A result of the existence with three types of interior points (Q1947785)
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scientific article; zbMATH DE number 6158175
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A result of the existence with three types of interior points |
scientific article; zbMATH DE number 6158175 |
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A result of the existence with three types of interior points (English)
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26 April 2013
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The paper introduces a function \(t(k)\), which is the smallest integer such that for every finite point set in the plane in general position (i.e. no three on a line), which has \(t(k)\) interior points, the point set has a subset, such that the interior of the convex hull of this subset contains exactly \(k\), \(k+1\), or \(k+2\) from the interior points of the original point set. The author suggests that these \(t(k)\) numbers can be useful at estimating bounds for some variants of the Erdős-Szekeres theorem. The main result of the paper is that \(t(6)=10\).
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planar point set
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Erdős-Szekeres theorem
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empty triangle
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interior point
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deficient point set
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\((x,y)\)-splitters
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