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A characterization of Sturmian morphisms

  • Jean Berstel
  • Patrice Séébold
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)

Abstract

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.

Keywords

Characteristic Sequence Irrational Number Symbolic Dynamic Empty Word Infinite Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

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

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