On the Palindromic Complexity of Words by Substitution of Letter Power in Modulo-recurrent Words

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Résumé

Let us consider a modulo-recurrent word and an integer k ≥ 1. In steps of k, we substitute one letter of this word by a
power of letter. Then, we obtain a new family of words derived from modulo-recurrent words. After giving the expressions
of the classic complexity functions of these words, we give a necessary condition for a factor of the substituted word to
be a palindrome. Next, we establish a relationship between the palindromic complexity functions of the substituted word
and the modulo-recurrent word. Finally, we determine their palindromic complexity functions for the Sturmian words.

Mots-clés

Sturmian words, modulo-recurrent, substitution, complexity function, palindrome