A little more about morphic Sturmian words
Institut Gaspard Monge,
Cité Descartes, 5, boulevard Descartes, Champs-sur-Marne,
77454 Marne-la-Vallée Cedex 2, France; email@example.com
Accepted: 19 September 2005
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.
Mathematics Subject Classification: 68R15 / 68Q45
Key words: Sturmian words / infinite words / iterated morphisms / combinatorics of words.
© EDP Sciences, 2006