A characterization of matroidal systems of inequalities (Q1118603)

We consider the polyhedron \(Conv\{x\in \{0,1\}^ n: Mx\leq b\}\), where M is a \(p\times n\) matrix of zeroes and ones and b is a nonnegative integer vector. We give a characterization of such polyhedra whose extreme points are the incidence vectors of the family of independent sets of a matroid and extend our result to polyhedra which are the convex hull of integral polymatroids. We also introduce some new classes of integral matroid polyhedra which extend a result of Edmonds.