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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: [mg49663] RE: [mg49650] Q: extract all k-tuple from a list of n elements
  • From: "David Park" <djmp at earthlink.net>
  • Date: Tue, 27 Jul 2004 07:00:40 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Klaus,

Is this what you are looking for?

Needs["DiscreteMath`Combinatorica`"];

2-tuples from a set of 3 elements:

KSubsets[{i, j, k}, 2]
{{i, j}, {i, k}, {j, k}}

3-tuples from a set of 5 elements:

KSubsets[{a, b, c, d, e}, 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}}

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 


From: Klaus Duellmann [mailto:klaus.duellmann at arcor.de]
To: mathgroup 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?

Any help is appreciated.

Regards,

Klaus




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