Unambiguous 1-Uniform Morphisms

TL;DR

This paper investigates the existence of unambiguous 1-uniform morphisms for any given word, focusing on whether each word can be uniquely mapped by such simple morphisms.

Contribution

It introduces the concept of unambiguous 1-uniform morphisms and studies their existence for arbitrary words.

Findings

Characterization of words admitting unambiguous 1-uniform morphisms

Conditions under which such morphisms exist for given words

Theoretical framework for analyzing morphism unambiguity

Abstract

A morphism h is unambiguous with respect to a word w if there is no other morphism g that maps w to the same image as h. In the present paper we study the question of whether, for any given word, there exists an unambiguous 1-uniform morphism, i.e., a morphism that maps every letter in the word to an image of length 1.