Remarks on the upper bound theorem.
type: Item
instance of: scholarly article
title: Remarks on the upper bound theorem.
zbMATH Open document ID: 1042.52006
DOI: 10.1016/S0097-3165(03)00137-7
author: Isabella Novik
published in: Journal of Combinatorial Theory. Series A
publication date: 2004-01-06T00:00:00Z
review text: An extension of the known upper bound theorem for convex polytopes in \(\mathbb{R}^d\) is the so-called strong upper bound theorem due to Gil Kalai, holding for the boundary complexes of simplicial polytopes and their full-dimensional subcomplexes. The author gives an extension of this theorem for even-dimensional simplicial manifolds. As a second result, the paper contains an upper bound theorem for odd-dimensional, centrally symmetric simplicial complexes (i.e., simplicial complexes for which there exists an involution \(\psi: K\to K\) that fixes none of their faces).
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 2022051
zbMATH Keywords: upper bound theorem
zbMATH Keywords: simplicial manifold
zbMATH Keywords: simplicial complex
zbMATH Keywords: simplicial polytope
zbMATH Keywords: strong upper bound theorem
zbMATH Keywords: \(k\)-neighbourly polytope
reviewed by: Horst Martini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2022051