Dozenten: Dr. Mihyun Kang und Manuel Bodirsky
Termine
Beginn der Vorlesung: 13.04.2004| VL | Dienstag | 13:00 - 15:00 | (RUD 26, 1.303) |
|---|---|---|---|
| Donnerstag | 13:00 - 15:00 | (RUD 26, 1.303) | |
| Sprechzeit | Dienstag | 10:30 - 11:30 | (RUD 25, 4.410/1) |
Zuordnung
- Hauptstudium, Halbkurs
- Theoretische Informatik
Voraussetzungen
- Grundlagen der Analysis
- Grundlagen der diskreten Mathematik
- fundierte Englisch-Kenntnisse
Inhalte und Lernziele
Generating functions are an important tool in enumerative combinatorics. This course is a gentle introduction to generating functions, illustrated by many examples and applications. It will deal with formal power series, analytic properties of functions represented as power series and several techniques to derive asymptotics of the coefficients of generating functions. We apply them to the enumeration of trees, partitions, and other structures, and show how to solve recurrences with generating functions.
The participants will learn how to use generating functions to enumerate combinatorial objects and derive the asymtotics. They will master the topics through exercise assignments, individual projects and oral presentations.
Empfohlene Literatur
- , Generalfunctionology, 2nd ed., Boston, Academic Press, 1994.
- , Asymptotic enumeration methods in Handbook of Combinatorics, vol. 2, R. L. Graham, M. Groetschel, and L. Lovasz, eds., Elsevier, 1995, pp. 1063-1229
