An improved bound for k-sets in four dimensions

Authors:
Micha Sharir
Affiliations:
School of computer science, tel aviv university, tel aviv 69978, israel and courant institute of mathematical sciences, new york university, new york, ny 10012, usa (e-mail: michas@post.tau.ac.il)
Venue:
Combinatorics, Probability and Computing
Year:
2011

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Abstract

We show that the number of halving sets of a set of n points in ℝ4 is O(n4−1/18), improving the previous bound of [10] with a simpler (albeit similar) proof.