A note on the avoidability of binary patterns with variables and reversals

TL;DR

This paper characterizes all unary and binary patterns with variables and reversals, extending avoidability results to ensure the generation of aperiodic words, building on recent studies of such variables.

Contribution

It provides a comprehensive characterization of patterns with variables and reversals, extending avoidability results to include aperiodic words.

Findings

Characterization of unary and binary patterns with reversals

Extension of avoidability to enforce aperiodic words

Results align with recent studies in the area

Abstract

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular cases. We show that the results are not surprising at all in the general case, and extend the avoidability of these patterns to enforce aperiodic words.