On biembedding an idempotent Latin square with its transpose
D. M. Donovan, T. S. Griggs and C. Psomas Received: July 7, 2011;
Revised: September 28, 2012;
Accepted: October 6, 2012
Abstract.
Let L be an idempotent Latin square of side n, thought of as a set of ordered triples (i, j, k) where L(i, j) = k. Let I be the set of triples (i, i, i). We consider the problem of biembedding the triples of L - I with the triples of L' - I, where L' is the transpose of L, in an orientable surface. We construct such embeddings for all doubly even values of n.
Keywords:
Latin square; idempotent; SOLS; orientable surface; biembedding.
AMS Subject classification:
Primary: 05B15, 05C10
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