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In algebra, an alternating polynomial is a polynomial f {\displaystyle f} such that if one switches any two of the variables, the polynomial changes sign:
Equivalently, if one permutes the variables, the polynomial changes in value by the sign of the permutation:
More generally, a polynomial f {\displaystyle f} is said to be alternating in x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} if it changes sign if one switches any two of the x i {\displaystyle x_{i}} , leaving the y j {\displaystyle y_{j}} fixed.