kramtus51

2021-12-08

Given cyclic permutations:

$\sigma =\left(123\right)$ ,${\sigma}_{2}=\left(45\right)$ ,

then what are the inverse cycles$\sigma}^{-1$ , $\sigma}_{2}^{-1$

then what are the inverse cycles

Melinda McCombs

Beginner2021-12-09Added 38 answers

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).

For the question: (123)−1=(321)=(132).

Hector Roberts

Beginner2021-12-10Added 31 answers

You have that $\sigma}_{1$ is the cycle:

$1\mapsto 2$

$2\mapsto 3$

$3\mapsto 1$

And the incverse cycle will look like:

$2\mapsto 1$

$3\mapsto 2$

$1\mapsto 3$

And the incverse cycle will look like: