An Improved Bound for \sl k -Sets in Three Dimensions |
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| Authors: | M Sharir S Smorodinsky G Tardos |
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| Institution: | (1) School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel \{sharir, shakhar\}@math.tau.ac.il , IL;(2) Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA , US;(3) Rényi Institute of the Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.hu, HU |
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| Abstract: | We prove that the maximum number of k -sets in a set S of n points in \Bbb R
3
is O(nk
3/2
) . This improves substantially the previous best known upper bound of O(nk
5/3
) (see 7] and 1]).
Received November 30, 1999, and in revised form July 24, 2000. Online publication February 26, 2001. |
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| Keywords: | |
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