Geodesic
Self-describing sequences and the Catalan family tree
The electronic journal of combinatorics, Tome 10 (2003)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We introduce a transformation of finite integer sequences, show that every sequence eventually stabilizes under this transformation and that the number of fixed points is counted by the Catalan numbers. The sequences that are fixed are precisely those that describe themselves — every term $t$ is equal to the number of previous terms that are smaller than $t$. In addition, we provide an easy way to enumerate all these self-describing sequences by organizing them in a Catalan tree with a specific labelling system.
DOI : 10.37236/1745
Classification : 05A15, 05C05, 11Y55 
@article{10_37236_1745,
     author = {Zoran \v{S}uniƙ},
     title = {Self-describing sequences and the {Catalan} family tree},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1745},
     zbl = {1028.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1745/}
}
TY  - JOUR
AU  - Zoran Šuniƙ
TI  - Self-describing sequences and the Catalan family tree
JO  - The electronic journal of combinatorics
PY  - 2003
VL  - 10
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1745/
DO  - 10.37236/1745
ID  - 10_37236_1745
ER  - 
%0 Journal Article
%A Zoran Šuniƙ
%T Self-describing sequences and the Catalan family tree
%J The electronic journal of combinatorics
%D 2003
%V 10
%U http://geodesic.mathdoc.fr/articles/10.37236/1745/
%R 10.37236/1745
%F 10_37236_1745
Zoran Šuniƙ. Self-describing sequences and the Catalan family tree. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1745

Cité par Sources :