Fixing and hindering systems in combinatorial geometry
type: Item
instance of: scholarly article
title: Fixing and hindering systems in combinatorial geometry
zbMATH Open document ID: 0962.52001
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/231177
full work available at URL: 20.html
review text: Let \(F\) be a set in the boundary of a convex body \(M\subset \mathbb{R}^n\). The set \(F\) is a fixing system (a hindering system) for \(M\) if for every (oriented) direction here is a nontrivial translation \(t\) in this direction such that \(tF\cap \text{int} M\neq \emptyset\) (respectively, \(tF\cap M\neq \emptyset)\). The paper is concerned with various estimates for the minimal cardinality of fixing systems (hindering systems) and the maximal cardinality of primitive fixing systems (primitive hindering systems). Several of the new results are for \(d\)-convex bodies in a Minkowski space \((\mathbb{R}^n\) with a norm).
reviewed by: Rolf Schneider
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 1460296
zbMATH Keywords: \(d\)-convex bodies
zbMATH Keywords: fixing system
zbMATH Keywords: hindering system
author: V. G. Boltyanski
author: Horst Martini
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1460296