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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

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Table of Contents

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Front/Back Matter

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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