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Packages for computing with symmetric functions, and combinatorics

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Mathematica-packages

Packages for computing with symmetric functions, and combinatorics

These are all work in progress, but some of these packages might be useful for those who prefers Mathematica over Sage.

SymmetricFunctions.m

This is a package for working with symmetric functions, see https://www.symmetricfunctions.com/. It has the core bases, as well as Jack and Macdonald polynomials, LLT polynomials, SchurP and SchurQ functions, the Hall inner product, plethysm and the Delta operator.

This also has support for working multiple alphabets, which is useful when dealing with plethysm calculus.

Compare with Stembridge's sf package for Maple, or Curtis Greene's symfun13 package.

See the SymmetricFunctions-Introduction.nb for a brief introduction.

Updates

  • 2023-08-08 Code added for storing transition matrices between sessions.
  • 2020-08-25 Finished big refactoring. Many functions are now more intuitive, and basis conversion is quicker.

CombinatoricTools.m

Functions for permutation statistics (major index, inversions, Bruhat order, etc.), compositions, partitions, q-analogs, the Foata map, and various helper functions.

NewTableaux.m

Functions for generating standard Young tableaux, semi-standard Young tableaux, RSK, promotion and crystal operators.

CatalanObjects.m

Various different families of Catalan objects, and ways to draw them.

ChromaticFunctions.m

Chromatic (quasi)symmetric functions and LLT polynomials associated with unit interval graphs. Various functions related to unit-interval graphs.

GTPatterns.m

Methods for generating GT-patterns (Gelfand-Tsetlin patterns) which are in bijection with semi-standard Young tableaux.

MacdonaldPolynomials.m

This is an older package, and not very up to date. It has Schubert polynomials, permuted-basement Macdonald polynomials, and various non-symmetric polynomials.

Tex2WebUtilities.m

I use this mainly for generating the bibliography on the Symmetric functions catalog. It can parse .bib-files and produce an associative array of the data. There are also functions for converting ytableau syntax to HTML.

PosetData.m

This is a file which mainly contains non-isomorphic posets.

TreesData.m

This is a file which mainly contains non-isomorphic trees.

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