Geodesic
Parametrization of solutions of some equations of squares in a free monoid
Diskretnaya Matematika, Tome 11 (1999) no. 3, pp. 133-148 
G. S. Makanin; T. A. Makanina. Parametrization of solutions of some equations of squares in a free monoid. Diskretnaya Matematika, Tome 11 (1999) no. 3, pp. 133-148. http://geodesic.mathdoc.fr/item/DM_1999_11_3_a11/
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     author = {G. S. Makanin and T. A. Makanina},
     title = {Parametrization of solutions of some equations of squares in a free monoid},
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     pages = {133--148},
     year = {1999},
     volume = {11},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1999_11_3_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce parametrizing functions $Fa$, $La$, $Do$ of word variables, natural number variables, and variables whose values are finite sequences of natural number variables. By means of parametrizing functions $Fa$, $La$, $Do$ we give finite formulas for the family of solutions of the equation $$ x_1^2x_2^2x_3^2=x_4^2 $$ in a free monoid.The research was supported by the Russian Foundation for Basic Research, grant 98–01–00885.