Abstract:We study the classical complexity of k to k insertion words of a letter in Sturmian words. Then, we determine the Abelian complexity and palindromic complexity of these words. Finally, we show that the k to k insertion of a letter x in Sturmian words preserves the palindromic richness of Sturmian words if and only if k = 1.

In this paper, we define from an infinite word u, the word by k to k erasure of a letter and the word of the erased letters. Then, we study the classical complexity and the palindromic complexity of these words in the case of modulo-recurrent words and more specifically in the Sturmian case.