Repetition factorization of automatic sequences
Formal Languages and Automata Theory
2023-11-30 v2 Discrete Mathematics
Combinatorics
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.
Cite
@article{arxiv.2311.14961,
title = {Repetition factorization of automatic sequences},
author = {Jeffrey Shallit and Xinhao Xu},
journal= {arXiv preprint arXiv:2311.14961},
year = {2023}
}