 
Summary: Symmetric Functions
Putnam Practice
September 7, 2005
Although there is no general formula that takes us from coefficients
c0, c1, ..., cn of the polynomial equation
c0xn
+ c1xn1
+ ... + cn = 0
to its roots x1, ...xn, there are formulas that take us from c0, c1, ...cn to a
large and important class of symmetric functions. A symmetric function
of x1, ..., xn is one whose value is unchanged if x1, x2, ..., xn are permuted
arbitrarily. For example, the following are symmetric functions of three
variables:
Q(x1, x2, x3) = x3
1 + x3
2 + x3
3
R(x1, x2, x3) =
x1 + x2
x3
