Majorization classes of integral matrices

The class A(R,S) of (0,1)-matrices with given row and column sum vectors R and S is well studied. Here we introduce and investigate the more general class A(B|S) of integral matrices with given column sum vector S and with rows that satisfy majorization constraints: each row is majorized by a given vector (a row in B). A characterization of nonemptyness of this class was recently given. We present algorithms for constructing a matrix in A(B|S), and study several properties of such classes. For instance, we show connectedness using certain transformations that generalize interchanges for (0,1)-matrices.