qtSkewKostkaPolynomials: Skew qt-Kostka polynomials

In jack: Jack, Zonal, Schur, and Other Symmetric Polynomials

Skew qt-Kostka polynomials

Description

Skew qt-Kostka polynomials associated to a given skew partition.

Usage

qtSkewKostkaPolynomials(lambda, mu)

Arguments

lambda, mu

integer partitions defining the skew partition: lambda is the outer partition and mu is the inner partition (so mu must be a subpartition of lambda)

Value

A list. The skew qt-Kostka polynomials are usually denoted by K_{\lambda/\mu, \nu}(q, t) where q and t denote the two variables, \lambda and \mu are the two integer partitions defining the skew partition, and \nu is an integer partition. One obtains the skew Kostka-Foulkes polynomials by substituting q with 0. For given partitions \lambda and \mu, the function returns the polynomials K_{\lambda/\mu, \nu}(q, t) as qspray objects for all partitions \nu of the same weight as the skew partition. The generated list is a list of lists with two elements: the integer partition \nu and the polynomial.

jack documentation built on Sept. 11, 2024, 6:34 p.m.