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February 11th, 2017, 02:46 PM   #1
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Permutation $(132)(45)$ as a product of transpositions.

Hi,

I have this permutation, expressed as product of transpositions:
$\sigma = (132)(45) = (12)(13)(45) = (31)(32)(45)(12)(12)$

I understand that $(132)(45) = (12)(13)(45)$,
is obtained keeping locked the $1$ in the first cycle and pairing it first with $2$ at the third position, and then with $3$ in the second position.
Then, leaving intact $(45)$ since it is already a cycle of two elements.

but, how to obtain $(31)(32)(45)(12)(12)$?

Can you help me? Thanks!
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