Doubly stochastic matrices and the Bruhat order

Czechoslovak Mathematical Journal

Richard ¹  A. ²  Brualdi³ 

[1] Department of Mathematics, 480 Lincoln Drive, University of Wisconsin, Madison, Wisconsin 53706, USA;Department of Mathematics, University of Oslo, Moltke Moes vei 35, 0851 Oslo, Norway;Programa de Engenharia de Produção/COPPE, Av. Athos da Silveira Ramos, 149, Centro de Tecnologia, Universidade Federal do Rio de Janeiro, CEP: 21941-909, Rio de Janeiro, RJ, Brazil

关键词: Bruhat order;    doubly stochastic matrix;    face;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order $n$ which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class $\Omega_n$ of doubly stochastic matrices (convex hull of $n\times n$ permutation matrices). An alternative description of this partial order is given. We define a class of special faces of $\Omega_n$ induced by permutation matrices, which we call Bruhat faces. Several examples of Bruhat faces are given and several results are presented.

【 授权许可】

Unknown