Symmetric Polynomial - Alternating Polynomials

Alternating Polynomials

Analogous to symmetric polynomials are alternating polynomials: polynomials that, rather than being invariant under permutation of the entries, change according to the sign of the permutation.

These are all products of the Vandermonde polynomial and a symmetric polynomial, and form a quadratic extension of the ring of symmetric polynomials: the Vandermonde polynomial is a square root of the discriminant.