Explore: Hall Polynomials

where the latter is the Schur P polynomials. Expanding the Schur polynomials in terms of the Hall–Littlewood polynomials, one has s λ ( x ) = ∑ μ K λ μ

a polynomial. In this context other collections of specific symmetric polynomials, such as complete homogeneous, power sum, and Schur polynomials play

In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed

Hall algebra, and Hall polynomials Hall subgroup Hall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage theorem Hall word

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}

Philip Hall (1959), both of whom published no more than brief summaries of their work. The Hall polynomials are the structure constants of the Hall algebra

elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible

For more details on the derivation see and. The Hall polynomials are the structure constants of the Hall algebra. In addition to the product, the coproduct

generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor