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arXiv · 1712.07919

A Note on Flips in Diagonal Rectangulations

Jean Cardinal·Vera Sacristán·Rodrigo I. Silveira
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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.

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Jean Cardinal, Vera Sacristán, Rodrigo I. Silveira. 2017-12-21. A Note on Flips in Diagonal Rectangulations. https://doi.org/10.23638/dmtcs-20-2-14

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