Difference between revisions of "Symmetric sum"
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Latest revision as of 12:52, 8 October 2023
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 sometimes used to denote the sum of
over all
subsets of size
in
.
See also
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