Enumerative Combinatorics: Volume 1 / Edition 1by Richard P. Stanley
Pub. Date: 04/28/1997
Publisher: Cambridge University Press
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. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory including jeu de taquin and the Littlewood-Richardson rule. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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.
Table of ContentsWhat is enumerative combinatorics?
Partially ordered sets
Rational generating functions
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