Discrete & Computational Geometry

, Volume 26, Issue 2, pp 187–194

Point Sets with Many k-Sets

  • G. Tóth

DOI: 10.1007/s004540010022

Cite this article as:
Tóth, G. Discrete Comput Geom (2001) 26: 187. doi:10.1007/s004540010022


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.

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • G. Tóth
    • 1
  1. 1.Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA and Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364 Budapest, Hungary geza@math-inst.huUSA