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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.
A family (X, B1), (X, B2), …, (X, Bq) of q STS(ν)s is a λ-fold large set of STS(v) and denoted by LSTSλ(ν) if every 3-subset of X is contained in exactly λ STS(ν)s of the collection. It is indecomposable and denoted by IDLSTSλ(ν) if there exists no LSTSλ′ (ν) contained in the collection for any λ′ < λ. In 1995, Griggs and Rosa posed a problem: For which values of λ > 1 and orders ν...
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