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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```

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