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90 reviewsContents: • Trees and the Composition of Generating Functions • Algebraic, D-finite, and Noncommutative Generating Functions • Symmetric Functions • Appendix 1 Knuth Equivalence, Jeu de Taquin, and the Littlewood–Richardson Rule • Appendix 2 The Characters of GL(n, ℂ) • Bibliography • Index
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and 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 and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule.
The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
• New edition includes over 150 new exercises on symmetric functions, most with solutions
• Shows the broad applicability of the material to many other areas of mathematics
• Features a section with 66 combinatorial interpretations of Catalan numbers that will appeal to amateur as well as professional mathematicians
Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
