Ring of symmetric functions: Difference between revisions

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Revision as of 05:02, 26 April 2012

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{{ main | Symmetric polynomial }}

The study of symmetric functions is based on that of symmetric polynomials. In a [[polynomial ring]] in some finite set of indeterminates, there is an action by ring [[automorphism]]s of the [[symmetric group]] on (the indices of) the indeterminates (simultaneaouslysimultaneously substituting each of them for another according to the permutation used). The invariants for this action form the subring of symmetric polynomials. If the indeterminates are ''X''₁,…,''X''_''n'', then examples of such symmetric polynomials are

: <math>X_1+X_2+\cdots+X_n, \, </math>