Embedding a Latin square with transversal into a projective space

作者：Pretorius Lou M^*; Swanepoel Konrad J

来源：Journal of Combinatorial Theory - Series A, 2011, 118(5): 1674-1683.

DOI：10.1016/j.jcta.2011.01.013

• Latin square
• Desarguesian projective plane
• Projective space
• Finite geometry
• Transversal
• MOLS

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 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.

• 出版日期2011-7