Study on the non-periodicity of the generalized Thue-Morse sequences generated by cyclic permutations

2013/05/10 by Eiji Miyanohara, Miyanohara, Eiji
Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1305.2274

This paper has been withdrawn by the author. This article is included in my other article 'E. MIyanohara arXiv:1404.4153. Please ignore this article

openalex publication_date 2013/05/10 · arxiv created 2015/02/25 · arxiv updated 2015/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

First we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutations and p-adic system, and consider the necessary-sufficient condition that it is non-periodic. Moreover if the generalized Thue-Morse sequence is not periodic, then all equally spaced subsequences of the generalized Thue-Morse sequences are not periodic. Finally we apply recently combinatorial transcendence results to the generalized non-periodic Thue-Morse sequence, we can found many transcendental numbers.

Citations

• Transcendence of digital expansions and continued fractions generated by a cyclic permutation and k-adic expansion

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