Binary Morphisms to Ultimately Periodic Words

TL;DR

This paper characterizes binary morphisms that transform infinite words into ultimately periodic words, showing that such morphisms must map 0 and 1 to commuting words, thus providing a classification criterion.

Contribution

It introduces a classification of binary morphisms based on the commutation property of their images, linking morphism structure to periodicity of the resulting words.

Findings

Morphisms mapping non-ultimately periodic words to ultimately periodic words have commuting images of 0 and 1.

The paper provides a necessary condition for such morphisms to produce ultimately periodic words.

This classification aids in understanding the structure of morphisms related to periodicity in infinite words.

Abstract

This paper classifies binary morphisms that map to ultimately periodic words. In particular, if a morphism h maps an infinite non-ultimately periodic word to an ultimately periodic word then it must be true that h(0) commutes with h(1).