An invariant property of balls in arrangements of hyperplanes

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

    Research output: Contribution to journalArticlepeer-review


    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 & Computational Geometry
    Issue number1
    StatePublished - Dec 1993

    ASJC Scopus subject areas

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


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