English

Avoidance bases for formulas with reversal

Combinatorics 2018-04-13 v2

Abstract

In the interest of studying formulas with reversal of high avoidability index, we find nn-avoidance bases for formulas with reversal for n{1,2,3}n\in\{1,2,3\}. We demonstrate that there is a unique formula with reversal in each of these three bases of highest avoidability index n+2n+2; these formulas are xxxx, xyxyRxyx\cdot y^R, and xyzxyRzRxyzx\cdot y^R\cdot z^R, which belong to an infinite family of formulas with reversal that has been the subject of recent study by the authors.

Cite

@article{arxiv.1711.08025,
  title  = {Avoidance bases for formulas with reversal},
  author = {James Currie and Lucas Mol and Narad Rampersad},
  journal= {arXiv preprint arXiv:1711.08025},
  year   = {2018}
}

Comments

23 pages, version 2 contains minor revisions suggested by reviewers

R2 v1 2026-06-22T22:53:17.984Z