**University Lecture Series**

Volume: 41;
2008;
167 pp;
Softcover

MSC: Primary 05;

Print ISBN: 978-0-8218-4411-3

Product Code: ULECT/41

List Price: $42.00

AMS Member Price: $33.60

MAA Member Price: $37.80

**Electronic ISBN: 978-1-4704-2185-4
Product Code: ULECT/41.E**

List Price: $42.00

AMS Member Price: $33.60

MAA Member Price: $37.80

#### Supplemental Materials

# The \(q,t\)-Catalan Numbers and the Space of Diagonal Harmonics: With an Appendix on the Combinatorics of Macdonald Polynomials

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*James Haglund*

This book contains detailed descriptions of the many exciting recent
developments in the combinatorics of the space of diagonal harmonics, a
topic at the forefront of current research in algebraic combinatorics.
These developments led in turn to some surprising discoveries in the
combinatorics of Macdonald polynomials, which are described in Appendix A.
The book is appropriate as a text for a topics course in algebraic
combinatorics, a volume for self-study, or a reference text for
researchers in any area which involves symmetric functions or lattice path
combinatorics.

The book contains expository discussions of some topics in the theory of
symmetric functions, such as the practical uses of plethystic
substitutions, which are not treated in depth in other texts. Exercises
are interspersed throughout the text in strategic locations, with full
solutions given in Appendix C.

#### Readership

Graduate students and research mathematicians interested in combinatorics.

#### Reviews & Endorsements

Overall the book is an excellent introduction into the combinatorial side of a beautiful and very active area of research.

-- Zentralblatt MATH

The explanations of the combinatorics are very lucid, and well thought out examples are provided at nearly every step.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics: With an Appendix on the Combinatorics of Macdonald Polynomials

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Chapter 1. Introduction to q-Analogues and Symmetric Functions 110 free
- Chapter 2. Macdonald Polynomials and the Space of Diagonal Harmonics 2736
- Chapter 3. The q, t-Catalan Numbers 4150
- Chapter 4. The q, t-Schröder Polynomial 5968
- Chapter 5. Parking Functions and the Hilbert Series 7786
- Chapter 6. The Shuffle Conjecture 91100
- Chapter 7. The Proof of the q, t-Schröder Theorem 113122
- Appendix A. The Combinatorics of Macdonald Polynomials 123132
- Appendix B. The Loehr-Warrington Conjecture 141150
- Appendix C. Solutions to Exercises 147156
- Bibliography 163172
- Back Cover Back Cover1178