
TL;DR
This paper introduces a new combinatorial approach to enumerate generic rectangulations by establishing a bijection with a specific class of pattern-avoiding permutations.
Contribution
It provides the first explicit bijection between generic rectangulations and a class of pattern-avoiding permutations, advancing the enumeration of these tilings.
Findings
Established a bijection between generic rectangulations and pattern-avoiding permutations.
Initiated the enumeration of generic rectangulations up to combinatorial equivalence.
Connected rectangulation enumeration to permutation pattern avoidance.
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.
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