A function f on n variables x₁,x₂,…,x_n is skew-symmetric, or alternating, if f changes sign when two variables x_i and x_j are swapped. Equivalently,

for all permutations σ‎ of n variables; here sgn(σ‎) denotes the parity of σ‎, 1 if σ‎ is even and −1 if σ‎ is odd. See elementary symmetric polynomial.