p. 11 - 20 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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |