Ela Some Subpolytopes of the Birkhoff Polytope∗
نویسنده
چکیده
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 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.
منابع مشابه
Subpolytopes of Cyclic Polytopes
A remarkable result of I. Shemer [4] states that the combinatorial structure of a neighbourly 2m-polytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic 2m-polytope is cyclic. In this note, we present a direct proof of this consequence that also yields that certain subpolytopes of a cyclic (2m+ 1)-polytope are cyclic.
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