SchurCombination

Expression of a symmetric polynomial as a linear combination
 of some Schur polynomials.

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

SchurCombination function

<dl><dt>qspray</dt>
<dd>a <code>qspray</code> object defining a symmetric polynomial</dd>
<dt>check</dt>
<dd>Boolean, whether to check the symmetry of <code>qspray</code></dd></dl>

Arguments

Symmetric polynomial in terms of the Schur polynomials — SchurCombination

<dl>

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


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

</dl>

SchurCombination: Symmetric polynomial in terms of the Schur polynomials

Description

Usage

Value

Arguments

See Also