Symmetric polynomial
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Revision 354
7/8/2026, 2:19:31 PM · Ancient Tree
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A symmetric polynomial is a [[polynomial|polynomial]] $P\in k[X_{1},\ldots,X_{n}]$ such that, for every [[permutation|permutation]] $\sigma \in S_{n}$:2
$$P(X_{\sigma(1)},\ldots,X_{\sigma(n)})=P(X_{1},\ldots,X_{n}).$$Revision 353
7/8/2026, 2:19:27 PM · Ancient Tree
Concept edited
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A symmetric polynomial is a [[polynomial|polynomial]] $P\in k[X_{1},\ldots,X_{n}]$ such that, for every [[permutation|permutation]] $\sigma$:1
A symmetric polynomial is a [[polynomial|polynomial]] $P\in k[X_{1},\ldots,X_{n}]$ such that, for every [[permutation|permutation]] $\sigma \in S_{n}$:2
$$P(X_{\sigma(1)},\ldots,X_{\sigma(n)})=P(X_{1},\ldots,X_{n}).$$Revision 348
7/8/2026, 2:06:43 PM · Ancient Tree
Concept created
A symmetric polynomial is a [[polynomial|polynomial]] $P\in k[X_{1},\ldots,X_{n}]$ such that, for every [[permutation|permutation]] $\sigma$:
$$P(X_{\sigma(1)},\ldots,X_{\sigma(n)})=P(X_{1},\ldots,X_{n}).$$