90 citations · 212 across the 5 of their papers we have counts for
5 papers
Antinorms and Radon curves
Horst Martini, Konrad J. Swanepoel
In this paper we consider two notions that have been discovered and rediscovered by geometers and analysts since 1917 up to the present day: Radon curves and antinorms. A Radon cur…
Largest family without A union B contained in C intersect D
Annalisa De Bonis, Gyula O. H. Katona, Konrad J. Swanepoel
Let F be a family of subsets of an n-element set not containing four distinct members such that A union B is contained in C intersect D. It is proved that the maximum size of F und…
Equilateral sets in finite-dimensional normed spaces
Konrad J. Swanepoel
This is an expository paper on the largest size of equilateral sets in finite-dimensional normed spaces.
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…
A problem of Kusner on equilateral sets
Konrad J. Swanepoel
R. B. Kusner [R. Guy, Amer. Math. Monthly 90 (1983), 196--199] asked whether a set of vectors in a d-dimensional real vector space such that the l-p distance between any pair is 1,…