A symmetric polynomial is a polynomial P (X 1, X 2,..., X n) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally, P is a symmetric polynomial if for any permutation σ of the subscripts 1, 2,..., n, one has P (X σ(1), X σ(2),..., X σ(n)) = P (X 1, X 2,..., X n).