ELA, Volume 15, pp. 1-7, January 2006, abstract.
Some Subpolytopes of the Birkhoff Polytope
Eduardo Marques de Sa
Some special subsets of the set of uniformly tapered doubly
stochastic matrices are considered. It is proved that each
such subset is a convex polytope 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 R^n 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.