Prove that the probability that two elements of the symmetric group $\displaystyle S_n,$ chosen randomly with replacement, commute is $\displaystyle \frac{P(n)}{n!},$ where $\displaystyle P(n)$ is the partition function.

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- Nov 11th 2009, 07:53 AMNonCommAlgProbabilistic Group Theory
Prove that the probability that two elements of the symmetric group $\displaystyle S_n,$ chosen randomly with replacement, commute is $\displaystyle \frac{P(n)}{n!},$ where $\displaystyle P(n)$ is the partition function.

- Nov 15th 2009, 10:59 PMSampras