### Abstract

Let ℋ be a collection of n hyperplanes in d-space in general position. For each tuple of d+1 hyperplanes of ℋ consider the open ball inscribed in the simplex that they form. Let ℬ_{ k} denote the number of such balls intersected by exactly k hyperplanes, for k=0, 1,..., n-d-1. We show that {Mathematical expression}.

Original language | English (US) |
---|---|

Pages (from-to) | 421-425 |

Number of pages | 5 |

Journal | Discrete and Computational Geometry |

Volume | 10 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1993 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Discrete and Computational Geometry*,

*10*(1), 421-425. https://doi.org/10.1007/BF02573987

**An invariant property of balls in arrangements of hyperplanes.** / Aronov, Boris; Naiman, Daniel Q.; Pach, János; Sharir, Micha.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 10, no. 1, pp. 421-425. https://doi.org/10.1007/BF02573987

}

TY - JOUR

T1 - An invariant property of balls in arrangements of hyperplanes

AU - Aronov, Boris

AU - Naiman, Daniel Q.

AU - Pach, János

AU - Sharir, Micha

PY - 1993/12

Y1 - 1993/12

N2 - Let ℋ be a collection of n hyperplanes in d-space in general position. For each tuple of d+1 hyperplanes of ℋ consider the open ball inscribed in the simplex that they form. Let ℬ k denote the number of such balls intersected by exactly k hyperplanes, for k=0, 1,..., n-d-1. We show that {Mathematical expression}.

AB - Let ℋ be a collection of n hyperplanes in d-space in general position. For each tuple of d+1 hyperplanes of ℋ consider the open ball inscribed in the simplex that they form. Let ℬ k denote the number of such balls intersected by exactly k hyperplanes, for k=0, 1,..., n-d-1. We show that {Mathematical expression}.

UR - http://www.scopus.com/inward/record.url?scp=51649145899&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649145899&partnerID=8YFLogxK

U2 - 10.1007/BF02573987

DO - 10.1007/BF02573987

M3 - Article

AN - SCOPUS:51649145899

VL - 10

SP - 421

EP - 425

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -