejpam-1773	17	3	byildiz�fatih.edu.tr	ORG
ejpam-1773	18	1	89	CARDINAL
ejpam-1773	18	2	2013	DATE
ejpam-1773	19	1	s. dougherty	PERSON
ejpam-1773	20	1	j. pure	PERSON
ejpam-1773	20	2	6	CARDINAL
ejpam-1773	20	3	89	CARDINAL
ejpam-1773	20	4	rk	ORG
ejpam-1773	20	5	2k	CARDINAL
ejpam-1773	21	1	rk	ORG
ejpam-1773	23	1	section 2	LAW
ejpam-1773	24	1	section 3	LAW
ejpam-1773	24	2	rk	NORP
ejpam-1773	24	3	k 6= k′	ORG
ejpam-1773	25	1	section 4	LAW
ejpam-1773	28	1	section 5	LAW
ejpam-1773	28	2	1	CARDINAL
ejpam-1773	28	3	2	CARDINAL
ejpam-1773	29	1	one	CARDINAL
ejpam-1773	29	2	1	CARDINAL
ejpam-1773	29	3	2	CARDINAL
ejpam-1773	30	1	section 6	LAW
ejpam-1773	30	2	quaternionic	NORP
ejpam-1773	31	1	extremal	GPE
ejpam-1773	31	2	k. 2	PERSON
ejpam-1773	31	3	1	CARDINAL
ejpam-1773	33	1	0,uiu	CARDINAL
ejpam-1773	34	1	j = u jui〉	PERSON
ejpam-1773	35	1	1	CARDINAL
ejpam-1773	37	1	0,uiu	CARDINAL
ejpam-1773	37	2	j = u jui〉	PERSON
ejpam-1773	37	3	2	CARDINAL
ejpam-1773	39	1	k.	PERSON
ejpam-1773	39	2	1,2	CARDINAL
ejpam-1773	40	1	3	CARDINAL
ejpam-1773	40	2	1	CARDINAL
ejpam-1773	41	1	∈	ORG
ejpam-1773	42	1	4	CARDINAL
ejpam-1773	44	1	uk	GPE
ejpam-1773	44	2	2(2	CARDINAL
ejpam-1773	48	1	11	CARDINAL
ejpam-1773	49	1	11	CARDINAL
ejpam-1773	50	1	s. dougherty	PERSON
ejpam-1773	51	1	j. pure	PERSON
ejpam-1773	51	2	6	CARDINAL
ejpam-1773	51	3	89	CARDINAL
ejpam-1773	51	4	rk	ORG
ejpam-1773	51	5	1	CARDINAL
ejpam-1773	53	1	0 or can be∞. we	DATE
ejpam-1773	53	2	rn k .	FAC
ejpam-1773	58	1	0	CARDINAL
ejpam-1773	59	1	11	CARDINAL
ejpam-1773	61	1	⊆	CARDINAL
ejpam-1773	61	2	6	CARDINAL
ejpam-1773	62	1	∈ rn k−1	ORG
ejpam-1773	62	2	f2	ORG
ejpam-1773	63	1	lee	PERSON
ejpam-1773	64	1	lee	PERSON
ejpam-1773	65	1	2	CARDINAL
ejpam-1773	66	1	lee weight	PERSON
ejpam-1773	66	2	i.	PERSON
ejpam-1773	66	3	one	CARDINAL
ejpam-1773	67	1	2|a|	CARDINAL
ejpam-1773	67	2	1,2	CARDINAL
ejpam-1773	68	1	k}	PERSON
ejpam-1773	72	1	5	CARDINAL
ejpam-1773	72	2	non-zero	CARDINAL
ejpam-1773	75	1	xn−wt(c	DATE
ejpam-1773	76	1	6	CARDINAL
ejpam-1773	76	2	lee weight	PERSON
ejpam-1773	76	3	zle(c	ORG
ejpam-1773	76	4	7	CARDINAL
ejpam-1773	76	5	lee	PERSON
ejpam-1773	77	1	7	CARDINAL
ejpam-1773	78	1	s. dougherty	PERSON
ejpam-1773	79	1	j. pure	PERSON
ejpam-1773	79	2	6	CARDINAL
ejpam-1773	79	3	89	CARDINAL
ejpam-1773	79	4	π j	ORG
ejpam-1773	79	5	π j	ORG
ejpam-1773	82	1	π j	ORG
ejpam-1773	82	2	k	PERSON
ejpam-1773	82	3	j ≤ k	PERSON
ejpam-1773	82	4	π j	ORG
ejpam-1773	82	5	k	PERSON
ejpam-1773	83	1	j,k(c ′	WORK_OF_ART
ejpam-1773	84	1	1	CARDINAL
ejpam-1773	85	1	k(c	PERSON
ejpam-1773	88	1	w=	PERSON
ejpam-1773	91	1	π j	ORG
ejpam-1773	91	2	k	PERSON
ejpam-1773	92	1	k(vi)π j	PERSON
ejpam-1773	93	1	0	CARDINAL
ejpam-1773	94	1	π j	ORG
ejpam-1773	95	1	〈π j	PERSON
ejpam-1773	95	2	0	CARDINAL
ejpam-1773	98	1	r2	GPE
ejpam-1773	99	1	π2,1	ORG
ejpam-1773	99	2	zero	CARDINAL
ejpam-1773	100	1	2	CARDINAL
ejpam-1773	102	1	1	CARDINAL
ejpam-1773	112	1	j ⊕	PERSON
ejpam-1773	113	1	j||c	PERSON
ejpam-1773	114	1	22	CARDINAL
ejpam-1773	114	2	22	CARDINAL
ejpam-1773	115	1	22	CARDINAL
ejpam-1773	116	1	w	ORG
ejpam-1773	117	1	u j+1v′,w+ u j+1w′]	PERSON
ejpam-1773	122	1	j.	PERSON
ejpam-1773	123	1	w ∈	PERSON
ejpam-1773	123	2	0	CARDINAL
ejpam-1773	124	1	w ∈	PERSON
ejpam-1773	124	2	w ∈	ORG
ejpam-1773	125	1	1	CARDINAL
ejpam-1773	127	1	π j	ORG
ejpam-1773	129	1	7	CARDINAL
ejpam-1773	130	1	1	CARDINAL
ejpam-1773	131	1	1	CARDINAL
ejpam-1773	131	2	k ≥ i. s. dougherty	ORG
ejpam-1773	132	1	j. pure	PERSON
ejpam-1773	132	2	6	CARDINAL
ejpam-1773	132	3	89	CARDINAL
ejpam-1773	134	1	2	CARDINAL
ejpam-1773	135	1	w	GPE
ejpam-1773	136	1	∈	ORG
ejpam-1773	139	1	3	CARDINAL
ejpam-1773	141	1	1	CARDINAL
ejpam-1773	141	2	1	CARDINAL
ejpam-1773	141	3	4	CARDINAL
ejpam-1773	141	4	7	CARDINAL
ejpam-1773	142	1	1,2	CARDINAL
ejpam-1773	145	1	1,2	CARDINAL
ejpam-1773	147	1	k}	PERSON
ejpam-1773	147	2	1,2	CARDINAL
ejpam-1773	149	1	1,2	CARDINAL
ejpam-1773	151	1	1	CARDINAL
ejpam-1773	151	2	{k	PERSON
ejpam-1773	153	1	2	CARDINAL
ejpam-1773	154	1	cb =	ORG
ejpam-1773	154	2	1	CARDINAL
ejpam-1773	154	3	⊆	CARDINAL
ejpam-1773	154	4	0	CARDINAL
ejpam-1773	155	1	lee	PERSON
ejpam-1773	158	1	2|a|	CARDINAL
ejpam-1773	160	1	lemma	ORG
ejpam-1773	160	2	7	CARDINAL
ejpam-1773	161	1	2	CARDINAL
ejpam-1773	165	1	4	CARDINAL
ejpam-1773	166	1	2kn	ORDINAL
ejpam-1773	167	1	i. proof	PERSON
ejpam-1773	168	1	lemma 2	ORG
ejpam-1773	169	1	10	CARDINAL
ejpam-1773	170	1	4	CARDINAL
ejpam-1773	170	2	n ≡ 22	ORG
ejpam-1773	172	1	s. dougherty	PERSON
ejpam-1773	173	1	j. pure	PERSON
ejpam-1773	173	2	6	CARDINAL
ejpam-1773	173	3	89	CARDINAL
ejpam-1773	173	4	106 94	CARDINAL
ejpam-1773	173	5	2	CARDINAL
ejpam-1773	175	1	2	CARDINAL
ejpam-1773	176	1	2k−2n	CARDINAL
ejpam-1773	177	1	1	CARDINAL
ejpam-1773	177	2	1	CARDINAL
ejpam-1773	179	1	3	CARDINAL
ejpam-1773	182	1	1	CARDINAL
ejpam-1773	183	1	1	CARDINAL
ejpam-1773	185	1	2k	CARDINAL
ejpam-1773	185	2	2	CARDINAL
ejpam-1773	186	1	8	CARDINAL
ejpam-1773	187	1	first	ORDINAL
ejpam-1773	187	2	1	CARDINAL
ejpam-1773	188	1	1	CARDINAL
ejpam-1773	188	2	1 ∈	CARDINAL
ejpam-1773	188	3	6=	CARDINAL
ejpam-1773	188	4	1	CARDINAL
ejpam-1773	189	1	uk	GPE
ejpam-1773	190	1	u1u2,u1u3	GPE
ejpam-1773	192	1	uk	GPE
ejpam-1773	193	1	uk	GPE
ejpam-1773	196	1	1,2	CARDINAL
ejpam-1773	197	1	1	CARDINAL
ejpam-1773	197	2	2k−1− 1	DATE
ejpam-1773	198	1	uk	GPE
ejpam-1773	198	2	22k−1	CARDINAL
ejpam-1773	198	3	22k	DATE
ejpam-1773	200	1	2	CARDINAL
ejpam-1773	200	2	lee	PERSON
ejpam-1773	200	3	4	CARDINAL
ejpam-1773	200	4	lee	PERSON
ejpam-1773	200	5	4	CARDINAL
ejpam-1773	201	1	5	CARDINAL
ejpam-1773	202	1	k = 1	PERSON
ejpam-1773	202	2	6	CARDINAL
ejpam-1773	203	1	k = 2.	PERSON
ejpam-1773	203	2	4n	CARDINAL
ejpam-1773	204	1	r2	GPE
ejpam-1773	205	1	2	CARDINAL
ejpam-1773	205	2	r2	GPE
ejpam-1773	206	1	2	CARDINAL
ejpam-1773	207	1	lee weight	PERSON
ejpam-1773	207	2	1+ 14z4 + z8	DATE
ejpam-1773	210	1	6	CARDINAL
ejpam-1773	211	1	s. dougherty	PERSON
ejpam-1773	212	1	j. pure	PERSON
ejpam-1773	212	2	6	CARDINAL
ejpam-1773	212	3	89	CARDINAL
ejpam-1773	214	1	1	CARDINAL
ejpam-1773	214	2	22k	DATE
ejpam-1773	216	1	∑ a⊆{1,2,	PERSON
ejpam-1773	217	1	2k	CARDINAL
ejpam-1773	219	1	∑	LAW
ejpam-1773	220	1	9	CARDINAL
ejpam-1773	220	2	22k	DATE
ejpam-1773	220	3	22k	DATE
ejpam-1773	221	1	10	CARDINAL
ejpam-1773	222	1	1+us	CARDINAL
ejpam-1773	222	2	1≤	CARDINAL
ejpam-1773	222	3	1+ us)α	QUANTITY
ejpam-1773	223	1	〈mk	PERSON
ejpam-1773	225	1	11	CARDINAL
ejpam-1773	225	2	−1	DATE
ejpam-1773	231	1	12	CARDINAL
ejpam-1773	231	2	22k	DATE
ejpam-1773	232	1	1p	CARDINAL
ejpam-1773	232	2	1	CARDINAL
ejpam-1773	232	3	1	CARDINAL
ejpam-1773	232	4	1	CARDINAL
ejpam-1773	234	1	1)y	CARDINAL
ejpam-1773	235	1	8	CARDINAL
ejpam-1773	236	1	lee weight	PERSON
ejpam-1773	237	1	lee	PERSON
ejpam-1773	237	2	8	CARDINAL
ejpam-1773	237	3	24	CARDINAL
ejpam-1773	238	1	lee weight	PERSON
ejpam-1773	238	2	1+ z2	QUANTITY
ejpam-1773	238	3	8	CARDINAL
ejpam-1773	239	1	s. dougherty	PERSON
ejpam-1773	240	1	j. pure	PERSON
ejpam-1773	240	2	6	CARDINAL
ejpam-1773	240	3	89	CARDINAL
ejpam-1773	240	4	1	CARDINAL
ejpam-1773	240	5	2 5.1	CARDINAL
ejpam-1773	241	1	1	CARDINAL
ejpam-1773	241	2	first	ORDINAL
ejpam-1773	241	3	1	CARDINAL
ejpam-1773	241	4	uk	GPE
ejpam-1773	241	5	1 6=	CARDINAL
ejpam-1773	241	6	0	CARDINAL
ejpam-1773	243	1	first	ORDINAL
ejpam-1773	243	2	r2 k−1	GPE
ejpam-1773	243	3	uk	GPE
ejpam-1773	244	1	13	CARDINAL
ejpam-1773	244	2	rn k	FAC
ejpam-1773	244	3	r2n k−1	GPE
ejpam-1773	245	1	lemma	ORG
ejpam-1773	247	1	3	CARDINAL
ejpam-1773	248	1	1	CARDINAL
ejpam-1773	248	2	2	CARDINAL
ejpam-1773	250	1	uk	GPE
ejpam-1773	252	1	uk	GPE
ejpam-1773	253	1	x(b	PRODUCT
ejpam-1773	256	1	7	CARDINAL
ejpam-1773	257	1	1	CARDINAL
ejpam-1773	257	2	uk	GPE
ejpam-1773	260	1	first	ORDINAL
ejpam-1773	260	2	uk	GPE
ejpam-1773	260	3	uk	GPE
ejpam-1773	260	4	0	CARDINAL
ejpam-1773	262	1	a′	ORG
ejpam-1773	263	1	a′	ORG
ejpam-1773	265	1	3	CARDINAL
ejpam-1773	265	2	a′	ORG
ejpam-1773	265	3	a′	ORG
ejpam-1773	266	1	a′	ORG
ejpam-1773	266	2	a′	ORG
ejpam-1773	266	3	22k−1	CARDINAL
ejpam-1773	267	1	1	CARDINAL
ejpam-1773	267	2	22k−1	CARDINAL
ejpam-1773	269	1	4	CARDINAL
ejpam-1773	270	1	1	CARDINAL
ejpam-1773	270	2	1 ≤	QUANTITY
ejpam-1773	272	1	rk	ORG
ejpam-1773	272	2	0	CARDINAL
ejpam-1773	274	1	1	CARDINAL
ejpam-1773	277	1	s. dougherty	PERSON
ejpam-1773	278	1	j. pure	PERSON
ejpam-1773	278	2	6	CARDINAL
ejpam-1773	278	3	89	CARDINAL
ejpam-1773	278	4	106 97	CARDINAL
ejpam-1773	278	5	8	CARDINAL
ejpam-1773	279	1	7	CARDINAL
ejpam-1773	280	1	one	CARDINAL
ejpam-1773	280	2	at least two	CARDINAL
ejpam-1773	280	3	rk	NORP
ejpam-1773	280	4	k ≥ 2	ORG
ejpam-1773	280	5	2	CARDINAL
ejpam-1773	282	1	⊆	CARDINAL
ejpam-1773	283	1	ub	ORG
ejpam-1773	283	2	6=	CARDINAL
ejpam-1773	283	3	0	CARDINAL
ejpam-1773	284	1	ub	ORG
ejpam-1773	285	1	ub	ORG
ejpam-1773	286	1	ub	ORG
ejpam-1773	287	1	uk	GPE
ejpam-1773	289	1	uk	GPE
ejpam-1773	289	2	ub	ORG
ejpam-1773	290	1	∈	ORG
ejpam-1773	290	2	c⊥.	PERSON
ejpam-1773	290	3	6∈	CARDINAL
ejpam-1773	293	1	one	CARDINAL
ejpam-1773	293	2	1	CARDINAL
ejpam-1773	293	3	6∈	CARDINAL
ejpam-1773	294	1	ub	ORG
ejpam-1773	300	1	2,3	CARDINAL
ejpam-1773	301	1	s.	PERSON
ejpam-1773	303	1	uk	GPE
ejpam-1773	306	1	aus = u1usa1 +	PERSON
ejpam-1773	308	1	usas−1	GPE
ejpam-1773	309	1	uk	GPE
ejpam-1773	309	2	us−1	ORG
ejpam-1773	314	1	one	CARDINAL
ejpam-1773	314	2	1	CARDINAL
ejpam-1773	314	3	k ≥ 2	ORG
ejpam-1773	316	1	9	CARDINAL
ejpam-1773	319	1	1,2	CARDINAL
ejpam-1773	322	1	〈ud1	PERSON
ejpam-1773	324	1	uds 〉	PERSON
ejpam-1773	324	2	1	CARDINAL
ejpam-1773	328	1	0	CARDINAL
ejpam-1773	329	1	j. hence	PERSON
ejpam-1773	330	1	∑ ub	PERSON
ejpam-1773	330	2	∈	ORG
ejpam-1773	330	3	c⊥.	GPE
ejpam-1773	330	4	i.	PERSON
ejpam-1773	330	5	i.	PERSON
ejpam-1773	332	1	1,2	CARDINAL
ejpam-1773	334	1	at least ⌈	CARDINAL
ejpam-1773	334	2	2	CARDINAL
ejpam-1773	334	3	〈ud1	PERSON
ejpam-1773	335	1	uds 〉	PERSON
ejpam-1773	335	2	∈	ORG
ejpam-1773	336	1	s. dougherty	PERSON
ejpam-1773	337	1	j. pure	PERSON
ejpam-1773	337	2	6	CARDINAL
ejpam-1773	337	3	89	CARDINAL
ejpam-1773	337	4	2 + 1	CARDINAL
ejpam-1773	338	1	k−	PERSON
ejpam-1773	339	1	2	CARDINAL
ejpam-1773	340	1	k 2	ORG
ejpam-1773	340	2	2	CARDINAL
ejpam-1773	341	1	∈	ORG
ejpam-1773	342	1	5.2	CARDINAL
ejpam-1773	342	2	2	CARDINAL
ejpam-1773	342	3	first	ORDINAL
ejpam-1773	342	4	k ≥ 1	ORG
ejpam-1773	342	5	1	CARDINAL
ejpam-1773	342	6	0	CARDINAL
ejpam-1773	344	1	2	CARDINAL
ejpam-1773	345	1	first	ORDINAL
ejpam-1773	346	1	1	CARDINAL
ejpam-1773	347	1	2	CARDINAL
ejpam-1773	348	1	uk	GPE
ejpam-1773	348	2	k ≥ 2.	ORG
ejpam-1773	349	1	4	CARDINAL
ejpam-1773	351	1	1,1+u1u2	CARDINAL
ejpam-1773	352	1	uk	GPE
ejpam-1773	352	2	1,1+u1u2	CARDINAL
ejpam-1773	355	1	rk	NORP
ejpam-1773	356	1	1	CARDINAL
ejpam-1773	356	2	first	ORDINAL
ejpam-1773	358	1	uk	GPE
ejpam-1773	358	2	22k	DATE
ejpam-1773	359	1	22k+1	CARDINAL
ejpam-1773	359	2	22k	DATE
ejpam-1773	361	1	4	CARDINAL
ejpam-1773	361	2	first	ORDINAL
ejpam-1773	362	1	uk	GPE
ejpam-1773	363	1	uk	GPE
ejpam-1773	363	2	0	CARDINAL
ejpam-1773	365	1	uk	GPE
ejpam-1773	367	1	uk	GPE
ejpam-1773	370	1	uk	GPE
ejpam-1773	371	1	wl(a	PERSON
ejpam-1773	372	1	lee	PERSON
ejpam-1773	372	2	4	CARDINAL
ejpam-1773	372	3	lee	PERSON
ejpam-1773	374	1	uk	GPE
ejpam-1773	375	1	wl(a	ORG
ejpam-1773	376	1	uk	GPE
ejpam-1773	377	1	+wl(a+	PERCENT
ejpam-1773	378	1	uk	GPE
ejpam-1773	378	2	2k	CARDINAL
ejpam-1773	378	3	7	CARDINAL
ejpam-1773	379	1	k ≥ 2 this	ORG
ejpam-1773	379	2	4	CARDINAL
ejpam-1773	380	1	2	CARDINAL
ejpam-1773	380	2	2	CARDINAL
ejpam-1773	381	1	2k+1	CARDINAL
ejpam-1773	381	2	2k	DATE
ejpam-1773	381	3	4	CARDINAL
ejpam-1773	382	1	k = 2	PERSON
ejpam-1773	382	2	3	CARDINAL
ejpam-1773	384	1	s. dougherty	PERSON
ejpam-1773	385	1	j. pure	PERSON
ejpam-1773	385	2	6	CARDINAL
ejpam-1773	385	3	89	CARDINAL
ejpam-1773	386	1	2	CARDINAL
ejpam-1773	386	2	1,1+u1u2+u3	CARDINAL
ejpam-1773	387	1	uk	GPE
ejpam-1773	388	1	lee	PERSON
ejpam-1773	389	1	4	CARDINAL
ejpam-1773	391	1	3	CARDINAL
ejpam-1773	392	1	2	CARDINAL
ejpam-1773	392	2	rk	ORG
ejpam-1773	394	1	2	CARDINAL
ejpam-1773	394	2	one	CARDINAL
ejpam-1773	396	1	uk	GPE
ejpam-1773	396	2	zero	CARDINAL
ejpam-1773	396	3	22k−1	CARDINAL
ejpam-1773	397	1	second	ORDINAL
ejpam-1773	398	1	6	CARDINAL
ejpam-1773	399	1	3	CARDINAL
ejpam-1773	400	1	z[i	PRODUCT
ejpam-1773	402	1	∑ viui	PERSON
ejpam-1773	402	2	14	CARDINAL
ejpam-1773	403	1	∈	ORG
ejpam-1773	404	1	one	CARDINAL
ejpam-1773	404	2	u·v ∈	ORG
ejpam-1773	406	1	l ⊆ l∗	ORG
ejpam-1773	407	1	n(v	ORG
ejpam-1773	410	1	o	DATE
ejpam-1773	410	2	15	CARDINAL
ejpam-1773	410	3	1	CARDINAL
ejpam-1773	410	4	1	CARDINAL
ejpam-1773	410	5	1	CARDINAL
ejpam-1773	410	6	o	DATE
ejpam-1773	410	7	16	CARDINAL
ejpam-1773	410	8	1	CARDINAL
ejpam-1773	411	1	o	DATE
ejpam-1773	411	2	17	CARDINAL
ejpam-1773	413	1	s. dougherty	PERSON
ejpam-1773	414	1	j. pure	PERSON
ejpam-1773	414	2	6	CARDINAL
ejpam-1773	414	3	89	CARDINAL
ejpam-1773	416	1	1p	CARDINAL
ejpam-1773	416	2	∈	ORG
ejpam-1773	416	3	2o	CARDINAL
ejpam-1773	417	1	18	CARDINAL
ejpam-1773	418	1	1p 2	QUANTITY
ejpam-1773	419	1	∈	ORG
ejpam-1773	419	2	2o	CARDINAL
ejpam-1773	420	1	19	CARDINAL
ejpam-1773	421	1	1p 2 h−1	TIME
ejpam-1773	421	2	∈	ORG
ejpam-1773	421	3	2o	CARDINAL
ejpam-1773	422	1	20	CARDINAL
ejpam-1773	422	2	4	CARDINAL
ejpam-1773	427	1	first	ORDINAL
ejpam-1773	427	2	2	CARDINAL
ejpam-1773	428	1	2	CARDINAL
ejpam-1773	428	2	u1+u2+u1u2	CARDINAL
ejpam-1773	429	1	second	ORDINAL
ejpam-1773	429	2	6	CARDINAL
ejpam-1773	430	1	third	ORDINAL
ejpam-1773	430	2	1	CARDINAL
ejpam-1773	430	3	3	CARDINAL
ejpam-1773	431	1	2	CARDINAL
ejpam-1773	435	1	∈	ORG
ejpam-1773	435	2	rk−2	NORP
ejpam-1773	436	1	φk−2(α0	GPE
ejpam-1773	442	1	2	CARDINAL
ejpam-1773	443	1	10	CARDINAL
ejpam-1773	444	1	k ≥ 2.	ORG
ejpam-1773	445	1	2k−2n	CARDINAL
ejpam-1773	448	1	4	CARDINAL
ejpam-1773	448	2	11	CARDINAL
ejpam-1773	449	1	2	CARDINAL
ejpam-1773	449	2	j ≤ k.	PERSON
ejpam-1773	449	3	2k−2n	CARDINAL
ejpam-1773	449	4	2k−1n	CARDINAL
ejpam-1773	449	5	λr(φk(c	ORG
ejpam-1773	450	1	2kn	ORDINAL
ejpam-1773	452	1	4	CARDINAL
ejpam-1773	452	2	10	CARDINAL
ejpam-1773	453	1	7	CARDINAL
ejpam-1773	453	2	extremal	PERSON
ejpam-1773	453	3	section 5	LAW
ejpam-1773	453	4	r2 k−1	GPE
ejpam-1773	454	1	j. pure	PERSON
ejpam-1773	454	2	6	CARDINAL
ejpam-1773	454	3	89	CARDINAL
ejpam-1773	454	4	uk	GPE
ejpam-1773	455	1	rn k	FAC
ejpam-1773	455	2	r2n k−1	GPE
ejpam-1773	456	1	two	CARDINAL
ejpam-1773	456	2	0	CARDINAL
ejpam-1773	458	1	c2,d1	NORP
ejpam-1773	458	2	0	CARDINAL
ejpam-1773	459	1	21	CARDINAL
ejpam-1773	459	2	k−1	GPE
ejpam-1773	459	3	k−1	GPE
ejpam-1773	460	1	c2,d1	NORP
ejpam-1773	460	2	k−1	GPE
ejpam-1773	461	1	0	CARDINAL
ejpam-1773	461	2	21	CARDINAL
ejpam-1773	462	1	5	CARDINAL
ejpam-1773	463	1	2n	CARDINAL
ejpam-1773	466	1	2n	CARDINAL
ejpam-1773	467	1	4	CARDINAL
ejpam-1773	467	2	12	CARDINAL
ejpam-1773	468	1	2kn	ORDINAL
ejpam-1773	469	1	2n	CARDINAL
ejpam-1773	471	1	linear	ORG
ejpam-1773	472	1	4.4	CARDINAL
ejpam-1773	472	2	7	CARDINAL
ejpam-1773	472	3	1	CARDINAL
ejpam-1773	473	1	k. hence	PERSON
ejpam-1773	475	1	s. dougherty	PERSON
ejpam-1773	476	1	j. pure	PERSON
ejpam-1773	476	2	6	CARDINAL
ejpam-1773	476	3	89	CARDINAL
ejpam-1773	477	1	8	CARDINAL
ejpam-1773	477	2	4	DATE
ejpam-1773	477	3	4	CARDINAL
ejpam-1773	477	4	3	CARDINAL
ejpam-1773	478	1	1	CARDINAL
ejpam-1773	478	2	1+ 14z4 + z8	DATE
ejpam-1773	482	1	7.3	CARDINAL
ejpam-1773	483	1	16	CARDINAL
ejpam-1773	483	2	8	DATE
ejpam-1773	483	3	4	CARDINAL
ejpam-1773	483	4	16	CARDINAL
ejpam-1773	483	5	4	CARDINAL
ejpam-1773	484	1	1	CARDINAL
ejpam-1773	485	1	lee weight	PERSON
ejpam-1773	486	1	1+ 28z4 + 198z8+ 28z12	MONEY
ejpam-1773	487	1	16,8,4	CARDINAL
ejpam-1773	488	1	r3	ORG
ejpam-1773	489	1	1+	QUANTITY
ejpam-1773	489	2	1+	QUANTITY
ejpam-1773	489	3	1+	QUANTITY
ejpam-1773	490	1	7.4	CARDINAL
ejpam-1773	491	1	3	CARDINAL
ejpam-1773	492	1	c3	PERSON
ejpam-1773	492	2	lee weight	PERSON
ejpam-1773	493	1	1+ 759z8 + 2576z12+ 759z16+ z24	DATE
ejpam-1773	495	1	6	CARDINAL
ejpam-1773	495	2	1,0,0,1+ u1u2,u2,u1 + u2	MONEY
ejpam-1773	495	3	0,1,0,u2	CARDINAL
ejpam-1773	495	4	1+	QUANTITY
ejpam-1773	496	1	1	CARDINAL
ejpam-1773	499	1	s. dougherty	PERSON
ejpam-1773	500	1	j. pure	PERSON
ejpam-1773	500	2	6	CARDINAL
ejpam-1773	500	3	89	CARDINAL
ejpam-1773	500	4	103 7.5	CARDINAL
ejpam-1773	501	1	32	CARDINAL
ejpam-1773	501	2	16	DATE
ejpam-1773	501	3	8	CARDINAL
ejpam-1773	501	4	1	CARDINAL
ejpam-1773	501	5	{uiu juk	PERSON
ejpam-1773	504	1	9	CARDINAL
ejpam-1773	504	2	lee weight	PERSON
ejpam-1773	504	3	lc4	ORG
ejpam-1773	505	1	1+ 620z8+ 13888z12+ 36518z16+ 1388z20+ 620z24	DATE
ejpam-1773	509	1	2	CARDINAL
ejpam-1773	509	2	1,1+	MONEY
ejpam-1773	509	3	ψ4(e	DATE
ejpam-1773	510	1	9	CARDINAL
ejpam-1773	511	1	2k	CARDINAL
ejpam-1773	511	2	2k−1	CARDINAL
ejpam-1773	511	3	2⌈	CARDINAL
ejpam-1773	511	4	2	CARDINAL
ejpam-1773	512	1	128,64,16	CARDINAL
ejpam-1773	513	1	7.6	CARDINAL
ejpam-1773	513	2	40	CARDINAL
ejpam-1773	513	3	20	DATE
ejpam-1773	513	4	c5	ORG
ejpam-1773	514	1	1+	CARDINAL
ejpam-1773	514	2	1+	CARDINAL
ejpam-1773	514	3	0	CARDINAL
ejpam-1773	514	4	 	ORG
ejpam-1773	514	5	    .	ORG
ejpam-1773	515	1	c5	ORG
ejpam-1773	515	2	10	CARDINAL
ejpam-1773	515	3	1+ 125z8+ 1664z10+ 10720z12+	DATE
ejpam-1773	517	1	27	CARDINAL
ejpam-1773	518	1	7.7	CARDINAL
ejpam-1773	518	2	44	CARDINAL
ejpam-1773	518	3	22	DATE
ejpam-1773	518	4	11	CARDINAL
ejpam-1773	519	1	1+ u2 1+ u1	CARDINAL
ejpam-1773	519	2	1+ u2 1+	DATE
ejpam-1773	519	3	1+ u2 1+	CARDINAL
ejpam-1773	519	4	1+ u2 u1 1+	QUANTITY
ejpam-1773	519	5	1+	QUANTITY
ejpam-1773	519	6	1+ u2 +	DATE
ejpam-1773	519	7	1+	CARDINAL
ejpam-1773	519	8	0	CARDINAL
ejpam-1773	519	9	0 1 u1 1+ u1 u1	QUANTITY
ejpam-1773	519	10	1+	CARDINAL
ejpam-1773	519	11	u2 u2  	PERSON
ejpam-1773	520	1	11	CARDINAL
ejpam-1773	520	2	1+ 104z8 + 512z10 +	CARDINAL
ejpam-1773	522	1	44,22,8	CARDINAL
ejpam-1773	522	2	216	CARDINAL
ejpam-1773	522	3	32	DATE
ejpam-1773	522	4	52	DATE
ejpam-1773	523	1	s. dougherty	PERSON
ejpam-1773	524	1	j. pure	PERSON
ejpam-1773	524	2	6	CARDINAL
ejpam-1773	524	3	89	CARDINAL
ejpam-1773	524	4	7.8	CARDINAL
ejpam-1773	525	1	56	CARDINAL
ejpam-1773	525	2	28	CARDINAL
ejpam-1773	525	3	12	CARDINAL
ejpam-1773	525	4	56	CARDINAL
ejpam-1773	525	5	56	CARDINAL
ejpam-1773	525	6	only one	CARDINAL
ejpam-1773	525	7	1+8190z12+	DATE
ejpam-1773	527	1	two	CARDINAL
ejpam-1773	527	2	r2	ORG
ejpam-1773	527	3	one	CARDINAL
ejpam-1773	527	4	c7	PERSON
ejpam-1773	527	5	14	CARDINAL
ejpam-1773	528	1	1+	CARDINAL
ejpam-1773	528	2	1+ u2	QUANTITY
ejpam-1773	528	3	1,u1,u1	DATE
ejpam-1773	528	4	1	CARDINAL
ejpam-1773	528	5	1+	QUANTITY
ejpam-1773	528	6	1+	QUANTITY
ejpam-1773	528	7	1	CARDINAL
ejpam-1773	528	8	1+	QUANTITY
ejpam-1773	528	9	1+ u1 +	QUANTITY
ejpam-1773	528	10	1	CARDINAL
ejpam-1773	528	11	1+	QUANTITY
ejpam-1773	528	12	1+	CARDINAL
ejpam-1773	528	13	1+	QUANTITY
ejpam-1773	528	14	1+	QUANTITY
ejpam-1773	528	15	1+	QUANTITY
ejpam-1773	528	16	1+	CARDINAL
ejpam-1773	530	1	1+	QUANTITY
ejpam-1773	530	2	1+	QUANTITY
ejpam-1773	530	3	1+ u2	QUANTITY
ejpam-1773	531	1	0,1,u1+ u2 +	DATE
ejpam-1773	531	2	1+	QUANTITY
ejpam-1773	531	3	1,u1	DATE
ejpam-1773	531	4	1+	DATE
ejpam-1773	531	5	1	CARDINAL
ejpam-1773	532	1	1+	QUANTITY
ejpam-1773	532	2	56,28,12	CARDINAL
ejpam-1773	532	3	4	CARDINAL
ejpam-1773	532	4	7	CARDINAL
ejpam-1773	533	1	4	CARDINAL
ejpam-1773	533	2	1+	DATE
ejpam-1773	533	3	1+	QUANTITY
ejpam-1773	533	4	1+ u2 +	DATE
ejpam-1773	533	5	1+ u2 +	DATE
ejpam-1773	533	6	1+	DATE
ejpam-1773	534	1	1+	QUANTITY
ejpam-1773	534	2	1+ u1 +	QUANTITY
ejpam-1773	534	3	1+	QUANTITY
ejpam-1773	534	4	1+	QUANTITY
ejpam-1773	534	5	0,u1 +	DATE
ejpam-1773	536	1	56,28,12	CARDINAL
ejpam-1773	536	2	8	CARDINAL
ejpam-1773	537	1	7.9	CARDINAL
ejpam-1773	538	1	64	CARDINAL
ejpam-1773	538	2	32	DATE
ejpam-1773	538	3	12	CARDINAL
ejpam-1773	538	4	8	CARDINAL
ejpam-1773	538	5	4	CARDINAL
ejpam-1773	538	6	1+ u1 +	QUANTITY
ejpam-1773	538	7	1+	QUANTITY
ejpam-1773	538	8	1+	DATE
ejpam-1773	538	9	1+ u2 + u1u2	QUANTITY
ejpam-1773	538	10	1+	QUANTITY
ejpam-1773	538	11	1+	QUANTITY
ejpam-1773	538	12	1+ u1 +	QUANTITY
ejpam-1773	538	13	1+	QUANTITY
ejpam-1773	538	14	1	CARDINAL
ejpam-1773	538	15	1+ u2 +	DATE
ejpam-1773	538	16	1+ u1 +	QUANTITY
ejpam-1773	539	1	1+	QUANTITY
ejpam-1773	540	1	105	CARDINAL
ejpam-1773	540	2	lee weight	PERSON
ejpam-1773	540	3	1+1888z12+20736z14	QUANTITY
ejpam-1773	541	1	64,32,12	CARDINAL
ejpam-1773	541	2	8	CARDINAL
ejpam-1773	546	1	2k	CARDINAL
ejpam-1773	550	1	extremal	GPE
ejpam-1773	550	2	rk	NORP
ejpam-1773	553	1	1	CARDINAL
ejpam-1773	553	2	e. bannai	PERSON
ejpam-1773	553	3	s.t. dougherty	PERSON
ejpam-1773	553	4	m. harada	PERSON
ejpam-1773	553	5	m. oura	PERSON
ejpam-1773	554	1	45:1194-1205	DATE
ejpam-1773	554	2	1999	DATE
ejpam-1773	555	1	2	CARDINAL
ejpam-1773	555	2	y.j. choie	GPE
ejpam-1773	555	3	s.t.	PERSON
ejpam-1773	555	4	dougherty.	ORG
ejpam-1773	556	1	15:129-147, 2004	DATE
ejpam-1773	557	1	3	CARDINAL
ejpam-1773	557	2	conway	GPE
ejpam-1773	557	3	n.j.a	ORG
ejpam-1773	558	1	2nd	ORDINAL
ejpam-1773	558	2	new york	GPE
ejpam-1773	558	3	1993	DATE
ejpam-1773	559	1	4	CARDINAL
ejpam-1773	559	2	j. h. conway	PERSON
ejpam-1773	559	3	n. j. a. sloane	PERSON
ejpam-1773	561	1	ny	GPE
ejpam-1773	561	2	3rd	ORDINAL
ejpam-1773	561	3	1998	DATE
ejpam-1773	562	1	5	CARDINAL
ejpam-1773	562	2	dougherty	GPE
ejpam-1773	562	3	t. a. gulliver	PERSON
ejpam-1773	562	4	m. harada	PERSON
ejpam-1773	563	1	algebraic combinatorics	ORG
ejpam-1773	563	2	9:233–250	CARDINAL
ejpam-1773	563	3	1999	DATE
ejpam-1773	564	1	106	CARDINAL
ejpam-1773	565	1	6	CARDINAL
ejpam-1773	565	2	dougherty	ORG
ejpam-1773	565	3	m. harada	PERSON
ejpam-1773	566	1	45:32-45, 1999	DATE
ejpam-1773	567	1	7	CARDINAL
ejpam-1773	567	2	dougherty	ORG
ejpam-1773	567	3	b. yıldız	PERSON
ejpam-1773	567	4	s. karadeniz	ORG
ejpam-1773	567	5	rk	ORG
ejpam-1773	567	6	17:205–219, 2011	DATE
ejpam-1773	568	1	8	CARDINAL
ejpam-1773	568	2	macwilliams	PERSON
ejpam-1773	568	3	n.j.a	ORG
ejpam-1773	570	1	amsterdam	GPE
ejpam-1773	570	2	north-holland	GPE
ejpam-1773	570	3	1977	DATE
ejpam-1773	571	1	9	CARDINAL
ejpam-1773	571	2	g. nebe	PERSON
ejpam-1773	571	3	e. m.	PERSON
ejpam-1773	571	4	n. j. a. sloane	PERSON
ejpam-1773	573	1	springerverlag, 2006	DATE
ejpam-1773	574	1	10	CARDINAL
ejpam-1773	574	2	e.m.	GPE
ejpam-1773	575	1	44:134–139	CARDINAL
ejpam-1773	575	2	1998	DATE
ejpam-1773	576	1	11	CARDINAL
ejpam-1773	578	1	american journal of mathematics	ORG
ejpam-1773	578	2	121:555-575	CARDINAL
ejpam-1773	578	3	1999	DATE