Enumerative Combinatorics, Volume 2 - Hardcover

Stanley, Richard P.

Hardcover

ISBN 10: 0521560691 ISBN 13: 9780521560696

Publisher: Cambridge University Press, 1999

Synopsis

This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

About this title

Book Description

This is the second volume of a two-volume work on the subject of enumerative combinatorics, an area of mathematics with connections to many other topics within and outside of mathematics, such as computer science, spectroscopy, algebraic geometry, algebraic topology, and representation theory. Many topics covered (in particular, the theory of symmetric functions) are not available in any other textbook at this level, and the usefulness of the book is enhanced by over 250 exercises with solutions.Although primarily intended as a textbook for graduate students and a resource for professional mathematicians, some parts of the book will be accessible to mathematics undergraduates and even interested amateurs.

About the Author

Richard P. Stanley is a Professor of Applied Mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. In addition to the seminal two-volume book Enumerative Combinatorics, he is the author of Combinatorics and Commutative Algebra (1983) as well as more than 100 research articles in mathematics. Among Stanley's many distinctions are membership in the National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition and the 2003 Schock Prize.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1999
• Language: English
• ISBN 10: 0521560691
• ISBN 13: 9780521560696
• Binding: Hardcover
• Number of pages: 600