A unified interpretation of several combinatorial dualities

A unified interpretation of several combinatorial dualities

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Article ID: iaor20091303
Country: Netherlands
Volume: 5
Issue: 2
Start Page Number: 337
End Page Number: 349
Publication Date: May 2008
Journal: Discrete Optimization
Authors: ,
Keywords: duality
Abstract:

Several combinatorial structures exhibit a duality relation that yields interesting theorems, and, sometimes, useful explanations or interpretations of results that do not concern duality explicitly. We present a common characterization of the duality relations associated with matroids, clutters (Sperner families), oriented matroids, and weakly oriented matroids. The same conditions characterize the orthogonality relation on certain families of vector spaces. This leads to a notion of abstract duality.

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