Abstract
A method of solving equations of the form \( {g^{{y_1}}} \cdot h \cdot {g^{{y_2}}} \cdot h \cdot \ldots \cdot {g^{{y_1}}} \cdot h \cdot {g^{{y_{l + 1}}}} = \sigma \) in the symmetric group S n is proposed, where h is a transposition, g is a full cycle, and σ × S n . The method is based on building all sets of generalized inversions of the bottom line of the substitution σ by means of a system of Boolean equations associated with σ. An example of solving an equation in a group S6 is given.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 1, pp. 31–51, 2009.
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Zubov, A.Y. On the representation of substitutions as products of a transposition and a full cycle. J Math Sci 166, 710–724 (2010). https://doi.org/10.1007/s10958-010-9887-z
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DOI: https://doi.org/10.1007/s10958-010-9887-z