JOURNAL BROWSE
Search
Advanced SearchSearch Tips
MINIMUM PERMANENTS ON DOUBLY STOCHASTIC MATRICES WITH PRESCRIBED ZEROS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 2,  2013, pp.211-223
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.2.211
 Title & Authors
MINIMUM PERMANENTS ON DOUBLY STOCHASTIC MATRICES WITH PRESCRIBED ZEROS
Song, Seok-Zun;
  PDF(new window)
 Abstract
We consider permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing identity submatrix. We determine the minimum permanents and minimizing matrices on the given faces of the polytope using the contraction method.
 Keywords
permanent;doubly stochastic matrix;barycentric;cohesive matrix;
 Language
English
 Cited by
 References
1.
R. A. Brualdi, An interesting face of the polytope of doubly stochastic matrices, Linear and Multilinear Algebra, 17 (1985), 5-18. crossref(new window)

2.
R. A. Brualdi and B. L. Shader, Minimum permanents on special faces of the polytope of doubly stochastic matrices, Linear Algebra Appl. 201 (1994), 103-111. crossref(new window)

3.
G. P. Egorycev, The solution of the van der Waerden problem for permanents, Dokl. Akad. Nauk. SSSR 258 (1981), 1041-1044.

4.
D. I. Falikman, A proof of vander Waerden's conjecture on the permanent of a doubly stochastic matrix, Mat. Zametki 29 (1981), 31-38, Translated in Math. Notes 29 (1981), 475-479.

5.
T. H. Foregger, On the minimum value of the permanent of a nearly decomposable doubly stochastic matrix, Linear Algebra Appl. 32 (1980), 75-85. crossref(new window)

6.
K. Pula, S. Z. Song and I. M. Wanless, Minimum permanents on two faces of the polytope of doubly stochastic matrices, Linear Algebra Appl. 434 (2011), 232-238. crossref(new window)

7.
S. Z. Song, Minimum permanents on certain faces of matrices containing an identity submatrix, Linear Algebra Appl. 108 (1988), 263-280. crossref(new window)

8.
S. Z. Song, Minimum permanents on a face of the polytope of doubly stochastic matrices, Linear Algebra Appl. 259 (1997), 169-182. crossref(new window)

9.
S. Z. Song, Minimum permanents and minimizing matrices on certain doubly stochastic matrices, Linear Algebra Appl. 162-164 (1992), 786-790.