kramtus51

2021-12-08

Given cyclic permutations:
$\sigma =\left(123\right)$,${\sigma }_{2}=\left(45\right)$,
then what are the inverse cycles ${\sigma }^{-1}$, ${\sigma }_{2}^{-1}$

Melinda McCombs

To find the inverse of a permutation just write it backwards. If $\tau =\left(1243\right)\left(67\right)$ then ${\tau }^{-1}=\left(76\right)\left(3421\right)$ which can then be rewritten as ${\tau }^{-1}=\left(1342\right)\left(67\right)$.
For the question: (123)−1=(321)=(132).

Hector Roberts

You have that ${\sigma }_{1}$ is the cycle:
$1↦2$
$2↦3$
$3↦1$
And the incverse cycle will look like:
$2↦1$
$3↦2$
$1↦3$

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