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On parity vectors of Latin squares

Donovan, D. M.; Grannell, M. J.; Griggs, T. S. and Lefevre, J. G. (2010). On parity vectors of Latin squares. Graphs and Combinatorics, 26(5) pp. 673–684.

URL: http://dx.doi.org/10.1007/s00373-010-0942-9
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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.

Item Type: Journal Article
Copyright Holders: 2010 Springer
ISSN: 0911-0119
Keywords: Latin square; orientable surface; biembedding; parity vector; group; Steiner quasigroup; Steiner loop
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 24610
Depositing User: Mike Grannell
Date Deposited: 09 Nov 2010 23:07
Last Modified: 30 Nov 2012 10:37
URI: http://oro.open.ac.uk/id/eprint/24610
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