A Note on Flips in Diagonal Rectangulations

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 rectangulatio...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Discrete mathematics and theoretical computer science Jg. 20 no. 2; H. Combinatorics
Hauptverfasser:	Cardinal, Jean, Sacristán, Vera, Silveira, Rodrigo I.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Discrete Mathematics & Theoretical Computer Science 09.11.2018
Schlagworte:	computer science - computational geometry computer science - discrete mathematics mathematics - combinatorics
ISSN:	1365-8050, 1365-8050
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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.
ISSN:	1365-8050 1365-8050
DOI:	10.23638/DMTCS-20-2-14