Increasing Forests and Quadrangulations via a Bijective Approach
Probability
2014-01-16 v3 Discrete Mathematics
Combinatorics
Abstract
In this work, we expose four bijections each allowing to increase (or decrease) one parameter in either uniform random forests with a fixed number of edges and trees, or quadrangulations with a boundary having a fixed number of faces and a fixed boundary length. In particular, this gives a way to sample a uniform quadrangulation with n + 1 faces from a uniform quadrangulation with n faces or a uniform forest with n+1 edges and p trees from a uniform forest with n edges and p trees.
Cite
@article{arxiv.1203.2365,
title = {Increasing Forests and Quadrangulations via a Bijective Approach},
author = {Jérémie Bettinelli},
journal= {arXiv preprint arXiv:1203.2365},
year = {2014}
}