Extension Equivalence of Oriented Matroids

Bachem, Achim and Kern, Walter (1986) Extension Equivalence of Oriented Matroids.
Published in: European Journal of Combinatorics Vol. 7. pp. 193-197.

Abstract

The point extensions of a matroid M are in one-to-one correspondence to the set of all linear subclasses of M which, ordered by inclusion, form the so called extension lattice of M. Two matroids are said to be extension equivalent if their extension lattices are isomorphic. In this paper we show that for two extension equivalent (oriented) matroids M, and M' of equal rank M * is an adjoint of M iff M * is an adjoint of M' and use this result to prove: M is represetable over the field F if and only if M' is.


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ZAIK Number: zpr84-005
Depositing User: Archive Admin
Date Deposited: 02 Apr 2001 00:00
Last Modified: 25 Oct 2011 09:15
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/5