KostaFoulkesPolynomial

Kostka-Foulkes polynomial for two given partitions.

Schur polynomials appear in combinatorics and zonal
polynomials appear in random matrix theory. They are particular cases
of Jack polynomials. This package allows to compute these polynomials
and other symmetric multivariate polynomials: flagged Schur
polynomials, factorial Schur polynomials, t-Schur polynomials,
Hall-Littlewood polynomials, Macdonald polynomials, and modified
Macdonald polynomials. In addition, it can compute the Kostka-Jack
numbers, the Kostka-Foulkes polynomials, the Kostka-Macdonald
polynomials, and the Hall polynomials. Mainly based on Demmel &
Koev's paper (2006) <doi:10.1090/S0025-5718-05-01780-1> and
Macdonald's book (1995) <doi:10.1093/oso/9780198534891.003.0001>.

Stc3<a9>phane Laurent

jack

Jack, Zonal, Schur, and Other Symmetric Polynomials

Stéphane Laurent

KostaFoulkesPolynomial function

<dl><dt>lambda, mu</dt>
<dd>integer partitions; in order for the Kostka-Foulkes
polynomial to be non-zero, a necessary condition is that <code>lambda</code>
and <code>mu</code> have the same weight; more precisely, <code>mu</code> must
be dominated by <code>lambda</code></dd></dl>

Arguments

Kostka-Foulkes polynomial — KostaFoulkesPolynomial

<dl>

<dt>lambda, mu</dt>
<dd>integer partitions; in order for the Kostka-Foulkes
polynomial to be non-zero, a necessary condition is that <code>lambda</code>
and <code>mu</code> have the same weight; more precisely, <code>mu</code> must
be dominated by <code>lambda</code></dd>

</dl>

KostaFoulkesPolynomial: Kostka-Foulkes polynomial

Description

Usage

Value

Arguments