The spectrum for large sets of resolvable idempotent Latin squares

Abstract

AbstractAn idempotent Latin square of order is called resolvable and denoted by RILS(v) if the off‐diagonal cells can be resolved into disjoint transversals. A large set of resolvable idempotent Latin squares of order , briefly LRILS(v), is a collection of RILS(v)s pairwise agreeing on only the main diagonal. In this article, an LRILS(v) is constructed for by using multiplier automorphism groups. Hence, there exists an LRILS(v) for any positive integer , except .