K-sets in four dimensions

Jiri Matousek; Micha Sharir; Shakhar Smorodinsky; Uli Wagner

doi:10.1007/s00454-005-1200-4

K-sets in four dimensions

Jiri Matousek, Micha Sharir, Shakhar Smorodinsky, Uli Wagner

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We show, with an elementary proof, that the number of halving simplices in a set of n points in ⁴ in general position is O(n^4-2/45). This improves the previous bound of O(n^4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

Original language	English
Pages (from-to)	177-191
Number of pages	15
Journal	Discrete and Computational Geometry
Volume	35
Issue number	2
DOIs	https://doi.org/10.1007/s00454-005-1200-4
State	Published - 1 Jan 2006
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-005-1200-4

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title = "K-sets in four dimensions",

abstract = "We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.",

author = "Jiri Matousek and Micha Sharir and Shakhar Smorodinsky and Uli Wagner",

year = "2006",

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doi = "10.1007/s00454-005-1200-4",

language = "English",

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T1 - K-sets in four dimensions

AU - Matousek, Jiri

AU - Sharir, Micha

AU - Smorodinsky, Shakhar

AU - Wagner, Uli

PY - 2006/1/1

Y1 - 2006/1/1

N2 - We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

AB - We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

UR - https://www.scopus.com/pages/publications/31144440702

U2 - 10.1007/s00454-005-1200-4

DO - 10.1007/s00454-005-1200-4

M3 - Article

AN - SCOPUS:31144440702

SN - 0179-5376

VL - 35

SP - 177

EP - 191

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

K-sets in four dimensions

Abstract

ASJC Scopus subject areas

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