Projective Equivalences of k-neighbourly Polytopes

2013/03/15 by Garcia-Colin, Natalia, Larman, David · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1303.3675

Abstract

We prove the following theorem, which is related to McMullen's problem on projective transformations of polytopes; let 2≤ k≤ \lfloor(d)/(2)\rfloor and ν(d, k) be the largest number such that any set of ν(d,k) points lying in general position in ℝ^d can be mapped by a permissible projective transformation onto the vertices of a k-neighborly polytope, then d + \lceil(d)/(k)\rceil +1 ≤ ν(d, k) < 2d-k +1.

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