(adsbygoogle = window.adsbygoogle || []).push({}); Permutations (last question of sheet, yay!!)

1. The problem statement, all variables and given/known data[/b]

[tex]\eta[/tex]:=

(1 2 ... n-1 n)

(n n-1 ... 2 1)

[tex]\in[/tex]S[tex]_{n}[/tex] for any n[tex]\in[/tex]N

n.b That should be 2 lines all in one large bracket btw

a.) Determine its sign.

b.) Let n [tex]\geq[/tex]1. Let <a1,...,as> [tex]\in[/tex]Sn be a cycle and let [tex]\sigma[/tex][tex]\in[/tex]Sn be arbitrary. Show that

[tex]\sigma\circ[/tex] <a1,...,as> [tex]\circ[/tex][tex]\sigma^{-1}[/tex] = <[tex]\sigma[/tex](a1),...,[tex]\sigma[/tex](as)> in Sn.

2. Relevant equations

3. The attempt at a solution

I get the sign of the permutation to be (-1)^n/2

I don;t know how to do the second part, any ideas?

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# Homework Help: Permutations (last question of sheet, yay )

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