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Article

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

Mathematical notes. 2017. Vol. 101. No. 1. P. 203-207.
Belov A., Chernyat’ev A.

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.