English

On possible growth of Toeplitz languages

Combinatorics 2010-12-30 v2

Abstract

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

Keywords

Cite

@article{arxiv.1003.1489,
  title  = {On possible growth of Toeplitz languages},
  author = {Julien Cassaigne and Anna Frid and Fedor Petrov},
  journal= {arXiv preprint arXiv:1003.1489},
  year   = {2010}
}

Comments

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

R2 v1 2026-06-21T14:54:45.765Z