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The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics: With an Appendix on the Combinatorics of Macdonald Polynomials
About this Title
James Haglund, University of Pennsylvania, Philadelphia, Philadelphia, PA
Publication: University Lecture Series
Publication Year:
2008; Volume 41
ISBNs: 978-0-8218-4411-3 (print); 978-1-4704-2185-4 (online)
DOI: https://doi.org/10.1090/ulect/041
MathSciNet review: MR2371044
MSC: Primary 05E05; Secondary 05A05, 05A30, 33D52
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction to $q$-analogues and symmetric functions
- Chapter 2. Macdonald polynomials and the space of diagonal harmonics
- Chapter 3. The $q, t$-Catalan numbers
- Chapter 4. The $q, t$-Schröder polynomial
- Chapter 5. Parking functions and the Hilbert series
- Chapter 6. The shuffle conjecture
- Chapter 7. The proof of the $q, t$-Schröder theorem
- Appendix A. The combinatorics of Macdonald polynomials
- Appendix B. The Loehr-Warrington conjecture
- Appendix C. Solutions to exercises