Tree-decorated planar maps
Combinatorics
2020-04-09 v2 Probability
Abstract
We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with a simple boundary. As a consequence, we count the number of tree decorated triangulations and quadrangulations with a given amount of faces and for a given size of the tree. Finally, we generalise the bijection to study other types of decorated planar maps and obtain explicit counting formulas for them.
Cite
@article{arxiv.1901.04981,
title = {Tree-decorated planar maps},
author = {Luis Fredes and Avelio Sepúlveda},
journal= {arXiv preprint arXiv:1901.04981},
year = {2020}
}
Comments
19 pages, 7 figures