On Parity Vectors of Latin Squares |
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Authors: | D M Donovan M J Grannell T S Griggs J G Lefevre |
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Institution: | 1. Centre for Discrete Mathematics and Computing, University of Queensland, St. Lucia, 4072, Australia 2. Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
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Abstract: | The parity vectors of two Latin squares of the same side n provide a necessary condition for the two squares to be biembeddable in an orientable surface. We investigate constraints
on the parity vector of a Latin square resulting from structural properties of the square, and show how the parity vector
of a direct product may be obtained from the parity vectors of the constituent factors. Parity vectors for Cayley tables of
all Abelian groups, some non-Abelian groups, Steiner quasigroups and Steiner loops are determined. Finally, we give a lower
bound on the number of main classes of Latin squares of side n that admit no self-embeddings. |
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