Geodesic
On a new collection of words in the Catalan family
Journal of integer sequences, Tome 17 (2014) no. 7
In this note, we provide a bijection between a new collection of words on nonnegative integers of length $n$ and Dyck paths of length $2n-2$, thus proving that this collection belongs to the Catalan family. The surprising key step in this bijection is the zeta map which is an important map in the study of $q,t$-Catalan numbers. Finally we discuss an alternative approach to this new collection of words using two statistics on planted trees that turn out to be closely related to the Tutte polynomial on the Catalan matroid.
Classification : 05A19
Keywords: bijective combinatorics, Catalan numbers, combinatorial statistics 
@article{JIS_2014__17_7_a0,
     author = {Stump,  Christian},
     title = {On a new collection of words in the {Catalan} family},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {7},
     zbl = {1297.05031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a0/}
}
TY  - JOUR
AU  - Stump,  Christian
TI  - On a new collection of words in the Catalan family
JO  - Journal of integer sequences
PY  - 2014
VL  - 17
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a0/
LA  - en
ID  - JIS_2014__17_7_a0
ER  - 
%0 Journal Article
%A Stump,  Christian
%T On a new collection of words in the Catalan family
%J Journal of integer sequences
%D 2014
%V 17
%N 7
%U http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a0/
%G en
%F JIS_2014__17_7_a0
Stump,  Christian. On a new collection of words in the Catalan family. Journal of integer sequences, Tome 17 (2014) no. 7. http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a0/