id	sid	eid	entity	type
ap-10600	1	1	acta polytechnica https://doi.org/10.14311/ap.2025.65.0534 acta polytechnica	ORG
ap-10600	1	2	65(5):534–538	CARDINAL
ap-10600	1	3	2025	DATE
ap-10600	1	4	2025	CARDINAL
ap-10600	2	1	4.0	CARDINAL
ap-10600	2	2	the czech technical university	ORG
ap-10600	2	3	prague	GPE
ap-10600	2	4	l’ubomíra dvořáková∗	ORG
ap-10600	2	5	edita pelantová czech technical university	ORG
ap-10600	2	6	prague	GPE
ap-10600	2	7	13	CARDINAL
ap-10600	2	8	120	CARDINAL
ap-10600	2	9	prague	GPE
ap-10600	2	10	czech	NORP
ap-10600	2	11	∗	CARDINAL
ap-10600	3	1	alphabet	GPE
ap-10600	3	2	one	CARDINAL
ap-10600	3	3	two	CARDINAL
ap-10600	3	4	k.	PERSON
ap-10600	3	5	integer k	PERSON
ap-10600	3	6	alphabet	GPE
ap-10600	6	1	1	CARDINAL
ap-10600	7	1	first	ORDINAL
ap-10600	8	1	1	CARDINAL
ap-10600	8	2	2	DATE
ap-10600	11	1	fa = lim	ORG
ap-10600	12	1	∈	ORG
ap-10600	12	2	fa	ORG
ap-10600	12	3	1	CARDINAL
ap-10600	13	1	w0w1	PERSON
ap-10600	14	1	wi	ORG
ap-10600	14	2	|w|	FAC
ap-10600	14	3	w	GPE
ap-10600	15	1	w	ORG
ap-10600	15	2	u = u0u1u2	ORG
ap-10600	18	1	n → n	ORG
ap-10600	21	1	two	CARDINAL
ap-10600	21	2	w	PERSON
ap-10600	21	3	∈	ORG
ap-10600	23	1	1	CARDINAL
ap-10600	23	2	1	CARDINAL
ap-10600	24	1	1	CARDINAL
ap-10600	25	1	1	CARDINAL
ap-10600	26	1	fa	ORG
ap-10600	28	1	1	CARDINAL
ap-10600	29	1	hedlund	PERSON
ap-10600	29	2	fa	ORG
ap-10600	30	1	1	CARDINAL
ap-10600	31	1	1	CARDINAL
ap-10600	32	1	2–4	CARDINAL
ap-10600	33	1	2	CARDINAL
ap-10600	34	1	one	CARDINAL
ap-10600	35	1	5	CARDINAL
ap-10600	35	2	zero	CARDINAL
ap-10600	37	1	6	CARDINAL
ap-10600	38	1	1	CARDINAL
ap-10600	40	1	3	CARDINAL
ap-10600	40	2	1	CARDINAL
ap-10600	40	3	11	CARDINAL
ap-10600	41	1	1	CARDINAL
ap-10600	42	1	k ∈ n	ORG
ap-10600	42	2	f1	PERSON
ap-10600	42	3	f2	ORG
ap-10600	43	1	1	CARDINAL
ap-10600	44	1	k ∈ n	ORG
ap-10600	44	2	1	CARDINAL
ap-10600	44	3	0	CARDINAL
ap-10600	45	1	2	CARDINAL
ap-10600	45	2	1	CARDINAL
ap-10600	46	1	11	CARDINAL
ap-10600	46	2	2	CARDINAL
ap-10600	46	3	3	CARDINAL
ap-10600	47	1	8	CARDINAL
ap-10600	47	2	3	CARDINAL
ap-10600	48	1	2	CARDINAL
ap-10600	49	1	c(n	ORG
ap-10600	49	2	534 https://doi.org/10.14311/ap.2025.65.0534 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en	DATE
ap-10600	50	1	65	CARDINAL
ap-10600	51	1	5/2025	CARDINAL
ap-10600	51	2	0	CARDINAL
ap-10600	51	3	1	CARDINAL
ap-10600	52	1	3	CARDINAL
ap-10600	52	2	2	CARDINAL
ap-10600	54	1	2	CARDINAL
ap-10600	55	1	9	CARDINAL
ap-10600	55	2	10–12	CARDINAL
ap-10600	57	1	2	CARDINAL
ap-10600	62	1	3	CARDINAL
ap-10600	63	1	2	CARDINAL
ap-10600	64	1	2	CARDINAL
ap-10600	66	1	2	CARDINAL
ap-10600	66	2	two	CARDINAL
ap-10600	66	3	ψ(uv	GPE
ap-10600	66	4	∈	ORG
ap-10600	67	1	ψ(u	ORG
ap-10600	68	1	j ∈	PERSON
ap-10600	68	2	1	CARDINAL
ap-10600	68	3	2	DATE
ap-10600	70	1	k ∈ n	PERSON
ap-10600	72	1	13	CARDINAL
ap-10600	74	1	13	CARDINAL
ap-10600	74	2	lim	PERSON
ap-10600	74	3	#{kn	MONEY
ap-10600	76	1	kn)n∈n	PRODUCT
ap-10600	80	1	14	CARDINAL
ap-10600	81	1	3	CARDINAL
ap-10600	85	1	15	CARDINAL
ap-10600	86	1	one	CARDINAL
ap-10600	89	1	14	CARDINAL
ap-10600	90	1	16	CARDINAL
ap-10600	90	2	17	CARDINAL
ap-10600	91	1	3	CARDINAL
ap-10600	92	1	4	CARDINAL
ap-10600	94	1	o(a) n and o(b) n	ORG
ap-10600	96	1	two	CARDINAL
ap-10600	96	2	two	CARDINAL
ap-10600	98	1	n = o(b	ORG
ap-10600	107	1	5	CARDINAL
ap-10600	107	2	56)ω	CARDINAL
ap-10600	107	3	aabaababaabaababaababaabaababaabaab	PERSON
ap-10600	108	1	12513615416215361451621531645126135	DATE
ap-10600	108	2	π(54162153614	PERSON
ap-10600	109	1	535	CARDINAL
ap-10600	109	2	dvořáková	ORG
ap-10600	109	3	edita pelantová acta polytechnica	ORG
ap-10600	109	4	6	CARDINAL
ap-10600	110	1	j ∈	PERSON
ap-10600	110	2	fa	ORG
ap-10600	110	3	γ	GPE
ap-10600	110	4	7	DATE
ap-10600	112	1	5	CARDINAL
ap-10600	113	1	18	CARDINAL
ap-10600	114	1	8	CARDINAL
ap-10600	115	1	more than one	CARDINAL
ap-10600	116	1	two	CARDINAL
ap-10600	117	1	9	CARDINAL
ap-10600	118	1	1	CARDINAL
ap-10600	120	1	two	CARDINAL
ap-10600	121	1	5	CARDINAL
ap-10600	121	2	1	CARDINAL
ap-10600	121	3	6	CARDINAL
ap-10600	121	4	1	CARDINAL
ap-10600	122	1	10	CARDINAL
ap-10600	123	1	1	CARDINAL
ap-10600	123	2	2	DATE
ap-10600	125	1	f⃗v	ORG
ap-10600	126	1	1	CARDINAL
ap-10600	127	1	3	CARDINAL
ap-10600	127	2	only one	CARDINAL
ap-10600	127	3	1 2	CARDINAL
ap-10600	127	4	1 2	CARDINAL
ap-10600	127	5	1	CARDINAL
ap-10600	127	6	12)ω	CARDINAL
ap-10600	127	7	3)ω	CARDINAL
ap-10600	128	1	2	CARDINAL
ap-10600	129	1	4	CARDINAL
ap-10600	129	2	three	CARDINAL
ap-10600	129	3	•	CARDINAL
ap-10600	129	4	12)ω	ORDINAL
ap-10600	129	5	34)ω	CARDINAL
ap-10600	129	6	1 2	CARDINAL
ap-10600	129	7	1 2	CARDINAL
ap-10600	129	8	1	CARDINAL
ap-10600	129	9	1 2	CARDINAL
ap-10600	129	10	1	CARDINAL
ap-10600	129	11	1 2	CARDINAL
ap-10600	129	12	•	CARDINAL
ap-10600	129	13	123)ω	CARDINAL
ap-10600	129	14	4)ω	CARDINAL
ap-10600	129	15	1 3	CARDINAL
ap-10600	129	16	1 3	CARDINAL
ap-10600	129	17	•	CARDINAL
ap-10600	129	18	4)ω	CARDINAL
ap-10600	129	19	1 2	CARDINAL
ap-10600	129	20	1 4	DATE
ap-10600	129	21	1 4	CARDINAL
ap-10600	129	22	1	CARDINAL
ap-10600	130	1	2	CARDINAL
ap-10600	130	2	3	CARDINAL
ap-10600	131	1	11	CARDINAL
ap-10600	132	1	1	CARDINAL
ap-10600	133	1	3	CARDINAL
ap-10600	133	2	two	CARDINAL
ap-10600	135	1	3	CARDINAL
ap-10600	135	2	#	CARDINAL
ap-10600	135	3	2	CARDINAL
ap-10600	135	4	#	CARDINAL
ap-10600	135	5	2	CARDINAL
ap-10600	135	6	8	CARDINAL
ap-10600	135	7	two	CARDINAL
ap-10600	136	1	γ.	GPE
ap-10600	137	1	6	CARDINAL
ap-10600	140	1	1	CARDINAL
ap-10600	140	2	lemma 11	ORG
ap-10600	140	3	1	CARDINAL
ap-10600	141	1	12	CARDINAL
ap-10600	143	1	two	CARDINAL
ap-10600	143	2	two	CARDINAL
ap-10600	147	1	∈	ORG
ap-10600	149	1	= π(u	ORG
ap-10600	150	1	|u′|	PRODUCT
ap-10600	152	1	|u′|a	CARDINAL
ap-10600	153	1	0 ≤ n ≤	QUANTITY
ap-10600	153	2	aj	PERSON
ap-10600	154	1	aj+m	PERSON
ap-10600	154	2	|aj	DATE
ap-10600	159	1	4	CARDINAL
ap-10600	160	1	2	CARDINAL
ap-10600	161	1	2	CARDINAL
ap-10600	162	1	19	CARDINAL
ap-10600	163	1	13	CARDINAL
ap-10600	164	1	1	CARDINAL
ap-10600	164	2	fa	ORG
ap-10600	164	3	0	CARDINAL
ap-10600	164	4	1	CARDINAL
ap-10600	165	1	n ∈ n	PRODUCT
ap-10600	166	1	⌈(1	GPE
ap-10600	166	2	14	DATE
ap-10600	167	1	1	CARDINAL
ap-10600	167	2	f(2	PERSON
ap-10600	170	1	1	CARDINAL
ap-10600	170	2	1	CARDINAL
ap-10600	170	3	2	DATE
ap-10600	172	1	1	CARDINAL
ap-10600	173	1	f(i	PERSON
ap-10600	173	2	1	CARDINAL
ap-10600	173	3	2	DATE
ap-10600	174	1	2	CARDINAL
ap-10600	175	1	k = ⌈log2 d⌉	ORG
ap-10600	175	2	536	CARDINAL
ap-10600	176	1	65	CARDINAL
ap-10600	177	1	5/2025	CARDINAL
ap-10600	177	2	3	CARDINAL
ap-10600	178	1	1)d−1	CARDINAL
ap-10600	180	1	1	CARDINAL
ap-10600	180	2	1ω	CARDINAL
ap-10600	181	1	2	CARDINAL
ap-10600	184	1	1 α f(i	QUANTITY
ap-10600	184	2	1	CARDINAL
ap-10600	184	3	2	DATE
ap-10600	185	1	1 1	CARDINAL
ap-10600	186	1	+ 1	DATE
ap-10600	188	1	d.	NORP
ap-10600	189	1	1	CARDINAL
ap-10600	189	2	⌉+1)+	NORP
ap-10600	192	1	1	CARDINAL
ap-10600	192	2	2	DATE
ap-10600	192	3	+ 1	DATE
ap-10600	193	1	∈	ORG
ap-10600	193	2	kb	ORG
ap-10600	193	3	1	CARDINAL
ap-10600	193	4	1	CARDINAL
ap-10600	194	1	1	CARDINAL
ap-10600	195	1	6	CARDINAL
ap-10600	196	1	f(i	PERSON
ap-10600	197	1	1	CARDINAL
ap-10600	197	2	α)f	NORP
ap-10600	197	3	f(i	PERSON
ap-10600	197	4	12	CARDINAL
ap-10600	197	5	1 +	DATE
ap-10600	197	6	2	CARDINAL
ap-10600	197	7	1 +	DATE
ap-10600	197	8	1 +	DATE
ap-10600	199	1	1 +	DATE
ap-10600	201	1	2	CARDINAL
ap-10600	201	2	1)⌉	CARDINAL
ap-10600	201	3	1	CARDINAL
ap-10600	201	4	1	CARDINAL
ap-10600	202	1	+ 1	DATE
ap-10600	203	1	2⌈log2	CARDINAL
ap-10600	203	2	1	CARDINAL
ap-10600	204	1	3	CARDINAL
ap-10600	205	1	lemma 13	ORG
ap-10600	205	2	1	CARDINAL
ap-10600	205	3	1	CARDINAL
ap-10600	206	1	1	CARDINAL
ap-10600	206	2	1	CARDINAL
ap-10600	206	3	1)⌈d2	CARDINAL
ap-10600	206	4	1)⌊d2	CARDINAL
ap-10600	206	5	1)d−1	CARDINAL
ap-10600	206	6	5	CARDINAL
ap-10600	206	7	1	CARDINAL
ap-10600	207	1	14	DATE
ap-10600	209	1	2	CARDINAL
ap-10600	210	1	1	CARDINAL
ap-10600	211	1	f(i	PERSON
ap-10600	212	1	14	CARDINAL
ap-10600	212	2	1)d−1	CARDINAL
ap-10600	212	3	1	CARDINAL
ap-10600	213	1	3	CARDINAL
ap-10600	213	2	f(i	GPE
ap-10600	213	3	14	CARDINAL
ap-10600	214	1	4	CARDINAL
ap-10600	214	2	f(i	GPE
ap-10600	216	1	5	CARDINAL
ap-10600	217	1	0	CARDINAL
ap-10600	217	2	1]d	DATE
ap-10600	217	3	two	CARDINAL
ap-10600	219	1	0	CARDINAL
ap-10600	219	2	1]d	DATE
ap-10600	219	3	0	CARDINAL
ap-10600	222	1	20	CARDINAL
ap-10600	224	1	21	CARDINAL
ap-10600	224	2	1	CARDINAL
ap-10600	225	1	andrieu	PERSON
ap-10600	225	2	9	CARDINAL
ap-10600	225	3	•	CARDINAL
ap-10600	225	4	2	CARDINAL
ap-10600	225	5	3	DATE
ap-10600	225	6	4	CARDINAL
ap-10600	225	7	•	CARDINAL
ap-10600	225	8	3	CARDINAL
ap-10600	225	9	4	DATE
ap-10600	229	1	∈ rd	ORG
ap-10600	229	2	cubic billiard	FAC
ap-10600	229	3	14 537	CARDINAL
ap-10600	229	4	dvořáková	ORG
ap-10600	229	5	edita pelantová acta polytechnica	ORG
ap-10600	230	1	3	CARDINAL
ap-10600	234	1	1	CARDINAL
ap-10600	234	2	m. morse	PERSON
ap-10600	235	1	g. a. hedlund	PERSON
ap-10600	237	1	sturmian	PERSON
ap-10600	238	1	american journal of mathematics 62(1):1–42, 1940	ORG
ap-10600	240	1	2	CARDINAL
ap-10600	241	1	balková	PERSON
ap-10600	241	2	e. pelantová	PERSON
ap-10600	241	3	starosta	PERSON
ap-10600	243	1	rairo	PERSON
ap-10600	243	2	44(4):443–470, 2010	DATE
ap-10600	245	1	3	CARDINAL
ap-10600	245	2	k. saari	PERSON
ap-10600	245	3	l. q. zamboni	PERSON
ap-10600	246	1	abelian	NORP
ap-10600	247	1	london	GPE
ap-10600	248	1	https://doi.org/10.1112/jlms/jdq063	PERSON
ap-10600	248	2	4	CARDINAL
ap-10600	248	3	l. vuillon	PERSON
ap-10600	250	1	european journal of combinatorics 22(2):263–275, 2001	ORG
ap-10600	251	1	5	CARDINAL
ap-10600	251	2	starosta	PERSON
ap-10600	253	1	b. boston	GPE
ap-10600	254	1	1–23	CARDINAL
ap-10600	255	1	birkhäuser,	ORG
ap-10600	255	2	boston	GPE
ap-10600	255	3	2013	DATE
ap-10600	257	1	6	CARDINAL
ap-10600	257	2	a. zorich	PERSON
ap-10600	259	1	ergodic	ORG
ap-10600	259	2	17(6):1477–1499, 1997	DATE
ap-10600	261	1	7	CARDINAL
ap-10600	261	2	p. hubert	PERSON
ap-10600	263	1	242(1–2):91–108	CARDINAL
ap-10600	263	2	2000	DATE
ap-10600	264	1	https://doi.org/10.1016/s0304-3975(98)00202-3	CARDINAL
ap-10600	265	1	8	CARDINAL
ap-10600	265	2	l. dvořáková	PERSON
ap-10600	265	3	z. masáková	PERSON
ap-10600	265	4	e. pelantová	PERSON
ap-10600	266	1	2	CARDINAL
ap-10600	267	1	68(6):1537–1555	CARDINAL
ap-10600	267	2	2024	DATE
ap-10600	269	1	9	CARDINAL
ap-10600	269	2	m. andrieu	PERSON
ap-10600	269	3	l. vivion	PERSON
ap-10600	270	1	hypercubic billiard	LOC
ap-10600	271	1	18th	ORDINAL
ap-10600	272	1	prague	GPE
ap-10600	272	2	2022	CARDINAL
ap-10600	273	1	10	CARDINAL
ap-10600	273	2	i. shiokawa	PERSON
ap-10600	273	3	j.-i	GPE
ap-10600	274	1	tamura	PERSON
ap-10600	275	1	de la société mathématique de france 122(1):1–	ORG
ap-10600	275	2	12, 1994	DATE
ap-10600	276	1	11	CARDINAL
ap-10600	276	2	i. shiokawa	PERSON
ap-10600	276	3	j.-i	GPE
ap-10600	277	1	tamura	PERSON
ap-10600	277	2	rauzy	PERSON
ap-10600	277	3	billiards	GPE
ap-10600	278	1	tokyo	GPE
ap-10600	278	2	17(1):211–218, 1994	DATE
ap-10600	280	1	12	CARDINAL
ap-10600	280	2	n. bedaride	PERSON
ap-10600	280	3	p. hubert	PERSON
ap-10600	282	1	annales de l’institut	ORG
ap-10600	282	2	57(3):719–738	CARDINAL
ap-10600	282	3	2007	DATE
ap-10600	283	1	13	CARDINAL
ap-10600	283	2	m. queffélec	PERSON
ap-10600	286	1	heidelberg	GPE
ap-10600	286	2	2nd	ORDINAL
ap-10600	286	3	2010	DATE
ap-10600	287	1	14	CARDINAL
ap-10600	289	1	kôkyûroku bessatsu b46:81–123	ORG
ap-10600	289	2	2014	DATE
ap-10600	290	1	15	CARDINAL
ap-10600	292	1	307(1):47–75, 2003	DATE
ap-10600	294	1	16	CARDINAL
ap-10600	294	2	j. cassaigne	PERSON
ap-10600	295	1	un algorithme de fractions	ORG
ap-10600	295	2	de complexité linéaire	ORG
ap-10600	295	3	2015	DATE
ap-10600	296	1	liafa	ORG
ap-10600	296	2	paris	GPE
ap-10600	297	1	17	CARDINAL
ap-10600	297	2	j. cassaigne	PERSON
ap-10600	297	3	s. labbé	PERSON
ap-10600	297	4	j. leroy	PERSON
ap-10600	298	1	2n	CARDINAL
ap-10600	298	2	combinatorics	ORG
ap-10600	298	3	2022	CARDINAL
ap-10600	299	1	https://doi.org/10.2140/moscow.2022.11.287	ORG
ap-10600	300	1	18	CARDINAL
ap-10600	300	2	m. newman	PERSON
ap-10600	302	1	191(4):279–282, 1971	DATE
ap-10600	303	1	19	CARDINAL
ap-10600	303	2	m. lothaire	PERSON
ap-10600	304	1	algebraic combinatorics	ORG
ap-10600	306	1	cambridge university press	ORG
ap-10600	306	2	cambridge	GPE
ap-10600	306	3	2002	DATE
ap-10600	308	1	20	CARDINAL
ap-10600	310	1	309(8):2053–2066	CARDINAL
ap-10600	310	2	2009	DATE
ap-10600	311	1	21	CARDINAL
ap-10600	311	2	l. vuillon	PERSON
ap-10600	313	1	bulletin	PERSON
ap-10600	313	2	belgian	NORP
ap-10600	313	3	simon stevin 10(5):787–805, 2003	PERSON
ap-10600	314	1	538	CARDINAL
ap-10600	314	2	https://doi.org/10.1112/jlms/jdq063	PERSON
ap-10600	315	1	https://doi.org/10.1017/cbo9781107326019	PRODUCT
ap-10600	315	2	65(5):534–538	CARDINAL
ap-10600	315	3	1 introduction	QUANTITY
ap-10600	315	4	2	CARDINAL
ap-10600	315	5	3	CARDINAL
ap-10600	315	6	4	CARDINAL
ap-10600	315	7	2 5	CARDINAL