SkewJackPol

Computes a skew Jack polynomial with a given 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

SkewJackPol function

<dl><dt>n</dt>
<dd>positive integer, the number of variables</dd>
<dt>lambda</dt>
<dd>outer integer partition of the skew partition</dd>
<dt>mu</dt>
<dd>inner integer partition of the skew partition; it must be a
subpartition of <code>lambda</code></dd>
<dt>alpha</dt>
<dd>the Jack parameter, any object coercible to a <code>bigq</code>
number</dd>
<dt>which</dt>
<dd>which skew Jack polynomial, <code>"J"</code>, <code>"P"</code>, <code>"Q"</code>
or <code>"C"</code></dd></dl>

Arguments

Skew Jack polynomial — SkewJackPol

<dl>

<dt>n</dt>
<dd>positive integer, the number of variables</dd>


<dt>lambda</dt>
<dd>outer integer partition of the skew partition</dd>


<dt>mu</dt>
<dd>inner integer partition of the skew partition; it must be a
subpartition of <code>lambda</code></dd>


<dt>alpha</dt>
<dd>the Jack parameter, any object coercible to a <code>bigq</code>
number</dd>


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

</dl>

SkewJackPol: Skew Jack polynomial

Description

Usage

Value

Arguments

See Also

Examples