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March 23rd, 2015, 09:08 AM   #1
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Cycle index

How to show that the cycle index for the cyclic group $C_n$ (the group of rotations of regular $n$-gon) is

$$P_{C_n} (t_1 , \ldots ,t_n)= \frac{1}{n} \sum_{d|n} \phi (d) t_{d}^{\frac{n}{d}}$$, where $\phi$ is the Euler function.
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