SoftcoverISBN:  9780821844113 
Product Code:  ULECT/41 
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AMS Member Price:  $36.00 
eBookISBN:  9781470421854 
Product Code:  ULECT/41.E 
List Price:  $42.00 
MAA Member Price:  $37.80 
AMS Member Price:  $33.60 
SoftcoverISBN:  9780821844113 
eBookISBN:  9781470421854 
Product Code:  ULECT/41.B 
List Price:  $87.00$66.00 
MAA Member Price:  $78.30$59.40 
AMS Member Price:  $69.60$52.80 
Softcover ISBN:  9780821844113 
Product Code:  ULECT/41 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
eBook ISBN:  9781470421854 
Product Code:  ULECT/41.E 
List Price:  $42.00 
MAA Member Price:  $37.80 
AMS Member Price:  $33.60 
Softcover ISBN:  9780821844113 
eBookISBN:  9781470421854 
Product Code:  ULECT/41.B 
List Price:  $87.00$66.00 
MAA Member Price:  $78.30$59.40 
AMS Member Price:  $69.60$52.80 

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 selfstudy, 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.

Table of Contents

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 LoehrWarrington conjecture

Appendix C. Solutions to exercises


Additional Material

Reviews

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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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 selfstudy, 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 LoehrWarrington 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