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kriegor May 18th, 2012 08:26 AM

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?

mehoul May 21st, 2012 11:47 PM

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

mehoul May 22nd, 2012 01:19 AM

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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