Mathematical Notes

, Volume 101, Issue 1–2, pp 203–207 | Cite as

Description of normal bases of boundary algebras and factor languages of slow growth

Volume 101, Number 2, February, 2017
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Abstract

For an algebra A, denote by VA(n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let TA(n) = VA(n) − VA(n − 1). An algebra is said to be boundary if TA(n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function TL(n) is the number of subwords of length n in L. We also describe the factor languages such that TL(n) ≤ n + const.

Keywords

normal basis Sturm sequence growth function monomial algebra factor language 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Bar-Ilan UniversityRamat GanIsrael
  2. 2.Moscow Institute of Physics and Technology (State University)DolgoprudnyRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia

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