Bijective Counting of Tree-Rooted Maps and Shuffles of Parenthesis Systems

@article{Bernardi2007BijectiveCO,
  title={Bijective Counting of Tree-Rooted Maps and Shuffles of Parenthesis Systems},
  author={Olivier Bernardi},
  journal={Electr. J. Comb.},
  year={2007},
  volume={14}
}
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size n is CnCn+1 where Cn = 1 n+1 ( 2n n ) is the nh Catalan number. We present a (long awaited) simple bijection which explains this result. Then, we prove that our bijection is isomorphic to a former recursive construction on shuffles of parenthesis systems due to Cori, Dulucq and Viennot. 
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