Avoidability index for binary patterns with reversal

TL;DR

This paper introduces the avoidability index for binary patterns with reversal, determining the minimal number of symbols needed to avoid certain pattern repetitions in words.

Contribution

It provides a systematic method to compute the avoidability index for patterns over an extended alphabet including reversals.

Findings

Calculated avoidability indices for various binary patterns with reversal

Established bounds for avoidability indices in specific pattern classes

Extended classical avoidability results to patterns with reversal

Abstract

For every pattern $p$ over the alphabet $\{x,y,x^R,y^R\}$, we specify the least $k$ such that $p$ is $k$-avoidable.