Question

Question about permutations.

Answer 1

Prove that:
\[sgn(\sigma)=sgn(\sigma^{-1})\forall \sigma \in S_n\]

Answer 2

what's \(S_n\)?

Answer 3

\[ 1 = sgn(e) \ \ \ \ \ \ \ \ \ \ \ \ \ \hbox{ where e is the identity permutation} \]
\[ = sgn(\sigma \sigma^{-1}) \]
\[ = sgn(\sigma).sgn(\sigma^{-1}) \]
And now you have it.

Answer 4

Indeed! I figured it was a simple one but I wanted to post something xD

Answer 5

who can answer my question? or it's too hard?

Answer 6

oh, S_n is the group of permutation on n objects.

Answer 7

are you speaking about same permutation as in combinatorics \[nPk=\frac{n!}{(n-k)!}\] because I hardly understand it here

Answer 8

No, I'm talking about this:
http://en.wikipedia.org/wiki/Permutation_group

Answer 9

The symmetric group right?

Answer 10

Yes