https://www.math.aau.at/talks/164/pdf

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.