Cell complexities in hyperplane arrangements

Boris Aronov, Micha Sharir

    Research output: Contribution to journalArticle

    Abstract

    We derive improved bounds on the complexity, i.e., the total number of faces of all dimensions, of many cells in arrangements of hyperplanes in higher dimensions, and use these bounds to obtain a very simple proof of an earlier bound, due to Aronov, Matoušek, and Sharir, on the sum of squares of cell complexities in such an arrangement.

    Original languageEnglish (US)
    Pages (from-to)107-115
    Number of pages9
    JournalDiscrete and Computational Geometry
    Volume32
    Issue number1
    DOIs
    StatePublished - 2004

    Fingerprint

    Hyperplane Arrangement
    Cell
    Arrangement of Hyperplanes
    Sum of squares
    Higher Dimensions
    Arrangement
    Face

    ASJC Scopus subject areas

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

    Cite this

    Cell complexities in hyperplane arrangements. / Aronov, Boris; Sharir, Micha.

    In: Discrete and Computational Geometry, Vol. 32, No. 1, 2004, p. 107-115.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Sharir, Micha. / Cell complexities in hyperplane arrangements. In: Discrete and Computational Geometry. 2004 ; Vol. 32, No. 1. pp. 107-115.
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