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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 lettersin such a way that it remains morphic and Sturmian.Yasutomi (1997) has proved that these were the sole possible additions andthat, 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.

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References

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