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Apologies if this is too basic, but given a permutation matrix $M$, is there any parameter or formula based on $M$ that gives the disjoint cycle decomposition, or at least the conjugacy class, of the corresponding permutation?

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    If you actually want to find a cycle decomposition, this probably isn't the way to do it. What is the intended application?2011-02-15
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    @Qiaochu Yuan: I know. I'm not actually interested in finding the dcd, I just want to prove a relation between two different constructions and it seems that expressing permutations as matrices may make things easier in this case.2011-02-15

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