Universität Wien

803332 VO Combinatorics (2005S)

Combinatorics

0.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Erstmals am 3. März 2005

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 03.03. 09:15 - 10:45 Seminarraum
  • Monday 07.03. 10:00 - 11:30 Seminarraum
  • Thursday 10.03. 09:15 - 10:45 Seminarraum
  • Monday 14.03. 10:00 - 11:30 Seminarraum
  • Thursday 17.03. 09:15 - 10:45 Seminarraum
  • Monday 04.04. 10:00 - 11:30 Seminarraum
  • Thursday 07.04. 09:15 - 10:45 Seminarraum
  • Monday 11.04. 10:00 - 11:30 Seminarraum
  • Thursday 14.04. 09:15 - 10:45 Seminarraum
  • Monday 18.04. 10:00 - 11:30 Seminarraum
  • Thursday 21.04. 09:15 - 10:45 Seminarraum
  • Monday 25.04. 10:00 - 11:30 Seminarraum
  • Thursday 28.04. 09:15 - 10:45 Seminarraum
  • Monday 02.05. 10:00 - 11:30 Seminarraum
  • Monday 09.05. 10:00 - 11:30 Seminarraum
  • Thursday 12.05. 09:15 - 10:45 Seminarraum
  • Thursday 19.05. 09:15 - 10:45 Seminarraum
  • Monday 23.05. 10:00 - 11:30 Seminarraum
  • Monday 30.05. 10:00 - 11:30 Seminarraum
  • Thursday 02.06. 09:15 - 10:45 Seminarraum
  • Monday 06.06. 10:00 - 11:30 Seminarraum
  • Thursday 09.06. 09:15 - 10:45 Seminarraum
  • Monday 13.06. 10:00 - 11:30 Seminarraum
  • Thursday 16.06. 09:15 - 10:45 Seminarraum
  • Monday 20.06. 10:00 - 11:30 Seminarraum
  • Thursday 23.06. 09:15 - 10:45 Seminarraum
  • Monday 27.06. 10:00 - 11:30 Seminarraum
  • Thursday 30.06. 09:15 - 10:45 Seminarraum

Information

Aims, contents and method of the course

This course depends on the course Discrete Mathematics. There are no other prerequisites.
The following themes will be treated: Combinatorial constructions which correspond to operations on formal power series in the case of ordinary and exponential generating functions, the exponential formula and its applications, the Lagrange formula, tree structures and related themes (some different proofs of Cayley's formula on labelled trees, oriented trees and the matrix-tree theorem, plane or ordered trees, binary trees, Dyck paths, Catalan numbers), Polya's theory on the enumeration of
equivalence classes of combinatorial objects, partially ordered sets ( Dilworth's theorem, Moebius function of posets, Sperner's theorem,
Hall's marriage theorem), flows and networks ( theorems of Ford-Fulkerson, Menger, Koenig and Hall) and an introduction to the
theory of integer partitions (q-binomial coefficients, the triple product identity of Jacobi, Euler's pentagonal number theorem, the
identities of Rogers - Ramanujan).

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Für die Vorlesung habe ich die folgenden Werke herangezogen:

*Martin Aigner & Günter M. Ziegler, *Das BUCH der Beweise, 2. Auflage,
Springer 2004*
*

*George E. Andrews & Kimmo Erikson, *Integer Partitions, Cambridge
University Press 2004*
*

*F. Bergeron, G. Labelle & P. Leroux, * Combinatorial Species and Tree-like Structures, Cambridge University Press 1998*
*

*Peter J. Cameron*, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press 1994

*Philippe Flajolet & Robert Sedgewick, *Analytic Combinatorics,

Hier sind vor allem die Kapitel I-III für die Vorlesung relevant. Das
Buch ist in Vorbereitung und kann vorläufig noch von der Homepage von Flajolet heruntergeladen werden:
http://algo.inria.fr/flajolet/Publications/books.html

*Richard P. Stanley, *Enumerative Combinatorics, Volume 2, Cambridge University Press 2001

Association in the course directory

Last modified: Mo 07.09.2020 15:50