On possible growth of Toeplitz languages

We consider a new family of factorial languages whose subword complexity grows as $Θ(n^α)$, where $α$ is the root of some transcendent equation. Analytical methods and in particular, a corollary of the Wiener-Pitt theorem, are used to find the asymptotic growth of the complexity. Factorial languages considered are languages of arithmetical factors of some Toeplitz words. So, we describe a new family of words with an unusual growth of arithmetical complexity.

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