Re: All permutations of a sequence

• To: mathgroup at smc.vnet.net
• Subject: [mg76341] Re: All permutations of a sequence
• From: "digrpat" <digrpat at aol.com>
• Date: Sun, 20 May 2007 02:24:12 -0400 (EDT)
• References: <f2h8t7\$v4\$1@smc.vnet.net> <f2jupj\$d3m\$1@smc.vnet.net> <f2mfqr\$mkg\$1@smc.vnet.net>

```my original suggestion was to be:

<< DiscreteMath`Combinatorica`

allpermutations[list_List] :=
Drop[MinimumChangePermutations[list], -Length[list]!/2]

but wrongly decided that simple Permutations should work. Maybe
MinimumChangePermutations doesn't work either, some sort of test would be
necessary...

"Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com> wrote in message
news:f2mfqr\$mkg\$1 at smc.vnet.net...
> digrpat wrote:
>
>> "Virgil Stokes" <vs at it.uu.se> wrote in message
>> news:f2h8t7\$v4\$1 at smc.vnet.net...
>>> I would like to get all unique permutations of a sequence (e.g.
>>> {1,2,3,4,5,6,7,8,9,10,11,12,13}) with the constraint that all sequences
>>> that have an opposite ordering are not included (e.g. {13, 12,
>>> 11,10,9,8,6,5,4,3,2,1}) would not be included.
>>>
>>> Are there some Mathematica commands that can be used to efficiently
>>> generate these permutations?
>>>
>>> --V. Stokes
> >
> > permutationlist = {1, 2, 3, 4, 5, 6,}
> >
> > allpermutations[list_List] := Drop[Permutations[list], -Length[list]!/2]
> >
> > allpermutations[permutationlist]
>
> Hi,
>
> I am afraid that the solution is not that simple (at least with
> Mathematica version 5.2). Although he above code works fine for a list
> of length 2 or 3, it does not return a correct result for a list of 4 or
> more elements.
>
> For instance, as you can see in the example below, none of the
> permutations of the forms {3, _, _, 4} or {4, _, _, 3} are present in
> the first half of the permuted list.
>
> In[1]:=
> lst = {1, 2, 3, 4};
> perm = Permutations[lst]
> lower = Drop[perm, -Length[lst]!/2]
> upper = Drop[perm, Length[lst]!/2]
> upper == Sort[Reverse /@ lower]
> Complement[upper, Reverse /@ lower]
>
> Out[2]=
> {{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4},
>   {1, 3, 4, 2}, {1, 4, 2, 3}, {1, 4, 3, 2},
>   {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}}
>
> Out[3]=
> {{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4},
>   {1, 3, 4, 2}, {1, 4, 2, 3}, {1, 4, 3, 2},
>   {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1, 4},
>   {2, 3, 4, 1}, {2, 4, 1, 3}, {2, 4, 3, 1}}
>
> Out[4]=
> {{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}}
>
> Out[5]=
> False
>
> Out[6]=
> {{3, 1, 2, 4}, {3, 2, 1, 4}, {4, 1, 2, 3},
>   {4, 2, 1, 3}}
>
> In[7]:=
> \$Version
>
> Out[7]=
> "5.2 for Microsoft Windows (June 20, 2005)"
>
> Regards,
> Jean-Marc
>
>

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