Minimum permanent on faces of staircase type of the polytope of doubly stochastic matrices

Abstract

Let Ωn denote the set of all n × n doubly stochastic matrices Γ or an n × n 10. 11-matrix D- [dn ]. let In this paper, we consider I he face Ω(D) of Ωn for D an n × n staircase matrix, and determine the minimum permanent and the set of all minimizing matrices on Ω(D). We find the barycenter of Ω(D) and show that the barycenter is a minimizing matrix on Ω (D). It is also proved that the staircase matrices are maximal with respect to the minimization of permanent.