Geodesic
Recursive generation of $k$-ary trees
Journal of integer sequences, Tome 12 (2009) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we present a construction of every $k$-ary tree using a forest of $(k - 1)$-ary trees satisfying a particular condition. We use this method recursively for the construction of the set of $k$-ary trees from the set of $(k - 1)$-Dyck paths, thus obtaining a new bijection $\phi $ between these two sets. Furthermore, we introduce a new order on $[k]^{*}$ which is used for the full description of this bijection. Finally, we study some new statistics on $k$-ary trees which are transferred by $\phi $ to statistics concerning the occurrence of strings in $(k - 1)$-Dyck paths.
Classification : 05A15, 05A19
Keywords: generalized Dyck words, k-ary trees, k-Catalan numbers 
@article{JIS_2009__12_7_a5,
     author = {Manes, K. and Sapounakis, A. and Tasoulas, I. and Tsikouras, P.},
     title = {Recursive generation of $k$-ary trees},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {12},
     number = {7},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a5/}
}
TY  - JOUR
AU  - Manes, K.
AU  - Sapounakis, A.
AU  - Tasoulas, I.
AU  - Tsikouras, P.
TI  - Recursive generation of $k$-ary trees
JO  - Journal of integer sequences
PY  - 2009
VL  - 12
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a5/
LA  - en
ID  - JIS_2009__12_7_a5
ER  - 
%0 Journal Article
%A Manes, K.
%A Sapounakis, A.
%A Tasoulas, I.
%A Tsikouras, P.
%T Recursive generation of $k$-ary trees
%J Journal of integer sequences
%D 2009
%V 12
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a5/
%G en
%F JIS_2009__12_7_a5
Manes, K.; Sapounakis, A.; Tasoulas, I.; Tsikouras, P. Recursive generation of $k$-ary trees. Journal of integer sequences, Tome 12 (2009) no. 7. http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a5/