Generic rectangulations
Abstract
A rectangulation is a tiling of a rectangle by a finite number of rectangles. The rectangulation is called generic if no four of its rectangles share a single corner. We initiate the enumeration of generic rectangulations up to combinatorial equivalence by establishing an explicit bijection between generic rectangulations and a set of permutations defined by a pattern-avoidance condition analogous to the definition of the twisted Baxter permutations.
Keywords
Cite
@article{arxiv.1105.3093,
title = {Generic rectangulations},
author = {Nathan Reading},
journal= {arXiv preprint arXiv:1105.3093},
year = {2026}
}
Comments
Final version to appear in Eur. J. Combinatorics. Since v2, I became aware of literature on generic rectangulations under the name rectangular drawings. There are results on asymptotic enumeration and computations counting generic rectangulations with n rectangles for many n. This result answers an open question posed in the rectangular drawings literature. See "Note added in proof."