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A little more about morphic Sturmian words

Published online by Cambridge University Press:  18 October 2006

Isabelle Fagnot
Isabelle Fagnot*
Affiliation:
Institut Gaspard Monge, Cité Descartes, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France; [email protected]
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Abstract

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.

Keywords

Sturmian wordsinfinite wordsiterated morphismscombinatorics of words.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 3: Word Avoidability Complexity And Morphisms (WACAM) , July 2006 , pp. 511 - 518
Copyright
© EDP Sciences, 2006

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References

Allauzen, C., Une caractérisation simple des nombres de Sturm. J. Théor. Nombres Bordeaux 10 (1998) 237–241. CrossRef
Berstel, J. and Séébold, P., A remark on morphic sturmian words. Theor. Inform. Appl. 28 (1994) 255–263. CrossRef
J. Berstel and P. Séébold, Algebraic combinatorics on Words, chapter Sturmian words. Cambridge University Press (2002).
V. Berthé, H. Ei, S. Ito and H. Rao, Invertible susbtitutions and Sturmian words: an application of Rauzy fractals. Preprint.
Crisp, D., Moran, W., Pollington, A. and Shiue, P., Substitution invariant cutting sequences. J. Théor. Nombres Bordeaux 5 (1993) 123–137. CrossRef
Justin, J. and Pirillo, G., Episturmian words: Shifts, morphisms and numeration systems. Inter. J. Found. Comput. Sci. 15 (2004) 329–348. CrossRef
Mignosi, F. and Séébold, P., Morphismes sturmiens et règles de Rauzy. J. Théor. Nombres Bordeaux 5 (1993) 221–233. CrossRef
Parvaix, B., Propriétés d'invariance des mots sturmiens. J. Théor. Nombres Bordeaux 9 (1997) 351–369. CrossRef
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.