Parametrization of the solutions of the equation x 1 x 2 … x n−1 x n = x n x n−1 … x 2 x 2 in a free monoid
Геннадий Семенович Маканин · Mathematical Notes · 2011
A parametrizing function 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 Sm, we construct formulas that provide all the solutions of the equation $x_1 x_2 ...x_{n - 1} x_n = x_n x_{n - 1} ...x_2 x_1 $ in a free monoid 〈a 1, a 2, …, a ω 〉 and only them.