prof. Ing. Zuzana Masáková, Ph.D.

Nekonečná slova kódující výměnu tří intervalů a jejich invariantnost na substituce

Zobecněné řetězové zlomky

Aritmetika v soustavách s kvartickou bází

Regular journal papers

1. L. Dvořáková, Z. Masáková, E. Pelantová, 2-balanced sequences coding rectangle exchange transformation, to appear in Theory of Computing Systems (2024), 19pp.
2. Z. Masáková, E. Pelantová, Periodicity and pure periodicity in alternate base systems, to appear in Research in Number Theory (2024), 16pp.
3. Z. Masáková, E. Pelantová, On Midy's Theorem in non-integer bases, Communications in Mathematics 33 (2025), no. 2, Paper no. 1, 17pp. https://arXiv:2401.03874
4. E. Charlier, C. Cisternino, Z. Masáková, E. Pelantová, Spectrum, algebraicity and normalization in alternate bases, Journal of Number Theory 249 (2023), 470-499.
5. Z. Masáková, T. Vávra, F. Veneziano, Finiteness and periodicity of continued fractions over quadratic number fields, Bull. Soc. Math. France 150 No.1 (2022), 77-109.
6. P. Ambrož, Z. Masáková, E. Pelantová, Lattice bounded distance equivalence for 1D Delone sets with finite local complexity, Journal of Geometry and Symmetry in Physics 59 (2021), 1-29.
7. Z. Masáková, J. Mazáč, E. Pelantová, On generalized self-similarities of cut-and-project sets, Linear Algebra and Applications 625 (2021), 279-321.
8. Z. Masáková, E. Vandomme, Redundance in the Signed $m$-Bonacci Numeration System, Journal of Integer Sequences 24 (2021), Article 21.7.2
9. P. Ambrož, Z. Masáková, E. Pelantová, Morphisms generating antipalindromic words, Europ. J. Combin. 89 (2020), 103160.
10. P. Ambrož, O. Kadlec, Z. Masáková, E. Pelantová, Palindromic length of words and morphisms in class P, Theor. Comput. Sci. 780 (2019), 74-83.
11. K. Hare, Z. Masáková, T. Vávra, On the spectra of Pisot-cyclotomic numbers, Lett. Math. Phys. 108 (2018), 1729–1756.
12. Z. Masáková, J. Mazáč, On self-similarities of cut-and-project sets, Acta Polytechnica 57 (2017), 430-445.
13. Z. Masáková, M. Tinková, Finiteness in real cubic fields, Acta Math. Hungar. 153 (2017), 318–333.
14. Z. Masáková, E. Pelantová, Š. Starosta, Exchange of three intervals: substitutions and palindromicity, European J. Combin. 62 (2017), 217-231.
15. S. Baker, Z. Masáková, E. Pelantová, T. Vávra, On periodic representations in non-Pisot bases, Monats. Mathematik 184 (2017), 1-19.
16. Z. Masáková, E. Pelantová, Š. Starosta, Itineraries induced by exchange of three intervals, Acta Polytechnica 56 (2016), 462-471.
17. Z. Masáková, K. Pastirčáková, E. Pelantová, Description of spectra of quadratic Pisot units, J. Num. Theory 150 (2015), 168-190. http://dx.doi.org/10.1016/j.jnt.2014.11.011
18. D. Dombek, Z. Masáková, T. Vávra, Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems, J. Théorie Nombres de Bordeaux 27, (2015), 745-768.
19. D. Dombek, Z. Masáková, V. Ziegler, On distinct unit generated fields that are totally complex, J. Num. Theory 148 (2015), 311-327. http://dx.doi.org/10.1016/j.jnt.2014.09.029
20. T. Komatsu, Z. Masáková, E. Pelantová, Higher order identities for Fibonacci numbers, Fibonacci Quart. 52 (2014), 150-163.
21. Z. Masáková, T. Vávra, Integers in number systems with positive and negative quadratic Pisot base, RAIRO Theor. Inform. Appl. 48 (2014), 341-367.
22. Z. Masáková, E. Pelantová, Itineraries induced by exchange of two intervals, Acta Polytechnica 53 (2013), 444-449.
23. Z. Masáková, E. Pelantová, Optimal Number Representations in Negative Bases, Acta Math. Hungar. 140 (2013), 329-340. arXiv:1208.1413v1 [math.NT]
24. T. Hejda, Z. Masáková, E. Pelantová, The greedy and lazy representations of numbers in negative base systems, Kybernetika 49 (2013), 258-279. arXiv:1110.6327v2 [math.NT]
25. Z. Masáková, E. Pelantová, Purely periodic expansions in systems with negative base, Acta Math. Hungar. 139 (2013), 208-227. arXiv:1202.1948v1 [math.NT]
26. P. Ambrož, D. Dombek, Z. Masáková, E. Pelantová, Numbers with integer expansion in the numeration system with negative base, Funct. Approx. Comment. Math., 47 (2012), 241-266. arXiv:0912.4597v3 [math.NT]
27. P. Ambrož, A. Frid, Z. Masáková, E. Pelantová, On the number of factors in codings of three interval exchange, Discrete Math. Theor. Comput. Sci. 13 (2011), 51-66. ArXiv 0904.2258v1 [math.CO]
28. D. Dombek, Z. Masáková, E. Pelantová, Number representation using generalized (-beta)-transformation, Theor. Comp. Sci 412 (2011), 6653-6665.
29. Z. Masáková, E. Pelantová, Ito-Sadahiro numbers vs. Parry numbers, Acta Polytechnica 51 (2011), 59-64.
30. Z. Masáková, E. Pelantová, T. Vávra, Arithmetics in number systems with negative base, Theor. Comp. Sci. 412 (2011), 835-845.
31. D. Lenz, Z. Masáková, E. Pelantová, Note on powers in three interval exchange transformations, Theor. Comp. Sci. 412 (2011), 3788-3794
32. Z. Masáková, T. Vávra, Arithmetics in numeration systems with negative quadratic base, Kybernetika 47 (2011), 74-92.
33. P. Ambrož, Z. Masáková, E. Pelantová, Morphisms fixing words associated with exchange of three intervals RAIRO Theor. Inform. Appl. 44 (2010), 3-17.
34. M. Grundland, J. Patera, Z. Masáková, N. Dodgson, Image Sampling with Quasicrystals Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 (2009), Article Number: 075
35. Z. Masáková, E. Pelantová, Relation between powers of factors and the recurrence function characterizing Sturmian words Theor. Comp. Sci. 410 (2009), 3589-3596. DOI: 10.1016/j.tcs.2009.04.003
36. Ľ. Balková, Z. Masáková, Palindromic complexity of infinite words associated with non-simple Parry numbers RAIRO Theor. Inform. Appl. 43 (2009), 145-163. DOI: 10.1051/ita:2008005
37. P. Baláži, Z. Masáková, E. Pelantová, Characterization of substitution invariant 3iet words, Integers - Electronic Journal of Combinatorial Number Theory 8 (2008), #A20, 21pp.
38. P. Arnoux, V. Berthé, Z. Masáková, E. Pelantová, Sturm numbers and substitution invariance of 3iet words, Integers - Electronic Journal of Combinatorial Number Theory 8 (2008), #A14, 17pp.
39. P. Ambrož, Z. Masáková, E. Pelantová, Matrices of 3iet preserving morphisms, Theor. Comp. Sci. 400 (2008), 113–136.
40. Z. Masáková, E. Pelantová, Selfmatching properties of Beatty sequences, Acta Polytechnica 47 No.2-3, (2007), 21-24.
41. J. Bernat, Z. Masáková, E. Pelantová, Affine factor complexity of infinite words associated with simple Parry numbers, Theor. Comp. Sci. 389 (2007), 12-25.
42. C. Frougny, Z. Masáková, E. Pelantová, Infinite left special branches in words associated with beta expansions, Discrete Math. Theor. Comput. Sci. 9 (2007), 125-144.
43. P. Ambrož, Z. Masáková, E. Pelantová, Addition and multiplication of beta-expansions in generalized Tribonacci base, Discrete Math. Theor. Comput. Sci. 9 (2007), 73 – 88.
44. P. Kocábová, Z. Masáková, E. Pelantová, Ambiguity in the m-Bonacci numeration system, Discrete Math. Theor. Comput. Sci. 9 (2007), 109-124.
45. P. Baláži, Z. Masáková, E. Pelantová, Factor versus palindromic complexity of uniformly recurrent infinite words, Theoret. Comp. Sci. 380 (2007), 266-275.
46. P. Ambrož, Ch. Frougny, Z. Masáková, E. Pelantová, Palindromic complexity of infinite words associated to simple Parry numbers, Annales de l‘Institut Fourier, 56 (2006), 2131-2160.
47. J.P. Gazeau, Z. Masáková, E. Pelantová, Nested quasicrystalline discretization of the line, IRMA Lectures in Mathematics and Theoretical Physics, Vol. 10, Ed. L. Nyssen, EMS (2006), 79-132. math-ph/0601026
48. P. Baláži, Z. Masáková, E. Pelantová, Complete characterization of substitution invariant Sturmian sequences, Integers - Electronic Journal of Combinatorial Number Theory 5 (2005), #A14, 23pp.
49. P. Kocábová, Z. Masáková, E. Pelantová, Integers with maximal number of Fibonacci representations, RAIRO Theor. Inf. Appl. 39 (2005), 343-358.
50. Z. Masáková, J. Patera, J. Zich, Classification of Voronoi and Delone tiles of quasicrystals III:; decagonal acceptance window of any size, J. Phys. A: Math. Gen. 38 (2005), 1947-1960.
51. Z. Masáková, Propriétés arithmétiques et combinatoires des β-entiers, Ann. Sci. Math. Québec 28 (2004), 153--164.
52. L. Balková, Z. Masáková, E. Pelantová, The Meyer property of cut-and-project sets, J. Phys. A.: Math. Gen. 37 (2004), 8853-8864.
53. C. Frougny, Z. Masáková, E. Pelantová Complexity of infinite words associated with beta-expansions, RAIRO Theor. Inf. and Appl. 38 (2004), pp. 162-184; Corrigendum RAIRO Theor. Inf. and Appl. 38 (2004), pp. 269-271.
54. L.S. Guimond, Z. Masáková, E. Pelantová, Arithmetics on beta-expansions, Acta Arith. 112 (2004), pp. 23-40.
55. L.S. Guimond, Z. Masáková, E. Pelantová, Combinatorial properties of infinite words associated with cut and project sequences, J. Théor. Nombres Bordeaux 15 (2003), pp. 697-725.
56. P. Ambrož, Ch. Frougny, Z. Masáková, E. Pelantová, Arithmetics on number systems with irrational bases, Bull. Soc. Math. Belg. 10 (2003) pp. 641-659.
57. Z. Masáková, J. Patera, J. Zich, Classification of Voronoi and Delone tiles in quasicrystals: I. General method, J. Phys. A: Math. Gen. 36 (2003) pp. 1869-1894.
58. 9. Z. Masáková, J. Patera, J. Zich, Classification of Voronoi and Delone tiles of quasicrystals: II. Circular acceptance window of arbitrary size, J. Phys. A: Math. Gen. 36 (2003) pp. 1895-1912.
59. Z. Masáková, J. Patera, E. Pelantová, Exceptional algebraic properties of three quadratic irrationalities observed in quasicrystals, Canadian J. Phys. 79 (2001) pp. 687-696.
60. Z. Masáková, E. Pelantová, M. Svobodová, Characterization of cut-and-project sets using a binary operation, Lett. Math. Phys. 54 (2000) pp. 1-10.
61. Z. Masáková, J. Patera and E. Pelantová, Substitution rules for aperiodic sequences of the cut and project type J. Phys. A: Math. Gen. 33 (2000) pp. 8867-8886.
62. Z. Masáková, J. Patera, E. Pelantová, Selfsimilar Delone sets and quasicrystals, J. Phys. A: Math. Gen. 31 (1998) pp. 4927-4946.
63. Z. Masáková, J. Patera, E. Pelantová, Minimal distances in quasicrystals, J. Phys. A: Math. Gen. 31 (1998) pp. 1539-1552.
64. Z. Masáková, J. Patera, E. Pelantová, Inflation centers of the cut and project quasicrystals, J. Phys. A: Math. Gen. 31 (1998) pp. 1443-1453.

Contributions in conference proceedings

1. Z. Masáková, E. Pelantová, K. Studeničová, Rewriting rules for arithmetics in alternate base systems, Proceedings of DLT 2023, Umea, Sweden, LNCS (2023).
2. Z. Masáková, J. Mazáč, Pentagonal quasicrystals and their linear self-similarities, J. Phys. -- Conference Series 1458 (2020), 012010.
3. P. Ambrož, Z. Masáková, Description of Voronoi tiles in quasicrystals with 8-fold symmetry, J. Phys. -- Conference Series 1458 (2020), 012007
4. P. Ambrož, Z. Masáková, J. Mazáč, Linear mappings as self-similarities of mathematical models of quasicrystals, J. Phys. -- Conference Series 1194, (2019), 012005.
5. Z. Masáková, E. Pelantová, Š. Starosta, Interval Exchange Words and the Question of Hof, Knill, and Simon, Proceedings of DLT 2015, Liverpool, LNCS 9168 (2015), 377–388.
6. Z. Masáková, E. Pelantová, Enumerating Abelian Returns to Prefixes of Sturmian Words, Proceedings of WORDS 2013, Turku, LNCS 8079 (2013), 193-204.
7. T. Hejda, Z. Masáková, E. Pelantová, On the negative base greedy and lazy representations, In "14eme Journées Montoises d'Informatique Théorique", 2012.
8. P. Ambrož, D. Dombek, Z. Masáková, E. Pelantová, Numbers with integer expansions in the numeration system with negative base, in Proceedings of the 13th Mons Theoretical Computer Days, Amiens, September 6-10, 2010, U.F.R. Sciences (2010) 1-8.
9. E. Pelantová, Z. Masáková, Quasicrystals: algebraic, combinatorial and geometrical aspects, in From Numbers and Languages to (Quantum) Cryptography, NATO School "Physics and Computer Science", Vol. 7, Edited by: J.-P. Gazeau, J. Nešetril and B. Rovan (2007) 113-131.
10. Ľ. Balková, Z. Masáková, The covering problem related to quasicrystals, Proceedings of the XIth International Conference on Symmetry Methods in Physics, Prague 2004, Eds. Č. Burdík, O. Navrátil, S. Pošta, 2004, 11pp.
11. Z. Masáková, Propriétés arithmétiques et combinatoires des beta-entiers, Comptes rendus de la conférence internationale Maroc-Québec, Mai 2003 "Théorie de nombres et applications", 2004, pp. 163-172.
12. Z. Masáková, Substitution Systems for mathematical models of quasicrystals, Proceedings of Workshop 2001, Prague, CTU, 2001, vol. 5, A. 24-25.
13. Z. Masáková, E. Pelantová, Cut and project sequences and substitution rules, Proc. of the international conference Aperiodic 2000, in Ferroelectrics 250 No. 1-4 (2001), pp. 165-168.
14. Z. Masáková, J. Patera, E. Pelantová, Lattice-like properties of quasicrystal models with quadratic irrationalities, Proceedings of Quantum Theory and Symmetries, Goslar, 1999, Eds. H.D. Doebner, V.K. Dobrev, J.D. Hennig, W. Luecke, World Scientific, 2000, pp. 499-509.
15. Z. Masáková, J. Patera, E. Pelantová, Acceptance windows compatible with a quasicrystal fragment, From quasicrystals to more complex systems ed. F. Axel, F. Denoyer, J.-P. Gazeau, Lecture Notes of the Winter School Order, Chance and Risk, Les Houches, March 1998, Springer 2000, pp. 167-193.
16. Z. Masáková, Quasiperiodic self-similar structures in Modern Applied Mathematics Techniques in Circuits, Systems and Control, Proc. of the 3rd international IMACS IEEE conferrence in Athens, July 4 - 8, 1999, Ed. N. E. Mastorakis, WSES-press 1999, pp. 94-99.
17. Z. Masáková, E. Pelantová, Quasicrystals, tilings and scaling symmetries, Proc. of the international workshop Self-similar systems in Dubna, July 30 - August 7, 1998, Eds. V. B. Priezzhev, V. P. Spiridonov, JINR Dubna 1999, pp. 189-202.
18. Z. Masáková, J. Patera, E. Pelantová, Internal and external quasicrystal inflation centers, Conf. Proceedings Symmetry Methods in Physics, Dubna 1997, Russ. J. Nuc. Phys. 10 (1998) pp. 2085-2089.
19. Z. Masáková, J. Patera, E. Pelantová, Scaling invariances of quasicrystalline sets, Conf. Proc. of the 5th Wigner Symposium, Vienna 1997, Eds. P. Kasperkovitch and D. Grau, World Scientific, Singapore, (1998) pp. 94-96.

Reports and preprints

1. E. Charlier, C. Cisternino, Z. Masáková, E. Pelantová, Substitutions and Cantor real numeration systems, preprint (2023), 23pp., https://arXiv:2312.13767
2. Z. Masáková, E. Pelantová, K. Studeničová, Finiteness property in Cantor real numeration systems, preprint (2023), full version of the contribution of DLT 2023. https://arxiv.org/abs/2302.10708
3. Z. Masáková, J. Patera, E. Pelantová, s-convexity, model sets and their relation, MSRI Preprint No. 1999-040 (1999)
4. Z. Masáková, E. Pelantová, A note on periodic s-convex sets, preprint (1999)
5. L.-S. Guimond, Z. Masáková, J. Patera, E. Pelantová, Deterministically broken periodicity of linear congruential generators using quasi-crystals, preprint CRM-2620 (1999).
6. Z. Masáková, J. Patera, E. Pelantová, Quadratic Irrationalities and Geometric Properties of One Dimensional Quasicrystals, preprint CRM-2565 (1998)

Popularization articles

1. Z. Masáková, Prvočísla v akci, Rozhledy Rozhledy matematicko-fyzikální, JČMF, 90 (2015), 66-77.
2. Z. Masáková, E. Pelantová, Tigří počítání, Pražská technika 6/2009, 16-17.
3. Z. Masáková, J. Patera, E. Pelantová, Projekce vícerozměrných krystalografických mřížek jako matematický model pro kvazikrystaly, Českosl. čas. pro fyziku 53 (2003) pp. 325-329.
4. Z. Masáková, E. Pelantová, M. Svobodová Rozklad množiny přirozených čísel pomocí zlatého řezu, Rozhledy matematicko-fyzikální 78 (2001) pp. 8-15.

Edited proceedings and special issues

1. Doktorandské dny 2023. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2023)
2. Doktorandské dny 2022. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2022)
3. Doktorandské dny 2021. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2021)
4. Doktorandské dny 2020. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2020)
5. Doktorandské dny 2019. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2019)
6. Doktorandské dny 2018. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2018)
7. Doktorandské dny 2017. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2017)
8. Doktorandské dny 2016. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2016)
9. Doktorandské dny 2015. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2015)
10. Doktorandské dny 2014. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2014)
11. Doktorandské dny 2013. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2013)
12. Special issue: Words 2011. Selected papers from the eight international conference on combinatorics on words Words 2011 held in Prague, September 2011. Edited by Z. Masáková and Š. Holub, International Journal of Foundations of Computer Science 23 (2012), no. 7. pp. 1579-1729.
13. Doktorandské dny 2012. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2012)
14. ISCAMI and Analytic and algebraic methods 2011. Special issue devoted to papers from conferences AAMP VIII and ISCAMI 2011 held in Prague, March 2011, and Malenovice, May 2011. Edited by K. Klouda, Z. Masáková, R. Mesiar and M. Štěpnička, Kybernetika 48 (2012), no. 3. pp. 357-586.
15. Doktorandské dny 2011. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2011)
16. WORDS 2011, Proceedings of the 8th International Conference Words 2011, Prague, September 12-16, 2011. Edited by P. Ambrož, Š. Holub and Z. Masáková, Electronic Proceedings in Theoretical Computer Science 63 (2011) 276p.
17. Doktorandské dny 2010. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2010)
18. Doktorandské dny 2009. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2009)
19. Doktorandské dny 2008. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2008)
20. Doktorandské dny 2007. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2007)
21. Doktorandské dny 2006. Sborník. Editoři P. Ambrož a Z. Masáková, ČVUT Praha (2006)
22. DI-CRM Workshop on Mathematical Physics. Papers from the workshop held at the Czech Technical University, Prague, June 18-21, 2000. Edited by Z. Masáková, E. Pelantová and J. Tolar. Czechoslovak J. Phys. 51 (2001), no. 4. pp. 281-428.

Lecture material

1. Z. Masáková, E. Pelantová, Teorie čísel, skriptum Czech Technical University, 2010, druhé vydání 2017.
2. Z. Masáková, Diskrétní matematika, eletronicky 2014.

Theses

1. Z. Masáková, Arithmetic and combinatorial properties of beta-integers, habilitační práce, Czech Technical University, 2005.
2. Z. Masáková, Aperiodic Delone sets with self-similarities, Ph.D. thesis at the Czech Technical University, 2000.
3. Z. Masáková, Confronting quasicrystal experiments with a rigorous model, M.Sc. thesis at the Czech Technical University, 1998