2026-08-01T05:16:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23105 2025-10-02T12:37:41Z ddc:004 open_access

On Palindromic Periodicities Fici, Gabriele Shallit, Jeffrey Simpson, Jamie Combinatorics on words Palindrome Symmetric word Palindromic periodicity Walnut Thue-Morse word Sturmian word Episturmian word 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 infinite periodic 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 distinct palindromic periodicities. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Gabriele Fici and Jeffrey Shallit and Jamie Simpson 2025 Is Part Of LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2025.11 urn:nbn:de:0030-drops-231051 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.11 eng https://creativecommons.org/licenses/by/4.0/legalcode