New sets with large Borsuk numbers (Q1406552)
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scientific article; zbMATH DE number 1974989
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New sets with large Borsuk numbers |
scientific article; zbMATH DE number 1974989 |
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New sets with large Borsuk numbers (English)
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4 September 2003
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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.
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Borsuk's conjecture
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spherical codes
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few distance sets
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