Universität Wien

250105 VO Topics in Combinatorics (2017W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

On Mondays we already start at 9:30.

  • Montag 02.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 05.10. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 09.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 12.10. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 16.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 19.10. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 23.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 30.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 06.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 09.11. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 13.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 16.11. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 20.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 23.11. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 27.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 30.11. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 04.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 07.12. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 11.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 14.12. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 08.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 11.01. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 15.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 18.01. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 22.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 25.01. 12:45 - 13:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 29.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

Generating Functions

Generating functions - that is, formal power series whose
coefficients count combinatorial objects - form one of the
most important tools in Enumerative Combinatorics. Their
significance is however not restricted to enumeration
since (formal or not) power series occur as well in many
other contexts. Consequently, a thorough understanding of
the character of generating functions (power series) is
crucial for various tasks one would like to master with
the help of generating functions, such as the manipulation
of these series, the extraction of coefficients, or the
(computationally) effective computation of these coefficients.

We shall discuss the following classes of power series
and their coefficient sequences:

* rational power series
* algebraic power series
* differentially finite power series
* differentially algebraic power series

how they are related to each other, and what one can do with them.
On the way, we shall see many (mainly combinatorial)
examples, and I shall allow myself several excursions
(such as a discussion of diagonals of power series),
also taking algorithmic aspects into account.

The basic source for this course will be Chapter 6 in
Richard Stanley's book "Enumerative Combinatorics, vol.2"
(Cambridge University Press). It will be complemented by
various other sources that will be announced as we move
along in the course (and also be posted here).

Art der Leistungskontrolle und erlaubte Hilfsmittel

oral exam

Mindestanforderungen und Beurteilungsmaßstab

course in "Discrete Mathematics"

Prüfungsstoff

Literatur

Richard Stanley: "Enumerative Combinatorics, vol.2", Chapter 6,
plus further sources to be announced later.

Zuordnung im Vorlesungsverzeichnis

MALV

Letzte Änderung: Mo 07.09.2020 15:40