RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2017, Volume 101, Issue 2, Pages 181–185 (Mi mz11408)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00548
This work was supported by the Russian Foundation for Basic Research under grant 14-01-00548.


DOI: https://doi.org/10.4213/mzm11408

Full text: PDF file (457 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2017, 101:2, 203–207

Bibliographic databases:

UDC: 512+519.17+517.987
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

Citation in format AMSBIB
\Bibitem{BelChe17}
\by A.~Ya.~Belov, A.~L.~Chernyatiev
\paper Description of Normal Bases of Boundary Algebras and Factor Languages of Slow Growth
\jour Mat. Zametki
\yr 2017
\vol 101
\issue 2
\pages 181--185
\mathnet{http://mi.mathnet.ru/mz11408}
\crossref{https://doi.org/10.4213/mzm11408}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3608016}
\elib{http://elibrary.ru/item.asp?id=28172139}
\transl
\jour Math. Notes
\yr 2017
\vol 101
\issue 2
\pages 203--207
\crossref{https://doi.org/10.1134/S0001434617010242}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000396392700024}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85015622926}


Linking options:
  • http://mi.mathnet.ru/eng/mz11408
  • https://doi.org/10.4213/mzm11408
  • http://mi.mathnet.ru/eng/mz/v101/i2/p181

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:165
    References:106
    First page:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020