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...

it is an alternating polynomial, not a symmetric polynomial. The defining property of the Vandermonde polynomial is that it is alternating in the entries...

property of this invariant states that the Jones polynomial of an alternating link is an alternating polynomial. This property was proved by Morwen Thistlethwaite...

symmetric polynomial is a polynomial P(X1, X2, ..., Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally...

In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that...

_{n}}\end{matrix}}\right]} are alternating polynomials by properties of the determinant. A polynomial is alternating if it changes sign under any transposition...

symmetric functions are polynomial functions, which are given by the symmetric polynomials. A related notion is alternating polynomials, which change sign...

of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...

of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...

In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct...