On the generalization of the study of a letter power substitution on modulo-recurrent words

TL;DR

This paper investigates the complexity of infinite words generated by a specific substitution process involving powers of external letters, focusing on modulo-recurrent and Sturmian words, and establishes their complexity functions.

Contribution

It introduces and analyzes the complexity of k-to-k power letter substitutions on modulo-recurrent and Sturmian words, expanding understanding of their structural properties.

Findings

Derived the complexity function for k-to-k power letter substituted words.

Extended the analysis to modulo-recurrent and Sturmian words.

Provided new insights into the structural behavior of these substituted words.

Abstract

Let us consider an infinite word and $k\geq 1$ an integer. By steps of $k$, we substitute a letter ofthis infinite word by the power of an external letter. The new word obtaining by this process is called $k$ to $k$ substitution of a power letter. After the application of this new notion on modulo-reccurent words and in particular on Sturmian words. We establish the complexity function of those words.