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An idempotent Latin square of order v 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 v, briefly LRILS(v), is a collection of 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...
Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. If the second square is the transpose of the first one, we say that the first square is r-self-orthogonal, denoted by r-SOLS(v). It has been proved that for any integer v⩾28, there exists an r-SOLS(v) if and only if v⩽r⩽v2 and r∉{v+1,v2-1}. In this paper, we give an almost complete solution...
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