충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제22권4호
  • /
  • Pages.843-851
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  • 2009
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

CONSTRUCTIONS OF (0,1)-MATRIX WITH PERMANENT k

  • Park, Se-Won (Department of Mathematics, Shingyeong University)
  • 투고 : 2009.11.05
  • 심사 : 2009.11.24
  • 발행 : 2009.12.30
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초록

The purpose of this paper is to show that for each integer k where $1{\geq}k{\geq}2^{n-1}$, there exists an $n{\times}n(0,1)$-matrix A with exactly PerA = k. Thus we introduce a constructive approch for such matrices. Using the permanent of (0,1)-matrix, we decomposed the number n! with an linear combination of the power of 2. That coefficient is an stiring number.

키워드

참고문헌

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  2. T. H. Foregger On the minimum value of the permanent of a nearly decomposable doubly stocastic matric, Linear Algebra Appl. 32 (1980), 75-85. https://doi.org/10.1016/0024-3795(80)90008-7
  3. S. G. Hwang Minimum permanent on faces of staircase type of the polytope of doubly stocastic matrices, Linear Algebra Appl. 18 (1985), 271-306.
  4. D. Konig. Theorie der endlichen und unendlichen Graphn, Leipzig, 1936
  5. M. Marcus and H. Minc. Modern University Algebra, New York, 1966
  6. M. Muir. On a class of permanent symmetric fucntions, Proc. Roy. Soc. Edinburgh 11 (1882), 111-120