Lawrence Oriented Matroids and a Problem of McMullen on Projective Equivalences of Polytopes

✍ Scribed by J.L. Ramı́rez Alfonsı́n

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 107 KB
• Volume: 22
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2000.0492

✦ Synopsis

Consider the following question introduced by McMullen: Determine the largest integer n = f (d) such that any set of n points in general position in the affine d-space R d can be mapped by a projective transformation onto the vertices of a convex polytope. It is known that 2d + 1 ≤ f (d) < (d + 1)(d + 2)/2 and it is conjectured that f (d) = 2d + 1. In this paper, we show that f (d) < 2d + d+1 2 by using a well-known oriented matroid generalization of the above problem.