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.