Abstract
Denote by the convex polytope of doubly substochastic matrices and by the convex polytope of doubly stochastic matrices. We generalize the Bruhat order for permutation matrices and doubly stochastic matrices to the subpermutation matrices and doubly substochastic matrices, respectively. Moreover we study the Bruhat shadow of a subpermutation matrix and the Bruhat faces of . The relations between the Bruhat faces in and those in are also given.
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