Some subpolytopes of the Birkhoff polytope

Abstract

Some special subsets of the set of uniformly tapered doubly stochastic matrices
are considered. It is proved that each such subset is a convexpolytope and its extreme points are
determined. A minimality result for the whole set of uniformly tapered doubly stochastic matrices is
also given. It is well known that if x and y are nonnegative vectors of Rⁿ and x is weakly majorized
by y, there exists a doubly substochastic matrix S such that x = Sy. A special choice for such S
is exhibited, as a product of doubly stochastic and diagonal substochastic matrices of a particularly
simple structure.