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arXiv · 1707.02741

A Set of Sequences of Complexity $2n+1$

Julien Cassaigne·Sébastien Labbé·Julien Leroy
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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.

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Julien Cassaigne, Sébastien Labbé, Julien Leroy. 2017-07-10. A Set of Sequences of Complexity $2n+1$. https://doi.org/10.1007/978-3-319-66396-8_14

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