Hearing Talk Andrei Asinowski M.Sc.Ph.D. in Mathematics

A rectangulation is a partition of a rectangle into rectangles. There are two natural ways to define „structurally identical“ rectangulations: via rectangle–segment contacts (the weak equivalence), and via rectangle–rectangle contacts (the strong equivalence). Guillotine rectangulations are rectangulations with a simple recursive structure. In this talk, I will briefly present recent results concerning combinatorics of rectangulations:

(1) A uniform treatment of representation of weak and strong rectangulations by posets and permutations,

(2) A permutation class in bijection with strong guillotine rectangulations,

(3) Enumeration of weak guillotine rectangulations that avoid certain patterns.

This research was conducted as a part of the project Generic Rectangulations funded by FWF.
Parts (1) and (2) are based on a joint work with Jean Cardinal, Stefan Felsner, and Éric Fusy, part (3) is based on a joint work with Cyril Banderier.