Indecomposable set-theoretical solutions to the Yang--Baxter equation on a set of size $pq$

Abstract

Let $p$ and $q$ be different prime numbers. Using recent results of Cedó and Okniński, we describe isomorphism classes of indecomposable set-theoretic solutions to the Yang--Baxter equation of cardinality $pq$.

Results are already contained in the paper [Jedliĉka, Premysl; Pilitowska, Agata; Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group. J. Combin. Theory Ser. A 197 (2023), Paper No. 105753, 35 pp.]