Alternating polynomial
In algebra, an alternating polynomial is a polynomial f ( x 1 , … , x n ) {\displaystyle f(x_{1},\dots ,x_{n})} such that if one switches any two of the variables, the polynomial changes sign: f ( x 1 , … , x j , … , x i , … , x n ) = − f ( x 1 , … , x i , … , x j , … , x n ) . {\displaystyle f(x_{1},\dots ,x_{j},\dots ,x_{i},\dots ,x_{n})=-f(x_{1},\dots ,x_{i},\dots ,x_{j},\dots ,x_{n}).} Equivalently, if one permutes the variables, the polynomial changes in value by the sign of the permutation: f ( x σ ( 1 ) , … , x σ ( n ) ) = s g n ( σ ) f ( x 1 , … , x n ) .