Embedding a Latin square with transversal into a projective space
Combinatorics
2011-08-26 v2
Abstract
A Latin square of side n defines in a natural way a finite geometry on 3n points, with three lines of size n and n^2 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, n^2-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 n^2 lines of size k. Extending work of Bruen and Colbourn (J. Combin. Th. Ser. A 92 (2000), 88-94), we characterise embeddings of these finite geometries into projective spaces over skew fields.
Cite
@article{arxiv.1005.3460,
title = {Embedding a Latin square with transversal into a projective space},
author = {Lou M. Pretorius and Konrad J. Swanepoel},
journal= {arXiv preprint arXiv:1005.3460},
year = {2011}
}
Comments
11 pages. This is the revised final preprint version. Added journal reference and doi