We prove a long standing conjecture of Duval in the special case of 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},
volume = {36},
year = {2002},
pages = {1-3},
doi = {10.1051/ita:2002001},
mrnumber = {1928155},
zbl = {1013.68152},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2002__36_1_1_0}
}
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) pp. 1-3. doi : 10.1051/ita:2002001. http://gdmltest.u-ga.fr/item/ITA_2002__36_1_1_0/
[1] and, Représentation géométrique des suites de complexité Bull. Soc. Math. France 119 (1991) 199-215. | Numdam | MR 1116845 | Zbl 0789.28011
[2] and, Une Caractérisation des mots périodiques. Discrete Math. 25 (1979) 1-5. | MR 522741 | Zbl 0407.68087
[3] , 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] and, 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] , 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] and, Morphismes sturmiens et règles de Rauzy. J. Théorie des Nombres de Bordeaux 5 (1993) 221-233. | Numdam | MR 1265903 | Zbl 0797.11029
[8] , 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] and, A generalization of Sturmian sequences; combinatorial structure and transcendence. Acta Arith. 95 (2000). | MR 1785413 | Zbl 0953.11007