On the Index of Sturmian Words

  • Jean Berstel


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.


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

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  • Jean Berstel

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