Some Remarks on Palindromic Periodicities
Gabriele Fici, Jeffrey Shallit, Jamie Simpson

TL;DR
This paper investigates palindromic periodicities in various classical infinite words, analyzing their properties and identifying words with minimal palindromic periodicities.
Contribution
It provides new results on the occurrence and structure of palindromic periodicities in well-known infinite words and characterizes words with minimal such periodicities.
Findings
Identified palindromic periodicities in Sturmian, episturmian, Thue-Morse, and other words.
Proved structural properties of words with minimal palindromic periodicities.
Established connections between palindromic periodicities and classical infinite words.
Abstract
We say a finite word is a palindromic periodicity if there exist two palindromes and such that and is a prefix of the word . 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.
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Taxonomy
TopicsAnalytic and geometric function theory · Graph theory and applications
