Enumerative Combinatorics: Volume 2: 62 (Cambridge Studies in Advanced Mathematics, Series Number 62)
Cambridge University Press, 3/23/2010
EAN 9780521789875, ISBN10: 0521789877
Paperback, 600 pages, 22.9 x 15.2 x 3.8 cm
Language: English
Originally published in English
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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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.
5. Composition of generating functions
6. Algebraic, D-finite, and noncommutative generating functions
7. Symmetric functions
Appendix Sergey Fomin.