Enumerative Combinatorics: Volume 2
Series: Cambridge Studies in Advanced Mathematics; 62;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 13 January 1999
- ISBN 9780521560696
- Binding Hardback
- No. of pages600 pages
- Size 237x160x38 mm
- Weight 1045 g
- Language English 0
Categories
Short description:
An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.
MoreLong 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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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.
'This magnificent two-volume work is best described by a quote from Gian-Carlo Rota's Forward to Volume 2: I find it impossible to predict when Richard Stanley's two-volume exposition of combinatorics may be superseded. No one will dare try, let alone be able, to match the thoroughness of coverage, the care for detail, the definitiveness of proof, the elegance of presentation.' J. E. Graver
Table of Contents:
5. Composition of generating functions; 6. Algebraic, D
-finite, and noncommutative generating functions; 7. Symmetric functions; Appendix Sergey Fomin.
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