# Polynomials

### Some articles on polynomials, polynomial:

Alternating Polynomial - Relation To Symmetric Polynomials
... Products of symmetric and alternating polynomials (in the same variables ) behave thus the product of two symmetric polynomials is symmetric, the product of a symmetric polynomial ... Thus, the direct sum of the spaces of symmetric and alternating polynomials forms a superalgebra (a -graded algebra), where the symmetric polynomials are the even part, and the ... This grading is unrelated to the grading of polynomials by degree ...
Charlier Polynomials
... In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier ... hypergeometric function by where are Laguerre polynomials ...
Alternating Polynomial - Unstable
... Alternating polynomials are an unstable phenomenon (in the language of stable homotopy theory) the ring of symmetric polynomials in n variables can be obtained from the ring of symmetric polynomials in ... However, this is not the case for alternating polynomials, in particular the Vandermonde polynomial ...
Capelli's Identity - Relations With Representation Theory - Case m = 1 and Representation Sk Cn
... we have xi1, which is abbreviated as xi In particular, for the polynomials of the first degree it is seen that Hence the action of restricted to the space of ... the representation theory point of view, the subspace of polynomials of first degree is a subrepresentation of the Lie algebra, which we identified with the standard representation in ... it is seen that the differential operators preserve the degree of the polynomials, and hence the polynomials of each fixed degree form a subrepresentation of the Lie algebra ...