A Note on the Weak-Zone-Theorem

Hochstättler, Winfried (1993) A Note on the Weak-Zone-Theorem.
Published in: Congressus Numerantium Vol. 98. pp. 95-103.

Abstract

In a recent paper J. Matousek gave a simple proof of a weak form of the zone theorem which estimates the number of facets in the zone of a (Pseudo-)Hyperplane arrangement. In the Pseudo-Case he gave the full proof only for the 3-dimensional case. In this short note we want to point out, that his proof in fact uses Linear Programming duality and so can be generalized easily to all dimensions using duality of Oriented Matroids.


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Item Type: Article
Citations: 3 (Google Scholar) |
Uncontrolled Keywords: arrangement of pseudo hyperplanes computational geometry duality linear programming oriented matroids
Subjects:
  • 68-XX Computer science > 68Uxx Computing methodologies and applications > 68U05 Computer graphics; computational geometry

  • 05-XX Combinatorics > 05Bxx Designs and configurations > 05B35 Matroids, geometric lattices

  • 90-XX Operations research, mathematical programming > 90Cxx Mathematical programming > 90C05 Linear programming

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    Divisions: Mathematical Institute
    Related URLs:
    Deposit Information:
    ZAIK Number: zpr92-110
    Depositing User: Winfried Hochstättler
    Date Deposited: 02 Apr 2001 00:00
    Last Modified: 19 Dec 2011 09:45
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/110