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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 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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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.
Combinatorial enumeration problems. --- Enumeration problems, Combinatorial --- Combinatorial analysis --- Analyse combinatoire --- Combinatorial enumeration problems --- Problèmes combinatoires d'énumération --- 519.1 --- 519.1 Combinatorics. Graph theory --- Combinatorics. Graph theory
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517.51 --- 515.7 --- Numbers, Complex --- Functions of a real variable. Real functions --- 517.51 Functions of a real variable. Real functions --- Functional analysis --- Functions --- Analysis (Mathematics) --- Functional calculus --- Differential equations --- Mathematical analysis --- Mathematics --- Set theory --- Calculus --- Calculus of variations --- Functional equations --- Integral equations --- Measure theory. Mathematical integration --- Analyse fonctionnelle --- Fonctions (Mathématiques) --- Functional analysis. --- Calcul différentiel --- Calcul intégral --- Mesure et integration --- Topologie generale --- Traite d'analyse mathematique
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Calculus of variations. --- Calcul des variations. --- Calculus of variations
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Analyse mathématique --- Mathematical analysis. --- Calcul des variations
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Analyse mathématique --- Mathematical analysis. --- Analyse fonctionnelle --- Functional analysis. --- Mesure, Théorie de la
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Analyse fonctionnelle --- Functional analysis --- Espaces linéaires normés. --- Normed linear spaces
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Analyse mathématique. --- Mathematical analysis --- Calculus, Integral --- Lebesgue integral --- Calcul intégral. --- Lebesgue, Intégrale de.
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