, Volume 26, Issue 2, pp 187-194
Date: 01 Jan 2001

Point Sets with Many k -Sets

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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.