The wheels of the OLS polytope: Facets and separation

Orthogonal Latin squares (OLS) are fundamental combinatorial objects with important theoretical properties and interesting applications. OLS can be represented by integer points satisfying a certain system of equalities. The convex hull of these points is the OLS polytope. This paper adds to the description of the OLS polytope by providing non-trivial facets arising from wheels. Specifically, for each wheel of size five, we identify the variables that can be added to the induced inequality, thus obtaining all distinct families of maximally lifted wheel inequalities. Each of these families induces facets of the OLS polytope which can be efficiently separated in polynomial time.