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.
Item Type: | Article |
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Citations: | 1 (Google Scholar) | |
Uncontrolled Keywords: | geometric lattices modular sublattices pseudomodular lattices |
Subjects: |
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Divisions: | Mathematical Institute |
Related URLs: |
ZAIK Number: | zpr90-090 |
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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 |