symbolicJackCombination

Expression of a symmetric polynomial as a linear combination
 of Jack polynomials with a symbolic Jack parameter.

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

symbolicJackCombination function

<dl><dt>qspray</dt>
<dd>a <code>qspray</code> object or a <code>symbolicQspray</code> object
defining a symmetric polynomial</dd>
<dt>which</dt>
<dd>which Jack polynomials, <code>"J"</code>, <code>"P"</code>, <code>"Q"</code> or
<code>"C"</code></dd>
<dt>check</dt>
<dd>Boolean, whether to check the symmetry</dd></dl>

Arguments

Symmetric polynomial in terms of symbolic Jack polynomials — symbolicJackCombination

<dl>

<dt>qspray</dt>
<dd>a <code>qspray</code> object or a <code>symbolicQspray</code> object
defining a symmetric polynomial</dd>


<dt>which</dt>
<dd>which Jack polynomials, <code>"J"</code>, <code>"P"</code>, <code>"Q"</code> or
<code>"C"</code></dd>


<dt>check</dt>
<dd>Boolean, whether to check the symmetry</dd>

</dl>

symbolicJackCombination: Symmetric polynomial in terms of symbolic Jack polynomials

Description

Usage

Value

Arguments