On the number of halving planes |
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| Authors: | I. Bárány Z. Füredi L. Lovász |
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| Affiliation: | (1) Hungarian Academy of Sciences, P.O.B. 127, 1364 Budapest, Hungary;(2) Department of Computer Science, Eötvös Loránd University, Múzeum krt. 6.-8., 1088 Budapest, Hungary;(3) Princeton University, 08544 Princeton, NJ, USA |
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| Abstract: | LetS   3 be ann-set in general position. A plane containing three of the points is called a halving plane if it dissectsS into two parts of equal cardinality. It is proved that the number of halving planes is at mostO(n2.998).As a main tool, for every setY ofn points in the plane a setN of sizeO(n4) is constructed such that the points ofN are distributed almost evenly in the triangles determined byY.Research supported partly by the Hungarian National Foundation for Scientific Research grant No. 1812 |
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| Keywords: | 52 A 37 |
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