PERMANENTS OF DOUBLY STOCHASTIC FERRERS MATRICES

  • Hwang, Suk-Geun (Department of mathematics Education Kyungpook National University) ;
  • Pyo, Sung-Soo (Department of mathematics Education Kyungpook National University)
  • Published : 1999.09.01

Abstract

The minimum permanent and the set of minimizing matrices over the face of the polytope 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 n are presented in terms of row sum vectors along with simple proofs.

Keywords

References

  1. J. Combin. Theory(A) v.22 The covex polyhedron of doubly stochastic matrices:Ⅰ.Applications of the permanent function R. A. Brualdi;P. M. Gibson
  2. Combinatorial Matrix Theory R. A. Brualdi;H. J. Ryser
  3. Linear Algebra Appl. v.32 On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix T. H. Foregger
  4. Linear Algebra Appl. v.18 Minimum permanent on faces of staircase type of the polytope of double stochastic matrices S.-G. Hwang
  5. Linear Algebra Appl. v.253 A face of the polytope of doubly stochastic matrices associated with certain matrix espansions S.-G. Hwang;S.-J. Shin
  6. Linear and Multilinear Algebra v.15 Minimum permanents of doubly stochastic matrices with prescribed zero entries H. Minc