Geometric permutations and common transversals
type: Item
instance of: scholarly article
title: Geometric permutations and common transversals
zbMATH Open document ID: 0606.52001
DOI: 10.1007/BF02187708
author: B. George
published in: Discrete \& Computational Geometry
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131003
review text: Let \({\mathcal F}\) be a finite family of disjoint convex subsets of the plane and p(\({\mathcal F})\) the family of all geometric permutations of \({\mathcal F}\). For the notion of geometric permutation and other results see the paper of the first two authors and \textit{J. Zaks} [Discrete Math. 54, 271-284 (1985; Zbl 0561.52002). In this paper the authors give the following two results: (1) n-1 \(\leq \max | p({\mathcal F})| \leq \left( \begin{matrix} n\\ 2\end{matrix} \right)\), where the maximum is taken over all families of n pairwise disjoint convex sets. (2) \(| p({\mathcal F})| \leq 8\), for every family \({\mathcal F}\) of at least 11 pairwise disjoint translates of a convex set. The authors notice that in the paper mentioned above the lower bound in (1) has been improved to 2n-2.
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 3979919
zbMATH Keywords: family of disjoint convex subsets of the plane
zbMATH Keywords: geometric permutations
zbMATH Keywords: translates
reviewed by: Dorin Andrica
MaRDI profile type: Publication
cites work: Q5341481
cites work: On common transversals
cites work: Geometric permutations for convex sets
cites work: A Problem of Geometry in R n
cites work: Symmetric twins and common transversals
cites work: Two counterexamples concerning transversals for convex subsets of the plane
OpenAlex ID: W1976350480
description: scientific article; zbMATH DE number 3979919