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

Akgün, Ö.; Mereb, M.; Vendramin, L.

doi:10.1090/mcom/3696

Enumeration of set-theoretic solutions to the Yang–Baxter equation
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by Ö. Akgün, M. Mereb and L. Vendramin HTML | PDF

Math. Comp. 91 (2022), 1469-1481 Request permission

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 321,931 involutive solutions of size nine, 4,895,272 involutive solutions of size ten and 422,449,480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.

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