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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- Sturm sequence
- factor language
- growth function
- monomial algebra
- normal basis