# What are polynomials?

### Some articles on polynomials, polynomial:

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 ... However, this is not the case for alternating polynomials, in particular the Vandermonde polynomial ...
Charlier Polynomials
... In mathematics, Charlier polynomials (also called Poissonâ€“Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier ... are given in terms of the generalized hypergeometric function by where are Laguerre polynomials ...
Capelli's Identity - Relations With Representation Theory - Case m = 1 and Representation Sk Cn
... 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 first-order polynomials is exactly the ... 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 ...
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 ... 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 alternating polynomials are the odd part ... This grading is unrelated to the grading of polynomials by degree ...