Blossoming bijection for higher-genus maps
Abstract
In 1997, Schaeffer described a bijection between Eulerian planar maps and some trees. In this work we generalize his work to a bijection between bicolorable maps on a surface of any fixed genus and some unicellular maps with the same genus. An important step of this construction is to exhibit a canonical orientation for maps, that allows to apply the same local opening algorithm as Schaeffer. As an important byproduct, we obtain the first bijective proof of a result of Bender and Canfield from 1991, when they proved that the generating series of maps in higher genus is a rational function of the generating series of planar maps.
Keywords
Cite
@article{arxiv.1711.05606,
title = {Blossoming bijection for higher-genus maps},
author = {Mathias Lepoutre},
journal= {arXiv preprint arXiv:1711.05606},
year = {2018}
}
Comments
This is the long version of this work. It is 29 pages long and has 15 figures. This work will be presented in a talk at FPSAC 2018