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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2004, Volume 195, Number 2, Pages 41–90 (Mi msb800)  

This article is cited in 2 scientific papers (total in 3 papers)

Finite parametrization of solutions of equations in a free monoid. I

G. S. Makanin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Complete solutions of all primitively parametrizable basis equations in a free monoid are written out. Parametrizing functions Fi, Th, Ro are introduced depending on word variables, positive integer variables, and variables whose values are finite sequences of positive-integer variables. Finite formulae for the family of solutions of all Fi-, Th-, Ro-parametrizable basis equations of the form $x_1x_2x_3x_4=\psi(x_1,x_2,x_3)$ in a free monoid are written out with the help of the parametrizing functions.

DOI: https://doi.org/10.4213/sm800

Full text: PDF file (387 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2004, 195:2, 187–235

Bibliographic databases:

UDC: 519.4
MSC: Primary 20M05; Secondary 03D40, 68R15
Received: 16.12.2002

Citation: G. S. Makanin, “Finite parametrization of solutions of equations in a free monoid. I”, Mat. Sb., 195:2 (2004), 41–90; Sb. Math., 195:2 (2004), 187–235

Citation in format AMSBIB
\Bibitem{Mak04}
\by G.~S.~Makanin
\paper Finite parametrization of solutions of equations in a free
monoid.~I
\jour Mat. Sb.
\yr 2004
\vol 195
\issue 2
\pages 41--90
\mathnet{http://mi.mathnet.ru/msb800}
\crossref{https://doi.org/10.4213/sm800}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2068951}
\zmath{https://zbmath.org/?q=an:1073.20049}
\transl
\jour Sb. Math.
\yr 2004
\vol 195
\issue 2
\pages 187--235
\crossref{https://doi.org/10.1070/SM2004v195n02ABEH000800}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000221431900011}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-2542518541}


Linking options:
  • http://mi.mathnet.ru/eng/msb800
  • https://doi.org/10.4213/sm800
  • http://mi.mathnet.ru/eng/msb/v195/i2/p41

    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
    Cycle of papers

    This publication is cited in the following articles:
    1. G. S. Makanin, “Finite parametrization of solutions of equations in a free monoid. II”, Sb. Math., 195:4 (2004), 521–552  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. G. S. Makanin, “Parametrization of the Solutions of the Equation $x_1x_2…x_{n-1}x_n=x_nx_{n-1}…x_2x_1$ in a Free Monoid”, Math. Notes, 89:6 (2011), 839–844  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. S. I. Adian, “On the studies of Gennadii Semënovich Makanin on algorithmic questions of the theory of groups and semigroups”, Russian Math. Surveys, 73:3 (2018), 553–568  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:283
    Full text:123
    References:42
    First page:1

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