SkewMacdonaldPol

Returns the skew Macdonald polynomial associated to
 the given skew partition.

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

SkewMacdonaldPol function

<dl><dt>n</dt>
<dd>number of variables, a positive integer</dd>
<dt>lambda, mu</dt>
<dd>integer partitions defining the skew partition:
<code>lambda</code> is the outer partition and <code>mu</code> is the inner partition
(so <code>mu</code> must be a subpartition of <code>lambda</code>)</dd>
<dt>which</dt>
<dd>which skew Macdonald polynomial, <code>"P"</code>, <code>"Q"</code>
or <code>"J"</code></dd></dl>

Arguments

Skew Macdonald polynomial — SkewMacdonaldPol

<dl>

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


<dt>lambda, mu</dt>
<dd>integer partitions defining the skew partition:
<code>lambda</code> is the outer partition and <code>mu</code> is the inner partition
(so <code>mu</code> must be a subpartition of <code>lambda</code>)</dd>


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

</dl>

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SkewMacdonaldPol: Skew Macdonald polynomial

Description

Usage

Value

Arguments