Latin Square Thue-Morse Sequences are Overlap-Free

TL;DR

This paper introduces a new morphism based on Latin squares that generalizes the Thue-Morse sequence and proves that its fixed points are overlap-free, extending previous results in combinatorics on words.

Contribution

It defines a novel morphism derived from Latin squares and proves that its fixed points are overlap-free, generalizing earlier work on Thue-Morse sequences.

Findings

Fixed points of the new morphism are overlap-free sequences.

The morphism generalizes the classical Thue-Morse morphism.

Extends previous results by Allouche-Shallit and Frid.

Abstract

We define a morphism based upon a Latin square that generalizes the Thue-Morse morphism. We prove that fixed points of this morphism are overlap-free sequences generalizing results of Allouche - Shallit and Frid.