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arXiv · 2311.14961

Repetition factorization of automatic sequences

Jeffrey Shallit·Xinhao Xu
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Abstract

Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several (generalized) automatic sequences, including the infinite Fibonacci word, the Thue-Morse word, paperfolding words, and the Rudin-Shapiro sequence.

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Jeffrey Shallit, Xinhao Xu. 2023-11-29. Repetition factorization of automatic sequences. https://arxiv.org/abs/2311.14961

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