A Guided Tour through Oriented Matroid Axioms

Bachem, Achim and Kern, Walter (1993) A Guided Tour through Oriented Matroid Axioms.
Published in: Acta mathematicae applicatae sinica Vol. 9 (2). pp. 125-134.

Abstract

Oriented Matroids arise as a natural combinatorial abstraction of linear algebra and geometry. Some of the topics were foreseen by Rockafellar. Later, oriented matroids were independently discovered by Bland, Dress and Las Vergnas. As with matroids oriented matroids can be developed from many different axiom systems. In this survey we shall concentrate on some of the more important ones and show how one system can be deduced from the other. Moreover we show how these axiom systems computationally relate to each other proving that none of them can be used to check one side of the well known Farkas' Lemma.


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Content information:
Item Type: Article
Citations: 3 (Google Scholar) |
Uncontrolled Keywords: axiom systems Farkas lemma oriented matroids
Subjects:
  • 05-XX Combinatorics > 05Bxx Designs and configurations > 05B35 Matroids, geometric lattices

  • 52-XX Convex and discrete geometry > 52Bxx Polytopes and polyhedra > 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)

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    Divisions: Mathematical Institute
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    Deposit Information:
    ZAIK Number: zpr89-064
    Depositing User: Archive Admin
    Date Deposited: 02 Apr 2001 00:00
    Last Modified: 15 Nov 2011 10:49
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/64