Geodesic
Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 181-185

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For an algebra $A$, denote by $V_A(n)$ the dimension of the vector space spanned by the monomials whose length does not exceed $n$. Let $T_A(n)=V_A(n)-V_A(n-1)$. An algebra is said to be boundary if $T_A(n)-n\mathrm{const}$. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let $\mathscr L$ be a factor language over a finite alphabet $\mathscr A$. The growth function $T_{\mathscr L}(n)$ is the number of subwords of length $n$ in $\mathscr L$. We also describe the factor languages such that $T_{\mathscr L}(n)\le n+\mathrm{const}$.
Keywords: normal basis, Sturm sequence, growth function, factor language.
Mots-clés : monomial algebra 
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     author = {A. Ya. Belov and A. L. Chernyatiev},
     title = {Description of {Normal} {Bases} of {Boundary} {Algebras} and {Factor} {Languages} of {Slow} {Growth}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {2},
     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a2/}
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A. Ya. Belov; A. L. Chernyatiev. Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 181-185. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a2/