Bijective counting of tree-rooted maps and shuffles of parenthesis systems
Combinatorics
2009-06-18 v1
Abstract
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long awaited) simple bijection which explains this result. We prove that our bijection is isomorphic to a former recursive construction on shuffles of parenthesis systems due to Cori, Dulucq and Viennot.
Keywords
Cite
@article{arxiv.math/0601684,
title = {Bijective counting of tree-rooted maps and shuffles of parenthesis systems},
author = {Olivier Bernardi},
journal= {arXiv preprint arXiv:math/0601684},
year = {2009}
}