Doubly stochastic matrices and the Bruhat order

作者：Brualdi Richard A^*; Dahl Geir; Fritscher Eliseu

来源：Czechoslovak Mathematical Journal, 2016, 66(3): 681-700.

DOI：10.1007/s10587-016-0286-6

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 nxn 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.

• 出版日期2016-9