Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

Functions for parametrization of solutions of an equation in a free monoid

Author(s): Gennady S. Makanin; Tatiana A. Makanina
Journal: Trans. Amer. Math. Soc. 352 (2000), 1-54.
MSC (1991): Primary 20M05; Secondary 03D40, 20F10
Posted: March 29, 1999
MathSciNet review: 1491869
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Abstract | References | Similar articles | Additional information

Abstract: In this paper we introduce recursive functions

$\begin{align*}&{}^{\mathbf{Fi}}(x_1,x_2)^{\lambda _1,\dotsc,\lambda _s}\qquad(s\ge 0), &{}^{\mathbf{Th}}(x_1,x_2,x_3)_i^{\lambda _1,\dotsc,\lambda _{2s}} \qquad(i=1,2,3;s\ge 0), &{}^{\mathbf{Ro}}(x_1,x_2,x_3)_i^{\mu _1,\dotsc,\mu _s}\qquad(i=1,2,3;s\ge 0) \end{align*}$

of the word variables , natural number variables $\lambda _k$ and variables $\mu _k$ whose values are finite sequences of natural number variables. By means of these functions we give finite expressions for the family of solutions of the equation

$\begin{displaymath}x_1x_2x_3x_4=\zeta(x_1,x_2,x_3)x_5,\end{displaymath}$

where $\zeta(x_1,x_2,x_3)$ is an arbitrary word in the alphabet , in a free monoid.

References:

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