On Parity Vectors of Latin Squares

D. M. Donovan, M. J. Grannell, T. S. Griggs, J. G. Lefevre
2010 Graphs and Combinatorics  
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
more » ... ner 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.
doi:10.1007/s00373-010-0942-9 fatcat:nmcvdn55crcpllqaf2xzizc2ua