Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Point Sets with Many k-Sets

Abstract

For any n , k , n\geq 2k>0 , we construct a set of n points in the plane with \(ne^{\Omega({\sqrt{\log k}})}\) k -sets. This improves the bounds of Erdős, Lovász, et al. As a consequence, we also improve the lower bound for the number of halving hyperplanes in higher dimensions.

Author information

Additional information

Received September 10, 1999, and in revised form January 27, 2000.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tóth, G. Point Sets with Many k-Sets. Discrete Comput Geom 26, 187–194 (2001). https://doi.org/10.1007/s004540010022

Download citation