The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series)

Softcover

ISBN 10: 0821844113 ISBN 13: 9780821844113

Publisher: American Mathematical Society, 2007

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.

Review:

"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