A lower bound theorem for polytope pairs
type: Item
instance of: scholarly article
title: A lower bound theorem for polytope pairs
zbMATH Open document ID: 0598.52005
DOI: 10.1016/0097-3165(85)90068-8
author: M. R. Emamy-Khansary
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: Let (P,F) be a pair of polytopes of class (d,n,u), i.e. P is a simple d- polytope in \({\mathbb{R}}^ d\) with n facets, F is a facet of P such that precisely u facets of P intersect F. If k denote the number of vertices of P not in F, the author gives a sharp upper bound for the number of vertices of the facet F in terms of k, n, and u, thus generalizing a result of \textit{V. Klee} [Acta. Math. 133, 1-25 (1974; Zbl 0307.90042)] who gave a proof for \(u=n-1\). This theorem implies Barnette's result on the lower bound of the number of vertices of a simple d-polytope in terms of the number of its facets.
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 3964868
zbMATH Keywords: upper bound of vertices
zbMATH Keywords: truncation-polytope
zbMATH Keywords: pair of polytopes
zbMATH Keywords: simple d-polytope
reviewed by: Bernd Kind
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90068-8
OpenAlex ID: W2144723754
cites work: The minimum number of vertices of a simple polytope
cites work: A proof of the lower bound conjecture for convex polytopes
cites work: Q5547252
cites work: Polytope pairs and their relationship to linear programming
cites work: A comparison of primal and dual methods of linear programming
cites work: A generalized lower‐bound conjecture for simplicial polytopes
cites work: Incidence graphs of convex polytopes
description: scientific article; zbMATH DE number 3964868