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| Softcover ISBN: | 978-0-8218-4411-3 |
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| Softcover ISBN: | 978-0-8218-4411-3 |
| Product Code: | ULECT/41 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-2185-4 |
| Product Code: | ULECT/41.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-0-8218-4411-3 |
| eBook ISBN: | 978-1-4704-2185-4 |
| Product Code: | ULECT/41.B |
| List Price: | $134.00 $101.50 |
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Book DetailsUniversity Lecture SeriesVolume: 41; 2008; 167 ppMSC: Primary 05
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.
ReadershipGraduate students and research mathematicians interested in combinatorics.
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Table of Contents
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Chapters
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Chapter 1. Introduction to $q$-analogues and symmetric functions
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Chapter 2. Macdonald polynomials and the space of diagonal harmonics
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Chapter 3. The $q, t$-Catalan numbers
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Chapter 4. The $q, t$-Schröder polynomial
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Chapter 5. Parking functions and the Hilbert series
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Chapter 6. The shuffle conjecture
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Chapter 7. The proof of the $q, t$-Schröder theorem
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Appendix A. The combinatorics of Macdonald polynomials
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Appendix B. The Loehr-Warrington conjecture
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Appendix C. Solutions to exercises
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Graduate students and research mathematicians interested in combinatorics.
-
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
-
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
