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MathGroup Archive 2004

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Re: Q: extract all k-tuple from a list of n elements

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49658] Re: Q: extract all k-tuple from a list of n elements
  • From: astanoff_otez_ceci at yahoo.fr (astanoff)
  • Date: Tue, 27 Jul 2004 07:00:35 -0400 (EDT)
  • References: <ce2fv9$8rm$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Klaus Duellmann wrote:

> Question: How can I extract all k-tuple from a list of n elements 
> (without considering permutations of the k-tuple)?

> Example: For the special case k=3 one solution would be

> Flatten[Table[{i, j, k}, {i, 1, n - 2}, {j, i + 1, n - 1}, {k, j + 1, 
> n}], 2];

> A generalization of this solution for all k >=1 would involve to create 
> 'automatically' a table of dimension k, but how can this be implemented?

> Any help is appreciated.

> Regards,

> Klaus

--

A colleague of mine gave me this recursive solution 
(seems rather cryptic but it works) :
 
tuple[k_Integer /; k>1]:=
  tuple[k]=
    Union[Sort /@ ((Function[{x},{Sequence@@First[x],#}& /@ Last[x]] /@
                ({#,DeleteCases[tuple[1],Alternatives@@#]}& /@ tuple[k-1]))
            //Flatten[#,1]&)]


test :
tuple[1]={"a","b","c","d","e"};
tuple[3]
{{a,b,c},{a,b,d},{a,b,e},{a,c,d},{a,c,e},{a,d,e},{b,c,d},{b,c,e},{b,d,e},{c,d,
    e}}

hth
v.a.


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