Geodesic
A Note on Flips in Diagonal Rectangulations
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2

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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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     author = {Cardinal, Jean and Sacrist\'an, Vera and Silveira, Rodrigo I.},
     title = {A {Note} on {Flips} in {Diagonal} {Rectangulations}},
     journal = {Discrete mathematics & theoretical computer science},
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     language = {en},
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Cardinal, Jean; Sacristán, Vera; Silveira, Rodrigo I. A Note on Flips in Diagonal Rectangulations. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2. doi: 10.23638/DMTCS-20-2-14

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