Counting facets and incidences
type: Item
instance of: scholarly article
title: Counting facets and incidences
zbMATH Open document ID: 0747.68092
DOI: 10.1007/BF02187848
author: Pankaj K. Agarwal
author: Boris Aronov
published in: Discrete \& Computational Geometry
publication date: 1992-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/131201
review text: The authors show a tight bound on the maximum number of facets bounding \(n^{d-2}\leq m\leq n^ d\) distinct cells in arrangements on \(n\) hyperplanes in \(R^ d\). This yields a tight bound on the number of incidences between \(n\) hyperplanes in \(R^ d\) and \(m\) vertices in their arrangement. The same technique is employed to obtain a tight bound on the number of faces bounding all nonconvex cells in arrangements of triangles in \(R^ 3\). Some open questions are given.
reviewed by: Hans-Dietrich Hecker
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 54914
zbMATH Keywords: tight bounds
zbMATH Keywords: facets
zbMATH Keywords: arrangements
MaRDI profile type: Publication
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OpenAlex ID: W2037597410
Wikidata QID: Q56454603
description: scientific article; zbMATH DE number 54914