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Doctormatt (talk | contribs) simpler initial example; article does not address the notion of being symmetric on a proper subset of variables |
Doctormatt (talk | contribs) removed "too technical" tag, since the one issue mentioned on the talk page was addressed |
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{{About|general properties of symmetric functions|the ring of symmetric functions in algebraic combinatorics|ring of symmetric functions}}
In [[mathematics]], a '''symmetric function of ''n'' variables''' is one whose value given n [[argument of a function|arguments]] is the same no matter the order of the 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 pairs <math>(x_1,x_2)</math> in the ___domain of <math>f</math>. While this notion can apply to any type of function whose ''n'' arguments have the same ___domain set, it is most often used for [[polynomial function]]s, in which case these are the functions given by [[symmetric polynomials]]. There is very little systematic theory of symmetric non-polynomial functions of ''n'' variables, so this sense is little-used, except as a general definition.
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