Majorization-constrained doubly stochastic matrices (Q1863545)

The authors study the structure and properties of the subpolytopes \(\Omega_n(d)\) of the Birkhoff polytope \(\Omega_n\) 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, the authors study the (not necessarily convex) set \(\Omega_n^*(d)\) of matrices in \(\Omega_n\) whose rows and columns majorize \(d\).