Universität Wien

250121 VO Topics in Combinatorics (2022W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
VOR-ORT

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
Für diese LV an-/abmelden

Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

(oral) exam at the end

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

Literatur

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.

Zuordnung im Vorlesungsverzeichnis

MALV

Letzte Änderung: Do 23.02.2023 12:29