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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. While this notion can apply to any type of function whose ''n'' arguments live in the same 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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==References==
* Joseph P. S. Kung, [[Gian-Carlo Rota]], & Catherine H. Yan (2009) ''Combinatorics: The Rota Way'', §5.1 Symmetric functions, pp 222–5, [[Cambridge University Press]] ISBN 978-0-521-73794-4 .
[[Category:Symmetric functions| ]]
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