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

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.

13 pages, 8 tables. Accepted for publication in Mathematics of Computation

References in corpus (3)

• Semigroups of I-type
• Bi-skew braces and Hopf Galois structures
• Retractability of set theoretic solutions of the Yang-Baxter equation

Cited by in corpus (6)

• Construction and the ergodicity properties of dual unitary quantum circuits
• Skew braces: a brief survey
• Incremental SAT-Based Enumeration of Solutions to the Yang-Baxter Equation
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation
• Composable Constraint Models for Permutation Enumeration
• On the enumeration of finite $L$-algebras