On Pseudomodular Matroids and Adjoints
Alfter, Marion and Hochstättler, Winfried
(1995)
On Pseudomodular Matroids and Adjoints.
Published in:
Discrete applied mathematics Vol. 60 (1-3).
pp. 3-11.
Abstract
There are two concepts of duality in combinatorial geometry. A set theoretical one, generalizing the structure of two orthocomplementary vector spaces and a lattice theoretical concept of an adjoint, that mimics duality between points and hyperplanes. The latter - usually called polarity - seems to make sense almost only in the linear case. In fact the only non-linear combinatorial geometries known to admit an adjoint were of rank 3. Moreover, N. E. Mnëv conjectured that in higher ranks there would exist no non-linear oriented matroid that has an oriented adjoint. At least with unoriented matroids this is not true. In this paper we present a class of rank 4 matroids with adjoint including a non-linear example.
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Item Type: | Article |
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Citations: | 5 (Google Scholar) | |
Uncontrolled Keywords: | adjoints matroids pseudomodularity |
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Divisions: | Mathematical Institute |
Additional Information: | ARIDAM VI and VII (New Brunswick, NJ, 1991/1992) |
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ZAIK Number: | zpr92-109 |
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Depositing User: | Winfried Hochstättler |
Date Deposited: | 02 Apr 2001 00:00 |
Last Modified: | 19 Jan 2012 10:49 |
URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/109 |