Abstract
We consider the generalized Thue-Morse word on the alphabet Σ = {0, 1, 2}. The object of the research is arithmetic progressions in this word, which are sequences consisting of identical symbols. Let A(d) be a function equal to the maximum length of an arithmetic progression with the difference d in the generalized Thue-Morse word. If n, d are positive integers and d is less than 3n, then the upper bound for A(d) is 3n + 6 and is attained with the difference d = 3n − 1.
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Parshina, O. G. (2015). On arithmetic progressions in the generalized Thue-Morse word. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9304, pp. 191–196). Springer Verlag. https://doi.org/10.1007/978-3-319-23660-5_16
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