Universität Wien
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250121 VO Topics in Combinatorics (2022W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
ON-SITE

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 04.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 06.12. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.12. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Enumeration of Tilings

The enumeration of tilings of regions by given tiles (such as dominoes, rhombi, etc.) may have its origin in recreational mathematics, but has been intensively studied since at least 50 years in combinatorics and statistical physics (there, in the guise of the dimer model) alike. The prototypical example of a tiling enumeration problem is the problem of finding the number of ways to cover an m x n chessboard completely by dominoes (2x1 tiles). Given that one of m or n is even, it turns out that this number is given by a closed formula that is somewhat surprising in its complexity.

The goal of this course is to provide an introduction into this fascinating area, mainly from the point of view of Enumerative Combinatorics. (At the end, I may also briefly touch upon - equally fascinating - probabilistic aspects.) We shall encounter various techniques to enumerate tilings, as for example condensation, non-intersecting lattice paths, Kasteleyn determinants, Ciucu's matchings factorization theorem. Since determinants play a predominant role here, we shall also learn a few tricks how to evaluate determinants.
Guessing formulas for the terms of a sequence (a(n)) from its first few values will also be discussed.

It will not be necessary to have already attended the "Combinatorics" course.

Assessment and permitted materials

(oral) exam at the end

Minimum requirements and assessment criteria

Examination topics

Reading list

On the website for the course,

https://www.mat.univie.ac.at/~kratt/akkomb/

relevant literature and other material will be put as the course moves along.

Association in the course directory

MALV

Last modified: Th 23.02.2023 12:29