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 Mat. Zametki, 2017, Volume 101, Issue 2, Pages 181–185 (Mi mz11408)

Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth

A. Ya. Belovab, A. L. Chernyatievc

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Bar-Ilan University, Ramat Gan, Israel
c National Research University "Higher School of Economics" (HSE), Moscow

Abstract: 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 $T_A(n)-n<\mathrm{const}$. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let $\mathscr L$ be a factor language over a finite alphabet $\mathscr A$. The growth function $T_{\mathscr L}(n)$ is the number of subwords of length $n$ in $\mathscr L$. We also describe the factor languages such that $T_{\mathscr L}(n)\le n+\mathrm{const}$.

Keywords: normal basis, Sturm sequence, growth function, monomial algebra, factor language.

 Funding Agency Grant Number Russian Foundation for Basic Research 14-01-00548 This work was supported by the Russian Foundation for Basic Research under grant 14-01-00548.

DOI: https://doi.org/10.4213/mzm11408

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English version:
Mathematical Notes, 2017, 101:2, 203–207

Bibliographic databases:

UDC: 512+519.17+517.987

Citation: A. Ya. Belov, A. L. Chernyatiev, “Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth”, Mat. Zametki, 101:2 (2017), 181–185; Math. Notes, 101:2 (2017), 203–207

Citation in format AMSBIB
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