Very strange permutation problem

[betty2301]

Homework Statement

~

Homework Equations

product of permutation

The Attempt at a Solution

i have difficulty understanding this q.
why in $\sigma$ there are b1b2...bn new element?
why can i insert $\tau$ in the permutation "matrix"?$\tau$itself is a "matrix"??

 

[jbunniii]

It's not a matrix. It is the two-line notation for a permutation. See here for more details:

http://en.wikipedia.org/wiki/Permutation

This is not a strange problem; in fact it's one of the most standard and fundamental facts about permutations.

 

[betty2301]

It's not a matrix. It is the two-line notation for a permutation. See here for more details:

http://en.wikipedia.org/wiki/Permutation

This is not a strange problem; in fact it's one of the most standard and fundamental facts about permutations.

i know this is not a matrix that's why i write "matrix".
help!

 

[betty2301]

is $\tau$ a transposition or any permutation?

 

[jbunniii]

is $\tau$ a transposition or any permutation?

$\tau$ can be any permutation. (That is exactly what $\forall \tau \in S_n$ means.)

Remember that $\tau \sigma \tau^{-1}$ is a composition of three permutations, in the following order: first $\tau^{-1}$, then $\sigma$, then $\tau$. If the "input" set of elements is $\tau(a_1), ..., \tau(a_n)$, then just follow what each stage of the composition does to these elements. Try not to overthink it - this is actually a very easy problem.