Geodesic
Asymptotics of the average height of 2-watermelons with a wall
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
We generalize the classical work of de Bruijn, Knuth and Rice (giving the asymptotics of the average height of Dyck paths of length $n$) to the case of $p$–watermelons with a wall (i.e., to a certain family of $p$ nonintersecting Dyck paths; simple Dyck paths being the special case $p=1$.) An exact enumeration formula for the average height is easily obtained by standard methods and well–known results. However, straightforwardly computing the asymptotics turns out to be quite complicated. Therefore, we work out the details only for the simple case $p=2$.
DOI : 10.37236/982
Classification : 05A16
Mots-clés : dyck paths, average height, exact enumeration formula, 2-watermelons 
Markus Fulmek. Asymptotics of the average height of 2-watermelons with a wall. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/982
@article{10_37236_982,
     author = {Markus Fulmek},
     title = {Asymptotics of the average height of 2-watermelons with a wall},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/982},
     zbl = {1158.05304},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/982/}
}
TY  - JOUR
AU  - Markus Fulmek
TI  - Asymptotics of the average height of 2-watermelons with a wall
JO  - The electronic journal of combinatorics
PY  - 2007
VL  - 14
UR  - http://geodesic.mathdoc.fr/articles/10.37236/982/
DO  - 10.37236/982
ID  - 10_37236_982
ER  - 
%0 Journal Article
%A Markus Fulmek
%T Asymptotics of the average height of 2-watermelons with a wall
%J The electronic journal of combinatorics
%D 2007
%V 14
%U http://geodesic.mathdoc.fr/articles/10.37236/982/
%R 10.37236/982
%F 10_37236_982

Cité par Sources :