

Counting Cycles of a Permutation in Parallel - profquail
http://rjlipton.wordpress.com/2009/09/04/counting-cycles-of-a-permutation-in-parallel/

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Leon
This has really become my favorite blog. Lipton is great to read to get a
survey of different math/cc topics. Plus he's holding out hope P=NP!

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btilly
For anyone who is curious why the theorem is true, here is a quick sketch of a
possible proof.

First prove that both sides of the equation are (mod 2) invariant if you swap
the labeling of (i, i+1). (That is if we keep the permutation alone and swap
the two labels, we don't change either side.) This allows us to rewrite any
permutation so that it takes a canonical form where each cycle takes the form
i -> i+1 -> ... -> i+j -> i. Then prove the theorem for permutations of that
form.

