New sets with large Borsuk numbers
type: Item
instance of: scholarly article
title: New sets with large Borsuk numbers
zbMATH Open document ID: 1028.52012
DOI: 10.1016/S0012-365X(02)00833-6
author: Aicke Hinrichs
author: Christian Richter
published in: Discrete Mathematics
publication date: 2003-09-04T00:00:00Z
review text: The authors construct finite sets in \(\mathbb{R}^{n}\), \(n\geq 298\), which cannot be partitioned into \(n+11\) parts of smaller diameter, thus decreasing the smallest dimension in which Borsuk's conjecture is known to be false. The construction is based on cardinality estimates of certain spherical codes and yields subsets of the unit sphere.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1974989
zbMATH Keywords: Borsuk's conjecture
zbMATH Keywords: spherical codes
zbMATH Keywords: few distance sets
reviewed by: Johann Linhart
MaRDI profile type: Publication
Wikidata QID: Q57382989
cites work: Q4219187
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cites work: Sets with large Borsuk number
description: scientific article; zbMATH DE number 1974989