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of to .

Symmetry

A symmetric function is a function that is unchanged when two variables and are interchanged:

:

where and are each one of . For example:

:

is symmetric in since interchanging any pair of leaves unchanged, but is not symmetric in all of , since interchanging with or or gives a different function.

Function composition

Suppose the functions

:

or more compactly , are all defined on a domain

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