Tree-Decorated Planar Maps

@article{Fredes2020TreeDecoratedPM,
  title={Tree-Decorated Planar Maps},
  author={Luis Fredes and Avelio Sep'ulveda},
  journal={Electron. J. Comb.},
  year={2020},
  volume={27},
  pages={P1.66}
}
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. 
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