# Point sets with many $k$-sets

## ABSTRACT

For any $n$, $k$, $n\ge 2k>0$, we construct a set of $n$ points in the plane with $ne^{\Omega\left({\sqrt{\log k}}\right)}$ $k$-sets. This improves the bounds of Erd\H os, Lov\'asz, et al. As a consequence, we also improve the lower bound of Edelsbrunner for the number of halving hyperplanes in higher dimensions.

Speaker's Contact Info: toth(at-sign)math.mit.edu