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
Frank.Bennett@msvu.ca

Department of Computer Science, University of Iowa, Iowa City, IA 52240, USA
hazhang@ihgp.ih.lucent.com

Department of Math., Suzhou University, Suzhou 215006, P.R. China
lzhu@nsad.suda.edu.cn

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


References

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