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
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.
|Additional Information:||© 2011 Elsevier Inc.|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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