Pretorius, Lou M. and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2011)
*Embedding a Latin square with transversal into a projective space.*
Journal of Combinatorial Theory, Series A, 118 (5).
pp. 1674-1683.
ISSN 0097-3165

## Abstract

A Latin square of side n defines in a natural way a finite geometry on 3. n points, with three lines of size n and n2 lines of size 3. A Latin square of side n with a transversal similarly defines a finite geometry on 3n+1 points, with three lines of size n, n2-n lines of size 3, and n concurrent lines of size 4. A collection of k mutually orthogonal Latin squares defines a geometry on kn points, with k lines of size n and n2 lines of size k. Extending the work of Bruen and Colbourn [A.A. Bruen, C.J. Colbourn, Transversal designs in classical planes and spaces, J. Combin. Theory Ser. A 92 (2000) 88-94], we characterise embeddings of these finite geometries into projective spaces over skew fields.

Item Type: | Article |
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Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |

Additional Information: | © 2011 Elsevier Inc. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 30 Mar 2011 13:24 |

Last Modified: | 20 Feb 2021 04:35 |

URI: | http://eprints.lse.ac.uk/id/eprint/33718 |

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