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combinatorics of words.

RAIRO - Theoretical Informatics and Applications (1)

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A little more about morphic Sturmian words
Isabelle Fagnot
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 3 / July 2006

Published online by Cambridge University Press:

18 October 2006, pp. 511-518

Print publication:

July 2006
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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.