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"?\tauitself 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.