Avoidance bases for formulas with reversal
Abstract
In the interest of studying formulas with reversal of high avoidability index, we find $n$-avoidance bases for formulas with reversal for $n\in\{1,2,3\}$. We demonstrate that there is a unique formula with reversal in each of these three bases of highest avoidability index $n+2$; these formulas are $xx$, $xyx\cdot y^R$, and $xyzx\cdot y^R\cdot z^R$, which belong to an infinite family of formulas with reversal that has been the subject of recent study by the authors.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.08025
- arXiv:
- arXiv:1711.08025
- Bibcode:
- 2017arXiv171108025C
- Keywords:
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- Mathematics - Combinatorics;
- 68R15
- E-Print:
- 23 pages, version 2 contains minor revisions suggested by reviewers