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An Improved Bound for k-Sets in Four Dimensions

Published online by Cambridge University Press:  20 May 2010

MICHA SHARIR
MICHA SHARIR*
Affiliation:
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)
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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 1 , January 2011 , pp. 119 - 129
Copyright
Copyright © Cambridge University Press 2010

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