### Abstract

Let S ⊂ℝ^{3} be an n-set in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most O(n^{2.998}). As a main tool, for every set Y of n points in the plane a set N of size O(n^{4}) is constructed such that the points of N are distributed almost evenly in the triangles determined by Y.

Original language | English |
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Pages (from-to) | 175-183 |

Number of pages | 9 |

Journal | Combinatorica |

Volume | 10 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1990 |

### Fingerprint

### Keywords

- AMS subject classification (1980): 52A37

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

*10*(2), 175-183. https://doi.org/10.1007/BF02123008

**On the number of halving planes.** / Bárány, I.; Füredi, Z.; Lovász, L.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 10, no. 2, pp. 175-183. https://doi.org/10.1007/BF02123008

}

TY - JOUR

T1 - On the number of halving planes

AU - Bárány, I.

AU - Füredi, Z.

AU - Lovász, L.

PY - 1990/6

Y1 - 1990/6

N2 - Let S ⊂ℝ3 be an n-set in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most O(n2.998). As a main tool, for every set Y of n points in the plane a set N of size O(n4) is constructed such that the points of N are distributed almost evenly in the triangles determined by Y.

AB - Let S ⊂ℝ3 be an n-set in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most O(n2.998). As a main tool, for every set Y of n points in the plane a set N of size O(n4) is constructed such that the points of N are distributed almost evenly in the triangles determined by Y.

KW - AMS subject classification (1980): 52A37

UR - http://www.scopus.com/inward/record.url?scp=0012998135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012998135&partnerID=8YFLogxK

U2 - 10.1007/BF02123008

DO - 10.1007/BF02123008

M3 - Article

AN - SCOPUS:0012998135

VL - 10

SP - 175

EP - 183

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 2

ER -