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Embedding a Latin square with transversal into a projective space

Pretorius, Lou M. and Swanepoel, Konrad (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

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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
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2011 Elsevier Inc.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 30 Mar 2011 13:24
URL: http://eprints.lse.ac.uk/33718/

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