Title: Indecomposable set-theoretical solutions to the Yang-Baxter equation of size $p^2$

Abstract: The quantum Yang-Baxter equation is a braiding condition on complex vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. A combinatorial approach is the investigation of set-theoretic solutions to the Yang--Baxter equation and their associated algebraic structures. In this article, we focus on indecomposable set-theoretic solutions to the Yang--Baxter equation. More specifically, we give a full classification of those which are of size $p^2$.