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

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 ofletter. Then, we obtaina newfamily of wordsderived frommodulo recurrent words. After givingthe 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.