Journal of the
Korean Mathematical Society JKMS

The minimum permanent and the set of minimizing matrices over the face of the polytope $\Omega_n$ of all doubly stochastic matrices of order $n$ determined by any staircase matrix was determined in [4] in terms of some parameter called frame. A staircase matrix can be described very simply as a Ferrers matrix by its row sum vector. In this paper, some simple exposition of the permanent minimization problem over the faces determined by Ferrers matrices of the polytope of $ \Omega_n$ are presented in terms of row sum vectors along with simple proofs.

Keywords: permanent, staircase matrix, Ferrers matrix, doubly stochastic matrix

MSC numbers: 15A15, 15A51