Cardinal, Jean and Sacristán, Vera and Silveira, Rodrigo I. - A Note on Flips in Diagonal Rectangulations

dmtcs:4315 - Discrete Mathematics & Theoretical Computer Science, November 9, 2018, vol. 20 no. 2 -
A Note on Flips in Diagonal Rectangulations

Authors: Cardinal, Jean and Sacristán, Vera and Silveira, Rodrigo I.

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.

Volume: vol. 20 no. 2
Section: Combinatorics
Published on: November 9, 2018
Submitted on: February 26, 2018
Keywords: Mathematics - Combinatorics,Computer Science - Computational Geometry,Computer Science - Discrete Mathematics


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