Euclidean Intersection Properties

Bachem, Achim and Wanka, Alfred (1989) Euclidean Intersection Properties.
Published in: Journal of combinatorial theory : Series B Vol. 47 (1). pp. 10-19.

Abstract

There are matroids which have Euclidean and non-Euclidean orientations and there are also matroids whose inherent structure does not allow any Euclidean orientation. In this paper we discuss some lattice theoretic properties of matroids which when used in an oriented version guarantee Euclideanness. These properties depend all on the existence of intersections of certain flats (which is equivalent to Euclideanness interpreted in the Las Vergnas notation of oriented matroids). We introduce three classes of matroids having various intersection properties and show that two of them cannot be characterized by excluding finitely many minors.


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Content information:
Item Type: Article
Citations: 7 (Google Scholar) | 2 (Web of Science)
Uncontrolled Keywords: Euclidean orientations intersection properties lattices oriented matroids
Subjects:
  • 05-XX Combinatorics > 05Bxx Designs and configurations > 05B35 Matroids, geometric lattices

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    Divisions: Mathematical Institute
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    Deposit Information:
    ZAIK Number: zpr86-025
    Depositing User: Archive Admin
    Date Deposited: 02 Apr 2001 00:00
    Last Modified: 09 Jan 2012 11:46
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/25