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

What is it about?

For an algebra $A$ let $V_A(n)$ denote the dimension of the vector space generated by monomials of length at most $n$. Let $T_A(n)=V_A(n)-V_A(n-1)$. We call an algebra a boundary algebra if $T_A(n)-n<{\rm const}$. In this paper we describe normal bases for algebras with slow growth and for boundary algebras. "Let ${\Cal L}$ be a factor language over a finite alphabet ${\Cal A}$. The growth function $T_{\Cal L}(n)$ is the number of subwords of length $n$ in ${\Cal L}$. We also describe factor languages such that $T_{\Cal L}(n)\leq n+{\rm const}$.

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