Further results on large sets of resolvable idempotent Latin squares

摘要

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, it is established that there exists an LRILS(v) for any positive integer v≥3, except for v=6, and except possibly for v∈{14,20,22,26,28,34,35,38,40,42,46,50,55,62}.