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 \(ba^2ba^2baba^2bab\) balanced. As a consequence, weakly Sturmian morphisms are Sturmian. An application to infinite words associated to irrational numbers is given.
For the entire collection see [Zbl 0825.00085].


11B85 Automata sequences
68R15 Combinatorics on words