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May 18th, 2012, 09:26 AM   #1
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Edge coloring of the cube

I didn't know exactly which forum branch to choose for this problem:

We have a cube and we are coloring its edges. There are three colors available. We say that the two colorings are the same if one can obtain a second by turning cube and permuting colors. Find the number of different colorings.

Any ideas?
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May 22nd, 2012, 12:47 AM   #2
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Re: Edge coloring of the cube

Hi, I think that you could find ideas in Polya's 1937 paper, which was reprinted as a book. Here is the reference : G. Pólya; R. C. Read (1987). Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. New York: Springer-Verlag. ISBN 0-387-96413-4. MR0884155
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May 22nd, 2012, 02:19 AM   #3
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Re: Edge coloring of the cube

the solution is there : http://en.wikipedia.org/wiki/P%C3%B3lya ... on_theorem up to the permutations of colors
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