A characterization of Sturmian morphisms
- Cite this paper as:
- Berstel J., Séébold P. (1993) A characterization of Sturmian morphisms. In: Borzyszkowski A.M., Sokołowski S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg
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 ba2ba2baba2bab balanced. As a consequence, weakly Sturmian morphisms are Sturmian. An application to infinite words associated to irrational numbers is given.
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