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Jan 16, 2022 at 15:11 vote accept mathoverflowUser
Jan 16, 2022 at 11:01 comment added Martin Rubey It should be possible to extend this a bit. If $n=p^k$ is a prime power, there seem to be actions of $C_k$ and $C_{k-1}$. In this case, the cyclic sieving polynomial is $\sum_{i=0}^k \frac{1-q^{p^i}}{1-q}$. If $n=3k$ such that $k$ is in oeis.org/A215800 there seems to be an (additional) action of $C_3$.
Jan 16, 2022 at 8:41 history edited Martin Rubey CC BY-SA 4.0
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Jan 16, 2022 at 8:12 comment added mathoverflowUser thanks for your answer.
Jan 15, 2022 at 23:07 history answered Martin Rubey CC BY-SA 4.0