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Mat. Zametki, 2011, Volume 89, Issue 6, Pages 879–884 (Mi mz9158)  

This article is cited in 1 scientific paper (total in 2 paper)

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

G. S. Makanin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A parametrizing function $\mathrm{Sm}$ is introduced. The parametrizing function is a recursive function depending on lexicographic variables, natural variables, and variables whose values are finite sequences of natural variables. Using the function $\mathrm{Sm}$, we construct formulas that provide all the solutions of the equation
$$ x_1x_2…x_{n-1}x_n=x_nx_{n-1}…x_2x_1 $$
in a free monoid $\langle a_1,a_2,…,a_\omega\rangle$ and only them.

Keywords: free monoid, parametrizing function, recursive function, lexicographic variable, list of words

DOI: https://doi.org/10.4213/mzm9158

Full text: PDF file (404 kB)
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English version:
Mathematical Notes, 2011, 89:6, 839–844

Bibliographic databases:

UDC: 512
Received: 08.09.2009
Revised: 13.07.2010

Citation: 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”, Mat. Zametki, 89:6 (2011), 879–884; Math. Notes, 89:6 (2011), 839–844

Citation in format AMSBIB
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\by G.~S.~Makanin
\paper Parametrization of the Solutions of the Equation $x_1x_2\dots x_{n-1}x_n=x_nx_{n-1}\dots x_2x_1$ in a Free Monoid
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 6
\pages 879--884
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\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 6
\pages 839--844
\crossref{https://doi.org/10.1134/S0001434611050257}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959660083}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Sh. Malkhasyan, “Pseudosymmetric Equations in a Free Monoid”, Math. Notes, 95:4 (2014), 520–529  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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
  • Математические заметки Mathematical Notes
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