Enumerative Combinatorics

Volume 2

Enumerative Combinatorics

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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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


"...sure to become a standard as an introductory graduate text in combinatorics."
Bulletin of the AMS"

"As a researcher, Stanley has few peers in combinatorics...the trove of exercises with solutions will form a vital resource; indeed, exercise 6.19 on the Catalan numbers, in 66 (!) parts, justifies the investment by itself. Both volumes highly recommended for all libraries."

"Volume 2 not only lives up to the high standards set by Volume 1, but surpasses them... Stanley's book is a valuable contribution to enumerative combinatorics. Beginners will find it an accessible introduction to the subject, and experts will still find much to learn from it."
Mathematical Reviews

'… an authoritative account of enumerative combinatorics.' George E. Andrews, Bulletin of the London Mathematical Society

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


Winner of the 2001 Leroy A. Steele Prize for Mathematical Exposition