Tree-decorated planar maps
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.04981
- arXiv:
- arXiv:1901.04981
- Bibcode:
- 2019arXiv190104981F
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Probability
- E-Print:
- 19 pages, 7 figures