A family of formulas with reversal of high avoidability index

TL;DR

This paper introduces an infinite family of formulas with reversal, demonstrating their avoidability index ranges between 4 and 5, and highlighting the simplicity and size of these formulas compared to previously known complex formulas.

Contribution

The paper presents a new infinite family of formulas with reversal, establishing bounds on their avoidability index and showing many have an index of 5, expanding understanding of avoidability with reversal.

Findings

Several family members have avoidability index 5

The family is large and structurally simple

Bounds on avoidability index between 4 and 5

Abstract

We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting due to its size and the simple structure of its members. For each $k\in\{4,5\}$, there are several previously known avoidable formulas (without reversal) of avoidability index $k$, but they are small in number and they all have rather complex structure.