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Circuit-Cocircuit Reversing Systems in Regular Matroids
Emeric Gioan
CNRS, LIRMM, 161 rue Ada,34392 Montpellier Cedex 5, France
Emeric.Gioan@lirmm.fr
Annals of Combinatorics 12 (2) p.171-182 June, 2008
AMS Subject Classification: 05A99, 05B35, 52C40, 82C22
Abstract:
We consider that two orientations of a regular matroid are equivalent if one can be obtained from the other by successive reorientations of positive circuits and/or positive cocircuits. We study the
inductive deletion-contraction structure of these equivalence classes in the set of orientations, and we enumerate these classes as evaluations of the Tutte polynomial. This generalizes the results in digraphs from a previous paper.
Keywords: oriented matroid, regular matroid, circuit reorientation, Tutte polynomial, duality

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