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: 673-684. doi:10.1007/s00373-010-0942-9

Author Donovan, D. M.
Grannell, M. J.
Griggs, T. S.
Lefevre, J. G.
Title On parity vectors of Latin squares
Journal name Graphs and Combinatorics   Check publisher's open access policy
ISSN 0911-0119
Publication date 2010-09
Sub-type Article (original research)
DOI 10.1007/s00373-010-0942-9
Volume 26
Issue 5
Start page 673
End page 684
Total pages 12
Place of publication Tokyo, Japan
Publisher Springer Japan KK
Collection year 2011
Language eng
Formatted 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. © 2010 Springer.
Keyword Latin square
Orientable surface
Parity vector
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published under Original Paper

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
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Created: Sun, 12 Sep 2010, 00:04:12 EST