Abstract:
In 2011, Makanin obtained the general solution of the symmetric equation
$$
x_1x_2\dotsb x_{n-1}x_n=x_nx_{n-1}\dotsb x_2x_1
$$
in a free monoid. In the present paper, a generalization of this result is given. Namely, we shall describe the general solution of the so-called pseudosymmetric equations in a free monoid which are obtained from the symmetric equations by transposing one (any) pair of adjacent variables.
Keywords:pseudosymmetric equation, free monoid, recursive function (recursion), lexicographic variable.
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