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{{About|general properties of symmetric functions|the ring of symmetric functions in algebraic combinatorics|ring of symmetric functions}}
{{technical|date=March 2013}}
In [[mathematics]], a '''symmetric function of ''n'' variables''' is one whose value at any ''n''-[[tuple]] of [[argument of a function|arguments]] is the same as its value at any [[permutation]] of that ''n''-tuple (e.g. if <math>f(\bold{x})=f(x_1,x_2,x_3)</math>, the function can be symmetric on all its variables, or just on <math>(x_1,x_2)</math>, <math>(x_2,x_3)</math>, or <math>(x_1,x_3)</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.
== Symmetrization ==
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