Combinatorics Seminar

Enumeration of tilings and graphical condensation

Tri Lai, University of Nebraska

Thursday, December 7th, 2023
3:25 PM - 4:25 PM
Hylan 1101

The enumeration of tilings is the mathematical study concerning the total number of ways to cover a certain region with similar pieces so that there are no gaps or overlaps. The study dates back to the early 1900s when MacMahon proved his classical theorem about plane partitions, which are in bijection with lozenge tilings of a hexagon. Enumeration of tilings has become a vibrant subfield in algebraic and enumeration combinatorics with applications and connections to various areas, including symmetric functions, statistical mechanics, cluster algebra, and probability. We also talk about a powerful method of enumerating tilings, namely Eric Kuo’s graphical condensation.

Event contact: iosevich at gmail dot com