Email this article Description of normal bases of boundary algebras and factor languages of slow growth
- Authors: Belov A.Y.1,2, Chernyat’ev A.L.3
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Affiliations:
- Bar-Ilan University
- Moscow Institute of Physics and Technology (State University)
- National Research University Higher School of Economics
- Issue: Vol 101, No 1-2 (2017)
- Pages: 203-207
- Section: Volume 101, Number 2, February, 2017
- URL: https://journals.rcsi.science/0001-4346/article/view/149978
- DOI: https://doi.org/10.1134/S0001434617010242
- ID: 149978
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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.
About the authors
A. Ya. Belov
Bar-Ilan University; Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: kanelster@gmail.com
Israel, Ramat Gan; Dolgoprudny, Moscow Oblast
A. L. Chernyat’ev
National Research University Higher School of Economics
Email: kanelster@gmail.com
Russian Federation, Moscow
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