Enumerative Combinatorics (The Wadsworth & Brooks/Cole Mathematics Series) - Softcover

Stanley, Richard

Softcover

ISBN 10: 146159765X ISBN 13: 9781461597650

Publisher: Springer, 2012

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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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

Enumerative combinatorics deals with the basic problem of counting how many objects have a given property. Since this problem arises in many areas of mathematics and science the subject is of great applicability. This book provides an introduction to the subject at a level suitable for graduate students and research mathematicians. The author has made a special effort, by providing extensive exercises with solutions, to show the broad applicability of enumerative combinatorics to other areas of mathematics.

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.

Gian-Carlo Rota (1932 1999) was a Professor of Applied Mathematics and Natural Philosophy at the Massachusetts Institute of Technology. He was a member of the National Academy of Science. He was awarded the 1988 Steele Prize of the American Mathematical Society for his 1964 paper 'On the Foundations of Combinatorial Theory I. Theory of Moebius Functions.' He was the founding editor of the Journal of Combinatorial Theory.

Edition details

• Publisher: Springer
• Publication date: 2012
• Language: English
• ISBN 10: 146159765X
• ISBN 13: 9781461597650
• Binding: Paperback
• Number of pages: 319