A bound on local minima of arrangements that implies the upper bound theorem
type: Item
instance of: scholarly article
title: A bound on local minima of arrangements that implies the upper bound theorem
zbMATH Open document ID: 0792.52006
DOI: 10.1007/BF02573988
author: Kenneth L. Clarkson
published in: Discrete \& Computational Geometry
publication date: 1994-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/131283
review text: The \(i\)-level of a simple arrangement of hyperplanes in \(E^ d\) is the boundary of the set of all points that are below at most \(i\) hyperplanes. Author proves an upper bound for the number of local minima of the \(i\)- level. From this he deduces by linear programming duality the Upper Bound Theorem for convex polytopes.
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 488285
zbMATH Keywords: dual linear program
zbMATH Keywords: upper bound theorem
zbMATH Keywords: arrangement of hyperplanes
zbMATH Keywords: convex polytopes
reviewed by: Christoph Schulz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 488285