Re: Permutations...

• To: mathgroup at smc.vnet.net
• Subject: [mg95780] Re: Permutations...
• From: Mariano Suárez-Alvarez <mariano.suarezalvarez at gmail.com>
• Date: Tue, 27 Jan 2009 06:57:59 -0500 (EST)
• References: <glk869\$oc9\$1@smc.vnet.net>

```On Jan 26, 9:52 am, bruno... at libero.it wrote:
> 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?

It is not at all evident what you mean by "rotations"
and "translations". Unless you can give more details
about what you really mean, it's a bit hard to guess...

-- m

```

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