The Lattices of Matroid Bases and Exact Matroid Bases

Rieder, Jörg (1991) The Lattices of Matroid Bases and Exact Matroid Bases.
Published in: Archiv der Mathematik : ADM Vol. 56 (6). pp. 616-623.

Abstract

Let M be a matroid on E and R be a subset of E. We show that the lattice generated by the incidence vectors of the bases of M is always that of a partition matroid. If we consider only bases B satisfying vert B cap R vert =p, it is proved that the corresponding lattice is the intersection of the basis lattice of M with the hyperplane arising from the condition vert R cap B vert =p.


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Content information:
Item Type: Article
Citations: 5 (Google Scholar) | 3 (Web of Science)
Uncontrolled Keywords: matroid bases
Subjects:
  • 05-XX Combinatorics > 05Bxx Designs and configurations > 05B35 Matroids, geometric lattices

  • Divisions: Mathematical Institute
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    Deposit Information:
    ZAIK Number: zpr88-050
    Depositing User: Archive Admin
    Date Deposited: 02 Apr 2001 00:00
    Last Modified: 17 Nov 2011 14:18
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/50