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: | Bland Robert G., Dietrich Brenda L. |
Keywords: | duality |
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.