Enumerative Combinatorics: Volume 2 (Cambridge Studies in Advanced Mathematics)

Stanley, Richard P.

Cambridge University Press（2001/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 600 p.
• 言語 ENG
• 商品コード 9780521789875
• DDC分類 511.62

基本説明

New in paperback. Hardcover is out of print. This second volume of a basic introduction covers the composition of generating functions, trees, algebraic generating functions, D-Finite generating functions, et al.

Full Description

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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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

Contents

5. Composition of generating functions; 6. Algebraic, D-finite, and noncommutative generating functions; 7. Symmetric functions; Appendix Sergey Fomin.