Rank and symbolic complexity

@inproceedings{Ferenczi2006RankAS,
  title={Rank and symbolic complexity},
  author={S{\'e}bastien Ferenczi},
  year={2006}
}
We investigate the relation between the complexity function of a sequence, that is the number p(n) of its factors of length n, and the rank of the associated dynamical system, that is the number of Rokhlin towers required to approximate it. We prove that if the rank is one, then lim infn→+∞ p(n) n2 ≤ 1 2 , but give examples with lim supn→+∞ p(n) G(n) = 1 for any prescribed function G with G(n) = o(a) for every a > 1. We give exact computations for examples of the ”staircase” type, which are… CONTINUE READING

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