A combinatorial property of points and ellipsoids
type: Item
instance of: scholarly article
title: A combinatorial property of points and ellipsoids
zbMATH Open document ID: 0697.52005
DOI: 10.1007/BF02187798
author: Imre Bárány
author: D. G. Larman
published in: Discrete \& Computational Geometry
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131125
review text: Let \({\mathbb{R}}^ d\) be d-dimensional Euclidean space. The authors prove that there exists a constant \(c_ d>0\) with the following property: for every finite set \(X\subset {\mathbb{R}}^ d\) there is \(Y\subset X\) with at most \(\lfloor (1/4)d(d+3)\rfloor +1\) points such that the arbitrary ellipsoid \(E\supset Y\) contains at least \(c_ d| X|\) points. It is also shown that the bound of the number of points of Y is best possible.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 4142920
zbMATH Keywords: quadric
zbMATH Keywords: ellipsoid
zbMATH Keywords: points
MaRDI profile type: Publication
cites work: A combinatorial result about points and balls in Euclidean space
cites work: On a Problem of Sidon in Additive Number Theory, and on some Related Problems
cites work: Q3254327
cites work: A combinatorial result on points and circles on the plane
OpenAlex ID: W1973020432
description: scientific article; zbMATH DE number 4142920