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Re: Cycle index for rotation

Hi,

What are "C hat", b and r? I'm totally ignorant about the usage of the cycle index, but I do know about the dihedral group. Rotation of the square through 180 degrees does not yield a product of two 4 cycles, but a permutation which is the product of four 2 cycles. See the attachment for the computation of the cycle index.

Attachment 28527

Re: Cycle index for rotation

The C hat computes the number of possible colorings of corners with different distributions of red and blue.

But your answer showed that I made a mistake in my calculation; thank you.