A little more about morphic sturmian words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 511-518.

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.

DOI : https://doi.org/10.1051/ita:2006031
Classification : 68R15,  68Q45
Mots clés : sturmian words, infinite words, iterated morphisms, combinatorics of words
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     title = {A little more about morphic sturmian words},
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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] C. Allauzen, Une caractérisation simple des nombres de Sturm. J. Théor. Nombres Bordeaux 10 (1998) 237-241. | Numdam | Zbl 0930.11051

[2] J. Berstel and P. Séébold, A remark on morphic sturmian words. Theor. Inform. Appl. 28 (1994) 255-263. | Numdam | Zbl 0883.68104

[3] J. Berstel and P. Séébold, Algebraic combinatorics on Words, chapter Sturmian words. Cambridge University Press (2002). | MR 1905123

[4] V. Berthé, H. Ei, S. Ito and H. Rao, Invertible susbtitutions and Sturmian words: an application of Rauzy fractals. Preprint.

[5] D. Crisp, W. Moran, A. Pollington and P. Shiue, Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux 5 (1993) 123-137. | Numdam | Zbl 0786.11041

[6] J. Justin and G. Pirillo, Episturmian words: Shifts, morphisms and numeration systems. Inter. J. Found. Comput. Sci. 15 (2004) 329-348. | Zbl 1067.68115

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

[8] B. Parvaix, 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

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