29 citations · 40 across the 5 of their papers we have counts for
5 papers
Embedding a Latin square with transversal into a projective space
Lou M. Pretorius, Konrad J. Swanepoel
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 si…
The Sylvester-Gallai Theorem, colourings and algebra
L. M. Pretorius, K. J. Swanepoel
Our point of departure is the following simple common generalisation of the Sylvester-Gallai theorem and the Motzkin-Rabin theorem: Let S be a finite set of points in the plane, wi…
Sylvester-Gallai Theorems for Complex Numbers and Quaternions
Noam Elkies, Lou M. Pretorius, Konrad J. Swanepoel
A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theo…
Blocking sets in small finite linear spaces II
L. M. Pretorius, K. J. Swanepoel
The contents of this paper has been incorporated into math.CO/0308288.
Blocking sets in small finite linear spaces
L. M. Pretorius, K. J. Swanepoel
We classify all finite linear spaces on at most 15 points admitting a blocking set. There are no such spaces on 11 or fewer points, one on 12 points, one on 13 points, two on 14 po…