Large sets of resolvable idempotent Latin squares

An idempotent Latin square of order v is called resolvable and denoted by RILS ( v ) if the v ( v − 1 ) off-diagonal cells can be resolved into v − 1 disjoint transversals. A large set of resolvable idempotent Latin squares of order v , briefly LRILS ( v ) , is a collection of v − 2 RILS ( v ) s pairwise agreeing on only the main diagonal. In this paper we display some recursive and direct constructions for LRILSs.