On possible growths of Toeplitz languages |
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Authors: | J. Cassaigne A. E. Frid F. V. Petrov |
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Affiliation: | 1.Luminy Institute of Mathematics,Marseille,France;2.Sobolev Institute of Mathematics,Novosibirsk,Russia;3.St. Petersburg Division of the Steklov Mathematical Institute,St. Petersburg,Russia |
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Abstract: | We consider a new family of factorial languages whose subword complexity grows as Φ(n α ), where α is the only positive root of some transcendental equation. The asymptotic growth of the complexity function of these languages is studied by discrete and analytical methods, a corollary of the Wiener-Pitt theorem inclusive. The factorial languages considered are also languages of arithmetical factors of infinite words; so, we describe a new family of infinite words with an unusual growth of arithmetical complexity. |
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