Difference between revisions of "Symmetric sum"
(roman lettering seems appropriate for the "sym" subscript) |
(→See also) |
||
(One intermediate revision by one other user not shown) | |||
Line 12: | Line 12: | ||
*[[Cyclic sum]] | *[[Cyclic sum]] | ||
*[[Muirhead's Inequality]] | *[[Muirhead's Inequality]] | ||
− | + | *[[PaperMath’s sum]] | |
{{stub}} | {{stub}} | ||
− | [[Category: | + | [[Category:Algebra]] |
[[Category:Definition]] | [[Category:Definition]] |
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
This article is a stub. Help us out by expanding it.