On weighted sums of numbers of convex polygons in point sets

Clemens Huemer, Deborah Oliveros, Pablo Pérez-Lantero +2

Let $S$ be a set of $n$ points in general position in the plane, and let $X_{k,\ell }(S)$ be the number of convex $k$-gons with vertices in $S$ that have exactly $\ell$ points of $S…