Enumerative combinatorics
著者
書誌事項
Enumerative combinatorics
（Cambridge studies in advanced mathematics, 49,
Cambridge University Press, 1997-1999
- v. 1 : hardcover
- v. 2 : hardcover
大学図書館所蔵 全77件
-
v. 1 : hardcover410.8//C14//076915100107364,15100107372,15100107695,
v. 2 : hardcover410.8//C14//392415100139243
注記
Originally published: Monterey, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, c1986-. (The Wadsworth & Brooks/Cole mathematics series)
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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v. 1 : hardcover ISBN 9780521553094
内容説明
This book is the first of a two-volume basic introduction to enumerative combinatorics at a level suitable for graduate students and research mathematicians. It concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. The book covers those parts of enumerative combinatorics of greatest applicability to other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods (including the Principle of Inclusion-Exclusion), partially ordered sets, and rational generating functions. There are a large number of exercises, almost all with solutions, which greatly augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
目次
- 1. What is enumerative combinatorics?
- 2. Sieve methods
- 3. Partially ordered sets
- 4. Rational generating functions.
- 巻冊次
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v. 2 : hardcover ISBN 9780521560696
内容説明
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.
目次
- 5. Composition of generating functions
- 6. Algebraic, D-finite, and noncommutative generating functions
- 7. Symmetric functions
- Appendix Sergey Fomin.
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