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.Comment: 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.