From geometry to generating functions: rectangulations and permutations
Discrete Mathematics
2024-04-02 v2 Computational Geometry
Formal Languages and Automata Theory
Combinatorics
Abstract
We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and M\"utze. We also analyze a new class of rectangulations, called whirls, using a generating tree.
Keywords
Cite
@article{arxiv.2401.05558,
title = {From geometry to generating functions: rectangulations and permutations},
author = {Andrei Asinowski and Cyril Banderier},
journal= {arXiv preprint arXiv:2401.05558},
year = {2024}
}
Comments
To appear in the proceedings of FPSAC 2024 (to be published in the S\'eminaire Lotharingien de Combinatoire)