Convex Sets of Doubly Stochastic Matrices

Abstract Let Ω denote the set of all n by n doubly stochastic matrices and let m be a positive integer. Then the set Ω m = {A ϵ Ω : 0 ⩽ a ij ⩽ 1 m , 1 ⩽ i, j ≤ n} is the convex hull of the matrices in Ω m having exactly m entries equal to 1 m in each row and column and the other entries equal to zero.