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

• To: mathgroup at smc.vnet.net
• Subject: [mg49671] Re: Q: extract all k-tuple from a list of n elements
• From: koopman at sfu.ca (Ray Koopman)
• Date: Tue, 27 Jul 2004 07:00:54 -0400 (EDT)
• References: <ce2fv9\$8rm\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Klaus Duellmann <klaus.duellmann at arcor.de> wrote in message
news:<ce2fv9\$8rm\$1 at smc.vnet.net>...
> 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?

In:= subsets[n_,k_] := ToExpression["Flatten[Table[" <>
ToString[Table["i"<>ToString[j],{j,k}]] <>
Table[ ", {i"<>ToString[j] <>
If[j==1, ",", ",i"<>ToString[j-1]<>"+1,"] <>
ToString[n+j-k] <> "}", {j,k}] <>
"]," <> ToString[k-1] <> "]"]

In:= subsets[5,3]
Out= {{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5},
{1, 4, 5}, {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}}

```

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