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Keywords:
Bruhat order; doubly stochastic matrix; face
Bruhat order; doubly stochastic matrix; face
Summary:
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.
References:
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