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On Palindromic Periodicities

Authors Gabriele Fici , Jeffrey Shallit , Jamie Simpson

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics on words
Keywords
  • Combinatorics on words
  • Palindrome
  • Symmetric word
  • Palindromic periodicity
  • Walnut
  • Thue-Morse word
  • Sturmian word
  • Episturmian word

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Abstract

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.

Cite As Get BibTex

Gabriele Fici, Jeffrey Shallit, and Jamie Simpson. On Palindromic Periodicities. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.11

Author Details

Gabriele Fici
  • Dipartimento di Matematica e Informatica, University of Palermo, Italy
Jeffrey Shallit
  • School of Computer Science, University of Waterloo, Canada
Jamie Simpson
  • 130 Preston Point Rd, East Fremantle, WA 6158, Australia

Funding

  • Fici, Gabriele: Project MUR PRIN 2022 APML - 20229BCXNW.
  • Shallit, Jeffrey: Funded by NSERC under grants 2018-04118 and 2024-03725.

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