Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes
type: Item
instance of: scholarly article
title: Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes
zbMATH Open document ID: 0790.52003
DOI: 10.1007/BF01202351
author: Y. S. Kupitz
published in: Combinatorica
publication date: 1994-01-13T00:00:00Z
review text: Let \(k\) be any natural number. The author shows that each subset \(V\) of Euclidean 3-space \(E^ 3\) (which spans \(E^ 3\) affinely) with at least \(4k+1\) points possesses some subset spanning a plane \(J\) such that each open half-space determined by \(J\) contains at least \(k\) points of \(V\).
reviewed by: Bernd Kind
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 484130
zbMATH Keywords: Helly-type
zbMATH Keywords: separation of points
MaRDI profile type: Publication
cites work: Partitions of mass-distributions and of convex bodies by hyperplanes
cites work: On a generalization of the Gallai-Sylvester theorem
full work available at URL: https://doi.org/10.1007/bf01202351
OpenAlex ID: W2000501530
description: scientific article; zbMATH DE number 484130