k-Sets in Four Dimensions

Discrete & Computational Geometry - Tập 35 - Trang 177-191 - 2005
Jiri Matousek1, Micha Sharir2,3, Shakhar Smorodinsky3, Uli Wagner1
1Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Prague 1, Czech Republic
2School of Computer Science, Tel Aviv University, Tel Aviv, Israel
3Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA

Tóm tắt

We show, with an elementary proof, that the number of halving simplices in a set of n points in ℝ4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/13^{4}). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

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Discrete & Computational Geometry

Tập 35

177-191

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