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Authors: Ruy Fabila-Monroy, Clemens Huemer and Dieter Mitsche

Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty non-convex four-gons with vertices from S is 12n2logn + o(n2logn) and the expected number of empty convex four-gons with vertices from S is Θ(n2).

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