Regularity of the Circuit Lattice of Oriented Matroids
نویسندگان
چکیده
For the signed circuits of a regular oriented matroid (and more particular of a digraph) the above questions have been studied very well in past. From graph theory it is known that the dimension of the circuit space of a connected digraph is |E| − |V | + 1, that the circuit space L(C) is regular and that the elementary circuits {C(B, e)}e∈E\B form a basis of L(C) for any basis B of O. For general oriented matroids question 1 is a known problem (see Björner et al. [1, 4.45(d)]) but the other problems have not been considered in the literature yet. Furthermore, we extend the set of questions by a fifth, coming from the theory of nowhere-zero flows in a digraph:
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