Geodesic
A characterization of balanced episturmian sequences
The electronic journal of combinatorics, Tome 14 (2007)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

It is well-known that Sturmian sequences are the non ultimately periodic sequences that are balanced over a 2-letter alphabet. They are also characterized by their complexity: they have exactly $(n+1)$ distinct factors of length $n$. A natural generalization of Sturmian sequences is the set of infinite episturmian sequences. These sequences are not necessarily balanced over a $k$-letter alphabet, nor are they necessarily aperiodic. In this paper, we characterize balanced episturmian sequences, periodic or not, and prove Fraenkel's conjecture for the special case of episturmian sequences. It appears that balanced episturmian sequences are all ultimately periodic and they can be classified in 3 families.
DOI : 10.37236/951
Classification : 68R15
Mots-clés : Sturmian sequences 
@article{10_37236_951,
     author = {Genevi\`eve Paquin and Laurent Vuillon},
     title = {A characterization of balanced episturmian sequences},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/951},
     zbl = {1121.68091},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/951/}
}
TY  - JOUR
AU  - Geneviève Paquin
AU  - Laurent Vuillon
TI  - A characterization of balanced episturmian sequences
JO  - The electronic journal of combinatorics
PY  - 2007
VL  - 14
UR  - http://geodesic.mathdoc.fr/articles/10.37236/951/
DO  - 10.37236/951
ID  - 10_37236_951
ER  - 
%0 Journal Article
%A Geneviève Paquin
%A Laurent Vuillon
%T A characterization of balanced episturmian sequences
%J The electronic journal of combinatorics
%D 2007
%V 14
%U http://geodesic.mathdoc.fr/articles/10.37236/951/
%R 10.37236/951
%F 10_37236_951
Geneviève Paquin; Laurent Vuillon. A characterization of balanced episturmian sequences. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/951

Cité par Sources :