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A characterization of Sturmian morphisms. (English) Zbl 0925.11026
Borzyszkowski, Andrzej M. (ed.) et al., Mathematical foundations of computer science 1993. 18th international symposium, MFCS ’93, Gdańsk, Poland, August/ September 1993. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 711, 281-290 (1993).
Summary: A morphism is called Sturmian if it preserves all Sturmian (infinite) words. It is weakly Sturmian if it preserves at least one Sturmian word. We prove that a morphism is Sturmian if and only if it keeps the word ba 2 ba 2 baba 2 bab balanced. As a consequence, weakly Sturmian morphisms are Sturmian. An application to infinite words associated to irrational numbers is given.
MSC:
11B85Automata sequences
68R15Combinatorics on words