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Permanent of a matrix A = $\|a_{i,j}\|_{i,j=1}^{n}$ is defined as $$ \mathrm{Perm}(A) = \sum\limits_{\sigma \in S_{n}} a_{1,\sigma_{1}},\ldots,a_{n,\sigma_{n}} $$ Is there some representation for permanent of Vandermonde's matrix similar to its determinant? Is there some numerical methods for computing Vandermonde's permanent that uses the particularity of Vandermonde's matrix?

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  • $\begingroup$ No, but i have to evaluate it using computer. In general, I can use Ryser's formula ($O(n2^n)$ operations), but it doesn't use the particularity of Wandermonde's matrix. $\endgroup$ – Appliqué Oct 26 '11 at 20:29
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    $\begingroup$ An apropos paper. (At least you can bound your permanent...) $\endgroup$ – J. M. is a poor mathematician Oct 26 '11 at 23:13

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