Zonal

Evaluates a zonal polynomial. The zonal polynomials are the
 Jack \(C\)-polynomials with Jack parameter \(\alpha=Z\).

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

Zonal function

<dl><dt>x</dt>
<dd>values of the variables, a vector of <code>bigq</code> numbers, or a
vector that can be coerced as such (e.g. <code>c("2", "5/3")</code>)</dd>
<dt>lambda</dt>
<dd>an integer partition, given as a vector of decreasing
integers</dd></dl>

Arguments

Evaluation of zonal polynomial - C++ implementation — Zonal

<dl>

<dt>x</dt>
<dd>values of the variables, a vector of <code>bigq</code> numbers, or a
vector that can be coerced as such (e.g. <code>c("2", "5/3")</code>)</dd>


<dt>lambda</dt>
<dd>an integer partition, given as a vector of decreasing
integers</dd>

</dl>

Zonal: Evaluation of zonal polynomial - C++ implementation

Description

Usage

Value

Arguments

Examples