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

  • A. Ya. Belov
  • A. L. Chernyat’ev
Volume 101, Number 2, February, 2017


For an algebra A, denote by V A (n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let T A (n) = V A (n) − V A (n − 1). An algebra is said to be boundary if T A (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 T L (n) is the number of subwords of length n in L. We also describe the factor languages such that T L (n) ≤ n + const.


normal basis Sturm sequence growth function monomial algebra factor language 


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© 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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