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jack (version 6.1.0)

qtSkewKostkaPolynomials: Skew qt-Kostka polynomials

Description

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

Usage

qtSkewKostkaPolynomials(lambda, mu)

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.

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)