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Sibirsk. Mat. Zh., 2011, Volume 52, Number 1, Pages 81–94 (Mi smj2179)  

On possible growths of Toeplitz languages

J. Cassaignea, F. V. Petrovb, A. E. Fridc

a Institut de Mathématiques de Luminy, Marseille Cedex, France
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

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

Keywords: subword complexity, arithmetical complexity, combinatorics on words, Toeplitz words, asymptotic combinatorics, analytical methods in combinatorics, Tauberian theorems, Wiener–Pitt theorem.

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English version:
Siberian Mathematical Journal, 2011, 52:1, 63–73

Bibliographic databases:

UDC: 519.115.8
Received: 10.03.2010

Citation: J. Cassaigne, F. V. Petrov, A. E. Frid, “On possible growths of Toeplitz languages”, Sibirsk. Mat. Zh., 52:1 (2011), 81–94; Siberian Math. J., 52:1 (2011), 63–73

Citation in format AMSBIB
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\paper On possible growths of Toeplitz languages
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\issue 1
\pages 81--94
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\jour Siberian Math. J.
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\pages 63--73
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