Polynomials

Some articles on polynomials, polynomial:

Capelli's Identity - Relations With Representation Theory - Case m = 1 and Representation Sk Cn
... 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 ... So, from 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 ... 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 ...
Complete Homogeneous Symmetric Polynomial - Properties - Relation With The Elementary Symmetric Polynomials
... between the elementary symmetric polynomials and the complete homogeneous ones which is valid for all m > 0, and any number of variables n ... it holds is from an identity of formal power series in t for the elementary symmetric polynomials, analogous to the one given above for the complete homogeneous ones (this is actually an identity of ... by the generating function for the complete homogeneous symmetric polynomials, one obtains the constant series 1, and the relation between the elementary and complete homogeneous polynomials follows from comparing ...
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 ... 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 ...