FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 1, PAGES 31-51

On the representation of substitutions as products of a transposition and a full cycle

A. Yu. Zubov

Abstract

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A method of solving equations of the form $gy$₁ × h × g^y₂ × h × ¼ × g^y_l × h × g^y_l+1= s in the symmetric group $S$_n is proposed, where $h$ is a transposition, $g$ is a full cycle, and $$s Î S_n. The method is based on building all sets of generalized inversions of the bottom line of the substitution $$s by means of a system of Boolean equations associated with $$s. An example of solving an equation in a group $S$₆ is given.

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Last modified: December 2, 2009