The blocking numbers of convex bodies
type: Item
instance of: scholarly article
title: The blocking numbers of convex bodies
zbMATH Open document ID: 0960.52004
author: N. Delaunay
published in: Discrete \& Computational Geometry
publication date: 2001-05-17T00:00:00Z
review text: The blocking number \(b(K)\) of a convex body \(K\) in Euclidean \(n\)-space \(\mathbb{R}^n\) is defined as the smallest possible number of disjoint translates of \(K\) which touch from outside the boundary of \(K\) and which prevent any additional disjoint translate of \(K\) from touching \(K\) from outside. The authors present a lower bound of the blocking number of each centrally symmetric convex body \(C\) based on the so-called \(M\)-curvature of \(C\). They also prove that there are infinitely many dimensions \(n\) such that a centrally symmetric convex body \(C\subset\mathbb{R}^n\) and a subspace \(R\) can be found with \(b(C)\leq b(C\cap R)+1\). It is shown that the blocking number of an \(n\)-dimensional cube is \(2^n\). Moreover, the blocking number of a three-dimensional ball is 6, and of a four-dimensional ball is 9.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 1507674
zbMATH Keywords: curvature
zbMATH Keywords: blocking number
zbMATH Keywords: translates
zbMATH Keywords: lower bound
zbMATH Keywords: centrally symmetric convex body
zbMATH Keywords: cube
zbMATH Keywords: ball
MaRDI profile type: Publication
full work available at URL: s004540010032
OpenAlex ID: W1985734458
DOI: 10.1007/S004540010032
description: scientific article; zbMATH DE number 1507674