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Point Sets with Many k-Sets


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.

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

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Tóth, G. Point Sets with Many k-Sets. Discrete Comput Geom 26, 187–194 (2001).

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