Very strange permutation problem

[betty2301]

Homework Statement

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Homework Equations

product of permutation

The Attempt at a Solution

i have difficulty understanding this q.
why in [itex]\sigma[/itex] there are b1b2...bn new element?
why can i insert [itex]\tau[/itex] in the permutation "matrix"?[itex]\tau[/itex]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 [itex]\tau[/itex] a transposition or any permutation?

 

[jbunniii]

is [itex]\tau[/itex] a transposition or any permutation?

[itex]\tau[/itex] can be any permutation. (That is exactly what [itex]\forall \tau \in S_n[/itex] means.)

Remember that [itex]\tau \sigma \tau^{-1}[/itex] is a composition of three permutations, in the following order: first [itex]\tau^{-1}[/itex], then [itex]\sigma[/itex], then [itex]\tau[/itex]. If the "input" set of elements is [itex]\tau(a_1), ..., \tau(a_n)[/itex], 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.