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Probability thatn random points are in convex position |
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| Authors: | P Valtr |
| Institution: | 1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic 2. Graduiertenkolleg “Algorithmische Diskrete Mathematik”, Fachbereich Mathematik und Informatik, Freie Universit?t Berlin, Takustrasse 9, 14195, Berlin, Germany |
| Abstract: | We show thatn random points chosen independently and uniformly from a parallelogram are in convex position with probability $$\left( {\frac{{\left( {\begin{array}{*{20}c} {2n - 2} \\ {n - 1} \\ \end{array} } \right)}}{{n!}}} \right)^2 $$ . A finite set of points in the plane is calledconvex if its points are vertices of a convex polygon. In this paper we show the following results: |
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