Weak abelian periodicity of infinite words

TL;DR

This paper investigates the properties of weak abelian periodicity in infinite words, exploring its relationship with balance and frequency, and providing conditions for fixed points of morphisms and minimal subshifts.

Contribution

It establishes necessary and sufficient conditions for weak abelian periodicity in fixed points of uniform binary morphisms and analyzes its role in minimal subshifts.

Findings

Characterization of weak abelian periodicity in fixed points of morphisms

Conditions linking weak abelian periodicity with balance and frequency

Insights into weak abelian periodicity in minimal subshifts

Abstract

We say that an infinite word w is weak abelian periodic if it can be factorized into finite words with the same frequencies of letters. In the paper we study properties of weak abelian periodicity, its relations with balance and frequency. We establish necessary and sufficient conditions for weak abelian periodicity of fixed points of uniform binary morphisms. Also, we discuss weak abelian periodicity in minimal subshifts.