A Note on Flips in Diagonal Rectangulations
Abstract
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equivalence classes of rectangulations, related to so-called flip graphs on triangulations and other families of geometric partitions. In this note, we consider a family of flip operations on the equivalence classes of diagonal rectangulations, and their interpretation as transpositions in the associated Baxter permutations, avoiding the vincular patterns { 3{14}2, 2{41}3 }. This complements results from Law and Reading (JCTA, 2012) and provides a complete characterization of flip operations on diagonal rectangulations, in both geometric and combinatorial terms.
Cite
@article{arxiv.1712.07919,
title = {A Note on Flips in Diagonal Rectangulations},
author = {Jean Cardinal and Vera Sacristán and Rodrigo I. Silveira},
journal= {arXiv preprint arXiv:1712.07919},
year = {2023}
}