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

A. Ya Belov; A. L. Chernyat’ev

doi:10.1134/S0001434617010242

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

A. Ya Belov
, A. L. Chernyat’ev

Department of Mathematics

Moscow Institute of Physics and Technology
Higher School of Economics

Research output: Contribution to journal › Article › peer-review

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 < 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.

Original language	English
Pages (from-to)	203-207
Number of pages	5
Journal	Mathematical Notes
Volume	101
Issue number	1-2
DOIs	https://doi.org/10.1134/S0001434617010242
State	Published - 1 Jan 2017

Bibliographical note

Publisher Copyright:
© 2017, Pleiades Publishing, Ltd.

Keywords

Sturm sequence
factor language
growth function
monomial algebra
normal basis

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10.1134/S0001434617010242

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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.",

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AU - Chernyat’ev, A. L.

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N2 - 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.

AB - 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.

KW - Sturm sequence

KW - factor language

KW - growth function

KW - monomial algebra

KW - normal basis

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JO - Mathematical Notes

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ER -

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

Abstract

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Keywords

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