For any n, k, n ≥ 2k > 0, we construct a set of n points in the plane with neΩ(√logk) k-sets. This improves the bounds of Erdos, Lovász, et al. As a consequence, we also improve the lower bound for the number of halving hyperplanes in higher dimensions.
CITATION STYLE
Tóth, G. (2001). Point sets with many k-sets. Discrete and Computational Geometry, 26(2), 187–194. https://doi.org/10.1007/s004540010022
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