English

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