An invariant property of balls in arrangements of hyperplanes

Boris Aronov, Daniel Q. Naiman, János Pach, Micha Sharir

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Pages (from-to)421-425
    Number of pages5
    JournalDiscrete and Computational Geometry
    Volume10
    Issue number1
    DOIs
    StatePublished - Dec 1993

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    ASJC Scopus subject areas

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

    Cite this

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

    In: Discrete and Computational Geometry, Vol. 10, No. 1, 12.1993, p. 421-425.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Naiman, Daniel Q. ; Pach, János ; Sharir, Micha. / An invariant property of balls in arrangements of hyperplanes. In: Discrete and Computational Geometry. 1993 ; Vol. 10, No. 1. pp. 421-425.
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