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^{yl} × h
× g^{yl+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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k091/k09103h.htm

Last modified: December 2, 2009