no. 1
A note on a conjecture of Duval and sturmian words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 1-3.

We prove a long standing conjecture of Duval in the special case of sturmian words.

DOI : https://doi.org/10.1051/ita:2002001
Classification : 68R15,  37B10
Mots clés : bordered words, sturmian words 
@article{ITA_2002__36_1_1_0,
     author = {Mignosi, Filippo and Zamboni, Luca Q.},
     title = {A note on a conjecture of {Duval} and sturmian words},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {1--3},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {1},
     year = {2002},
     doi = {10.1051/ita:2002001},
     zbl = {1013.68152},
     mrnumber = {1928155},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2002001/}
}
TY  - JOUR
AU  - Mignosi, Filippo
AU  - Zamboni, Luca Q.
TI  - A note on a conjecture of Duval and sturmian words
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2002
DA  - 2002///
SP  - 1
EP  - 3
VL  - 36
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2002001/
UR  - https://zbmath.org/?q=an%3A1013.68152
UR  - https://www.ams.org/mathscinet-getitem?mr=1928155
UR  - https://doi.org/10.1051/ita:2002001
DO  - 10.1051/ita:2002001
LA  - en
ID  - ITA_2002__36_1_1_0
ER  - 
Mignosi, Filippo; Zamboni, Luca Q. A note on a conjecture of Duval and sturmian words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 1-3. doi : 10.1051/ita:2002001. http://www.numdam.org/articles/10.1051/ita:2002001/

[1] P. Arnoux and G. Rauzy, Représentation géométrique des suites de complexité 2n+1. Bull. Soc. Math. France 119 (1991) 199-215. | Numdam | MR 1116845 | Zbl 0789.28011

[2] R. Assous and M. Pouzet, Une Caractérisation des mots périodiques. Discrete Math. 25 (1979) 1-5. | MR 522741 | Zbl 0407.68087

[3] J.P. Duval, Relationship between the Period of a Finite Word and the Length of its Unbordered Segments. Discrete Math. 40 (1982) 31-44. | MR 676710 | Zbl 0475.68038

[4] A. Ehrenfeucht and D.M. Silberger, Periodicity and Unbordered Segments of words. Discrete Math. 26 (1979) 101-109. | MR 535237 | Zbl 0416.20051

[5] Lothaire, Algebraic Combinatorics on Words, Chap. 9 Periodicity, Chap. 3 Sturmian Words. Cambridge University Press (to appear). Available at http://www-igm.univ-mlv.fr/berstel | MR 1905123 | Zbl 1001.68093

[6] G. Pirillo, A rather curious characteristic property of standard Sturmian words, to appear in Algebraic Combinatorics, edited by G. Rota, D. Senato and H. Crapo. Springer-Verlag Italia, Milano (in press). | MR 1854493 | Zbl 0966.68167

[7] F. Mignosi and P. Séébold, Morphismes sturmiens et règles de Rauzy. J. Théorie des Nombres de Bordeaux 5 (1993) 221-233. | Numdam | MR 1265903 | Zbl 0797.11029

[8] G. Rauzy, Mots infinis en arithmétique, in Automata on Infinite Words, edited by M. Nivat and D. Perrin. Lecture Notes in Comput. Sci. 192 (1985) 167-171. | MR 814741 | Zbl 0613.10044

[9] R. Risley and L.Q. Zamboni, A generalization of Sturmian sequences; combinatorial structure and transcendence. Acta Arith. 95 (2000). | MR 1785413 | Zbl 0953.11007

Cité par Sources :