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

TL;DR

This paper classifies indecomposable set-theoretic solutions to the Yang--Baxter equation for sets of size pq, where p and q are distinct primes, building on recent algebraic results.

Contribution

It provides a complete description of isomorphism classes of such solutions for sets of size pq, advancing understanding of their structure.

Findings

Classification of solutions for size pq

Identification of isomorphism classes

Extension of recent algebraic results

Abstract

Let $p$ and $q$ be different prime numbers. Using recent results of Ced\'o and Okni\'nski, we describe isomorphism classes of indecomposable set-theoretic solutions to the Yang--Baxter equation of cardinality $pq$.