Symmetric Function

A Symmetric Function is a Function that is restricted to the Commutativity Property (whose mapping is unchanged for any Permutation of its Input Sets).

• Example(s):
  • A Distance Metric Function.
  • …
• Counter-Example(s):
  • An Anti-Symmetric Function.
• See: Symmetric Relation, Symmetric Operation.

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References

2009

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  • In mathematics, the term "symmetric function" can mean two different things. A symmetric function of n variables is one whose value at any n-tuple of 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 functions, in which case these are the functions given by symmetric polynomials. There is hardly any systematic theory of symmetric non-polynomial functions of n variables, which are therefore not considered in this article.

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