Some articles on power sum symmetric, symmetric, power, power sum, sum, powers, sums:
... In mathematics, specifically in commutative algebra, the power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational ... However, not every symmetric polynomial with integral coefficients is generated by integral combinations of products of power-sum polynomials they are a generating set over the rationals, but not over the integers ...
... For each integer k ≥ 1, the monomial symmetric polynomial m(k,0,…,0)(X1, …, Xn) is of special interest, and called the power sum symmetric polynomial ... More precisely, Any symmetric polynomial in X1, …, Xn can be expressed as a polynomial expression with rational coefficients in the power sum symmetric polynomials p1(X1, …, Xn), …, pn(X1, …, Xn) ... In particular, the remaining power sum polynomials pk(X1, …, Xn) for k > n can be so expressed in the first n power sum polynomials for example In contrast to the situation for the ...
... The power sum symmetric polynomial of degree k in variables x1.. ... is the sum of all kth powers of the variables ... are Thus, for each nonnegative integer, there exists exactly one power sum symmetric polynomial of degree in variables ...
... It should be noted that the name "symmetric function" for elements of ΛR is a misnomer in neither construction the elements are functions, and in fact ... of Λ (unlike those of Λn) are no longer polynomials they are formal infinite sums of monomials ... We have therefore reverted to the older terminology of symmetric functions ...
Famous quotes containing the words power and/or sum:
“He had come down, He said, to clean the earth
Of the dirtiness of war.
Now tell of why His power failed Him there?
His power did not fail. It was that, simply,
He found how much the people wanted war.”
—Gwendolyn Brooks (b. 1917)
“The real risks for any artist are taken ... in pushing the work to the limits of what is possible, in the attempt to increase the sum of what it is possible to think. Books become good when they go to this edge and risk falling over itwhen they endanger the artist by reason of what he has, or has not, artistically dared.”
—Salman Rushdie (b. 1947)