A problem of McMullen on the projective equivalences of polytopes
type: Item
instance of: scholarly article
title: A problem of McMullen on the projective equivalences of polytopes
zbMATH Open document ID: 0573.52009
DOI: 10.1016/S0195-6698(85)80006-8
author: Raul Cordovil
author: Ilda P. Silva
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: In terms of convexity for oriented matroids the authors give a version of the following problem of McMullen [cf. Contributions to geometry, Proc. Symp., Siegen 1978, 92-130 (1979; Zbl 0445.52006)]: ''Determine the largest number \(\partial (d)\) of points, lying in general position in \(R^ d\), which may be mapped by a permissible projective transformation onto the set of vertices of a convex polytope''. It is proved, that for every orientation \(\Theta\) of the uniform matroid \(U_{2r-1,r}\) with \(r\geq 3\), there is an acyclic reorientation, such that all 2r-1 points are extreme. This result generalizes the inequality of Larman \(\partial (r-1)\geq 2r-1\) for the above problem of McMullen.
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 52A01
zbMATH DE Number: 3915110
zbMATH Keywords: problem of McMullen
zbMATH Keywords: projective transformation
zbMATH Keywords: convex polytope
reviewed by: Valeriu Soltan
MaRDI profile type: Publication
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full work available at URL: s0195-6698(85)80006-8
OpenAlex ID: W2011599629
description: scientific article; zbMATH DE number 3915110