|
Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth
A. Ya. Belovab, A. L. Chernyatievc a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Bar-Ilan University, Ramat Gan, Israel
c National Research University "Higher School of Economics" (HSE), Moscow
Abstract:
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, monomial algebra, factor language.
Received: 09.12.2015
Citation:
A. Ya. Belov, A. L. Chernyatiev, “Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth”, Mat. Zametki, 101:2 (2017), 181–185; Math. Notes, 101:2 (2017), 203–207
Linking options:
https://www.mathnet.ru/eng/mzm11408https://doi.org/10.4213/mzm11408 https://www.mathnet.ru/eng/mzm/v101/i2/p181
|
Statistics & downloads: |
Abstract page: | 325 | Full-text PDF : | 29 | References: | 120 | First page: | 17 |
|