On the extreme points of the majorization polytope Ω3(y x)

Let Ωn denote the set of all doubly stochastic matrices. For x, y Rn such that y is majorized by x, let Ωn(y x)={S Ωny=Sx Then Ωn(y x) forms a convex subpolytope of Ωn. We determine the extreme points and the number of extreme points of the polytope Ω3(y x).