id	sid	tid	token	lemma	pos
ap-10600	1	1	acta	acta	PROPN
ap-10600	1	2	polytechnica	polytechnica	PROPN
ap-10600	1	3	https://doi.org/10.14311/ap.2025.65.0534	https://doi.org/10.14311/ap.2025.65.0534	PROPN
ap-10600	1	4	acta	acta	PROPN
ap-10600	1	5	polytechnica	polytechnica	PROPN
ap-10600	1	6	65(5):534–538	65(5):534–538	PROPN
ap-10600	1	7	,	,	PUNCT
ap-10600	1	8	2025	2025	NUM
ap-10600	1	9	©	©	ADP
ap-10600	1	10	2025	2025	NUM
ap-10600	1	11	the	the	DET
ap-10600	1	12	author(s	author(s	NOUN
ap-10600	1	13	)	)	PUNCT
ap-10600	1	14	.	.	PUNCT
ap-10600	2	1	licensed	license	VERB
ap-10600	2	2	under	under	ADP
ap-10600	2	3	a	a	DET
ap-10600	2	4	cc	cc	NOUN
ap-10600	2	5	-	-	PUNCT
ap-10600	2	6	by	by	ADP
ap-10600	2	7	4.0	4.0	NUM
ap-10600	2	8	licence	licence	NOUN
ap-10600	2	9	published	publish	VERB
ap-10600	2	10	by	by	ADP
ap-10600	2	11	the	the	DET
ap-10600	2	12	czech	czech	PROPN
ap-10600	2	13	technical	technical	PROPN
ap-10600	2	14	university	university	PROPN
ap-10600	2	15	in	in	ADP
ap-10600	2	16	prague	prague	PROPN
ap-10600	2	17	frequencies	frequency	NOUN
ap-10600	2	18	of	of	ADP
ap-10600	2	19	letters	letter	NOUN
ap-10600	2	20	in	in	ADP
ap-10600	2	21	infinite	infinite	ADJ
ap-10600	2	22	k	k	ADV
ap-10600	2	23	-	-	ADJ
ap-10600	2	24	balanced	balanced	ADJ
ap-10600	2	25	sequences	sequence	NOUN
ap-10600	2	26	l’ubomíra	l’ubomíra	NOUN
ap-10600	2	27	dvořáková∗	dvořáková∗	PROPN
ap-10600	2	28	,	,	PUNCT
ap-10600	2	29	edita	edita	PROPN
ap-10600	2	30	pelantová	pelantová	PROPN
ap-10600	2	31	czech	czech	PROPN
ap-10600	2	32	technical	technical	PROPN
ap-10600	2	33	university	university	PROPN
ap-10600	2	34	in	in	ADP
ap-10600	2	35	prague	prague	PROPN
ap-10600	2	36	,	,	PUNCT
ap-10600	2	37	faculty	faculty	NOUN
ap-10600	2	38	of	of	ADP
ap-10600	2	39	nuclear	nuclear	ADJ
ap-10600	2	40	sciences	science	NOUN
ap-10600	2	41	and	and	CCONJ
ap-10600	2	42	physical	physical	ADJ
ap-10600	2	43	engineering	engineering	NOUN
ap-10600	2	44	,	,	PUNCT
ap-10600	2	45	department	department	NOUN
ap-10600	2	46	of	of	ADP
ap-10600	2	47	mathematics	mathematic	NOUN
ap-10600	2	48	,	,	PUNCT
ap-10600	2	49	trojanova	trojanova	X
ap-10600	2	50	13	13	NUM
ap-10600	2	51	,	,	PUNCT
ap-10600	2	52	120	120	NUM
ap-10600	2	53	00	00	NUM
ap-10600	2	54	prague	prague	PROPN
ap-10600	2	55	,	,	PUNCT
ap-10600	2	56	czech	czech	PROPN
ap-10600	2	57	republic	republic	NOUN
ap-10600	2	58	∗	∗	NOUN
ap-10600	2	59	corresponding	correspond	VERB
ap-10600	2	60	author	author	NOUN
ap-10600	2	61	:	:	PUNCT
ap-10600	2	62	lubomira.dvorakova@fjfi.cvut.cz	lubomira.dvorakova@fjfi.cvut.cz	ADJ
ap-10600	2	63	abstract	abstract	ADJ
ap-10600	2	64	.	.	PUNCT
ap-10600	3	1	the	the	DET
ap-10600	3	2	frequency	frequency	NOUN
ap-10600	3	3	of	of	ADP
ap-10600	3	4	letters	letter	NOUN
ap-10600	3	5	in	in	ADP
ap-10600	3	6	a	a	DET
ap-10600	3	7	symbolic	symbolic	ADJ
ap-10600	3	8	sequence	sequence	NOUN
ap-10600	3	9	u	u	NOUN
ap-10600	3	10	over	over	ADP
ap-10600	3	11	a	a	DET
ap-10600	3	12	finite	finite	ADJ
ap-10600	3	13	alphabet	alphabet	NOUN
ap-10600	3	14	is	be	AUX
ap-10600	3	15	one	one	NUM
ap-10600	3	16	of	of	ADP
ap-10600	3	17	the	the	DET
ap-10600	3	18	basic	basic	ADJ
ap-10600	3	19	characteristics	characteristic	NOUN
ap-10600	3	20	of	of	ADP
ap-10600	3	21	u.	u.	NOUN
ap-10600	3	22	the	the	DET
ap-10600	3	23	notion	notion	NOUN
ap-10600	3	24	of	of	ADP
ap-10600	3	25	k	k	ADJ
ap-10600	3	26	-	-	PUNCT
ap-10600	3	27	balancedness	balancedness	NOUN
ap-10600	3	28	captures	capture	VERB
ap-10600	3	29	the	the	DET
ap-10600	3	30	property	property	NOUN
ap-10600	3	31	that	that	PRON
ap-10600	3	32	the	the	DET
ap-10600	3	33	number	number	NOUN
ap-10600	3	34	of	of	ADP
ap-10600	3	35	any	any	DET
ap-10600	3	36	letter	letter	NOUN
ap-10600	3	37	occurring	occur	VERB
ap-10600	3	38	in	in	ADP
ap-10600	3	39	two	two	NUM
ap-10600	3	40	arbitrary	arbitrary	ADJ
ap-10600	3	41	factors	factor	NOUN
ap-10600	3	42	of	of	ADP
ap-10600	3	43	u	u	NOUN
ap-10600	3	44	of	of	ADP
ap-10600	3	45	equal	equal	ADJ
ap-10600	3	46	length	length	NOUN
ap-10600	3	47	differs	differ	VERB
ap-10600	3	48	at	at	ADP
ap-10600	3	49	most	most	ADJ
ap-10600	3	50	by	by	ADP
ap-10600	3	51	k.	k.	PROPN
ap-10600	3	52	for	for	ADP
ap-10600	3	53	a	a	DET
ap-10600	3	54	fixed	fix	VERB
ap-10600	3	55	integer	integer	NOUN
ap-10600	3	56	k	k	PROPN
ap-10600	3	57	and	and	CCONJ
ap-10600	3	58	alphabet	alphabet	PROPN
ap-10600	3	59	size	size	NOUN
ap-10600	3	60	d	d	PROPN
ap-10600	3	61	∈	∈	PROPN
ap-10600	3	62	n	n	CCONJ
ap-10600	3	63	,	,	PUNCT
ap-10600	3	64	we	we	PRON
ap-10600	3	65	discuss	discuss	VERB
ap-10600	3	66	possible	possible	ADJ
ap-10600	3	67	frequencies	frequency	NOUN
ap-10600	3	68	of	of	ADP
ap-10600	3	69	letters	letter	NOUN
ap-10600	3	70	in	in	ADP
ap-10600	3	71	k	k	ADV
ap-10600	3	72	-	-	ADJ
ap-10600	3	73	balanced	balanced	ADJ
ap-10600	3	74	d	d	ADJ
ap-10600	3	75	-	-	ADJ
ap-10600	3	76	ary	ary	ADJ
ap-10600	3	77	sequences	sequence	NOUN
ap-10600	3	78	.	.	PUNCT
ap-10600	4	1	for	for	ADP
ap-10600	4	2	the	the	DET
ap-10600	4	3	size	size	NOUN
ap-10600	4	4	d	d	PROPN
ap-10600	4	5	of	of	ADP
ap-10600	4	6	the	the	DET
ap-10600	4	7	alphabet	alphabet	NOUN
ap-10600	4	8	,	,	PUNCT
ap-10600	4	9	we	we	PRON
ap-10600	4	10	introduce	introduce	VERB
ap-10600	4	11	the	the	DET
ap-10600	4	12	notion	notion	NOUN
ap-10600	4	13	of	of	ADP
ap-10600	4	14	balancedness	balancedness	NOUN
ap-10600	4	15	threshold	threshold	NOUN
ap-10600	4	16	bt	bt	PROPN
ap-10600	4	17	(	(	PUNCT
ap-10600	4	18	d	d	NOUN
ap-10600	4	19	)	)	PUNCT
ap-10600	4	20	and	and	CCONJ
ap-10600	4	21	provide	provide	VERB
ap-10600	4	22	an	an	DET
ap-10600	4	23	upper	upper	ADJ
ap-10600	4	24	bound	bind	VERB
ap-10600	4	25	on	on	ADP
ap-10600	4	26	it	it	PRON
ap-10600	4	27	,	,	PUNCT
ap-10600	4	28	where	where	SCONJ
ap-10600	4	29	bt	bt	PROPN
ap-10600	4	30	(	(	PUNCT
ap-10600	4	31	d	d	NOUN
ap-10600	4	32	)	)	PUNCT
ap-10600	4	33	is	be	AUX
ap-10600	4	34	the	the	DET
ap-10600	4	35	minimum	minimum	NOUN
ap-10600	4	36	k	k	NOUN
ap-10600	4	37	such	such	ADJ
ap-10600	4	38	that	that	SCONJ
ap-10600	4	39	there	there	PRON
ap-10600	4	40	exists	exist	VERB
ap-10600	4	41	a	a	DET
ap-10600	4	42	k	k	ADV
ap-10600	4	43	-	-	ADJ
ap-10600	4	44	balanced	balanced	ADJ
ap-10600	4	45	sequence	sequence	NOUN
ap-10600	4	46	over	over	ADP
ap-10600	4	47	a	a	DET
ap-10600	4	48	d	d	NOUN
ap-10600	4	49	-	-	PUNCT
ap-10600	4	50	letter	letter	NOUN
ap-10600	4	51	alphabet	alphabet	NOUN
ap-10600	4	52	for	for	ADP
ap-10600	4	53	all	all	DET
ap-10600	4	54	possible	possible	ADJ
ap-10600	4	55	letter	letter	NOUN
ap-10600	4	56	frequencies	frequency	NOUN
ap-10600	4	57	.	.	PUNCT
ap-10600	5	1	keywords	keyword	NOUN
ap-10600	5	2	:	:	PUNCT
ap-10600	5	3	letter	letter	NOUN
ap-10600	5	4	frequency	frequency	NOUN
ap-10600	5	5	,	,	PUNCT
ap-10600	5	6	balanced	balanced	ADJ
ap-10600	5	7	sequences	sequence	NOUN
ap-10600	5	8	,	,	PUNCT
ap-10600	5	9	balancedness	balancedness	NOUN
ap-10600	5	10	threshold	threshold	NOUN
ap-10600	5	11	,	,	PUNCT
ap-10600	5	12	factor	factor	NOUN
ap-10600	5	13	complexity	complexity	NOUN
ap-10600	5	14	.	.	PUNCT
ap-10600	6	1	1	1	X
ap-10600	6	2	.	.	X
ap-10600	6	3	introduction	introduction	NOUN
ap-10600	6	4	this	this	DET
ap-10600	6	5	paper	paper	NOUN
ap-10600	6	6	is	be	AUX
ap-10600	6	7	devoted	devote	VERB
ap-10600	6	8	to	to	ADP
ap-10600	6	9	studying	study	VERB
ap-10600	6	10	the	the	DET
ap-10600	6	11	relation	relation	NOUN
ap-10600	6	12	between	between	ADP
ap-10600	6	13	frequencies	frequency	NOUN
ap-10600	6	14	of	of	ADP
ap-10600	6	15	letters	letter	NOUN
ap-10600	6	16	and	and	CCONJ
ap-10600	6	17	k	k	NOUN
ap-10600	6	18	-	-	NOUN
ap-10600	6	19	balancedness	balancedness	NOUN
ap-10600	6	20	in	in	ADP
ap-10600	6	21	sequences	sequence	NOUN
ap-10600	6	22	(	(	PUNCT
ap-10600	6	23	also	also	ADV
ap-10600	6	24	called	call	VERB
ap-10600	6	25	infinite	infinite	ADJ
ap-10600	6	26	words	word	NOUN
ap-10600	6	27	)	)	PUNCT
ap-10600	6	28	.	.	PUNCT
ap-10600	7	1	let	let	VERB
ap-10600	7	2	us	we	PRON
ap-10600	7	3	first	first	ADV
ap-10600	7	4	introduce	introduce	VERB
ap-10600	7	5	these	these	DET
ap-10600	7	6	notions	notion	NOUN
ap-10600	7	7	.	.	PUNCT
ap-10600	8	1	consider	consider	VERB
ap-10600	8	2	a	a	DET
ap-10600	8	3	sequence	sequence	NOUN
ap-10600	8	4	u	u	NOUN
ap-10600	8	5	=	=	NOUN
ap-10600	8	6	u0u1u2	u0u1u2	X
ap-10600	8	7	·	·	PUNCT
ap-10600	8	8	·	·	PUNCT
ap-10600	8	9	·	·	PUNCT
ap-10600	8	10	of	of	ADP
ap-10600	8	11	symbols	symbol	NOUN
ap-10600	8	12	from	from	ADP
ap-10600	8	13	a	a	DET
ap-10600	8	14	finite	finite	ADJ
ap-10600	8	15	alphabet	alphabet	NOUN
ap-10600	8	16	a	a	PROPN
ap-10600	8	17	=	=	X
ap-10600	8	18	{	{	PUNCT
ap-10600	8	19	1	1	NUM
ap-10600	8	20	,	,	PUNCT
ap-10600	8	21	2	2	NUM
ap-10600	8	22	,	,	PUNCT
ap-10600	8	23	.	.	PUNCT
ap-10600	8	24	.	.	PUNCT
ap-10600	9	1	.	.	PUNCT
ap-10600	10	1	,	,	PUNCT
ap-10600	10	2	d	d	X
ap-10600	10	3	}	}	PUNCT
ap-10600	10	4	.	.	PUNCT
ap-10600	11	1	the	the	DET
ap-10600	11	2	frequency	frequency	NOUN
ap-10600	11	3	of	of	ADP
ap-10600	11	4	a	a	DET
ap-10600	11	5	letter	letter	NOUN
ap-10600	11	6	a	a	PRON
ap-10600	11	7	in	in	ADP
ap-10600	11	8	u	u	NOUN
ap-10600	11	9	is	be	AUX
ap-10600	11	10	the	the	DET
ap-10600	11	11	limit	limit	NOUN
ap-10600	11	12	(	(	PUNCT
ap-10600	11	13	if	if	SCONJ
ap-10600	11	14	it	it	PRON
ap-10600	11	15	exists	exist	VERB
ap-10600	11	16	):	):	PUNCT
ap-10600	11	17	fa	fa	PROPN
ap-10600	11	18	=	=	SYM
ap-10600	11	19	lim	lim	PROPN
ap-10600	11	20	n→∞	n→∞	X
ap-10600	11	21	#	#	SYM
ap-10600	11	22	{	{	PUNCT
ap-10600	11	23	i	i	PRON
ap-10600	11	24	<	<	X
ap-10600	11	25	n	n	PROPN
ap-10600	11	26	:	:	PUNCT
ap-10600	11	27	ui	ui	PROPN
ap-10600	11	28	=	=	PUNCT
ap-10600	11	29	a	a	PROPN
ap-10600	11	30	}	}	PUNCT
ap-10600	11	31	n	n	NOUN
ap-10600	11	32	.	.	PUNCT
ap-10600	12	1	if	if	SCONJ
ap-10600	12	2	every	every	DET
ap-10600	12	3	letter	letter	NOUN
ap-10600	12	4	a	a	DET
ap-10600	12	5	∈	∈	NOUN
ap-10600	12	6	a	a	PRON
ap-10600	12	7	has	have	VERB
ap-10600	12	8	a	a	DET
ap-10600	12	9	well	well	ADV
ap-10600	12	10	-	-	PUNCT
ap-10600	12	11	defined	define	VERB
ap-10600	12	12	frequency	frequency	NOUN
ap-10600	12	13	in	in	ADP
ap-10600	12	14	u	u	NOUN
ap-10600	12	15	,	,	PUNCT
ap-10600	12	16	then	then	ADV
ap-10600	12	17	∑	∑	PUNCT
ap-10600	12	18	a∈a	a∈a	ADJ
ap-10600	12	19	fa	fa	PROPN
ap-10600	12	20	=	=	SYM
ap-10600	12	21	1	1	X
ap-10600	12	22	.	.	PUNCT
ap-10600	13	1	the	the	DET
ap-10600	13	2	vector	vector	NOUN
ap-10600	13	3	f⃗u	f⃗u	PROPN
ap-10600	13	4	=	=	PUNCT
ap-10600	13	5	(	(	PUNCT
ap-10600	13	6	fa)a∈a	fa)a∈a	NUM
ap-10600	13	7	is	be	AUX
ap-10600	13	8	called	call	VERB
ap-10600	13	9	the	the	DET
ap-10600	13	10	frequency	frequency	NOUN
ap-10600	13	11	vector	vector	NOUN
ap-10600	13	12	of	of	ADP
ap-10600	13	13	u.	u.	NOUN
ap-10600	13	14	a	a	DET
ap-10600	13	15	word	word	NOUN
ap-10600	13	16	w	w	PROPN
ap-10600	13	17	=	=	SYM
ap-10600	13	18	w0w1	w0w1	X
ap-10600	13	19	·	·	PUNCT
ap-10600	13	20	·	·	PUNCT
ap-10600	14	1	·	·	PUNCT
ap-10600	14	2	wn−1	wn−1	ADJ
ap-10600	14	3	over	over	ADP
ap-10600	14	4	a	a	PRON
ap-10600	14	5	is	be	AUX
ap-10600	14	6	a	a	DET
ap-10600	14	7	finite	finite	ADJ
ap-10600	14	8	sequence	sequence	NOUN
ap-10600	14	9	of	of	ADP
ap-10600	14	10	letters	letter	NOUN
ap-10600	14	11	wi	wi	PROPN
ap-10600	14	12	from	from	ADP
ap-10600	14	13	a.	a.	NOUN
ap-10600	14	14	its	its	PRON
ap-10600	14	15	length	length	NOUN
ap-10600	14	16	|w|	|w|	NOUN
ap-10600	14	17	equals	equal	VERB
ap-10600	14	18	n.	n.	NOUN
ap-10600	14	19	to	to	PART
ap-10600	14	20	denote	denote	VERB
ap-10600	14	21	the	the	DET
ap-10600	14	22	number	number	NOUN
ap-10600	14	23	of	of	ADP
ap-10600	14	24	occurrences	occurrence	NOUN
ap-10600	14	25	of	of	ADP
ap-10600	14	26	a	a	DET
ap-10600	14	27	letter	letter	NOUN
ap-10600	14	28	a	a	PRON
ap-10600	14	29	in	in	ADP
ap-10600	14	30	w	w	PROPN
ap-10600	14	31	,	,	PUNCT
ap-10600	14	32	we	we	PRON
ap-10600	14	33	use	use	VERB
ap-10600	14	34	|w|a	|w|a	PROPN
ap-10600	14	35	.	.	PUNCT
ap-10600	15	1	the	the	DET
ap-10600	15	2	set	set	NOUN
ap-10600	15	3	of	of	ADP
ap-10600	15	4	all	all	DET
ap-10600	15	5	words	word	NOUN
ap-10600	15	6	over	over	ADP
ap-10600	15	7	the	the	DET
ap-10600	15	8	alphabet	alphabet	NOUN
ap-10600	15	9	a	a	X
ap-10600	15	10	(	(	PUNCT
ap-10600	15	11	including	include	VERB
ap-10600	15	12	the	the	DET
ap-10600	15	13	empty	empty	ADJ
ap-10600	15	14	word	word	NOUN
ap-10600	15	15	)	)	PUNCT
ap-10600	15	16	is	be	AUX
ap-10600	15	17	denoted	denote	VERB
ap-10600	15	18	a∗.	a∗.	NOUN
ap-10600	15	19	the	the	DET
ap-10600	15	20	word	word	NOUN
ap-10600	15	21	w	w	NOUN
ap-10600	15	22	is	be	AUX
ap-10600	15	23	a	a	DET
ap-10600	15	24	factor	factor	NOUN
ap-10600	15	25	of	of	ADP
ap-10600	15	26	u	u	NOUN
ap-10600	15	27	=	=	PROPN
ap-10600	15	28	u0u1u2	u0u1u2	X
ap-10600	15	29	·	·	PUNCT
ap-10600	15	30	·	·	PUNCT
ap-10600	15	31	·	·	PUNCT
ap-10600	16	1	if	if	SCONJ
ap-10600	16	2	there	there	PRON
ap-10600	16	3	exists	exist	VERB
ap-10600	16	4	i	i	PRON
ap-10600	16	5	∈	∈	PROPN
ap-10600	16	6	n	n	PRON
ap-10600	16	7	such	such	ADJ
ap-10600	16	8	that	that	PRON
ap-10600	16	9	w	w	PROPN
ap-10600	16	10	=	=	SYM
ap-10600	16	11	uiui+1	uiui+1	PROPN
ap-10600	16	12	·	·	PUNCT
ap-10600	16	13	·	·	PUNCT
ap-10600	16	14	·	·	PUNCT
ap-10600	16	15	ui+|w|−1	ui+|w|−1	PROPN
ap-10600	16	16	.	.	NOUN
ap-10600	17	1	we	we	PRON
ap-10600	17	2	say	say	VERB
ap-10600	17	3	that	that	SCONJ
ap-10600	17	4	the	the	DET
ap-10600	17	5	sequence	sequence	NOUN
ap-10600	17	6	u	u	NOUN
ap-10600	17	7	is	be	AUX
ap-10600	17	8	recurrent	recurrent	ADJ
ap-10600	17	9	if	if	SCONJ
ap-10600	17	10	every	every	DET
ap-10600	17	11	factor	factor	NOUN
ap-10600	17	12	of	of	ADP
ap-10600	17	13	u	u	PROPN
ap-10600	17	14	occurs	occur	VERB
ap-10600	17	15	in	in	ADP
ap-10600	17	16	u	u	NOUN
ap-10600	17	17	infinitely	infinitely	ADV
ap-10600	17	18	many	many	ADJ
ap-10600	17	19	times	time	NOUN
ap-10600	17	20	.	.	PUNCT
ap-10600	18	1	the	the	DET
ap-10600	18	2	language	language	NOUN
ap-10600	18	3	l(u	l(u	PROPN
ap-10600	18	4	)	)	PUNCT
ap-10600	18	5	of	of	ADP
ap-10600	18	6	a	a	DET
ap-10600	18	7	sequence	sequence	NOUN
ap-10600	18	8	u	u	NOUN
ap-10600	18	9	is	be	AUX
ap-10600	18	10	the	the	DET
ap-10600	18	11	set	set	NOUN
ap-10600	18	12	of	of	ADP
ap-10600	18	13	factors	factor	NOUN
ap-10600	18	14	occurring	occur	VERB
ap-10600	18	15	in	in	ADP
ap-10600	18	16	u.	u.	PROPN
ap-10600	18	17	the	the	DET
ap-10600	18	18	factor	factor	NOUN
ap-10600	18	19	complexity	complexity	NOUN
ap-10600	18	20	of	of	ADP
ap-10600	18	21	a	a	DET
ap-10600	18	22	sequence	sequence	NOUN
ap-10600	18	23	u	u	NOUN
ap-10600	18	24	is	be	AUX
ap-10600	18	25	the	the	DET
ap-10600	18	26	mapping	mapping	NOUN
ap-10600	18	27	c	c	NOUN
ap-10600	18	28	:	:	PUNCT
ap-10600	18	29	n	n	X
ap-10600	18	30	→	→	SYM
ap-10600	18	31	n	n	CCONJ
ap-10600	18	32	,	,	PUNCT
ap-10600	18	33	where	where	SCONJ
ap-10600	18	34	:	:	PUNCT
ap-10600	18	35	c(n	c(n	NUM
ap-10600	18	36	)	)	PUNCT
ap-10600	19	1	=	=	PUNCT
ap-10600	19	2	#	#	SYM
ap-10600	19	3	{	{	PUNCT
ap-10600	19	4	w	w	PROPN
ap-10600	19	5	∈	∈	PROPN
ap-10600	19	6	l(u	l(u	PROPN
ap-10600	19	7	)	)	PUNCT
ap-10600	19	8	:	:	PUNCT
ap-10600	20	1	|w|	|w|	VERB
ap-10600	20	2	=	=	SYM
ap-10600	20	3	n	n	CCONJ
ap-10600	20	4	}	}	PUNCT
ap-10600	20	5	.	.	PUNCT
ap-10600	21	1	we	we	PRON
ap-10600	21	2	say	say	VERB
ap-10600	21	3	that	that	SCONJ
ap-10600	21	4	u	u	PROPN
ap-10600	21	5	is	be	AUX
ap-10600	21	6	k	k	NOUN
ap-10600	21	7	-	-	ADJ
ap-10600	21	8	balanced	balanced	ADJ
ap-10600	21	9	if	if	SCONJ
ap-10600	21	10	for	for	ADP
ap-10600	21	11	any	any	DET
ap-10600	21	12	two	two	NUM
ap-10600	21	13	factors	factor	NOUN
ap-10600	21	14	v	v	ADP
ap-10600	21	15	,	,	PUNCT
ap-10600	21	16	w	w	NOUN
ap-10600	21	17	of	of	ADP
ap-10600	21	18	u	u	NOUN
ap-10600	21	19	of	of	ADP
ap-10600	21	20	the	the	DET
ap-10600	21	21	same	same	ADJ
ap-10600	21	22	length	length	NOUN
ap-10600	21	23	and	and	CCONJ
ap-10600	21	24	for	for	ADP
ap-10600	21	25	any	any	DET
ap-10600	21	26	letter	letter	NOUN
ap-10600	21	27	a	a	DET
ap-10600	21	28	∈	∈	PROPN
ap-10600	21	29	a	a	DET
ap-10600	21	30	holds∣∣|v|a	holds∣∣|v|a	ADJ
ap-10600	21	31	−	−	NOUN
ap-10600	21	32	|w|a	|w|a	NOUN
ap-10600	21	33	∣∣	∣∣	X
ap-10600	21	34	≤	≤	PROPN
ap-10600	21	35	k.	k.	PROPN
ap-10600	22	1	obviously	obviously	ADV
ap-10600	22	2	,	,	PUNCT
ap-10600	22	3	a	a	DET
ap-10600	22	4	k	k	ADV
ap-10600	22	5	-	-	ADJ
ap-10600	22	6	balanced	balanced	ADJ
ap-10600	22	7	sequence	sequence	NOUN
ap-10600	22	8	is	be	AUX
ap-10600	22	9	k	k	NOUN
ap-10600	22	10	-	-	ADJ
ap-10600	22	11	balanced	balanced	ADJ
ap-10600	22	12	for	for	ADP
ap-10600	22	13	any	any	DET
ap-10600	22	14	k	k	PROPN
ap-10600	22	15	>	>	X
ap-10600	22	16	k.	k.	PROPN
ap-10600	23	1	the	the	DET
ap-10600	23	2	study	study	NOUN
ap-10600	23	3	of	of	ADP
ap-10600	23	4	1	1	NUM
ap-10600	23	5	-	-	PUNCT
ap-10600	23	6	balanced	balanced	ADJ
ap-10600	23	7	sequences	sequence	NOUN
ap-10600	23	8	over	over	ADP
ap-10600	23	9	a	a	DET
ap-10600	23	10	binary	binary	ADJ
ap-10600	23	11	alphabet	alphabet	NOUN
ap-10600	23	12	{	{	PUNCT
ap-10600	23	13	a	a	PROPN
ap-10600	23	14	,	,	PUNCT
ap-10600	23	15	b	b	NOUN
ap-10600	23	16	}	}	PUNCT
ap-10600	23	17	was	be	AUX
ap-10600	23	18	initiated	initiate	VERB
ap-10600	23	19	by	by	ADP
ap-10600	23	20	hedlund	hedlund	PROPN
ap-10600	23	21	and	and	CCONJ
ap-10600	23	22	morse	morse	NOUN
ap-10600	23	23	[	[	X
ap-10600	23	24	1	1	NUM
ap-10600	23	25	]	]	PUNCT
ap-10600	23	26	.	.	PUNCT
ap-10600	24	1	they	they	PRON
ap-10600	24	2	showed	show	VERB
ap-10600	24	3	that	that	SCONJ
ap-10600	24	4	1	1	NUM
ap-10600	24	5	-	-	PUNCT
ap-10600	24	6	balancedness	balancedness	NOUN
ap-10600	24	7	requires	require	VERB
ap-10600	24	8	some	some	DET
ap-10600	24	9	particular	particular	ADJ
ap-10600	24	10	properties	property	NOUN
ap-10600	24	11	of	of	ADP
ap-10600	24	12	the	the	DET
ap-10600	24	13	sequence	sequence	NOUN
ap-10600	24	14	.	.	PUNCT
ap-10600	25	1	if	if	SCONJ
ap-10600	25	2	a	a	DET
ap-10600	25	3	1	1	NUM
ap-10600	25	4	-	-	PUNCT
ap-10600	25	5	balanced	balanced	ADJ
ap-10600	25	6	sequence	sequence	NOUN
ap-10600	25	7	is	be	AUX
ap-10600	25	8	eventually	eventually	ADV
ap-10600	25	9	periodic	periodic	ADJ
ap-10600	25	10	,	,	PUNCT
ap-10600	25	11	then	then	ADV
ap-10600	26	1	fa	fa	PROPN
ap-10600	27	1	and	and	CCONJ
ap-10600	27	2	fb	fb	INTJ
ap-10600	27	3	are	be	AUX
ap-10600	27	4	rational	rational	ADJ
ap-10600	27	5	.	.	PUNCT
ap-10600	28	1	in	in	ADP
ap-10600	28	2	the	the	DET
ap-10600	28	3	opposite	opposite	ADJ
ap-10600	28	4	case	case	NOUN
ap-10600	28	5	,	,	PUNCT
ap-10600	28	6	a	a	DET
ap-10600	28	7	1	1	NUM
ap-10600	28	8	-	-	PUNCT
ap-10600	28	9	balanced	balanced	ADJ
ap-10600	28	10	sequence	sequence	NOUN
ap-10600	28	11	is	be	AUX
ap-10600	28	12	called	call	VERB
ap-10600	28	13	sturmian	sturmian	NOUN
ap-10600	28	14	.	.	PUNCT
ap-10600	29	1	hedlund	hedlund	PROPN
ap-10600	29	2	and	and	CCONJ
ap-10600	29	3	morse	morse	PROPN
ap-10600	29	4	proved	prove	VERB
ap-10600	29	5	that	that	SCONJ
ap-10600	29	6	for	for	ADP
ap-10600	29	7	each	each	DET
ap-10600	29	8	positive	positive	ADJ
ap-10600	29	9	vector	vector	NOUN
ap-10600	29	10	(	(	PUNCT
ap-10600	29	11	fa	fa	NOUN
ap-10600	29	12	,	,	PUNCT
ap-10600	29	13	fb	fb	NOUN
ap-10600	29	14	)	)	PUNCT
ap-10600	29	15	,	,	PUNCT
ap-10600	29	16	where	where	SCONJ
ap-10600	29	17	fa	fa	INTJ
ap-10600	30	1	+	+	NUM
ap-10600	30	2	fb	fb	NOUN
ap-10600	30	3	=	=	SYM
ap-10600	30	4	1	1	NUM
ap-10600	31	1	,	,	PUNCT
ap-10600	31	2	there	there	PRON
ap-10600	31	3	exists	exist	VERB
ap-10600	31	4	a	a	DET
ap-10600	31	5	1	1	NUM
ap-10600	31	6	-	-	PUNCT
ap-10600	31	7	balanced	balanced	ADJ
ap-10600	31	8	sequence	sequence	NOUN
ap-10600	31	9	with	with	ADP
ap-10600	31	10	such	such	ADJ
ap-10600	31	11	letter	letter	NOUN
ap-10600	31	12	frequencies	frequency	NOUN
ap-10600	31	13	.	.	PUNCT
ap-10600	32	1	the	the	DET
ap-10600	32	2	class	class	NOUN
ap-10600	32	3	of	of	ADP
ap-10600	32	4	sturmian	sturmian	NOUN
ap-10600	32	5	sequences	sequence	NOUN
ap-10600	32	6	is	be	AUX
ap-10600	32	7	the	the	DET
ap-10600	32	8	most	most	ADV
ap-10600	32	9	studied	studied	ADJ
ap-10600	32	10	class	class	NOUN
ap-10600	32	11	of	of	ADP
ap-10600	32	12	sequences	sequence	NOUN
ap-10600	32	13	and	and	CCONJ
ap-10600	32	14	there	there	PRON
ap-10600	32	15	exist	exist	VERB
ap-10600	32	16	a	a	DET
ap-10600	32	17	lot	lot	NOUN
ap-10600	32	18	of	of	ADP
ap-10600	32	19	equivalent	equivalent	ADJ
ap-10600	32	20	definitions	definition	NOUN
ap-10600	32	21	of	of	ADP
ap-10600	32	22	sturmian	sturmian	ADJ
ap-10600	32	23	sequences	sequence	NOUN
ap-10600	32	24	,	,	PUNCT
ap-10600	32	25	see	see	VERB
ap-10600	32	26	[	[	X
ap-10600	32	27	2–4	2–4	NUM
ap-10600	32	28	]	]	PUNCT
ap-10600	32	29	.	.	PUNCT
ap-10600	33	1	these	these	DET
ap-10600	33	2	equivalent	equivalent	ADJ
ap-10600	33	3	definitions	definition	NOUN
ap-10600	33	4	allow	allow	VERB
ap-10600	33	5	sturmian	sturmian	ADJ
ap-10600	33	6	sequences	sequence	NOUN
ap-10600	33	7	to	to	PART
ap-10600	33	8	be	be	AUX
ap-10600	33	9	generalised	generalise	VERB
ap-10600	33	10	to	to	ADP
ap-10600	33	11	larger	large	ADJ
ap-10600	33	12	alphabets	alphabet	NOUN
ap-10600	33	13	in	in	ADP
ap-10600	33	14	many	many	ADJ
ap-10600	33	15	different	different	ADJ
ap-10600	33	16	ways	way	NOUN
ap-10600	33	17	,	,	PUNCT
ap-10600	33	18	see	see	VERB
ap-10600	33	19	[	[	X
ap-10600	33	20	2	2	NUM
ap-10600	33	21	]	]	PUNCT
ap-10600	33	22	.	.	PUNCT
ap-10600	34	1	on	on	ADP
ap-10600	34	2	the	the	DET
ap-10600	34	3	one	one	NUM
ap-10600	34	4	hand	hand	NOUN
ap-10600	34	5	,	,	PUNCT
ap-10600	34	6	one	one	NUM
ap-10600	34	7	of	of	ADP
ap-10600	34	8	the	the	DET
ap-10600	34	9	most	most	ADV
ap-10600	34	10	usual	usual	ADJ
ap-10600	34	11	generalisations	generalisation	NOUN
ap-10600	34	12	are	be	AUX
ap-10600	34	13	the	the	DET
ap-10600	34	14	arnoux	arnoux	NOUN
ap-10600	34	15	-	-	PUNCT
ap-10600	34	16	rauzy	rauzy	NOUN
ap-10600	34	17	sequences	sequence	NOUN
ap-10600	34	18	,	,	PUNCT
ap-10600	34	19	however	however	ADV
ap-10600	34	20	,	,	PUNCT
ap-10600	34	21	it	it	PRON
ap-10600	34	22	is	be	AUX
ap-10600	34	23	known	know	VERB
ap-10600	34	24	that	that	SCONJ
ap-10600	34	25	the	the	DET
ap-10600	34	26	letter	letter	NOUN
ap-10600	34	27	frequencies	frequency	NOUN
ap-10600	34	28	of	of	ADP
ap-10600	34	29	any	any	DET
ap-10600	34	30	arnoux	arnoux	NOUN
ap-10600	34	31	-	-	PUNCT
ap-10600	34	32	rauzy	rauzy	NOUN
ap-10600	34	33	sequence	sequence	NOUN
ap-10600	34	34	belong	belong	VERB
ap-10600	34	35	to	to	ADP
ap-10600	34	36	the	the	DET
ap-10600	34	37	rauzy	rauzy	NOUN
ap-10600	34	38	gasket	gasket	NOUN
ap-10600	35	1	[	[	X
ap-10600	35	2	5	5	NUM
ap-10600	35	3	]	]	PUNCT
ap-10600	35	4	,	,	PUNCT
ap-10600	35	5	which	which	PRON
ap-10600	35	6	is	be	AUX
ap-10600	35	7	a	a	DET
ap-10600	35	8	fractal	fractal	ADJ
ap-10600	35	9	set	set	NOUN
ap-10600	35	10	of	of	ADP
ap-10600	35	11	lebesgue	lebesgue	ADJ
ap-10600	35	12	measure	measure	NOUN
ap-10600	35	13	zero	zero	NUM
ap-10600	35	14	.	.	PUNCT
ap-10600	36	1	on	on	ADP
ap-10600	36	2	the	the	DET
ap-10600	36	3	other	other	ADJ
ap-10600	36	4	hand	hand	NOUN
ap-10600	36	5	,	,	PUNCT
ap-10600	36	6	for	for	ADP
ap-10600	36	7	any	any	DET
ap-10600	36	8	given	give	VERB
ap-10600	36	9	letter	letter	NOUN
ap-10600	36	10	frequencies	frequency	NOUN
ap-10600	36	11	,	,	PUNCT
ap-10600	36	12	one	one	PRON
ap-10600	36	13	can	can	AUX
ap-10600	36	14	construct	construct	VERB
ap-10600	36	15	a	a	DET
ap-10600	36	16	sequence	sequence	NOUN
ap-10600	36	17	of	of	ADP
ap-10600	36	18	sublinear	sublinear	NOUN
ap-10600	36	19	factor	factor	NOUN
ap-10600	36	20	complexity	complexity	NOUN
ap-10600	36	21	by	by	ADP
ap-10600	36	22	coding	code	VERB
ap-10600	36	23	a	a	DET
ap-10600	36	24	d	d	ADJ
ap-10600	36	25	-	-	PUNCT
ap-10600	36	26	interval	interval	NOUN
ap-10600	36	27	exchange	exchange	NOUN
ap-10600	36	28	transformation	transformation	NOUN
ap-10600	36	29	.	.	PUNCT
ap-10600	37	1	it	it	PRON
ap-10600	37	2	is	be	AUX
ap-10600	37	3	,	,	PUNCT
ap-10600	37	4	however	however	ADV
ap-10600	37	5	,	,	PUNCT
ap-10600	37	6	known	know	VERB
ap-10600	37	7	[	[	X
ap-10600	37	8	6	6	NUM
ap-10600	37	9	]	]	PUNCT
ap-10600	37	10	that	that	SCONJ
ap-10600	37	11	such	such	DET
ap-10600	37	12	a	a	DET
ap-10600	37	13	generalisation	generalisation	NOUN
ap-10600	37	14	of	of	ADP
ap-10600	37	15	sturmian	sturmian	ADJ
ap-10600	37	16	sequences	sequence	NOUN
ap-10600	37	17	to	to	ADP
ap-10600	37	18	d	d	VERB
ap-10600	37	19	-	-	PUNCT
ap-10600	37	20	ary	ary	ADJ
ap-10600	37	21	alphabet	alphabet	NOUN
ap-10600	37	22	is	be	AUX
ap-10600	37	23	almost	almost	ADV
ap-10600	37	24	always	always	ADV
ap-10600	37	25	unbalanced	unbalanced	ADJ
ap-10600	37	26	.	.	PUNCT
ap-10600	38	1	1	1	NUM
ap-10600	38	2	-	-	PUNCT
ap-10600	38	3	balanced	balance	VERB
ap-10600	38	4	sequences	sequence	NOUN
ap-10600	38	5	over	over	ADP
ap-10600	38	6	alphabets	alphabet	NOUN
ap-10600	38	7	of	of	ADP
ap-10600	38	8	size	size	NOUN
ap-10600	38	9	d	d	X
ap-10600	38	10	were	be	AUX
ap-10600	38	11	described	describe	VERB
ap-10600	38	12	by	by	ADP
ap-10600	38	13	hubert	hubert	PROPN
ap-10600	39	1	[	[	X
ap-10600	39	2	7	7	NUM
ap-10600	39	3	]	]	PUNCT
ap-10600	39	4	.	.	PUNCT
ap-10600	40	1	the	the	DET
ap-10600	40	2	description	description	NOUN
ap-10600	40	3	implies	imply	VERB
ap-10600	40	4	that	that	SCONJ
ap-10600	40	5	for	for	ADP
ap-10600	40	6	d	d	PROPN
ap-10600	40	7	≥	≥	NUM
ap-10600	40	8	3	3	NUM
ap-10600	40	9	,	,	PUNCT
ap-10600	40	10	the	the	DET
ap-10600	40	11	frequency	frequency	NOUN
ap-10600	40	12	vector	vector	NOUN
ap-10600	40	13	(	(	PUNCT
ap-10600	40	14	fa)a∈a	fa)a∈a	NUM
ap-10600	40	15	of	of	ADP
ap-10600	40	16	1	1	NUM
ap-10600	40	17	-	-	PUNCT
ap-10600	40	18	balanced	balanced	ADJ
ap-10600	40	19	sequences	sequence	NOUN
ap-10600	40	20	takes	take	VERB
ap-10600	40	21	only	only	ADV
ap-10600	40	22	a	a	DET
ap-10600	40	23	specific	specific	ADJ
ap-10600	40	24	form	form	NOUN
ap-10600	40	25	,	,	PUNCT
ap-10600	40	26	see	see	VERB
ap-10600	40	27	lemma	lemma	PROPN
ap-10600	40	28	11	11	NUM
ap-10600	40	29	.	.	PUNCT
ap-10600	41	1	this	this	DET
ap-10600	41	2	fact	fact	NOUN
ap-10600	41	3	motivates	motivate	VERB
ap-10600	41	4	our	our	PRON
ap-10600	41	5	definition	definition	NOUN
ap-10600	41	6	of	of	ADP
ap-10600	41	7	balancedness	balancedness	NOUN
ap-10600	41	8	threshold	threshold	NOUN
ap-10600	41	9	for	for	ADP
ap-10600	41	10	an	an	DET
ap-10600	41	11	alphabet	alphabet	NOUN
ap-10600	41	12	of	of	ADP
ap-10600	41	13	size	size	NOUN
ap-10600	41	14	d.	d.	PROPN
ap-10600	41	15	definition	definition	NOUN
ap-10600	41	16	1	1	NUM
ap-10600	41	17	.	.	PUNCT
ap-10600	42	1	we	we	PRON
ap-10600	42	2	say	say	VERB
ap-10600	42	3	that	that	SCONJ
ap-10600	42	4	k	k	PROPN
ap-10600	42	5	∈	∈	PROPN
ap-10600	42	6	n	n	PRON
ap-10600	42	7	is	be	AUX
ap-10600	42	8	frequency	frequency	NOUN
ap-10600	42	9	restrictive	restrictive	ADJ
ap-10600	42	10	for	for	ADP
ap-10600	42	11	d	d	PROPN
ap-10600	42	12	if	if	SCONJ
ap-10600	42	13	there	there	PRON
ap-10600	42	14	exists	exist	VERB
ap-10600	42	15	a	a	DET
ap-10600	42	16	positive	positive	ADJ
ap-10600	42	17	vector	vector	NOUN
ap-10600	42	18	f⃗	f⃗	NOUN
ap-10600	42	19	=	=	SYM
ap-10600	42	20	(	(	PUNCT
ap-10600	42	21	f1	f1	NOUN
ap-10600	42	22	,	,	PUNCT
ap-10600	42	23	f2	f2	PROPN
ap-10600	42	24	,	,	PUNCT
ap-10600	42	25	.	.	PUNCT
ap-10600	42	26	.	.	PUNCT
ap-10600	42	27	.	.	PUNCT
ap-10600	43	1	,	,	PUNCT
ap-10600	43	2	fd	fd	PROPN
ap-10600	43	3	)	)	PUNCT
ap-10600	43	4	with	with	ADP
ap-10600	43	5	∑	∑	ADV
ap-10600	43	6	i∈a	i∈a	ADJ
ap-10600	43	7	fi	fi	NOUN
ap-10600	43	8	=	=	NOUN
ap-10600	43	9	1	1	NUM
ap-10600	43	10	such	such	ADJ
ap-10600	43	11	that	that	SCONJ
ap-10600	43	12	no	no	DET
ap-10600	43	13	k	k	ADV
ap-10600	43	14	-	-	ADJ
ap-10600	43	15	balanced	balanced	ADJ
ap-10600	43	16	d	d	ADJ
ap-10600	43	17	-	-	ADJ
ap-10600	43	18	ary	ary	ADJ
ap-10600	43	19	sequence	sequence	NOUN
ap-10600	43	20	has	have	VERB
ap-10600	43	21	the	the	DET
ap-10600	43	22	frequency	frequency	NOUN
ap-10600	43	23	vector	vector	NOUN
ap-10600	43	24	f⃗	f⃗	NOUN
ap-10600	43	25	.	.	PUNCT
ap-10600	44	1	balancedness	balancedness	NOUN
ap-10600	44	2	threshold	threshold	NOUN
ap-10600	44	3	bt	bt	PROPN
ap-10600	44	4	(	(	PUNCT
ap-10600	44	5	d	d	NOUN
ap-10600	44	6	)	)	PUNCT
ap-10600	44	7	is	be	AUX
ap-10600	44	8	the	the	DET
ap-10600	44	9	minimum	minimum	ADJ
ap-10600	44	10	k	k	PROPN
ap-10600	44	11	∈	∈	PROPN
ap-10600	44	12	n	n	PRON
ap-10600	44	13	such	such	ADJ
ap-10600	44	14	that	that	SCONJ
ap-10600	44	15	k	k	PROPN
ap-10600	44	16	is	be	AUX
ap-10600	44	17	not	not	PART
ap-10600	44	18	frequency	frequency	NOUN
ap-10600	44	19	restrictive	restrictive	ADJ
ap-10600	44	20	for	for	ADP
ap-10600	44	21	d.	d.	PROPN
ap-10600	44	22	obviously	obviously	ADV
ap-10600	44	23	,	,	PUNCT
ap-10600	44	24	bt	bt	PROPN
ap-10600	44	25	(	(	PUNCT
ap-10600	44	26	1	1	NUM
ap-10600	44	27	)	)	PUNCT
ap-10600	44	28	=	=	SYM
ap-10600	44	29	0	0	X
ap-10600	44	30	.	.	PUNCT
ap-10600	45	1	it	it	PRON
ap-10600	45	2	follows	follow	VERB
ap-10600	45	3	from	from	ADP
ap-10600	45	4	the	the	DET
ap-10600	45	5	result	result	NOUN
ap-10600	45	6	by	by	ADP
ap-10600	45	7	hedlund	hedlund	PROPN
ap-10600	45	8	and	and	CCONJ
ap-10600	45	9	morse	morse	VERB
ap-10600	45	10	that	that	SCONJ
ap-10600	45	11	bt	bt	PROPN
ap-10600	45	12	(	(	PUNCT
ap-10600	45	13	2	2	NUM
ap-10600	45	14	)	)	PUNCT
ap-10600	45	15	=	=	SYM
ap-10600	45	16	1	1	X
ap-10600	45	17	.	.	X
ap-10600	46	1	in	in	ADP
ap-10600	46	2	lemma	lemma	PROPN
ap-10600	46	3	11	11	NUM
ap-10600	46	4	,	,	PUNCT
ap-10600	46	5	we	we	PRON
ap-10600	46	6	explain	explain	VERB
ap-10600	46	7	why	why	SCONJ
ap-10600	46	8	bt	bt	PROPN
ap-10600	46	9	(	(	PUNCT
ap-10600	46	10	d	d	PROPN
ap-10600	46	11	)	)	PUNCT
ap-10600	46	12	≥	≥	NOUN
ap-10600	46	13	2	2	NUM
ap-10600	46	14	for	for	ADP
ap-10600	46	15	every	every	DET
ap-10600	46	16	d	d	PROPN
ap-10600	46	17	≥	≥	NOUN
ap-10600	46	18	3	3	NUM
ap-10600	46	19	.	.	PUNCT
ap-10600	47	1	in	in	ADP
ap-10600	47	2	[	[	X
ap-10600	47	3	8	8	NUM
ap-10600	47	4	]	]	PUNCT
ap-10600	47	5	,	,	PUNCT
ap-10600	47	6	the	the	DET
ap-10600	47	7	sequence	sequence	NOUN
ap-10600	47	8	coding	code	VERB
ap-10600	47	9	rectangle	rectangle	NOUN
ap-10600	47	10	exchange	exchange	NOUN
ap-10600	47	11	transformation	transformation	NOUN
ap-10600	47	12	is	be	AUX
ap-10600	47	13	used	use	VERB
ap-10600	47	14	to	to	PART
ap-10600	47	15	prove	prove	VERB
ap-10600	47	16	bt	bt	NOUN
ap-10600	47	17	(	(	PUNCT
ap-10600	47	18	3	3	NUM
ap-10600	47	19	)	)	PUNCT
ap-10600	48	1	=	=	SYM
ap-10600	48	2	2	2	X
ap-10600	48	3	.	.	PUNCT
ap-10600	49	1	moreover	moreover	ADV
ap-10600	49	2	,	,	PUNCT
ap-10600	49	3	the	the	DET
ap-10600	49	4	factor	factor	NOUN
ap-10600	49	5	complexity	complexity	NOUN
ap-10600	49	6	of	of	ADP
ap-10600	49	7	such	such	ADJ
ap-10600	49	8	ternary	ternary	ADJ
ap-10600	49	9	sequences	sequence	NOUN
ap-10600	49	10	satisfies	satisfie	NOUN
ap-10600	49	11	c(n	c(n	PROPN
ap-10600	49	12	)	)	PUNCT
ap-10600	49	13	≤	≤	NOUN
ap-10600	49	14	534	534	NUM
ap-10600	49	15	https://doi.org/10.14311/ap.2025.65.0534	https://doi.org/10.14311/ap.2025.65.0534	NOUN
ap-10600	49	16	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10600	49	17	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10600	49	18	vol	vol	NOUN
ap-10600	49	19	.	.	PROPN
ap-10600	50	1	65	65	NUM
ap-10600	50	2	no	no	NOUN
ap-10600	50	3	.	.	PUNCT
ap-10600	51	1	5/2025	5/2025	NUM
ap-10600	51	2	frequencies	frequency	NOUN
ap-10600	51	3	of	of	ADP
ap-10600	51	4	letters	letter	NOUN
ap-10600	51	5	in	in	ADP
ap-10600	51	6	infinite	infinite	ADJ
ap-10600	51	7	k	k	ADV
ap-10600	51	8	-	-	ADJ
ap-10600	51	9	balanced	balanced	ADJ
ap-10600	51	10	sequences	sequence	NOUN
ap-10600	51	11	αn2	αn2	NOUN
ap-10600	51	12	(	(	PUNCT
ap-10600	51	13	1	1	NUM
ap-10600	51	14	+	+	NUM
ap-10600	51	15	o(1	o(1	NOUN
ap-10600	51	16	)	)	PUNCT
ap-10600	51	17	)	)	PUNCT
ap-10600	51	18	,	,	PUNCT
ap-10600	51	19	for	for	ADP
ap-10600	51	20	parameter	parameter	NOUN
ap-10600	51	21	α	α	PROPN
ap-10600	51	22	∈	∈	PROPN
ap-10600	51	23	(	(	PUNCT
ap-10600	51	24	0	0	NUM
ap-10600	51	25	,	,	PUNCT
ap-10600	51	26	1	1	NUM
ap-10600	51	27	)	)	PUNCT
ap-10600	51	28	.	.	PUNCT
ap-10600	52	1	the	the	DET
ap-10600	52	2	equality	equality	NOUN
ap-10600	52	3	bt	bt	PROPN
ap-10600	52	4	(	(	PUNCT
ap-10600	52	5	3	3	NUM
ap-10600	52	6	)	)	PUNCT
ap-10600	52	7	=	=	SYM
ap-10600	52	8	2	2	NUM
ap-10600	52	9	follows	follow	VERB
ap-10600	52	10	also	also	ADV
ap-10600	52	11	from	from	ADP
ap-10600	52	12	the	the	DET
ap-10600	52	13	properties	property	NOUN
ap-10600	52	14	of	of	ADP
ap-10600	52	15	ternary	ternary	ADJ
ap-10600	52	16	hypercubic	hypercubic	ADJ
ap-10600	52	17	billiard	billiard	PROPN
ap-10600	52	18	sequences	sequence	NOUN
ap-10600	52	19	.	.	PUNCT
ap-10600	53	1	this	this	DET
ap-10600	53	2	class	class	NOUN
ap-10600	53	3	contains	contain	VERB
ap-10600	53	4	sequences	sequence	NOUN
ap-10600	53	5	of	of	ADP
ap-10600	53	6	any	any	DET
ap-10600	53	7	given	give	VERB
ap-10600	53	8	letter	letter	NOUN
ap-10600	53	9	frequencies	frequency	NOUN
ap-10600	53	10	.	.	PUNCT
ap-10600	54	1	they	they	PRON
ap-10600	54	2	are	be	AUX
ap-10600	54	3	2	2	NUM
ap-10600	54	4	-	-	PUNCT
ap-10600	54	5	balanced	balanced	ADJ
ap-10600	55	1	[	[	X
ap-10600	55	2	9	9	NUM
ap-10600	55	3	]	]	PUNCT
ap-10600	55	4	and	and	CCONJ
ap-10600	55	5	under	under	ADP
ap-10600	55	6	an	an	DET
ap-10600	55	7	additional	additional	ADJ
ap-10600	55	8	condition	condition	NOUN
ap-10600	55	9	on	on	ADP
ap-10600	55	10	momentum	momentum	NOUN
ap-10600	55	11	,	,	PUNCT
ap-10600	55	12	their	their	PRON
ap-10600	55	13	factor	factor	NOUN
ap-10600	55	14	complexity	complexity	NOUN
ap-10600	55	15	equals	equal	VERB
ap-10600	55	16	n2	n2	NOUN
ap-10600	55	17	+	+	CCONJ
ap-10600	55	18	n+	n+	NUM
ap-10600	55	19	1	1	NUM
ap-10600	55	20	,	,	PUNCT
ap-10600	55	21	see	see	VERB
ap-10600	55	22	[	[	X
ap-10600	55	23	10–12	10–12	NUM
ap-10600	55	24	]	]	PUNCT
ap-10600	55	25	.	.	PUNCT
ap-10600	56	1	the	the	DET
ap-10600	56	2	main	main	ADJ
ap-10600	56	3	contribution	contribution	NOUN
ap-10600	56	4	of	of	ADP
ap-10600	56	5	this	this	DET
ap-10600	56	6	paper	paper	NOUN
ap-10600	56	7	is	be	AUX
ap-10600	56	8	the	the	DET
ap-10600	56	9	upper	upper	ADJ
ap-10600	56	10	bound	bind	VERB
ap-10600	56	11	on	on	ADP
ap-10600	56	12	the	the	DET
ap-10600	56	13	balancedness	balancedness	NOUN
ap-10600	56	14	threshold	threshold	NOUN
ap-10600	56	15	.	.	PUNCT
ap-10600	57	1	theorem	theorem	NOUN
ap-10600	57	2	2	2	NUM
ap-10600	57	3	.	.	PUNCT
ap-10600	58	1	let	let	VERB
ap-10600	58	2	d	d	PRON
ap-10600	58	3	be	be	AUX
ap-10600	58	4	a	a	DET
ap-10600	58	5	positive	positive	ADJ
ap-10600	58	6	integer	integer	NOUN
ap-10600	58	7	.	.	PUNCT
ap-10600	59	1	then	then	ADV
ap-10600	59	2	bt	bt	X
ap-10600	59	3	(	(	PUNCT
ap-10600	59	4	d	d	NOUN
ap-10600	59	5	)	)	PUNCT
ap-10600	59	6	≤	≤	NOUN
ap-10600	60	1	⌈log2	⌈log2	DET
ap-10600	60	2	d⌉.	d⌉.	NOUN
ap-10600	60	3	on	on	ADP
ap-10600	60	4	top	top	NOUN
ap-10600	60	5	of	of	ADP
ap-10600	60	6	it	it	PRON
ap-10600	60	7	,	,	PUNCT
ap-10600	60	8	we	we	PRON
ap-10600	60	9	discuss	discuss	VERB
ap-10600	60	10	factor	factor	NOUN
ap-10600	60	11	complexity	complexity	NOUN
ap-10600	60	12	of	of	ADP
ap-10600	60	13	d	d	PROPN
ap-10600	60	14	-	-	ADJ
ap-10600	60	15	ary	ary	PROPN
ap-10600	60	16	sequences	sequence	NOUN
ap-10600	60	17	used	use	VERB
ap-10600	60	18	in	in	ADP
ap-10600	60	19	the	the	DET
ap-10600	60	20	proof	proof	NOUN
ap-10600	60	21	of	of	ADP
ap-10600	60	22	the	the	DET
ap-10600	60	23	above	above	ADJ
ap-10600	60	24	theorem	theorem	NOUN
ap-10600	60	25	.	.	PUNCT
ap-10600	61	1	getting	get	VERB
ap-10600	61	2	a	a	DET
ap-10600	61	3	lower	low	ADJ
ap-10600	61	4	bound	bind	VERB
ap-10600	61	5	on	on	ADP
ap-10600	61	6	bt	bt	PROPN
ap-10600	61	7	(	(	PUNCT
ap-10600	61	8	d	d	NOUN
ap-10600	61	9	)	)	PUNCT
ap-10600	61	10	is	be	AUX
ap-10600	61	11	beyond	beyond	ADP
ap-10600	61	12	our	our	PRON
ap-10600	61	13	means	mean	NOUN
ap-10600	61	14	.	.	PUNCT
ap-10600	62	1	it	it	PRON
ap-10600	62	2	is	be	AUX
ap-10600	62	3	unclear	unclear	ADJ
ap-10600	62	4	whether	whether	SCONJ
ap-10600	62	5	,	,	PUNCT
ap-10600	62	6	for	for	ADP
ap-10600	62	7	some	some	DET
ap-10600	62	8	d	d	PROPN
ap-10600	62	9	∈	∈	PROPN
ap-10600	62	10	n	n	CCONJ
ap-10600	62	11	,	,	PUNCT
ap-10600	62	12	bt	bt	PROPN
ap-10600	62	13	(	(	PUNCT
ap-10600	62	14	d	d	PROPN
ap-10600	62	15	)	)	PUNCT
ap-10600	62	16	≥	≥	NOUN
ap-10600	62	17	3	3	NUM
ap-10600	62	18	holds	hold	NOUN
ap-10600	62	19	.	.	PUNCT
ap-10600	63	1	the	the	DET
ap-10600	63	2	characterisation	characterisation	NOUN
ap-10600	63	3	of	of	ADP
ap-10600	63	4	2	2	NUM
ap-10600	63	5	-	-	PUNCT
ap-10600	63	6	balanced	balanced	ADJ
ap-10600	63	7	sequences	sequence	NOUN
ap-10600	63	8	,	,	PUNCT
ap-10600	63	9	which	which	PRON
ap-10600	63	10	would	would	AUX
ap-10600	63	11	be	be	AUX
ap-10600	63	12	helpful	helpful	ADJ
ap-10600	63	13	for	for	ADP
ap-10600	63	14	this	this	DET
ap-10600	63	15	purpose	purpose	NOUN
ap-10600	63	16	,	,	PUNCT
ap-10600	63	17	is	be	AUX
ap-10600	63	18	still	still	ADV
ap-10600	63	19	missing	miss	VERB
ap-10600	63	20	.	.	PUNCT
ap-10600	64	1	2	2	X
ap-10600	64	2	.	.	X
ap-10600	64	3	frequencies	frequency	NOUN
ap-10600	64	4	and	and	CCONJ
ap-10600	64	5	balancedness	balancedness	NOUN
ap-10600	64	6	in	in	ADP
ap-10600	64	7	fixed	fix	VERB
ap-10600	64	8	points	point	NOUN
ap-10600	64	9	of	of	ADP
ap-10600	64	10	morphism	morphism	NOUN
ap-10600	64	11	in	in	ADP
ap-10600	64	12	combinatorics	combinatoric	NOUN
ap-10600	64	13	on	on	ADP
ap-10600	64	14	words	word	NOUN
ap-10600	64	15	,	,	PUNCT
ap-10600	64	16	sequences	sequence	NOUN
ap-10600	64	17	with	with	ADP
ap-10600	64	18	some	some	DET
ap-10600	64	19	required	require	VERB
ap-10600	64	20	properties	property	NOUN
ap-10600	64	21	are	be	AUX
ap-10600	64	22	usually	usually	ADV
ap-10600	64	23	looked	look	VERB
ap-10600	64	24	up	up	ADP
ap-10600	64	25	among	among	ADP
ap-10600	64	26	morphic	morphic	ADJ
ap-10600	64	27	sequences	sequence	NOUN
ap-10600	64	28	.	.	PUNCT
ap-10600	65	1	let	let	VERB
ap-10600	65	2	us	we	PRON
ap-10600	65	3	recall	recall	VERB
ap-10600	65	4	what	what	PRON
ap-10600	65	5	is	be	AUX
ap-10600	65	6	known	know	VERB
ap-10600	65	7	on	on	ADP
ap-10600	65	8	letter	letter	NOUN
ap-10600	65	9	frequencies	frequency	NOUN
ap-10600	65	10	and	and	CCONJ
ap-10600	65	11	balancedness	balancedness	NOUN
ap-10600	65	12	of	of	ADP
ap-10600	65	13	such	such	ADJ
ap-10600	65	14	sequences	sequence	NOUN
ap-10600	65	15	.	.	PUNCT
ap-10600	66	1	it	it	PRON
ap-10600	66	2	clarifies	clarify	VERB
ap-10600	66	3	why	why	SCONJ
ap-10600	66	4	such	such	ADJ
ap-10600	66	5	sequences	sequence	NOUN
ap-10600	66	6	can	can	AUX
ap-10600	66	7	not	not	PART
ap-10600	66	8	be	be	AUX
ap-10600	66	9	used	use	VERB
ap-10600	66	10	in	in	ADP
ap-10600	66	11	the	the	DET
ap-10600	66	12	proof	proof	NOUN
ap-10600	66	13	of	of	ADP
ap-10600	66	14	theorem	theorem	NOUN
ap-10600	66	15	2	2	NUM
ap-10600	66	16	.	.	PUNCT
ap-10600	66	17	given	give	VERB
ap-10600	66	18	two	two	NUM
ap-10600	66	19	alphabets	alphabet	NOUN
ap-10600	66	20	a	a	DET
ap-10600	66	21	,	,	PUNCT
ap-10600	66	22	b	b	NOUN
ap-10600	66	23	,	,	PUNCT
ap-10600	66	24	then	then	ADV
ap-10600	66	25	a	a	DET
ap-10600	66	26	morphism	morphism	NOUN
ap-10600	66	27	is	be	AUX
ap-10600	66	28	a	a	DET
ap-10600	66	29	map	map	NOUN
ap-10600	66	30	ψ	ψ	X
ap-10600	66	31	:	:	PUNCT
ap-10600	66	32	a∗	a∗	PROPN
ap-10600	66	33	→	→	SYM
ap-10600	66	34	b∗	b∗	ADJ
ap-10600	66	35	such	such	ADJ
ap-10600	66	36	that	that	DET
ap-10600	66	37	ψ(uv	ψ(uv	NOUN
ap-10600	66	38	)	)	PUNCT
ap-10600	66	39	=	=	SYM
ap-10600	66	40	ψ(u)ψ(v	ψ(u)ψ(v	NOUN
ap-10600	66	41	)	)	PUNCT
ap-10600	66	42	for	for	ADP
ap-10600	66	43	all	all	DET
ap-10600	66	44	words	word	NOUN
ap-10600	66	45	u	u	NOUN
ap-10600	66	46	,	,	PUNCT
ap-10600	66	47	v	v	PROPN
ap-10600	66	48	∈	∈	PROPN
ap-10600	66	49	a∗	a∗	NOUN
ap-10600	66	50	,	,	PUNCT
ap-10600	66	51	where	where	SCONJ
ap-10600	66	52	uv	uv	NOUN
ap-10600	66	53	means	mean	VERB
ap-10600	66	54	concatenation	concatenation	NOUN
ap-10600	66	55	of	of	ADP
ap-10600	66	56	the	the	DET
ap-10600	66	57	words	word	NOUN
ap-10600	66	58	u	u	NOUN
ap-10600	66	59	and	and	CCONJ
ap-10600	66	60	v.	v.	ADP
ap-10600	66	61	the	the	DET
ap-10600	66	62	morphism	morphism	NOUN
ap-10600	66	63	ψ	ψ	PROPN
ap-10600	66	64	can	can	AUX
ap-10600	66	65	be	be	AUX
ap-10600	66	66	naturally	naturally	ADV
ap-10600	66	67	extended	extend	VERB
ap-10600	66	68	to	to	ADP
ap-10600	66	69	a	a	DET
ap-10600	66	70	sequence	sequence	NOUN
ap-10600	66	71	u	u	NOUN
ap-10600	66	72	=	=	NOUN
ap-10600	66	73	u0u1u2	u0u1u2	X
ap-10600	66	74	·	·	PUNCT
ap-10600	66	75	·	·	PUNCT
ap-10600	66	76	·	·	PUNCT
ap-10600	66	77	over	over	ADP
ap-10600	66	78	a	a	PRON
ap-10600	66	79	by	by	ADP
ap-10600	66	80	setting	set	VERB
ap-10600	66	81	ψ(u	ψ(u	NOUN
ap-10600	66	82	)	)	PUNCT
ap-10600	66	83	=	=	SYM
ap-10600	66	84	ψ(u0)ψ(u1)ψ(u2	ψ(u0)ψ(u1)ψ(u2	NOUN
ap-10600	66	85	)	)	PUNCT
ap-10600	66	86	·	·	PUNCT
ap-10600	66	87	·	·	PUNCT
ap-10600	66	88	·	·	PUNCT
ap-10600	66	89	.	.	PUNCT
ap-10600	67	1	a	a	DET
ap-10600	67	2	fixed	fix	VERB
ap-10600	67	3	point	point	NOUN
ap-10600	67	4	of	of	ADP
ap-10600	67	5	a	a	DET
ap-10600	67	6	morphism	morphism	NOUN
ap-10600	67	7	ψ	ψ	NOUN
ap-10600	67	8	:	:	PUNCT
ap-10600	67	9	a∗	a∗	PROPN
ap-10600	67	10	→	→	SYM
ap-10600	67	11	a∗	a∗	PROPN
ap-10600	67	12	is	be	AUX
ap-10600	67	13	a	a	DET
ap-10600	67	14	sequence	sequence	NOUN
ap-10600	67	15	u	u	NOUN
ap-10600	67	16	such	such	ADJ
ap-10600	67	17	that	that	SCONJ
ap-10600	67	18	ψ(u	ψ(u	PROPN
ap-10600	67	19	)	)	PUNCT
ap-10600	67	20	=	=	PUNCT
ap-10600	68	1	u.	u.	NOUN
ap-10600	68	2	we	we	PRON
ap-10600	68	3	associate	associate	VERB
ap-10600	68	4	to	to	ADP
ap-10600	68	5	a	a	DET
ap-10600	68	6	morphism	morphism	NOUN
ap-10600	68	7	ψ	ψ	NOUN
ap-10600	68	8	:	:	PUNCT
ap-10600	68	9	a∗	a∗	PROPN
ap-10600	68	10	→	→	SYM
ap-10600	68	11	a∗	a∗	NOUN
ap-10600	68	12	the	the	DET
ap-10600	68	13	incidence	incidence	NOUN
ap-10600	68	14	matrix	matrix	NOUN
ap-10600	68	15	mψ	mψ	NOUN
ap-10600	68	16	defined	define	VERB
ap-10600	68	17	for	for	ADP
ap-10600	68	18	each	each	DET
ap-10600	68	19	i	i	PRON
ap-10600	68	20	,	,	PUNCT
ap-10600	68	21	j	j	PROPN
ap-10600	68	22	∈	∈	PROPN
ap-10600	68	23	{	{	PUNCT
ap-10600	68	24	1	1	NUM
ap-10600	68	25	,	,	PUNCT
ap-10600	68	26	2	2	NUM
ap-10600	68	27	,	,	PUNCT
ap-10600	68	28	.	.	PUNCT
ap-10600	68	29	.	.	PUNCT
ap-10600	68	30	.	.	PUNCT
ap-10600	69	1	,	,	PUNCT
ap-10600	69	2	d	d	X
ap-10600	69	3	}	}	PUNCT
ap-10600	69	4	as	as	ADP
ap-10600	69	5	(	(	PUNCT
ap-10600	69	6	mψ)ij	mψ)ij	PROPN
ap-10600	69	7	=	=	PUNCT
ap-10600	69	8	|ψ(j)|i	|ψ(j)|i	NOUN
ap-10600	69	9	.	.	PUNCT
ap-10600	70	1	a	a	DET
ap-10600	70	2	morphism	morphism	NOUN
ap-10600	70	3	ψ	ψ	NOUN
ap-10600	70	4	is	be	AUX
ap-10600	70	5	primitive	primitive	ADJ
ap-10600	70	6	if	if	SCONJ
ap-10600	70	7	the	the	DET
ap-10600	70	8	matrix	matrix	NOUN
ap-10600	70	9	mψ	mψ	NOUN
ap-10600	70	10	is	be	AUX
ap-10600	70	11	primitive	primitive	ADJ
ap-10600	70	12	,	,	PUNCT
ap-10600	70	13	i.e.	i.e.	X
ap-10600	70	14	,	,	PUNCT
ap-10600	70	15	there	there	PRON
ap-10600	70	16	exists	exist	VERB
ap-10600	70	17	k	k	PROPN
ap-10600	70	18	∈	∈	PROPN
ap-10600	70	19	n	n	PRON
ap-10600	70	20	such	such	ADJ
ap-10600	70	21	that	that	SCONJ
ap-10600	70	22	mk	mk	PROPN
ap-10600	70	23	ψ	ψ	NOUN
ap-10600	70	24	is	be	AUX
ap-10600	70	25	a	a	DET
ap-10600	70	26	positive	positive	ADJ
ap-10600	70	27	matrix	matrix	NOUN
ap-10600	70	28	.	.	PUNCT
ap-10600	71	1	in	in	ADP
ap-10600	71	2	the	the	DET
ap-10600	71	3	sequel	sequel	NOUN
ap-10600	71	4	,	,	PUNCT
ap-10600	71	5	we	we	PRON
ap-10600	71	6	limit	limit	VERB
ap-10600	71	7	our	our	PRON
ap-10600	71	8	consideration	consideration	NOUN
ap-10600	71	9	to	to	ADP
ap-10600	71	10	the	the	DET
ap-10600	71	11	fixed	fix	VERB
ap-10600	71	12	points	point	NOUN
ap-10600	71	13	of	of	ADP
ap-10600	71	14	primitive	primitive	ADJ
ap-10600	71	15	morphisms	morphism	NOUN
ap-10600	71	16	.	.	PUNCT
ap-10600	72	1	frequencies	frequency	NOUN
ap-10600	72	2	of	of	ADP
ap-10600	72	3	letters	letter	NOUN
ap-10600	72	4	in	in	ADP
ap-10600	72	5	any	any	DET
ap-10600	72	6	fixed	fix	VERB
ap-10600	72	7	point	point	NOUN
ap-10600	72	8	of	of	ADP
ap-10600	72	9	a	a	DET
ap-10600	72	10	primitive	primitive	ADJ
ap-10600	72	11	morphism	morphism	NOUN
ap-10600	72	12	are	be	AUX
ap-10600	72	13	given	give	VERB
ap-10600	72	14	by	by	ADP
ap-10600	72	15	the	the	DET
ap-10600	72	16	coordinates	coordinate	NOUN
ap-10600	72	17	of	of	ADP
ap-10600	72	18	a	a	DET
ap-10600	72	19	unique	unique	ADJ
ap-10600	72	20	positive	positive	ADJ
ap-10600	72	21	eigenvector	eigenvector	NOUN
ap-10600	72	22	of	of	ADP
ap-10600	72	23	norm	norm	NOUN
ap-10600	72	24	one	one	NUM
ap-10600	72	25	corresponding	correspond	VERB
ap-10600	72	26	to	to	ADP
ap-10600	72	27	the	the	DET
ap-10600	72	28	spectral	spectral	ADJ
ap-10600	72	29	radius	radius	NOUN
ap-10600	72	30	[	[	X
ap-10600	72	31	13	13	NUM
ap-10600	72	32	]	]	PUNCT
ap-10600	72	33	.	.	PUNCT
ap-10600	73	1	therefore	therefore	ADV
ap-10600	73	2	,	,	PUNCT
ap-10600	73	3	the	the	DET
ap-10600	73	4	letter	letter	NOUN
ap-10600	73	5	frequencies	frequency	NOUN
ap-10600	73	6	belong	belong	VERB
ap-10600	73	7	to	to	ADP
ap-10600	73	8	an	an	DET
ap-10600	73	9	algebraic	algebraic	ADJ
ap-10600	73	10	field	field	NOUN
ap-10600	73	11	of	of	ADP
ap-10600	73	12	order	order	NOUN
ap-10600	73	13	no	no	ADV
ap-10600	73	14	greater	great	ADJ
ap-10600	73	15	than	than	SCONJ
ap-10600	73	16	d.	d.	PROPN
ap-10600	73	17	the	the	DET
ap-10600	73	18	same	same	ADJ
ap-10600	73	19	is	be	AUX
ap-10600	73	20	true	true	ADJ
ap-10600	73	21	for	for	ADP
ap-10600	73	22	morphic	morphic	ADJ
ap-10600	73	23	sequences	sequence	NOUN
ap-10600	73	24	,	,	PUNCT
ap-10600	73	25	i.e.	i.e.	X
ap-10600	73	26	,	,	PUNCT
ap-10600	73	27	morphic	morphic	ADJ
ap-10600	73	28	images	image	NOUN
ap-10600	73	29	of	of	ADP
ap-10600	73	30	fixed	fix	VERB
ap-10600	73	31	points	point	NOUN
ap-10600	73	32	.	.	PUNCT
ap-10600	74	1	the	the	DET
ap-10600	74	2	letters	letter	NOUN
ap-10600	74	3	in	in	ADP
ap-10600	74	4	any	any	DET
ap-10600	74	5	morphic	morphic	ADJ
ap-10600	74	6	sequence	sequence	NOUN
ap-10600	74	7	u	u	NOUN
ap-10600	74	8	have	have	VERB
ap-10600	74	9	the	the	DET
ap-10600	74	10	socalled	socalled	ADJ
ap-10600	74	11	uniform	uniform	ADJ
ap-10600	74	12	letter	letter	NOUN
ap-10600	74	13	frequencies	frequency	NOUN
ap-10600	74	14	[	[	PUNCT
ap-10600	74	15	13	13	NUM
ap-10600	74	16	]	]	PUNCT
ap-10600	74	17	:	:	PUNCT
ap-10600	74	18	for	for	ADP
ap-10600	74	19	any	any	DET
ap-10600	74	20	sequence	sequence	NOUN
ap-10600	74	21	(	(	PUNCT
ap-10600	74	22	kn)n∈n	kn)n∈n	NOUN
ap-10600	74	23	of	of	ADP
ap-10600	74	24	non	non	ADJ
ap-10600	74	25	-	-	ADJ
ap-10600	74	26	negative	negative	ADJ
ap-10600	74	27	integers	integer	NOUN
ap-10600	74	28	,	,	PUNCT
ap-10600	74	29	the	the	DET
ap-10600	74	30	limit	limit	NOUN
ap-10600	74	31	:	:	PUNCT
ap-10600	74	32	lim	lim	PROPN
ap-10600	74	33	n→∞	n→∞	NOUN
ap-10600	74	34	#	#	SYM
ap-10600	74	35	{	{	PUNCT
ap-10600	74	36	kn	kn	NOUN
ap-10600	74	37	≤	≤	PROPN
ap-10600	75	1	i	i	PRON
ap-10600	75	2	<	<	X
ap-10600	75	3	kn	kn	PROPN
ap-10600	75	4	+	+	CCONJ
ap-10600	75	5	n	n	CCONJ
ap-10600	75	6	:	:	PUNCT
ap-10600	75	7	ui	ui	PROPN
ap-10600	76	1	=	=	PUNCT
ap-10600	76	2	a	a	PRON
ap-10600	76	3	}	}	PUNCT
ap-10600	76	4	n	n	NOUN
ap-10600	76	5	exists	exist	VERB
ap-10600	76	6	and	and	CCONJ
ap-10600	76	7	is	be	AUX
ap-10600	76	8	the	the	DET
ap-10600	76	9	same	same	ADJ
ap-10600	76	10	for	for	ADP
ap-10600	76	11	any	any	DET
ap-10600	76	12	choice	choice	NOUN
ap-10600	76	13	of	of	ADP
ap-10600	76	14	(	(	PUNCT
ap-10600	76	15	kn)n∈n	kn)n∈n	NOUN
ap-10600	76	16	.	.	PUNCT
ap-10600	77	1	the	the	DET
ap-10600	77	2	definition	definition	NOUN
ap-10600	77	3	of	of	ADP
ap-10600	77	4	letter	letter	NOUN
ap-10600	77	5	frequency	frequency	NOUN
ap-10600	77	6	in	in	ADP
ap-10600	77	7	the	the	DET
ap-10600	77	8	introduction	introduction	NOUN
ap-10600	77	9	is	be	AUX
ap-10600	77	10	restricted	restrict	VERB
ap-10600	77	11	to	to	ADP
ap-10600	77	12	the	the	DET
ap-10600	77	13	study	study	NOUN
ap-10600	77	14	of	of	ADP
ap-10600	77	15	the	the	DET
ap-10600	77	16	limit	limit	NOUN
ap-10600	77	17	for	for	ADP
ap-10600	77	18	the	the	DET
ap-10600	77	19	sequence	sequence	NOUN
ap-10600	77	20	(	(	PUNCT
ap-10600	77	21	kn	kn	PROPN
ap-10600	77	22	)	)	PUNCT
ap-10600	77	23	=	=	PUNCT
ap-10600	78	1	(	(	PUNCT
ap-10600	78	2	0	0	NUM
ap-10600	78	3	)	)	PUNCT
ap-10600	78	4	.	.	PUNCT
ap-10600	79	1	the	the	DET
ap-10600	79	2	relation	relation	NOUN
ap-10600	79	3	of	of	ADP
ap-10600	79	4	balancedness	balancedness	NOUN
ap-10600	79	5	and	and	CCONJ
ap-10600	79	6	uniform	uniform	ADJ
ap-10600	79	7	letter	letter	NOUN
ap-10600	79	8	frequency	frequency	NOUN
ap-10600	79	9	was	be	AUX
ap-10600	79	10	described	describe	VERB
ap-10600	79	11	by	by	ADP
ap-10600	79	12	berthé	berthé	ADJ
ap-10600	79	13	and	and	CCONJ
ap-10600	79	14	delecroix	delecroix	NOUN
ap-10600	80	1	[	[	X
ap-10600	80	2	14	14	NUM
ap-10600	80	3	]	]	PUNCT
ap-10600	80	4	.	.	PUNCT
ap-10600	81	1	theorem	theorem	NOUN
ap-10600	81	2	3	3	NUM
ap-10600	81	3	.	.	PUNCT
ap-10600	82	1	a	a	DET
ap-10600	82	2	sequence	sequence	NOUN
ap-10600	82	3	u	u	NOUN
ap-10600	82	4	over	over	ADP
ap-10600	82	5	an	an	DET
ap-10600	82	6	alphabet	alphabet	NOUN
ap-10600	82	7	a	a	PRON
ap-10600	82	8	is	be	AUX
ap-10600	82	9	kbalanced	kbalance	VERB
ap-10600	82	10	for	for	ADP
ap-10600	82	11	some	some	DET
ap-10600	82	12	k	k	PROPN
ap-10600	82	13	∈	∈	PROPN
ap-10600	82	14	n	n	CCONJ
ap-10600	82	15	if	if	SCONJ
ap-10600	83	1	and	and	CCONJ
ap-10600	83	2	only	only	ADV
ap-10600	83	3	if	if	SCONJ
ap-10600	83	4	it	it	PRON
ap-10600	83	5	has	have	VERB
ap-10600	83	6	uniform	uniform	ADJ
ap-10600	83	7	letter	letter	NOUN
ap-10600	83	8	frequencies	frequency	NOUN
ap-10600	83	9	and	and	CCONJ
ap-10600	83	10	there	there	PRON
ap-10600	83	11	exists	exist	VERB
ap-10600	83	12	a	a	DET
ap-10600	83	13	constant	constant	ADJ
ap-10600	83	14	b	b	NOUN
ap-10600	83	15	such	such	ADJ
ap-10600	83	16	that	that	PRON
ap-10600	83	17	for	for	ADP
ap-10600	83	18	any	any	DET
ap-10600	83	19	factor	factor	NOUN
ap-10600	83	20	w	w	PROPN
ap-10600	83	21	of	of	ADP
ap-10600	83	22	u	u	PROPN
ap-10600	83	23	,	,	PUNCT
ap-10600	83	24	we	we	PRON
ap-10600	83	25	have	have	VERB
ap-10600	83	26	∣∣|w|a	∣∣|w|a	PROPN
ap-10600	83	27	−	−	PROPN
ap-10600	83	28	fa|w|	fa|w|	NOUN
ap-10600	83	29	∣∣	∣∣	NUM
ap-10600	83	30	≤	≤	NUM
ap-10600	83	31	b	b	NOUN
ap-10600	83	32	for	for	ADP
ap-10600	83	33	every	every	DET
ap-10600	83	34	letter	letter	NOUN
ap-10600	83	35	a	a	DET
ap-10600	83	36	∈	∈	NOUN
ap-10600	83	37	a.	a.	NOUN
ap-10600	83	38	in	in	ADP
ap-10600	83	39	general	general	ADJ
ap-10600	83	40	,	,	PUNCT
ap-10600	83	41	proving	prove	VERB
ap-10600	83	42	that	that	SCONJ
ap-10600	83	43	a	a	DET
ap-10600	83	44	sequence	sequence	NOUN
ap-10600	83	45	u	u	NOUN
ap-10600	83	46	is	be	AUX
ap-10600	83	47	k	k	NOUN
ap-10600	83	48	-	-	ADJ
ap-10600	83	49	balanced	balanced	ADJ
ap-10600	83	50	for	for	ADP
ap-10600	83	51	some	some	DET
ap-10600	83	52	k	k	PROPN
ap-10600	83	53	may	may	AUX
ap-10600	83	54	be	be	AUX
ap-10600	83	55	a	a	DET
ap-10600	83	56	complicated	complicated	ADJ
ap-10600	83	57	problem	problem	NOUN
ap-10600	83	58	.	.	PUNCT
ap-10600	84	1	determine	determine	VERB
ap-10600	84	2	the	the	DET
ap-10600	84	3	minimum	minimum	NOUN
ap-10600	84	4	such	such	ADJ
ap-10600	84	5	k	k	PROPN
ap-10600	84	6	is	be	AUX
ap-10600	84	7	even	even	ADV
ap-10600	84	8	more	more	ADV
ap-10600	84	9	difficult	difficult	ADJ
ap-10600	84	10	.	.	PUNCT
ap-10600	85	1	if	if	SCONJ
ap-10600	85	2	u	u	NOUN
ap-10600	85	3	is	be	AUX
ap-10600	85	4	a	a	DET
ap-10600	85	5	fixed	fix	VERB
ap-10600	85	6	point	point	NOUN
ap-10600	85	7	of	of	ADP
ap-10600	85	8	a	a	DET
ap-10600	85	9	primitive	primitive	ADJ
ap-10600	85	10	morphism	morphism	NOUN
ap-10600	85	11	,	,	PUNCT
ap-10600	85	12	then	then	ADV
ap-10600	85	13	it	it	PRON
ap-10600	85	14	is	be	AUX
ap-10600	85	15	possible	possible	ADJ
ap-10600	85	16	to	to	PART
ap-10600	85	17	decide	decide	VERB
ap-10600	85	18	about	about	ADP
ap-10600	85	19	k	k	NOUN
ap-10600	85	20	-	-	NOUN
ap-10600	85	21	balancedness	balancedness	NOUN
ap-10600	85	22	using	use	VERB
ap-10600	85	23	a	a	DET
ap-10600	85	24	result	result	NOUN
ap-10600	85	25	by	by	ADP
ap-10600	85	26	adamczewski	adamczewski	PROPN
ap-10600	85	27	[	[	X
ap-10600	85	28	15	15	NUM
ap-10600	85	29	]	]	PUNCT
ap-10600	85	30	.	.	PUNCT
ap-10600	86	1	it	it	PRON
ap-10600	86	2	says	say	VERB
ap-10600	86	3	that	that	SCONJ
ap-10600	86	4	if	if	SCONJ
ap-10600	86	5	all	all	PRON
ap-10600	86	6	eigenvalues	eigenvalue	VERB
ap-10600	86	7	but	but	CCONJ
ap-10600	86	8	one	one	NUM
ap-10600	86	9	of	of	ADP
ap-10600	86	10	the	the	DET
ap-10600	86	11	incidence	incidence	NOUN
ap-10600	86	12	matrix	matrix	NOUN
ap-10600	86	13	lie	lie	NOUN
ap-10600	86	14	in	in	ADP
ap-10600	86	15	the	the	DET
ap-10600	86	16	interior	interior	NOUN
ap-10600	86	17	of	of	ADP
ap-10600	86	18	the	the	DET
ap-10600	86	19	unit	unit	NOUN
ap-10600	86	20	ball	ball	NOUN
ap-10600	86	21	centred	centre	VERB
ap-10600	86	22	at	at	ADP
ap-10600	86	23	the	the	DET
ap-10600	86	24	origin	origin	NOUN
ap-10600	86	25	,	,	PUNCT
ap-10600	86	26	then	then	ADV
ap-10600	86	27	u	u	NOUN
ap-10600	86	28	is	be	AUX
ap-10600	86	29	k	k	NOUN
ap-10600	86	30	-	-	ADJ
ap-10600	86	31	balanced	balanced	ADJ
ap-10600	86	32	.	.	PUNCT
ap-10600	87	1	moreover	moreover	ADV
ap-10600	87	2	,	,	PUNCT
ap-10600	87	3	an	an	DET
ap-10600	87	4	algorithm	algorithm	NOUN
ap-10600	87	5	computing	compute	VERB
ap-10600	87	6	the	the	DET
ap-10600	87	7	minimum	minimum	ADJ
ap-10600	87	8	value	value	NOUN
ap-10600	87	9	of	of	ADP
ap-10600	87	10	k	k	PROPN
ap-10600	87	11	is	be	AUX
ap-10600	87	12	provided	provide	VERB
ap-10600	87	13	ibidem	ibidem	PROPN
ap-10600	87	14	.	.	PUNCT
ap-10600	88	1	since	since	SCONJ
ap-10600	88	2	the	the	DET
ap-10600	88	3	letter	letter	NOUN
ap-10600	88	4	frequencies	frequency	NOUN
ap-10600	88	5	in	in	ADP
ap-10600	88	6	morphic	morphic	ADJ
ap-10600	88	7	sequences	sequence	NOUN
ap-10600	88	8	are	be	AUX
ap-10600	88	9	always	always	ADV
ap-10600	88	10	algebraic	algebraic	ADJ
ap-10600	88	11	numbers	number	NOUN
ap-10600	88	12	,	,	PUNCT
ap-10600	88	13	they	they	PRON
ap-10600	88	14	can	can	AUX
ap-10600	88	15	not	not	PART
ap-10600	88	16	cover	cover	VERB
ap-10600	88	17	all	all	DET
ap-10600	88	18	possible	possible	ADJ
ap-10600	88	19	candidates	candidate	NOUN
ap-10600	88	20	for	for	ADP
ap-10600	88	21	f⃗	f⃗	NOUN
ap-10600	88	22	.	.	PUNCT
ap-10600	89	1	a	a	DET
ap-10600	89	2	very	very	ADV
ap-10600	89	3	important	important	ADJ
ap-10600	89	4	generalisation	generalisation	NOUN
ap-10600	89	5	of	of	ADP
ap-10600	89	6	morphic	morphic	ADJ
ap-10600	89	7	sequences	sequence	NOUN
ap-10600	89	8	is	be	AUX
ap-10600	89	9	represented	represent	VERB
ap-10600	89	10	by	by	ADP
ap-10600	89	11	s	s	NOUN
ap-10600	89	12	-	-	PUNCT
ap-10600	89	13	adic	adic	ADJ
ap-10600	89	14	systems	system	NOUN
ap-10600	89	15	,	,	PUNCT
ap-10600	89	16	see	see	VERB
ap-10600	89	17	for	for	ADP
ap-10600	89	18	example	example	NOUN
ap-10600	89	19	[	[	X
ap-10600	89	20	14	14	NUM
ap-10600	89	21	]	]	PUNCT
ap-10600	89	22	.	.	PUNCT
ap-10600	90	1	an	an	DET
ap-10600	90	2	s	s	ADJ
ap-10600	90	3	-	-	ADJ
ap-10600	90	4	adic	adic	ADJ
ap-10600	90	5	system	system	NOUN
ap-10600	90	6	introduced	introduce	VERB
ap-10600	90	7	by	by	ADP
ap-10600	90	8	cassaigne	cassaigne	NOUN
ap-10600	90	9	in	in	ADP
ap-10600	90	10	[	[	X
ap-10600	90	11	16	16	NUM
ap-10600	90	12	]	]	PUNCT
ap-10600	90	13	allows	allow	VERB
ap-10600	90	14	constructing	construct	VERB
ap-10600	90	15	ternary	ternary	ADJ
ap-10600	90	16	sequences	sequence	NOUN
ap-10600	90	17	with	with	ADP
ap-10600	90	18	prescribed	prescribed	ADJ
ap-10600	90	19	letter	letter	NOUN
ap-10600	90	20	frequencies	frequency	NOUN
ap-10600	90	21	that	that	PRON
ap-10600	90	22	are	be	AUX
ap-10600	90	23	almost	almost	ADV
ap-10600	90	24	always	always	ADV
ap-10600	90	25	k	k	ADV
ap-10600	90	26	-	-	ADJ
ap-10600	90	27	balanced	balanced	ADJ
ap-10600	90	28	for	for	ADP
ap-10600	90	29	some	some	DET
ap-10600	90	30	constant	constant	ADJ
ap-10600	90	31	k	k	NOUN
ap-10600	90	32	,	,	PUNCT
ap-10600	90	33	as	as	SCONJ
ap-10600	90	34	proven	prove	VERB
ap-10600	90	35	in	in	ADP
ap-10600	90	36	[	[	X
ap-10600	90	37	17	17	NUM
ap-10600	90	38	]	]	SYM
ap-10600	90	39	.	.	PUNCT
ap-10600	91	1	3	3	X
ap-10600	91	2	.	.	X
ap-10600	91	3	colouring	colouring	NOUN
ap-10600	91	4	of	of	ADP
ap-10600	91	5	sequences	sequence	NOUN
ap-10600	91	6	in	in	ADP
ap-10600	91	7	this	this	DET
ap-10600	91	8	section	section	NOUN
ap-10600	91	9	,	,	PUNCT
ap-10600	91	10	we	we	PRON
ap-10600	91	11	describe	describe	VERB
ap-10600	91	12	a	a	DET
ap-10600	91	13	construction	construction	NOUN
ap-10600	91	14	that	that	PRON
ap-10600	91	15	enables	enable	VERB
ap-10600	91	16	us	we	PRON
ap-10600	91	17	to	to	PART
ap-10600	91	18	create	create	VERB
ap-10600	91	19	sequences	sequence	NOUN
ap-10600	91	20	with	with	ADP
ap-10600	91	21	prescribed	prescribed	ADJ
ap-10600	91	22	letter	letter	NOUN
ap-10600	91	23	frequencies	frequency	NOUN
ap-10600	91	24	.	.	PUNCT
ap-10600	92	1	definition	definition	NOUN
ap-10600	92	2	4	4	NUM
ap-10600	92	3	.	.	PUNCT
ap-10600	93	1	let	let	VERB
ap-10600	93	2	u	u	PRON
ap-10600	93	3	=	=	NOUN
ap-10600	93	4	u0u1u2	u0u1u2	X
ap-10600	93	5	·	·	PUNCT
ap-10600	93	6	·	·	PUNCT
ap-10600	93	7	·	·	PUNCT
ap-10600	93	8	be	be	AUX
ap-10600	93	9	a	a	DET
ap-10600	93	10	sequence	sequence	NOUN
ap-10600	93	11	over	over	ADP
ap-10600	93	12	the	the	DET
ap-10600	93	13	alphabet	alphabet	NOUN
ap-10600	93	14	{	{	PUNCT
ap-10600	93	15	a	a	PROPN
ap-10600	93	16	,	,	PUNCT
ap-10600	93	17	b	b	NOUN
ap-10600	93	18	}	}	PUNCT
ap-10600	93	19	.	.	PUNCT
ap-10600	94	1	denote	denote	VERB
ap-10600	94	2	by	by	ADP
ap-10600	94	3	o(a	o(a	NOUN
ap-10600	94	4	)	)	PUNCT
ap-10600	94	5	n	n	NOUN
ap-10600	94	6	and	and	CCONJ
ap-10600	94	7	o(b	o(b	PROPN
ap-10600	94	8	)	)	PUNCT
ap-10600	94	9	n	n	CCONJ
ap-10600	94	10	the	the	DET
ap-10600	94	11	nth	nth	NOUN
ap-10600	94	12	occurrence	occurrence	NOUN
ap-10600	94	13	of	of	ADP
ap-10600	94	14	the	the	DET
ap-10600	94	15	letters	letter	NOUN
ap-10600	94	16	a	a	PRON
ap-10600	94	17	and	and	CCONJ
ap-10600	94	18	b	b	NOUN
ap-10600	94	19	in	in	ADP
ap-10600	94	20	u	u	NOUN
ap-10600	94	21	,	,	PUNCT
ap-10600	94	22	respectively	respectively	ADV
ap-10600	94	23	.	.	PUNCT
ap-10600	95	1	let	let	VERB
ap-10600	95	2	a	a	PRON
ap-10600	95	3	=	=	X
ap-10600	95	4	a0a1a2	a0a1a2	X
ap-10600	95	5	·	·	PUNCT
ap-10600	95	6	·	·	PUNCT
ap-10600	95	7	·	·	PUNCT
ap-10600	96	1	and	and	CCONJ
ap-10600	96	2	b	b	X
ap-10600	96	3	=	=	SYM
ap-10600	96	4	b0b1b2	b0b1b2	PROPN
ap-10600	96	5	·	·	PUNCT
ap-10600	96	6	·	·	PUNCT
ap-10600	96	7	·	·	PUNCT
ap-10600	96	8	be	be	AUX
ap-10600	96	9	two	two	NUM
ap-10600	96	10	sequences	sequence	NOUN
ap-10600	96	11	over	over	ADP
ap-10600	96	12	two	two	NUM
ap-10600	96	13	disjoint	disjoint	NOUN
ap-10600	96	14	alphabets	alphabet	NOUN
ap-10600	96	15	a	a	PRON
ap-10600	96	16	and	and	CCONJ
ap-10600	96	17	b	b	NOUN
ap-10600	96	18	,	,	PUNCT
ap-10600	96	19	respectively	respectively	ADV
ap-10600	96	20	.	.	PUNCT
ap-10600	97	1	colouring	colouring	NOUN
ap-10600	97	2	of	of	ADP
ap-10600	97	3	u	u	NOUN
ap-10600	97	4	by	by	ADP
ap-10600	97	5	a	a	PRON
ap-10600	97	6	and	and	CCONJ
ap-10600	97	7	b	b	NOUN
ap-10600	97	8	is	be	AUX
ap-10600	97	9	a	a	DET
ap-10600	97	10	sequence	sequence	NOUN
ap-10600	97	11	v	v	NOUN
ap-10600	97	12	=	=	SYM
ap-10600	97	13	v0v1v2	v0v1v2	X
ap-10600	97	14	·	·	PUNCT
ap-10600	97	15	·	·	PUNCT
ap-10600	97	16	·	·	PUNCT
ap-10600	98	1	over	over	ADP
ap-10600	98	2	a	a	DET
ap-10600	98	3	∪	∪	NOUN
ap-10600	98	4	b	b	NOUN
ap-10600	98	5	such	such	ADJ
ap-10600	98	6	that	that	PRON
ap-10600	98	7	for	for	ADP
ap-10600	98	8	every	every	DET
ap-10600	98	9	n	n	PRON
ap-10600	98	10	∈	∈	PROPN
ap-10600	98	11	n	n	CCONJ
ap-10600	98	12	the	the	DET
ap-10600	98	13	n	n	ADV
ap-10600	98	14	th	th	X
ap-10600	98	15	entry	entry	NOUN
ap-10600	98	16	of	of	ADP
ap-10600	98	17	v	v	NOUN
ap-10600	98	18	is	be	AUX
ap-10600	98	19	:	:	PUNCT
ap-10600	98	20	vn	vn	PROPN
ap-10600	98	21	=	=	SYM
ap-10600	98	22	{	{	PUNCT
ap-10600	98	23	an	an	PRON
ap-10600	98	24	,	,	PUNCT
ap-10600	98	25	if	if	SCONJ
ap-10600	98	26	n	n	ADV
ap-10600	98	27	=	=	SYM
ap-10600	98	28	o(a	o(a	PROPN
ap-10600	98	29	)	)	PUNCT
ap-10600	98	30	n	n	NOUN
ap-10600	98	31	,	,	PUNCT
ap-10600	98	32	bn	bn	INTJ
ap-10600	98	33	,	,	PUNCT
ap-10600	98	34	if	if	SCONJ
ap-10600	98	35	n	n	PRON
ap-10600	98	36	=	=	SYM
ap-10600	98	37	o(b	o(b	PROPN
ap-10600	98	38	)	)	PUNCT
ap-10600	98	39	n	n	CCONJ
ap-10600	98	40	.	.	PUNCT
ap-10600	99	1	we	we	PRON
ap-10600	99	2	denote	denote	VERB
ap-10600	99	3	v	v	NOUN
ap-10600	99	4	=	=	SYM
ap-10600	99	5	colour(u	colour(u	PROPN
ap-10600	99	6	,	,	PUNCT
ap-10600	99	7	a	a	DET
ap-10600	99	8	,	,	PUNCT
ap-10600	99	9	b	b	NOUN
ap-10600	99	10	)	)	PUNCT
ap-10600	99	11	.	.	PUNCT
ap-10600	100	1	less	less	ADV
ap-10600	100	2	formally	formally	ADV
ap-10600	100	3	:	:	PUNCT
ap-10600	100	4	v	v	NOUN
ap-10600	100	5	is	be	AUX
ap-10600	100	6	obtained	obtain	VERB
ap-10600	100	7	from	from	ADP
ap-10600	100	8	the	the	DET
ap-10600	100	9	sequence	sequence	NOUN
ap-10600	100	10	u	u	NOUN
ap-10600	100	11	over	over	ADP
ap-10600	100	12	{	{	PUNCT
ap-10600	100	13	a	a	DET
ap-10600	100	14	,	,	PUNCT
ap-10600	100	15	b	b	NOUN
ap-10600	100	16	}	}	PUNCT
ap-10600	100	17	by	by	ADP
ap-10600	100	18	replacing	replace	VERB
ap-10600	100	19	the	the	DET
ap-10600	100	20	letters	letter	NOUN
ap-10600	100	21	a	a	DET
ap-10600	100	22	’s	’s	NOUN
ap-10600	100	23	in	in	ADP
ap-10600	100	24	u	u	NOUN
ap-10600	100	25	step	step	NOUN
ap-10600	100	26	by	by	ADP
ap-10600	100	27	step	step	NOUN
ap-10600	100	28	by	by	ADP
ap-10600	100	29	entries	entry	NOUN
ap-10600	100	30	of	of	ADP
ap-10600	100	31	the	the	DET
ap-10600	100	32	sequence	sequence	NOUN
ap-10600	100	33	a0a1a2	a0a1a2	X
ap-10600	100	34	·	·	PUNCT
ap-10600	100	35	·	·	PUNCT
ap-10600	100	36	·	·	PUNCT
ap-10600	100	37	and	and	CCONJ
ap-10600	100	38	analogously	analogously	ADV
ap-10600	100	39	,	,	PUNCT
ap-10600	100	40	the	the	DET
ap-10600	100	41	letters	letter	NOUN
ap-10600	100	42	b	b	PROPN
ap-10600	100	43	’s	’s	X
ap-10600	100	44	in	in	ADP
ap-10600	100	45	u	u	NOUN
ap-10600	100	46	are	be	AUX
ap-10600	100	47	replaced	replace	VERB
ap-10600	100	48	by	by	ADP
ap-10600	100	49	entries	entry	NOUN
ap-10600	100	50	of	of	ADP
ap-10600	100	51	the	the	DET
ap-10600	100	52	sequence	sequence	NOUN
ap-10600	100	53	b0b1b2	b0b1b2	PROPN
ap-10600	100	54	·	·	PUNCT
ap-10600	100	55	·	·	PUNCT
ap-10600	100	56	·	·	PUNCT
ap-10600	100	57	.	.	PUNCT
ap-10600	101	1	for	for	ADP
ap-10600	101	2	v	v	NOUN
ap-10600	101	3	=	=	SYM
ap-10600	101	4	colour(u	colour(u	PROPN
ap-10600	101	5	,	,	PUNCT
ap-10600	101	6	a	a	DET
ap-10600	101	7	,	,	PUNCT
ap-10600	101	8	b	b	NOUN
ap-10600	101	9	)	)	PUNCT
ap-10600	101	10	we	we	PRON
ap-10600	101	11	use	use	VERB
ap-10600	101	12	the	the	DET
ap-10600	101	13	notation	notation	NOUN
ap-10600	101	14	π(v	π(v	NOUN
ap-10600	101	15	)	)	PUNCT
ap-10600	101	16	=	=	SYM
ap-10600	101	17	u	u	NOUN
ap-10600	101	18	and	and	CCONJ
ap-10600	101	19	π(v	π(v	NOUN
ap-10600	101	20	)	)	PUNCT
ap-10600	102	1	=	=	SYM
ap-10600	102	2	u	u	NOUN
ap-10600	102	3	for	for	ADP
ap-10600	102	4	any	any	DET
ap-10600	102	5	v	v	PROPN
ap-10600	102	6	∈	∈	PROPN
ap-10600	102	7	l(v	l(v	NOUN
ap-10600	102	8	)	)	PUNCT
ap-10600	102	9	and	and	CCONJ
ap-10600	102	10	the	the	DET
ap-10600	102	11	corresponding	correspond	VERB
ap-10600	102	12	u	u	PROPN
ap-10600	102	13	∈	∈	PROPN
ap-10600	102	14	l(u	l(u	PROPN
ap-10600	102	15	)	)	PUNCT
ap-10600	102	16	.	.	PUNCT
ap-10600	103	1	we	we	PRON
ap-10600	103	2	say	say	VERB
ap-10600	103	3	that	that	SCONJ
ap-10600	103	4	u	u	PROPN
ap-10600	103	5	(	(	PUNCT
ap-10600	103	6	resp	resp	NOUN
ap-10600	103	7	.	.	PUNCT
ap-10600	104	1	u	u	NOUN
ap-10600	104	2	)	)	PUNCT
ap-10600	104	3	is	be	AUX
ap-10600	104	4	a	a	DET
ap-10600	104	5	projection	projection	NOUN
ap-10600	104	6	of	of	ADP
ap-10600	104	7	v	v	NOUN
ap-10600	104	8	(	(	PUNCT
ap-10600	104	9	resp	resp	NOUN
ap-10600	104	10	.	.	PUNCT
ap-10600	105	1	v	v	X
ap-10600	105	2	)	)	PUNCT
ap-10600	105	3	.	.	PUNCT
ap-10600	106	1	the	the	DET
ap-10600	106	2	map	map	NOUN
ap-10600	106	3	π	π	X
ap-10600	106	4	:	:	PUNCT
ap-10600	106	5	l(v	l(v	NOUN
ap-10600	106	6	)	)	PUNCT
ap-10600	106	7	→	→	SYM
ap-10600	106	8	l(u	l(u	PROPN
ap-10600	106	9	)	)	PUNCT
ap-10600	106	10	is	be	AUX
ap-10600	106	11	clearly	clearly	ADV
ap-10600	106	12	a	a	DET
ap-10600	106	13	morphism	morphism	NOUN
ap-10600	106	14	.	.	PUNCT
ap-10600	106	15	example	example	NOUN
ap-10600	107	1	5	5	NUM
ap-10600	107	2	.	.	PUNCT
ap-10600	107	3	let	let	VERB
ap-10600	107	4	u	u	PRON
ap-10600	107	5	be	be	AUX
ap-10600	107	6	a	a	DET
ap-10600	107	7	sequence	sequence	NOUN
ap-10600	107	8	over	over	ADP
ap-10600	107	9	{	{	PUNCT
ap-10600	107	10	a	a	DET
ap-10600	107	11	,	,	PUNCT
ap-10600	107	12	b	b	NOUN
ap-10600	107	13	}	}	PUNCT
ap-10600	107	14	and	and	CCONJ
ap-10600	107	15	a	a	PRON
ap-10600	107	16	=	=	X
ap-10600	107	17	(	(	PUNCT
ap-10600	107	18	121314)ω	121314)ω	NUM
ap-10600	107	19	and	and	CCONJ
ap-10600	107	20	b	b	X
ap-10600	107	21	=	=	SYM
ap-10600	107	22	(	(	PUNCT
ap-10600	107	23	56)ω	56)ω	NUM
ap-10600	107	24	,	,	PUNCT
ap-10600	107	25	then	then	ADV
ap-10600	107	26	:	:	PUNCT
ap-10600	107	27	u	u	NOUN
ap-10600	107	28	=	=	PROPN
ap-10600	107	29	aabaababaabaababaababaabaababaabaab	aabaababaabaababaababaabaababaabaab	PROPN
ap-10600	107	30	·	·	PUNCT
ap-10600	107	31	·	·	PUNCT
ap-10600	107	32	·	·	PUNCT
ap-10600	108	1	v	v	X
ap-10600	108	2	=	=	SYM
ap-10600	108	3	12513615416215361451621531645126135	12513615416215361451621531645126135	NUM
ap-10600	108	4	·	·	PUNCT
ap-10600	108	5	·	·	PUNCT
ap-10600	108	6	·	·	PUNCT
ap-10600	108	7	we	we	PRON
ap-10600	108	8	have	have	VERB
ap-10600	108	9	π(54162153614	π(54162153614	NOUN
ap-10600	108	10	)	)	PUNCT
ap-10600	108	11	=	=	PUNCT
ap-10600	108	12	baabaababaa	baabaababaa	NOUN
ap-10600	108	13	.	.	PUNCT
ap-10600	109	1	535	535	NUM
ap-10600	109	2	l’ubomíra	l’ubomíra	PROPN
ap-10600	109	3	dvořáková	dvořáková	PROPN
ap-10600	109	4	,	,	PUNCT
ap-10600	109	5	edita	edita	PROPN
ap-10600	109	6	pelantová	pelantová	PROPN
ap-10600	109	7	acta	acta	PROPN
ap-10600	109	8	polytechnica	polytechnica	PROPN
ap-10600	109	9	remark	remark	NOUN
ap-10600	109	10	6	6	NUM
ap-10600	109	11	.	.	PUNCT
ap-10600	109	12	frequencies	frequency	NOUN
ap-10600	109	13	of	of	ADP
ap-10600	109	14	letters	letter	NOUN
ap-10600	109	15	in	in	ADP
ap-10600	109	16	v	v	NOUN
ap-10600	109	17	=	=	SYM
ap-10600	109	18	colour(u	colour(u	PROPN
ap-10600	109	19	,	,	PUNCT
ap-10600	109	20	a	a	DET
ap-10600	109	21	,	,	PUNCT
ap-10600	109	22	b	b	NOUN
ap-10600	109	23	)	)	PUNCT
ap-10600	109	24	can	can	AUX
ap-10600	109	25	be	be	AUX
ap-10600	109	26	easily	easily	ADV
ap-10600	109	27	computed	compute	VERB
ap-10600	109	28	from	from	ADP
ap-10600	109	29	frequencies	frequency	NOUN
ap-10600	109	30	of	of	ADP
ap-10600	109	31	letters	letter	NOUN
ap-10600	109	32	in	in	ADP
ap-10600	109	33	u	u	NOUN
ap-10600	109	34	,	,	PUNCT
ap-10600	109	35	a	a	PRON
ap-10600	109	36	,	,	PUNCT
ap-10600	109	37	and	and	CCONJ
ap-10600	109	38	b	b	X
ap-10600	109	39	:	:	PUNCT
ap-10600	109	40	if	if	SCONJ
ap-10600	109	41	they	they	PRON
ap-10600	109	42	exist	exist	VERB
ap-10600	109	43	.	.	PUNCT
ap-10600	110	1	for	for	ADP
ap-10600	110	2	example	example	NOUN
ap-10600	110	3	,	,	PUNCT
ap-10600	110	4	the	the	DET
ap-10600	110	5	letter	letter	NOUN
ap-10600	110	6	j	j	PROPN
ap-10600	110	7	∈	∈	PROPN
ap-10600	110	8	a	a	PRON
ap-10600	110	9	has	have	VERB
ap-10600	110	10	the	the	DET
ap-10600	110	11	frequency	frequency	NOUN
ap-10600	110	12	faγ	faγ	NOUN
ap-10600	110	13	in	in	ADP
ap-10600	110	14	v	v	NOUN
ap-10600	110	15	,	,	PUNCT
ap-10600	110	16	where	where	SCONJ
ap-10600	110	17	fa	fa	PROPN
ap-10600	110	18	is	be	AUX
ap-10600	110	19	the	the	DET
ap-10600	110	20	frequency	frequency	NOUN
ap-10600	110	21	of	of	ADP
ap-10600	110	22	the	the	DET
ap-10600	110	23	letter	letter	NOUN
ap-10600	110	24	a	a	PRON
ap-10600	110	25	in	in	ADP
ap-10600	110	26	u	u	NOUN
ap-10600	110	27	and	and	CCONJ
ap-10600	110	28	γ	γ	NOUN
ap-10600	110	29	is	be	AUX
ap-10600	110	30	the	the	DET
ap-10600	110	31	frequency	frequency	NOUN
ap-10600	110	32	of	of	ADP
ap-10600	110	33	the	the	DET
ap-10600	110	34	letter	letter	NOUN
ap-10600	110	35	j	j	PROPN
ap-10600	110	36	in	in	ADP
ap-10600	110	37	a.	a.	NOUN
ap-10600	110	38	definition	definition	NOUN
ap-10600	110	39	7	7	NUM
ap-10600	110	40	.	.	PUNCT
ap-10600	111	1	a	a	DET
ap-10600	111	2	sequence	sequence	NOUN
ap-10600	111	3	a	a	PRON
ap-10600	111	4	is	be	AUX
ap-10600	111	5	a	a	DET
ap-10600	111	6	constant	constant	ADJ
ap-10600	111	7	gap	gap	NOUN
ap-10600	111	8	sequence	sequence	NOUN
ap-10600	111	9	if	if	SCONJ
ap-10600	111	10	for	for	ADP
ap-10600	111	11	each	each	DET
ap-10600	111	12	letter	letter	NOUN
ap-10600	111	13	a	a	DET
ap-10600	111	14	occurring	occur	VERB
ap-10600	111	15	in	in	ADP
ap-10600	111	16	a	a	DET
ap-10600	111	17	the	the	DET
ap-10600	111	18	distance	distance	NOUN
ap-10600	111	19	between	between	ADP
ap-10600	111	20	any	any	DET
ap-10600	111	21	consecutive	consecutive	ADJ
ap-10600	111	22	occurrences	occurrence	NOUN
ap-10600	111	23	of	of	ADP
ap-10600	111	24	a	a	PRON
ap-10600	111	25	in	in	ADP
ap-10600	111	26	a	a	PRON
ap-10600	111	27	is	be	AUX
ap-10600	111	28	constant	constant	ADJ
ap-10600	111	29	.	.	PUNCT
ap-10600	112	1	example	example	NOUN
ap-10600	112	2	5	5	NUM
ap-10600	112	3	shows	show	VERB
ap-10600	112	4	constant	constant	ADJ
ap-10600	112	5	gap	gap	NOUN
ap-10600	112	6	sequences	sequence	NOUN
ap-10600	112	7	a	a	PRON
ap-10600	112	8	and	and	CCONJ
ap-10600	112	9	b.	b.	NOUN
ap-10600	113	1	the	the	DET
ap-10600	113	2	next	next	ADJ
ap-10600	113	3	result	result	NOUN
ap-10600	113	4	comes	come	VERB
ap-10600	113	5	from	from	ADP
ap-10600	113	6	[	[	X
ap-10600	113	7	18	18	NUM
ap-10600	113	8	]	]	PUNCT
ap-10600	113	9	.	.	PUNCT
ap-10600	114	1	lemma	lemma	PROPN
ap-10600	114	2	8	8	NUM
ap-10600	114	3	.	.	PUNCT
ap-10600	115	1	let	let	VERB
ap-10600	115	2	a	a	PRON
ap-10600	115	3	be	be	AUX
ap-10600	115	4	a	a	DET
ap-10600	115	5	constant	constant	ADJ
ap-10600	115	6	gap	gap	NOUN
ap-10600	115	7	sequence	sequence	NOUN
ap-10600	115	8	over	over	ADP
ap-10600	115	9	an	an	DET
ap-10600	115	10	alphabet	alphabet	NOUN
ap-10600	115	11	a	a	PRON
ap-10600	115	12	containing	contain	VERB
ap-10600	115	13	more	more	ADJ
ap-10600	115	14	than	than	ADP
ap-10600	115	15	one	one	NUM
ap-10600	115	16	letter	letter	NOUN
ap-10600	115	17	.	.	PUNCT
ap-10600	116	1	then	then	ADV
ap-10600	116	2	a	a	PRON
ap-10600	116	3	contains	contain	VERB
ap-10600	116	4	two	two	NUM
ap-10600	116	5	distinct	distinct	ADJ
ap-10600	116	6	letters	letter	NOUN
ap-10600	116	7	having	have	VERB
ap-10600	116	8	the	the	DET
ap-10600	116	9	same	same	ADJ
ap-10600	116	10	frequency	frequency	NOUN
ap-10600	116	11	.	.	PUNCT
ap-10600	117	1	theorem	theorem	NOUN
ap-10600	117	2	9	9	NUM
ap-10600	117	3	(	(	PUNCT
ap-10600	117	4	[	[	X
ap-10600	117	5	7	7	NUM
ap-10600	117	6	]	]	NUM
ap-10600	117	7	)	)	PUNCT
ap-10600	117	8	.	.	PUNCT
ap-10600	118	1	a	a	DET
ap-10600	118	2	recurrent	recurrent	ADJ
ap-10600	118	3	aperiodic	aperiodic	ADJ
ap-10600	118	4	sequence	sequence	NOUN
ap-10600	118	5	v	v	NOUN
ap-10600	118	6	is	be	AUX
ap-10600	118	7	1	1	NUM
ap-10600	118	8	-	-	PUNCT
ap-10600	118	9	balanced	balanced	ADJ
ap-10600	118	10	if	if	SCONJ
ap-10600	119	1	and	and	CCONJ
ap-10600	119	2	only	only	ADV
ap-10600	119	3	if	if	SCONJ
ap-10600	119	4	v	v	NUM
ap-10600	119	5	=	=	SYM
ap-10600	119	6	colour(u	colour(u	PROPN
ap-10600	119	7	,	,	PUNCT
ap-10600	119	8	a	a	DET
ap-10600	119	9	,	,	PUNCT
ap-10600	119	10	b	b	NOUN
ap-10600	119	11	)	)	PUNCT
ap-10600	119	12	for	for	ADP
ap-10600	119	13	some	some	DET
ap-10600	119	14	sturmian	sturmian	ADJ
ap-10600	119	15	sequence	sequence	NOUN
ap-10600	119	16	u	u	NOUN
ap-10600	119	17	and	and	CCONJ
ap-10600	120	1	constant	constant	ADJ
ap-10600	120	2	gap	gap	NOUN
ap-10600	120	3	sequences	sequence	NOUN
ap-10600	120	4	a	a	PRON
ap-10600	120	5	,	,	PUNCT
ap-10600	120	6	b	b	NOUN
ap-10600	120	7	over	over	ADP
ap-10600	120	8	two	two	NUM
ap-10600	120	9	disjoint	disjoint	ADJ
ap-10600	120	10	alphabets	alphabet	NOUN
ap-10600	120	11	.	.	PUNCT
ap-10600	121	1	example	example	NOUN
ap-10600	121	2	5	5	NUM
ap-10600	121	3	shows	show	VERB
ap-10600	121	4	a	a	DET
ap-10600	121	5	1	1	NUM
ap-10600	121	6	-	-	PUNCT
ap-10600	121	7	balanced	balanced	ADJ
ap-10600	121	8	sequence	sequence	NOUN
ap-10600	121	9	v.	v.	ADP
ap-10600	121	10	using	use	VERB
ap-10600	121	11	remark	remark	NOUN
ap-10600	121	12	6	6	NUM
ap-10600	121	13	,	,	PUNCT
ap-10600	121	14	we	we	PRON
ap-10600	121	15	can	can	AUX
ap-10600	121	16	describe	describe	VERB
ap-10600	121	17	the	the	DET
ap-10600	121	18	form	form	NOUN
ap-10600	121	19	of	of	ADP
ap-10600	121	20	the	the	DET
ap-10600	121	21	frequency	frequency	NOUN
ap-10600	121	22	vector	vector	NOUN
ap-10600	121	23	in	in	ADP
ap-10600	121	24	1	1	NUM
ap-10600	121	25	-	-	PUNCT
ap-10600	121	26	balanced	balanced	ADJ
ap-10600	121	27	ternary	ternary	ADJ
ap-10600	121	28	and	and	CCONJ
ap-10600	121	29	quaternary	quaternary	ADJ
ap-10600	121	30	sequences	sequence	NOUN
ap-10600	121	31	.	.	PUNCT
ap-10600	122	1	observation	observation	NOUN
ap-10600	122	2	10	10	NUM
ap-10600	122	3	.	.	PUNCT
ap-10600	123	1	let	let	VERB
ap-10600	123	2	v	v	NOUN
ap-10600	123	3	=	=	SYM
ap-10600	123	4	colour(u	colour(u	PROPN
ap-10600	123	5	,	,	PUNCT
ap-10600	123	6	a	a	DET
ap-10600	123	7	,	,	PUNCT
ap-10600	123	8	b	b	NOUN
ap-10600	123	9	)	)	PUNCT
ap-10600	123	10	be	be	AUX
ap-10600	123	11	a	a	DET
ap-10600	123	12	1balanced	1balanced	NUM
ap-10600	123	13	sequence	sequence	NOUN
ap-10600	123	14	over	over	ADP
ap-10600	123	15	an	an	DET
ap-10600	123	16	alphabet	alphabet	NOUN
ap-10600	123	17	{	{	PUNCT
ap-10600	123	18	1	1	NUM
ap-10600	123	19	,	,	PUNCT
ap-10600	123	20	2	2	NUM
ap-10600	123	21	,	,	PUNCT
ap-10600	123	22	.	.	PUNCT
ap-10600	123	23	.	.	PUNCT
ap-10600	124	1	.	.	PUNCT
ap-10600	125	1	,	,	PUNCT
ap-10600	125	2	d	d	X
ap-10600	125	3	}	}	PUNCT
ap-10600	125	4	,	,	PUNCT
ap-10600	125	5	where	where	SCONJ
ap-10600	125	6	α	α	NOUN
ap-10600	125	7	is	be	AUX
ap-10600	125	8	the	the	DET
ap-10600	125	9	frequency	frequency	NOUN
ap-10600	125	10	of	of	ADP
ap-10600	125	11	a	a	PRON
ap-10600	125	12	in	in	ADP
ap-10600	125	13	u.	u.	NOUN
ap-10600	125	14	then	then	ADV
ap-10600	125	15	the	the	DET
ap-10600	125	16	frequency	frequency	NOUN
ap-10600	125	17	vector	vector	NOUN
ap-10600	125	18	f⃗v	f⃗v	NOUN
ap-10600	125	19	takes	take	VERB
ap-10600	125	20	on	on	ADP
ap-10600	125	21	the	the	DET
ap-10600	125	22	following	follow	VERB
ap-10600	125	23	values	value	NOUN
ap-10600	125	24	.	.	PUNCT
ap-10600	126	1	(	(	PUNCT
ap-10600	126	2	1	1	NUM
ap-10600	126	3	.	.	PUNCT
ap-10600	126	4	)	)	PUNCT
ap-10600	127	1	for	for	ADP
ap-10600	127	2	d	d	PROPN
ap-10600	127	3	=	=	SYM
ap-10600	127	4	3	3	NUM
ap-10600	127	5	,	,	PUNCT
ap-10600	127	6	we	we	PRON
ap-10600	127	7	have	have	VERB
ap-10600	127	8	only	only	ADV
ap-10600	127	9	one	one	NUM
ap-10600	127	10	frequency	frequency	NOUN
ap-10600	127	11	vector	vector	NOUN
ap-10600	127	12	f⃗v	f⃗v	NOUN
ap-10600	127	13	=	=	SYM
ap-10600	127	14	(	(	PUNCT
ap-10600	127	15	α	α	NOUN
ap-10600	127	16	1	1	NUM
ap-10600	127	17	2	2	NUM
ap-10600	127	18	,	,	PUNCT
ap-10600	127	19	α	α	NOUN
ap-10600	127	20	1	1	NUM
ap-10600	127	21	2	2	NUM
ap-10600	127	22	,	,	PUNCT
ap-10600	127	23	1	1	NUM
ap-10600	127	24	−	−	NOUN
ap-10600	127	25	α	α	X
ap-10600	127	26	)	)	PUNCT
ap-10600	127	27	(	(	PUNCT
ap-10600	127	28	up	up	ADP
ap-10600	127	29	to	to	ADP
ap-10600	127	30	certain	certain	ADJ
ap-10600	127	31	letter	letter	NOUN
ap-10600	127	32	permutations	permutation	NOUN
ap-10600	127	33	)	)	PUNCT
ap-10600	127	34	corresponding	correspond	VERB
ap-10600	127	35	to	to	ADP
ap-10600	127	36	a	a	DET
ap-10600	127	37	=	=	PUNCT
ap-10600	127	38	(	(	PUNCT
ap-10600	127	39	12)ω	12)ω	NUM
ap-10600	127	40	and	and	CCONJ
ap-10600	127	41	b	b	X
ap-10600	127	42	=	=	SYM
ap-10600	127	43	(	(	PUNCT
ap-10600	127	44	3)ω	3)ω	PROPN
ap-10600	127	45	.	.	PUNCT
ap-10600	128	1	(	(	PUNCT
ap-10600	128	2	2	2	NUM
ap-10600	128	3	.	.	PUNCT
ap-10600	128	4	)	)	PUNCT
ap-10600	129	1	for	for	ADP
ap-10600	129	2	d	d	PROPN
ap-10600	129	3	=	=	SYM
ap-10600	129	4	4	4	NUM
ap-10600	129	5	,	,	PUNCT
ap-10600	129	6	we	we	PRON
ap-10600	129	7	have	have	VERB
ap-10600	129	8	three	three	NUM
ap-10600	129	9	possibilities	possibility	NOUN
ap-10600	129	10	(	(	PUNCT
ap-10600	129	11	up	up	ADP
ap-10600	129	12	to	to	ADP
ap-10600	129	13	certain	certain	ADJ
ap-10600	129	14	letter	letter	NOUN
ap-10600	129	15	permutations	permutation	NOUN
ap-10600	129	16	):	):	PUNCT
ap-10600	129	17	•	•	ADP
ap-10600	129	18	if	if	SCONJ
ap-10600	129	19	a	a	PRON
ap-10600	129	20	=	=	X
ap-10600	129	21	(	(	PUNCT
ap-10600	129	22	12)ω	12)ω	NUM
ap-10600	129	23	,	,	PUNCT
ap-10600	129	24	b	b	X
ap-10600	129	25	=	=	SYM
ap-10600	129	26	(	(	PUNCT
ap-10600	129	27	34)ω	34)ω	NUM
ap-10600	129	28	,	,	PUNCT
ap-10600	129	29	then	then	ADV
ap-10600	129	30	:	:	PUNCT
ap-10600	129	31	f⃗v	f⃗v	PROPN
ap-10600	129	32	=	=	SYM
ap-10600	129	33	(	(	PUNCT
ap-10600	129	34	α	α	NOUN
ap-10600	129	35	1	1	NUM
ap-10600	129	36	2	2	NUM
ap-10600	129	37	,	,	PUNCT
ap-10600	129	38	α	α	NOUN
ap-10600	129	39	1	1	NUM
ap-10600	129	40	2	2	NUM
ap-10600	129	41	,	,	PUNCT
ap-10600	129	42	(	(	PUNCT
ap-10600	129	43	1	1	NUM
ap-10600	129	44	−	−	NOUN
ap-10600	129	45	α	α	NUM
ap-10600	129	46	)	)	PUNCT
ap-10600	129	47	1	1	NUM
ap-10600	129	48	2	2	NUM
ap-10600	129	49	,	,	PUNCT
ap-10600	129	50	(	(	PUNCT
ap-10600	129	51	1	1	NUM
ap-10600	129	52	−	−	NOUN
ap-10600	129	53	α	α	NUM
ap-10600	129	54	)	)	PUNCT
ap-10600	129	55	1	1	NUM
ap-10600	129	56	2	2	NUM
ap-10600	129	57	)	)	PUNCT
ap-10600	129	58	,	,	PUNCT
ap-10600	129	59	•	•	INTJ
ap-10600	129	60	if	if	SCONJ
ap-10600	129	61	a	a	PRON
ap-10600	129	62	=	=	X
ap-10600	129	63	(	(	PUNCT
ap-10600	129	64	123)ω	123)ω	NUM
ap-10600	129	65	,	,	PUNCT
ap-10600	129	66	b	b	X
ap-10600	129	67	=	=	SYM
ap-10600	129	68	(	(	PUNCT
ap-10600	129	69	4)ω	4)ω	INTJ
ap-10600	129	70	,	,	PUNCT
ap-10600	129	71	then	then	ADV
ap-10600	129	72	:	:	PUNCT
ap-10600	129	73	f⃗v	f⃗v	PROPN
ap-10600	129	74	=	=	SYM
ap-10600	129	75	(	(	PUNCT
ap-10600	129	76	α	α	NOUN
ap-10600	129	77	1	1	NUM
ap-10600	129	78	3	3	NUM
ap-10600	129	79	,	,	PUNCT
ap-10600	129	80	α	α	PROPN
ap-10600	129	81	1	1	NUM
ap-10600	129	82	3	3	NUM
ap-10600	129	83	,	,	PUNCT
ap-10600	129	84	α	α	PROPN
ap-10600	129	85	1	1	NUM
ap-10600	129	86	3	3	NUM
ap-10600	129	87	,	,	PUNCT
ap-10600	129	88	1	1	NUM
ap-10600	129	89	−	−	PROPN
ap-10600	129	90	α	α	NOUN
ap-10600	129	91	)	)	PUNCT
ap-10600	129	92	,	,	PUNCT
ap-10600	129	93	•	•	INTJ
ap-10600	129	94	if	if	SCONJ
ap-10600	129	95	a	a	PRON
ap-10600	129	96	=	=	X
ap-10600	129	97	(	(	PUNCT
ap-10600	129	98	1213)ω	1213)ω	NUM
ap-10600	129	99	,	,	PUNCT
ap-10600	129	100	b	b	NOUN
ap-10600	129	101	=	=	SYM
ap-10600	129	102	(	(	PUNCT
ap-10600	129	103	4)ω	4)ω	INTJ
ap-10600	129	104	,	,	PUNCT
ap-10600	129	105	then	then	ADV
ap-10600	129	106	:	:	PUNCT
ap-10600	129	107	f⃗v	f⃗v	PROPN
ap-10600	129	108	=	=	SYM
ap-10600	129	109	(	(	PUNCT
ap-10600	129	110	α	α	NOUN
ap-10600	129	111	1	1	NUM
ap-10600	129	112	2	2	NUM
ap-10600	129	113	,	,	PUNCT
ap-10600	129	114	α	α	PROPN
ap-10600	129	115	1	1	NUM
ap-10600	129	116	4	4	NUM
ap-10600	129	117	,	,	PUNCT
ap-10600	129	118	α	α	PROPN
ap-10600	129	119	1	1	NUM
ap-10600	129	120	4	4	NUM
ap-10600	129	121	,	,	PUNCT
ap-10600	129	122	1	1	NUM
ap-10600	129	123	−	−	NOUN
ap-10600	129	124	α	α	NOUN
ap-10600	129	125	)	)	PUNCT
ap-10600	129	126	.	.	PUNCT
ap-10600	130	1	the	the	DET
ap-10600	130	2	following	follow	VERB
ap-10600	130	3	lemma	lemma	PROPN
ap-10600	130	4	implies	imply	VERB
ap-10600	130	5	that	that	SCONJ
ap-10600	130	6	bt	bt	PROPN
ap-10600	130	7	(	(	PUNCT
ap-10600	130	8	d	d	PROPN
ap-10600	130	9	)	)	PUNCT
ap-10600	130	10	≥	≥	NOUN
ap-10600	130	11	2	2	NUM
ap-10600	130	12	for	for	ADP
ap-10600	130	13	d	d	PROPN
ap-10600	130	14	≥	≥	NUM
ap-10600	130	15	3	3	NUM
ap-10600	130	16	.	.	PUNCT
ap-10600	131	1	lemma	lemma	PROPN
ap-10600	131	2	11	11	NUM
ap-10600	131	3	.	.	PUNCT
ap-10600	132	1	let	let	VERB
ap-10600	132	2	v	v	PART
ap-10600	132	3	be	be	AUX
ap-10600	132	4	a	a	DET
ap-10600	132	5	d	d	NOUN
ap-10600	132	6	-	-	ADJ
ap-10600	132	7	ary	ary	ADJ
ap-10600	132	8	1	1	NUM
ap-10600	132	9	-	-	PUNCT
ap-10600	132	10	balanced	balanced	ADJ
ap-10600	132	11	sequence	sequence	NOUN
ap-10600	132	12	,	,	PUNCT
ap-10600	132	13	where	where	SCONJ
ap-10600	132	14	v	v	NOUN
ap-10600	132	15	=	=	SYM
ap-10600	132	16	colour(u	colour(u	PROPN
ap-10600	132	17	,	,	PUNCT
ap-10600	132	18	a	a	DET
ap-10600	132	19	,	,	PUNCT
ap-10600	132	20	b	b	NOUN
ap-10600	132	21	)	)	PUNCT
ap-10600	132	22	,	,	PUNCT
ap-10600	132	23	u	u	NOUN
ap-10600	132	24	is	be	AUX
ap-10600	132	25	a	a	DET
ap-10600	132	26	sturmian	sturmian	NOUN
ap-10600	132	27	sequence	sequence	NOUN
ap-10600	132	28	over	over	ADP
ap-10600	132	29	{	{	PUNCT
ap-10600	132	30	a	a	DET
ap-10600	132	31	,	,	PUNCT
ap-10600	132	32	b	b	NOUN
ap-10600	132	33	}	}	PUNCT
ap-10600	132	34	and	and	CCONJ
ap-10600	132	35	a	a	DET
ap-10600	132	36	,	,	PUNCT
ap-10600	132	37	b	b	NOUN
ap-10600	132	38	are	be	AUX
ap-10600	132	39	constant	constant	ADJ
ap-10600	132	40	gap	gap	NOUN
ap-10600	132	41	sequences	sequence	NOUN
ap-10600	132	42	over	over	ADP
ap-10600	132	43	disjoint	disjoint	NOUN
ap-10600	132	44	alphabets	alphabet	NOUN
ap-10600	132	45	a	a	PRON
ap-10600	132	46	and	and	CCONJ
ap-10600	132	47	b.	b.	NOUN
ap-10600	133	1	if	if	SCONJ
ap-10600	133	2	d	d	PROPN
ap-10600	133	3	≥	≥	NOUN
ap-10600	133	4	3	3	NUM
ap-10600	133	5	,	,	PUNCT
ap-10600	133	6	then	then	ADV
ap-10600	133	7	v	v	NOUN
ap-10600	133	8	contains	contain	VERB
ap-10600	133	9	two	two	NUM
ap-10600	133	10	distinct	distinct	ADJ
ap-10600	133	11	letters	letter	NOUN
ap-10600	133	12	of	of	ADP
ap-10600	133	13	the	the	DET
ap-10600	133	14	same	same	ADJ
ap-10600	133	15	frequency	frequency	NOUN
ap-10600	133	16	.	.	PUNCT
ap-10600	134	1	proof	proof	NOUN
ap-10600	134	2	.	.	PUNCT
ap-10600	135	1	denote	denote	VERB
ap-10600	135	2	α	α	PRON
ap-10600	135	3	the	the	DET
ap-10600	135	4	frequency	frequency	NOUN
ap-10600	135	5	of	of	ADP
ap-10600	135	6	the	the	DET
ap-10600	135	7	letter	letter	NOUN
ap-10600	135	8	a	a	PRON
ap-10600	135	9	in	in	ADP
ap-10600	135	10	u.	u.	NOUN
ap-10600	135	11	if	if	SCONJ
ap-10600	135	12	d	d	PROPN
ap-10600	135	13	≥	≥	NOUN
ap-10600	135	14	3	3	NUM
ap-10600	135	15	,	,	PUNCT
ap-10600	135	16	then	then	ADV
ap-10600	135	17	either	either	CCONJ
ap-10600	135	18	#	#	SYM
ap-10600	135	19	a	a	DET
ap-10600	135	20	≥	≥	NUM
ap-10600	135	21	2	2	NUM
ap-10600	135	22	or	or	CCONJ
ap-10600	135	23	#	#	SYM
ap-10600	135	24	b	b	NOUN
ap-10600	135	25	≥	≥	NUM
ap-10600	135	26	2	2	NUM
ap-10600	135	27	.	.	PUNCT
ap-10600	135	28	consequently	consequently	ADV
ap-10600	135	29	,	,	PUNCT
ap-10600	135	30	by	by	ADP
ap-10600	135	31	lemma	lemma	PROPN
ap-10600	135	32	8	8	NUM
ap-10600	135	33	,	,	PUNCT
ap-10600	135	34	either	either	CCONJ
ap-10600	135	35	a	a	PRON
ap-10600	135	36	or	or	CCONJ
ap-10600	135	37	b	b	NOUN
ap-10600	135	38	contains	contain	VERB
ap-10600	135	39	two	two	NUM
ap-10600	135	40	distinct	distinct	ADJ
ap-10600	135	41	letters	letter	NOUN
ap-10600	135	42	i	i	PRON
ap-10600	135	43	,	,	PUNCT
ap-10600	135	44	j	j	PROPN
ap-10600	135	45	such	such	ADJ
ap-10600	135	46	that	that	SCONJ
ap-10600	135	47	they	they	PRON
ap-10600	135	48	have	have	VERB
ap-10600	135	49	the	the	DET
ap-10600	135	50	same	same	ADJ
ap-10600	135	51	frequency	frequency	NOUN
ap-10600	135	52	in	in	ADP
ap-10600	135	53	a	a	DET
ap-10600	135	54	,	,	PUNCT
ap-10600	135	55	resp	resp	NOUN
ap-10600	135	56	.	.	PUNCT
ap-10600	136	1	b	b	X
ap-10600	136	2	,	,	PUNCT
ap-10600	136	3	say	say	VERB
ap-10600	136	4	γ	γ	X
ap-10600	136	5	.	.	PROPN
ap-10600	137	1	then	then	ADV
ap-10600	137	2	,	,	PUNCT
ap-10600	137	3	by	by	ADP
ap-10600	137	4	remark	remark	NOUN
ap-10600	137	5	6	6	NUM
ap-10600	137	6	,	,	PUNCT
ap-10600	137	7	fi	fi	NOUN
ap-10600	137	8	=	=	NOUN
ap-10600	137	9	fj	fj	PROPN
ap-10600	137	10	=	=	SYM
ap-10600	137	11	αγ	αγ	PROPN
ap-10600	137	12	,	,	PUNCT
ap-10600	137	13	resp	resp	NOUN
ap-10600	137	14	.	.	PUNCT
ap-10600	137	15	fi	fi	NOUN
ap-10600	138	1	=	=	NOUN
ap-10600	138	2	fj	fj	PROPN
ap-10600	139	1	=	=	PUNCT
ap-10600	140	1	(	(	PUNCT
ap-10600	140	2	1	1	NUM
ap-10600	140	3	−α)γ	−α)γ	ADV
ap-10600	140	4	,	,	PUNCT
ap-10600	140	5	are	be	AUX
ap-10600	140	6	the	the	DET
ap-10600	140	7	frequencies	frequency	NOUN
ap-10600	140	8	of	of	ADP
ap-10600	140	9	letters	letter	NOUN
ap-10600	140	10	i	i	PRON
ap-10600	140	11	and	and	CCONJ
ap-10600	140	12	j	j	PROPN
ap-10600	140	13	in	in	ADP
ap-10600	140	14	v.	v.	PROPN
ap-10600	140	15	as	as	ADP
ap-10600	140	16	a	a	DET
ap-10600	140	17	consequence	consequence	NOUN
ap-10600	140	18	of	of	ADP
ap-10600	140	19	lemma	lemma	PROPN
ap-10600	140	20	11	11	NUM
ap-10600	140	21	,	,	PUNCT
ap-10600	140	22	we	we	PRON
ap-10600	140	23	can	can	AUX
ap-10600	140	24	see	see	VERB
ap-10600	140	25	that	that	SCONJ
ap-10600	140	26	the	the	DET
ap-10600	140	27	frequency	frequency	NOUN
ap-10600	140	28	vectors	vector	NOUN
ap-10600	140	29	of	of	ADP
ap-10600	140	30	1	1	NUM
ap-10600	140	31	-	-	PUNCT
ap-10600	140	32	balanced	balanced	ADJ
ap-10600	140	33	sequences	sequence	NOUN
ap-10600	140	34	do	do	AUX
ap-10600	140	35	not	not	PART
ap-10600	140	36	take	take	VERB
ap-10600	140	37	on	on	ADP
ap-10600	140	38	all	all	DET
ap-10600	140	39	possible	possible	ADJ
ap-10600	140	40	values	value	NOUN
ap-10600	140	41	.	.	PUNCT
ap-10600	141	1	lemma	lemma	PROPN
ap-10600	141	2	12	12	NUM
ap-10600	141	3	.	.	PUNCT
ap-10600	142	1	let	let	VERB
ap-10600	142	2	u	u	PRON
ap-10600	142	3	be	be	AUX
ap-10600	142	4	an	an	DET
ap-10600	142	5	ℓ-balanced	ℓ-balance	VERB
ap-10600	142	6	sequence	sequence	NOUN
ap-10600	142	7	over	over	ADP
ap-10600	142	8	{	{	PUNCT
ap-10600	142	9	a	a	DET
ap-10600	142	10	,	,	PUNCT
ap-10600	142	11	b	b	NOUN
ap-10600	142	12	}	}	PUNCT
ap-10600	142	13	,	,	PUNCT
ap-10600	142	14	and	and	CCONJ
ap-10600	142	15	a	a	DET
ap-10600	142	16	=	=	X
ap-10600	142	17	a0a1a2	a0a1a2	X
ap-10600	142	18	·	·	PUNCT
ap-10600	142	19	·	·	PUNCT
ap-10600	142	20	·	·	PUNCT
ap-10600	143	1	and	and	CCONJ
ap-10600	143	2	b	b	X
ap-10600	143	3	=	=	SYM
ap-10600	143	4	b0b1b2	b0b1b2	PROPN
ap-10600	143	5	·	·	PUNCT
ap-10600	143	6	·	·	PUNCT
ap-10600	143	7	·	·	PUNCT
ap-10600	143	8	be	be	AUX
ap-10600	143	9	two	two	NUM
ap-10600	143	10	k	k	ADV
ap-10600	143	11	-	-	ADJ
ap-10600	143	12	balanced	balanced	ADJ
ap-10600	143	13	sequences	sequence	NOUN
ap-10600	143	14	over	over	ADP
ap-10600	143	15	two	two	NUM
ap-10600	143	16	disjoint	disjoint	NOUN
ap-10600	143	17	alphabets	alphabet	NOUN
ap-10600	143	18	a	a	PRON
ap-10600	143	19	and	and	CCONJ
ap-10600	143	20	b	b	NOUN
ap-10600	143	21	,	,	PUNCT
ap-10600	143	22	respectively	respectively	ADV
ap-10600	143	23	.	.	PUNCT
ap-10600	144	1	then	then	ADV
ap-10600	144	2	v	v	X
ap-10600	144	3	=	=	SYM
ap-10600	144	4	colour(u	colour(u	PROPN
ap-10600	144	5	,	,	PUNCT
ap-10600	144	6	a	a	DET
ap-10600	144	7	,	,	PUNCT
ap-10600	144	8	b	b	NOUN
ap-10600	144	9	)	)	PUNCT
ap-10600	144	10	is	be	AUX
ap-10600	144	11	(	(	PUNCT
ap-10600	144	12	k	k	X
ap-10600	144	13	+	+	CCONJ
ap-10600	144	14	ℓ)-balanced	ℓ)-balanced	ADJ
ap-10600	144	15	.	.	PUNCT
ap-10600	145	1	proof	proof	NOUN
ap-10600	145	2	.	.	PUNCT
ap-10600	146	1	let	let	VERB
ap-10600	146	2	u	u	NOUN
ap-10600	146	3	,	,	PUNCT
ap-10600	146	4	v	v	PART
ap-10600	146	5	be	be	AUX
ap-10600	146	6	factors	factor	NOUN
ap-10600	146	7	of	of	ADP
ap-10600	146	8	v	v	NUM
ap-10600	146	9	of	of	ADP
ap-10600	146	10	the	the	DET
ap-10600	146	11	same	same	ADJ
ap-10600	146	12	length	length	NOUN
ap-10600	146	13	.	.	PUNCT
ap-10600	147	1	we	we	PRON
ap-10600	147	2	want	want	VERB
ap-10600	147	3	to	to	PART
ap-10600	147	4	prove	prove	VERB
ap-10600	147	5	that	that	SCONJ
ap-10600	147	6	for	for	ADP
ap-10600	147	7	each	each	DET
ap-10600	147	8	letter	letter	NOUN
ap-10600	147	9	c	c	PROPN
ap-10600	147	10	∈	∈	PROPN
ap-10600	147	11	a	a	DET
ap-10600	147	12	∪	∪	ADJ
ap-10600	147	13	b:∣∣|u|c	b:∣∣|u|c	NOUN
ap-10600	147	14	−	−	PUNCT
ap-10600	147	15	|v|c	|v|c	PROPN
ap-10600	147	16	∣∣	∣∣	X
ap-10600	147	17	≤	≤	PUNCT
ap-10600	147	18	k	k	PROPN
ap-10600	148	1	+	+	PROPN
ap-10600	148	2	ℓ	ℓ	PROPN
ap-10600	148	3	.	.	PUNCT
ap-10600	149	1	wlog	wlog	PROPN
ap-10600	149	2	let	let	VERB
ap-10600	149	3	c	c	PROPN
ap-10600	149	4	∈	∈	PROPN
ap-10600	149	5	a.	a.	NOUN
ap-10600	149	6	denote	denote	VERB
ap-10600	149	7	u′	u′	PROPN
ap-10600	149	8	=	=	SYM
ap-10600	149	9	π(u	π(u	PROPN
ap-10600	149	10	)	)	PUNCT
ap-10600	149	11	and	and	CCONJ
ap-10600	149	12	v′	v′	NOUN
ap-10600	149	13	=	=	SYM
ap-10600	149	14	π(v	π(v	NOUN
ap-10600	149	15	)	)	PUNCT
ap-10600	149	16	.	.	PUNCT
ap-10600	150	1	clearly	clearly	ADV
ap-10600	150	2	,	,	PUNCT
ap-10600	150	3	|u′|	|u′|	PROPN
ap-10600	150	4	=	=	SYM
ap-10600	150	5	|v′|	|v′|	PROPN
ap-10600	150	6	.	.	PUNCT
ap-10600	151	1	thanks	thank	NOUN
ap-10600	151	2	to	to	ADP
ap-10600	151	3	ℓ-balancedness	ℓ-balancedness	NOUN
ap-10600	151	4	of	of	ADP
ap-10600	151	5	u	u	PROPN
ap-10600	151	6	,	,	PUNCT
ap-10600	151	7	we	we	PRON
ap-10600	151	8	have	have	VERB
ap-10600	151	9	∣∣|u′|a	∣∣|u′|a	PRON
ap-10600	151	10	−	−	NOUN
ap-10600	151	11	|v′|a	|v′|a	PRON
ap-10600	151	12	∣∣	∣∣	X
ap-10600	151	13	≤	≤	NUM
ap-10600	151	14	ℓ.	ℓ.	NOUN
ap-10600	151	15	let	let	VERB
ap-10600	151	16	πa	πa	ADP
ap-10600	151	17	:	:	PUNCT
ap-10600	151	18	(	(	PUNCT
ap-10600	151	19	a	a	DET
ap-10600	151	20	∪	∪	ADJ
ap-10600	151	21	b)∗	b)∗	PROPN
ap-10600	151	22	→	→	SYM
ap-10600	151	23	a∗	a∗	PROPN
ap-10600	151	24	be	be	AUX
ap-10600	151	25	a	a	DET
ap-10600	151	26	morphism	morphism	NOUN
ap-10600	151	27	such	such	ADJ
ap-10600	151	28	that	that	SCONJ
ap-10600	151	29	πa(x	πa(x	NOUN
ap-10600	151	30	)	)	PUNCT
ap-10600	151	31	=	=	PUNCT
ap-10600	152	1	x	x	X
ap-10600	152	2	if	if	SCONJ
ap-10600	152	3	x	x	SYM
ap-10600	152	4	∈	∈	PROPN
ap-10600	152	5	a	a	PRON
ap-10600	152	6	and	and	CCONJ
ap-10600	152	7	πa(x	πa(x	NOUN
ap-10600	152	8	)	)	PUNCT
ap-10600	152	9	=	=	SYM
ap-10600	152	10	ε	ε	PROPN
ap-10600	152	11	if	if	SCONJ
ap-10600	152	12	x	x	PROPN
ap-10600	152	13	∈	∈	PROPN
ap-10600	152	14	b.	b.	NOUN
ap-10600	152	15	it	it	PRON
ap-10600	152	16	holds	hold	VERB
ap-10600	152	17	that	that	SCONJ
ap-10600	152	18	for	for	ADP
ap-10600	152	19	each	each	DET
ap-10600	152	20	factor	factor	NOUN
ap-10600	152	21	w	w	PROPN
ap-10600	152	22	of	of	ADP
ap-10600	152	23	v	v	NOUN
ap-10600	152	24	,	,	PUNCT
ap-10600	152	25	the	the	DET
ap-10600	152	26	word	word	NOUN
ap-10600	152	27	πa(w	πa(w	PUNCT
ap-10600	152	28	)	)	PUNCT
ap-10600	152	29	is	be	AUX
ap-10600	152	30	a	a	DET
ap-10600	152	31	factor	factor	NOUN
ap-10600	152	32	of	of	ADP
ap-10600	152	33	a.	a.	NOUN
ap-10600	152	34	by	by	ADP
ap-10600	152	35	definition	definition	NOUN
ap-10600	152	36	of	of	ADP
ap-10600	152	37	πa	πa	PROPN
ap-10600	152	38	,	,	PUNCT
ap-10600	152	39	we	we	PRON
ap-10600	152	40	have	have	VERB
ap-10600	152	41	|u|c	|u|c	ADV
ap-10600	152	42	=	=	SYM
ap-10600	152	43	|πa(u)|c	|πa(u)|c	NOUN
ap-10600	152	44	,	,	PUNCT
ap-10600	152	45	|v|c	|v|c	PROPN
ap-10600	152	46	=	=	SYM
ap-10600	152	47	|πa(v)|c	|πa(v)|c	X
ap-10600	152	48	and	and	CCONJ
ap-10600	152	49	by	by	ADP
ap-10600	152	50	definition	definition	NOUN
ap-10600	152	51	of	of	ADP
ap-10600	152	52	colouring	colouring	NOUN
ap-10600	152	53	,	,	PUNCT
ap-10600	152	54	|πa(u)|	|πa(u)|	NOUN
ap-10600	152	55	=	=	SYM
ap-10600	152	56	|u′|a	|u′|a	PROPN
ap-10600	152	57	,	,	PUNCT
ap-10600	152	58	|πa(v)|	|πa(v)|	PROPN
ap-10600	152	59	=	=	SYM
ap-10600	152	60	|v′|a	|v′|a	PROPN
ap-10600	152	61	.	.	PUNCT
ap-10600	153	1	since	since	SCONJ
ap-10600	153	2	|u′|a	|u′|a	NUM
ap-10600	153	3	and	and	CCONJ
ap-10600	153	4	|v′|a	|v′|a	PRON
ap-10600	153	5	differ	differ	VERB
ap-10600	153	6	at	at	ADP
ap-10600	153	7	most	most	ADJ
ap-10600	153	8	by	by	ADP
ap-10600	153	9	ℓ	ℓ	NOUN
ap-10600	153	10	,	,	PUNCT
ap-10600	153	11	the	the	DET
ap-10600	153	12	words	word	NOUN
ap-10600	153	13	πa(u	πa(u	NUM
ap-10600	153	14	)	)	PUNCT
ap-10600	153	15	and	and	CCONJ
ap-10600	153	16	πa(v	πa(v	NUM
ap-10600	153	17	)	)	PUNCT
ap-10600	153	18	are	be	AUX
ap-10600	153	19	factors	factor	NOUN
ap-10600	153	20	of	of	ADP
ap-10600	153	21	a	a	PRON
ap-10600	153	22	whose	whose	DET
ap-10600	153	23	lengths	length	NOUN
ap-10600	153	24	differ	differ	VERB
ap-10600	153	25	at	at	ADV
ap-10600	153	26	most	most	ADJ
ap-10600	153	27	by	by	ADP
ap-10600	153	28	ℓ.	ℓ.	NOUN
ap-10600	153	29	wlog	wlog	PROPN
ap-10600	153	30	assume	assume	VERB
ap-10600	153	31	|πa(u)|	|πa(u)|	PROPN
ap-10600	153	32	=	=	SYM
ap-10600	153	33	|πa(v)|	|πa(v)|	PROPN
ap-10600	153	34	+	+	CCONJ
ap-10600	153	35	n	n	CCONJ
ap-10600	153	36	,	,	PUNCT
ap-10600	153	37	where	where	SCONJ
ap-10600	153	38	0	0	NUM
ap-10600	153	39	≤	≤	NOUN
ap-10600	153	40	n	n	PRON
ap-10600	153	41	≤	≤	NOUN
ap-10600	153	42	ℓ.	ℓ.	NOUN
ap-10600	153	43	then	then	ADV
ap-10600	153	44	πa(u	πa(u	PUNCT
ap-10600	153	45	)	)	PUNCT
ap-10600	153	46	=	=	SYM
ap-10600	153	47	ai	ai	VERB
ap-10600	153	48	·	·	PUNCT
ap-10600	153	49	·	·	PUNCT
ap-10600	153	50	·	·	PUNCT
ap-10600	153	51	ai+m+n	ai+m+n	NOUN
ap-10600	153	52	and	and	CCONJ
ap-10600	153	53	πa(v	πa(v	NOUN
ap-10600	153	54	)	)	PUNCT
ap-10600	153	55	=	=	SYM
ap-10600	153	56	aj	aj	PROPN
ap-10600	153	57	·	·	PUNCT
ap-10600	153	58	·	·	PUNCT
ap-10600	153	59	·	·	PUNCT
ap-10600	154	1	aj+m	aj+m	NOUN
ap-10600	154	2	for	for	ADP
ap-10600	154	3	some	some	DET
ap-10600	154	4	i	i	PROPN
ap-10600	154	5	,	,	PUNCT
ap-10600	154	6	j	j	PROPN
ap-10600	154	7	,	,	PUNCT
ap-10600	154	8	m	m	PROPN
ap-10600	154	9	∈	∈	PROPN
ap-10600	154	10	n.	n.	NOUN
ap-10600	154	11	then	then	ADV
ap-10600	154	12	using	use	VERB
ap-10600	154	13	k	k	NOUN
ap-10600	154	14	-	-	NOUN
ap-10600	154	15	balancedness	balancedness	NOUN
ap-10600	154	16	of	of	ADP
ap-10600	154	17	a	a	DET
ap-10600	154	18	we	we	PRON
ap-10600	154	19	get:∣∣|πa(u)|c	get:∣∣|πa(u)|c	PUNCT
ap-10600	154	20	−	−	PROPN
ap-10600	154	21	|πa(v)|c	|πa(v)|c	X
ap-10600	154	22	∣∣	∣∣	NUM
ap-10600	154	23	≤	≤	NUM
ap-10600	154	24	∣∣|ai	∣∣|ai	NOUN
ap-10600	154	25	·	·	PUNCT
ap-10600	154	26	·	·	PUNCT
ap-10600	154	27	·	·	PUNCT
ap-10600	154	28	ai+m|c	ai+m|c	VERB
ap-10600	154	29	−	−	PROPN
ap-10600	154	30	|aj	|aj	SYM
ap-10600	154	31	·	·	PUNCT
ap-10600	154	32	·	·	PUNCT
ap-10600	154	33	·	·	PUNCT
ap-10600	155	1	aj+m|c	aj+m|c	ADP
ap-10600	155	2	∣∣	∣∣	X
ap-10600	155	3	+	+	CCONJ
ap-10600	155	4	|ai+m+1	|ai+m+1	PROPN
ap-10600	155	5	·	·	PUNCT
ap-10600	155	6	·	·	PUNCT
ap-10600	155	7	·	·	PUNCT
ap-10600	155	8	ai+m+n|c	ai+m+n|c	VERB
ap-10600	155	9	≤	≤	PUNCT
ap-10600	156	1	k	k	PROPN
ap-10600	157	1	+	+	CCONJ
ap-10600	157	2	n	n	CCONJ
ap-10600	157	3	≤	≤	NOUN
ap-10600	157	4	k	k	NOUN
ap-10600	157	5	+	+	PUNCT
ap-10600	157	6	ℓ.	ℓ.	NOUN
ap-10600	157	7	since	since	SCONJ
ap-10600	157	8	|u|c	|u|c	PROPN
ap-10600	157	9	=	=	SYM
ap-10600	157	10	|πa(u)|c	|πa(u)|c	PROPN
ap-10600	157	11	and	and	CCONJ
ap-10600	157	12	|v|c	|v|c	PROPN
ap-10600	157	13	=	=	SYM
ap-10600	157	14	|πa(v)|c	|πa(v)|c	PROPN
ap-10600	157	15	,	,	PUNCT
ap-10600	157	16	we	we	PRON
ap-10600	157	17	have	have	AUX
ap-10600	157	18	proven	prove	VERB
ap-10600	157	19	that	that	SCONJ
ap-10600	157	20	∣∣|u|c	∣∣|u|c	ADV
ap-10600	157	21	−	−	ADP
ap-10600	158	1	|v|c	|v|c	PROPN
ap-10600	158	2	∣∣	∣∣	X
ap-10600	158	3	≤	≤	PUNCT
ap-10600	158	4	k	k	PROPN
ap-10600	159	1	+	+	CCONJ
ap-10600	159	2	ℓ.	ℓ.	NOUN
ap-10600	159	3	4	4	NUM
ap-10600	159	4	.	.	PUNCT
ap-10600	160	1	proof	proof	NOUN
ap-10600	160	2	of	of	ADP
ap-10600	160	3	theorem	theorem	NOUN
ap-10600	160	4	2	2	NUM
ap-10600	160	5	in	in	ADP
ap-10600	160	6	this	this	DET
ap-10600	160	7	section	section	NOUN
ap-10600	161	1	,	,	PUNCT
ap-10600	161	2	we	we	PRON
ap-10600	161	3	prove	prove	VERB
ap-10600	161	4	a	a	DET
ap-10600	161	5	statement	statement	NOUN
ap-10600	161	6	having	having	AUX
ap-10600	161	7	theorem	theorem	VERB
ap-10600	161	8	2	2	NUM
ap-10600	161	9	as	as	ADP
ap-10600	161	10	its	its	PRON
ap-10600	161	11	direct	direct	ADJ
ap-10600	161	12	consequence	consequence	NOUN
ap-10600	161	13	.	.	PUNCT
ap-10600	162	1	we	we	PRON
ap-10600	162	2	make	make	VERB
ap-10600	162	3	use	use	NOUN
ap-10600	162	4	of	of	ADP
ap-10600	162	5	the	the	DET
ap-10600	162	6	knowledge	knowledge	NOUN
ap-10600	162	7	of	of	ADP
ap-10600	162	8	the	the	DET
ap-10600	162	9	number	number	NOUN
ap-10600	162	10	of	of	ADP
ap-10600	162	11	occurrences	occurrence	NOUN
ap-10600	162	12	of	of	ADP
ap-10600	162	13	letters	letter	NOUN
ap-10600	162	14	in	in	ADP
ap-10600	162	15	sturmian	sturmian	ADJ
ap-10600	162	16	sequences	sequence	NOUN
ap-10600	162	17	,	,	PUNCT
ap-10600	162	18	provided	provide	VERB
ap-10600	162	19	in	in	ADP
ap-10600	162	20	[	[	X
ap-10600	162	21	19	19	NUM
ap-10600	162	22	]	]	PUNCT
ap-10600	162	23	.	.	PUNCT
ap-10600	163	1	lemma	lemma	PROPN
ap-10600	163	2	13	13	NUM
ap-10600	163	3	.	.	PUNCT
ap-10600	164	1	let	let	VERB
ap-10600	164	2	u	u	PRON
ap-10600	164	3	be	be	AUX
ap-10600	164	4	a	a	DET
ap-10600	164	5	1	1	NUM
ap-10600	164	6	-	-	PUNCT
ap-10600	164	7	balanced	balanced	ADJ
ap-10600	164	8	sequence	sequence	NOUN
ap-10600	164	9	over	over	ADP
ap-10600	164	10	the	the	DET
ap-10600	164	11	alphabet	alphabet	NOUN
ap-10600	164	12	{	{	PUNCT
ap-10600	164	13	a	a	PROPN
ap-10600	164	14	,	,	PUNCT
ap-10600	164	15	b	b	NOUN
ap-10600	164	16	}	}	PUNCT
ap-10600	164	17	and	and	CCONJ
ap-10600	164	18	fa	fa	X
ap-10600	164	19	=	=	SYM
ap-10600	164	20	α	α	PROPN
ap-10600	164	21	∈	∈	PROPN
ap-10600	164	22	(	(	PUNCT
ap-10600	164	23	0	0	NUM
ap-10600	164	24	,	,	PUNCT
ap-10600	164	25	1	1	NUM
ap-10600	164	26	)	)	PUNCT
ap-10600	164	27	.	.	PUNCT
ap-10600	165	1	then	then	ADV
ap-10600	165	2	any	any	DET
ap-10600	165	3	factor	factor	NOUN
ap-10600	165	4	u	u	NOUN
ap-10600	165	5	of	of	ADP
ap-10600	165	6	length	length	NOUN
ap-10600	165	7	n	n	ADP
ap-10600	165	8	∈	∈	PROPN
ap-10600	165	9	n	n	NOUN
ap-10600	165	10	either	either	CCONJ
ap-10600	165	11	contains	contain	VERB
ap-10600	165	12	⌈αn⌉	⌈αn⌉	NOUN
ap-10600	165	13	letters	letter	NOUN
ap-10600	165	14	a	a	PRON
ap-10600	165	15	and	and	CCONJ
ap-10600	165	16	⌊(1	⌊(1	NUM
ap-10600	166	1	−	−	PROPN
ap-10600	166	2	α)n⌋	α)n⌋	NOUN
ap-10600	166	3	letters	letter	NOUN
ap-10600	166	4	b	b	NOUN
ap-10600	166	5	,	,	PUNCT
ap-10600	166	6	or	or	CCONJ
ap-10600	166	7	u	u	NOUN
ap-10600	166	8	contains	contain	VERB
ap-10600	166	9	⌊αn⌋	⌊αn⌋	NOUN
ap-10600	166	10	letters	letter	NOUN
ap-10600	166	11	a	a	PRON
ap-10600	166	12	and	and	CCONJ
ap-10600	166	13	⌈(1	⌈(1	NOUN
ap-10600	166	14	−	−	PROPN
ap-10600	166	15	α)n⌉	α)n⌉	ADJ
ap-10600	166	16	letters	letter	NOUN
ap-10600	166	17	b.	b.	PROPN
ap-10600	166	18	theorem	theorem	PROPN
ap-10600	166	19	14	14	NUM
ap-10600	166	20	.	.	PUNCT
ap-10600	167	1	let	let	VERB
ap-10600	167	2	d	d	PROPN
ap-10600	167	3	∈	∈	PROPN
ap-10600	167	4	n	n	CCONJ
ap-10600	167	5	,	,	PUNCT
ap-10600	167	6	d	d	PRON
ap-10600	167	7	≥	≥	NUM
ap-10600	167	8	1	1	NUM
ap-10600	167	9	,	,	PUNCT
ap-10600	167	10	and	and	CCONJ
ap-10600	167	11	f(1	f(1	PROPN
ap-10600	167	12	)	)	PUNCT
ap-10600	167	13	,	,	PUNCT
ap-10600	167	14	f(2	f(2	PROPN
ap-10600	167	15	)	)	PUNCT
ap-10600	167	16	,	,	PUNCT
ap-10600	167	17	.	.	PUNCT
ap-10600	167	18	.	.	PUNCT
ap-10600	168	1	.	.	PUNCT
ap-10600	169	1	,	,	PUNCT
ap-10600	169	2	f(d	f(d	PROPN
ap-10600	169	3	)	)	PUNCT
ap-10600	169	4	be	be	AUX
ap-10600	169	5	positive	positive	ADJ
ap-10600	169	6	numbers	number	NOUN
ap-10600	169	7	such	such	ADJ
ap-10600	169	8	that	that	DET
ap-10600	169	9	f(1	f(1	PROPN
ap-10600	169	10	)	)	PUNCT
ap-10600	169	11	+	+	PUNCT
ap-10600	170	1	f(2	f(2	PROPN
ap-10600	170	2	)	)	PUNCT
ap-10600	170	3	+	+	NUM
ap-10600	170	4	·	·	PUNCT
ap-10600	170	5	·	·	PUNCT
ap-10600	170	6	·	·	PUNCT
ap-10600	170	7	+	+	NUM
ap-10600	170	8	f(d	f(d	PROPN
ap-10600	170	9	)	)	PUNCT
ap-10600	170	10	=	=	SYM
ap-10600	170	11	1	1	X
ap-10600	170	12	.	.	PUNCT
ap-10600	170	13	then	then	ADV
ap-10600	170	14	there	there	PRON
ap-10600	170	15	exists	exist	VERB
ap-10600	170	16	an	an	DET
ap-10600	170	17	infinite	infinite	ADJ
ap-10600	170	18	sequence	sequence	NOUN
ap-10600	170	19	v	v	NOUN
ap-10600	170	20	over	over	ADP
ap-10600	170	21	the	the	DET
ap-10600	170	22	alphabet	alphabet	NOUN
ap-10600	170	23	{	{	PUNCT
ap-10600	170	24	1	1	NUM
ap-10600	170	25	,	,	PUNCT
ap-10600	170	26	2	2	NUM
ap-10600	170	27	,	,	PUNCT
ap-10600	170	28	.	.	PUNCT
ap-10600	170	29	.	.	PUNCT
ap-10600	171	1	.	.	PUNCT
ap-10600	172	1	,	,	PUNCT
ap-10600	172	2	d	d	X
ap-10600	172	3	}	}	PUNCT
ap-10600	172	4	such	such	ADJ
ap-10600	172	5	that	that	SCONJ
ap-10600	172	6	:	:	PUNCT
ap-10600	172	7	(	(	PUNCT
ap-10600	172	8	1	1	NUM
ap-10600	172	9	.	.	PUNCT
ap-10600	172	10	)	)	PUNCT
ap-10600	173	1	the	the	DET
ap-10600	173	2	frequency	frequency	NOUN
ap-10600	173	3	of	of	ADP
ap-10600	173	4	the	the	DET
ap-10600	173	5	letter	letter	NOUN
ap-10600	173	6	i	i	PRON
ap-10600	173	7	in	in	ADP
ap-10600	173	8	v	v	NUM
ap-10600	173	9	is	be	AUX
ap-10600	173	10	f(i	f(i	NUM
ap-10600	173	11	)	)	PUNCT
ap-10600	173	12	for	for	ADP
ap-10600	173	13	each	each	DET
ap-10600	173	14	i	i	PRON
ap-10600	173	15	∈	∈	PROPN
ap-10600	173	16	{	{	PUNCT
ap-10600	173	17	1	1	NUM
ap-10600	173	18	,	,	PUNCT
ap-10600	173	19	2	2	NUM
ap-10600	173	20	,	,	PUNCT
ap-10600	173	21	.	.	PUNCT
ap-10600	173	22	.	.	PUNCT
ap-10600	173	23	.	.	PUNCT
ap-10600	174	1	,	,	PUNCT
ap-10600	174	2	d	d	X
ap-10600	174	3	}	}	PUNCT
ap-10600	174	4	,	,	PUNCT
ap-10600	174	5	(	(	PUNCT
ap-10600	174	6	2	2	NUM
ap-10600	174	7	.	.	PUNCT
ap-10600	174	8	)	)	PUNCT
ap-10600	175	1	v	v	NOUN
ap-10600	175	2	is	be	AUX
ap-10600	175	3	k	k	NOUN
ap-10600	175	4	-	-	ADJ
ap-10600	175	5	balanced	balanced	ADJ
ap-10600	175	6	with	with	ADP
ap-10600	175	7	k	k	X
ap-10600	175	8	=	=	PUNCT
ap-10600	175	9	⌈log2	⌈log2	PROPN
ap-10600	175	10	d⌉	d⌉	PROPN
ap-10600	175	11	,	,	PUNCT
ap-10600	175	12	536	536	NUM
ap-10600	175	13	vol	vol	NOUN
ap-10600	175	14	.	.	PUNCT
ap-10600	176	1	65	65	NUM
ap-10600	176	2	no	no	NOUN
ap-10600	176	3	.	.	PUNCT
ap-10600	177	1	5/2025	5/2025	NUM
ap-10600	177	2	frequencies	frequency	NOUN
ap-10600	177	3	of	of	ADP
ap-10600	177	4	letters	letter	NOUN
ap-10600	177	5	in	in	ADP
ap-10600	177	6	infinite	infinite	ADJ
ap-10600	177	7	k	k	ADV
ap-10600	177	8	-	-	ADJ
ap-10600	177	9	balanced	balanced	ADJ
ap-10600	177	10	sequences	sequence	NOUN
ap-10600	177	11	(	(	PUNCT
ap-10600	177	12	3	3	NUM
ap-10600	177	13	.	.	PUNCT
ap-10600	177	14	)	)	PUNCT
ap-10600	178	1	the	the	DET
ap-10600	178	2	factor	factor	NOUN
ap-10600	178	3	complexity	complexity	NOUN
ap-10600	178	4	of	of	ADP
ap-10600	178	5	v	v	NOUN
ap-10600	178	6	satisfies	satisfie	NOUN
ap-10600	178	7	:	:	PUNCT
ap-10600	178	8	cv(n	cv(n	X
ap-10600	178	9	)	)	PUNCT
ap-10600	178	10	≤	≤	NOUN
ap-10600	178	11	(	(	PUNCT
ap-10600	178	12	n+	n+	NUM
ap-10600	178	13	1)d−1	1)d−1	NUM
ap-10600	178	14	.	.	PUNCT
ap-10600	179	1	proof	proof	NOUN
ap-10600	179	2	.	.	PUNCT
ap-10600	180	1	we	we	PRON
ap-10600	180	2	proceed	proceed	VERB
ap-10600	180	3	by	by	ADP
ap-10600	180	4	induction	induction	NOUN
ap-10600	180	5	on	on	ADP
ap-10600	180	6	d.	d.	PROPN
ap-10600	180	7	if	if	SCONJ
ap-10600	180	8	d	d	PROPN
ap-10600	180	9	=	=	SYM
ap-10600	180	10	1	1	NUM
ap-10600	180	11	,	,	PUNCT
ap-10600	180	12	then	then	ADV
ap-10600	180	13	we	we	PRON
ap-10600	180	14	put	put	VERB
ap-10600	180	15	v	v	NOUN
ap-10600	180	16	=	=	SYM
ap-10600	180	17	1ω	1ω	NUM
ap-10600	180	18	.	.	PUNCT
ap-10600	181	1	let	let	VERB
ap-10600	181	2	d	d	X
ap-10600	181	3	≥	≥	NUM
ap-10600	181	4	2	2	X
ap-10600	181	5	.	.	PUNCT
ap-10600	182	1	we	we	PRON
ap-10600	182	2	denote	denote	VERB
ap-10600	182	3	α	α	NOUN
ap-10600	182	4	=	=	SYM
ap-10600	182	5	f(1)+f(2)+	f(1)+f(2)+	PROPN
ap-10600	182	6	·	·	PUNCT
ap-10600	182	7	·	·	PUNCT
ap-10600	182	8	·	·	PUNCT
ap-10600	183	1	+	+	NOUN
ap-10600	183	2	f(⌈d2	f(⌈d2	NOUN
ap-10600	183	3	⌉	⌉	NOUN
ap-10600	183	4	)	)	PUNCT
ap-10600	183	5	and	and	CCONJ
ap-10600	183	6	:	:	PUNCT
ap-10600	183	7	f	f	PROPN
ap-10600	183	8	′(i	′(i	PROPN
ap-10600	183	9	)	)	PUNCT
ap-10600	183	10	=	=	SYM
ap-10600	184	1			NOUN
ap-10600	184	2	1	1	NUM
ap-10600	184	3	α	α	NOUN
ap-10600	184	4	f(i	f(i	PROPN
ap-10600	184	5	)	)	PUNCT
ap-10600	184	6	for	for	ADP
ap-10600	184	7	i	i	PROPN
ap-10600	184	8	=	=	SYM
ap-10600	184	9	1	1	NUM
ap-10600	184	10	,	,	PUNCT
ap-10600	184	11	2	2	NUM
ap-10600	184	12	,	,	PUNCT
ap-10600	184	13	.	.	PUNCT
ap-10600	184	14	.	.	PUNCT
ap-10600	184	15	.	.	PUNCT
ap-10600	185	1	,	,	PUNCT
ap-10600	185	2	⌈d2⌉	⌈d2⌉	PROPN
ap-10600	185	3	,	,	PUNCT
ap-10600	185	4	1	1	NUM
ap-10600	185	5	1	1	NUM
ap-10600	185	6	−	−	NOUN
ap-10600	185	7	α	α	DET
ap-10600	185	8	f(i	f(i	PROPN
ap-10600	185	9	)	)	PUNCT
ap-10600	185	10	for	for	ADP
ap-10600	185	11	i	i	PRON
ap-10600	185	12	=	=	SYM
ap-10600	186	1	⌈d2⌉	⌈d2⌉	PROPN
ap-10600	186	2	+	+	NUM
ap-10600	186	3	1	1	NUM
ap-10600	186	4	,	,	PUNCT
ap-10600	186	5	.	.	PUNCT
ap-10600	186	6	.	.	PUNCT
ap-10600	187	1	.	.	PUNCT
ap-10600	188	1	,	,	PUNCT
ap-10600	188	2	d.	d.	PROPN
ap-10600	188	3	obviously	obviously	ADV
ap-10600	188	4	:	:	PUNCT
ap-10600	188	5	f	f	PROPN
ap-10600	188	6	′(1)+	′(1)+	X
ap-10600	188	7	·	·	PUNCT
ap-10600	188	8	·	·	PUNCT
ap-10600	188	9	·	·	PUNCT
ap-10600	189	1	+	+	NOUN
ap-10600	189	2	f	f	X
ap-10600	189	3	′(⌈d2	′(⌈d2	PROPN
ap-10600	189	4	⌉	⌉	NOUN
ap-10600	189	5	)	)	PUNCT
ap-10600	189	6	=	=	SYM
ap-10600	189	7	1	1	NUM
ap-10600	189	8	=	=	SYM
ap-10600	189	9	f	f	X
ap-10600	189	10	′(⌈d2	′(⌈d2	PROPN
ap-10600	189	11	⌉+1)+	⌉+1)+	PROPN
ap-10600	189	12	·	·	PUNCT
ap-10600	189	13	·	·	PUNCT
ap-10600	189	14	·	·	PUNCT
ap-10600	190	1	+	+	NOUN
ap-10600	190	2	f	f	NOUN
ap-10600	190	3	′(d	′(d	NOUN
ap-10600	190	4	)	)	PUNCT
ap-10600	190	5	.	.	PUNCT
ap-10600	191	1	by	by	ADP
ap-10600	191	2	induction	induction	NOUN
ap-10600	191	3	hypothesis	hypothesis	NOUN
ap-10600	191	4	,	,	PUNCT
ap-10600	191	5	there	there	PRON
ap-10600	191	6	exist	exist	VERB
ap-10600	191	7	a	a	DET
ap-10600	191	8	kabalanced	kabalanced	ADJ
ap-10600	191	9	sequence	sequence	NOUN
ap-10600	192	1	a	a	DET
ap-10600	192	2	=	=	X
ap-10600	192	3	a0a1a2	a0a1a2	X
ap-10600	192	4	·	·	PUNCT
ap-10600	192	5	·	·	PUNCT
ap-10600	192	6	·	·	PUNCT
ap-10600	192	7	over	over	ADP
ap-10600	192	8	the	the	DET
ap-10600	192	9	alphabet	alphabet	NOUN
ap-10600	192	10	a	a	PROPN
ap-10600	192	11	=	=	X
ap-10600	192	12	{	{	PUNCT
ap-10600	192	13	1	1	NUM
ap-10600	192	14	,	,	PUNCT
ap-10600	192	15	2	2	NUM
ap-10600	192	16	,	,	PUNCT
ap-10600	192	17	.	.	PUNCT
ap-10600	192	18	.	.	PUNCT
ap-10600	192	19	.	.	PUNCT
ap-10600	192	20	,	,	PUNCT
ap-10600	192	21	⌈d2	⌈d2	ADP
ap-10600	192	22	⌉	⌉	NOUN
ap-10600	192	23	}	}	PUNCT
ap-10600	192	24	with	with	ADP
ap-10600	192	25	the	the	DET
ap-10600	192	26	frequencies	frequency	NOUN
ap-10600	192	27	of	of	ADP
ap-10600	192	28	letters	letter	NOUN
ap-10600	192	29	f	f	PROPN
ap-10600	192	30	′(i	′(i	PROPN
ap-10600	192	31	)	)	PUNCT
ap-10600	192	32	for	for	ADP
ap-10600	192	33	each	each	PRON
ap-10600	192	34	i	i	PRON
ap-10600	192	35	∈	∈	PROPN
ap-10600	192	36	a	a	PRON
ap-10600	192	37	and	and	CCONJ
ap-10600	192	38	ka	ka	X
ap-10600	192	39	=	=	NOUN
ap-10600	192	40	⌈log2⌈d2	⌈log2⌈d2	PROPN
ap-10600	192	41	⌉⌉	⌉⌉	ADV
ap-10600	192	42	and	and	CCONJ
ap-10600	192	43	a	a	DET
ap-10600	192	44	kbbalanced	kbbalanced	ADJ
ap-10600	192	45	sequence	sequence	NOUN
ap-10600	192	46	b	b	NOUN
ap-10600	192	47	=	=	SYM
ap-10600	192	48	b0b1b2	b0b1b2	PROPN
ap-10600	192	49	·	·	PUNCT
ap-10600	192	50	·	·	PUNCT
ap-10600	192	51	·	·	PUNCT
ap-10600	192	52	over	over	ADP
ap-10600	192	53	the	the	DET
ap-10600	192	54	alphabet	alphabet	PROPN
ap-10600	192	55	b	b	PROPN
ap-10600	192	56	=	=	NOUN
ap-10600	192	57	{	{	PUNCT
ap-10600	192	58	⌈d2	⌈d2	NOUN
ap-10600	192	59	⌉	⌉	ADJ
ap-10600	192	60	+	+	NOUN
ap-10600	192	61	1	1	NUM
ap-10600	192	62	,	,	PUNCT
ap-10600	192	63	.	.	PUNCT
ap-10600	192	64	.	.	PUNCT
ap-10600	192	65	.	.	PUNCT
ap-10600	193	1	,	,	PUNCT
ap-10600	193	2	d	d	X
ap-10600	193	3	}	}	PUNCT
ap-10600	193	4	with	with	ADP
ap-10600	193	5	the	the	DET
ap-10600	193	6	frequencies	frequency	NOUN
ap-10600	193	7	of	of	ADP
ap-10600	193	8	letters	letter	NOUN
ap-10600	193	9	f	f	PROPN
ap-10600	193	10	′(i	′(i	PROPN
ap-10600	193	11	)	)	PUNCT
ap-10600	193	12	for	for	ADP
ap-10600	193	13	each	each	DET
ap-10600	193	14	i	i	PROPN
ap-10600	193	15	∈	∈	PROPN
ap-10600	193	16	b	b	PROPN
ap-10600	193	17	and	and	CCONJ
ap-10600	193	18	kb	kb	PROPN
ap-10600	193	19	=	=	PRON
ap-10600	193	20	⌈log2⌊d2	⌈log2⌊d2	PRON
ap-10600	193	21	⌋⌉.	⌋⌉.	NOUN
ap-10600	193	22	let	let	VERB
ap-10600	193	23	u	u	PRON
ap-10600	193	24	be	be	AUX
ap-10600	193	25	a	a	DET
ap-10600	193	26	1	1	NUM
ap-10600	193	27	-	-	PUNCT
ap-10600	193	28	balanced	balanced	ADJ
ap-10600	193	29	sequence	sequence	NOUN
ap-10600	193	30	over	over	ADP
ap-10600	193	31	the	the	DET
ap-10600	193	32	alphabet	alphabet	NOUN
ap-10600	193	33	{	{	PUNCT
ap-10600	193	34	a	a	PROPN
ap-10600	193	35	,	,	PUNCT
ap-10600	193	36	b	b	NOUN
ap-10600	193	37	}	}	PUNCT
ap-10600	193	38	with	with	ADP
ap-10600	193	39	frequencies	frequency	NOUN
ap-10600	193	40	of	of	ADP
ap-10600	193	41	letters	letter	NOUN
ap-10600	193	42	α	α	NOUN
ap-10600	193	43	and	and	CCONJ
ap-10600	193	44	1	1	NUM
ap-10600	193	45	−	−	PROPN
ap-10600	193	46	α	α	NOUN
ap-10600	193	47	,	,	PUNCT
ap-10600	193	48	respectively	respectively	ADV
ap-10600	193	49	.	.	PUNCT
ap-10600	194	1	then	then	ADV
ap-10600	194	2	the	the	DET
ap-10600	194	3	sequence	sequence	NOUN
ap-10600	194	4	v	v	NOUN
ap-10600	194	5	=	=	SYM
ap-10600	194	6	colour(u	colour(u	PROPN
ap-10600	194	7	,	,	PUNCT
ap-10600	194	8	a	a	DET
ap-10600	194	9	,	,	PUNCT
ap-10600	194	10	b	b	NOUN
ap-10600	194	11	)	)	PUNCT
ap-10600	194	12	is	be	AUX
ap-10600	194	13	over	over	ADP
ap-10600	194	14	the	the	DET
ap-10600	194	15	alphabet	alphabet	NOUN
ap-10600	194	16	{	{	PUNCT
ap-10600	194	17	1	1	NUM
ap-10600	194	18	,	,	PUNCT
ap-10600	194	19	.	.	PUNCT
ap-10600	194	20	.	.	PUNCT
ap-10600	194	21	.	.	PUNCT
ap-10600	195	1	,	,	PUNCT
ap-10600	195	2	d	d	X
ap-10600	195	3	}	}	PUNCT
ap-10600	195	4	,	,	PUNCT
ap-10600	195	5	and	and	CCONJ
ap-10600	195	6	by	by	ADP
ap-10600	195	7	remark	remark	NOUN
ap-10600	195	8	6	6	NUM
ap-10600	195	9	,	,	PUNCT
ap-10600	195	10	the	the	DET
ap-10600	195	11	frequencies	frequency	NOUN
ap-10600	195	12	of	of	ADP
ap-10600	195	13	letters	letter	NOUN
ap-10600	195	14	are	be	AUX
ap-10600	195	15	αf	αf	ADP
ap-10600	195	16	′(i	′(i	NOUN
ap-10600	195	17	)	)	PUNCT
ap-10600	196	1	=	=	SYM
ap-10600	196	2	f(i	f(i	PROPN
ap-10600	196	3	)	)	PUNCT
ap-10600	197	1	for	for	ADP
ap-10600	197	2	i	i	PRON
ap-10600	197	3	∈	∈	PROPN
ap-10600	197	4	a	a	PRON
ap-10600	197	5	and	and	CCONJ
ap-10600	197	6	(	(	PUNCT
ap-10600	197	7	1	1	NUM
ap-10600	197	8	−	−	NOUN
ap-10600	197	9	α)f	α)f	ADJ
ap-10600	197	10	′(i	′(i	NOUN
ap-10600	197	11	)	)	PUNCT
ap-10600	197	12	=	=	SYM
ap-10600	197	13	f(i	f(i	PROPN
ap-10600	197	14	)	)	PUNCT
ap-10600	197	15	for	for	ADP
ap-10600	197	16	i	i	PROPN
ap-10600	197	17	∈	∈	PROPN
ap-10600	197	18	b.	b.	PROPN
ap-10600	197	19	lemma	lemma	PROPN
ap-10600	197	20	12	12	NUM
ap-10600	197	21	implies	imply	VERB
ap-10600	197	22	that	that	SCONJ
ap-10600	197	23	v	v	X
ap-10600	197	24	=	=	SYM
ap-10600	197	25	colour(u	colour(u	PROPN
ap-10600	197	26	,	,	PUNCT
ap-10600	197	27	a	a	DET
ap-10600	197	28	,	,	PUNCT
ap-10600	197	29	b	b	NOUN
ap-10600	197	30	)	)	PUNCT
ap-10600	197	31	is	be	AUX
ap-10600	197	32	k	k	NOUN
ap-10600	197	33	-	-	ADJ
ap-10600	197	34	balanced	balanced	ADJ
ap-10600	197	35	,	,	PUNCT
ap-10600	197	36	with	with	ADP
ap-10600	197	37	k	k	PROPN
ap-10600	197	38	=	=	SYM
ap-10600	197	39	1	1	NUM
ap-10600	197	40	+	+	NUM
ap-10600	197	41	⌈log2⌈d2	⌈log2⌈d2	PROPN
ap-10600	197	42	⌉⌉.	⌉⌉.	X
ap-10600	197	43	to	to	PART
ap-10600	197	44	complete	complete	VERB
ap-10600	197	45	the	the	DET
ap-10600	197	46	proof	proof	NOUN
ap-10600	197	47	of	of	ADP
ap-10600	197	48	item	item	NOUN
ap-10600	197	49	(	(	PUNCT
ap-10600	197	50	2	2	NUM
ap-10600	197	51	.	.	NUM
ap-10600	197	52	)	)	PUNCT
ap-10600	197	53	,	,	PUNCT
ap-10600	197	54	we	we	PRON
ap-10600	197	55	have	have	VERB
ap-10600	197	56	to	to	PART
ap-10600	197	57	show	show	VERB
ap-10600	197	58	that	that	SCONJ
ap-10600	197	59	1	1	NUM
ap-10600	197	60	+	+	NUM
ap-10600	197	61	⌈log2⌈d2	⌈log2⌈d2	NUM
ap-10600	197	62	⌉⌉	⌉⌉	ADV
ap-10600	197	63	≤	≤	NUM
ap-10600	197	64	⌈log2	⌈log2	ADV
ap-10600	197	65	d⌉.	d⌉.	NOUN
ap-10600	197	66	if	if	SCONJ
ap-10600	197	67	d	d	NOUN
ap-10600	197	68	is	be	AUX
ap-10600	197	69	even	even	ADV
ap-10600	197	70	,	,	PUNCT
ap-10600	197	71	then	then	ADV
ap-10600	197	72	1	1	NUM
ap-10600	197	73	+	+	NUM
ap-10600	197	74	⌈log2⌈d2	⌈log2⌈d2	NUM
ap-10600	198	1	⌉⌉	⌉⌉	ADP
ap-10600	198	2	=	=	PUNCT
ap-10600	198	3	⌈log2	⌈log2	NOUN
ap-10600	198	4	d⌉.	d⌉.	NOUN
ap-10600	198	5	for	for	ADP
ap-10600	198	6	d	d	X
ap-10600	198	7	odd	odd	ADJ
ap-10600	198	8	,	,	PUNCT
ap-10600	198	9	we	we	PRON
ap-10600	198	10	demonstrate	demonstrate	VERB
ap-10600	198	11	the	the	DET
ap-10600	198	12	required	require	VERB
ap-10600	198	13	inequality	inequality	NOUN
ap-10600	198	14	by	by	ADP
ap-10600	198	15	contradiction	contradiction	NOUN
ap-10600	198	16	.	.	PUNCT
ap-10600	199	1	assume	assume	VERB
ap-10600	199	2	that	that	SCONJ
ap-10600	199	3	1	1	NUM
ap-10600	199	4	+	+	NUM
ap-10600	199	5	⌈log2⌈d2	⌈log2⌈d2	NUM
ap-10600	199	6	⌉⌉	⌉⌉	ADV
ap-10600	199	7	>	>	PUNCT
ap-10600	199	8	⌈log2	⌈log2	ADJ
ap-10600	199	9	d⌉.	d⌉.	NOUN
ap-10600	199	10	as	as	SCONJ
ap-10600	199	11	d	d	PROPN
ap-10600	199	12	is	be	AUX
ap-10600	199	13	odd	odd	ADJ
ap-10600	199	14	,	,	PUNCT
ap-10600	199	15	we	we	PRON
ap-10600	199	16	know	know	VERB
ap-10600	199	17	that	that	PRON
ap-10600	199	18	:	:	PUNCT
ap-10600	200	1	log2	log2	PROPN
ap-10600	201	1	d	d	X
ap-10600	201	2	<	<	X
ap-10600	201	3	⌈log2	⌈log2	X
ap-10600	201	4	d⌉	d⌉	PROPN
ap-10600	201	5	≤	≤	NUM
ap-10600	201	6	⌈log2⌈d2	⌈log2⌈d2	NUM
ap-10600	201	7	⌉⌉	⌉⌉	ADP
ap-10600	201	8	=	=	PUNCT
ap-10600	201	9	⌈log2	⌈log2	SYM
ap-10600	201	10	d+1	d+1	PROPN
ap-10600	201	11	2	2	NUM
ap-10600	201	12	⌉	⌉	PRON
ap-10600	201	13	=	=	PUNCT
ap-10600	201	14	⌈log2(d+	⌈log2(d+	ADJ
ap-10600	201	15	1)⌉	1)⌉	NUM
ap-10600	201	16	−	−	NOUN
ap-10600	201	17	1	1	NUM
ap-10600	201	18	<	<	X
ap-10600	201	19	log2(d+	log2(d+	PROPN
ap-10600	201	20	1	1	NUM
ap-10600	201	21	)	)	PUNCT
ap-10600	201	22	.	.	PUNCT
ap-10600	202	1	therefore	therefore	ADV
ap-10600	202	2	we	we	PRON
ap-10600	202	3	have	have	VERB
ap-10600	202	4	d	d	X
ap-10600	202	5	<	<	X
ap-10600	202	6	2⌈log2	2⌈log2	NUM
ap-10600	202	7	d⌉	d⌉	NOUN
ap-10600	202	8	<	<	X
ap-10600	202	9	d	d	X
ap-10600	202	10	+	+	NOUN
ap-10600	202	11	1	1	NUM
ap-10600	202	12	.	.	PUNCT
ap-10600	203	1	the	the	DET
ap-10600	203	2	numbers	number	NOUN
ap-10600	203	3	d	d	NOUN
ap-10600	203	4	,	,	PUNCT
ap-10600	203	5	2⌈log2	2⌈log2	NUM
ap-10600	203	6	d⌉	d⌉	NUM
ap-10600	203	7	and	and	CCONJ
ap-10600	203	8	d+	d+	NOUN
ap-10600	203	9	1	1	NUM
ap-10600	203	10	are	be	AUX
ap-10600	203	11	integers	integer	NOUN
ap-10600	203	12	,	,	PUNCT
ap-10600	203	13	which	which	PRON
ap-10600	203	14	leads	lead	VERB
ap-10600	203	15	to	to	ADP
ap-10600	203	16	a	a	DET
ap-10600	203	17	contradiction	contradiction	NOUN
ap-10600	203	18	.	.	PUNCT
ap-10600	204	1	to	to	PART
ap-10600	204	2	show	show	VERB
ap-10600	204	3	item	item	NOUN
ap-10600	204	4	(	(	PUNCT
ap-10600	204	5	3	3	NUM
ap-10600	204	6	.	.	NUM
ap-10600	204	7	)	)	PUNCT
ap-10600	204	8	,	,	PUNCT
ap-10600	204	9	we	we	PRON
ap-10600	204	10	proceed	proceed	VERB
ap-10600	204	11	again	again	ADV
ap-10600	204	12	by	by	ADP
ap-10600	204	13	induction	induction	NOUN
ap-10600	204	14	on	on	ADP
ap-10600	204	15	d.	d.	PROPN
ap-10600	204	16	let	let	VERB
ap-10600	204	17	u	u	PRON
ap-10600	204	18	be	be	AUX
ap-10600	204	19	a	a	DET
ap-10600	204	20	fixed	fix	VERB
ap-10600	204	21	factor	factor	NOUN
ap-10600	204	22	of	of	ADP
ap-10600	204	23	length	length	NOUN
ap-10600	204	24	n	n	CCONJ
ap-10600	204	25	in	in	ADP
ap-10600	204	26	the	the	DET
ap-10600	204	27	1balanced	1balanced	NUM
ap-10600	204	28	sequence	sequence	NOUN
ap-10600	204	29	u.	u.	VERB
ap-10600	204	30	the	the	DET
ap-10600	204	31	frequencies	frequency	NOUN
ap-10600	204	32	of	of	ADP
ap-10600	204	33	letters	letter	NOUN
ap-10600	204	34	in	in	ADP
ap-10600	204	35	u	u	PROPN
ap-10600	204	36	are	be	AUX
ap-10600	204	37	α	α	PRON
ap-10600	204	38	and	and	CCONJ
ap-10600	204	39	(	(	PUNCT
ap-10600	204	40	1	1	NUM
ap-10600	204	41	−	−	PROPN
ap-10600	204	42	α	α	NOUN
ap-10600	204	43	)	)	PUNCT
ap-10600	204	44	.	.	PUNCT
ap-10600	205	1	by	by	ADP
ap-10600	205	2	lemma	lemma	PROPN
ap-10600	205	3	13	13	NUM
ap-10600	205	4	,	,	PUNCT
ap-10600	205	5	the	the	DET
ap-10600	205	6	factor	factor	NOUN
ap-10600	205	7	u	u	NOUN
ap-10600	205	8	either	either	CCONJ
ap-10600	205	9	contains	contain	VERB
ap-10600	205	10	⌈αn⌉	⌈αn⌉	NOUN
ap-10600	205	11	letters	letter	NOUN
ap-10600	205	12	a	a	PRON
ap-10600	205	13	and	and	CCONJ
ap-10600	205	14	⌊(1	⌊(1	NUM
ap-10600	205	15	−	−	PROPN
ap-10600	205	16	α)n⌋	α)n⌋	NOUN
ap-10600	205	17	letters	letter	NOUN
ap-10600	205	18	b	b	NOUN
ap-10600	205	19	,	,	PUNCT
ap-10600	205	20	or	or	CCONJ
ap-10600	205	21	u	u	NOUN
ap-10600	205	22	contains	contain	VERB
ap-10600	205	23	⌊αn⌋	⌊αn⌋	NOUN
ap-10600	205	24	letters	letter	NOUN
ap-10600	205	25	a	a	DET
ap-10600	205	26	and	and	CCONJ
ap-10600	205	27	⌈(1−α)n⌉	⌈(1−α)n⌉	PROPN
ap-10600	205	28	letters	letter	NOUN
ap-10600	205	29	b.	b.	NOUN
ap-10600	205	30	hence	hence	ADV
ap-10600	205	31	the	the	DET
ap-10600	205	32	factor	factor	NOUN
ap-10600	205	33	u	u	NOUN
ap-10600	205	34	equals	equal	VERB
ap-10600	205	35	the	the	DET
ap-10600	205	36	projection	projection	NOUN
ap-10600	205	37	π(v	π(v	NOUN
ap-10600	205	38	)	)	PUNCT
ap-10600	205	39	for	for	ADP
ap-10600	205	40	at	at	ADP
ap-10600	205	41	most	most	ADJ
ap-10600	205	42	ca(⌈αn⌉	ca(⌈αn⌉	ADJ
ap-10600	205	43	)	)	PUNCT
ap-10600	205	44	×	×	NOUN
ap-10600	205	45	cb(⌈(1	cb(⌈(1	NOUN
ap-10600	205	46	−α)n⌉	−α)n⌉	NOUN
ap-10600	205	47	)	)	PUNCT
ap-10600	205	48	factors	factor	NOUN
ap-10600	205	49	v	v	ADP
ap-10600	205	50	in	in	ADP
ap-10600	205	51	v.	v.	ADV
ap-10600	205	52	since	since	SCONJ
ap-10600	205	53	u	u	NOUN
ap-10600	205	54	has	have	VERB
ap-10600	205	55	at	at	ADP
ap-10600	205	56	most	most	ADJ
ap-10600	205	57	n+	n+	ADP
ap-10600	205	58	1	1	NUM
ap-10600	205	59	factors	factor	NOUN
ap-10600	205	60	of	of	ADP
ap-10600	205	61	length	length	NOUN
ap-10600	205	62	n	n	CCONJ
ap-10600	205	63	,	,	PUNCT
ap-10600	205	64	we	we	PRON
ap-10600	205	65	have	have	VERB
ap-10600	205	66	:	:	PUNCT
ap-10600	205	67	cv(n	cv(n	X
ap-10600	205	68	)	)	PUNCT
ap-10600	205	69	≤	≤	NOUN
ap-10600	205	70	(	(	PUNCT
ap-10600	205	71	n+	n+	NOUN
ap-10600	205	72	1	1	NUM
ap-10600	205	73	)	)	PUNCT
ap-10600	205	74	ca(⌈αn⌉	ca(⌈αn⌉	NOUN
ap-10600	205	75	)	)	PUNCT
ap-10600	205	76	cb(⌈(1	cb(⌈(1	NOUN
ap-10600	205	77	−	−	NOUN
ap-10600	205	78	α)n⌉	α)n⌉	ADJ
ap-10600	205	79	)	)	PUNCT
ap-10600	205	80	.	.	PUNCT
ap-10600	206	1	using	use	VERB
ap-10600	206	2	the	the	DET
ap-10600	206	3	induction	induction	NOUN
ap-10600	206	4	hypothesis	hypothesis	NOUN
ap-10600	206	5	and	and	CCONJ
ap-10600	206	6	simple	simple	ADJ
ap-10600	206	7	inequalities	inequality	NOUN
ap-10600	206	8	⌈αn⌉	⌈αn⌉	VERB
ap-10600	206	9	≤	≤	NUM
ap-10600	206	10	n	n	CCONJ
ap-10600	206	11	and	and	CCONJ
ap-10600	206	12	⌈(1	⌈(1	PROPN
ap-10600	206	13	−	−	PROPN
ap-10600	206	14	α)n⌉	α)n⌉	ADJ
ap-10600	206	15	≤	≤	NOUN
ap-10600	206	16	n	n	CCONJ
ap-10600	206	17	,	,	PUNCT
ap-10600	206	18	we	we	PRON
ap-10600	206	19	conclude	conclude	VERB
ap-10600	206	20	:	:	PUNCT
ap-10600	206	21	cv(n	cv(n	X
ap-10600	206	22	)	)	PUNCT
ap-10600	206	23	≤	≤	NOUN
ap-10600	206	24	(	(	PUNCT
ap-10600	206	25	n+	n+	NOUN
ap-10600	206	26	1	1	NUM
ap-10600	206	27	)	)	PUNCT
ap-10600	206	28	ca(n	ca(n	NOUN
ap-10600	206	29	)	)	PUNCT
ap-10600	206	30	cb(n	cb(n	SYM
ap-10600	206	31	)	)	PUNCT
ap-10600	206	32	≤	≤	NOUN
ap-10600	206	33	(	(	PUNCT
ap-10600	206	34	n+	n+	NOUN
ap-10600	206	35	1	1	NUM
ap-10600	206	36	)	)	PUNCT
ap-10600	206	37	(	(	PUNCT
ap-10600	206	38	n+	n+	NUM
ap-10600	206	39	1)⌈d2	1)⌈d2	NUM
ap-10600	206	40	⌉−1	⌉−1	PROPN
ap-10600	206	41	(	(	PUNCT
ap-10600	206	42	n+	n+	NUM
ap-10600	206	43	1)⌊d2	1)⌊d2	NUM
ap-10600	206	44	⌋−1	⌋−1	NOUN
ap-10600	206	45	=	=	SYM
ap-10600	206	46	(	(	PUNCT
ap-10600	206	47	n+	n+	NUM
ap-10600	206	48	1)d−1	1)d−1	NUM
ap-10600	206	49	.	.	NOUN
ap-10600	206	50	5	5	NUM
ap-10600	206	51	.	.	NOUN
ap-10600	206	52	comments	comment	NOUN
ap-10600	206	53	and	and	CCONJ
ap-10600	206	54	questions	question	NOUN
ap-10600	206	55	(	(	PUNCT
ap-10600	206	56	1	1	NUM
ap-10600	206	57	.	.	PUNCT
ap-10600	206	58	)	)	PUNCT
ap-10600	207	1	the	the	DET
ap-10600	207	2	bound	bound	ADJ
ap-10600	207	3	we	we	PRON
ap-10600	207	4	found	find	VERB
ap-10600	207	5	on	on	ADP
ap-10600	207	6	the	the	DET
ap-10600	207	7	factor	factor	NOUN
ap-10600	207	8	complexity	complexity	NOUN
ap-10600	207	9	of	of	ADP
ap-10600	207	10	the	the	DET
ap-10600	207	11	sequence	sequence	NOUN
ap-10600	207	12	v	v	NOUN
ap-10600	207	13	constructed	construct	VERB
ap-10600	207	14	in	in	ADP
ap-10600	207	15	the	the	DET
ap-10600	207	16	proof	proof	NOUN
ap-10600	207	17	of	of	ADP
ap-10600	207	18	theorem	theorem	ADJ
ap-10600	207	19	14	14	NUM
ap-10600	207	20	is	be	AUX
ap-10600	207	21	not	not	PART
ap-10600	207	22	optimal	optimal	ADJ
ap-10600	207	23	.	.	PUNCT
ap-10600	208	1	what	what	PRON
ap-10600	208	2	is	be	AUX
ap-10600	208	3	the	the	DET
ap-10600	208	4	optimal	optimal	ADJ
ap-10600	208	5	upper	upper	ADJ
ap-10600	208	6	bound	bind	VERB
ap-10600	208	7	?	?	PUNCT
ap-10600	209	1	(	(	PUNCT
ap-10600	209	2	2	2	NUM
ap-10600	209	3	.	.	PUNCT
ap-10600	209	4	)	)	PUNCT
ap-10600	210	1	a	a	DET
ap-10600	210	2	1	1	NUM
ap-10600	210	3	-	-	PUNCT
ap-10600	210	4	balanced	balance	VERB
ap-10600	210	5	binary	binary	ADJ
ap-10600	210	6	sequence	sequence	NOUN
ap-10600	210	7	u	u	NOUN
ap-10600	210	8	is	be	AUX
ap-10600	210	9	either	either	CCONJ
ap-10600	210	10	sturmian	sturmian	NOUN
ap-10600	210	11	or	or	CCONJ
ap-10600	210	12	periodic	periodic	NOUN
ap-10600	210	13	.	.	PUNCT
ap-10600	211	1	if	if	SCONJ
ap-10600	211	2	some	some	DET
ap-10600	211	3	ratio	ratio	NOUN
ap-10600	211	4	f(i	f(i	PROPN
ap-10600	211	5	)	)	PUNCT
ap-10600	211	6	:	:	PUNCT
ap-10600	212	1	f(j	f(j	NOUN
ap-10600	212	2	)	)	PUNCT
ap-10600	212	3	in	in	ADP
ap-10600	212	4	the	the	DET
ap-10600	212	5	assumptions	assumption	NOUN
ap-10600	212	6	of	of	ADP
ap-10600	212	7	theorem	theorem	NOUN
ap-10600	212	8	14	14	NUM
ap-10600	212	9	is	be	AUX
ap-10600	212	10	rational	rational	ADJ
ap-10600	212	11	,	,	PUNCT
ap-10600	212	12	we	we	PRON
ap-10600	212	13	can	can	AUX
ap-10600	212	14	reduce	reduce	VERB
ap-10600	212	15	the	the	DET
ap-10600	212	16	degree	degree	NOUN
ap-10600	212	17	of	of	ADP
ap-10600	212	18	the	the	DET
ap-10600	212	19	polynomial	polynomial	NOUN
ap-10600	212	20	in	in	ADP
ap-10600	212	21	the	the	DET
ap-10600	212	22	upper	upper	ADJ
ap-10600	212	23	bound	bind	VERB
ap-10600	212	24	(	(	PUNCT
ap-10600	212	25	n+	n+	NUM
ap-10600	212	26	1)d−1	1)d−1	NUM
ap-10600	212	27	at	at	ADP
ap-10600	212	28	least	least	ADJ
ap-10600	212	29	by	by	ADP
ap-10600	212	30	1	1	NUM
ap-10600	212	31	.	.	PUNCT
ap-10600	213	1	(	(	PUNCT
ap-10600	213	2	3	3	NUM
ap-10600	213	3	.	.	PUNCT
ap-10600	213	4	)	)	PUNCT
ap-10600	213	5	when	when	SCONJ
ap-10600	213	6	all	all	DET
ap-10600	213	7	frequencies	frequency	NOUN
ap-10600	213	8	f(i	f(i	NUM
ap-10600	213	9	)	)	PUNCT
ap-10600	213	10	in	in	ADP
ap-10600	213	11	the	the	DET
ap-10600	213	12	assumptions	assumption	NOUN
ap-10600	213	13	of	of	ADP
ap-10600	213	14	theorem	theorem	ADJ
ap-10600	213	15	14	14	NUM
ap-10600	213	16	are	be	AUX
ap-10600	213	17	rational	rational	ADJ
ap-10600	213	18	,	,	PUNCT
ap-10600	213	19	our	our	PRON
ap-10600	213	20	construction	construction	NOUN
ap-10600	213	21	gives	give	VERB
ap-10600	213	22	a	a	DET
ap-10600	213	23	periodic	periodic	ADJ
ap-10600	213	24	sequence	sequence	NOUN
ap-10600	213	25	v.	v.	ADP
ap-10600	213	26	how	how	SCONJ
ap-10600	213	27	to	to	PART
ap-10600	213	28	determine	determine	VERB
ap-10600	213	29	its	its	PRON
ap-10600	213	30	period	period	NOUN
ap-10600	213	31	?	?	PUNCT
ap-10600	214	1	(	(	PUNCT
ap-10600	214	2	4	4	NUM
ap-10600	214	3	.	.	PUNCT
ap-10600	214	4	)	)	PUNCT
ap-10600	214	5	given	give	VERB
ap-10600	214	6	rational	rational	ADJ
ap-10600	214	7	frequencies	frequency	NOUN
ap-10600	214	8	f(i	f(i	NUM
ap-10600	214	9	)	)	PUNCT
ap-10600	215	1	=	=	PUNCT
ap-10600	215	2	pi	pi	NOUN
ap-10600	215	3	qi	qi	PROPN
ap-10600	215	4	,	,	PUNCT
ap-10600	215	5	how	how	SCONJ
ap-10600	215	6	many	many	ADJ
ap-10600	215	7	steps	step	NOUN
ap-10600	215	8	are	be	AUX
ap-10600	215	9	needed	need	VERB
ap-10600	215	10	to	to	PART
ap-10600	215	11	construct	construct	VERB
ap-10600	215	12	a	a	DET
ap-10600	215	13	prefix	prefix	NOUN
ap-10600	215	14	of	of	ADP
ap-10600	215	15	v	v	NOUN
ap-10600	215	16	of	of	ADP
ap-10600	215	17	length	length	NOUN
ap-10600	215	18	n	n	CCONJ
ap-10600	215	19	?	?	PUNCT
ap-10600	216	1	(	(	PUNCT
ap-10600	216	2	5	5	NUM
ap-10600	216	3	.	.	PUNCT
ap-10600	216	4	)	)	PUNCT
ap-10600	217	1	a	a	DET
ap-10600	217	2	cubic	cubic	ADJ
ap-10600	217	3	billiard	billiard	NOUN
ap-10600	217	4	sequence	sequence	NOUN
ap-10600	217	5	in	in	ADP
ap-10600	217	6	dimension	dimension	NOUN
ap-10600	217	7	d	d	X
ap-10600	217	8	(	(	PUNCT
ap-10600	217	9	also	also	ADV
ap-10600	217	10	called	call	VERB
ap-10600	217	11	hypercubic	hypercubic	ADJ
ap-10600	217	12	billiard	billiard	NOUN
ap-10600	217	13	sequence	sequence	NOUN
ap-10600	217	14	)	)	PUNCT
ap-10600	217	15	is	be	AUX
ap-10600	217	16	a	a	DET
ap-10600	217	17	coding	coding	NOUN
ap-10600	217	18	of	of	ADP
ap-10600	217	19	the	the	DET
ap-10600	217	20	sequence	sequence	NOUN
ap-10600	217	21	of	of	ADP
ap-10600	217	22	the	the	DET
ap-10600	217	23	faces	face	NOUN
ap-10600	217	24	successively	successively	ADV
ap-10600	217	25	hit	hit	VERB
ap-10600	217	26	by	by	ADP
ap-10600	217	27	a	a	DET
ap-10600	217	28	billiard	billiard	NOUN
ap-10600	217	29	ball	ball	NOUN
ap-10600	217	30	moving	move	VERB
ap-10600	217	31	inside	inside	ADP
ap-10600	217	32	the	the	DET
ap-10600	217	33	unit	unit	NOUN
ap-10600	217	34	hypercube	hypercube	NOUN
ap-10600	217	35	[	[	X
ap-10600	217	36	0	0	NUM
ap-10600	217	37	,	,	PUNCT
ap-10600	217	38	1]d	1]d	NUM
ap-10600	217	39	,	,	PUNCT
ap-10600	217	40	where	where	SCONJ
ap-10600	217	41	two	two	NUM
ap-10600	217	42	parallel	parallel	ADJ
ap-10600	217	43	faces	face	NOUN
ap-10600	217	44	are	be	AUX
ap-10600	217	45	encoded	encode	VERB
ap-10600	217	46	by	by	ADP
ap-10600	217	47	the	the	DET
ap-10600	217	48	same	same	ADJ
ap-10600	217	49	letter	letter	NOUN
ap-10600	217	50	.	.	PUNCT
ap-10600	218	1	these	these	PRON
ap-10600	218	2	d	d	ADJ
ap-10600	218	3	-	-	PUNCT
ap-10600	218	4	ary	ary	PROPN
ap-10600	218	5	sequences	sequence	NOUN
ap-10600	218	6	are	be	AUX
ap-10600	218	7	parametrised	parametrise	VERB
ap-10600	218	8	by	by	ADP
ap-10600	218	9	the	the	DET
ap-10600	218	10	initial	initial	ADJ
ap-10600	218	11	position	position	NOUN
ap-10600	218	12	x	x	X
ap-10600	218	13	∈	∈	PROPN
ap-10600	219	1	[	[	X
ap-10600	219	2	0	0	NUM
ap-10600	219	3	,	,	PUNCT
ap-10600	219	4	1]d	1]d	NUM
ap-10600	219	5	and	and	CCONJ
ap-10600	219	6	the	the	DET
ap-10600	219	7	initial	initial	ADJ
ap-10600	219	8	momentum	momentum	NOUN
ap-10600	219	9	θ	θ	PROPN
ap-10600	219	10	∈	∈	PROPN
ap-10600	219	11	rd	rd	PROPN
ap-10600	219	12	\	\	PROPN
ap-10600	219	13	{	{	PUNCT
ap-10600	219	14	0	0	NUM
ap-10600	219	15	}	}	PUNCT
ap-10600	219	16	of	of	ADP
ap-10600	219	17	the	the	DET
ap-10600	219	18	ball	ball	NOUN
ap-10600	219	19	.	.	PUNCT
ap-10600	220	1	the	the	DET
ap-10600	220	2	vector	vector	NOUN
ap-10600	220	3	of	of	ADP
ap-10600	220	4	letter	letter	NOUN
ap-10600	220	5	frequencies	frequency	NOUN
ap-10600	220	6	corresponds	correspond	VERB
ap-10600	220	7	to	to	ADP
ap-10600	220	8	the	the	DET
ap-10600	220	9	vector	vector	NOUN
ap-10600	220	10	of	of	ADP
ap-10600	220	11	initial	initial	ADJ
ap-10600	220	12	momentum	momentum	NOUN
ap-10600	220	13	,	,	PUNCT
ap-10600	220	14	up	up	ADP
ap-10600	220	15	to	to	ADP
ap-10600	220	16	a	a	DET
ap-10600	220	17	dilatation	dilatation	NOUN
ap-10600	220	18	,	,	PUNCT
ap-10600	220	19	and	and	CCONJ
ap-10600	220	20	a	a	DET
ap-10600	220	21	change	change	NOUN
ap-10600	220	22	in	in	ADP
ap-10600	220	23	the	the	DET
ap-10600	220	24	signs	sign	NOUN
ap-10600	220	25	of	of	ADP
ap-10600	220	26	certain	certain	ADJ
ap-10600	220	27	components	component	NOUN
ap-10600	220	28	.	.	PUNCT
ap-10600	221	1	under	under	ADP
ap-10600	221	2	an	an	DET
ap-10600	221	3	additional	additional	ADJ
ap-10600	221	4	condition	condition	NOUN
ap-10600	221	5	on	on	ADP
ap-10600	221	6	momentum	momentum	NOUN
ap-10600	221	7	,	,	PUNCT
ap-10600	221	8	the	the	DET
ap-10600	221	9	factor	factor	NOUN
ap-10600	221	10	complexity	complexity	NOUN
ap-10600	221	11	of	of	ADP
ap-10600	221	12	cubic	cubic	ADJ
ap-10600	221	13	billiard	billiard	NOUN
ap-10600	221	14	sequences	sequence	NOUN
ap-10600	221	15	in	in	ADP
ap-10600	221	16	dimension	dimension	NOUN
ap-10600	221	17	d	d	NOUN
ap-10600	221	18	satisfies	satisfy	VERB
ap-10600	221	19	c(n	c(n	PROPN
ap-10600	221	20	)	)	PUNCT
ap-10600	222	1	=	=	SYM
ap-10600	222	2	nd−1(1	nd−1(1	X
ap-10600	222	3	+	+	PUNCT
ap-10600	222	4	o(1	o(1	NOUN
ap-10600	222	5	)	)	PUNCT
ap-10600	222	6	)	)	PUNCT
ap-10600	222	7	,	,	PUNCT
ap-10600	222	8	see	see	VERB
ap-10600	222	9	[	[	X
ap-10600	222	10	20	20	NUM
ap-10600	222	11	]	]	PUNCT
ap-10600	222	12	.	.	PUNCT
ap-10600	223	1	vuillon	vuillon	PROPN
ap-10600	224	1	[	[	X
ap-10600	224	2	21	21	NUM
ap-10600	224	3	]	]	PUNCT
ap-10600	224	4	proved	prove	VERB
ap-10600	224	5	that	that	SCONJ
ap-10600	224	6	any	any	DET
ap-10600	224	7	cubic	cubic	ADJ
ap-10600	224	8	billiard	billiard	NOUN
ap-10600	224	9	sequence	sequence	NOUN
ap-10600	224	10	in	in	ADP
ap-10600	224	11	dimension	dimension	NOUN
ap-10600	224	12	d	d	PROPN
ap-10600	224	13	,	,	PUNCT
ap-10600	224	14	whose	whose	DET
ap-10600	224	15	momentum	momentum	NOUN
ap-10600	224	16	has	have	VERB
ap-10600	224	17	rationally	rationally	ADV
ap-10600	224	18	independent	independent	ADJ
ap-10600	224	19	components	component	NOUN
ap-10600	224	20	,	,	PUNCT
ap-10600	224	21	is	be	AUX
ap-10600	224	22	d−	d−	PROPN
ap-10600	224	23	1	1	NUM
ap-10600	224	24	balanced	balanced	ADJ
ap-10600	224	25	.	.	PUNCT
ap-10600	225	1	andrieu	andrieu	PROPN
ap-10600	225	2	and	and	CCONJ
ap-10600	225	3	vivion	vivion	NOUN
ap-10600	225	4	[	[	X
ap-10600	225	5	9	9	NUM
ap-10600	225	6	]	]	PUNCT
ap-10600	225	7	further	far	ADV
ap-10600	225	8	specified	specify	VERB
ap-10600	225	9	that	that	SCONJ
ap-10600	225	10	:	:	PUNCT
ap-10600	225	11	•	•	NOUN
ap-10600	225	12	for	for	ADP
ap-10600	225	13	d	d	PROPN
ap-10600	225	14	∈	∈	PROPN
ap-10600	225	15	{	{	PUNCT
ap-10600	225	16	2	2	NUM
ap-10600	225	17	,	,	PUNCT
ap-10600	225	18	3	3	NUM
ap-10600	225	19	,	,	PUNCT
ap-10600	225	20	4	4	NUM
ap-10600	225	21	}	}	PUNCT
ap-10600	225	22	,	,	PUNCT
ap-10600	225	23	any	any	DET
ap-10600	225	24	cubic	cubic	ADJ
ap-10600	225	25	billiard	billiard	NOUN
ap-10600	225	26	sequence	sequence	NOUN
ap-10600	225	27	in	in	ADP
ap-10600	225	28	dimension	dimension	NOUN
ap-10600	225	29	d	d	ADP
ap-10600	225	30	generated	generate	VERB
ap-10600	225	31	by	by	ADP
ap-10600	225	32	a	a	DET
ap-10600	225	33	momentum	momentum	NOUN
ap-10600	225	34	with	with	ADP
ap-10600	225	35	rationally	rationally	ADV
ap-10600	225	36	independent	independent	ADJ
ap-10600	225	37	components	component	NOUN
ap-10600	225	38	is	be	AUX
ap-10600	225	39	not	not	PART
ap-10600	225	40	d	d	ADV
ap-10600	225	41	−	−	PROPN
ap-10600	225	42	2	2	NUM
ap-10600	225	43	balanced	balanced	ADJ
ap-10600	225	44	,	,	PUNCT
ap-10600	225	45	•	•	ADV
ap-10600	225	46	for	for	ADP
ap-10600	225	47	d	d	PROPN
ap-10600	225	48	≥	≥	NUM
ap-10600	225	49	5	5	NUM
ap-10600	225	50	,	,	PUNCT
ap-10600	225	51	for	for	ADP
ap-10600	225	52	every	every	DET
ap-10600	225	53	c	c	PROPN
ap-10600	225	54	∈	∈	PROPN
ap-10600	225	55	{	{	PUNCT
ap-10600	225	56	3	3	NUM
ap-10600	225	57	,	,	PUNCT
ap-10600	225	58	4	4	NUM
ap-10600	225	59	,	,	PUNCT
ap-10600	225	60	.	.	PUNCT
ap-10600	225	61	.	.	PUNCT
ap-10600	225	62	.	.	PUNCT
ap-10600	226	1	,	,	PUNCT
ap-10600	227	1	d	d	X
ap-10600	227	2	−	−	NOUN
ap-10600	228	1	1	1	NUM
ap-10600	228	2	}	}	PUNCT
ap-10600	228	3	,	,	PUNCT
ap-10600	228	4	there	there	PRON
ap-10600	228	5	exists	exist	VERB
ap-10600	228	6	a	a	DET
ap-10600	228	7	cubic	cubic	ADJ
ap-10600	228	8	billiard	billiard	NOUN
ap-10600	228	9	sequence	sequence	NOUN
ap-10600	228	10	in	in	ADP
ap-10600	228	11	dimension	dimension	NOUN
ap-10600	228	12	d	d	ADP
ap-10600	228	13	generated	generate	VERB
ap-10600	228	14	by	by	ADP
ap-10600	228	15	a	a	DET
ap-10600	228	16	momentum	momentum	NOUN
ap-10600	228	17	with	with	ADP
ap-10600	228	18	rationally	rationally	ADV
ap-10600	228	19	independent	independent	ADJ
ap-10600	228	20	components	component	NOUN
ap-10600	228	21	that	that	PRON
ap-10600	228	22	is	be	AUX
ap-10600	228	23	c	c	NOUN
ap-10600	228	24	-	-	PUNCT
ap-10600	228	25	balanced	balanced	ADJ
ap-10600	228	26	,	,	PUNCT
ap-10600	228	27	but	but	CCONJ
ap-10600	228	28	not	not	PART
ap-10600	228	29	(	(	PUNCT
ap-10600	228	30	c	c	X
ap-10600	228	31	−	−	PROPN
ap-10600	228	32	1)-balanced	1)-balanced	ADJ
ap-10600	228	33	.	.	PUNCT
ap-10600	229	1	we	we	PRON
ap-10600	229	2	can	can	AUX
ap-10600	229	3	conclude	conclude	VERB
ap-10600	229	4	that	that	PRON
ap-10600	229	5	for	for	ADP
ap-10600	229	6	certain	certain	ADJ
ap-10600	229	7	frequency	frequency	NOUN
ap-10600	229	8	vectors	vector	NOUN
ap-10600	229	9	f⃗	f⃗	VERB
ap-10600	229	10	∈	∈	PROPN
ap-10600	229	11	rd	rd	PROPN
ap-10600	229	12	,	,	PUNCT
ap-10600	229	13	the	the	DET
ap-10600	229	14	corresponding	corresponding	ADJ
ap-10600	229	15	cubic	cubic	ADJ
ap-10600	229	16	billiard	billiard	NOUN
ap-10600	229	17	sequence	sequence	NOUN
ap-10600	229	18	in	in	ADP
ap-10600	229	19	dimension	dimension	NOUN
ap-10600	229	20	d	d	X
ap-10600	229	21	is	be	AUX
ap-10600	229	22	(	(	PUNCT
ap-10600	229	23	d−	d−	PROPN
ap-10600	229	24	1)-balanced	1)-balanced	PROPN
ap-10600	229	25	but	but	CCONJ
ap-10600	229	26	not	not	PART
ap-10600	229	27	(	(	PUNCT
ap-10600	229	28	d−	d−	PROPN
ap-10600	229	29	2)-balanced	2)-balanced	NUM
ap-10600	229	30	,	,	PUNCT
ap-10600	229	31	while	while	SCONJ
ap-10600	229	32	for	for	ADP
ap-10600	229	33	the	the	DET
ap-10600	229	34	same	same	ADJ
ap-10600	229	35	f⃗	f⃗	NOUN
ap-10600	229	36	,	,	PUNCT
ap-10600	229	37	the	the	DET
ap-10600	229	38	colouring	colouring	NOUN
ap-10600	229	39	procedure	procedure	NOUN
ap-10600	229	40	we	we	PRON
ap-10600	229	41	use	use	VERB
ap-10600	229	42	in	in	ADP
ap-10600	229	43	the	the	DET
ap-10600	229	44	proof	proof	NOUN
ap-10600	229	45	of	of	ADP
ap-10600	229	46	theorem	theorem	ADJ
ap-10600	229	47	14	14	NUM
ap-10600	229	48	537	537	NUM
ap-10600	229	49	l’ubomíra	l’ubomíra	PROPN
ap-10600	229	50	dvořáková	dvořáková	PROPN
ap-10600	229	51	,	,	PUNCT
ap-10600	229	52	edita	edita	PROPN
ap-10600	229	53	pelantová	pelantová	PROPN
ap-10600	229	54	acta	acta	PROPN
ap-10600	229	55	polytechnica	polytechnica	PROPN
ap-10600	229	56	provides	provide	VERB
ap-10600	229	57	a	a	DET
ap-10600	229	58	sequence	sequence	NOUN
ap-10600	229	59	which	which	PRON
ap-10600	229	60	is	be	AUX
ap-10600	229	61	⌈log2	⌈log2	PRON
ap-10600	229	62	d⌉-balanced	d⌉-balance	VERB
ap-10600	229	63	.	.	PUNCT
ap-10600	230	1	in	in	ADP
ap-10600	230	2	other	other	ADJ
ap-10600	230	3	words	word	NOUN
ap-10600	230	4	,	,	PUNCT
ap-10600	230	5	in	in	ADP
ap-10600	230	6	the	the	DET
ap-10600	230	7	case	case	NOUN
ap-10600	230	8	of	of	ADP
ap-10600	230	9	d	d	PROPN
ap-10600	230	10	>	>	X
ap-10600	230	11	3	3	NUM
ap-10600	230	12	,	,	PUNCT
ap-10600	230	13	we	we	PRON
ap-10600	230	14	construct	construct	VERB
ap-10600	230	15	a	a	DET
ap-10600	230	16	sequence	sequence	NOUN
ap-10600	230	17	which	which	PRON
ap-10600	230	18	is	be	AUX
ap-10600	230	19	less	less	ADV
ap-10600	230	20	imbalanced	imbalanced	ADJ
ap-10600	230	21	.	.	PUNCT
ap-10600	231	1	acknowledgements	acknowledgement	NOUN
ap-10600	231	2	both	both	DET
ap-10600	231	3	authors	author	NOUN
ap-10600	231	4	are	be	AUX
ap-10600	231	5	aware	aware	ADJ
ap-10600	231	6	of	of	ADP
ap-10600	231	7	how	how	SCONJ
ap-10600	231	8	significantly	significantly	ADV
ap-10600	231	9	prof	prof	PROPN
ap-10600	231	10	.	.	PUNCT
ap-10600	232	1	havlíček	havlíček	PROPN
ap-10600	232	2	influenced	influence	VERB
ap-10600	232	3	their	their	PRON
ap-10600	232	4	scientific	scientific	ADJ
ap-10600	232	5	careers	career	NOUN
ap-10600	232	6	.	.	PUNCT
ap-10600	233	1	as	as	ADP
ap-10600	233	2	a	a	DET
ap-10600	233	3	teacher	teacher	NOUN
ap-10600	233	4	,	,	PUNCT
ap-10600	233	5	as	as	ADP
ap-10600	233	6	a	a	DET
ap-10600	233	7	coauthor	coauthor	NOUN
ap-10600	233	8	,	,	PUNCT
ap-10600	233	9	and	and	CCONJ
ap-10600	233	10	most	most	ADV
ap-10600	233	11	importantly	importantly	ADV
ap-10600	233	12	,	,	PUNCT
ap-10600	233	13	as	as	ADP
ap-10600	233	14	a	a	DET
ap-10600	233	15	person	person	NOUN
ap-10600	233	16	who	who	PRON
ap-10600	233	17	,	,	PUNCT
ap-10600	233	18	in	in	ADP
ap-10600	233	19	his	his	PRON
ap-10600	233	20	role	role	NOUN
ap-10600	233	21	as	as	ADP
ap-10600	233	22	dean	dean	NOUN
ap-10600	233	23	of	of	ADP
ap-10600	233	24	the	the	DET
ap-10600	233	25	faculty	faculty	NOUN
ap-10600	233	26	and	and	CCONJ
ap-10600	233	27	head	head	NOUN
ap-10600	233	28	of	of	ADP
ap-10600	233	29	the	the	DET
ap-10600	233	30	department	department	NOUN
ap-10600	233	31	of	of	ADP
ap-10600	233	32	mathematics	mathematic	NOUN
ap-10600	233	33	,	,	PUNCT
ap-10600	233	34	encouraged	encourage	VERB
ap-10600	233	35	his	his	PRON
ap-10600	233	36	colleagues	colleague	NOUN
ap-10600	233	37	to	to	PART
ap-10600	233	38	pursue	pursue	VERB
ap-10600	233	39	scientific	scientific	ADJ
ap-10600	233	40	endeavours	endeavour	NOUN
ap-10600	233	41	.	.	PUNCT
ap-10600	234	1	references	reference	NOUN
ap-10600	234	2	[	[	X
ap-10600	234	3	1	1	NUM
ap-10600	234	4	]	]	PUNCT
ap-10600	234	5	m.	m.	NOUN
ap-10600	234	6	morse	morse	PROPN
ap-10600	234	7	,	,	PUNCT
ap-10600	235	1	g.	g.	PROPN
ap-10600	235	2	a.	a.	PROPN
ap-10600	235	3	hedlund	hedlund	PROPN
ap-10600	235	4	.	.	PUNCT
ap-10600	236	1	symbolic	symbolic	PROPN
ap-10600	236	2	dynamics	dynamics	PROPN
ap-10600	236	3	ii	ii	PROPN
ap-10600	236	4	.	.	PUNCT
ap-10600	237	1	sturmian	sturmian	PROPN
ap-10600	237	2	trajectories	trajectory	NOUN
ap-10600	237	3	.	.	PUNCT
ap-10600	238	1	american	american	ADJ
ap-10600	238	2	journal	journal	PROPN
ap-10600	238	3	of	of	ADP
ap-10600	238	4	mathematics	mathematics	PROPN
ap-10600	238	5	62(1):1–42	62(1):1–42	NUM
ap-10600	238	6	,	,	PUNCT
ap-10600	238	7	1940	1940	NUM
ap-10600	238	8	.	.	PUNCT
ap-10600	239	1	https://doi.org/10.2307/2371431	https://doi.org/10.2307/2371431	X
ap-10600	240	1	[	[	X
ap-10600	240	2	2	2	NUM
ap-10600	240	3	]	]	X
ap-10600	240	4	l	l	NOUN
ap-10600	240	5	’	'	PUNCT
ap-10600	240	6	.	.	PUNCT
ap-10600	241	1	balková	balková	PROPN
ap-10600	241	2	,	,	PUNCT
ap-10600	241	3	e.	e.	PROPN
ap-10600	241	4	pelantová	pelantová	PROPN
ap-10600	241	5	,	,	PUNCT
ap-10600	241	6	š	š	PROPN
ap-10600	241	7	.	.	PUNCT
ap-10600	241	8	starosta	starosta	PROPN
ap-10600	241	9	.	.	PUNCT
ap-10600	242	1	sturmian	sturmian	PROPN
ap-10600	242	2	jungle	jungle	NOUN
ap-10600	242	3	(	(	PUNCT
ap-10600	242	4	or	or	CCONJ
ap-10600	242	5	garden	garden	NOUN
ap-10600	242	6	?	?	PUNCT
ap-10600	242	7	)	)	PUNCT
ap-10600	242	8	on	on	ADP
ap-10600	242	9	multiliteral	multiliteral	ADJ
ap-10600	242	10	alphabets	alphabet	NOUN
ap-10600	242	11	.	.	PUNCT
ap-10600	243	1	rairo	rairo	PROPN
ap-10600	243	2	–	–	PUNCT
ap-10600	243	3	theoretical	theoretical	ADJ
ap-10600	243	4	informatics	informatic	NOUN
ap-10600	243	5	and	and	CCONJ
ap-10600	243	6	applications	application	NOUN
ap-10600	243	7	44(4):443–470	44(4):443–470	PROPN
ap-10600	243	8	,	,	PUNCT
ap-10600	243	9	2010	2010	NUM
ap-10600	243	10	.	.	PUNCT
ap-10600	244	1	https://doi.org/10.1051/ita/2011002	https://doi.org/10.1051/ita/2011002	NOUN
ap-10600	245	1	[	[	X
ap-10600	245	2	3	3	X
ap-10600	245	3	]	]	X
ap-10600	245	4	g.	g.	NOUN
ap-10600	245	5	richomme	richomme	PROPN
ap-10600	245	6	,	,	PUNCT
ap-10600	245	7	k.	k.	PROPN
ap-10600	245	8	saari	saari	PROPN
ap-10600	245	9	,	,	PUNCT
ap-10600	245	10	l.	l.	PROPN
ap-10600	245	11	q.	q.	PROPN
ap-10600	245	12	zamboni	zamboni	PROPN
ap-10600	245	13	.	.	PUNCT
ap-10600	246	1	abelian	abelian	PROPN
ap-10600	246	2	complexity	complexity	NOUN
ap-10600	246	3	of	of	ADP
ap-10600	246	4	minimal	minimal	ADJ
ap-10600	246	5	subshifts	subshift	NOUN
ap-10600	246	6	.	.	PUNCT
ap-10600	247	1	journal	journal	NOUN
ap-10600	247	2	of	of	ADP
ap-10600	247	3	the	the	DET
ap-10600	247	4	london	london	PROPN
ap-10600	247	5	mathematical	mathematical	ADJ
ap-10600	247	6	society	society	NOUN
ap-10600	247	7	83(1):79–95	83(1):79–95	NUM
ap-10600	247	8	,	,	PUNCT
ap-10600	247	9	2011	2011	NUM
ap-10600	247	10	.	.	PUNCT
ap-10600	248	1	https://doi.org/10.1112/jlms/jdq063	https://doi.org/10.1112/jlms/jdq063	ADJ
ap-10600	248	2	[	[	X
ap-10600	248	3	4	4	X
ap-10600	248	4	]	]	X
ap-10600	248	5	l.	l.	PROPN
ap-10600	248	6	vuillon	vuillon	PROPN
ap-10600	248	7	.	.	PUNCT
ap-10600	249	1	a	a	DET
ap-10600	249	2	characterization	characterization	NOUN
ap-10600	249	3	of	of	ADP
ap-10600	249	4	sturmian	sturmian	ADJ
ap-10600	249	5	words	word	NOUN
ap-10600	249	6	by	by	ADP
ap-10600	249	7	return	return	NOUN
ap-10600	249	8	words	word	NOUN
ap-10600	249	9	.	.	PUNCT
ap-10600	250	1	european	european	ADJ
ap-10600	250	2	journal	journal	PROPN
ap-10600	250	3	of	of	ADP
ap-10600	250	4	combinatorics	combinatoric	NOUN
ap-10600	250	5	22(2):263–275	22(2):263–275	NUM
ap-10600	250	6	,	,	PUNCT
ap-10600	250	7	2001	2001	NUM
ap-10600	250	8	.	.	PUNCT
ap-10600	251	1	https://doi.org/10.1006/eujc.2000.0444	https://doi.org/10.1006/eujc.2000.0444	PROPN
ap-10600	251	2	[	[	X
ap-10600	251	3	5	5	NUM
ap-10600	251	4	]	]	PUNCT
ap-10600	251	5	p.	p.	NOUN
ap-10600	251	6	arnoux	arnoux	NOUN
ap-10600	251	7	,	,	PUNCT
ap-10600	251	8	š	š	PROPN
ap-10600	251	9	.	.	PUNCT
ap-10600	251	10	starosta	starosta	PROPN
ap-10600	251	11	.	.	PUNCT
ap-10600	252	1	the	the	DET
ap-10600	252	2	rauzy	rauzy	NOUN
ap-10600	252	3	gasket	gasket	NOUN
ap-10600	252	4	.	.	PUNCT
ap-10600	253	1	in	in	ADP
ap-10600	253	2	b.	b.	PROPN
ap-10600	253	3	boston	boston	PROPN
ap-10600	253	4	(	(	PUNCT
ap-10600	253	5	ed	ed	NOUN
ap-10600	253	6	.	.	PUNCT
ap-10600	253	7	)	)	PUNCT
ap-10600	253	8	,	,	PUNCT
ap-10600	253	9	further	further	ADJ
ap-10600	253	10	developments	development	NOUN
ap-10600	253	11	in	in	ADP
ap-10600	253	12	fractals	fractal	NOUN
ap-10600	253	13	and	and	CCONJ
ap-10600	253	14	related	relate	VERB
ap-10600	253	15	fields	field	NOUN
ap-10600	253	16	,	,	PUNCT
ap-10600	253	17	trends	trend	NOUN
ap-10600	253	18	in	in	ADP
ap-10600	253	19	mathematics	mathematic	NOUN
ap-10600	253	20	,	,	PUNCT
ap-10600	253	21	pp	pp	ADP
ap-10600	253	22	.	.	PUNCT
ap-10600	254	1	1–23	1–23	PROPN
ap-10600	254	2	.	.	PUNCT
ap-10600	255	1	birkhäuser	birkhäuser	PROPN
ap-10600	255	2	,	,	PUNCT
ap-10600	255	3	boston	boston	PROPN
ap-10600	255	4	,	,	PUNCT
ap-10600	255	5	2013	2013	NUM
ap-10600	255	6	.	.	PUNCT
ap-10600	256	1	https://doi.org/10.1007/978-0-8176-8400-6_1	https://doi.org/10.1007/978-0-8176-8400-6_1	NOUN
ap-10600	257	1	[	[	X
ap-10600	257	2	6	6	NUM
ap-10600	257	3	]	]	PUNCT
ap-10600	257	4	a.	a.	NOUN
ap-10600	257	5	zorich	zorich	PROPN
ap-10600	257	6	.	.	PUNCT
ap-10600	258	1	deviation	deviation	NOUN
ap-10600	258	2	for	for	ADP
ap-10600	258	3	interval	interval	NOUN
ap-10600	258	4	exchange	exchange	NOUN
ap-10600	258	5	transformations	transformation	NOUN
ap-10600	258	6	.	.	PUNCT
ap-10600	259	1	ergodic	ergodic	ADJ
ap-10600	259	2	theory	theory	NOUN
ap-10600	259	3	and	and	CCONJ
ap-10600	259	4	dynamical	dynamical	ADJ
ap-10600	259	5	systems	system	NOUN
ap-10600	259	6	17(6):1477–1499	17(6):1477–1499	NUM
ap-10600	259	7	,	,	PUNCT
ap-10600	259	8	1997	1997	NUM
ap-10600	259	9	.	.	PUNCT
ap-10600	260	1	https://doi.org/10.1017/s0143385797086215	https://doi.org/10.1017/s0143385797086215	NUM
ap-10600	261	1	[	[	X
ap-10600	261	2	7	7	X
ap-10600	261	3	]	]	X
ap-10600	261	4	p.	p.	PROPN
ap-10600	261	5	hubert	hubert	PROPN
ap-10600	261	6	.	.	PUNCT
ap-10600	262	1	suites	suit	VERB
ap-10600	262	2	équilibrées	équilibrées	PROPN
ap-10600	262	3	.	.	PUNCT
ap-10600	263	1	theoretical	theoretical	ADJ
ap-10600	263	2	computer	computer	NOUN
ap-10600	263	3	science	science	NOUN
ap-10600	263	4	242(1–2):91–108	242(1–2):91–108	NUM
ap-10600	263	5	,	,	PUNCT
ap-10600	263	6	2000	2000	NUM
ap-10600	263	7	.	.	PUNCT
ap-10600	264	1	https://doi.org/10.1016/s0304-3975(98)00202-3	https://doi.org/10.1016/s0304-3975(98)00202-3	VERB
ap-10600	265	1	[	[	X
ap-10600	265	2	8	8	NUM
ap-10600	265	3	]	]	X
ap-10600	265	4	l.	l.	PROPN
ap-10600	265	5	dvořáková	dvořáková	PROPN
ap-10600	265	6	,	,	PUNCT
ap-10600	265	7	z.	z.	PROPN
ap-10600	265	8	masáková	masáková	PROPN
ap-10600	265	9	,	,	PUNCT
ap-10600	265	10	e.	e.	PROPN
ap-10600	265	11	pelantová	pelantová	PROPN
ap-10600	265	12	.	.	PUNCT
ap-10600	266	1	2	2	NUM
ap-10600	266	2	-	-	PUNCT
ap-10600	266	3	balanced	balanced	ADJ
ap-10600	266	4	sequences	sequence	NOUN
ap-10600	266	5	coding	code	VERB
ap-10600	266	6	rectangle	rectangle	NOUN
ap-10600	266	7	exchange	exchange	NOUN
ap-10600	266	8	transformation	transformation	NOUN
ap-10600	266	9	.	.	PUNCT
ap-10600	267	1	theoretical	theoretical	ADJ
ap-10600	267	2	computer	computer	NOUN
ap-10600	267	3	science	science	NOUN
ap-10600	267	4	68(6):1537–1555	68(6):1537–1555	NUM
ap-10600	267	5	,	,	PUNCT
ap-10600	267	6	2024	2024	NUM
ap-10600	267	7	.	.	PUNCT
ap-10600	268	1	https://doi.org/10.1007/s00224-024-10188-6	https://doi.org/10.1007/s00224-024-10188-6	NUM
ap-10600	269	1	[	[	X
ap-10600	269	2	9	9	NUM
ap-10600	269	3	]	]	PUNCT
ap-10600	269	4	m.	m.	NOUN
ap-10600	269	5	andrieu	andrieu	PROPN
ap-10600	269	6	,	,	PUNCT
ap-10600	269	7	l.	l.	PROPN
ap-10600	269	8	vivion	vivion	PROPN
ap-10600	269	9	.	.	PUNCT
ap-10600	270	1	imbalances	imbalance	NOUN
ap-10600	270	2	in	in	ADP
ap-10600	270	3	hypercubic	hypercubic	ADJ
ap-10600	270	4	billiard	billiard	NOUN
ap-10600	270	5	words	word	NOUN
ap-10600	270	6	.	.	PUNCT
ap-10600	271	1	in	in	ADP
ap-10600	271	2	18th	18th	ADJ
ap-10600	271	3	mons	mon	NOUN
ap-10600	271	4	theoretical	theoretical	ADJ
ap-10600	271	5	computer	computer	NOUN
ap-10600	271	6	science	science	NOUN
ap-10600	271	7	days	day	NOUN
ap-10600	271	8	.	.	PUNCT
ap-10600	272	1	prague	prague	PROPN
ap-10600	272	2	,	,	PUNCT
ap-10600	272	3	2022	2022	NUM
ap-10600	272	4	.	.	PUNCT
ap-10600	273	1	[	[	X
ap-10600	273	2	10	10	NUM
ap-10600	273	3	]	]	X
ap-10600	273	4	p.	p.	NOUN
ap-10600	273	5	arnoux	arnoux	NOUN
ap-10600	273	6	,	,	PUNCT
ap-10600	273	7	c.	c.	PROPN
ap-10600	273	8	mauduit	mauduit	PROPN
ap-10600	273	9	,	,	PUNCT
ap-10600	273	10	i.	i.	PROPN
ap-10600	273	11	shiokawa	shiokawa	PROPN
ap-10600	273	12	,	,	PUNCT
ap-10600	273	13	j.-i	j.-i	PROPN
ap-10600	273	14	.	.	PUNCT
ap-10600	274	1	tamura	tamura	PROPN
ap-10600	274	2	.	.	PROPN
ap-10600	274	3	complexity	complexity	NOUN
ap-10600	274	4	of	of	ADP
ap-10600	274	5	sequences	sequence	NOUN
ap-10600	274	6	defined	define	VERB
ap-10600	274	7	by	by	ADP
ap-10600	274	8	billiard	billiard	NOUN
ap-10600	274	9	in	in	ADP
ap-10600	274	10	the	the	DET
ap-10600	274	11	cube	cube	NOUN
ap-10600	274	12	.	.	PUNCT
ap-10600	275	1	bulletin	bulletin	PROPN
ap-10600	275	2	de	de	PROPN
ap-10600	275	3	la	la	PROPN
ap-10600	275	4	société	société	PROPN
ap-10600	275	5	mathématique	mathématique	PROPN
ap-10600	275	6	de	de	PROPN
ap-10600	275	7	france	france	PROPN
ap-10600	275	8	122(1):1	122(1):1	PROPN
ap-10600	275	9	–	–	PUNCT
ap-10600	275	10	12	12	NUM
ap-10600	275	11	,	,	PUNCT
ap-10600	275	12	1994	1994	NUM
ap-10600	275	13	.	.	PUNCT
ap-10600	276	1	https://doi.org/10.24033/bsmf.2220	https://doi.org/10.24033/bsmf.2220	X
ap-10600	276	2	[	[	X
ap-10600	276	3	11	11	NUM
ap-10600	276	4	]	]	PUNCT
ap-10600	276	5	p.	p.	NOUN
ap-10600	276	6	arnoux	arnoux	NOUN
ap-10600	276	7	,	,	PUNCT
ap-10600	276	8	c.	c.	PROPN
ap-10600	276	9	mauduit	mauduit	PROPN
ap-10600	276	10	,	,	PUNCT
ap-10600	276	11	i.	i.	PROPN
ap-10600	276	12	shiokawa	shiokawa	PROPN
ap-10600	276	13	,	,	PUNCT
ap-10600	276	14	j.-i	j.-i	PROPN
ap-10600	276	15	.	.	PUNCT
ap-10600	277	1	tamura	tamura	PROPN
ap-10600	277	2	.	.	PROPN
ap-10600	277	3	rauzy	rauzy	PROPN
ap-10600	277	4	’s	’s	PART
ap-10600	277	5	conjecture	conjecture	NOUN
ap-10600	277	6	on	on	ADP
ap-10600	277	7	billiards	billiard	NOUN
ap-10600	277	8	in	in	ADP
ap-10600	277	9	the	the	DET
ap-10600	277	10	cube	cube	NOUN
ap-10600	277	11	.	.	PUNCT
ap-10600	278	1	tokyo	tokyo	PROPN
ap-10600	278	2	journal	journal	NOUN
ap-10600	278	3	of	of	ADP
ap-10600	278	4	mathematics	mathematics	PROPN
ap-10600	278	5	17(1):211–218	17(1):211–218	PROPN
ap-10600	278	6	,	,	PUNCT
ap-10600	278	7	1994	1994	NUM
ap-10600	278	8	.	.	PUNCT
ap-10600	279	1	https://doi.org/10.3836/tjm/1270128200	https://doi.org/10.3836/tjm/1270128200	PROPN
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ap-10600	280	2	12	12	NUM
ap-10600	280	3	]	]	X
ap-10600	280	4	n.	n.	NOUN
ap-10600	280	5	bedaride	bedaride	ADJ
ap-10600	280	6	,	,	PUNCT
ap-10600	280	7	p.	p.	PROPN
ap-10600	280	8	hubert	hubert	PROPN
ap-10600	280	9	.	.	PUNCT
ap-10600	281	1	billiard	billiard	PROPN
ap-10600	281	2	complexity	complexity	NOUN
ap-10600	281	3	in	in	ADP
ap-10600	281	4	the	the	DET
ap-10600	281	5	hypercube	hypercube	NOUN
ap-10600	281	6	.	.	PUNCT
ap-10600	282	1	annales	annales	PROPN
ap-10600	282	2	de	de	ADP
ap-10600	282	3	l’institut	l’institut	PROPN
ap-10600	282	4	fourier	fourier	NOUN
ap-10600	282	5	57(3):719–738	57(3):719–738	NUM
ap-10600	282	6	,	,	PUNCT
ap-10600	282	7	2007	2007	NUM
ap-10600	282	8	.	.	PUNCT
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ap-10600	283	3	13	13	NUM
ap-10600	283	4	]	]	PUNCT
ap-10600	283	5	m.	m.	NOUN
ap-10600	283	6	queffélec	queffélec	PROPN
ap-10600	283	7	.	.	PUNCT
ap-10600	284	1	substitution	substitution	NOUN
ap-10600	284	2	dynamical	dynamical	ADJ
ap-10600	284	3	systems	system	NOUN
ap-10600	284	4	–	–	PUNCT
ap-10600	284	5	spectral	spectral	ADJ
ap-10600	284	6	analysis	analysis	NOUN
ap-10600	284	7	.	.	PUNCT
ap-10600	285	1	lecture	lecture	NOUN
ap-10600	285	2	notes	note	NOUN
ap-10600	285	3	in	in	ADP
ap-10600	285	4	mathematics	mathematic	NOUN
ap-10600	285	5	.	.	PUNCT
ap-10600	286	1	springer	springer	NOUN
ap-10600	286	2	-	-	PUNCT
ap-10600	286	3	verlag	verlag	PROPN
ap-10600	286	4	,	,	PUNCT
ap-10600	286	5	heidelberg	heidelberg	PROPN
ap-10600	286	6	,	,	PUNCT
ap-10600	286	7	2nd	2nd	ADJ
ap-10600	286	8	edn	edn	PROPN
ap-10600	286	9	.	.	PUNCT
ap-10600	286	10	,	,	PUNCT
ap-10600	286	11	2010	2010	NUM
ap-10600	286	12	.	.	PUNCT
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ap-10600	287	3	14	14	NUM
ap-10600	287	4	]	]	X
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ap-10600	287	6	berthé	berthé	ADJ
ap-10600	287	7	,	,	PUNCT
ap-10600	287	8	v.	v.	ADP
ap-10600	287	9	delecroix	delecroix	NOUN
ap-10600	287	10	.	.	PUNCT
ap-10600	288	1	beyond	beyond	ADP
ap-10600	288	2	substitutive	substitutive	ADJ
ap-10600	288	3	dynamical	dynamical	ADJ
ap-10600	288	4	systems	system	NOUN
ap-10600	288	5	:	:	PUNCT
ap-10600	288	6	s	s	X
ap-10600	288	7	-	-	PUNCT
ap-10600	288	8	adic	adic	ADJ
ap-10600	288	9	expansions	expansion	NOUN
ap-10600	288	10	.	.	PUNCT
ap-10600	289	1	rims	rims	PROPN
ap-10600	289	2	kôkyûroku	kôkyûroku	PROPN
ap-10600	289	3	bessatsu	bessatsu	PROPN
ap-10600	289	4	b46:81–123	b46:81–123	NOUN
ap-10600	289	5	,	,	PUNCT
ap-10600	289	6	2014	2014	NUM
ap-10600	289	7	.	.	PUNCT
ap-10600	290	1	[	[	X
ap-10600	290	2	15	15	NUM
ap-10600	290	3	]	]	X
ap-10600	290	4	b.	b.	PROPN
ap-10600	290	5	adamczewski	adamczewski	PROPN
ap-10600	290	6	.	.	PUNCT
ap-10600	291	1	balances	balance	NOUN
ap-10600	291	2	for	for	ADP
ap-10600	291	3	fixed	fix	VERB
ap-10600	291	4	points	point	NOUN
ap-10600	291	5	of	of	ADP
ap-10600	291	6	primitive	primitive	ADJ
ap-10600	291	7	substitutions	substitution	NOUN
ap-10600	291	8	.	.	PUNCT
ap-10600	292	1	theoretical	theoretical	ADJ
ap-10600	292	2	computer	computer	NOUN
ap-10600	292	3	science	science	NOUN
ap-10600	292	4	307(1):47–75	307(1):47–75	NUM
ap-10600	292	5	,	,	PUNCT
ap-10600	292	6	2003	2003	NUM
ap-10600	292	7	.	.	PUNCT
ap-10600	293	1	https://doi.org/10.1016/s0304-3975(03)00092-6	https://doi.org/10.1016/s0304-3975(03)00092-6	PROPN
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ap-10600	294	2	16	16	NUM
ap-10600	294	3	]	]	PUNCT
ap-10600	294	4	j.	j.	PROPN
ap-10600	294	5	cassaigne	cassaigne	PROPN
ap-10600	294	6	.	.	PUNCT
ap-10600	295	1	un	un	PROPN
ap-10600	295	2	algorithme	algorithme	PROPN
ap-10600	295	3	de	de	PROPN
ap-10600	295	4	fractions	fraction	NOUN
ap-10600	295	5	continues	continue	VERB
ap-10600	295	6	de	de	X
ap-10600	295	7	complexité	complexité	NOUN
ap-10600	295	8	linéaire	linéaire	NOUN
ap-10600	295	9	,	,	PUNCT
ap-10600	295	10	2015	2015	NUM
ap-10600	295	11	.	.	PUNCT
ap-10600	296	1	dyna3s	dyna3s	ADJ
ap-10600	296	2	meeting	meeting	NOUN
ap-10600	296	3	,	,	PUNCT
ap-10600	296	4	liafa	liafa	PROPN
ap-10600	296	5	,	,	PUNCT
ap-10600	296	6	paris	paris	PROPN
ap-10600	296	7	.	.	PUNCT
ap-10600	297	1	[	[	X
ap-10600	297	2	17	17	NUM
ap-10600	297	3	]	]	PUNCT
ap-10600	297	4	j.	j.	PROPN
ap-10600	297	5	cassaigne	cassaigne	PROPN
ap-10600	297	6	,	,	PUNCT
ap-10600	297	7	s.	s.	PROPN
ap-10600	297	8	labbé	labbé	PROPN
ap-10600	297	9	,	,	PUNCT
ap-10600	297	10	j.	j.	PROPN
ap-10600	297	11	leroy	leroy	PROPN
ap-10600	297	12	.	.	PUNCT
ap-10600	298	1	almost	almost	ADV
ap-10600	298	2	everywhere	everywhere	ADV
ap-10600	298	3	balanced	balanced	ADJ
ap-10600	298	4	sequences	sequence	NOUN
ap-10600	298	5	of	of	ADP
ap-10600	298	6	complexity	complexity	NOUN
ap-10600	298	7	2n	2n	NUM
ap-10600	298	8	+	+	CCONJ
ap-10600	298	9	1	1	X
ap-10600	298	10	.	.	PUNCT
ap-10600	298	11	combinatorics	combinatoric	NOUN
ap-10600	298	12	and	and	CCONJ
ap-10600	298	13	number	number	NOUN
ap-10600	298	14	theory	theory	NOUN
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ap-10600	298	16	,	,	PUNCT
ap-10600	298	17	2022	2022	NUM
ap-10600	298	18	.	.	PUNCT
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ap-10600	300	1	[	[	X
ap-10600	300	2	18	18	NUM
ap-10600	300	3	]	]	PUNCT
ap-10600	300	4	m.	m.	NOUN
ap-10600	300	5	newman	newman	PROPN
ap-10600	300	6	.	.	PUNCT
ap-10600	301	1	roots	root	NOUN
ap-10600	301	2	of	of	ADP
ap-10600	301	3	unity	unity	NOUN
ap-10600	301	4	and	and	CCONJ
ap-10600	301	5	covering	covering	NOUN
ap-10600	301	6	sets	set	NOUN
ap-10600	301	7	.	.	PUNCT
ap-10600	302	1	mathematische	mathematische	PROPN
ap-10600	302	2	annalen	annalen	VERB
ap-10600	302	3	191(4):279–282	191(4):279–282	PROPN
ap-10600	302	4	,	,	PUNCT
ap-10600	302	5	1971	1971	NUM
ap-10600	302	6	.	.	PUNCT
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ap-10600	303	5	m.	m.	NOUN
ap-10600	303	6	lothaire	lothaire	NOUN
ap-10600	303	7	.	.	PUNCT
ap-10600	304	1	algebraic	algebraic	ADJ
ap-10600	304	2	combinatorics	combinatoric	NOUN
ap-10600	304	3	on	on	ADP
ap-10600	304	4	words	word	NOUN
ap-10600	304	5	.	.	PUNCT
ap-10600	305	1	encyclopedia	encyclopedia	NOUN
ap-10600	305	2	of	of	ADP
ap-10600	305	3	mathematics	mathematic	NOUN
ap-10600	305	4	and	and	CCONJ
ap-10600	305	5	its	its	PRON
ap-10600	305	6	applications	application	NOUN
ap-10600	305	7	.	.	PUNCT
ap-10600	306	1	cambridge	cambridge	PROPN
ap-10600	306	2	university	university	PROPN
ap-10600	306	3	press	press	PROPN
ap-10600	306	4	,	,	PUNCT
ap-10600	306	5	cambridge	cambridge	PROPN
ap-10600	306	6	,	,	PUNCT
ap-10600	306	7	2002	2002	NUM
ap-10600	306	8	.	.	PUNCT
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ap-10600	308	1	[	[	X
ap-10600	308	2	20	20	NUM
ap-10600	308	3	]	]	X
ap-10600	308	4	n.	n.	NOUN
ap-10600	308	5	bedaride	bedaride	ADJ
ap-10600	308	6	.	.	PUNCT
ap-10600	309	1	directional	directional	ADJ
ap-10600	309	2	complexity	complexity	NOUN
ap-10600	309	3	of	of	ADP
ap-10600	309	4	the	the	DET
ap-10600	309	5	hypercubic	hypercubic	ADJ
ap-10600	309	6	billiard	billiard	NOUN
ap-10600	309	7	.	.	PUNCT
ap-10600	310	1	discrete	discrete	ADJ
ap-10600	310	2	mathematics	mathematics	PROPN
ap-10600	310	3	309(8):2053–2066	309(8):2053–2066	PROPN
ap-10600	310	4	,	,	PUNCT
ap-10600	310	5	2009	2009	NUM
ap-10600	310	6	.	.	PUNCT
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ap-10600	311	3	21	21	NUM
ap-10600	311	4	]	]	X
ap-10600	311	5	l.	l.	PROPN
ap-10600	311	6	vuillon	vuillon	PROPN
ap-10600	311	7	.	.	PUNCT
ap-10600	312	1	balanced	balanced	ADJ
ap-10600	312	2	words	word	NOUN
ap-10600	312	3	.	.	PUNCT
ap-10600	313	1	bulletin	bulletin	NOUN
ap-10600	313	2	of	of	ADP
ap-10600	313	3	the	the	DET
ap-10600	313	4	belgian	belgian	ADJ
ap-10600	313	5	mathematical	mathematical	ADJ
ap-10600	313	6	society	society	NOUN
ap-10600	313	7	–	–	PUNCT
ap-10600	313	8	simon	simon	PROPN
ap-10600	313	9	stevin	stevin	PROPN
ap-10600	313	10	10(5):787–805	10(5):787–805	PROPN
ap-10600	313	11	,	,	PUNCT
ap-10600	313	12	2003	2003	NUM
ap-10600	313	13	.	.	PUNCT
ap-10600	314	1	https://doi.org/10.36045/bbms/1074791332	https://doi.org/10.36045/bbms/1074791332	PROPN
ap-10600	314	2	538	538	NUM
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ap-10600	314	5	https://doi.org/10.1112/jlms/jdq063	https://doi.org/10.1112/jlms/jdq063	ADJ
ap-10600	314	6	https://doi.org/10.1006/eujc.2000.0444	https://doi.org/10.1006/eujc.2000.0444	PROPN
ap-10600	314	7	https://doi.org/10.1007/978-0-8176-8400-6_1	https://doi.org/10.1007/978-0-8176-8400-6_1	PROPN
ap-10600	315	1	https://doi.org/10.1017/s0143385797086215	https://doi.org/10.1017/s0143385797086215	NUM
ap-10600	315	2	https://doi.org/10.1016/s0304-3975(98)00202-3	https://doi.org/10.1016/s0304-3975(98)00202-3	PROPN
ap-10600	315	3	https://doi.org/10.1007/s00224-024-10188-6	https://doi.org/10.1007/s00224-024-10188-6	NUM
ap-10600	315	4	https://doi.org/10.24033/bsmf.2220	https://doi.org/10.24033/bsmf.2220	NOUN
ap-10600	315	5	https://doi.org/10.3836/tjm/1270128200	https://doi.org/10.3836/tjm/1270128200	VERB
ap-10600	315	6	https://doi.org/10.5802/aif.2274	https://doi.org/10.5802/aif.2274	PROPN
ap-10600	315	7	https://doi.org/10.1007/978-3-642-11212-6	https://doi.org/10.1007/978-3-642-11212-6	PROPN
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ap-10600	315	10	https://doi.org/10.1007/bf01350330	https://doi.org/10.1007/bf01350330	PUNCT
ap-10600	315	11	https://doi.org/10.1017/cbo9781107326019	https://doi.org/10.1017/cbo9781107326019	PROPN
ap-10600	315	12	https://doi.org/10.1016/j.disc.2008.04.018	https://doi.org/10.1016/j.disc.2008.04.018	NOUN
ap-10600	315	13	https://doi.org/10.36045/bbms/1074791332	https://doi.org/10.36045/bbms/1074791332	PROPN
ap-10600	315	14	acta	acta	PROPN
ap-10600	315	15	polytechnica	polytechnica	PROPN
ap-10600	315	16	65(5):534–538	65(5):534–538	PROPN
ap-10600	315	17	,	,	PUNCT
ap-10600	315	18	2025	2025	NUM
ap-10600	315	19	1	1	NUM
ap-10600	315	20	introduction	introduction	NOUN
ap-10600	315	21	2	2	NUM
ap-10600	315	22	frequencies	frequency	NOUN
ap-10600	315	23	and	and	CCONJ
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ap-10600	315	25	in	in	ADP
ap-10600	315	26	fixed	fix	VERB
ap-10600	315	27	points	point	NOUN
ap-10600	315	28	of	of	ADP
ap-10600	315	29	morphism	morphism	NOUN
ap-10600	315	30	3	3	NUM
ap-10600	315	31	colouring	colouring	NOUN
ap-10600	315	32	of	of	ADP
ap-10600	315	33	sequences	sequence	NOUN
ap-10600	315	34	4	4	NUM
ap-10600	315	35	proof	proof	NOUN
ap-10600	315	36	of	of	ADP
ap-10600	315	37	theorem	theorem	ADJ
ap-10600	315	38	2	2	NUM
ap-10600	315	39	5	5	NUM
ap-10600	315	40	comments	comment	NOUN
ap-10600	315	41	and	and	CCONJ
ap-10600	315	42	questions	question	VERB
ap-10600	315	43	acknowledgements	acknowledgement	NOUN
ap-10600	315	44	references	reference	NOUN