대한수학회보 (Bulletin of the Korean Mathematical Society)
- 제33권1호
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- Pages.127-133
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- 1996
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- 1015-8634(pISSN)
- /
- 2234-3016(eISSN)
A cohesive matrix in a conjecture on permanents
- Hong, Sung-Min (Department of Mathematics, Gyeongsang National University, Chinju 660-701) ;
-
Jun, Young-Bae
(Department of Mathematics, Gyeongsang National University, Chinju 660-701)
;
- Kim, Seon-Jeons (Department of Mathematics, Gyeongsang National University, Chinju 660-701) ;
- Song, Seok-Zun (Department of Mathematics, Cheju National University, Cheju 690-756)
- 발행 : 1996.02.01
초록
Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative matrices whose row and column sums are all equal to 1. The permanent of a $n \times n$ matrix $A = [a_{ij}]$ is defined by $$ per(A) = \sum_{\sigma}^ a_{1\sigma(a)} \cdots a_{n\sigma(n)} $$ where $\sigma$ runs over all permutations of ${1, 2, \ldots, n}$.