Recurrence function of the generalized Thue–Morse word

Mahamadi Nana, Boucaré Kientéga and Idrissa Kaboré Notes on Number Theory and Discrete Mathematics Print ISSN 1310–5132, Online ISSN 2367–8275 Volume 32, 2026, Number 3 , Pages 590–609 DOI: 10.7546/nntdm.2026.32.3.590-609 Full paper (PDF, 272 Kb) Mahamadi Nana Département de Mathématiques, UFR Sciences et Techniques, Université Nazi Boni 01BP 1091 Bobo Dioulasso, Burkina Faso Boucaré Kientéga Département de Mathématiques, Informatique et Economie Appliquées, Institut Universitaire Professionnalisant, Université Daniel Ouezzin Coulibaly BP 176 D\’edougou, Burkina Faso Idrissa Kaboré Département de Mathématiques, UFR Sciences et Techniques, Université Nazi Boni 01BP 1091 Bobo Dioulasso, Burkina Faso This paper is devoted to the study of the recurrence function of q -ary Thue–Morse word t q . After giving the structure of singular factors, we describe the maximal return time of factors of t q . We conclude by determining the recurrence function of generalized Thue–Morse word. Ⓒ 2026 by the Authors. This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0) . Nana, M., Kientéga, B., & Kaboré, I. (2026). Recurrence function of the generalized Thue–Morse word. Notes on Number Theory and Discrete Mathematics , 32(3), 590-609, DOI: 10.7546/nntdm.2026.32.3.590-609.