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arXiv · 1802.10561

Entropy ratio for infinite sequences with positive entropy

C. Mauduit·C. -G. Moreira
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Abstract

The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given function $f$ with exponential growth, we introduced in [MM17] the notion of {\it word entropy} $E_W(f)$ associated to $f$ and we described the combinatorial structure of sets of infinite words with a complexity function bounded by $f$. The goal of this work is to give estimates on the word entropy $E_W(f)$ in terms of the limiting lower exponential growth rate of $f$.

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C. Mauduit, C. -G. Moreira. 2018-02-28. Entropy ratio for infinite sequences with positive entropy. https://arxiv.org/abs/1802.10561

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