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On biembedding an idempotent Latin square with its transpose

Author(s): D. M. Donovan | T. S. Griggs | C. Psomas

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXII;
Issue: 1;
Start page: 11;
Date: 2013;
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Keywords: Latin square | idempotent | SOLS | orientable surface | biembedding

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.
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