A lower bound for the number of polygonizations of \(N\) points in the plane (Q2713599)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A lower bound for the number of polygonizations of \(N\) points in the plane |
scientific article |
Statements
10 June 2001
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simple polygon
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polygonization
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point configuration
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A lower bound for the number of polygonizations of \(N\) points in the plane (English)
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Let \(\Phi (N)\) be the maximum number of simple polygons that can be drawn using as vertices a set \(V\) of \(N\) points in the plane, where the maximum is taken over all sets \(V\) of \(N\) points in the plane. It is shown that \(\Phi (N)^{1/N}\) is asymptotically greater than \(3.6\). This improves the previous lower bound of about 3.268; the best known upper bound is 1384000.
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