How many ways can you paint a regular Decagon with q colors?
I need to solve it with Burnside's lemma.
So far I managed to find only 2 symmetries, the identity, and this one.
I believe I miss the method, can someone solve, and try to explain how did he solve it?
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1Are you familiar with the Dihedral group? – Mark Apr 24 '21 at 23:46
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1Hint: a square has 8 symmetries, not just 2. – MJD Apr 25 '21 at 00:37
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2You actually have some of the other symmetries drawn on your image. – user3482749 Apr 25 '21 at 00:47
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I found no other method beside brute forcing all combinations. – Apr 25 '21 at 10:55
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2No one is saying so, but I imagine we're all talking about a regular decagon. – Gerry Myerson Apr 26 '21 at 03:14