The Radon number of the three-dimensional integer lattice (Q1423579)
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scientific article; zbMATH DE number 2051387
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Radon number of the three-dimensional integer lattice |
scientific article; zbMATH DE number 2051387 |
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The Radon number of the three-dimensional integer lattice (English)
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7 March 2004
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\textit{S. Onn} [SIAM J. Discrete Math. 4, No. 3, 436--447 (1991; Zbl 0735.52007)] proved that the Radon number \(r(d)\) of the \(d\)-dimensional integer lattice fulfills the inequalities \(5\cdot 2 ^{d-2} +1 \leq r(d) \leq d(2^ d -1) +3\). So in particular, \(11 \leq r(3) \leq 24\). The authors of the present note improve the right inequality up to \(r(3) \leq 17\).
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integer lattice
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Radon number
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Radon partition
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0.8547274
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0.85130596
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0.8419529
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0.8315027
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0.8266779
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0.8245624
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