On possible growth of Toeplitz languages

Abstract

We consider a new family of factorial languages whose subword complexity grows as $\Theta (n^{\alpha })$, where $\alpha$ 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.

Accepted to Siberian Mathematical Journal. Now in English, the Russian version is the previous one