In minisymposium: Nonnegative Matrices and MajorizationWed 10:30–11:00, Auditorium Max Weber
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order $n$. We introduce an extension of this, called the stochastic Bruhat order, for the larger class $\Omega_n$ of doubly stochastic matrices (i.e., nonnegative matrices with row and column sums 1). A characterization of this order is given, in terms of certain interchange operations. Moreover, several results on so-called Bruhat faces of $\Omega_n$ induced by permutation matrices, are given.