Alternating polynomial

In algebra, an alternating polynomial is a polynomial $f(x_1,\dots,x_n)$ 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 $f(x_1,\dots,x_n,y_1,\dots,y_t)$ is said to be alternating in $x_1,\dots,x_n$ if it changes sign if one switches any two of the $x_i$ , leaving the $y_j$ fixed.

单词	Alternating polynomial
释义	Alternating polynomial 英语百科 Alternating polynomial In algebra, an alternating polynomial is a polynomial $f(x_1,\dots,x_n)$ 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 $f(x_1,\dots,x_n,y_1,\dots,y_t)$ is said to be alternating in $x_1,\dots,x_n$ if it changes sign if one switches any two of the $x_i$ , leaving the $y_j$ fixed.
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