episciences.org_4315_1635090883
1635090883
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
11
09
2018
vol. 20 no. 2
Combinatorics
A Note on Flips in Diagonal Rectangulations
Jean
Cardinal
Vera
SacristÃ¡n
Rodrigo I.
Silveira
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.
11
09
2018
4315
arXiv:1712.07919
10.23638/DMTCS-20-2-14
https://dmtcs.episciences.org/4315