Tight bounds on the expected number of holes in random point sets

Martin Balko, Manfred Scheucher, Pavel Valtr

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…