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MathGroup Archive 2006

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Permutations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65508] Permutations
  • From: "King, Peter R" <peter.king at imperial.ac.uk>
  • Date: Thu, 6 Apr 2006 06:51:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I wish to be able to construct permutations by listing those positions
that are unaltered, all other pairs swapping. So if I start from
{a,b,c,d,e,f} and apply the rule {1,4} I get {a,c,b,d,f,e}. Note that
this is the only kind of permutation that I need. ie there is always at
least one pair of positions that aren't changed and in all other
positions neighbouring pairs are swapped (the only other kind of
permutation is where all pairs cross, I guess I can call this {} and it
gives {b,a,d,c,f,e}).

I am sure there is a trivial way of doing this (clearly I can construct
matrices and do it by multiplication of the vector - or I can extract
elements and swap the postions "by hand" but these seem unnecessarily
tedious). Any thoughts out there?

Many thanks in advance.


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