English

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

Combinatorics 2021-02-25 v1 Dynamical Systems

Abstract

We prove the existence of a ternary sequence of factor complexity 2n+12n+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.

Keywords

Cite

@article{arxiv.1707.02741,
  title  = {A Set of Sequences of Complexity $2n+1$},
  author = {Julien Cassaigne and Sébastien Labbé and Julien Leroy},
  journal= {arXiv preprint arXiv:1707.02741},
  year   = {2021}
}

Comments

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