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Simplicial cells in arrangements of hyperplanes

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Abstract

Let ℋ be an arrangement of n hyperplanes in P d, C(ℋ) its cell complex, and H any hyperplane of ℋ. It is proved: (1) If ℋ is not a near pencil then there are at least n−d−1 simplicial d-cells of C(ℋ), each having no facet in H. (2) There are at least d+1 simplicial d-cells of C(ℋ), each having a facet in H.

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Authors and Affiliations

  1. University of Washington, 98105, Seattle, Washington, USA

    R. W. Shannon

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  1. R. W. Shannon
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Material for this paper was taken from the author's doctoral dissertation.

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Shannon, R.W. Simplicial cells in arrangements of hyperplanes. Geom Dedicata 8, 179–187 (1979). https://doi.org/10.1007/BF00181486

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  • DOI: https://doi.org/10.1007/BF00181486

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