ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




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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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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Comenius University
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