Majorization permutahedra and (0,1)-matrices

A majorization permutahedron M(v) is a polytope associated with a majorization x⪯v in Rn, defined by M(v)={x∈Rn:x⪯v}. Several properties of these polytopes are investigated and a connection to discrete convexity is established. These results are used to obtain a generalization of the Gale–Ryser theorem for (0,1)-matrices with given line sums.