Universität Wien

250105 VO Topics in Combinatorics (2017W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

On Mondays we already start at 9:30.

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

Information

Aims, contents and method of the course

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).

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

course in "Discrete Mathematics"

Examination topics

Reading list

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

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:40