Annals of Combinatorics 1 (1997) 107-118

Holey Self-orthogonal Latin Squares with Symmetric Orthogonal Mates

F.E. Bennett, H. Zhang, and L. Zhu

Department of Math., Mount Saint Vincent University, Halifax, Nova Scotia B3M 2J6, Canada

Department of Computer Science, University of Iowa, Iowa City, IA 52240, USA

Department of Math., Suzhou University, Suzhou 215006, P.R. China

Received July 30, 1996

AMS Subject Classification: 05B15

Abstract. We improve the existence results for holey self-orthogonal Latin squares with symme- tric orthogonal mates (HSOLSSOMs) and show that the necessary conditions for the existence of a HSOLSSOM of type hn are also sufficient with at most 28 pairs (h, n) of possible exceptions.

Keywords: Latin square, orthogonal mate, holes, self-orthogonal Latin square


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