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.

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."

References in corpus (3)

• Bijections for Baxter Families and Related Objects
• Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations
• On the number of tilings of a square by rectangles

Cited by in corpus (9)

• A Note on Flips in Diagonal Rectangulations
• Rectangulotopes
• Noncrossing arc diagrams and canonical join representations
• Geometric realizations of the $s$-weak order and its lattice quotients
• Transformations of Rectangular Dualizable Graphs
• The Hopf algebra of generic rectangulations
• Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube
• Separating trees and simple congruences of the weak order
• A Theory of Rectangularly Dualizable Graphs