Planar maps and Tamari-like intervals

Wenjie Fang (Speaker)

Activity: Talk or presentationInvited talk at conference or symposiumScience to science

Description

Tamari lattice is a partial order defined on objects counted by Catalan numbers, such as binary trees and Dyck paths. It is a well-studied object in combinatorics, with several generalizations. In this talk, we will see how intervals in these Tamari-like lattices are related to planar maps. More precisely, we discovered a bijection between non-separable planar maps and intervals in the generalized Tamari lattice, which naturally extends to a bijection between bridgeless planar maps and intervals in the original Tamari lattice. We will also discuss the consequences of these bijections in enumerative and structural studies of the related objects.
PeriodOct 2017
Held at Workshop on "Enumerative Combinatorics"
Event typeConference
LocationVienna, Austria
Degree of RecognitionInternational

Keywords

  • Tamari interval
  • planar map
  • decorated tree
  • bijection