id	sid	tid	token	lemma	pos
ap-2169	1	1	acta	acta	PROPN
ap-2169	1	2	polytechnica	polytechnica	PROPN
ap-2169	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2169	1	4	/	/	SYM
ap-2169	1	5	ap.2014.54.0394	ap.2014.54.0394	PROPN
ap-2169	1	6	acta	acta	PROPN
ap-2169	1	7	polytechnica	polytechnica	PROPN
ap-2169	1	8	54(6):394–397	54(6):394–397	PROPN
ap-2169	1	9	,	,	PUNCT
ap-2169	1	10	2014	2014	NUM
ap-2169	1	11	©	©	PROPN
ap-2169	1	12	czech	czech	PROPN
ap-2169	1	13	technical	technical	PROPN
ap-2169	1	14	university	university	PROPN
ap-2169	1	15	in	in	ADP
ap-2169	1	16	prague	prague	PROPN
ap-2169	1	17	,	,	PUNCT
ap-2169	1	18	2014	2014	NUM
ap-2169	1	19	available	available	ADJ
ap-2169	1	20	online	online	ADV
ap-2169	1	21	at	at	ADP
ap-2169	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2169	1	23	automorphisms	automorphism	NOUN
ap-2169	1	24	of	of	ADP
ap-2169	1	25	algebras	algebras	PROPN
ap-2169	1	26	and	and	CCONJ
ap-2169	1	27	orthogonal	orthogonal	ADJ
ap-2169	1	28	polynomials	polynomial	NOUN
ap-2169	1	29	daniel	daniel	PROPN
ap-2169	1	30	gromada	gromada	PROPN
ap-2169	1	31	,	,	PUNCT
ap-2169	1	32	severin	severin	PROPN
ap-2169	1	33	pošta∗	pošta∗	PROPN
ap-2169	1	34	department	department	PROPN
ap-2169	1	35	of	of	ADP
ap-2169	1	36	mathematics	mathematic	NOUN
ap-2169	1	37	,	,	PUNCT
ap-2169	1	38	faculty	faculty	NOUN
ap-2169	1	39	of	of	ADP
ap-2169	1	40	nuclear	nuclear	ADJ
ap-2169	1	41	sciences	science	NOUN
ap-2169	1	42	and	and	CCONJ
ap-2169	1	43	physical	physical	ADJ
ap-2169	1	44	engineering	engineering	NOUN
ap-2169	1	45	,	,	PUNCT
ap-2169	1	46	czech	czech	PROPN
ap-2169	1	47	technical	technical	PROPN
ap-2169	1	48	university	university	PROPN
ap-2169	1	49	in	in	ADP
ap-2169	1	50	prague	prague	PROPN
ap-2169	1	51	,	,	PUNCT
ap-2169	1	52	trojanova	trojanova	X
ap-2169	1	53	13	13	NUM
ap-2169	1	54	,	,	PUNCT
ap-2169	1	55	cz-120	cz-120	PROPN
ap-2169	1	56	00	00	NUM
ap-2169	1	57	prague	prague	PROPN
ap-2169	1	58	,	,	PUNCT
ap-2169	1	59	czech	czech	PROPN
ap-2169	1	60	republic	republic	NOUN
ap-2169	1	61	∗	∗	NOUN
ap-2169	1	62	corresponding	correspond	VERB
ap-2169	1	63	author	author	NOUN
ap-2169	1	64	:	:	PUNCT
ap-2169	1	65	severin.posta@fjfi.cvut.cz	severin.posta@fjfi.cvut.cz	NOUN
ap-2169	1	66	abstract	abstract	NOUN
ap-2169	1	67	.	.	PUNCT
ap-2169	2	1	suitable	suitable	ADJ
ap-2169	2	2	automorphisms	automorphisms	PROPN
ap-2169	2	3	together	together	ADV
ap-2169	2	4	with	with	ADP
ap-2169	2	5	a	a	DET
ap-2169	2	6	complete	complete	ADJ
ap-2169	2	7	classification	classification	NOUN
ap-2169	2	8	of	of	ADP
ap-2169	2	9	representations	representation	NOUN
ap-2169	2	10	of	of	ADP
ap-2169	2	11	some	some	DET
ap-2169	2	12	algebras	algebra	NOUN
ap-2169	2	13	can	can	AUX
ap-2169	2	14	be	be	AUX
ap-2169	2	15	used	use	VERB
ap-2169	2	16	to	to	PART
ap-2169	2	17	generate	generate	VERB
ap-2169	2	18	some	some	DET
ap-2169	2	19	sets	set	NOUN
ap-2169	2	20	of	of	ADP
ap-2169	2	21	orthogonal	orthogonal	ADJ
ap-2169	2	22	polynomials	polynomial	NOUN
ap-2169	2	23	“	"	PUNCT
ap-2169	2	24	at	at	ADP
ap-2169	2	25	no	no	DET
ap-2169	2	26	cost	cost	NOUN
ap-2169	2	27	”	"	PUNCT
ap-2169	2	28	.	.	PUNCT
ap-2169	3	1	this	this	PRON
ap-2169	3	2	is	be	AUX
ap-2169	3	3	also	also	ADV
ap-2169	3	4	the	the	DET
ap-2169	3	5	case	case	NOUN
ap-2169	3	6	for	for	ADP
ap-2169	3	7	the	the	DET
ap-2169	3	8	nonstandard	nonstandard	ADJ
ap-2169	3	9	klimyk	klimyk	NOUN
ap-2169	3	10	-	-	PUNCT
ap-2169	3	11	gavrilik	gavrilik	NOUN
ap-2169	3	12	deformation	deformation	NOUN
ap-2169	3	13	u	u	NOUN
ap-2169	3	14	′q(so3	′q(so3	NUM
ap-2169	3	15	)	)	PUNCT
ap-2169	3	16	,	,	PUNCT
ap-2169	3	17	which	which	PRON
ap-2169	3	18	is	be	AUX
ap-2169	3	19	connected	connect	VERB
ap-2169	3	20	to	to	ADP
ap-2169	3	21	q	q	ADJ
ap-2169	3	22	-	-	PUNCT
ap-2169	3	23	racah	racah	ADJ
ap-2169	3	24	polynomials	polynomial	NOUN
ap-2169	3	25	.	.	PUNCT
ap-2169	4	1	keywords	keyword	NOUN
ap-2169	4	2	:	:	PUNCT
ap-2169	4	3	orthogonal	orthogonal	ADJ
ap-2169	4	4	polynomials	polynomial	NOUN
ap-2169	4	5	,	,	PUNCT
ap-2169	4	6	algebra	algebra	NOUN
ap-2169	4	7	representation	representation	NOUN
ap-2169	4	8	,	,	PUNCT
ap-2169	4	9	automorphism	automorphism	NOUN
ap-2169	4	10	.	.	PUNCT
ap-2169	5	1	1	1	X
ap-2169	5	2	.	.	X
ap-2169	5	3	introduction	introduction	NOUN
ap-2169	5	4	the	the	DET
ap-2169	5	5	connection	connection	NOUN
ap-2169	5	6	of	of	ADP
ap-2169	5	7	orthogonal	orthogonal	ADJ
ap-2169	5	8	polynomials	polynomial	NOUN
ap-2169	5	9	with	with	ADP
ap-2169	5	10	lie	lie	NOUN
ap-2169	5	11	algebras	algebra	NOUN
ap-2169	5	12	has	have	AUX
ap-2169	5	13	been	be	AUX
ap-2169	5	14	known	know	VERB
ap-2169	5	15	for	for	ADP
ap-2169	5	16	a	a	DET
ap-2169	5	17	long	long	ADJ
ap-2169	5	18	time	time	NOUN
ap-2169	5	19	(	(	PUNCT
ap-2169	5	20	see	see	VERB
ap-2169	5	21	[	[	X
ap-2169	5	22	1–4	1–4	NOUN
ap-2169	5	23	]	]	X
ap-2169	5	24	.	.	PUNCT
ap-2169	6	1	for	for	ADP
ap-2169	6	2	a	a	DET
ap-2169	6	3	nice	nice	ADJ
ap-2169	6	4	introduction	introduction	NOUN
ap-2169	6	5	and	and	CCONJ
ap-2169	6	6	a	a	DET
ap-2169	6	7	detailed	detailed	ADJ
ap-2169	6	8	historical	historical	ADJ
ap-2169	6	9	survey	survey	NOUN
ap-2169	6	10	see	see	VERB
ap-2169	6	11	[	[	X
ap-2169	6	12	5	5	NUM
ap-2169	6	13	]	]	PUNCT
ap-2169	6	14	and	and	CCONJ
ap-2169	6	15	references	reference	NOUN
ap-2169	6	16	therein	therein	ADV
ap-2169	6	17	)	)	PUNCT
ap-2169	6	18	.	.	PUNCT
ap-2169	7	1	having	having	AUX
ap-2169	7	2	available	available	ADJ
ap-2169	7	3	the	the	DET
ap-2169	7	4	classification	classification	NOUN
ap-2169	7	5	of	of	ADP
ap-2169	7	6	irreducible	irreducible	ADJ
ap-2169	7	7	representations	representation	NOUN
ap-2169	7	8	and	and	CCONJ
ap-2169	7	9	making	make	VERB
ap-2169	7	10	use	use	NOUN
ap-2169	7	11	of	of	ADP
ap-2169	7	12	some	some	DET
ap-2169	7	13	automorphisms	automorphism	NOUN
ap-2169	7	14	of	of	ADP
ap-2169	7	15	algebras	algebras	PROPN
ap-2169	7	16	,	,	PUNCT
ap-2169	7	17	one	one	PRON
ap-2169	7	18	can	can	AUX
ap-2169	7	19	obtain	obtain	VERB
ap-2169	7	20	sets	set	NOUN
ap-2169	7	21	of	of	ADP
ap-2169	7	22	orthogonal	orthogonal	ADJ
ap-2169	7	23	polynomials	polynomial	NOUN
ap-2169	7	24	for	for	ADP
ap-2169	7	25	free	free	ADJ
ap-2169	7	26	,	,	PUNCT
ap-2169	7	27	without	without	ADP
ap-2169	7	28	the	the	DET
ap-2169	7	29	need	need	NOUN
ap-2169	7	30	to	to	PART
ap-2169	7	31	proving	prove	VERB
ap-2169	7	32	their	their	PRON
ap-2169	7	33	properties	property	NOUN
ap-2169	7	34	manually	manually	ADV
ap-2169	7	35	.	.	PUNCT
ap-2169	8	1	the	the	DET
ap-2169	8	2	same	same	ADJ
ap-2169	8	3	is	be	AUX
ap-2169	8	4	true	true	ADJ
ap-2169	8	5	for	for	ADP
ap-2169	8	6	some	some	PRON
ap-2169	8	7	of	of	ADP
ap-2169	8	8	their	their	PRON
ap-2169	8	9	q	q	NOUN
ap-2169	8	10	-	-	PUNCT
ap-2169	8	11	analogs	analog	NOUN
ap-2169	8	12	.	.	PUNCT
ap-2169	9	1	we	we	PRON
ap-2169	9	2	show	show	VERB
ap-2169	9	3	this	this	DET
ap-2169	9	4	approach	approach	NOUN
ap-2169	9	5	on	on	ADP
ap-2169	9	6	a	a	DET
ap-2169	9	7	well	well	ADV
ap-2169	9	8	-	-	PUNCT
ap-2169	9	9	known	know	VERB
ap-2169	9	10	example	example	NOUN
ap-2169	9	11	of	of	ADP
ap-2169	9	12	the	the	DET
ap-2169	9	13	sl2	sl2	PROPN
ap-2169	9	14	algebra	algebra	PROPN
ap-2169	9	15	and	and	CCONJ
ap-2169	9	16	krawtchouk	krawtchouk	NOUN
ap-2169	9	17	polynomials	polynomial	NOUN
ap-2169	9	18	[	[	X
ap-2169	9	19	5	5	NUM
ap-2169	9	20	]	]	PUNCT
ap-2169	9	21	,	,	PUNCT
ap-2169	9	22	and	and	CCONJ
ap-2169	9	23	we	we	PRON
ap-2169	9	24	then	then	ADV
ap-2169	9	25	apply	apply	VERB
ap-2169	9	26	the	the	DET
ap-2169	9	27	same	same	ADJ
ap-2169	9	28	procedure	procedure	NOUN
ap-2169	9	29	to	to	ADP
ap-2169	9	30	the	the	DET
ap-2169	9	31	nonstandard	nonstandard	ADJ
ap-2169	9	32	klimyk	klimyk	NOUN
ap-2169	9	33	-	-	PUNCT
ap-2169	9	34	gavrilik	gavrilik	NOUN
ap-2169	9	35	deformation	deformation	NOUN
ap-2169	9	36	u	u	NOUN
ap-2169	9	37	′q(so3	′q(so3	NUM
ap-2169	9	38	)	)	PUNCT
ap-2169	9	39	,	,	PUNCT
ap-2169	9	40	for	for	ADP
ap-2169	9	41	which	which	PRON
ap-2169	9	42	the	the	DET
ap-2169	9	43	complete	complete	ADJ
ap-2169	9	44	classification	classification	NOUN
ap-2169	9	45	of	of	ADP
ap-2169	9	46	its	its	PRON
ap-2169	9	47	irreducible	irreducible	ADJ
ap-2169	9	48	representations	representation	NOUN
ap-2169	9	49	is	be	AUX
ap-2169	9	50	known	know	VERB
ap-2169	9	51	(	(	PUNCT
ap-2169	9	52	see	see	VERB
ap-2169	9	53	[	[	X
ap-2169	9	54	6–9	6–9	NOUN
ap-2169	9	55	]	]	PUNCT
ap-2169	9	56	)	)	PUNCT
ap-2169	9	57	.	.	PUNCT
ap-2169	10	1	2	2	X
ap-2169	10	2	.	.	NUM
ap-2169	10	3	lie	lie	NOUN
ap-2169	10	4	algebra	algebra	PROPN
ap-2169	10	5	sl2	sl2	PROPN
ap-2169	10	6	let	let	VERB
ap-2169	10	7	us	we	PRON
ap-2169	10	8	first	first	ADV
ap-2169	10	9	consider	consider	VERB
ap-2169	10	10	the	the	DET
ap-2169	10	11	lie	lie	NOUN
ap-2169	10	12	algebra	algebra	NOUN
ap-2169	10	13	sl2	sl2	PROPN
ap-2169	10	14	of	of	ADP
ap-2169	10	15	2×2	2×2	NUM
ap-2169	10	16	complex	complex	ADJ
ap-2169	10	17	matrices	matrix	NOUN
ap-2169	10	18	with	with	ADP
ap-2169	10	19	zero	zero	NUM
ap-2169	10	20	trace	trace	NOUN
ap-2169	10	21	.	.	PUNCT
ap-2169	11	1	it	it	PRON
ap-2169	11	2	has	have	VERB
ap-2169	11	3	the	the	DET
ap-2169	11	4	standard	standard	ADJ
ap-2169	11	5	chevalley	chevalley	ADJ
ap-2169	11	6	basis	basis	NOUN
ap-2169	11	7	e	e	NOUN
ap-2169	11	8	=	=	PUNCT
ap-2169	11	9	(	(	PUNCT
ap-2169	11	10	0	0	NUM
ap-2169	11	11	1	1	NUM
ap-2169	11	12	0	0	NUM
ap-2169	11	13	0	0	NUM
ap-2169	11	14	)	)	PUNCT
ap-2169	11	15	,	,	PUNCT
ap-2169	12	1	f	f	X
ap-2169	12	2	=	=	PRON
ap-2169	12	3	(	(	PUNCT
ap-2169	12	4	0	0	NUM
ap-2169	12	5	0	0	NUM
ap-2169	12	6	1	1	NUM
ap-2169	12	7	0	0	NUM
ap-2169	12	8	)	)	PUNCT
ap-2169	12	9	,	,	PUNCT
ap-2169	12	10	h	h	NOUN
ap-2169	12	11	=	=	PUNCT
ap-2169	12	12	(	(	PUNCT
ap-2169	12	13	1	1	NUM
ap-2169	12	14	0	0	NUM
ap-2169	12	15	0	0	NUM
ap-2169	12	16	−1	−1	NOUN
ap-2169	12	17	)	)	PUNCT
ap-2169	12	18	.	.	PUNCT
ap-2169	13	1	these	these	DET
ap-2169	13	2	matrices	matrix	NOUN
ap-2169	13	3	satisfy	satisfy	VERB
ap-2169	13	4	the	the	DET
ap-2169	13	5	commutation	commutation	NOUN
ap-2169	13	6	relations	relation	NOUN
ap-2169	14	1	[	[	X
ap-2169	14	2	h	h	X
ap-2169	14	3	,	,	PUNCT
ap-2169	14	4	e	e	X
ap-2169	14	5	]	]	X
ap-2169	14	6	=	=	SYM
ap-2169	14	7	2e	2e	NOUN
ap-2169	14	8	,	,	PUNCT
ap-2169	14	9	[	[	X
ap-2169	14	10	h	h	X
ap-2169	14	11	,	,	PUNCT
ap-2169	14	12	f	f	X
ap-2169	14	13	]	]	PUNCT
ap-2169	14	14	=	=	PUNCT
ap-2169	15	1	−2f	−2f	PROPN
ap-2169	15	2	,	,	PUNCT
ap-2169	15	3	[	[	X
ap-2169	15	4	e	e	X
ap-2169	15	5	,	,	PUNCT
ap-2169	15	6	f	f	X
ap-2169	15	7	]	]	X
ap-2169	15	8	=	=	SYM
ap-2169	15	9	h	h	NOUN
ap-2169	15	10	,	,	PUNCT
ap-2169	15	11	where	where	SCONJ
ap-2169	15	12	[	[	X
ap-2169	15	13	x	x	X
ap-2169	15	14	,	,	PUNCT
ap-2169	15	15	y	y	PROPN
ap-2169	15	16	]	]	X
ap-2169	15	17	=	=	PUNCT
ap-2169	16	1	xy	xy	PROPN
ap-2169	16	2	−	−	PROPN
ap-2169	17	1	yx	yx	PROPN
ap-2169	17	2	.	.	PUNCT
ap-2169	17	3	let	let	VERB
ap-2169	17	4	ϕ	ϕ	NOUN
ap-2169	17	5	be	be	AUX
ap-2169	17	6	a	a	DET
ap-2169	17	7	finite	finite	ADJ
ap-2169	17	8	-	-	ADJ
ap-2169	17	9	dimensional	dimensional	ADJ
ap-2169	17	10	irreducible	irreducible	ADJ
ap-2169	17	11	representation	representation	NOUN
ap-2169	17	12	of	of	ADP
ap-2169	17	13	sl2	sl2	PROPN
ap-2169	17	14	acting	act	VERB
ap-2169	17	15	on	on	ADP
ap-2169	17	16	the	the	DET
ap-2169	17	17	space	space	NOUN
ap-2169	17	18	vn+1	vn+1	PROPN
ap-2169	17	19	of	of	ADP
ap-2169	17	20	dimension	dimension	PROPN
ap-2169	17	21	n	n	PROPN
ap-2169	17	22	+	+	CCONJ
ap-2169	17	23	1	1	NUM
ap-2169	17	24	with	with	ADP
ap-2169	17	25	some	some	DET
ap-2169	17	26	fixed	fix	VERB
ap-2169	17	27	basis	basis	NOUN
ap-2169	17	28	via	via	ADP
ap-2169	17	29	the	the	DET
ap-2169	17	30	matrices	matrix	NOUN
ap-2169	17	31	h	h	NOUN
ap-2169	17	32	=	=	SYM
ap-2169	17	33	ϕ(h	ϕ(h	PROPN
ap-2169	17	34	)	)	PUNCT
ap-2169	18	1	=	=	SYM
ap-2169	18	2			ADJ
ap-2169	18	3	n	n	CCONJ
ap-2169	18	4	0	0	NUM
ap-2169	18	5	0	0	NUM
ap-2169	18	6	·	·	PUNCT
ap-2169	18	7	·	·	PUNCT
ap-2169	18	8	·	·	PUNCT
ap-2169	18	9	0	0	NUM
ap-2169	18	10	0	0	NUM
ap-2169	19	1	n	n	CCONJ
ap-2169	19	2	−	−	PROPN
ap-2169	20	1	2	2	NUM
ap-2169	20	2	0	0	NUM
ap-2169	20	3	0	0	NUM
ap-2169	20	4	0	0	NUM
ap-2169	20	5	0	0	NUM
ap-2169	20	6	n	n	CCONJ
ap-2169	20	7	−	−	PROPN
ap-2169	20	8	4	4	NUM
ap-2169	20	9	0	0	NUM
ap-2169	20	10	...	...	PUNCT
ap-2169	20	11	.	.	PUNCT
ap-2169	20	12	.	.	PUNCT
ap-2169	20	13	.	.	PUNCT
ap-2169	21	1	...	...	PUNCT
ap-2169	22	1	0	0	NUM
ap-2169	22	2	0	0	NUM
ap-2169	22	3	0	0	NUM
ap-2169	22	4	·	·	PUNCT
ap-2169	22	5	·	·	PUNCT
ap-2169	22	6	·	·	PUNCT
ap-2169	23	1	−n	−n	INTJ
ap-2169	23	2			PROPN
ap-2169	23	3	,	,	PUNCT
ap-2169	23	4	ϕ(e	ϕ(e	PROPN
ap-2169	23	5	)	)	PUNCT
ap-2169	23	6	=	=	PUNCT
ap-2169	24	1			ADJ
ap-2169	24	2	0	0	NUM
ap-2169	24	3	1	1	NUM
ap-2169	24	4	0	0	NUM
ap-2169	24	5	·	·	PUNCT
ap-2169	24	6	·	·	PUNCT
ap-2169	24	7	·	·	PUNCT
ap-2169	24	8	0	0	NUM
ap-2169	25	1	0	0	NUM
ap-2169	25	2	0	0	NUM
ap-2169	25	3	2	2	NUM
ap-2169	25	4	0	0	NUM
ap-2169	25	5	0	0	NUM
ap-2169	25	6	0	0	NUM
ap-2169	25	7	0	0	NUM
ap-2169	25	8	.	.	PUNCT
ap-2169	25	9	.	.	PUNCT
ap-2169	25	10	.	.	PUNCT
ap-2169	26	1	0	0	NUM
ap-2169	26	2	...	...	PUNCT
ap-2169	26	3	.	.	PUNCT
ap-2169	26	4	.	.	PUNCT
ap-2169	27	1	.	.	PUNCT
ap-2169	28	1	...	...	PUNCT
ap-2169	29	1	0	0	NUM
ap-2169	29	2	0	0	NUM
ap-2169	29	3	0	0	NUM
ap-2169	29	4	·	·	PUNCT
ap-2169	29	5	·	·	PUNCT
ap-2169	29	6	·	·	PUNCT
ap-2169	29	7	0	0	NUM
ap-2169	30	1			NOUN
ap-2169	30	2	,	,	PUNCT
ap-2169	30	3	ϕ(f	ϕ(f	PROPN
ap-2169	30	4	)	)	PUNCT
ap-2169	31	1	=	=	SYM
ap-2169	31	2			ADJ
ap-2169	31	3	0	0	NUM
ap-2169	31	4	0	0	NUM
ap-2169	31	5	0	0	NUM
ap-2169	31	6	·	·	PUNCT
ap-2169	31	7	·	·	PUNCT
ap-2169	31	8	·	·	PUNCT
ap-2169	31	9	0	0	NUM
ap-2169	32	1	n	n	CCONJ
ap-2169	32	2	0	0	NUM
ap-2169	32	3	0	0	NUM
ap-2169	32	4	0	0	NUM
ap-2169	32	5	0	0	NUM
ap-2169	33	1	n	n	CCONJ
ap-2169	34	1	−	−	PROPN
ap-2169	34	2	1	1	NUM
ap-2169	34	3	0	0	NUM
ap-2169	34	4	0	0	NUM
ap-2169	34	5	...	...	PUNCT
ap-2169	34	6	.	.	PUNCT
ap-2169	34	7	.	.	PUNCT
ap-2169	34	8	.	.	PUNCT
ap-2169	34	9	.	.	PUNCT
ap-2169	34	10	.	.	PUNCT
ap-2169	34	11	.	.	PUNCT
ap-2169	35	1	...	...	PUNCT
ap-2169	36	1	0	0	NUM
ap-2169	36	2	0	0	NUM
ap-2169	36	3	0	0	NUM
ap-2169	36	4	·	·	PUNCT
ap-2169	36	5	·	·	PUNCT
ap-2169	36	6	·	·	PUNCT
ap-2169	36	7	0	0	NUM
ap-2169	37	1			PRON
ap-2169	37	2	.	.	PUNCT
ap-2169	38	1	now	now	ADV
ap-2169	38	2	let	let	VERB
ap-2169	38	3	us	we	PRON
ap-2169	38	4	define	define	VERB
ap-2169	38	5	a	a	DET
ap-2169	38	6	matrix	matrix	NOUN
ap-2169	38	7	s	s	NOUN
ap-2169	38	8	as	as	ADP
ap-2169	38	9	s	s	NOUN
ap-2169	38	10	=	=	SYM
ap-2169	38	11	ϕ(e	ϕ(e	PROPN
ap-2169	38	12	)	)	PUNCT
ap-2169	39	1	+	+	CCONJ
ap-2169	39	2	ϕ(f	ϕ(f	X
ap-2169	39	3	)	)	PUNCT
ap-2169	39	4	=	=	SYM
ap-2169	39	5			ADJ
ap-2169	39	6	0	0	NUM
ap-2169	40	1	1	1	NUM
ap-2169	40	2	0	0	NUM
ap-2169	40	3	·	·	PUNCT
ap-2169	40	4	·	·	PUNCT
ap-2169	40	5	·	·	PUNCT
ap-2169	40	6	0	0	NUM
ap-2169	41	1	n	n	CCONJ
ap-2169	41	2	0	0	NUM
ap-2169	41	3	2	2	NUM
ap-2169	41	4	0	0	NUM
ap-2169	41	5	0	0	NUM
ap-2169	42	1	n	n	CCONJ
ap-2169	43	1	−	−	PROPN
ap-2169	43	2	1	1	NUM
ap-2169	43	3	0	0	NUM
ap-2169	43	4	.	.	PUNCT
ap-2169	43	5	.	.	PUNCT
ap-2169	44	1	.	.	PUNCT
ap-2169	44	2	0	0	NUM
ap-2169	44	3	...	...	PUNCT
ap-2169	44	4	.	.	PUNCT
ap-2169	44	5	.	.	PUNCT
ap-2169	45	1	.	.	PUNCT
ap-2169	45	2	.	.	PUNCT
ap-2169	46	1	.	.	PUNCT
ap-2169	46	2	.	.	PUNCT
ap-2169	47	1	...	...	PUNCT
ap-2169	48	1	0	0	NUM
ap-2169	48	2	0	0	NUM
ap-2169	48	3	0	0	NUM
ap-2169	48	4	·	·	PUNCT
ap-2169	48	5	·	·	PUNCT
ap-2169	48	6	·	·	PUNCT
ap-2169	48	7	0	0	NUM
ap-2169	49	1			PRON
ap-2169	49	2	.	.	PUNCT
ap-2169	50	1	making	make	VERB
ap-2169	50	2	use	use	NOUN
ap-2169	50	3	of	of	ADP
ap-2169	50	4	an	an	DET
ap-2169	50	5	automorphism	automorphism	NOUN
ap-2169	50	6	σ	σ	NOUN
ap-2169	50	7	sending	send	VERB
ap-2169	50	8	h→	h→	NOUN
ap-2169	50	9	e+	e+	PUNCT
ap-2169	50	10	f	f	PROPN
ap-2169	50	11	,	,	PUNCT
ap-2169	50	12	e→	e→	PROPN
ap-2169	50	13	1	1	NUM
ap-2169	50	14	2(h−	2(h−	PROPN
ap-2169	50	15	e+	e+	PUNCT
ap-2169	50	16	f	f	PROPN
ap-2169	50	17	)	)	PUNCT
ap-2169	50	18	,	,	PUNCT
ap-2169	50	19	f	f	PROPN
ap-2169	50	20	→	→	SYM
ap-2169	50	21	1	1	NUM
ap-2169	50	22	2(h+	2(h+	NOUN
ap-2169	50	23	e−	e−	PROPN
ap-2169	50	24	f	f	PROPN
ap-2169	50	25	)	)	PUNCT
ap-2169	50	26	and	and	CCONJ
ap-2169	50	27	taking	take	VERB
ap-2169	50	28	into	into	ADP
ap-2169	50	29	account	account	NOUN
ap-2169	50	30	the	the	DET
ap-2169	50	31	classification	classification	NOUN
ap-2169	50	32	of	of	ADP
ap-2169	50	33	irreducible	irreducible	ADJ
ap-2169	50	34	representations	representation	NOUN
ap-2169	50	35	of	of	ADP
ap-2169	50	36	the	the	DET
ap-2169	50	37	sl2	sl2	PROPN
ap-2169	50	38	algebra	algebra	PROPN
ap-2169	50	39	,	,	PUNCT
ap-2169	50	40	we	we	PRON
ap-2169	50	41	see	see	VERB
ap-2169	50	42	that	that	PRON
ap-2169	50	43	matrices	matrice	VERB
ap-2169	50	44	h	h	NOUN
ap-2169	50	45	and	and	CCONJ
ap-2169	50	46	s	s	PRON
ap-2169	50	47	form	form	NOUN
ap-2169	50	48	a	a	DET
ap-2169	50	49	so	so	ADV
ap-2169	50	50	-	-	PUNCT
ap-2169	50	51	called	call	VERB
ap-2169	50	52	leonard	leonard	PROPN
ap-2169	50	53	pair	pair	PROPN
ap-2169	50	54	(	(	PUNCT
ap-2169	50	55	a	a	DET
ap-2169	50	56	leonard	leonard	NOUN
ap-2169	50	57	pair	pair	NOUN
ap-2169	50	58	is	be	AUX
ap-2169	50	59	a	a	DET
ap-2169	50	60	pair	pair	NOUN
ap-2169	50	61	of	of	ADP
ap-2169	50	62	diagonalizable	diagonalizable	ADJ
ap-2169	50	63	finite	finite	ADJ
ap-2169	50	64	-	-	ADJ
ap-2169	50	65	dimensional	dimensional	ADJ
ap-2169	50	66	linear	linear	ADJ
ap-2169	50	67	transformations	transformation	NOUN
ap-2169	50	68	,	,	PUNCT
ap-2169	50	69	each	each	PRON
ap-2169	50	70	of	of	ADP
ap-2169	50	71	which	which	PRON
ap-2169	50	72	acts	act	VERB
ap-2169	50	73	in	in	ADP
ap-2169	50	74	an	an	DET
ap-2169	50	75	irreducible	irreducible	ADJ
ap-2169	50	76	tridiagonal	tridiagonal	ADJ
ap-2169	50	77	fashion	fashion	NOUN
ap-2169	50	78	on	on	ADP
ap-2169	50	79	an	an	DET
ap-2169	50	80	eigenbasis	eigenbasis	NOUN
ap-2169	50	81	for	for	ADP
ap-2169	50	82	the	the	DET
ap-2169	50	83	other	other	ADJ
ap-2169	50	84	one	one	NUM
ap-2169	50	85	)	)	PUNCT
ap-2169	50	86	.	.	PUNCT
ap-2169	51	1	particularly	particularly	ADV
ap-2169	51	2	,	,	PUNCT
ap-2169	51	3	they	they	PRON
ap-2169	51	4	have	have	VERB
ap-2169	51	5	the	the	DET
ap-2169	51	6	same	same	ADJ
ap-2169	51	7	eigenvalues	eigenvalue	NOUN
ap-2169	51	8	.	.	PUNCT
ap-2169	52	1	it	it	PRON
ap-2169	52	2	follows	follow	VERB
ap-2169	52	3	that	that	SCONJ
ap-2169	52	4	there	there	PRON
ap-2169	52	5	exists	exist	VERB
ap-2169	52	6	a	a	DET
ap-2169	52	7	matrix	matrix	NOUN
ap-2169	52	8	p	p	NOUN
ap-2169	53	1	such	such	DET
ap-2169	53	2	that	that	PRON
ap-2169	53	3	s	s	NOUN
ap-2169	53	4	=	=	SYM
ap-2169	53	5	php−1	php−1	NOUN
ap-2169	53	6	.	.	PUNCT
ap-2169	54	1	we	we	PRON
ap-2169	54	2	can	can	AUX
ap-2169	54	3	consider	consider	VERB
ap-2169	54	4	the	the	DET
ap-2169	54	5	rows	row	NOUN
ap-2169	54	6	of	of	ADP
ap-2169	54	7	p	p	NOUN
ap-2169	54	8	or	or	CCONJ
ap-2169	54	9	the	the	DET
ap-2169	54	10	columns	column	NOUN
ap-2169	54	11	of	of	ADP
ap-2169	54	12	p−1	p−1	PROPN
ap-2169	54	13	as	as	ADP
ap-2169	54	14	coordinate	coordinate	NOUN
ap-2169	54	15	vectors	vector	NOUN
ap-2169	54	16	of	of	ADP
ap-2169	54	17	a	a	DET
ap-2169	54	18	polynomial	polynomial	NOUN
ap-2169	54	19	.	.	PUNCT
ap-2169	55	1	the	the	DET
ap-2169	55	2	proposition	proposition	NOUN
ap-2169	55	3	is	be	AUX
ap-2169	55	4	that	that	SCONJ
ap-2169	55	5	kj(k	kj(k	PROPN
ap-2169	55	6	;	;	PUNCT
ap-2169	55	7	1/2	1/2	NUM
ap-2169	55	8	,	,	PUNCT
ap-2169	55	9	n	n	CCONJ
ap-2169	55	10	)	)	PUNCT
ap-2169	55	11	=	=	NOUN
ap-2169	56	1	[	[	X
ap-2169	56	2	p−1]kj	p−1]kj	X
ap-2169	56	3	=	=	SYM
ap-2169	56	4	(	(	PUNCT
ap-2169	56	5	n	n	X
ap-2169	56	6	j	j	NOUN
ap-2169	56	7	)	)	PUNCT
ap-2169	56	8	−1	−1	NOUN
ap-2169	56	9	pjk	pjk	NOUN
ap-2169	56	10	(	(	PUNCT
ap-2169	56	11	1	1	X
ap-2169	56	12	)	)	PUNCT
ap-2169	56	13	wherekn(x	wherekn(x	NOUN
ap-2169	56	14	;	;	PUNCT
ap-2169	56	15	p	p	NOUN
ap-2169	56	16	,	,	PUNCT
ap-2169	56	17	n	n	CCONJ
ap-2169	56	18	)	)	PUNCT
ap-2169	56	19	is	be	AUX
ap-2169	56	20	n	n	ADV
ap-2169	56	21	-	-	PUNCT
ap-2169	56	22	th	th	X
ap-2169	56	23	krawtchouk	krawtchouk	NOUN
ap-2169	56	24	polynomial	polynomial	ADJ
ap-2169	56	25	n	n	NOUN
ap-2169	56	26	=	=	SYM
ap-2169	56	27	0	0	NUM
ap-2169	56	28	,	,	PUNCT
ap-2169	56	29	1	1	NUM
ap-2169	56	30	,	,	PUNCT
ap-2169	56	31	.	.	PUNCT
ap-2169	56	32	.	.	PUNCT
ap-2169	57	1	.	.	PUNCT
ap-2169	58	1	,	,	PUNCT
ap-2169	58	2	n	n	CCONJ
ap-2169	58	3	with	with	ADP
ap-2169	58	4	parameters	parameter	NOUN
ap-2169	58	5	p	p	X
ap-2169	58	6	∈	∈	PROPN
ap-2169	58	7	(	(	PUNCT
ap-2169	58	8	0	0	NUM
ap-2169	58	9	,	,	PUNCT
ap-2169	58	10	1	1	NUM
ap-2169	58	11	)	)	PUNCT
ap-2169	58	12	and	and	CCONJ
ap-2169	58	13	n	n	PRON
ap-2169	58	14	∈	∈	PROPN
ap-2169	58	15	n0	n0	PROPN
ap-2169	58	16	.	.	PUNCT
ap-2169	59	1	the	the	DET
ap-2169	59	2	matrix	matrix	NOUN
ap-2169	59	3	p	p	NOUN
ap-2169	59	4	is	be	AUX
ap-2169	59	5	defined	define	VERB
ap-2169	59	6	by	by	ADP
ap-2169	59	7	a	a	DET
ap-2169	59	8	similarity	similarity	NOUN
ap-2169	59	9	relation	relation	NOUN
ap-2169	59	10	up	up	ADV
ap-2169	59	11	394	394	NUM
ap-2169	59	12	http://dx.doi.org/10.14311/ap.2014.54.0394	http://dx.doi.org/10.14311/ap.2014.54.0394	NOUN
ap-2169	59	13	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2169	59	14	vol	vol	NOUN
ap-2169	59	15	.	.	PUNCT
ap-2169	60	1	54	54	NUM
ap-2169	60	2	no	no	NOUN
ap-2169	60	3	.	.	PUNCT
ap-2169	61	1	6/2014	6/2014	NUM
ap-2169	61	2	automorphisms	automorphism	NOUN
ap-2169	61	3	of	of	ADP
ap-2169	61	4	algebras	algebras	PROPN
ap-2169	61	5	and	and	CCONJ
ap-2169	61	6	orthogonal	orthogonal	ADJ
ap-2169	61	7	polynomials	polynomial	NOUN
ap-2169	61	8	to	to	ADP
ap-2169	61	9	a	a	DET
ap-2169	61	10	multiplicative	multiplicative	ADJ
ap-2169	61	11	constant	constant	NOUN
ap-2169	61	12	.	.	PUNCT
ap-2169	62	1	equation	equation	NOUN
ap-2169	62	2	1	1	NUM
ap-2169	62	3	holds	hold	VERB
ap-2169	62	4	if	if	SCONJ
ap-2169	62	5	we	we	PRON
ap-2169	62	6	choose	choose	VERB
ap-2169	62	7	p00	p00	PROPN
ap-2169	62	8	=	=	SYM
ap-2169	62	9	1	1	NUM
ap-2169	62	10	.	.	PUNCT
ap-2169	63	1	the	the	DET
ap-2169	63	2	krawtchouk	krawtchouk	ADJ
ap-2169	63	3	polynomials	polynomial	NOUN
ap-2169	63	4	are	be	AUX
ap-2169	63	5	defined	define	VERB
ap-2169	63	6	by	by	ADP
ap-2169	63	7	means	mean	NOUN
ap-2169	63	8	of	of	ADP
ap-2169	63	9	the	the	DET
ap-2169	63	10	hypergeometric	hypergeometric	ADJ
ap-2169	63	11	function	function	NOUN
ap-2169	63	12	kn(x	kn(x	X
ap-2169	63	13	;	;	PUNCT
ap-2169	63	14	p	p	X
ap-2169	63	15	,	,	PUNCT
ap-2169	63	16	n	n	CCONJ
ap-2169	63	17	)	)	PUNCT
ap-2169	64	1	=	=	SYM
ap-2169	64	2	2f1	2f1	NUM
ap-2169	65	1	(	(	PUNCT
ap-2169	65	2	−n,−x	−n,−x	VERB
ap-2169	65	3	−n	−n	NOUN
ap-2169	65	4	∣∣∣∣	∣∣∣∣	NOUN
ap-2169	65	5	1	1	NUM
ap-2169	65	6	p	p	NOUN
ap-2169	65	7	)	)	PUNCT
ap-2169	66	1	=	=	SYM
ap-2169	66	2	n∑	n∑	NOUN
ap-2169	66	3	j=0	j=0	PROPN
ap-2169	66	4	(	(	PUNCT
ap-2169	66	5	−n)j(−x)j	−n)j(−x)j	PROPN
ap-2169	66	6	(	(	PUNCT
ap-2169	66	7	−n)j	−n)j	NOUN
ap-2169	66	8	1	1	NUM
ap-2169	66	9	pjj	pjj	ADV
ap-2169	66	10	!	!	PUNCT
ap-2169	67	1	where	where	SCONJ
ap-2169	67	2	(	(	PUNCT
ap-2169	67	3	a)j	a)j	X
ap-2169	67	4	=	=	SYM
ap-2169	67	5	j−1∏	j−1∏	ADP
ap-2169	67	6	k=0	k=0	PROPN
ap-2169	67	7	(	(	PUNCT
ap-2169	67	8	a+	a+	X
ap-2169	67	9	k	k	NOUN
ap-2169	67	10	)	)	PUNCT
ap-2169	67	11	and	and	CCONJ
ap-2169	67	12	(	(	PUNCT
ap-2169	67	13	a)0	a)0	PROPN
ap-2169	67	14	=	=	SYM
ap-2169	67	15	1	1	NUM
ap-2169	67	16	.	.	PUNCT
ap-2169	67	17	to	to	PART
ap-2169	67	18	show	show	VERB
ap-2169	67	19	(	(	PUNCT
ap-2169	67	20	1	1	NUM
ap-2169	67	21	)	)	PUNCT
ap-2169	67	22	,	,	PUNCT
ap-2169	67	23	we	we	PRON
ap-2169	67	24	can	can	AUX
ap-2169	67	25	use	use	VERB
ap-2169	67	26	the	the	DET
ap-2169	67	27	similarity	similarity	NOUN
ap-2169	67	28	relations	relation	NOUN
ap-2169	67	29	p−1s	p−1s	ADP
ap-2169	67	30	=	=	PROPN
ap-2169	67	31	hp−1	hp−1	PROPN
ap-2169	67	32	,	,	PUNCT
ap-2169	67	33	i.e.	i.e.	X
ap-2169	67	34	,	,	PUNCT
ap-2169	67	35	[	[	X
ap-2169	67	36	p−1s]kj	p−1s]kj	NOUN
ap-2169	67	37	=	=	SYM
ap-2169	67	38	j[p−1]k	j[p−1]k	PROPN
ap-2169	67	39	,	,	PUNCT
ap-2169	67	40	j−1	j−1	PROPN
ap-2169	67	41	+	+	CCONJ
ap-2169	67	42	(	(	PUNCT
ap-2169	67	43	n	n	CCONJ
ap-2169	67	44	−	−	PROPN
ap-2169	67	45	j)[p−1]k	j)[p−1]k	PROPN
ap-2169	67	46	,	,	PUNCT
ap-2169	67	47	j+1	j+1	NUM
ap-2169	67	48	,	,	PUNCT
ap-2169	67	49	[	[	X
ap-2169	67	50	hp−1]jk	hp−1]jk	X
ap-2169	67	51	=	=	SYM
ap-2169	67	52	(	(	PUNCT
ap-2169	67	53	n	n	CCONJ
ap-2169	67	54	−	−	PROPN
ap-2169	67	55	2k)[p−1]kj	2k)[p−1]kj	PROPN
ap-2169	67	56	,	,	PUNCT
ap-2169	67	57	construct	construct	VERB
ap-2169	67	58	a	a	DET
ap-2169	67	59	recurrence	recurrence	NOUN
ap-2169	67	60	relation	relation	NOUN
ap-2169	67	61	j[p−1]k	j[p−1]k	PROPN
ap-2169	67	62	,	,	PUNCT
ap-2169	67	63	j−1	j−1	PROPN
ap-2169	67	64	−	−	PROPN
ap-2169	67	65	(	(	PUNCT
ap-2169	67	66	n	n	NOUN
ap-2169	67	67	−	−	PROPN
ap-2169	67	68	2k)[p−1]k	2k)[p−1]k	NUM
ap-2169	67	69	,	,	PUNCT
ap-2169	67	70	j	j	PROPN
ap-2169	67	71	+	+	CCONJ
ap-2169	67	72	(	(	PUNCT
ap-2169	67	73	n	n	CCONJ
ap-2169	67	74	−	−	PROPN
ap-2169	67	75	j)[p−1]k	j)[p−1]k	PROPN
ap-2169	67	76	,	,	PUNCT
ap-2169	67	77	j+1	j+1	PROPN
ap-2169	67	78	=	=	SYM
ap-2169	67	79	0	0	NUM
ap-2169	67	80	(	(	PUNCT
ap-2169	67	81	2	2	NUM
ap-2169	67	82	)	)	PUNCT
ap-2169	67	83	and	and	CCONJ
ap-2169	67	84	compare	compare	VERB
ap-2169	67	85	it	it	PRON
ap-2169	67	86	with	with	ADP
ap-2169	67	87	general	general	ADJ
ap-2169	67	88	recurrence	recurrence	NOUN
ap-2169	67	89	for	for	ADP
ap-2169	67	90	krawtchouk	krawtchouk	ADJ
ap-2169	67	91	polynomials	polynomial	NOUN
ap-2169	67	92	,	,	PUNCT
ap-2169	67	93	j(p−	j(p−	VERB
ap-2169	67	94	1)kj−1(x)−	1)kj−1(x)−	NUM
ap-2169	67	95	(	(	PUNCT
ap-2169	67	96	j(p−	j(p−	VERB
ap-2169	67	97	1	1	NUM
ap-2169	67	98	)	)	PUNCT
ap-2169	67	99	+	+	CCONJ
ap-2169	67	100	(	(	PUNCT
ap-2169	67	101	j	j	PROPN
ap-2169	67	102	−n)p+	−n)p+	PROPN
ap-2169	67	103	x	x	SYM
ap-2169	67	104	)	)	PUNCT
ap-2169	67	105	kj(x	kj(x	PUNCT
ap-2169	67	106	)	)	PUNCT
ap-2169	68	1	+	+	CCONJ
ap-2169	68	2	(	(	PUNCT
ap-2169	68	3	j	j	PROPN
ap-2169	68	4	−n)pkj+1(x	−n)pkj+1(x	NOUN
ap-2169	68	5	)	)	PUNCT
ap-2169	69	1	=	=	SYM
ap-2169	69	2	0	0	PUNCT
ap-2169	69	3	(	(	PUNCT
ap-2169	69	4	3	3	NUM
ap-2169	69	5	)	)	PUNCT
ap-2169	69	6	where	where	SCONJ
ap-2169	69	7	kn(x	kn(x	X
ap-2169	69	8	)	)	PUNCT
ap-2169	69	9	=	=	SYM
ap-2169	69	10	kn(x	kn(x	X
ap-2169	69	11	;	;	PUNCT
ap-2169	69	12	p	p	X
ap-2169	69	13	,	,	PUNCT
ap-2169	69	14	n	n	CCONJ
ap-2169	69	15	)	)	PUNCT
ap-2169	69	16	for	for	ADP
ap-2169	69	17	fixed	fix	VERB
ap-2169	69	18	p	p	NOUN
ap-2169	69	19	and	and	CCONJ
ap-2169	69	20	n	n	PROPN
ap-2169	69	21	.	.	PUNCT
ap-2169	70	1	one	one	PRON
ap-2169	70	2	can	can	AUX
ap-2169	70	3	show	show	VERB
ap-2169	70	4	a	a	DET
ap-2169	70	5	similar	similar	ADJ
ap-2169	70	6	result	result	NOUN
ap-2169	70	7	for	for	ADP
ap-2169	70	8	the	the	DET
ap-2169	70	9	relation	relation	NOUN
ap-2169	70	10	sp	sp	ADP
ap-2169	70	11	=	=	NOUN
ap-2169	70	12	ph	ph	PROPN
ap-2169	70	13	.	.	PROPN
ap-2169	71	1	this	this	PRON
ap-2169	71	2	also	also	ADV
ap-2169	71	3	proves	prove	VERB
ap-2169	71	4	the	the	DET
ap-2169	71	5	relation	relation	NOUN
ap-2169	71	6	between	between	ADP
ap-2169	71	7	p−1	p−1	PROPN
ap-2169	71	8	and	and	CCONJ
ap-2169	71	9	p	p	NOUN
ap-2169	71	10	∗	∗	NOUN
ap-2169	71	11	,	,	PUNCT
ap-2169	71	12	which	which	PRON
ap-2169	71	13	can	can	AUX
ap-2169	71	14	be	be	AUX
ap-2169	71	15	written	write	VERB
ap-2169	71	16	as	as	ADP
ap-2169	71	17	p−1	p−1	PROPN
ap-2169	71	18	=	=	PROPN
ap-2169	71	19	p	p	X
ap-2169	71	20	∗g−1	∗g−1	PROPN
ap-2169	71	21	,	,	PUNCT
ap-2169	71	22	where	where	SCONJ
ap-2169	71	23	gjk	gjk	NOUN
ap-2169	71	24	=	=	PUNCT
ap-2169	71	25	δjk	δjk	X
ap-2169	71	26	(	(	PUNCT
ap-2169	71	27	n	n	X
ap-2169	71	28	j	j	PROPN
ap-2169	71	29	)	)	PUNCT
ap-2169	71	30	.	.	PUNCT
ap-2169	72	1	this	this	PRON
ap-2169	72	2	means	mean	VERB
ap-2169	72	3	that	that	SCONJ
ap-2169	72	4	p	p	NOUN
ap-2169	72	5	is	be	AUX
ap-2169	72	6	orthogonal	orthogonal	ADJ
ap-2169	72	7	with	with	ADP
ap-2169	72	8	respect	respect	NOUN
ap-2169	72	9	to	to	ADP
ap-2169	72	10	the	the	DET
ap-2169	72	11	inner	inner	ADJ
ap-2169	72	12	product	product	NOUN
ap-2169	72	13	defined	define	VERB
ap-2169	72	14	by	by	ADP
ap-2169	72	15	matrix	matrix	NOUN
ap-2169	72	16	g.	g.	PROPN
ap-2169	73	1	thus	thus	ADV
ap-2169	73	2	,	,	PUNCT
ap-2169	73	3	p−1	p−1	PROPN
ap-2169	73	4	is	be	AUX
ap-2169	73	5	orthogonal	orthogonal	ADJ
ap-2169	73	6	and	and	CCONJ
ap-2169	73	7	so	so	ADV
ap-2169	73	8	the	the	DET
ap-2169	73	9	columns	column	NOUN
ap-2169	73	10	of	of	ADP
ap-2169	73	11	p−1	p−1	PROPN
ap-2169	73	12	(	(	PUNCT
ap-2169	73	13	krawtchouk	krawtchouk	NOUN
ap-2169	73	14	polynomials	polynomial	NOUN
ap-2169	73	15	)	)	PUNCT
ap-2169	73	16	are	be	AUX
ap-2169	73	17	orthogonal	orthogonal	ADJ
ap-2169	73	18	with	with	ADP
ap-2169	73	19	respect	respect	NOUN
ap-2169	73	20	to	to	ADP
ap-2169	73	21	the	the	DET
ap-2169	73	22	inner	inner	ADJ
ap-2169	73	23	product	product	NOUN
ap-2169	73	24	defining	define	VERB
ap-2169	73	25	the	the	DET
ap-2169	73	26	orthogonality	orthogonality	NOUN
ap-2169	73	27	relation	relation	NOUN
ap-2169	74	1	n∑	n∑	PROPN
ap-2169	75	1	j=1	j=1	NOUN
ap-2169	75	2	(	(	PUNCT
ap-2169	75	3	n	n	CCONJ
ap-2169	75	4	j	j	PROPN
ap-2169	75	5	)	)	PUNCT
ap-2169	75	6	km(j)kn(j	km(j)kn(j	PROPN
ap-2169	75	7	)	)	PUNCT
ap-2169	75	8	=	=	SYM
ap-2169	75	9	hnδmn	hnδmn	NOUN
ap-2169	75	10	.	.	PUNCT
ap-2169	76	1	(	(	PUNCT
ap-2169	76	2	4	4	X
ap-2169	76	3	)	)	PUNCT
ap-2169	76	4	the	the	DET
ap-2169	76	5	inner	inner	ADJ
ap-2169	76	6	product	product	NOUN
ap-2169	76	7	is	be	AUX
ap-2169	76	8	of	of	ADP
ap-2169	76	9	course	course	NOUN
ap-2169	76	10	determined	determine	VERB
ap-2169	76	11	up	up	ADP
ap-2169	76	12	to	to	ADP
ap-2169	76	13	normalization	normalization	NOUN
ap-2169	76	14	(	(	PUNCT
ap-2169	76	15	(	(	PUNCT
ap-2169	76	16	4	4	X
ap-2169	76	17	)	)	PUNCT
ap-2169	76	18	can	can	AUX
ap-2169	76	19	be	be	AUX
ap-2169	76	20	multiplied	multiply	VERB
ap-2169	76	21	by	by	ADP
ap-2169	76	22	the	the	DET
ap-2169	76	23	arbitrary	arbitrary	ADJ
ap-2169	76	24	sequence	sequence	NOUN
ap-2169	76	25	an	an	NOUN
ap-2169	76	26	)	)	PUNCT
ap-2169	76	27	.	.	PUNCT
ap-2169	77	1	this	this	DET
ap-2169	77	2	result	result	NOUN
ap-2169	77	3	corresponds	correspond	VERB
ap-2169	77	4	with	with	ADP
ap-2169	77	5	the	the	DET
ap-2169	77	6	general	general	ADJ
ap-2169	77	7	orthogonality	orthogonality	NOUN
ap-2169	77	8	relation	relation	NOUN
ap-2169	77	9	for	for	ADP
ap-2169	77	10	krawtchouk	krawtchouk	ADJ
ap-2169	77	11	polynomials	polynomial	NOUN
ap-2169	77	12	(	(	PUNCT
ap-2169	77	13	see	see	VERB
ap-2169	77	14	[	[	X
ap-2169	77	15	10	10	NUM
ap-2169	77	16	]	]	SYM
ap-2169	77	17	)	)	PUNCT
ap-2169	78	1	n∑	n∑	PROPN
ap-2169	78	2	j=0	j=0	PROPN
ap-2169	78	3	(	(	PUNCT
ap-2169	78	4	n	n	CCONJ
ap-2169	78	5	j	j	NOUN
ap-2169	78	6	)	)	PUNCT
ap-2169	79	1	pj(1−	pj(1−	NOUN
ap-2169	79	2	p)n−jkm(j)kn(j	p)n−jkm(j)kn(j	NOUN
ap-2169	79	3	)	)	PUNCT
ap-2169	80	1	=	=	PUNCT
ap-2169	80	2	(	(	PUNCT
ap-2169	80	3	n	n	NOUN
ap-2169	80	4	n	n	CCONJ
ap-2169	80	5	)	)	PUNCT
ap-2169	81	1	−1(1−	−1(1−	NOUN
ap-2169	81	2	p	p	X
ap-2169	81	3	p	p	NOUN
ap-2169	81	4	)	)	PUNCT
ap-2169	81	5	n	n	NUM
ap-2169	81	6	δmn	δmn	NOUN
ap-2169	81	7	.	.	PUNCT
ap-2169	82	1	relation	relation	NOUN
ap-2169	82	2	(	(	PUNCT
ap-2169	82	3	4	4	X
ap-2169	82	4	)	)	PUNCT
ap-2169	82	5	can	can	AUX
ap-2169	82	6	be	be	AUX
ap-2169	82	7	derived	derive	VERB
ap-2169	82	8	,	,	PUNCT
ap-2169	82	9	not	not	PART
ap-2169	82	10	just	just	ADV
ap-2169	82	11	proven	prove	VERB
ap-2169	82	12	,	,	PUNCT
ap-2169	82	13	using	use	VERB
ap-2169	82	14	the	the	DET
ap-2169	82	15	properties	property	NOUN
ap-2169	82	16	of	of	ADP
ap-2169	82	17	the	the	DET
ap-2169	82	18	leonard	leonard	PROPN
ap-2169	82	19	pair	pair	PROPN
ap-2169	82	20	.	.	PUNCT
ap-2169	83	1	we	we	PRON
ap-2169	83	2	will	will	AUX
ap-2169	83	3	make	make	VERB
ap-2169	83	4	use	use	NOUN
ap-2169	83	5	of	of	ADP
ap-2169	83	6	the	the	DET
ap-2169	83	7	fact	fact	NOUN
ap-2169	83	8	that	that	SCONJ
ap-2169	83	9	s	s	VERB
ap-2169	83	10	has	have	AUX
ap-2169	83	11	n+1	n+1	PROPN
ap-2169	83	12	distinct	distinct	ADJ
ap-2169	83	13	eigenvalues	eigenvalue	NOUN
ap-2169	83	14	and	and	CCONJ
ap-2169	83	15	p	p	NOUN
ap-2169	83	16	diagonalizes	diagonalize	NOUN
ap-2169	83	17	s	s	PART
ap-2169	83	18	,	,	PUNCT
ap-2169	83	19	so	so	ADV
ap-2169	83	20	the	the	DET
ap-2169	83	21	columns	column	NOUN
ap-2169	83	22	of	of	ADP
ap-2169	83	23	p	p	NOUN
ap-2169	83	24	are	be	AUX
ap-2169	83	25	eigenvectors	eigenvector	NOUN
ap-2169	83	26	of	of	ADP
ap-2169	83	27	s.	s.	PROPN
ap-2169	83	28	if	if	SCONJ
ap-2169	83	29	we	we	PRON
ap-2169	83	30	find	find	VERB
ap-2169	83	31	an	an	DET
ap-2169	83	32	inner	inner	ADJ
ap-2169	83	33	product	product	NOUN
ap-2169	83	34	such	such	ADJ
ap-2169	83	35	that	that	SCONJ
ap-2169	83	36	s	s	PART
ap-2169	83	37	is	be	AUX
ap-2169	83	38	a	a	DET
ap-2169	83	39	matrix	matrix	NOUN
ap-2169	83	40	of	of	ADP
ap-2169	83	41	a	a	DET
ap-2169	83	42	self	self	NOUN
ap-2169	83	43	-	-	PUNCT
ap-2169	83	44	adjoint	adjoint	NOUN
ap-2169	83	45	operator	operator	NOUN
ap-2169	83	46	with	with	ADP
ap-2169	83	47	respect	respect	NOUN
ap-2169	83	48	to	to	ADP
ap-2169	83	49	this	this	DET
ap-2169	83	50	product	product	NOUN
ap-2169	83	51	,	,	PUNCT
ap-2169	83	52	then	then	ADV
ap-2169	83	53	p	p	NOUN
ap-2169	83	54	will	will	AUX
ap-2169	83	55	be	be	AUX
ap-2169	83	56	orthogonal	orthogonal	ADJ
ap-2169	83	57	with	with	ADP
ap-2169	83	58	respect	respect	NOUN
ap-2169	83	59	to	to	ADP
ap-2169	83	60	this	this	DET
ap-2169	83	61	product	product	NOUN
ap-2169	83	62	.	.	PUNCT
ap-2169	84	1	we	we	PRON
ap-2169	84	2	will	will	AUX
ap-2169	84	3	try	try	VERB
ap-2169	84	4	to	to	PART
ap-2169	84	5	find	find	VERB
ap-2169	84	6	a	a	DET
ap-2169	84	7	diagonal	diagonal	ADJ
ap-2169	84	8	matrix	matrix	NOUN
ap-2169	84	9	a	a	DET
ap-2169	84	10	=	=	SYM
ap-2169	84	11	diag(a0	diag(a0	X
ap-2169	84	12	,	,	PUNCT
ap-2169	84	13	.	.	PUNCT
ap-2169	84	14	.	.	PUNCT
ap-2169	85	1	.	.	PUNCT
ap-2169	86	1	,	,	PUNCT
ap-2169	86	2	an	an	PRON
ap-2169	86	3	)	)	PUNCT
ap-2169	86	4	,	,	PUNCT
ap-2169	86	5	such	such	ADJ
ap-2169	86	6	that	that	DET
ap-2169	86	7	a−1sa	a−1sa	NOUN
ap-2169	86	8	is	be	AUX
ap-2169	86	9	a	a	DET
ap-2169	86	10	hermitian	hermitian	ADJ
ap-2169	86	11	matrix	matrix	NOUN
ap-2169	86	12	,	,	PUNCT
ap-2169	86	13	and	and	CCONJ
ap-2169	86	14	so	so	ADV
ap-2169	86	15	it	it	PRON
ap-2169	86	16	is	be	AUX
ap-2169	86	17	a	a	DET
ap-2169	86	18	matrix	matrix	NOUN
ap-2169	86	19	of	of	ADP
ap-2169	86	20	the	the	DET
ap-2169	86	21	self	self	NOUN
ap-2169	86	22	-	-	PUNCT
ap-2169	86	23	adjoint	adjoint	NOUN
ap-2169	86	24	operator	operator	NOUN
ap-2169	86	25	in	in	ADP
ap-2169	86	26	the	the	DET
ap-2169	86	27	case	case	NOUN
ap-2169	86	28	of	of	ADP
ap-2169	86	29	a	a	DET
ap-2169	86	30	standard	standard	ADJ
ap-2169	86	31	inner	inner	ADJ
ap-2169	86	32	product	product	NOUN
ap-2169	86	33	.	.	PUNCT
ap-2169	87	1	after	after	ADP
ap-2169	87	2	a	a	DET
ap-2169	87	3	change	change	NOUN
ap-2169	87	4	of	of	ADP
ap-2169	87	5	basis	basis	NOUN
ap-2169	87	6	we	we	PRON
ap-2169	87	7	can	can	AUX
ap-2169	87	8	see	see	VERB
ap-2169	87	9	that	that	PRON
ap-2169	87	10	s	s	VERB
ap-2169	87	11	is	be	AUX
ap-2169	87	12	a	a	DET
ap-2169	87	13	self	self	NOUN
ap-2169	87	14	-	-	PUNCT
ap-2169	87	15	adjoint	adjoint	NOUN
ap-2169	87	16	operator	operator	NOUN
ap-2169	87	17	in	in	ADP
ap-2169	87	18	the	the	DET
ap-2169	87	19	case	case	NOUN
ap-2169	87	20	of	of	ADP
ap-2169	87	21	the	the	DET
ap-2169	87	22	inner	inner	ADJ
ap-2169	87	23	product	product	NOUN
ap-2169	87	24	defined	define	VERB
ap-2169	87	25	by	by	ADP
ap-2169	87	26	the	the	DET
ap-2169	87	27	matrix	matrix	NOUN
ap-2169	87	28	g	g	NOUN
ap-2169	87	29	=	=	SYM
ap-2169	87	30	a∗a	a∗a	PUNCT
ap-2169	87	31	=	=	SYM
ap-2169	87	32	diag(w0	diag(w0	PROPN
ap-2169	87	33	,	,	PUNCT
ap-2169	87	34	.	.	PUNCT
ap-2169	87	35	.	.	PUNCT
ap-2169	88	1	.	.	PUNCT
ap-2169	89	1	,	,	PUNCT
ap-2169	89	2	wn	wn	PROPN
ap-2169	89	3	)	)	PUNCT
ap-2169	89	4	.	.	PUNCT
ap-2169	90	1	thus	thus	ADV
ap-2169	90	2	,	,	PUNCT
ap-2169	90	3	we	we	PRON
ap-2169	90	4	require	require	VERB
ap-2169	90	5	[	[	X
ap-2169	90	6	a−1sa]j−1,j	a−1sa]j−1,j	NOUN
ap-2169	90	7	=	=	PUNCT
ap-2169	91	1	[	[	X
ap-2169	91	2	a−1sa]j	a−1sa]j	NOUN
ap-2169	91	3	,	,	PUNCT
ap-2169	91	4	j−1	j−1	PROPN
ap-2169	91	5	,	,	PUNCT
ap-2169	91	6	which	which	PRON
ap-2169	91	7	leads	lead	VERB
ap-2169	91	8	to	to	ADP
ap-2169	91	9	the	the	DET
ap-2169	91	10	condition	condition	NOUN
ap-2169	91	11	|aj	|aj	NOUN
ap-2169	91	12	|2	|2	NUM
ap-2169	91	13	=	=	SYM
ap-2169	91	14	|aj−1|2	|aj−1|2	PROPN
ap-2169	91	15	s̄j	s̄j	PROPN
ap-2169	91	16	,	,	PUNCT
ap-2169	91	17	j−1	j−1	PROPN
ap-2169	91	18	sj−1,j	sj−1,j	NOUN
ap-2169	91	19	=	=	PUNCT
ap-2169	91	20	|aj−1|2	|aj−1|2	PROPN
ap-2169	91	21	n	n	CCONJ
ap-2169	91	22	−	−	PROPN
ap-2169	91	23	j	j	PROPN
ap-2169	92	1	+	+	CCONJ
ap-2169	92	2	1	1	NUM
ap-2169	92	3	j	j	NOUN
ap-2169	92	4	.	.	PUNCT
ap-2169	93	1	this	this	DET
ap-2169	93	2	request	request	NOUN
ap-2169	93	3	is	be	AUX
ap-2169	93	4	fulfilled	fulfil	VERB
ap-2169	93	5	if	if	SCONJ
ap-2169	93	6	we	we	PRON
ap-2169	93	7	choose	choose	VERB
ap-2169	93	8	wj	wj	PROPN
ap-2169	93	9	=	=	PUNCT
ap-2169	93	10	|aj	|aj	NOUN
ap-2169	93	11	|2	|2	NUM
ap-2169	94	1	=	=	SYM
ap-2169	94	2	j∏	j∏	PROPN
ap-2169	94	3	k=1	k=1	PUNCT
ap-2169	95	1	n	n	CCONJ
ap-2169	96	1	−	−	PROPN
ap-2169	96	2	k	k	PROPN
ap-2169	97	1	+	+	CCONJ
ap-2169	97	2	1	1	NUM
ap-2169	97	3	k	k	NOUN
ap-2169	97	4	=	=	PUNCT
ap-2169	97	5	(	(	PUNCT
ap-2169	97	6	n	n	X
ap-2169	97	7	j	j	PROPN
ap-2169	97	8	)	)	PUNCT
ap-2169	97	9	.	.	PUNCT
ap-2169	98	1	3	3	X
ap-2169	98	2	.	.	X
ap-2169	98	3	algebra	algebra	VERB
ap-2169	98	4	u	u	NOUN
ap-2169	98	5	′q(so3	′q(so3	PUNCT
ap-2169	98	6	)	)	PUNCT
ap-2169	98	7	now	now	ADV
ap-2169	98	8	let	let	VERB
ap-2169	98	9	us	we	PRON
ap-2169	98	10	consider	consider	VERB
ap-2169	98	11	from	from	ADP
ap-2169	98	12	the	the	DET
ap-2169	98	13	same	same	ADJ
ap-2169	98	14	point	point	NOUN
ap-2169	98	15	of	of	ADP
ap-2169	98	16	view	view	NOUN
ap-2169	98	17	the	the	DET
ap-2169	98	18	algebra	algebra	NOUN
ap-2169	98	19	u	u	NOUN
ap-2169	98	20	′q(so3	′q(so3	NUM
ap-2169	98	21	)	)	PUNCT
ap-2169	98	22	,	,	PUNCT
ap-2169	98	23	a	a	DET
ap-2169	98	24	complex	complex	ADJ
ap-2169	98	25	associative	associative	ADJ
ap-2169	98	26	algebra	algebra	NOUN
ap-2169	98	27	generated	generate	VERB
ap-2169	98	28	by	by	ADP
ap-2169	98	29	three	three	NUM
ap-2169	98	30	elements	element	NOUN
ap-2169	98	31	i1	i1	PROPN
ap-2169	98	32	,	,	PUNCT
ap-2169	98	33	i2	i2	PROPN
ap-2169	98	34	and	and	CCONJ
ap-2169	98	35	i3	i3	NOUN
ap-2169	98	36	satisfying	satisfy	VERB
ap-2169	98	37	the	the	DET
ap-2169	98	38	relations	relation	NOUN
ap-2169	98	39	q1/2i1i2	q1/2i1i2	NOUN
ap-2169	98	40	−	−	PROPN
ap-2169	98	41	q−1/2i2i1	q−1/2i2i1	ADJ
ap-2169	98	42	=	=	SYM
ap-2169	98	43	i3	i3	NOUN
ap-2169	98	44	,	,	PUNCT
ap-2169	98	45	(	(	PUNCT
ap-2169	98	46	5	5	X
ap-2169	98	47	)	)	PUNCT
ap-2169	98	48	q1/2i2i3	q1/2i2i3	NOUN
ap-2169	98	49	−	−	PROPN
ap-2169	98	50	q−1/2i3i2	q−1/2i3i2	PROPN
ap-2169	98	51	=	=	PROPN
ap-2169	98	52	i1	i1	PROPN
ap-2169	98	53	,	,	PUNCT
ap-2169	98	54	(	(	PUNCT
ap-2169	98	55	6	6	X
ap-2169	98	56	)	)	PUNCT
ap-2169	98	57	q1/2i3i1	q1/2i3i1	NOUN
ap-2169	98	58	−	−	PROPN
ap-2169	98	59	q−1/2i1i3	q−1/2i1i3	X
ap-2169	98	60	=	=	PROPN
ap-2169	98	61	i2	i2	PROPN
ap-2169	98	62	.	.	PUNCT
ap-2169	99	1	(	(	PUNCT
ap-2169	99	2	7	7	X
ap-2169	99	3	)	)	PUNCT
ap-2169	99	4	let	let	VERB
ap-2169	99	5	us	we	PRON
ap-2169	99	6	assume	assume	VERB
ap-2169	99	7	that	that	SCONJ
ap-2169	99	8	q	q	NOUN
ap-2169	99	9	is	be	AUX
ap-2169	99	10	not	not	PART
ap-2169	99	11	the	the	DET
ap-2169	99	12	root	root	NOUN
ap-2169	99	13	of	of	ADP
ap-2169	99	14	unity	unity	NOUN
ap-2169	99	15	and	and	CCONJ
ap-2169	99	16	define	define	VERB
ap-2169	99	17	matrices	matrix	NOUN
ap-2169	99	18	ϕ(i1	ϕ(i1	NOUN
ap-2169	99	19	)	)	PUNCT
ap-2169	99	20	,	,	PUNCT
ap-2169	99	21	ϕ(i2	ϕ(i2	NOUN
ap-2169	99	22	)	)	PUNCT
ap-2169	99	23	,	,	PUNCT
ap-2169	99	24	ϕ(i3	ϕ(i3	NOUN
ap-2169	99	25	)	)	PUNCT
ap-2169	99	26	by	by	ADP
ap-2169	99	27	[	[	X
ap-2169	99	28	ϕ(i1)]j+1,j	ϕ(i1)]j+1,j	NOUN
ap-2169	99	29	=	=	PUNCT
ap-2169	100	1	[	[	X
ap-2169	100	2	2	2	NUM
ap-2169	100	3	m	m	NOUN
ap-2169	100	4	−	−	PROPN
ap-2169	100	5	j	j	NOUN
ap-2169	100	6	]	]	X
ap-2169	100	7	q−m+j	q−m+j	X
ap-2169	100	8	+	+	CCONJ
ap-2169	100	9	qm−j	qm−j	ADJ
ap-2169	100	10	,	,	PUNCT
ap-2169	100	11	[	[	X
ap-2169	100	12	ϕ(i1)]j−1,j	ϕ(i1)]j−1,j	X
ap-2169	100	13	=	=	PUNCT
ap-2169	101	1	−	−	PROPN
ap-2169	102	1	[	[	X
ap-2169	102	2	j	j	X
ap-2169	102	3	]	]	X
ap-2169	102	4	q−m+j	q−m+j	X
ap-2169	103	1	+	+	CCONJ
ap-2169	103	2	qm−j	qm−j	ADJ
ap-2169	103	3	,	,	PUNCT
ap-2169	104	1	[	[	X
ap-2169	104	2	ϕ(i1)]jk	ϕ(i1)]jk	X
ap-2169	104	3	=	=	SYM
ap-2169	104	4	0	0	NUM
ap-2169	104	5	for	for	ADP
ap-2169	104	6	k	k	PROPN
ap-2169	104	7	6=	6=	PROPN
ap-2169	104	8	j	j	PROPN
ap-2169	104	9	±	±	PROPN
ap-2169	104	10	1	1	NUM
ap-2169	104	11	,	,	PUNCT
ap-2169	104	12	[	[	X
ap-2169	104	13	ϕ(i3)]jk	ϕ(i3)]jk	X
ap-2169	104	14	=	=	SYM
ap-2169	104	15	i[−m	i[−m	PROPN
ap-2169	105	1	+	+	CCONJ
ap-2169	105	2	j]δjk	j]δjk	NOUN
ap-2169	105	3	,	,	PUNCT
ap-2169	105	4	wherem	wherem	ADJ
ap-2169	105	5	=	=	PUNCT
ap-2169	105	6	n/2	n/2	PROPN
ap-2169	105	7	and	and	CCONJ
ap-2169	105	8	[	[	X
ap-2169	105	9	ν	ν	X
ap-2169	105	10	]	]	X
ap-2169	105	11	=	=	SYM
ap-2169	105	12	(	(	PUNCT
ap-2169	105	13	qν−q−ν)/(q−q−1	qν−q−ν)/(q−q−1	NUM
ap-2169	105	14	)	)	PUNCT
ap-2169	105	15	.	.	PUNCT
ap-2169	106	1	(	(	PUNCT
ap-2169	106	2	the	the	DET
ap-2169	106	3	matrix	matrix	NOUN
ap-2169	106	4	ϕ(i2	ϕ(i2	NOUN
ap-2169	106	5	)	)	PUNCT
ap-2169	106	6	can	can	AUX
ap-2169	106	7	be	be	AUX
ap-2169	106	8	obtained	obtain	VERB
ap-2169	106	9	from	from	ADP
ap-2169	106	10	the	the	DET
ap-2169	106	11	third	third	ADJ
ap-2169	106	12	defining	define	VERB
ap-2169	106	13	relation	relation	NOUN
ap-2169	106	14	(	(	PUNCT
ap-2169	106	15	7	7	NUM
ap-2169	106	16	)	)	PUNCT
ap-2169	106	17	.	.	PUNCT
ap-2169	106	18	)	)	PUNCT
ap-2169	107	1	then	then	ADV
ap-2169	107	2	the	the	DET
ap-2169	107	3	triple	triple	ADJ
ap-2169	107	4	form	form	NOUN
ap-2169	107	5	is	be	AUX
ap-2169	107	6	an	an	PRON
ap-2169	107	7	irreducible	irreducible	ADJ
ap-2169	107	8	so	so	ADV
ap-2169	107	9	called	call	VERB
ap-2169	107	10	classical	classical	ADJ
ap-2169	107	11	representation	representation	NOUN
ap-2169	107	12	of	of	ADP
ap-2169	107	13	u	u	NOUN
ap-2169	107	14	′q(so3	′q(so3	NUM
ap-2169	107	15	)	)	PUNCT
ap-2169	107	16	of	of	ADP
ap-2169	107	17	dimension	dimension	NOUN
ap-2169	107	18	n	n	PROPN
ap-2169	107	19	+	+	NOUN
ap-2169	107	20	1	1	X
ap-2169	107	21	.	.	PUNCT
ap-2169	108	1	the	the	DET
ap-2169	108	2	matrices	matrix	NOUN
ap-2169	108	3	ϕ(i1	ϕ(i1	NOUN
ap-2169	108	4	)	)	PUNCT
ap-2169	108	5	and	and	CCONJ
ap-2169	108	6	ϕ(i3	ϕ(i3	NOUN
ap-2169	108	7	)	)	PUNCT
ap-2169	108	8	have	have	VERB
ap-2169	108	9	the	the	DET
ap-2169	108	10	same	same	ADJ
ap-2169	108	11	eigenvalues	eigenvalue	NOUN
ap-2169	108	12	,	,	PUNCT
ap-2169	108	13	which	which	PRON
ap-2169	108	14	follows	follow	VERB
ap-2169	108	15	from	from	ADP
ap-2169	108	16	the	the	DET
ap-2169	108	17	classification	classification	NOUN
ap-2169	108	18	of	of	ADP
ap-2169	108	19	all	all	DET
ap-2169	108	20	irreducible	irreducible	ADJ
ap-2169	108	21	representations	representation	NOUN
ap-2169	108	22	(	(	PUNCT
ap-2169	108	23	there	there	PRON
ap-2169	108	24	is	be	VERB
ap-2169	108	25	one	one	NUM
ap-2169	108	26	classical	classical	ADJ
ap-2169	108	27	representation	representation	NOUN
ap-2169	108	28	per	per	ADP
ap-2169	108	29	dimension	dimension	NOUN
ap-2169	108	30	,	,	PUNCT
ap-2169	108	31	see	see	VERB
ap-2169	108	32	[	[	X
ap-2169	108	33	9	9	NUM
ap-2169	108	34	]	]	PUNCT
ap-2169	108	35	)	)	PUNCT
ap-2169	108	36	and	and	CCONJ
ap-2169	108	37	from	from	ADP
ap-2169	108	38	the	the	DET
ap-2169	108	39	existence	existence	NOUN
ap-2169	108	40	of	of	ADP
ap-2169	108	41	a	a	DET
ap-2169	108	42	rotational	rotational	ADJ
ap-2169	108	43	automorphism	automorphism	NOUN
ap-2169	108	44	which	which	PRON
ap-2169	108	45	sends	send	VERB
ap-2169	108	46	i1	i1	PROPN
ap-2169	108	47	→	→	SYM
ap-2169	108	48	i2	i2	PROPN
ap-2169	108	49	,	,	PUNCT
ap-2169	108	50	i2	i2	PROPN
ap-2169	108	51	→	→	SYM
ap-2169	108	52	i3	i3	PROPN
ap-2169	108	53	,	,	PUNCT
ap-2169	108	54	i3	i3	NOUN
ap-2169	108	55	→	→	SYM
ap-2169	108	56	i1	i1	PROPN
ap-2169	108	57	.	.	PUNCT
ap-2169	109	1	thus	thus	ADV
ap-2169	109	2	,	,	PUNCT
ap-2169	109	3	we	we	PRON
ap-2169	109	4	can	can	AUX
ap-2169	109	5	construct	construct	VERB
ap-2169	109	6	matrix	matrix	NOUN
ap-2169	109	7	p	p	PRON
ap-2169	109	8	such	such	ADJ
ap-2169	109	9	that	that	DET
ap-2169	109	10	ϕ(i1	ϕ(i1	NOUN
ap-2169	109	11	)	)	PUNCT
ap-2169	110	1	=	=	SYM
ap-2169	110	2	pϕ(i3)p−1	pϕ(i3)p−1	NOUN
ap-2169	110	3	.	.	PUNCT
ap-2169	111	1	395	395	NUM
ap-2169	111	2	daniel	daniel	PROPN
ap-2169	111	3	gromada	gromada	PROPN
ap-2169	111	4	,	,	PUNCT
ap-2169	111	5	severin	severin	PROPN
ap-2169	111	6	pošta	pošta	PROPN
ap-2169	111	7	acta	acta	PROPN
ap-2169	111	8	polytechnica	polytechnica	PROPN
ap-2169	111	9	we	we	PRON
ap-2169	111	10	will	will	AUX
ap-2169	111	11	show	show	VERB
ap-2169	111	12	that	that	DET
ap-2169	111	13	matrix	matrix	NOUN
ap-2169	111	14	p	p	NOUN
ap-2169	111	15	corresponds	correspond	VERB
ap-2169	111	16	to	to	ADP
ap-2169	111	17	q	q	ADJ
ap-2169	111	18	-	-	PUNCT
ap-2169	111	19	racah	racah	ADJ
ap-2169	111	20	polynomials	polynomial	NOUN
ap-2169	111	21	.	.	PUNCT
ap-2169	112	1	the	the	DET
ap-2169	112	2	general	general	ADJ
ap-2169	112	3	q	q	ADJ
ap-2169	112	4	-	-	PUNCT
ap-2169	112	5	racah	racah	ADJ
ap-2169	112	6	polynomials	polynomial	NOUN
ap-2169	112	7	are	be	AUX
ap-2169	112	8	defined	define	VERB
ap-2169	112	9	by	by	ADP
ap-2169	112	10	means	mean	NOUN
ap-2169	112	11	of	of	ADP
ap-2169	112	12	hypergeometric	hypergeometric	ADJ
ap-2169	112	13	series	series	NOUN
ap-2169	112	14	as	as	ADP
ap-2169	112	15	rn	rn	PROPN
ap-2169	112	16	(	(	PUNCT
ap-2169	112	17	µ(x);α	µ(x);α	PROPN
ap-2169	112	18	,	,	PUNCT
ap-2169	112	19	β	β	X
ap-2169	112	20	,	,	PUNCT
ap-2169	112	21	γ	γ	PROPN
ap-2169	112	22	,	,	PUNCT
ap-2169	112	23	δ	δ	PROPN
ap-2169	112	24	|	|	NOUN
ap-2169	112	25	q	q	NOUN
ap-2169	112	26	)	)	PUNCT
ap-2169	113	1	=	=	SYM
ap-2169	113	2	4ϕ3	4ϕ3	NUM
ap-2169	113	3	(	(	PUNCT
ap-2169	113	4	q−n	q−n	PROPN
ap-2169	113	5	,	,	PUNCT
ap-2169	113	6	αβqn+1	αβqn+1	ADJ
ap-2169	113	7	,	,	PUNCT
ap-2169	113	8	q−x	q−x	ADJ
ap-2169	113	9	,	,	PUNCT
ap-2169	113	10	γδqx+1	γδqx+1	PROPN
ap-2169	113	11	αq	αq	ADP
ap-2169	113	12	,	,	PUNCT
ap-2169	113	13	βδq	βδq	ADV
ap-2169	113	14	,	,	PUNCT
ap-2169	113	15	γq	γq	ADP
ap-2169	113	16	∣∣∣∣	∣∣∣∣	NOUN
ap-2169	113	17	q	q	PROPN
ap-2169	113	18	;	;	PUNCT
ap-2169	113	19	q	q	X
ap-2169	113	20	)	)	PUNCT
ap-2169	113	21	=	=	PUNCT
ap-2169	114	1	∞∑	∞∑	NUM
ap-2169	114	2	k=0	k=0	NOUN
ap-2169	115	1	[	[	X
ap-2169	115	2	q−n]k[αβqn+1]k[q−x]k[γδqx+1]k	q−n]k[αβqn+1]k[q−x]k[γδqx+1]k	X
ap-2169	115	3	[	[	X
ap-2169	115	4	αq]k[βδq]k[γq]k	αq]k[βδq]k[γq]k	NUM
ap-2169	115	5	qk	qk	NOUN
ap-2169	115	6	[	[	X
ap-2169	115	7	q]k	q]k	NOUN
ap-2169	115	8	,	,	PUNCT
ap-2169	115	9	(	(	PUNCT
ap-2169	115	10	8)	8)	NUM
ap-2169	115	11	where	where	SCONJ
ap-2169	115	12	rn(x;α	rn(x;α	PROPN
ap-2169	115	13	,	,	PUNCT
ap-2169	115	14	β	β	X
ap-2169	115	15	,	,	PUNCT
ap-2169	115	16	γ	γ	PROPN
ap-2169	115	17	,	,	PUNCT
ap-2169	115	18	δ	δ	PROPN
ap-2169	115	19	|	|	ADV
ap-2169	115	20	q	q	NOUN
ap-2169	115	21	)	)	PUNCT
ap-2169	115	22	is	be	AUX
ap-2169	115	23	n	n	ADV
ap-2169	115	24	-	-	PUNCT
ap-2169	115	25	th	th	X
ap-2169	115	26	q	q	ADJ
ap-2169	115	27	-	-	PUNCT
ap-2169	115	28	racah	racah	NOUN
ap-2169	115	29	polynomial	polynomial	ADJ
ap-2169	115	30	with	with	ADP
ap-2169	115	31	parameters	parameter	NOUN
ap-2169	115	32	α	α	X
ap-2169	115	33	,	,	PUNCT
ap-2169	115	34	β	β	X
ap-2169	115	35	,	,	PUNCT
ap-2169	115	36	γ	γ	PROPN
ap-2169	115	37	,	,	PUNCT
ap-2169	115	38	δ	δ	PROPN
ap-2169	115	39	,	,	PUNCT
ap-2169	115	40	and	and	CCONJ
ap-2169	115	41	with	with	ADP
ap-2169	115	42	n	n	NOUN
ap-2169	115	43	=	=	SYM
ap-2169	115	44	0	0	NUM
ap-2169	115	45	,	,	PUNCT
ap-2169	115	46	1	1	NUM
ap-2169	115	47	,	,	PUNCT
ap-2169	115	48	.	.	PUNCT
ap-2169	115	49	.	.	PUNCT
ap-2169	116	1	.	.	PUNCT
ap-2169	117	1	,	,	PUNCT
ap-2169	117	2	n	n	X
ap-2169	117	3	,	,	PUNCT
ap-2169	117	4	where	where	SCONJ
ap-2169	117	5	n	n	PRON
ap-2169	117	6	is	be	AUX
ap-2169	117	7	a	a	DET
ap-2169	117	8	nonnegative	nonnegative	ADJ
ap-2169	117	9	integer	integer	NOUN
ap-2169	117	10	,	,	PUNCT
ap-2169	117	11	µ(x	µ(x	NOUN
ap-2169	117	12	)	)	PUNCT
ap-2169	117	13	=	=	SYM
ap-2169	117	14	q−x	q−x	ADJ
ap-2169	117	15	+	+	CCONJ
ap-2169	117	16	γδqx+1	γδqx+1	ADJ
ap-2169	117	17	,	,	PUNCT
ap-2169	117	18	[	[	X
ap-2169	117	19	a]k	a]k	ADP
ap-2169	117	20	=	=	SYM
ap-2169	117	21	k−1∏	k−1∏	PROPN
ap-2169	117	22	j=0	j=0	PROPN
ap-2169	117	23	(	(	PUNCT
ap-2169	117	24	1−	1−	NUM
ap-2169	117	25	aqj	aqj	NOUN
ap-2169	117	26	)	)	PUNCT
ap-2169	117	27	,	,	PUNCT
ap-2169	118	1	[	[	X
ap-2169	118	2	a]0	a]0	X
ap-2169	118	3	=	=	SYM
ap-2169	118	4	1	1	X
ap-2169	118	5	.	.	PUNCT
ap-2169	118	6	the	the	DET
ap-2169	118	7	parameters	parameter	NOUN
ap-2169	118	8	must	must	AUX
ap-2169	118	9	satisfy	satisfy	VERB
ap-2169	118	10	αq	αq	ADP
ap-2169	118	11	=	=	SYM
ap-2169	118	12	q−n	q−n	PROPN
ap-2169	118	13	or	or	CCONJ
ap-2169	118	14	βδq	βδq	PRON
ap-2169	118	15	=	=	SYM
ap-2169	118	16	q−n	q−n	NOUN
ap-2169	118	17	or	or	CCONJ
ap-2169	118	18	γq	γq	ADP
ap-2169	118	19	=	=	SYM
ap-2169	118	20	q−n	q−n	PROPN
ap-2169	118	21	.	.	PUNCT
ap-2169	119	1	in	in	ADP
ap-2169	119	2	the	the	DET
ap-2169	119	3	definition	definition	NOUN
ap-2169	119	4	of	of	ADP
ap-2169	119	5	basic	basic	ADJ
ap-2169	119	6	hypergeometric	hypergeometric	ADJ
ap-2169	119	7	orthogonal	orthogonal	ADJ
ap-2169	119	8	polynomials	polynomial	NOUN
ap-2169	119	9	it	it	PRON
ap-2169	119	10	is	be	AUX
ap-2169	119	11	usually	usually	ADV
ap-2169	119	12	assumed	assume	VERB
ap-2169	119	13	that	that	SCONJ
ap-2169	119	14	q	q	PUNCT
ap-2169	119	15	∈	∈	PROPN
ap-2169	119	16	(	(	PUNCT
ap-2169	119	17	0	0	NUM
ap-2169	119	18	,	,	PUNCT
ap-2169	119	19	1	1	NUM
ap-2169	119	20	)	)	PUNCT
ap-2169	119	21	.	.	PUNCT
ap-2169	120	1	however	however	ADV
ap-2169	120	2	,	,	PUNCT
ap-2169	120	3	in	in	ADP
ap-2169	120	4	this	this	DET
ap-2169	120	5	calculation	calculation	NOUN
ap-2169	120	6	it	it	PRON
ap-2169	120	7	is	be	AUX
ap-2169	120	8	sufficient	sufficient	ADJ
ap-2169	120	9	to	to	PART
ap-2169	120	10	assume	assume	VERB
ap-2169	120	11	q	q	X
ap-2169	120	12	∈	∈	PROPN
ap-2169	120	13	r	r	NOUN
ap-2169	120	14	\	\	PUNCT
ap-2169	120	15	{	{	PUNCT
ap-2169	120	16	−1	−1	NOUN
ap-2169	120	17	,	,	PUNCT
ap-2169	120	18	0	0	NUM
ap-2169	120	19	,	,	PUNCT
ap-2169	120	20	1	1	NUM
ap-2169	120	21	}	}	PUNCT
ap-2169	120	22	.	.	PUNCT
ap-2169	121	1	the	the	DET
ap-2169	121	2	correspondence	correspondence	NOUN
ap-2169	121	3	has	have	VERB
ap-2169	121	4	the	the	DET
ap-2169	121	5	following	follow	VERB
ap-2169	121	6	form	form	NOUN
ap-2169	121	7	−ijrj	−ijrj	X
ap-2169	122	1	(	(	PUNCT
ap-2169	122	2	µ(k);α	µ(k);α	NOUN
ap-2169	122	3	,	,	PUNCT
ap-2169	122	4	β	β	X
ap-2169	122	5	,	,	PUNCT
ap-2169	122	6	γ	γ	PROPN
ap-2169	122	7	,	,	PUNCT
ap-2169	122	8	δ	δ	PROPN
ap-2169	122	9	|	|	NOUN
ap-2169	122	10	q	q	NOUN
ap-2169	122	11	)	)	PUNCT
ap-2169	123	1	=	=	PUNCT
ap-2169	124	1	[	[	X
ap-2169	124	2	p−1]kj	p−1]kj	X
ap-2169	124	3	=	=	PUNCT
ap-2169	124	4	w−1	w−1	PROPN
ap-2169	124	5	j	j	PROPN
ap-2169	124	6	p̄jk	p̄jk	PROPN
ap-2169	124	7	,	,	PUNCT
ap-2169	124	8	(	(	PUNCT
ap-2169	124	9	9	9	X
ap-2169	124	10	)	)	PUNCT
ap-2169	124	11	where	where	SCONJ
ap-2169	124	12	i	i	PRON
ap-2169	124	13	is	be	AUX
ap-2169	124	14	an	an	DET
ap-2169	124	15	imaginary	imaginary	ADJ
ap-2169	124	16	unit	unit	NOUN
ap-2169	124	17	.	.	PUNCT
ap-2169	125	1	the	the	DET
ap-2169	125	2	weight	weight	NOUN
ap-2169	125	3	sequence	sequence	NOUN
ap-2169	125	4	and	and	CCONJ
ap-2169	125	5	parameters	parameter	NOUN
ap-2169	125	6	are	be	AUX
ap-2169	125	7	wj	wj	NOUN
ap-2169	125	8	=	=	PUNCT
ap-2169	126	1	[	[	X
ap-2169	126	2	q−n	q−n	X
ap-2169	126	3	]	]	X
ap-2169	126	4	j	j	PROPN
ap-2169	127	1	[	[	X
ap-2169	127	2	−q−n	−q−n	X
ap-2169	127	3	]	]	X
ap-2169	127	4	j	j	X
ap-2169	128	1	[	[	X
ap-2169	128	2	q]j	q]j	X
ap-2169	129	1	[	[	X
ap-2169	129	2	−q]j	−q]j	NOUN
ap-2169	129	3	1	1	NUM
ap-2169	129	4	+	+	CCONJ
ap-2169	129	5	q−n+2j	q−n+2j	PROPN
ap-2169	129	6	(	(	PUNCT
ap-2169	129	7	−q−n	−q−n	PROPN
ap-2169	129	8	)	)	PUNCT
ap-2169	129	9	j(1	j(1	PROPN
ap-2169	129	10	+	+	NUM
ap-2169	129	11	q−n	q−n	PROPN
ap-2169	129	12	)	)	PUNCT
ap-2169	129	13	,	,	PUNCT
ap-2169	129	14	α	α	X
ap-2169	129	15	=	=	PUNCT
ap-2169	130	1	β	β	X
ap-2169	130	2	=	=	SYM
ap-2169	130	3	−γ	−γ	NOUN
ap-2169	130	4	=	=	PUNCT
ap-2169	130	5	−δ	−δ	NOUN
ap-2169	130	6	=	=	SYM
ap-2169	130	7	iq	iq	NOUN
ap-2169	130	8	−n−1	−n−1	NUM
ap-2169	130	9	2	2	NUM
ap-2169	130	10	.	.	PUNCT
ap-2169	131	1	(	(	PUNCT
ap-2169	131	2	10	10	NUM
ap-2169	131	3	)	)	PUNCT
ap-2169	131	4	from	from	ADP
ap-2169	131	5	now	now	ADV
ap-2169	131	6	,	,	PUNCT
ap-2169	131	7	we	we	PRON
ap-2169	131	8	will	will	AUX
ap-2169	131	9	again	again	ADV
ap-2169	131	10	omit	omit	VERB
ap-2169	131	11	the	the	DET
ap-2169	131	12	parameters	parameter	NOUN
ap-2169	131	13	of	of	ADP
ap-2169	131	14	the	the	DET
ap-2169	131	15	polynomials	polynomial	NOUN
ap-2169	131	16	and	and	CCONJ
ap-2169	131	17	write	write	VERB
ap-2169	131	18	only	only	ADV
ap-2169	131	19	rn(µ(x	rn(µ(x	NOUN
ap-2169	131	20	)	)	PUNCT
ap-2169	131	21	)	)	PUNCT
ap-2169	131	22	instead	instead	ADV
ap-2169	131	23	of	of	ADP
ap-2169	131	24	rn(µ(x);α	rn(µ(x);α	PROPN
ap-2169	131	25	,	,	PUNCT
ap-2169	131	26	β	β	X
ap-2169	131	27	,	,	PUNCT
ap-2169	131	28	γ	γ	PROPN
ap-2169	131	29	,	,	PUNCT
ap-2169	131	30	δ	δ	PROPN
ap-2169	131	31	|	|	NOUN
ap-2169	131	32	q	q	NOUN
ap-2169	131	33	)	)	PUNCT
ap-2169	131	34	.	.	PUNCT
ap-2169	132	1	in	in	ADP
ap-2169	132	2	order	order	NOUN
ap-2169	132	3	to	to	PART
ap-2169	132	4	prove	prove	VERB
ap-2169	132	5	(	(	PUNCT
ap-2169	132	6	9	9	NUM
ap-2169	132	7	)	)	PUNCT
ap-2169	132	8	,	,	PUNCT
ap-2169	132	9	we	we	PRON
ap-2169	132	10	construct	construct	VERB
ap-2169	132	11	the	the	DET
ap-2169	132	12	recurrence	recurrence	NOUN
ap-2169	132	13	relation	relation	NOUN
ap-2169	132	14	and	and	CCONJ
ap-2169	132	15	compare	compare	VERB
ap-2169	132	16	it	it	PRON
ap-2169	132	17	to	to	ADP
ap-2169	132	18	the	the	DET
ap-2169	132	19	general	general	ADJ
ap-2169	132	20	form	form	NOUN
ap-2169	132	21	of	of	ADP
ap-2169	132	22	the	the	DET
ap-2169	132	23	recurrence	recurrence	NOUN
ap-2169	132	24	relation	relation	NOUN
ap-2169	132	25	for	for	ADP
ap-2169	132	26	q	q	ADJ
ap-2169	132	27	-	-	PUNCT
ap-2169	132	28	racah	racah	ADJ
ap-2169	132	29	polynomials	polynomial	NOUN
ap-2169	132	30	.	.	PUNCT
ap-2169	133	1	the	the	DET
ap-2169	133	2	equation	equation	NOUN
ap-2169	133	3	p−1ϕ(i1	p−1ϕ(i1	NOUN
ap-2169	133	4	)	)	PUNCT
ap-2169	134	1	=	=	PUNCT
ap-2169	134	2	ϕ(i3)p−1	ϕ(i3)p−1	PROPN
ap-2169	134	3	gives	give	VERB
ap-2169	134	4	us	we	PRON
ap-2169	134	5	the	the	DET
ap-2169	134	6	relation	relation	NOUN
ap-2169	134	7	−	−	PROPN
ap-2169	134	8	(	(	PUNCT
ap-2169	134	9	q−n+k	q−n+k	X
ap-2169	134	10	−	−	PROPN
ap-2169	135	1	q−k)rj	q−k)rj	PROPN
ap-2169	135	2	(	(	PUNCT
ap-2169	135	3	µ(k	µ(k	NOUN
ap-2169	135	4	)	)	PUNCT
ap-2169	135	5	)	)	PUNCT
ap-2169	136	1	=	=	PUNCT
ap-2169	136	2	−q	−q	ADJ
ap-2169	136	3	−n	−n	NOUN
ap-2169	136	4	(	(	PUNCT
ap-2169	136	5	1−	1−	NUM
ap-2169	136	6	q2n	q2n	CCONJ
ap-2169	136	7	)	)	PUNCT
ap-2169	136	8	1	1	NUM
ap-2169	137	1	+	+	CCONJ
ap-2169	137	2	q−n+2n	q−n+2n	ADJ
ap-2169	137	3	rj−1	rj−1	NOUN
ap-2169	137	4	(	(	PUNCT
ap-2169	137	5	µ(k	µ(k	NOUN
ap-2169	137	6	)	)	PUNCT
ap-2169	137	7	)	)	PUNCT
ap-2169	138	1	+	+	CCONJ
ap-2169	138	2	1−	1−	NUM
ap-2169	138	3	q−2n+2n	q−2n+2n	VERB
ap-2169	138	4	1	1	NUM
ap-2169	139	1	+	+	CCONJ
ap-2169	139	2	q−n+2n	q−n+2n	ADJ
ap-2169	139	3	rj+1	rj+1	NOUN
ap-2169	139	4	(	(	PUNCT
ap-2169	139	5	µ(k	µ(k	NOUN
ap-2169	139	6	)	)	PUNCT
ap-2169	139	7	)	)	PUNCT
ap-2169	139	8	.	.	PUNCT
ap-2169	140	1	(	(	PUNCT
ap-2169	140	2	11	11	X
ap-2169	140	3	)	)	PUNCT
ap-2169	140	4	we	we	PRON
ap-2169	140	5	can	can	AUX
ap-2169	140	6	see	see	VERB
ap-2169	140	7	that	that	SCONJ
ap-2169	140	8	this	this	DET
ap-2169	140	9	form	form	NOUN
ap-2169	140	10	corresponds	correspond	VERB
ap-2169	140	11	to	to	ADP
ap-2169	140	12	the	the	DET
ap-2169	140	13	general	general	ADJ
ap-2169	140	14	recurrence	recurrence	NOUN
ap-2169	140	15	(	(	PUNCT
ap-2169	140	16	see	see	VERB
ap-2169	140	17	[	[	X
ap-2169	140	18	10	10	NUM
ap-2169	140	19	]	]	SYM
ap-2169	140	20	)	)	PUNCT
ap-2169	140	21	−	−	PROPN
ap-2169	141	1	(	(	PUNCT
ap-2169	141	2	1−	1−	NUM
ap-2169	141	3	q−x)(1−	q−x)(1−	VERB
ap-2169	141	4	γδqx+1)rn	γδqx+1)rn	PROPN
ap-2169	141	5	(	(	PUNCT
ap-2169	141	6	µ(x	µ(x	X
ap-2169	141	7	)	)	PUNCT
ap-2169	141	8	)	)	PUNCT
ap-2169	142	1	=	=	SYM
ap-2169	142	2	anrn+1	anrn+1	NOUN
ap-2169	142	3	(	(	PUNCT
ap-2169	142	4	µ(x	µ(x	NOUN
ap-2169	142	5	)	)	PUNCT
ap-2169	142	6	)	)	PUNCT
ap-2169	142	7	−	−	PROPN
ap-2169	142	8	(	(	PUNCT
ap-2169	142	9	an	an	DET
ap-2169	142	10	+	+	NOUN
ap-2169	142	11	cn)rn	cn)rn	ADP
ap-2169	142	12	(	(	PUNCT
ap-2169	142	13	µ(x	µ(x	X
ap-2169	142	14	)	)	PUNCT
ap-2169	142	15	)	)	PUNCT
ap-2169	143	1	+	+	CCONJ
ap-2169	143	2	cnrn−1	cnrn−1	PROPN
ap-2169	143	3	(	(	PUNCT
ap-2169	143	4	µ(x	µ(x	PROPN
ap-2169	143	5	)	)	PUNCT
ap-2169	143	6	)	)	PUNCT
ap-2169	143	7	,	,	PUNCT
ap-2169	143	8	(	(	PUNCT
ap-2169	143	9	12	12	NUM
ap-2169	143	10	)	)	PUNCT
ap-2169	143	11	where	where	SCONJ
ap-2169	143	12	an	an	DET
ap-2169	143	13	=(	=(	NOUN
ap-2169	143	14	1−	1−	NUM
ap-2169	143	15	αqn+1)(1−	αqn+1)(1−	PROPN
ap-2169	143	16	αβqn+1	αβqn+1	PROPN
ap-2169	143	17	)	)	PUNCT
ap-2169	143	18	1−	1−	NUM
ap-2169	143	19	αβq2n+1	αβq2n+1	NOUN
ap-2169	143	20	(	(	PUNCT
ap-2169	143	21	1−	1−	NUM
ap-2169	143	22	βδqn+1)(1−	βδqn+1)(1−	PROPN
ap-2169	143	23	γqn+1	γqn+1	NUM
ap-2169	143	24	)	)	PUNCT
ap-2169	143	25	1−	1−	NUM
ap-2169	143	26	αβq2n+2	αβq2n+2	NUM
ap-2169	143	27	,	,	PUNCT
ap-2169	143	28	cn	cn	X
ap-2169	143	29	=	=	NOUN
ap-2169	143	30	q(1−	q(1−	NOUN
ap-2169	143	31	qn)(1−	qn)(1−	ADJ
ap-2169	143	32	βqn)(γ	βqn)(γ	NOUN
ap-2169	143	33	−	−	PROPN
ap-2169	143	34	αβqn)(δ	αβqn)(δ	NOUN
ap-2169	143	35	−	−	PROPN
ap-2169	143	36	αqn	αqn	NOUN
ap-2169	143	37	)	)	PUNCT
ap-2169	143	38	(	(	PUNCT
ap-2169	143	39	1−	1−	NUM
ap-2169	143	40	αβq2n)(1−	αβq2n)(1−	NUM
ap-2169	143	41	αβq2n+1	αβq2n+1	NOUN
ap-2169	143	42	)	)	PUNCT
ap-2169	143	43	,	,	PUNCT
ap-2169	143	44	if	if	SCONJ
ap-2169	143	45	the	the	DET
ap-2169	143	46	parameters	parameter	NOUN
ap-2169	143	47	are	be	AUX
ap-2169	143	48	set	set	VERB
ap-2169	143	49	up	up	ADP
ap-2169	143	50	the	the	DET
ap-2169	143	51	way	way	NOUN
ap-2169	143	52	as	as	ADP
ap-2169	143	53	in	in	ADP
ap-2169	143	54	(	(	PUNCT
ap-2169	143	55	10	10	NUM
ap-2169	143	56	)	)	PUNCT
ap-2169	143	57	.	.	PUNCT
ap-2169	144	1	the	the	DET
ap-2169	144	2	way	way	NOUN
ap-2169	144	3	of	of	ADP
ap-2169	144	4	deriving	derive	VERB
ap-2169	144	5	the	the	DET
ap-2169	144	6	weight	weight	NOUN
ap-2169	144	7	sequence	sequence	NOUN
ap-2169	144	8	is	be	AUX
ap-2169	144	9	similar	similar	ADJ
ap-2169	144	10	to	to	ADP
ap-2169	144	11	the	the	DET
ap-2169	144	12	former	former	ADJ
ap-2169	144	13	case	case	NOUN
ap-2169	144	14	.	.	PUNCT
ap-2169	145	1	we	we	PRON
ap-2169	145	2	again	again	ADV
ap-2169	145	3	try	try	VERB
ap-2169	145	4	to	to	PART
ap-2169	145	5	find	find	VERB
ap-2169	145	6	a	a	DET
ap-2169	145	7	diagonal	diagonal	ADJ
ap-2169	145	8	matrix	matrix	NOUN
ap-2169	145	9	a.	a.	NOUN
ap-2169	145	10	however	however	ADV
ap-2169	145	11	,	,	PUNCT
ap-2169	145	12	there	there	PRON
ap-2169	145	13	is	be	VERB
ap-2169	145	14	no	no	DET
ap-2169	145	15	diagonal	diagonal	ADJ
ap-2169	145	16	matrix	matrix	NOUN
ap-2169	145	17	that	that	PRON
ap-2169	145	18	transforms	transform	VERB
ap-2169	145	19	ϕ(i1	ϕ(i1	NOUN
ap-2169	145	20	)	)	PUNCT
ap-2169	145	21	to	to	ADP
ap-2169	145	22	a	a	DET
ap-2169	145	23	hermitian	hermitian	ADJ
ap-2169	145	24	matrix	matrix	NOUN
ap-2169	145	25	.	.	PUNCT
ap-2169	146	1	nevertheless	nevertheless	ADV
ap-2169	146	2	,	,	PUNCT
ap-2169	146	3	we	we	PRON
ap-2169	146	4	can	can	AUX
ap-2169	146	5	transform	transform	VERB
ap-2169	146	6	ϕ(i1	ϕ(i1	NOUN
ap-2169	146	7	)	)	PUNCT
ap-2169	146	8	to	to	ADP
ap-2169	146	9	a	a	DET
ap-2169	146	10	symmetric	symmetric	ADJ
ap-2169	146	11	matrix	matrix	NOUN
ap-2169	146	12	and	and	CCONJ
ap-2169	146	13	then	then	ADV
ap-2169	146	14	show	show	VERB
ap-2169	146	15	that	that	SCONJ
ap-2169	146	16	the	the	DET
ap-2169	146	17	transformed	transform	VERB
ap-2169	146	18	matrix	matrix	NOUN
ap-2169	146	19	is	be	AUX
ap-2169	146	20	normal	normal	ADJ
ap-2169	146	21	.	.	PUNCT
ap-2169	147	1	the	the	DET
ap-2169	147	2	elements	element	NOUN
ap-2169	147	3	of	of	ADP
ap-2169	147	4	a	a	DET
ap-2169	147	5	have	have	NOUN
ap-2169	147	6	to	to	PART
ap-2169	147	7	satisfy	satisfy	VERB
ap-2169	147	8	a2	a2	PROPN
ap-2169	147	9	j	j	PROPN
ap-2169	147	10	=	=	PROPN
ap-2169	147	11	a2	a2	PROPN
ap-2169	147	12	j−1	j−1	PROPN
ap-2169	148	1	[	[	X
ap-2169	148	2	ϕ(i1)]j	ϕ(i1)]j	PROPN
ap-2169	148	3	,	,	PUNCT
ap-2169	148	4	j−1	j−1	PROPN
ap-2169	149	1	[	[	X
ap-2169	149	2	ϕ(i1)]j−1,j	ϕ(i1)]j−1,j	NOUN
ap-2169	149	3	=	=	SYM
ap-2169	149	4	a2	a2	NOUN
ap-2169	149	5	j−1	j−1	PROPN
ap-2169	149	6	−(q2m−j+1	−(q2m−j+1	PROPN
ap-2169	149	7	−	−	PROPN
ap-2169	149	8	q−2m+j−1)(q−m+j	q−2m+j−1)(q−m+j	PROPN
ap-2169	149	9	+	+	X
ap-2169	149	10	qm−j	qm−j	ADJ
ap-2169	149	11	)	)	PUNCT
ap-2169	150	1	(	(	PUNCT
ap-2169	150	2	qj	qj	PROPN
ap-2169	150	3	−	−	PROPN
ap-2169	150	4	q−j)(q−m+j−1	q−j)(q−m+j−1	PROPN
ap-2169	150	5	+	+	CCONJ
ap-2169	150	6	qm−j+1	qm−j+1	PROPN
ap-2169	150	7	)	)	PUNCT
ap-2169	150	8	.	.	PUNCT
ap-2169	151	1	the	the	DET
ap-2169	151	2	elements	element	NOUN
ap-2169	151	3	are	be	AUX
ap-2169	151	4	determined	determine	VERB
ap-2169	151	5	up	up	ADP
ap-2169	151	6	to	to	ADP
ap-2169	151	7	a	a	DET
ap-2169	151	8	multiplicative	multiplicative	ADJ
ap-2169	151	9	constant	constant	NOUN
ap-2169	151	10	as	as	ADP
ap-2169	151	11	a	a	DET
ap-2169	151	12	product	product	NOUN
ap-2169	151	13	a2	a2	PROPN
ap-2169	151	14	j	j	PROPN
ap-2169	151	15	=	=	SYM
ap-2169	151	16	j∏	j∏	PROPN
ap-2169	151	17	k=1	k=1	PUNCT
ap-2169	152	1	−	−	PROPN
ap-2169	152	2	(	(	PUNCT
ap-2169	152	3	q2m−k+1	q2m−k+1	VERB
ap-2169	152	4	−	−	PROPN
ap-2169	152	5	q−2m+k−1)(q−m+k	q−2m+k−1)(q−m+k	PROPN
ap-2169	152	6	+	+	CCONJ
ap-2169	152	7	qm−k	qm−k	NOUN
ap-2169	152	8	)	)	PUNCT
ap-2169	152	9	(	(	PUNCT
ap-2169	152	10	qk	qk	AUX
ap-2169	152	11	−	−	PROPN
ap-2169	152	12	q−k)(q−m+k−1	q−k)(q−m+k−1	PROPN
ap-2169	152	13	+	+	CCONJ
ap-2169	152	14	qm−k+1	qm−k+1	NOUN
ap-2169	152	15	)	)	PUNCT
ap-2169	152	16	=	=	SYM
ap-2169	153	1	j∏	j∏	PROPN
ap-2169	153	2	k=1	k=1	PUNCT
ap-2169	153	3	q2	q2	PROPN
ap-2169	153	4	m	m	PROPN
ap-2169	153	5	(	(	PUNCT
ap-2169	153	6	1−	1−	NUM
ap-2169	153	7	q−4m+2k−2)(1	q−4m+2k−2)(1	NOUN
ap-2169	153	8	+	+	CCONJ
ap-2169	153	9	q−2m+2k	q−2m+2k	NOUN
ap-2169	153	10	)	)	PUNCT
ap-2169	153	11	(	(	PUNCT
ap-2169	153	12	1−	1−	NUM
ap-2169	153	13	q2k)(1	q2k)(1	NUM
ap-2169	153	14	+	+	SYM
ap-2169	153	15	q−2m+2k−2	q−2m+2k−2	PART
ap-2169	153	16	)	)	PUNCT
ap-2169	153	17	=	=	SYM
ap-2169	154	1	j∏	j∏	PROPN
ap-2169	154	2	k=1	k=1	X
ap-2169	154	3	(	(	PUNCT
ap-2169	154	4	1−	1−	NUM
ap-2169	154	5	q−n+k−1)(1	q−n+k−1)(1	NOUN
ap-2169	154	6	+	+	CCONJ
ap-2169	154	7	q−n+k−1)(1	q−n+k−1)(1	ADP
ap-2169	154	8	+	+	CCONJ
ap-2169	154	9	q−n+2k	q−n+2k	NOUN
ap-2169	154	10	)	)	PUNCT
ap-2169	154	11	q−n	q−n	PROPN
ap-2169	154	12	(	(	PUNCT
ap-2169	154	13	1−	1−	NUM
ap-2169	154	14	qk)(1	qk)(1	X
ap-2169	154	15	+	+	ADP
ap-2169	154	16	qk)(1	qk)(1	NOUN
ap-2169	154	17	+	+	NOUN
ap-2169	154	18	q−n+2k−2	q−n+2k−2	NOUN
ap-2169	154	19	)	)	PUNCT
ap-2169	154	20	=	=	NOUN
ap-2169	155	1	[	[	X
ap-2169	155	2	q−n	q−n	X
ap-2169	155	3	]	]	X
ap-2169	155	4	j	j	PROPN
ap-2169	156	1	[	[	X
ap-2169	156	2	−q−n	−q−n	X
ap-2169	156	3	]	]	X
ap-2169	156	4	j	j	X
ap-2169	157	1	[	[	X
ap-2169	157	2	q]j	q]j	X
ap-2169	158	1	[	[	X
ap-2169	158	2	−q]j	−q]j	NOUN
ap-2169	158	3	1	1	NUM
ap-2169	158	4	+	+	CCONJ
ap-2169	158	5	q−n+2j	q−n+2j	ADJ
ap-2169	158	6	(	(	PUNCT
ap-2169	158	7	q−n	q−n	PROPN
ap-2169	158	8	)	)	PUNCT
ap-2169	158	9	j(1	j(1	PROPN
ap-2169	158	10	+	+	NUM
ap-2169	158	11	q−n	q−n	NOUN
ap-2169	158	12	)	)	PUNCT
ap-2169	158	13	.	.	PUNCT
ap-2169	159	1	if	if	SCONJ
ap-2169	159	2	we	we	PRON
ap-2169	159	3	assume	assume	VERB
ap-2169	159	4	q	q	X
ap-2169	159	5	∈	∈	PROPN
ap-2169	159	6	(	(	PUNCT
ap-2169	159	7	0	0	NUM
ap-2169	159	8	,	,	PUNCT
ap-2169	159	9	1	1	NUM
ap-2169	159	10	)	)	PUNCT
ap-2169	159	11	then	then	ADV
ap-2169	159	12	for	for	SCONJ
ap-2169	159	13	all	all	DET
ap-2169	159	14	k	k	PROPN
ap-2169	159	15	≥	≥	NUM
ap-2169	159	16	1	1	NUM
ap-2169	159	17	the	the	DET
ap-2169	159	18	factor	factor	NOUN
ap-2169	159	19	1−	1−	NUM
ap-2169	159	20	q−n+k−1	q−n+k−1	NOUN
ap-2169	159	21	is	be	AUX
ap-2169	159	22	negative	negative	ADJ
ap-2169	159	23	whereas	whereas	SCONJ
ap-2169	159	24	the	the	DET
ap-2169	159	25	other	other	ADJ
ap-2169	159	26	factors	factor	NOUN
ap-2169	159	27	are	be	AUX
ap-2169	159	28	positive	positive	ADJ
ap-2169	159	29	.	.	PUNCT
ap-2169	160	1	therefore	therefore	ADV
ap-2169	160	2	,	,	PUNCT
ap-2169	160	3	|aj	|aj	NOUN
ap-2169	160	4	|2	|2	NUM
ap-2169	160	5	=	=	SYM
ap-2169	160	6	(	(	PUNCT
ap-2169	160	7	−1)ja2	−1)ja2	PROPN
ap-2169	160	8	j	j	PROPN
ap-2169	160	9	.	.	PUNCT
ap-2169	161	1	it	it	PRON
ap-2169	161	2	can	can	AUX
ap-2169	161	3	be	be	AUX
ap-2169	161	4	easily	easily	ADV
ap-2169	161	5	seen	see	VERB
ap-2169	161	6	that	that	SCONJ
ap-2169	161	7	this	this	PRON
ap-2169	161	8	holds	hold	VERB
ap-2169	161	9	for	for	ADP
ap-2169	161	10	all	all	DET
ap-2169	161	11	q	q	PROPN
ap-2169	161	12	∈	∈	PROPN
ap-2169	161	13	r\{−1	r\{−1	NOUN
ap-2169	161	14	,	,	PUNCT
ap-2169	161	15	0	0	NUM
ap-2169	161	16	,	,	PUNCT
ap-2169	161	17	1	1	NUM
ap-2169	161	18	}	}	PUNCT
ap-2169	161	19	by	by	ADP
ap-2169	161	20	similar	similar	ADJ
ap-2169	161	21	reasoning	reasoning	NOUN
ap-2169	161	22	.	.	PUNCT
ap-2169	162	1	finally	finally	ADV
ap-2169	162	2	,	,	PUNCT
ap-2169	162	3	we	we	PRON
ap-2169	162	4	have	have	VERB
ap-2169	162	5	|aj	|aj	NUM
ap-2169	162	6	|2	|2	NUM
ap-2169	162	7	=	=	SYM
ap-2169	162	8	wj	wj	NOUN
ap-2169	162	9	.	.	PUNCT
ap-2169	163	1	now	now	ADV
ap-2169	163	2	we	we	PRON
ap-2169	163	3	just	just	ADV
ap-2169	163	4	need	need	VERB
ap-2169	163	5	to	to	PART
ap-2169	163	6	verify	verify	VERB
ap-2169	163	7	that	that	PRON
ap-2169	163	8	b	b	X
ap-2169	163	9	:	:	PUNCT
ap-2169	163	10	=	=	SYM
ap-2169	163	11	a−1ϕ(i1)a	a−1ϕ(i1)a	ADV
ap-2169	163	12	is	be	AUX
ap-2169	163	13	normal	normal	ADJ
ap-2169	163	14	using	use	VERB
ap-2169	163	15	the	the	DET
ap-2169	163	16	fact	fact	NOUN
ap-2169	163	17	that	that	SCONJ
ap-2169	163	18	b	b	NOUN
ap-2169	163	19	is	be	AUX
ap-2169	163	20	symmetric	symmetric	ADJ
ap-2169	163	21	.	.	PUNCT
ap-2169	164	1	thus	thus	ADV
ap-2169	164	2	,	,	PUNCT
ap-2169	164	3	we	we	PRON
ap-2169	164	4	have	have	VERB
ap-2169	164	5	to	to	PART
ap-2169	164	6	verify	verify	VERB
ap-2169	164	7	∑	∑	PROPN
ap-2169	164	8	bjlb̄kl	bjlb̄kl	PROPN
ap-2169	164	9	=	=	PROPN
ap-2169	164	10	∑	∑	PUNCT
ap-2169	164	11	b̄jlbkl	b̄jlbkl	NOUN
ap-2169	164	12	.	.	PUNCT
ap-2169	165	1	we	we	PRON
ap-2169	165	2	can	can	AUX
ap-2169	165	3	just	just	ADV
ap-2169	165	4	show	show	VERB
ap-2169	165	5	that	that	SCONJ
ap-2169	165	6	for	for	ADP
ap-2169	165	7	all	all	DET
ap-2169	165	8	indices	index	NOUN
ap-2169	165	9	j	j	PROPN
ap-2169	165	10	,	,	PUNCT
ap-2169	165	11	k	k	PROPN
ap-2169	165	12	,	,	PUNCT
ap-2169	165	13	l	l	NOUN
ap-2169	165	14	we	we	PRON
ap-2169	165	15	have	have	VERB
ap-2169	165	16	bjlb̄kl	bjlb̄kl	PROPN
ap-2169	165	17	=	=	SYM
ap-2169	165	18	a−1	a−1	PROPN
ap-2169	165	19	j	j	PROPN
ap-2169	166	1	[	[	X
ap-2169	166	2	ϕ(i1)]jlalā−1	ϕ(i1)]jlalā−1	X
ap-2169	166	3	k	k	X
ap-2169	167	1	[	[	X
ap-2169	167	2	ϕ(i1)]klāl	ϕ(i1)]klāl	X
ap-2169	167	3	∈	∈	PROPN
ap-2169	167	4	r.	r.	PROPN
ap-2169	167	5	since	since	SCONJ
ap-2169	167	6	ϕ(i1	ϕ(i1	PROPN
ap-2169	167	7	)	)	PUNCT
ap-2169	167	8	is	be	AUX
ap-2169	167	9	real	real	ADJ
ap-2169	167	10	and	and	CCONJ
ap-2169	167	11	alāl	alāl	PROPN
ap-2169	167	12	=	=	PUNCT
ap-2169	167	13	|al|2	|al|2	PROPN
ap-2169	167	14	,	,	PUNCT
ap-2169	167	15	we	we	PRON
ap-2169	167	16	just	just	ADV
ap-2169	167	17	have	have	VERB
ap-2169	167	18	to	to	PART
ap-2169	167	19	decide	decide	VERB
ap-2169	167	20	whether	whether	SCONJ
ap-2169	167	21	ajak	ajak	ADV
ap-2169	167	22	is	be	AUX
ap-2169	167	23	real	real	ADJ
ap-2169	167	24	for	for	ADP
ap-2169	167	25	indices	index	NOUN
ap-2169	167	26	j	j	PROPN
ap-2169	167	27	,	,	PUNCT
ap-2169	167	28	k	k	PROPN
ap-2169	167	29	,	,	PUNCT
ap-2169	167	30	whose	whose	DET
ap-2169	167	31	difference	difference	NOUN
ap-2169	167	32	is	be	AUX
ap-2169	167	33	even	even	ADV
ap-2169	167	34	(	(	PUNCT
ap-2169	167	35	otherwise	otherwise	ADV
ap-2169	167	36	[	[	X
ap-2169	167	37	ϕ(i1)]jl	ϕ(i1)]jl	PROPN
ap-2169	167	38	or	or	CCONJ
ap-2169	167	39	[	[	X
ap-2169	167	40	ϕ(i1)]kl	ϕ(i1)]kl	PROPN
ap-2169	167	41	is	be	AUX
ap-2169	167	42	zero	zero	NUM
ap-2169	167	43	due	due	ADP
ap-2169	167	44	to	to	ADP
ap-2169	167	45	its	its	PRON
ap-2169	167	46	special	special	ADJ
ap-2169	167	47	form	form	NOUN
ap-2169	167	48	)	)	PUNCT
ap-2169	167	49	.	.	PUNCT
ap-2169	168	1	considering	consider	VERB
ap-2169	168	2	a2	a2	PROPN
ap-2169	168	3	j	j	PROPN
ap-2169	168	4	is	be	AUX
ap-2169	168	5	real	real	ADJ
ap-2169	168	6	and	and	CCONJ
ap-2169	168	7	alternates	alternate	NOUN
ap-2169	168	8	,	,	PUNCT
ap-2169	168	9	we	we	PRON
ap-2169	168	10	see	see	VERB
ap-2169	168	11	that	that	SCONJ
ap-2169	168	12	aj	aj	PROPN
ap-2169	168	13	and	and	CCONJ
ap-2169	168	14	ak	ak	PROPN
ap-2169	168	15	are	be	AUX
ap-2169	168	16	both	both	ADV
ap-2169	168	17	real	real	ADJ
ap-2169	168	18	or	or	CCONJ
ap-2169	168	19	purely	purely	ADV
ap-2169	168	20	imaginary	imaginary	ADJ
ap-2169	168	21	.	.	PUNCT
ap-2169	169	1	therefore	therefore	ADV
ap-2169	169	2	,	,	PUNCT
ap-2169	169	3	ajak	ajak	PROPN
ap-2169	169	4	∈	∈	PROPN
ap-2169	169	5	r.	r.	PROPN
ap-2169	169	6	4	4	NUM
ap-2169	169	7	.	.	PUNCT
ap-2169	170	1	conclusion	conclusion	NOUN
ap-2169	170	2	on	on	ADP
ap-2169	170	3	the	the	DET
ap-2169	170	4	example	example	NOUN
ap-2169	170	5	of	of	ADP
ap-2169	170	6	the	the	DET
ap-2169	170	7	algebra	algebra	NOUN
ap-2169	170	8	u	u	NOUN
ap-2169	170	9	′q(so3	′q(so3	PART
ap-2169	170	10	)	)	PUNCT
ap-2169	171	1	we	we	PRON
ap-2169	171	2	have	have	AUX
ap-2169	171	3	shown	show	VERB
ap-2169	171	4	that	that	SCONJ
ap-2169	171	5	the	the	DET
ap-2169	171	6	existence	existence	NOUN
ap-2169	171	7	of	of	ADP
ap-2169	171	8	a	a	DET
ap-2169	171	9	complete	complete	ADJ
ap-2169	171	10	classification	classification	NOUN
ap-2169	171	11	of	of	ADP
ap-2169	171	12	representations	representation	NOUN
ap-2169	171	13	together	together	ADV
ap-2169	171	14	with	with	ADP
ap-2169	171	15	a	a	DET
ap-2169	171	16	suitable	suitable	ADJ
ap-2169	171	17	use	use	NOUN
ap-2169	171	18	of	of	ADP
ap-2169	171	19	some	some	DET
ap-2169	171	20	automorphism	automorphism	NOUN
ap-2169	171	21	can	can	AUX
ap-2169	171	22	produce	produce	VERB
ap-2169	171	23	as	as	ADP
ap-2169	171	24	a	a	DET
ap-2169	171	25	by	by	ADP
ap-2169	171	26	-	-	PUNCT
ap-2169	171	27	product	product	NOUN
ap-2169	171	28	a	a	DET
ap-2169	171	29	set	set	NOUN
ap-2169	171	30	of	of	ADP
ap-2169	171	31	396	396	NUM
ap-2169	171	32	vol	vol	NOUN
ap-2169	171	33	.	.	PUNCT
ap-2169	172	1	54	54	NUM
ap-2169	172	2	no	no	NOUN
ap-2169	172	3	.	.	PUNCT
ap-2169	173	1	6/2014	6/2014	NUM
ap-2169	173	2	automorphisms	automorphism	NOUN
ap-2169	173	3	of	of	ADP
ap-2169	173	4	algebras	algebras	PROPN
ap-2169	173	5	and	and	CCONJ
ap-2169	173	6	orthogonal	orthogonal	ADJ
ap-2169	173	7	polynomials	polynomial	NOUN
ap-2169	173	8	orthogonal	orthogonal	ADJ
ap-2169	173	9	polynomials	polynomial	NOUN
ap-2169	173	10	(	(	PUNCT
ap-2169	173	11	see	see	VERB
ap-2169	173	12	also	also	ADV
ap-2169	173	13	[	[	X
ap-2169	173	14	11	11	NUM
ap-2169	173	15	]	]	NUM
ap-2169	173	16	)	)	PUNCT
ap-2169	173	17	.	.	PUNCT
ap-2169	174	1	because	because	SCONJ
ap-2169	174	2	the	the	DET
ap-2169	174	3	algebra	algebra	NOUN
ap-2169	174	4	u	u	NOUN
ap-2169	174	5	′q(so3	′q(so3	NUM
ap-2169	174	6	)	)	PUNCT
ap-2169	174	7	is	be	AUX
ap-2169	174	8	a	a	DET
ap-2169	174	9	special	special	ADJ
ap-2169	174	10	case	case	NOUN
ap-2169	174	11	of	of	ADP
ap-2169	174	12	askey	askey	NOUN
ap-2169	174	13	-	-	PUNCT
ap-2169	174	14	wilson	wilson	NOUN
ap-2169	174	15	algebra	algebra	PROPN
ap-2169	174	16	aw	aw	INTJ
ap-2169	174	17	(	(	PUNCT
ap-2169	174	18	3	3	NUM
ap-2169	174	19	)	)	PUNCT
ap-2169	174	20	,	,	PUNCT
ap-2169	174	21	introduced	introduce	VERB
ap-2169	174	22	by	by	ADP
ap-2169	174	23	zhedanov	zhedanov	PROPN
ap-2169	174	24	[	[	X
ap-2169	174	25	12	12	NUM
ap-2169	174	26	]	]	PUNCT
ap-2169	174	27	,	,	PUNCT
ap-2169	174	28	it	it	PRON
ap-2169	174	29	would	would	AUX
ap-2169	174	30	be	be	AUX
ap-2169	174	31	nice	nice	ADJ
ap-2169	174	32	to	to	PART
ap-2169	174	33	generalize	generalize	VERB
ap-2169	174	34	this	this	DET
ap-2169	174	35	approach	approach	NOUN
ap-2169	174	36	to	to	ADP
ap-2169	174	37	this	this	DET
ap-2169	174	38	case	case	NOUN
ap-2169	174	39	(	(	PUNCT
ap-2169	174	40	see	see	VERB
ap-2169	174	41	also	also	ADV
ap-2169	174	42	[	[	X
ap-2169	174	43	13–16	13–16	NUM
ap-2169	174	44	]	]	NUM
ap-2169	174	45	)	)	PUNCT
ap-2169	174	46	.	.	PUNCT
ap-2169	175	1	references	reference	NOUN
ap-2169	175	2	[	[	X
ap-2169	175	3	1	1	NUM
ap-2169	175	4	]	]	PUNCT
ap-2169	175	5	w.	w.	PROPN
ap-2169	175	6	miller	miller	PROPN
ap-2169	175	7	,	,	PUNCT
ap-2169	175	8	jr	jr	PROPN
ap-2169	175	9	.	.	PROPN
ap-2169	175	10	lie	lie	PROPN
ap-2169	175	11	theory	theory	NOUN
ap-2169	175	12	and	and	CCONJ
ap-2169	175	13	difference	difference	NOUN
ap-2169	175	14	equations	equation	NOUN
ap-2169	175	15	.	.	PUNCT
ap-2169	176	1	i.	i.	PROPN
ap-2169	176	2	j	j	PROPN
ap-2169	176	3	math	math	PROPN
ap-2169	176	4	anal	anal	PROPN
ap-2169	176	5	appl	appl	PROPN
ap-2169	176	6	28:383–399	28:383–399	PROPN
ap-2169	176	7	,	,	PUNCT
ap-2169	176	8	1969	1969	NUM
ap-2169	176	9	.	.	PUNCT
ap-2169	177	1	[	[	X
ap-2169	177	2	2	2	X
ap-2169	177	3	]	]	PUNCT
ap-2169	177	4	t.	t.	PROPN
ap-2169	177	5	h.	h.	PROPN
ap-2169	177	6	koornwinder	koornwinder	PROPN
ap-2169	177	7	.	.	PUNCT
ap-2169	178	1	krawtchouk	krawtchouk	PROPN
ap-2169	178	2	polynomials	polynomial	NOUN
ap-2169	178	3	,	,	PUNCT
ap-2169	178	4	a	a	DET
ap-2169	178	5	unification	unification	NOUN
ap-2169	178	6	of	of	ADP
ap-2169	178	7	two	two	NUM
ap-2169	178	8	different	different	ADJ
ap-2169	178	9	group	group	NOUN
ap-2169	178	10	theoretic	theoretic	NOUN
ap-2169	178	11	interpretations	interpretation	NOUN
ap-2169	178	12	.	.	PUNCT
ap-2169	179	1	siam	siam	PROPN
ap-2169	179	2	j	j	PROPN
ap-2169	179	3	math	math	PROPN
ap-2169	179	4	anal	anal	PROPN
ap-2169	179	5	13(6):1011–1023	13(6):1011–1023	NUM
ap-2169	179	6	,	,	PUNCT
ap-2169	179	7	1982	1982	NUM
ap-2169	179	8	.	.	PUNCT
ap-2169	180	1	doi:10.1137/0513072	doi:10.1137/0513072	NOUN
ap-2169	180	2	.	.	PUNCT
ap-2169	181	1	[	[	X
ap-2169	181	2	3	3	X
ap-2169	181	3	]	]	X
ap-2169	181	4	p.	p.	NOUN
ap-2169	181	5	feinsilver	feinsilver	ADV
ap-2169	181	6	.	.	PUNCT
ap-2169	182	1	lie	lie	PROPN
ap-2169	182	2	algebras	algebra	NOUN
ap-2169	182	3	and	and	CCONJ
ap-2169	182	4	recurrence	recurrence	NOUN
ap-2169	182	5	relations	relation	NOUN
ap-2169	182	6	.	.	PUNCT
ap-2169	183	1	i.	i.	PROPN
ap-2169	183	2	acta	acta	PROPN
ap-2169	183	3	appl	appl	PROPN
ap-2169	183	4	math	math	PROPN
ap-2169	183	5	13(3):291–333	13(3):291–333	PROPN
ap-2169	183	6	,	,	PUNCT
ap-2169	183	7	1988	1988	NUM
ap-2169	183	8	.	.	PUNCT
ap-2169	184	1	[	[	X
ap-2169	184	2	4	4	X
ap-2169	184	3	]	]	X
ap-2169	184	4	y.	y.	PROPN
ap-2169	184	5	i.	i.	PROPN
ap-2169	184	6	granovskĭı	granovskĭı	PROPN
ap-2169	184	7	,	,	PUNCT
ap-2169	184	8	a.	a.	PROPN
ap-2169	184	9	s.	s.	PROPN
ap-2169	184	10	zhedanov	zhedanov	PROPN
ap-2169	184	11	.	.	PUNCT
ap-2169	185	1	orthogonal	orthogonal	ADJ
ap-2169	185	2	polynomials	polynomial	NOUN
ap-2169	185	3	on	on	ADP
ap-2169	185	4	lie	lie	NOUN
ap-2169	185	5	algebras	algebras	PROPN
ap-2169	185	6	.	.	PUNCT
ap-2169	186	1	izv	izv	PROPN
ap-2169	186	2	vyssh	vyssh	PROPN
ap-2169	186	3	uchebn	uchebn	NOUN
ap-2169	186	4	zaved	zave	VERB
ap-2169	186	5	fiz	fiz	PROPN
ap-2169	186	6	29(5):60–66	29(5):60–66	NUM
ap-2169	186	7	,	,	PUNCT
ap-2169	186	8	1986	1986	NUM
ap-2169	186	9	.	.	PUNCT
ap-2169	187	1	[	[	X
ap-2169	187	2	5	5	NUM
ap-2169	187	3	]	]	PUNCT
ap-2169	187	4	k.	k.	PROPN
ap-2169	187	5	nomura	nomura	PROPN
ap-2169	187	6	,	,	PUNCT
ap-2169	187	7	p.	p.	PROPN
ap-2169	187	8	terwilliger	terwilliger	NOUN
ap-2169	187	9	.	.	PUNCT
ap-2169	188	1	krawtchouk	krawtchouk	PROPN
ap-2169	188	2	polynomials	polynomial	NOUN
ap-2169	188	3	,	,	PUNCT
ap-2169	188	4	the	the	DET
ap-2169	188	5	lie	lie	NOUN
ap-2169	188	6	algebra	algebra	PROPN
ap-2169	188	7	sl2	sl2	PROPN
ap-2169	188	8	,	,	PUNCT
ap-2169	188	9	and	and	CCONJ
ap-2169	188	10	leonard	leonard	PROPN
ap-2169	188	11	pairs	pair	NOUN
ap-2169	188	12	.	.	PUNCT
ap-2169	189	1	linear	linear	ADJ
ap-2169	189	2	algebra	algebra	PROPN
ap-2169	189	3	appl	appl	PROPN
ap-2169	189	4	437(1):345–375	437(1):345–375	PROPN
ap-2169	189	5	,	,	PUNCT
ap-2169	189	6	2012	2012	NUM
ap-2169	189	7	.	.	PUNCT
ap-2169	190	1	doi:10.1016	doi:10.1016	PROPN
ap-2169	190	2	/	/	SYM
ap-2169	190	3	j.laa.2012.02.006	j.laa.2012.02.006	PROPN
ap-2169	190	4	.	.	PUNCT
ap-2169	191	1	[	[	X
ap-2169	191	2	6	6	NUM
ap-2169	191	3	]	]	PUNCT
ap-2169	191	4	a.	a.	NOUN
ap-2169	191	5	m.	m.	NOUN
ap-2169	191	6	gavrilik	gavrilik	PROPN
ap-2169	191	7	,	,	PUNCT
ap-2169	191	8	n.	n.	PROPN
ap-2169	191	9	z.	z.	PROPN
ap-2169	191	10	iorgov	iorgov	PROPN
ap-2169	191	11	.	.	PUNCT
ap-2169	192	1	q	q	X
ap-2169	192	2	-	-	PUNCT
ap-2169	192	3	deformed	deform	VERB
ap-2169	192	4	algebras	algebra	NOUN
ap-2169	192	5	uq(son	uq(son	PROPN
ap-2169	192	6	)	)	PUNCT
ap-2169	192	7	and	and	CCONJ
ap-2169	192	8	their	their	PRON
ap-2169	192	9	representations	representation	NOUN
ap-2169	192	10	.	.	PUNCT
ap-2169	193	1	methods	method	NOUN
ap-2169	193	2	funct	funct	VERB
ap-2169	193	3	anal	anal	ADJ
ap-2169	193	4	topology	topology	NOUN
ap-2169	193	5	3(4):51–63	3(4):51–63	NUM
ap-2169	193	6	,	,	PUNCT
ap-2169	193	7	1997	1997	NUM
ap-2169	193	8	.	.	PUNCT
ap-2169	194	1	[	[	X
ap-2169	194	2	7	7	NUM
ap-2169	194	3	]	]	PUNCT
ap-2169	194	4	a.	a.	NOUN
ap-2169	194	5	m.	m.	NOUN
ap-2169	194	6	gavrilik	gavrilik	PROPN
ap-2169	194	7	,	,	PUNCT
ap-2169	194	8	n.	n.	PROPN
ap-2169	194	9	z.	z.	PROPN
ap-2169	194	10	iorgov	iorgov	PROPN
ap-2169	194	11	,	,	PUNCT
ap-2169	194	12	a.	a.	PROPN
ap-2169	194	13	u.	u.	PROPN
ap-2169	194	14	klimyk	klimyk	PROPN
ap-2169	194	15	.	.	PUNCT
ap-2169	195	1	nonstandard	nonstandard	ADJ
ap-2169	195	2	deformation	deformation	NOUN
ap-2169	195	3	u	u	NOUN
ap-2169	195	4	′	′	NOUN
ap-2169	195	5	q(son	q(son	NOUN
ap-2169	195	6	):	):	PUNCT
ap-2169	195	7	the	the	DET
ap-2169	195	8	embedding	embed	VERB
ap-2169	195	9	u	u	NOUN
ap-2169	195	10	′	′	NUM
ap-2169	195	11	q(son	q(son	NOUN
ap-2169	195	12	)	)	PUNCT
ap-2169	195	13	⊂	⊂	PROPN
ap-2169	195	14	uq(sln	uq(sln	PROPN
ap-2169	195	15	)	)	PUNCT
ap-2169	195	16	and	and	CCONJ
ap-2169	195	17	representations	representation	NOUN
ap-2169	195	18	.	.	PUNCT
ap-2169	196	1	in	in	ADP
ap-2169	196	2	symmetries	symmetry	NOUN
ap-2169	196	3	in	in	ADP
ap-2169	196	4	science	science	NOUN
ap-2169	196	5	,	,	PUNCT
ap-2169	196	6	x	x	X
ap-2169	196	7	(	(	PUNCT
ap-2169	196	8	bregenz	bregenz	PROPN
ap-2169	196	9	,	,	PUNCT
ap-2169	196	10	1997	1997	NUM
ap-2169	196	11	)	)	PUNCT
ap-2169	196	12	,	,	PUNCT
ap-2169	196	13	pp	pp	ADP
ap-2169	196	14	.	.	PUNCT
ap-2169	197	1	121–133	121–133	NUM
ap-2169	197	2	.	.	PUNCT
ap-2169	198	1	plenum	plenum	PROPN
ap-2169	198	2	,	,	PUNCT
ap-2169	198	3	new	new	PROPN
ap-2169	198	4	york	york	PROPN
ap-2169	198	5	,	,	PUNCT
ap-2169	198	6	1998	1998	NUM
ap-2169	198	7	.	.	PUNCT
ap-2169	199	1	[	[	X
ap-2169	199	2	8	8	NUM
ap-2169	199	3	]	]	PUNCT
ap-2169	199	4	a.	a.	NOUN
ap-2169	199	5	m.	m.	NOUN
ap-2169	199	6	gavrilik	gavrilik	PROPN
ap-2169	199	7	,	,	PUNCT
ap-2169	199	8	n.	n.	PROPN
ap-2169	199	9	z.	z.	PROPN
ap-2169	199	10	iorgov	iorgov	PROPN
ap-2169	199	11	.	.	PUNCT
ap-2169	200	1	representations	representation	NOUN
ap-2169	200	2	of	of	ADP
ap-2169	200	3	the	the	DET
ap-2169	200	4	nonstandard	nonstandard	ADJ
ap-2169	200	5	algebras	algebras	PROPN
ap-2169	200	6	uq(so(n	uq(so(n	NOUN
ap-2169	200	7	)	)	PUNCT
ap-2169	200	8	)	)	PUNCT
ap-2169	200	9	and	and	CCONJ
ap-2169	200	10	uq(so(n−	uq(so(n−	ADJ
ap-2169	200	11	1	1	NUM
ap-2169	200	12	,	,	PUNCT
ap-2169	200	13	1	1	NUM
ap-2169	200	14	)	)	PUNCT
ap-2169	200	15	)	)	PUNCT
ap-2169	200	16	in	in	ADP
ap-2169	200	17	gel′	gel′	NOUN
ap-2169	200	18	fand	fand	NOUN
ap-2169	200	19	-	-	PUNCT
ap-2169	200	20	tsetlin	tsetlin	PROPN
ap-2169	200	21	basis	basis	NOUN
ap-2169	200	22	.	.	PUNCT
ap-2169	201	1	ukraïn	ukraïn	ADJ
ap-2169	201	2	f̄ız	f̄ız	PROPN
ap-2169	201	3	zh	zh	PROPN
ap-2169	201	4	43(6	43(6	PROPN
ap-2169	201	5	-	-	PUNCT
ap-2169	201	6	7):791–797	7):791–797	NUM
ap-2169	201	7	,	,	PUNCT
ap-2169	201	8	1998	1998	NUM
ap-2169	201	9	.	.	PUNCT
ap-2169	202	1	international	international	ADJ
ap-2169	202	2	symposium	symposium	NOUN
ap-2169	202	3	on	on	ADP
ap-2169	202	4	mathematical	mathematical	ADJ
ap-2169	202	5	and	and	CCONJ
ap-2169	202	6	theoretical	theoretical	ADJ
ap-2169	202	7	physics	physics	NOUN
ap-2169	202	8	(	(	PUNCT
ap-2169	202	9	kyiv	kyiv	ADJ
ap-2169	202	10	,	,	PUNCT
ap-2169	202	11	1997	1997	NUM
ap-2169	202	12	)	)	PUNCT
ap-2169	202	13	.	.	PUNCT
ap-2169	203	1	[	[	X
ap-2169	203	2	9	9	NUM
ap-2169	203	3	]	]	PUNCT
ap-2169	203	4	m.	m.	NOUN
ap-2169	203	5	havlíček	havlíček	PROPN
ap-2169	203	6	,	,	PUNCT
ap-2169	203	7	s.	s.	PROPN
ap-2169	203	8	pošta	pošta	PROPN
ap-2169	203	9	.	.	PUNCT
ap-2169	204	1	on	on	ADP
ap-2169	204	2	the	the	DET
ap-2169	204	3	classification	classification	NOUN
ap-2169	204	4	of	of	ADP
ap-2169	204	5	irreducible	irreducible	ADJ
ap-2169	204	6	finite	finite	ADJ
ap-2169	204	7	-	-	ADJ
ap-2169	204	8	dimensional	dimensional	ADJ
ap-2169	204	9	representations	representation	NOUN
ap-2169	204	10	of	of	ADP
ap-2169	204	11	u	u	NOUN
ap-2169	204	12	′	′	NUM
ap-2169	204	13	q(so3	q(so3	ADV
ap-2169	204	14	)	)	PUNCT
ap-2169	204	15	algebra	algebra	NOUN
ap-2169	204	16	.	.	PUNCT
ap-2169	205	1	j	j	PROPN
ap-2169	205	2	math	math	PROPN
ap-2169	205	3	phys	phys	PROPN
ap-2169	205	4	42(1):472–500	42(1):472–500	PROPN
ap-2169	205	5	,	,	PUNCT
ap-2169	205	6	2001	2001	NUM
ap-2169	205	7	.	.	PUNCT
ap-2169	206	1	doi:10.1063/1.1328078	doi:10.1063/1.1328078	NOUN
ap-2169	206	2	.	.	PUNCT
ap-2169	207	1	[	[	X
ap-2169	207	2	10	10	NUM
ap-2169	207	3	]	]	X
ap-2169	207	4	r.	r.	PROPN
ap-2169	207	5	koekoek	koekoek	PROPN
ap-2169	207	6	,	,	PUNCT
ap-2169	207	7	r.	r.	PROPN
ap-2169	207	8	f.	f.	PROPN
ap-2169	207	9	swarttouw	swarttouw	PROPN
ap-2169	207	10	.	.	PUNCT
ap-2169	208	1	the	the	DET
ap-2169	208	2	askey	askey	NOUN
ap-2169	208	3	-	-	PUNCT
ap-2169	208	4	scheme	scheme	NOUN
ap-2169	208	5	of	of	ADP
ap-2169	208	6	hypergeometric	hypergeometric	ADJ
ap-2169	208	7	orthogonal	orthogonal	ADJ
ap-2169	208	8	polynomials	polynomial	NOUN
ap-2169	208	9	and	and	CCONJ
ap-2169	208	10	its	its	PRON
ap-2169	208	11	q	q	NOUN
ap-2169	208	12	-	-	PUNCT
ap-2169	208	13	analogue	analogue	NOUN
ap-2169	208	14	,	,	PUNCT
ap-2169	208	15	1996	1996	NUM
ap-2169	208	16	.	.	PUNCT
ap-2169	209	1	arxiv	arxiv	NOUN
ap-2169	209	2	:	:	PUNCT
ap-2169	209	3	math/9602214	math/9602214	ADJ
ap-2169	209	4	.	.	PUNCT
ap-2169	210	1	[	[	X
ap-2169	210	2	11	11	NUM
ap-2169	210	3	]	]	PUNCT
ap-2169	210	4	p.	p.	NOUN
ap-2169	210	5	terwilliger	terwilliger	NOUN
ap-2169	210	6	.	.	PUNCT
ap-2169	211	1	leonard	leonard	PROPN
ap-2169	211	2	pairs	pair	NOUN
ap-2169	211	3	and	and	CCONJ
ap-2169	211	4	the	the	DET
ap-2169	211	5	q	q	ADJ
ap-2169	211	6	-	-	PUNCT
ap-2169	211	7	racah	racah	ADJ
ap-2169	211	8	polynomials	polynomial	NOUN
ap-2169	211	9	.	.	PUNCT
ap-2169	212	1	linear	linear	ADJ
ap-2169	212	2	algebra	algebra	PROPN
ap-2169	212	3	appl	appl	PROPN
ap-2169	212	4	387:235–276	387:235–276	PROPN
ap-2169	212	5	,	,	PUNCT
ap-2169	212	6	2004	2004	NUM
ap-2169	212	7	.	.	PUNCT
ap-2169	213	1	doi:10.1016	doi:10.1016	PROPN
ap-2169	213	2	/	/	SYM
ap-2169	213	3	j.laa.2004.02.014	j.laa.2004.02.014	PROPN
ap-2169	213	4	.	.	PUNCT
ap-2169	214	1	[	[	X
ap-2169	214	2	12	12	NUM
ap-2169	214	3	]	]	PUNCT
ap-2169	214	4	a.	a.	PROPN
ap-2169	214	5	s.	s.	PROPN
ap-2169	214	6	zhedanov	zhedanov	PROPN
ap-2169	214	7	.	.	PUNCT
ap-2169	215	1	“	"	PUNCT
ap-2169	215	2	hidden	hidden	ADJ
ap-2169	215	3	symmetry	symmetry	NOUN
ap-2169	215	4	”	"	PUNCT
ap-2169	215	5	of	of	ADP
ap-2169	215	6	askey	askey	NOUN
ap-2169	215	7	-	-	PUNCT
ap-2169	215	8	wilson	wilson	NOUN
ap-2169	215	9	polynomials	polynomial	NOUN
ap-2169	215	10	.	.	PUNCT
ap-2169	216	1	teoret	teoret	PROPN
ap-2169	216	2	mat	mat	PROPN
ap-2169	216	3	fiz	fiz	PROPN
ap-2169	216	4	89(2):190–204	89(2):190–204	PROPN
ap-2169	216	5	,	,	PUNCT
ap-2169	216	6	1991	1991	NUM
ap-2169	216	7	.	.	PUNCT
ap-2169	217	1	doi:10.1007	doi:10.1007	PROPN
ap-2169	217	2	/	/	SYM
ap-2169	217	3	bf01015906	bf01015906	PROPN
ap-2169	217	4	.	.	PUNCT
ap-2169	218	1	[	[	X
ap-2169	218	2	13	13	NUM
ap-2169	218	3	]	]	PUNCT
ap-2169	218	4	p.	p.	NOUN
ap-2169	218	5	terwilliger	terwilliger	NOUN
ap-2169	218	6	.	.	PUNCT
ap-2169	219	1	the	the	DET
ap-2169	219	2	universal	universal	ADJ
ap-2169	219	3	askey	askey	PROPN
ap-2169	219	4	-	-	PUNCT
ap-2169	219	5	wilson	wilson	NOUN
ap-2169	219	6	algebra	algebra	PROPN
ap-2169	219	7	.	.	PUNCT
ap-2169	220	1	sigma	sigma	PROPN
ap-2169	220	2	symmetry	symmetry	PROPN
ap-2169	220	3	integrability	integrability	PROPN
ap-2169	220	4	geom	geom	PROPN
ap-2169	220	5	methods	method	NOUN
ap-2169	220	6	appl	appl	PROPN
ap-2169	220	7	7	7	NUM
ap-2169	220	8	:	:	PUNCT
ap-2169	220	9	paper	paper	NOUN
ap-2169	220	10	069	069	NUM
ap-2169	220	11	,	,	PUNCT
ap-2169	220	12	24	24	NUM
ap-2169	220	13	,	,	PUNCT
ap-2169	220	14	2011	2011	NUM
ap-2169	220	15	.	.	PUNCT
ap-2169	221	1	doi:10.3842	doi:10.3842	NOUN
ap-2169	221	2	/	/	SYM
ap-2169	221	3	sigma.2011.069	sigma.2011.069	PROPN
ap-2169	221	4	.	.	PUNCT
ap-2169	222	1	[	[	X
ap-2169	222	2	14	14	NUM
ap-2169	222	3	]	]	PUNCT
ap-2169	222	4	p.	p.	NOUN
ap-2169	222	5	terwilliger	terwilliger	NOUN
ap-2169	222	6	.	.	PUNCT
ap-2169	223	1	the	the	DET
ap-2169	223	2	universal	universal	ADJ
ap-2169	223	3	askey	askey	PROPN
ap-2169	223	4	-	-	PUNCT
ap-2169	223	5	wilson	wilson	NOUN
ap-2169	223	6	algebra	algebra	PROPN
ap-2169	223	7	and	and	CCONJ
ap-2169	223	8	the	the	DET
ap-2169	223	9	equitable	equitable	ADJ
ap-2169	223	10	presentation	presentation	NOUN
ap-2169	223	11	of	of	ADP
ap-2169	223	12	uq(sl2	uq(sl2	PROPN
ap-2169	223	13	)	)	PUNCT
ap-2169	223	14	.	.	PUNCT
ap-2169	224	1	sigma	sigma	PROPN
ap-2169	224	2	symmetry	symmetry	PROPN
ap-2169	224	3	integrability	integrability	PROPN
ap-2169	224	4	geom	geom	PROPN
ap-2169	224	5	methods	method	NOUN
ap-2169	224	6	appl	appl	PROPN
ap-2169	224	7	7	7	NUM
ap-2169	224	8	:	:	PUNCT
ap-2169	224	9	paper	paper	NOUN
ap-2169	224	10	099	099	NUM
ap-2169	224	11	,	,	PUNCT
ap-2169	224	12	26	26	NUM
ap-2169	224	13	,	,	PUNCT
ap-2169	224	14	2011	2011	NUM
ap-2169	224	15	.	.	PUNCT
ap-2169	225	1	[	[	X
ap-2169	225	2	15	15	NUM
ap-2169	225	3	]	]	X
ap-2169	225	4	p.	p.	NOUN
ap-2169	225	5	terwilliger	terwilliger	NOUN
ap-2169	225	6	,	,	PUNCT
ap-2169	225	7	a.	a.	NOUN
ap-2169	225	8	žitnik	žitnik	PROPN
ap-2169	225	9	.	.	PUNCT
ap-2169	226	1	distance	distance	NOUN
ap-2169	226	2	-	-	PUNCT
ap-2169	226	3	regular	regular	ADJ
ap-2169	226	4	graphs	graph	NOUN
ap-2169	226	5	of	of	ADP
ap-2169	226	6	q	q	ADJ
ap-2169	226	7	-	-	PUNCT
ap-2169	226	8	racah	racah	NOUN
ap-2169	226	9	type	type	NOUN
ap-2169	226	10	and	and	CCONJ
ap-2169	226	11	the	the	DET
ap-2169	226	12	universal	universal	ADJ
ap-2169	226	13	askey	askey	NOUN
ap-2169	226	14	–	–	PUNCT
ap-2169	226	15	wilson	wilson	PROPN
ap-2169	226	16	algebra	algebra	PROPN
ap-2169	226	17	.	.	PUNCT
ap-2169	227	1	j	j	PROPN
ap-2169	227	2	combin	combin	PROPN
ap-2169	227	3	theory	theory	NOUN
ap-2169	227	4	ser	ser	NOUN
ap-2169	227	5	a	a	DET
ap-2169	227	6	125:98–112	125:98–112	NUM
ap-2169	227	7	,	,	PUNCT
ap-2169	227	8	2014	2014	NUM
ap-2169	227	9	.	.	PUNCT
ap-2169	228	1	doi:10.1016	doi:10.1016	PROPN
ap-2169	228	2	/	/	SYM
ap-2169	228	3	j.jcta.2014.03.001	j.jcta.2014.03.001	NOUN
ap-2169	228	4	.	.	PUNCT
ap-2169	229	1	[	[	X
ap-2169	229	2	16	16	NUM
ap-2169	229	3	]	]	PUNCT
ap-2169	229	4	p.	p.	NOUN
ap-2169	229	5	terwilliger	terwilliger	NOUN
ap-2169	229	6	.	.	PUNCT
ap-2169	230	1	the	the	DET
ap-2169	230	2	universal	universal	ADJ
ap-2169	230	3	askey	askey	PROPN
ap-2169	230	4	-	-	PUNCT
ap-2169	230	5	wilson	wilson	NOUN
ap-2169	230	6	algebra	algebra	PROPN
ap-2169	230	7	and	and	CCONJ
ap-2169	230	8	daha	daha	NOUN
ap-2169	230	9	of	of	ADP
ap-2169	230	10	type	type	NOUN
ap-2169	230	11	(	(	PUNCT
ap-2169	230	12	c∨	c∨	NOUN
ap-2169	230	13	1	1	NUM
ap-2169	230	14	,	,	PUNCT
ap-2169	230	15	c1	c1	PROPN
ap-2169	230	16	)	)	PUNCT
ap-2169	230	17	.	.	PUNCT
ap-2169	231	1	sigma	sigma	PROPN
ap-2169	231	2	symmetry	symmetry	PROPN
ap-2169	231	3	integrability	integrability	PROPN
ap-2169	231	4	geom	geom	PROPN
ap-2169	231	5	methods	method	NOUN
ap-2169	231	6	appl	appl	PROPN
ap-2169	231	7	9	9	NUM
ap-2169	231	8	:	:	PUNCT
ap-2169	231	9	paper	paper	NOUN
ap-2169	231	10	047	047	NUM
ap-2169	231	11	,	,	PUNCT
ap-2169	231	12	40	40	NUM
ap-2169	231	13	,	,	PUNCT
ap-2169	231	14	2013	2013	NUM
ap-2169	231	15	.	.	PUNCT
ap-2169	232	1	397	397	NUM
ap-2169	232	2	http://dx.doi.org/10.1137/0513072	http://dx.doi.org/10.1137/0513072	NOUN
ap-2169	232	3	http://dx.doi.org/10.1016/j.laa.2012.02.006	http://dx.doi.org/10.1016/j.laa.2012.02.006	NOUN
ap-2169	232	4	http://dx.doi.org/10.1063/1.1328078	http://dx.doi.org/10.1063/1.1328078	PROPN
ap-2169	232	5	arxiv	arxiv	NOUN
ap-2169	232	6	:	:	PUNCT
ap-2169	232	7	math/9602214	math/9602214	PROPN
ap-2169	232	8	http://dx.doi.org/10.1016/j.laa.2004.02.014	http://dx.doi.org/10.1016/j.laa.2004.02.014	PROPN
ap-2169	232	9	http://dx.doi.org/10.1007/bf01015906	http://dx.doi.org/10.1007/bf01015906	VERB
ap-2169	232	10	http://dx.doi.org/10.3842/sigma.2011.069	http://dx.doi.org/10.3842/sigma.2011.069	ADP
ap-2169	232	11	http://dx.doi.org/10.1016/j.jcta.2014.03.001	http://dx.doi.org/10.1016/j.jcta.2014.03.001	PROPN
ap-2169	232	12	acta	acta	PROPN
ap-2169	232	13	polytechnica	polytechnica	PROPN
ap-2169	232	14	54(6):394–397	54(6):394–397	PROPN
ap-2169	232	15	,	,	PUNCT
ap-2169	232	16	2014	2014	NUM
ap-2169	232	17	1	1	NUM
ap-2169	232	18	introduction	introduction	NOUN
ap-2169	232	19	2	2	NUM
ap-2169	232	20	lie	lie	NOUN
ap-2169	232	21	algebra	algebra	NOUN
ap-2169	232	22	sl2	sl2	PROPN
ap-2169	232	23	3	3	NUM
ap-2169	232	24	algebra	algebra	NOUN
ap-2169	232	25	uq'(so3	uq'(so3	NOUN
ap-2169	232	26	)	)	PUNCT
ap-2169	232	27	4	4	NUM
ap-2169	232	28	conclusion	conclusion	NOUN
ap-2169	232	29	references	reference	NOUN