The number of 3-sets of a finite point set in the plane
Edgar A. Ramos · 1993
A 3-set of a finite set $S$ in the plane is a subset of $S$ of size 3 of the form $S~ \(ca ~h$, for some halfplane $h$. We give an upper bound \(lf11$n$/6\(rf + 3 for the number of 3-sets of any $S$ with $\(bvS\(bv=n~\(<=~6$. This almost matches the known lower bound \(lf11$n$/6\(rf.