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Permutations...

• To: mathgroup at smc.vnet.net
• Subject: [mg95770] Permutations...
• From: brunocam at libero.it
• Date: Mon, 26 Jan 2009 06:52:29 -0500 (EST)

Given 4 elements  (1 2 3 4)  we have 6 translatios:
1 2 3 4
1 3 2 4
1 4 2 3
2 1 3 4
3 1 2 4
4 3 2 1

Each translation can generate 4 rotations:
1 2 3 4   1 3 2 4   1 4 2 3
2 3 4 1   3 2 4 1   4 2 3 1
3 4 1 2   4 1 3 2   3 1 4 2
4 1 2 3   4 1 3 2   3 1 4 2
etc.

Then:
Translations = (4-1)! = 6
Rotations = 4 per translation
Permutations = Trans * Rot = 4! = 24

With Mathematica:
Permutations[Range[4]]  prints all 24 Permutations
How can I get the 6 Translations and the 18 Rotations separately?

Bruno