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Circuit-cocircuit reversing systems in regular matroids. (English) Zbl 1228.05111
Summary: 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.

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
05A99 Enumerative combinatorics
52C40 Oriented matroids in discrete geometry
82C22 Interacting particle systems in time-dependent statistical mechanics
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