### Abstract

The set P of n points in R^{d} in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

Original language | English (US) |
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Pages | 192-199 |

Number of pages | 8 |

DOIs | |

State | Published - 1998 |

Event | Proceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USA Duration: Jun 7 1998 → Jun 10 1998 |

### Other

Other | Proceedings of the 1998 14th Annual Symposium on Computational Geometry |
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City | Minneapolis, MN, USA |

Period | 6/7/98 → 6/10/98 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Andrzejak, A., Aronov, B., Har-Peled, S., Seidel, R., & Welzl, E. (1998).

*Results on k-sets and j-facets via continuous motion*. 192-199. Paper presented at Proceedings of the 1998 14th Annual Symposium on Computational Geometry, Minneapolis, MN, USA, . https://doi.org/10.1145/276884.276906