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

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.

arXiv comment12 pages, 11th International Conference on Words (Montreal, September 11-15, 2017)

References in corpus (4)

• Acyclic, connected and tree sets
• On some symmetric multidimensional continued fraction algorithms
• Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm
• Balancedness of Arnoux-Rauzy and Brun words

Cited by in corpus (2)

• Almost everywhere balanced sequences of complexity $2n+1$
• Fixed points of Sturmian morphisms and their derivated words