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

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.