Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

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SINGULAR FACTORS OF GENERALIZED THUE MORSE WORD

Authors

  • Boucaré Kientéga
  • Mahamadi Nana
  • Moussa Barro

Keywords:

infinite words, singular factor, bispecial factor, ancestor of a word

DOI:

https://doi.org/10.17654/0972087126023

Abstract

In this paper, we study the singular factors of Thue-Morse word over an alphabet of size q. At first, we determine the ancestors of factors of word  Then, we describe explicitly the singular factors by using ancestors. At last, we characterize the bispecial factors of  by using the singular factors.

Received: July 23, 2025
Accepted: September 10, 2025

References

[1] V. Berthé and M. Rigo, eds., Combinatorics, Automata and Number Theory, Encyclopedia of Mathematics and its Applications 135, Cambridge University Press, 2010.

[2] J. Cassaigne, Recurrence in infinite words, LNCS, Springer Verlag, 2001, 1-11.

[3] J. Cassaigne, Special Factors of Sequences with Linear Subword Complexity, in Developments in Language Theory II, World Scientific, 1996, pp. 25-34.

[4] J. Cassaigne, Limit values of the recurrence quotient of Sturmian sequences, Theoret. Comput. Sci. 218 (1999), 3-12.

[5] F. Durand, B. Host and Skau, Substitutional dynamical Bratelli diagrams and dimension groups, Ergodic Theory Dynam. System 19 (1999), 953-993.

[6] I. Kaboré and B. Kientéga, Some combinatorial properties of the ternary Thue-Morse word, In. J. Appl. Math. 31(18) (2018), 181-197.

[7] I. Kaboré and B. Kientéga, Abelian Complexity of Thue-Morse Word Over a Ternary Alphabet, Springer International Publishing AG 2017, S. Brlek et al., eds., WORDS 2017, LNCS 10432, 2017, pp. 132-143.

[8] I. Kaboré, B. Kientéga and M. Nana, Recurrence function of the ternary Thue-Morse word, Advances and Applications in Discrete Mathematics 39(1) (2023), 43-72.

[9] I. Kaboré, B. Kientéga and M. Nana, Bispecial factors and separator factors of generalized Thue-Morse word, RAMRES Sciences des Structures de la matière 8(1) (2024), 43-72.

[10] F. Mignosi and P. Séebold, If a DOL-language is k-power-free then it is circular, in: A. Lingas, R. Karlsson, S. Carlsson, eds., ICALP’ 93, Lect. Notes Comp. 700 (1993), 507-518.

[11] M. Morse, Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. 44 (1938), 632.

[12] Š. Starosta, Thue-Morse word and palindromic richness, Kibernetika 48(3) (2012), 361-370.

[13] A. Thue, Die gegenseilige lage gleicher Teile gewisser Zeichenreihen, Norske vid. selsk. Mat. Nat. Kl. 1 (1912), 1-67.

[14] Z.-X. Wen and Z.-Y. Wen, Some properties of the singular words of the Fibonacci word, European J. Combin. 15 (1994), 587-598.

Published

2025-11-21

Issue

Section

Articles

How to Cite

SINGULAR FACTORS OF GENERALIZED THUE MORSE WORD. (2025). Far East Journal of Mathematical Sciences (FJMS), 143(2), 375-398. https://doi.org/10.17654/0972087126023