Journal of Guangdong University of Technology ›› 2009, Vol. 26 ›› Issue (3): 92-95.

• Comprehensive Studies • Previous Articles    

The Permeant of (01)-Matrices

  

  1. 1.Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 51009,China;2.School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 43000,China
  • Online:2009-10-02 Published:2009-10-02

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Abstract: Based on the position of zero entries.it determines the extreme value of the permeant of(0,1)-matrices where the total number of 0′s is n+1.It presents the maximum value,the second largest value and the third largest value of permanents,and finds the matrices which can be used to attain these extreme values.

Key words: permanent； combinatorially equivalent； submatrix； permutation matrices；

[1] T.Muir.On a class of permanent symmetric functions, Proc.Roy. Soc. Edinburgh .

[2] Brualdi R A,Goldwasser J L,Michael T S.Maximum permanents of matrices of zeros and ones. Journal of Combinatorial Theory Series A . 1988

[3] Jerrum,M. R.,Sinclair,A. J.Approximating the permanent. SIAM Journal on Computing . 1989

[4] Seok-Zun Song Suk-Geun Hwang Seog-Hoon Rim and Gi-Sang Cheon.Extremes of permanents of (0,1)-matrices. Linear Algebra and Its Applications . 2003
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