Palindromes in infinite ternary words
Ľubomíra Dvořáková, Edita Pelantová, Štěpán Starosta · RAIRO - Theoretical Informatics and Applications · 2009
We study infinite words u over an alphabet satisfying the property , where denotes the number of palindromic factors of length n occurring in the language of u. We study also infinite words satisfying a stronger property : every palindrome of u has exactly one palindromic extension in u. For binary words, the properties and coincide and these properties characterize Sturmian words, i.e., words with the complexity C(n) = n + 1 for any . In this paper, we focus on ternary infinite words with the language closed under reversal. For such words u, we prove that if C(n) = 2n + 1 for any , then u satisfies the property and moreover u is rich in palindromes. Also a sufficient condition for the property is given. We construct a word demonstrating that on a ternary alphabet does not imply .