Fixed points avoiding Abelian $k$-powers

TL;DR

This paper proves that it is possible to algorithmically determine whether the fixed point of a morphism avoids Abelian k-powers, under broad conditions, contributing to the understanding of pattern avoidance in infinite words.

Contribution

It establishes the decidability of avoiding Abelian k-powers in fixed points of morphisms under general conditions, advancing the theory of pattern avoidance.

Findings

Decidability of Abelian k-power avoidance in fixed points

Applicable under broad conditions for morphisms

Enhances understanding of pattern avoidance in combinatorics on words

Abstract

We show that the problem of whether the fixed point of a morphism avoids Abelian $k$-powers is decidable under rather general conditions