Geodesic
Bijective counting of tree-rooted maps and shuffles of parenthesis systems
The electronic journal of combinatorics, Tome 14 (2007)

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl arXiv EuDML
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is ${\cal C}_{n} {\cal C}_{n+1}$ where ${\cal C}_{n}={1\over n+1}{2n \choose n}$ is the $n^{th}$ 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.
DOI : 10.37236/928
Classification : 05A15, 05C30
Mots-clés : Catalan number 
Olivier Bernardi. Bijective counting of tree-rooted maps and shuffles of parenthesis systems. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/928
@article{10_37236_928,
     author = {Olivier Bernardi},
     title = {Bijective counting of tree-rooted maps and shuffles of parenthesis systems},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/928},
     zbl = {1115.05002},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/928/}
}
TY  - JOUR
AU  - Olivier Bernardi
TI  - Bijective counting of tree-rooted maps and shuffles of parenthesis systems
JO  - The electronic journal of combinatorics
PY  - 2007
VL  - 14
UR  - http://geodesic.mathdoc.fr/articles/10.37236/928/
DO  - 10.37236/928
ID  - 10_37236_928
ER  - 
%0 Journal Article
%A Olivier Bernardi
%T Bijective counting of tree-rooted maps and shuffles of parenthesis systems
%J The electronic journal of combinatorics
%D 2007
%V 14
%U http://geodesic.mathdoc.fr/articles/10.37236/928/
%R 10.37236/928
%F 10_37236_928

Cité par Sources :