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