W. Watkins and R. Merris, Convex sets of doubly stochastic matrices, J. Combinatorial Theory 16 (1974), 129-130. Math Reviews 48#6139.

In 1946, G. Birkhoff showed that the set of n-by-n doubly stochastic matrices is the convex hull of the n! permutation matrices, i.e., of the n-by-n matrices with exactly one 1 in each row and column and all other entries equal to 0. This article extends Birkhoff's result along the following lines: Let m be a positive integer, m <= n. The set of n-by-n doubly stochastic matrices, each entry of which is at most 1/m, is the convex hull of the n-by-n matrices with exactly m entries in each row and column equal to 1/m, and all other entries equal to 0. Among the publications citing this article are