On Palindromic Periodicities

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.