On a sequence related to that of Thue–Morse and its applications

descriptionPublicationkeyboard_double_arrow_right Article 01 May 2007 English Publisher:Elsevier BVJournal:Discrete Mathematics, volume 307, pages 1,082-1,093 (issn: 0012-365X,

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Authors: Arturas Dubickas;

doi: 10.1016/j.disc.2006.08.001

On a sequence related to that of Thue–Morse and its applications

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Abstract

Let \((a_b)\) be the sequence of runlengths of the famous Thue-Morse sequence, i.e., \((a_n)= 1\,2\,1\,1\,2\,2\,2\,1\,1\,2\dots\). Using the generating function of this sequence and tools from combinatorics on words, the author obtains nice results in distribution modulo 1. For example: for any real number \(\varepsilon\neq 0\), the sequence \(\{\varepsilon(-{3\over 2})^n\}\) has a limit point larger than 0.466. Please note the reference [2] appeared [Ann. Math. (2) 165, 547--565 (2007; Zbl 1195.11094)].

Related Organizations

Vilnius University
Lithuania

Keywords

radix representation, Combinatorics on words, Thue–Morse sequence, Distribution modulo 1, Radix representation, distribution modulo 1, Words, words, Theoretical Computer Science, Discrete Mathematics and Combinatorics, Radix representation; digital problems, General theory of distribution modulo \(1\), Thue-Morse sequence

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