Adjoints and Duals of Matroids Linearly Representable over a Skew Field

Hochstättler, Winfried and Kromberg, Stephan (1996) Adjoints and Duals of Matroids Linearly Representable over a Skew Field.
Published in: Mathematica Scandinavica Vol. 78. pp. 5-12.

Abstract

Following an approach suggested by B. Lindström we prove that the dual of a matroid representable over a skew field is itself representable over the same field. Along the same line we show that any matroid within this class has an adjoint. As an application we derive an adjoint for the dual of the Non-Pappus-Matroid. Furthermore, we reprove a result by Alfter and Hochstättler concerning the existence of an adjoint for a certain eight point configuration and show that this configuration is linearly representable over a field if and only if the field is skew.


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Deposit Information:
ZAIK Number: zpr94-154
Depositing User: Winfried Hochstättler
Date Deposited: 02 Apr 2001 00:00
Last Modified: 19 Dec 2011 09:45
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/154