Enumerative Combinatorics, Volume 2
by Richard P. Stanley
Cambridge Studies in Advanced Mathematics (62)
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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 show more 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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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. show lessTags
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"Richard Stanley's Enumerative Combinatorics, Volume 1, appeared in 1986, and its interesting choice of topics, clear prose style, numerous exercises, and scholarly erudition quickly won it a large following. The long-awaited Volume 2 appeared in 1999, and it is an impressive work of scholarship that surpasses the high standards set by Volume 1."
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