March 23rd, 2015, 08:08 AM  #1 
Newbie Joined: Mar 2015 From: here Posts: 1 Thanks: 0  Cycle index
How to show that the cycle index for the cyclic group $C_n$ (the group of rotations of regular $n$gon) is $$P_{C_n} (t_1 , \ldots ,t_n)= \frac{1}{n} \sum_{dn} \phi (d) t_{d}^{\frac{n}{d}}$$, where $\phi$ is the Euler function. 

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