Pretorius, Lou M. (Lourens Martin)Swanepoel, Konrad Johann2011-03-032011-03-032011-07L.M. Pretorius, K.J. Swanepoel, Embedding a Latin square with transversal into a projective space, Journal of Combinatorial Theory, Series A, vol. 118, no. 5, pp. 1674-1683 (2011) doi:10.1016/j.jcta.2011.01.0130097-316510.1016/j.jcta.2011.01.013http://hdl.handle.net/2263/15954A Latin square of side n defines in a natural way a finite geometry on 3n 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.en© 2010 Elsevier Inc. All rights reserved.Latin squares and rectanglesDesarguesian projective planeFinite geometryTransversalMOLSMagic squaresProjective spacesPostprint Article