Symmetric sum
Revision as of 15:53, 17 June 2018 by Mathematrucker (talk | contribs) (Added in the definition of symmetric function and cleaned things up a bit.)
The symmetric sum of a function
of
variables is defined to be
, where
ranges over all permutations of
. More generally, a symmetric sum of
variables is a sum that is unchanged by any permutation of its variables. More generally still, a symmetric function of
variables is a function that is unchanged by any permutation of its variables.
Thus, the symmetric sum of a symmetric function satisfies
Any symmetric sum can be written as a polynomial of elementary symmetric sums.
See also
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