Enumeration of set-theoretic solutions to the Yang-Baxter equation

TL;DR

This paper employs Constraint Satisfaction techniques to systematically enumerate small set-theoretic solutions to the Yang-Baxter equation, revealing millions of solutions across various sizes and types.

Contribution

It introduces a novel computational approach to enumerate and construct set-theoretic solutions to the Yang-Baxter equation, including involutive solutions and biquandles.

Findings

321,931 involutive solutions of size nine

4,894,272 involutive solutions of size ten

422,449,480 non-involutive solutions of size eight

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.