Geodesic
Some subpolytopes of the Birkhoff polytope
The electronic journal of linear algebra, Tome 15 (2006), pp. 1-7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 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.
Classification : 15A39, 52B11
Keywords: doubly-stochastic matrices, inequalities, polytopes, majorization 
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     title = {Some subpolytopes of the {Birkhoff} polytope},
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Marques de Sá, Eduardo. Some subpolytopes of the Birkhoff polytope. The electronic journal of linear algebra, Tome 15 (2006), pp. 1-7. http://geodesic.mathdoc.fr/item/ELA_2006__15__a27/