The Q,T-Catalan Numbers and the Space of Diagonal Harmonics
2007
American Mathematical Society (Verlag)
978-0-8218-4411-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4411-3 (ISBN)
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Contains detailed descriptions of the many exciting developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of research in algebraic combinatorics. This book includes discussions of some topics in the theory of symmetric functions, such as the practical uses of plethystic substitutions.
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.
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.
Introduction to $q$-analogues and symmetric functions Macdonald polynomials and the space of diagonal harmonics The $q, t$-Catalan numbers The $q, t$-Schroder polynomial Parking functions and the Hilbert series The shuffle conjecture The proof of the $q, t$-Schroder theorem The combinatorics and Macdonald polynomials The Loehr-Warrington conjecture Solutions to exercises Bibliography.
| Erscheint lt. Verlag | 1.1.2008 |
|---|---|
| Reihe/Serie | University Lecture Series |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 323 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| ISBN-10 | 0-8218-4411-3 / 0821844113 |
| ISBN-13 | 978-0-8218-4411-3 / 9780821844113 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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