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 Mat. Sb., 2004, Volume 195, Number 4, Pages 65–96 (Mi msb814)

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

G. S. Makanin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In the preceding paper of the author parametrizing functions Fi, Th, Ro were introduced depending on word variables, positive-integer variables, and variables whose values are finite sequences of positive-integer variables. With the help of the parametrizing functions Fi, Th, Ro finite formulae are written out for the family of solutions of every equation of the form $\varphi(x_1,x_2,x_3) x_4=\psi(x_1,x_2,x_3) x_5$, where $\varphi(x_1,x_2,x_3)$ and $\psi(x_1,x_2,x_3)$ are arbitrary words in the alphabet $x_1$, $x_2$$x_3$ in a free monoid.

DOI: https://doi.org/10.4213/sm814

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English version:
Sbornik: Mathematics, 2004, 195:4, 521–552

Bibliographic databases:

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

Citation: G. S. Makanin, “Finite parametrization of solutions of equations in a free monoid. II”, Mat. Sb., 195:4 (2004), 65–96; Sb. Math., 195:4 (2004), 521–552

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb814
• https://doi.org/10.4213/sm814
• http://mi.mathnet.ru/eng/msb/v195/i4/p65

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This publication is cited in the following articles:
1. 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
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
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