Majorization-constrained doubly stochastic matrices Original Research Article

We study subpolytopes Ωn(d) of the Birkhoff polytope Ωn of doubly stochastic matrices of order n whose rows and columns (or just one row or just the main diagonal) are majorized by a given stochastic vector d. In addition, we consider the (not necessarily convex) set Ωn*(d) of matrices in Ωn whose rows and columns majorize d.