Gray code orders for $q$-ary words avoiding a given factor

TL;DR

This paper introduces Gray code orderings and algorithms for generating q-ary words that avoid specific factors, generalizing previous results and providing an alternative approach using generalized order relations and word matching techniques.

Contribution

It presents new Gray code orders and a generation algorithm for q-ary words avoiding a given factor, extending earlier work and offering an alternative to existing methods.

Findings

Provides Gray code orderings for factor-avoiding q-ary words

Develops a generating algorithm based on generalized BRGC order relations

Generalizes previous results and offers an alternative approach

Abstract

Based on BRGC inspired order relations we give Gray codes and a generating algorithm for $q$-ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and can be seen as an alternative to those of Squire published in 1996. Among the involved tools, we make use of generalized BRGC order relations, ultimate periodicity of infinite words, and word matching techniques.