Geodesic
On the representation of substitutions as products of a~transposition and a~full cycle
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 31-51.

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A method of solving equations of the form $g^{y_1}\cdot h\cdot g^{y_2}\cdot h\cdot\ldots\cdot g^{y_l}\cdot h\cdot g^{y_{l+1}}=\sigma$ in the symmetric group $\mathrm S_n$ is proposed, where $h$ is a transposition, $g$ is a full cycle, and $\sigma\in\mathrm S_n$. The method is based on building all sets of generalized inversions of the bottom line of the substitution $\sigma$ by means of a system of Boolean equations associated with $\sigma$. An example of solving an equation in a group $\mathrm S_6$ is given. 
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A. Yu. Zubov. On the representation of substitutions as products of a~transposition and a~full cycle. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 31-51. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a2/

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