Equation with permutations.

Asked Apr 25 '23 at 17:09

Active Apr 25 '23 at 21:44

Viewed 36 times

I have the following equation with permutations :

$x^2=(1 2 3)(4)$

I try to solve this by direct method with repeted tries, after i tested it's compatibility with the signature of the permutation, there is a better way to find the unknown permutation x? Something like the inverse of the permutation? Imention that the permutation in the right is given in cycle form :

$$\begin{pmatrix} 1 & 2 & 3 & 4\\ 2& 3 & 1 &4 \end{pmatrix}$$

edited Apr 25 '23 at 21:44

N. F. Taussig

76,571

asked Apr 25 '23 at 17:09

Alexandru Harai

Rotating a triangle clockwise twice is the same as rotating it counterclockwise once. For your specific problem, note that $(132)^2=(123)$. For the more general case of finding a square root of a permutation see the linked problem. – JMoravitz Apr 25 '23 at 17:28
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Does this answer your question? How to find the square root of a permutation – JMoravitz Apr 25 '23 at 17:28

Equation with permutations.

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