10.23638/DMTCS-20-2-14
Cardinal, Jean
Jean
Cardinal
SacristÃ¡n, Vera
Vera
SacristÃ¡n
Silveira, Rodrigo I.
Rodrigo I.
Silveira
A Note on Flips in Diagonal Rectangulations
episciences.org
2018
Mathematics - Combinatorics
Computer Science - Computational Geometry
Computer Science - Discrete Mathematics
contact@episciences.org
episciences.org
2018-02-26T16:41:12+01:00
2019-02-04T12:59:59+01:00
2018-11-09
eng
Journal article
https://dmtcs.episciences.org/4315
arXiv:1712.07919
1365-8050
PDF
1
Discrete Mathematics & Theoretical Computer Science ; vol. 20 no. 2 ; Combinatorics ; 1365-8050
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.