Danziger, Peter; Wanless, Ian M. and Webb, Bridget S.
(2011).
*Journal of Combinatorial Theory, Series A*, 118(3) pp. 796–807.

DOI (Digital Object Identifier) Link: | http://doi.org/10.1016/j.jcta.2010.11.011 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

We show for all n not in that there exists a latin square of order n that contains two entries γ_1 and γ_2 such that there are some transversals through γ_1 but they all include γ_2 as well. We use this result to show that if n>6 and n is not of the form 2p for a prime p greater or equal to 11 then there exists a latin square of order n that possesses an orthogonal mate but is not in any triple of MOLS. Such examples provide pairs of 2-maxMOLS.

Item Type: | Journal Article |
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Copyright Holders: | 2011 Elsevier |

ISSN: | 0097-3165 |

Keywords: | Latin square; Monogamous square; MOLS; maxMOLS; Transversal Latin square; Monogamous square; MOLS; maxMOLS; Transversal Latin square; Monogamous square; MOLS; maxMOLS; Transversal |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 25356 |

Depositing User: | Bridget Webb |

Date Deposited: | 27 Jan 2011 14:12 |

Last Modified: | 15 Jan 2016 15:25 |

URI: | http://oro.open.ac.uk/id/eprint/25356 |

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