Endliche Gruppenaktionen auf Funktionenmengen: Das Lemma von Burnside -- Repräsentantenkonstruktionen -- Anwendungen in der Musiktheorie

It is a book about Mathematics and Music. Mazzola uses methods from group theory and category theory to describe music theoretical problems. 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 There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results.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. Titel Inhaltsverzeichnis Figurenverzeichnis Tabellenverzeichnis Vorwort und Einleitung 1. Das Lemma von Burnside, angewendet auf Gruppenaktionen auf Funktionenmengen 1.1 Grundlagen 1.2 Endliche Gruppenaktionen auf Funktionenmengen 1.3 Die Diagonalsituation auf Y^X 1.4 Die Gruppenaktion von GxH auf Y^X 1.5 Die Gruppenaktionen nach (1.2.1) und (1.2.2) auf Y^X, Y^X_inj und Y^X_surj 1.6 Das Lemma von Cauchy-Frobenius 1.7 Anwendungen 2. Erzeugung von Orbit-Repräsentanten 2.1 Repräsentanten von k-Motiven 2.2 Eine weitere Konstruktionsaufgabe Literaturverzeichnis Index Enumerative combinatorics deals with the basic problem of counting how many objects have a given property, a subject of great applicability. This book provides an introduction at a level suitable for graduate students. Extensive exercises with solutions show connections to other areas of mathematics. Written for students with a basic knowledge of linear algebra and abstract algebra, this text contains a large number of exercises graded in difficulty, with solutions or references for almost all exercises. Guerino Mazzola ; Unter Mitarbeit Von Daniel Muzzulini ; Mit Einem Beitrag Von Georg Rainer Hofmann. Bibliography: P. [335]-342. The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Richard P. Stanley. Includes Bibliographies And Index.