Re: Permutations...
- To: mathgroup at smc.vnet.net
- Subject: [mg95793] Re: Permutations...
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Tue, 27 Jan 2009 07:00:28 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <glk869$oc9$1@smc.vnet.net>
In article <glk869$oc9$1 at smc.vnet.net>, brunocam 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?
>
> Bruno
You can get the translations by applying repeatedly *RotateLeft*. For
instance,
In[1]:= Table[RotateLeft[{1, 2, 3, 4}, n], {n, 0, 3}]
Out[1]= {{1, 2, 3, 4}, {2, 3, 4, 1}, {3, 4, 1, 2}, {4, 1, 2, 3}}
In[2]:= Table[RotateLeft[#, n], {n, 0, 3}] & /@ {{1, 2, 3, 4}, {1, 3,
2, 4}}
Out[2]=
{{{1, 2, 3, 4}, {2, 3, 4, 1}, {3, 4, 1, 2}, {4, 1, 2, 3}},
{{1, 3, 2, 4}, {3, 2, 4, 1}, {2, 4, 1, 3}, {4, 1, 3, 2}}}