Enumeration of set-theoretic solutions to the Yang-Baxter equation
Group Theory
2022-06-03 v2 Quantum Algebra
Abstract
We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang-Baxter equation of small size. We show that there are 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.
Keywords
Cite
@article{arxiv.2008.04483,
title = {Enumeration of set-theoretic solutions to the Yang-Baxter equation},
author = {Ö. Akgün and M. Mereb and L. Vendramin},
journal= {arXiv preprint arXiv:2008.04483},
year = {2022}
}
Comments
13 pages, 8 tables. Accepted for publication in Mathematics of Computation