Sturmian words and words with a critical exponent

Drew Vandeth

    Research output: Contribution to journalArticle

    30 Citations (Scopus)

    Abstract

    Let S be a standard Sturmian word that is a fixed point of a non-trivial homomorphism. Associated to the infinite word S is a unique irrational number β with 0 <β <1. We prove that the standard Sturmian word S contains no fractional power with exponent greater than Ω and that for any real number ε > 0 it contains a fractional power with exponent greater than Ω - ε; here Ω is a constant that depends on β. The constant Ω is given explicitly. Using these results we are able to give a short proof of Mignosi's theorem and give an exact evaluation of the maximal power that can occur in a standard Sturmian word.
    Original languageEnglish
    Pages (from-to)283-300
    Number of pages18
    JournalTheoretical Computer Science
    Volume242
    Issue number1-2
    DOIs
    Publication statusPublished - 2000

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    Keywords

    • Critical exponent
    • Lyndon-schutzenberger theorem
    • Sturmian words

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