Abstract
We prove the existence of a ternary sequence of factor complexity \(2n+1\) for any given vector of rationally independent letter frequencies. Such sequences are constructed from an infinite product of two substitutions according to a particular Multidimensional Continued Fraction algorithm. We show that this algorithm is conjugate to a well-known one, the Selmer algorithm. Experimentations (Baldwin, 1992) suggest that their second Lyapunov exponent is negative which presages finite balance properties.
J. Leroy—FNRS post-doctoral fellow.
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Acknowledgments
We are thankful to Valérie Berthé for her enthusiasm toward this project and for the referees for their thorough reading and pertinent suggestions.
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Cassaigne, J., Labbé, S., Leroy, J. (2017). A Set of Sequences of Complexity \(2n+1\) . In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_14
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DOI: https://doi.org/10.1007/978-3-319-66396-8_14
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