A unified interpretation of several combinatorial dualities

@article{bland-dietrich-07, 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.}, author = {Bland, R. and Dietrich, B.}, citeulike-article-id = {3872588}, doi = {10.1016/j.disopt.2006.08.002}, issn = {15725286}, journal = {Discrete Optimization}, keywords = {omatroids}, month = {May}, number = {2}, pages = {337--349}, posted-at = {2009-01-09 23:24:26}, priority = {4}, title = {A unified interpretation of several combinatorial dualities}, url = {http://dx.doi.org/10.1016/j.disopt.2006.08.002}, volume = {5}, year = {2008} }

TY - JOUR ID - bland-dietrich-07 L3 - citeulike-article-id:3872588 N2 - 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. IS - 2 JF - Discrete Optimization SN - 15725286 EP - 349 TI - A unified interpretation of several combinatorial dualities VL - 5 SP - 337 KW - omatroids AU - Bland, R AU - Dietrich, B PY - 2008/05// UR - http://dx.doi.org/10.1016/j.disopt.2006.08.002 ER -