qtSkewKostkaPolynomials {jack}R Documentation

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 Kλ/μ,ν(q,t)K_{\lambda/\mu, \nu}(q, t) where qq and tt denote the two variables, λ\lambda and μ\mu are the two integer partitions defining the skew partition, and ν\nu is an integer partition. One obtains the skew Kostka-Foulkes polynomials by substituting qq with 00. For given partitions λ\lambda and μ\mu, the function returns the polynomials Kλ/μ,ν(q,t)K_{\lambda/\mu, \nu}(q, t) as qspray objects for all partitions ν\nu of the same weight as the skew partition. The generated list is a list of lists with two elements: the integer partition ν\nu and the polynomial.


[Package jack version 6.1.0 Index]