The Morphisms With Unstackable Image Words

TL;DR

This paper explores the properties of overlap-free and square-free morphisms, introducing a new counterexample and generalizing key combinatorial properties to better classify these morphisms.

Contribution

It presents a counterexample to existing classifications and generalizes properties of the Leech square-free morphism for broader understanding.

Findings

Identified the Leech square-free morphism as a counterexample.

Generalized combinatorial properties of the Leech morphism.

Enhanced classification methods for overlap-free and square-free morphisms.

Abstract

In an attempt to classify all of the overlap-free morphisms constructively using the Latin-square morphism, we came across an interesting counterexample, the Leech square-free morphism. We generalize the combinatorial properties of the Leech square-free morphism to gain insights on a larger class of both overlap-free morphisms and square-free morphisms.