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Adding short description: "Function that is invariant under a permutation of its variables" (Shortdesc helper) |
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{{Short description|Function that is invariant under a permutation of its variables}}
{{About| general properties of symmetric functions of several real or complex variable|the ring of symmetric functions in algebraic combinatorics|ring of symmetric functions|symmetric functions on elements of a vector space |symmetric tensor}}
In [[mathematics]], a [[Function (mathematics)|function]] of ''n'' variables is '''symmetric''' if its value is the same no matter the order of its [[argument of a function|arguments]]. For example, if <math>f=f(x_1,x_2)</math> is a symmetric function, then <math>f(x_1,x_2)=f(x_2,x_1)</math> for all <math>x_1</math> and <math>x_2</math> such that <math>(x_1,x_2)</math> and <math>(x_2,x_1)</math> are in the [[Domain of a function|___domain]] of ''f''. The most commonly encountered symmetric functions are [[polynomial function]]s, which are given by the [[symmetric polynomial]]s.
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