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  • Cited by 1344
Cambridge University Press
Online publication date:
January 2010
Print publication year:
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Book 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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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to Volume 2: I find it impossible to predict when Richard Stanley’s two-volume exposition of combinatorics may be superseded.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

‘As a researcher, Stanley has few peers in combinatorics; as at once, to pack every page with information, connect with the reader’s intuition, and communicate the underlying, unifying philosophy of the subject.’

D. V. Feldman - University of New Hampshire

‘What else is to be added to our comments on this excellent book? Perhaps a quotation from G.-C. Rota’s foreword: ‘Every once in a long while, a textbook worthy of the name comes along … Weber, Bertini, van der Waerden, Feller, Dunford and Schwartz, Ahlfors, Stanley.’

Source: European Mathematical Society

‘… an authoritative account of enumerative combinatorics.’

George E. Andrews Source: Bulletin of the London Mathematical Society

'What else can be added to the comments upon this excellent book?'

Source: EMS Newsletter

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