Polynôme symétrique

Definition / General algebra /

Un polynôme symétrique est un polynôme $P\in k[X_{1},\ldots,X_{n}]$ tel que, pour tout permutation $\sigma \in S_{n}$ :
$P(X_{\sigma(1)},\ldots,X_{\sigma(n)})=P(X_{1},\ldots,X_{n}).$

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