Trapezoids and Deltoids in Wide Planar Point Sets

We call a set of n points in the Euclidean plane "wide" if at most root n of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is Omega (n(3) log n) and O(n(3) log(2) n) while for deltoids we have Omega (n(5/2)) and O(n(8/3) log n)