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Tight Bounds on the Expected Number of Holes in Random Point Sets
For integers $$d\ge 2$$ and $$k\ge d+1$$ , a k-hole in a set S of points in general position in $$\mathbb {R}^d$$ is a k-tuple of points from S in convex position such that the interior of their convex hull does not contain any point from S. For a convex …