Macdonald Polynomials

Purpose: This page is to make available some of the resources and results associated to the symmetric functions known as Macdonald polynomials (for the most part, type A only). There are some fantastic conjectures and results discovered all the time associated to this field and my main direction of interest is from their combinatorial perspective.  This hardly does them justice since there is a strong interest from a wide range of fields such as algebraic geometry, representation theory, mathematical physics, etc.

What's new?: I placed programs to compute ribbon operators and the ribbon rule in the Maple section. (11/5/01)  There is a graphical explanation of the statistics by Garsia and Haglund for the q,t-Catalan numbers. (9/7/00).


Symmetric Functions

  • Defintions of symbols used in this Web Site
  • Maple packages
  • TEX tables of q,t-Kostka polynomials
  • Table of specializations
  • A defintion of the operator nabla

  • Representation Theory

  • A statement of the n! Theorem
  • Macdonald Polynomials, The n! Conjecture, and Other Amenities (A. Garsia)
  • Harmonic Polynomials for the Symmetric Group and Macdonald Symmetric Polynomials (F. Bergeron)

  • Combinatorics

  • LATEX typeset cyclage posets
  • qt-analogs of sequences 
    1. Catalan numbers
    2. binomial coefficients
    3. number of rooted forests
    4. number of standard tableaux
  • qt-Kostka stats for standard tableau

  • Other

  • Reference for LATEX math symbols
  • Reference for LaTeX help

  • This web page is maintained by Mike Zabrocki. Contibutions are welcome (encouraged). Send me Maple packages, expositions, open problems, tools that you have for studying Macdonald Polynomials, notes on Macdonald, Hall-Littlewood, Jack symmetric functions and I will publish them to this site.

    Mike Zabrocki
    York University
    Web page: