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February 11th, 2017, 01:46 PM  #1 
Senior Member Joined: Jan 2013 From: Italy Posts: 153 Thanks: 7  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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$13245$, permutation, product, transpositions 
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