Symmetric sum
Revision as of 16:48, 17 June 2018 by Mathematrucker (talk | contribs) (Added subset interpretation of symmetric sum notation.)
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.
Any symmetric sum can be written as a polynomial of elementary symmetric sums.
A symmetric function of variables is a function that is unchanged by any permutation of its variables. The symmetric sum of a symmetric function
therefore satisfies
Given variables
and a symmetric function
with
, the notation
is also sometimes used to denote the sum of
over all
subsets of size
in
.
See also
This article is a stub. Help us out by expanding it.