From geometry to generating functions: rectangulations and permutations

Andrei Asinowski (1) , Cyril Banderier (2)

1 Alpen-Adria-Universität Klagenfurt [Klagenfurt, Austria]
2 LIPN - Laboratoire d'Informatique de Paris-Nord

We enumerate several classes of pattern-avoiding rectangulations. We establish bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and Mütze. We also analyze a new class of rectangulations, called whirls, using a generating tree.

Keywords: Rectangulations; permutations; pattern avoidance; generating functions

Domains: Mathematics [math]; Computer Science [cs]

Andrei Asinowski, Cyril Banderier. From geometry to generating functions: rectangulations and permutations. 2024. ⟨hal-04386564v1⟩