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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; fagnot@univ-mlv.fr
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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

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