Among sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic sturmian word is morphic, then it can be extended by the left with one or two letters in such a way that it remains morphic and sturmian. Yasutomi (1997) has proved that these were the sole possible additions and that, if we cut the first letters of such a word, it didn't remain morphic. In this paper, we give an elementary and combinatorial proof of this result.
Classification : 68R15, 68Q45
Mots clés : sturmian words, infinite words, iterated morphisms, combinatorics of words
@article{ITA_2006__40_3_511_0, author = {Fagnot, Isabelle}, title = {A little more about morphic sturmian words}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {511--518}, publisher = {EDP-Sciences}, volume = {40}, number = {3}, year = {2006}, doi = {10.1051/ita:2006031}, zbl = {1110.68118}, mrnumber = {2269208}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2006031/} }
TY - JOUR AU - Fagnot, Isabelle TI - A little more about morphic sturmian words JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 DA - 2006/// SP - 511 EP - 518 VL - 40 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2006031/ UR - https://zbmath.org/?q=an%3A1110.68118 UR - https://www.ams.org/mathscinet-getitem?mr=2269208 UR - https://doi.org/10.1051/ita:2006031 DO - 10.1051/ita:2006031 LA - en ID - ITA_2006__40_3_511_0 ER -
Fagnot, Isabelle. A little more about morphic sturmian words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 511-518. doi : 10.1051/ita:2006031. http://www.numdam.org/articles/10.1051/ita:2006031/
[1] Une caractérisation simple des nombres de Sturm. J. Théor. Nombres Bordeaux 10 (1998) 237-241. | Numdam | Zbl 0930.11051
,[2] A remark on morphic sturmian words. Theor. Inform. Appl. 28 (1994) 255-263. | Numdam | Zbl 0883.68104
and ,[3] Algebraic combinatorics on Words, chapter Sturmian words. Cambridge University Press (2002). | MR 1905123
and ,[4] Invertible susbtitutions and Sturmian words: an application of Rauzy fractals. Preprint.
, , and ,[5] Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux 5 (1993) 123-137. | Numdam | Zbl 0786.11041
, , and ,[6] Episturmian words: Shifts, morphisms and numeration systems. Inter. J. Found. Comput. Sci. 15 (2004) 329-348. | Zbl 1067.68115
and ,[7] Morphismes sturmiens et règles de Rauzy. J. Théor. Nombres Bordeaux 5 (1993) 221-233. | Numdam | Zbl 0797.11029
and ,[8] Propriétés d'invariance des mots sturmiens. J. Théor. Nombres Bordeaux 9 (1997) 351-369. | Numdam | Zbl 0904.11008
,[9] Shin-Ichi Yasutomi, On sturmian sequences which are invariant under some substitutions, in Number theory and its applications. Proceedings of the conference held at the RIMS, Kyoto, Japan, November 10-14, 1997, edited by Kanemitsu, Shigeru et al. Kluwer Acad. Publ. Dordrecht (1999) 347-373. | Zbl 0971.11007
Cité par Sources :