Modular Substructures in Pseudomodular Lattices

Dress, Andreas and Hochstättler, Winfried and Kern, Walter (1994) Modular Substructures in Pseudomodular Lattices.
Published in: Mathematica Scandinavica Vol. 74. pp. 9-16.

Abstract

Pseudomodular lattices have been used by the first author and L. Lovász [Combinatorica 7, 39-48 (1987)] in order to investigate combinatorial properties of algebraic matroids and were further analyzed by A. Björner and L. Lovász [Acta Sci. Math. 51, No. 3/4, 295-308 (1987)]. The purpose of our paper is to present local conditions, characterizing modular sublattices of a pseudomodular lattice. As an application, we derive a result by the second and the third author [Combinatorica 9, No. 2, 145-152 (1989)], implying that Lovász's min-max formula for matchings in projective geometries remains valid for pseudomodular lattices, and we discuss a relation with B. Lindstroems construction of subgeometries of full algebraic combinatorial geometries which are isomorphic to projective geometries over skew fields.


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Item Type: Article
Citations: 1 (Google Scholar) |
Uncontrolled Keywords: geometric lattices modular sublattices pseudomodular lattices
Subjects:
  • 05-XX Combinatorics > 05Bxx Designs and configurations > 05B35 Matroids, geometric lattices

  • 06-XX Order, lattices, ordered algebraic structures > 06Cxx Modular lattices, complemented lattices > 06C10 Semimodular lattices, geometric lattices

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    Divisions: Mathematical Institute
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    Deposit Information:
    ZAIK Number: zpr90-090
    Depositing User: Winfried Hochstättler
    Date Deposited: 02 Apr 2001 00:00
    Last Modified: 19 Jan 2012 11:11
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/90