A Note on Flips in Diagonal Rectangulations
Abstract
Rectangulations are partitions of a square into axisaligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of patternavoiding 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 socalled 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 arXiv:
 arXiv:1712.07919
 Bibcode:
 2017arXiv171207919C
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics
 EPrint:
 Discrete Mathematics &