On the number of halving planes

I. Bárány, Z. Füredi, L. Lovász

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)175-183
Number of pages9
JournalCombinatorica
Volume10
Issue number2
DOIs
Publication statusPublished - Jun 1990

Fingerprint

Dissect
Triangle
Cardinality

Keywords

  • AMS subject classification (1980): 52A37

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

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

In: Combinatorica, Vol. 10, No. 2, 06.1990, p. 175-183.

Research output: Contribution to journalArticle

Bárány, I. ; Füredi, Z. ; Lovász, L. / On the number of halving planes. In: Combinatorica. 1990 ; Vol. 10, No. 2. pp. 175-183.
@article{ff47db26126440019c9754699f2e7a39,
title = "On the number of halving planes",
abstract = "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.",
keywords = "AMS subject classification (1980): 52A37",
author = "I. B{\'a}r{\'a}ny and Z. F{\"u}redi and L. Lov{\'a}sz",
year = "1990",
month = "6",
doi = "10.1007/BF02123008",
language = "English",
volume = "10",
pages = "175--183",
journal = "Combinatorica",
issn = "0209-9683",
publisher = "Janos Bolyai Mathematical Society",
number = "2",

}

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 -