The maximum number of triangles in arrangements of pseudolines
type: Item
instance of: scholarly article
title: The maximum number of triangles in arrangements of pseudolines
zbMATH Open document ID: 0837.51001
author: Jean-Pierre Roudneff
published in: Journal of Combinatorial Theory. Series B
publication date: 1996-01-29T00:00:00Z
review text: The main result of this paper is the proof of the following conjecture of Grünbaum: any arrangement of \(n\geq 9\) pseudolines in the real projective plane has at most \({1 \over 3} n(n - 1)\) triangular faces. The result does not hold for \(n \leq 8\). The structure of extremal examples is explored and an infinite family of non simple arrangements with \({1 \over 3} n(n - 1)\) triangles is constructed. As an application, it is shown that the number of simplices in arrangements of \(n \geq 10\) pseudoplanes is always less than \({1 \over 12} n(n - 1) (n - 2)\).
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 839135
zbMATH Keywords: arrangement of pseudolines
zbMATH Keywords: cell complexes
zbMATH Keywords: combinatorial geometry
zbMATH Keywords: oriented matroids
MaRDI profile type: Publication
OpenAlex ID: W2017820487
DOI: 10.1006/JCTB.1996.0006
description: scientific article; zbMATH DE number 839135