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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto

contact


François Bergeron
University of Quebec in Montreal
MR ID: 35230
Reference #
OMN:202504.111460

Attributes

Posted date
2025-04-18 02:59:09
Revised date
2025-04-18 02:59:09
Level
   Graduate
Notes type
   Short Notes
Topic
   Algebra
      Group Theory
   Discrete Mathematics
      Combinatorics
   Topology
      Geometric Topology and Knot Theory

Macdonald Polynomials and Operators, and Catalan Combinatorics

Our main aim with these notes is to introduce the combinatorial and symmetric function tools
that relate to the description of the Poincar´e polynomial of the triply graded Khovanov-Rozansky
homology of torus links, a.k.a. the (reduced) “superpolynomial” of these links. These where written in the context of the AIM Research Community on Link Homology.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (680K) 04/18/25