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On the Index of Sturmian Words

  • Jean Berstel

Summary

An infinite word x has finite index if the exponents of the powers of primitive words that are factors of x are bounded. F. Mignosi has proved that a Sturmian word has finite index if and only if the coefficients of the continued fraction development of its slope are bounded. Mignosi’s proof relies on a delicate analysis of the approximation of the slope by rational numbers. We give here a proof based on combinatorial properties of words, and give some additional relations between the exponents and the slope.

Keywords

Finite Index Symbolic Dynamic Standard Sequence Continue Fraction Expansion Characteristic 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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© Springer-Verlag Berlin Heidelberg 1999

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  • Jean Berstel

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