Donovan, D. M.; Grannell, M. J.; Griggs, T. S. and Lefevre, J. G.
(2010).
*Graphs and Combinatorics*, 26(5) pp. 673–684.

URL: | http://dx.doi.org/10.1007/s00373-010-0942-9 |
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Google Scholar: | Look up in Google Scholar |

## 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 |
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Copyright Holders: | 2010 Springer |

ISSN: | 0911-0119 |

Keywords: | Latin square; orientable surface; biembedding; parity vector; group; Steiner quasigroup; Steiner loop |

Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 24610 |

Depositing User: | Mike Grannell |

Date Deposited: | 09 Nov 2010 23:07 |

Last Modified: | 04 Oct 2016 10:49 |

URI: | http://oro.open.ac.uk/id/eprint/24610 |

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