2024/07/15 by Gabriele Fici, Jeffrey Shallit, Fici, Gabriele +3 · 1 citation
Mathematics · #Analytic and geometric function theory #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2407.10564
We say a finite word x is a palindromic periodicity if there exist two palindromes p and s such that |x| ≥ |ps| and x is a prefix of the word (ps)ω= pspsps⋯. In this paper we examine the palindromic periodicities occurring in some classical infinite words, such as Sturmian words, episturmian words, the Thue-Morse word, the period-doubling word, the Rudin-Shapiro word, the paperfolding word, and the Tribonacci word, and prove a number of results about them. We also prove results about words with the smallest number of palindromic periodicities.