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On the number of halving planes (1990)

Bárány, I. ; Füredi, Z. ; Lovász, L.

Springer

Combinatorica 10 (1990), S. 175-183

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ISSN: 1439-6912

Keywords: 52 A 37

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract LetS ⊂ℝ3 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(n 2.998). As a main tool, for every setY ofn points in the plane a setN of sizeO(n 4) is constructed such that the points ofN are distributed almost evenly in the triangles determined byY.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02123008

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