Re: Permutations...
- To: mathgroup at smc.vnet.net
- Subject: [mg95853] Re: Permutations...
- From: Steven Siew <stevensiew2 at gmail.com>
- Date: Wed, 28 Jan 2009 06:43:14 -0500 (EST)
- References: <glk869$oc9$1@smc.vnet.net>
ans=Permutations[Range[4]]; > How can I get the 6 Translations and the 18 Rotations separately? trans=Select[ans,First[#] == 1 &] {{1,2,3,4},{1,2,4,3},{1,3,2,4},{1,3,4,2},{1,4,2,3},{1,4,3,2}} rotations=Complement[ans,trans] {{2,1,3,4},{2,1,4,3},{2,3,1,4},{2,3,4,1},{2,4,1,3},{2,4,3,1},{3,1,2,4}, {3,1,4,2},{3,2,1,4},{3,2,4,1},{3,4,1,2},{3,4,2,1},{4,1,2,3},{4,1,3,2}, {4,2,1,3},{4,2,3,1},{4,3,1,2},{4,3,2,1}} On Jan 26, 10:52 pm, 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? > > Bruno