Convex sets of some doubly stochastic matrices

AbstractLet Ω denote the set of all n by n doubly stochastic matrices. Let t be a real number such that 1t ⩾ 1n and let m be a real number such that 1m ⩽ 1 − 1t. The set Ωs = {A ϵ Ω : 1m ⩽ aij ⩽ 1t, 1 ⩽ i, j ⩽ n} is the convex hull of the matrices in Ωs having as many largest entries, namely, 1t, as possible in each row and column while filling out the remaining entries with the value 1m and if necessary at most one entry in each row and column which has a value between 1m and 1t