How to build a barricade
type: Item
instance of: scholarly article
title: How to build a barricade
zbMATH Open document ID: 0542.52010
DOI: 10.1007/BF01637278
author: János Pach
author: Vojtěch Rödl
author: Peter Frankl
published in: Monatshefte für Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178193
review text: Given a packing \(\mathcal C=\{C_i\mid i\in I\}\) of congruent copies of a strictly convex planar set \(C\) in a parallel strip \(S\) of width \(w\) and a straight line \(\ell\), let \(| \ell \cap \mathcal C|\) denote the sum of the lengths of the segments \(\ell \cap C_i\) over all \(i\in I\). It is proved that \[ \sup_{\mathcal C}\inf_{\ell}| \ell \cap {\mathcal C}| =(\delta(C)+o(1))w, \] where \(\delta (C)\) is the density of the densest packing of congruent copies of \(C\) in the plane. Some generalizations are also considered.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 3861937
zbMATH Keywords: densest packing
zbMATH Keywords: convex sets
zbMATH Keywords: independent random variables
MaRDI profile type: Publication
cites work: Q5824053
cites work: Noetherian modules and Noetherian injective rings
cites work: Q5618791
OpenAlex ID: W1994577906
description: scientific article; zbMATH DE number 3861937