Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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MINIMUM PERMANENTS ON DOUBLY STOCHASTIC MATRICES WITH PRESCRIBED ZEROS

  • Song, Seok-Zun (Department of Mathematics, Jeju National University)
  • Received : 2013.03.25
  • Accepted : 2013.04.06
  • Published : 2013.06.25
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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.

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References

  1. R. A. Brualdi, An interesting face of the polytope of doubly stochastic matrices, Linear and Multilinear Algebra, 17 (1985), 5-18. https://doi.org/10.1080/03081088508817637
  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. https://doi.org/10.1016/0024-3795(94)90109-0
  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. https://doi.org/10.1016/0024-3795(80)90008-7
  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. https://doi.org/10.1016/j.laa.2010.08.015
  7. S. Z. Song, Minimum permanents on certain faces of matrices containing an identity submatrix, Linear Algebra Appl. 108 (1988), 263-280. https://doi.org/10.1016/0024-3795(88)90192-9
  8. S. Z. Song, Minimum permanents on a face of the polytope of doubly stochastic matrices, Linear Algebra Appl. 259 (1997), 169-182. https://doi.org/10.1016/S0024-3795(96)00248-0
  9. S. Z. Song, Minimum permanents and minimizing matrices on certain doubly stochastic matrices, Linear Algebra Appl. 162-164 (1992), 786-790.