May 18th, 2012, 08:26 AM  #1 
Newbie Joined: Apr 2012 Posts: 18 Thanks: 0  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? 
May 21st, 2012, 11:47 PM  #2 
Senior Member Joined: Feb 2012 Posts: 144 Thanks: 16  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: SpringerVerlag. ISBN 0387964134. MR0884155

May 22nd, 2012, 01:19 AM  #3 
Senior Member Joined: Feb 2012 Posts: 144 Thanks: 16  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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