### Abstract

We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk^{3/2}). This improves substantially the previous best known upper bound of O(nk^{5/3}) (see [7] and [1]).

Original language | English |
---|---|

Pages (from-to) | 195-204 |

Number of pages | 10 |

Journal | Discrete & Computational Geometry |

Volume | 26 |

Issue number | 2 |

Publication status | Published - 2001 |

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### ASJC Scopus subject areas

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

### Cite this

*Discrete & Computational Geometry*,

*26*(2), 195-204.

**An improved bound for k-sets in three dimensions.** / Sharir, M.; Smorodinsky, S.; Tardos, G.

Research output: Contribution to journal › Article

*Discrete & Computational Geometry*, vol. 26, no. 2, pp. 195-204.

}

TY - JOUR

T1 - An improved bound for k-sets in three dimensions

AU - Sharir, M.

AU - Smorodinsky, S.

AU - Tardos, G.

PY - 2001

Y1 - 2001

N2 - We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk3/2). This improves substantially the previous best known upper bound of O(nk5/3) (see [7] and [1]).

AB - We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk3/2). This improves substantially the previous best known upper bound of O(nk5/3) (see [7] and [1]).

UR - http://www.scopus.com/inward/record.url?scp=0035612718&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035612718&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035612718

VL - 26

SP - 195

EP - 204

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -