An extension of the polytope of doubly stochastic matrices

We consider a class of matrices whose row and column sum vectors are majorized by given vectors b and c, and whose entries lie in the interval [0,?1]. This class generalizes the class of doubly stochastic matrices. We investigate the corresponding polytope Ω(b|c) of such matrices. Main results include a generalization of the Birkhoff–von Neumann theorem and a characterization of the faces, including edges, of Ω(b|c).