Unified bijections for planar maps

Combinatorics Seminar
Friday, February 3, 2012 - 15:05
1 hour (actually 50 minutes)
Skiles 005
Math, MIT
Planar maps are embeddings of connected planar graphs in the plane considered up to continuous deformation. We will present a ``master bijection'' for planar maps and show that it can be specialized in various ways in order to count several families of maps. More precisely, for each integer d we obtain a bijection between the family of maps of girth d and a family of decorated plane trees. This gives new counting results for maps of girth d counted according to the degree distribution of their faces. Our approach unifies and extends many known bijections. This is joint work with Eric Fusy.