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Maple functions for computing

Macdonald polynomials

This is an integrated package for studying symmetric functions

Includes limited functions for handling partitions

SF updated and should work
on all versions of Maple.

John Stembridge

This is a complete sytem for studying algebraic combinatorics

Symmetric Functions on different Alphabets, Free Module over symmetric polynomials, NonCommutative Symmetric Functions

Characters of Linear Groups, Schubert Polynomials, SYMmetric Functions, TABleaux, FREE algebra, hyperoctahedral Algebras

Symmetric Group Algebra, NilCoxeter Algebra, IDCoxeter Algebra, HEcKe Algebra, hyperoctahedral groups, Symmetric Groups

Classical Groups, PARTitions, COMPositions

Sébastien Veigneau, Alain Lascoux and Jean-Yves Thibon

defintions of Macdonald polynomials P_\mu[X;q,t], J_\mu[X;q,t], H_\mu[X;q,t]

Vertex operators for J & H basis to add row and column of size 2

Vertex operators for J & H that add a row of size 3 to a polynomial indexed by a two column shape

Functions to compute J & H basis that are FAST when the case is covered by the vertex operator formulas

Hall-Littlewood SFs and vertex operator

Vertex operator formulas are from:

M. A. Zabrocki, A Macdonald Vertex Operator and

Standard Tableaux Statistics for the Two-Column $(q,t)$-Kostka Coefficients,

Electron. J.
Combinat. 5,
R45 (1998), 46pp.

M. A. Zabrocki, Positivity for special cases of $(q,t)$-Kostka coefficients and standard tableaux statistics.

Functions for creating symmetric and non-symmetric Jack and Macdonald symmetric functions

Cherednick's double affine Hecke algebra functions

Provided by A. Lascoux

Determinental formulas for the Macdonald polynomials H_\mu[X;q,t] expanded in terms of s_\la[X/(1-q)] basis

Functions to expand these determinants

Formulas are from:

L. Lapointe, A. Lascoux, J. Morse, Determinantal expressions of Macdonald polynomials

Main functions:

operator that
adds a ribbon to the left of a Schur function

operators
that add a column on the homogeneous & Hall-Littlewood functions

q-deformations
of the ribbon operators

operators
that add a column on the Macdonald functions

Formulas are from:

Ribbon Operators
and Hall-Littlewood Symmetric Functions, Adv. in Math., 156 (2000),
pp. 33-43.

Vertex operators of the form \sum_i f_i g_i^\perp that add a column to elementary and homogeneous symmetric functions

Symmetric function operators to add a row or a sequence of columns to the monomial and forgotten symmetric functions

Symmetric function operators to add a row or a sequence of columns to the Schur symmetric functions.

Symmetric function operators to add a sequence of columns to the power symmetric functions.

For monomial, forgotten and Schur, the column operators has the property that if length(\la) > the length of the column being added then the result is 0.

Formulas are from:

M. A. Zabrocki, Vertex operators for standard bases of the symmetric functions.

A function to compute the operator nabla on arbitrary homogeneous symmetric functions

Many q,t analogs of sequences assocated with trees, Dyck paths and parking functions come from this operator, and included are the ones corresponding to n^n, (n+1)^(n-1), and the Catalan numbers

Formulas are from:

Explicit Plethystic Formulas for the Macdonald q,t-Kostka Coefficients (A. Garsia, M. Haiman and G. Tesler)

Identities and positivity conjectures for some remarkable operators in the theory of symmetric function (F. Bergeron, A. Garsia, M. Haiman, and G. Tesler)

Functions to compute the qt-Catalan numbers directly from the definition. It is possible to compute this way for much larger n than using the operator nabla.

Formulas are from:

A REMARKABLE q,t-CATALAN SEQUENCE
AND q-LAGRANGE INVERSION, Adriano
Garsia, Mark Haiman

Main functions:

These files
contain tables of q,t-Kostka polynomials up to degree 10, created with
the SF package.

John Stembridge

Main functions:

A Maple program
to compute the relevant formulas given in the paper listed below.

A table of
the functions k_gamma[X;q,t] in the paper, sufficient to compute K_{lambda,mu}(q,t)
up to partitions of size 12, and certain infinite families beyond this.

A maple script
to produce and save k_gamma's and intermediate computations in "alltables".

This directory contains Maple programs for computing q,t-Kostka polynomials
by means of the formulas given in the paper

A. M. Garsia and G. Tesler, Plethystic Formulas for Macdonald $q,t$-Kostka
Coefficients

Advances in Mathematics, volume 123, number 2, November 10, 1996, pp.
143-222.

If you have suggestions or other Maple functions/packages/efficiency improvements e-mail me at .