Geodesic
Recursive generation of \(k\)-ary trees
Journal of integer sequences, Tome 12 (2009) no. 7
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},
     year = {2009},
     volume = {12},
     number = {7},
     zbl = {1213.05014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_7_a5/}
}
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AU  - Sapounakis,  A.
AU  - Tasoulas,  I.
AU  - Tsikouras,  P.
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%A Tasoulas,  I.
%A Tsikouras,  P.
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%J Journal of integer sequences
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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/