A characterization of Sturmian morphisms

  • Jean Berstel
  • Patrice Séébold
Conference paper

DOI: 10.1007/3-540-57182-5_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)
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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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Jean Berstel
    • 1
  • Patrice Séébold
    • 2
  1. 1.Institut Blaise PascalLITPParis
  2. 2.LAMIFAAmiensFrance

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