Re: Listing the partitions of a set

• To: mathgroup at smc.vnet.net
• Subject: [mg65314] Re: [mg65282] Listing the partitions of a set
• From: "David Park" <djmp at earthlink.net>
• Date: Sat, 25 Mar 2006 05:17:55 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

What about...

Needs["DiscreteMath`Combinatorica`"]

?KSetPartitions

Flatten[KSetPartitions[{1, 2, 3, 4}, #] & /@ Range[4], 1]
Length[%]
{{{1, 2, 3, 4}}, {{1}, {2, 3, 4}}, {{1, 2}, {3, 4}}, {{1, 3, 4}, {2}}, {{1,
2,
3}, {4}}, {{1, 4}, {2, 3}}, {{1, 2, 4}, {3}}, {{1, 3}, {2,
4}}, {{1}, {2}, {3, 4}}, {{1}, {2, 3}, {4}}, {{1}, {2, 4}, {3}}, {{1,
2}, {3}, {4}}, {{1, 3}, {2}, {4}}, {{1,
4}, {2}, {3}}, {{1}, {2}, {3}, {4}}}
15

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

From: Richard Palmer [mailto:mapsinc at bellatlantic.net]
To: mathgroup at smc.vnet.net

Is there a simple way to list the partitions of a set?  For example, there
are 15 partitions on a set of 4 elements.  {{{1, 2, 3, 4}}, {1, {2, 3, 4}},
{{1, 3, 4}, 2}, {{1, 2, 4}, 3}, {{1, 2, 3},    4}, {{1, 2}, {3, 4}}, {{1,
3}, {2, 4}}, {{1, 4}, {2, 3}}, {1, 2, {3, 4}}, {1, 3, {2, 4}}, {1, 4, {2,
3}}, {2, 3, {1, 4}}, {2,    4, {1, 3}}, {3, 4, {1, 2}}, {1, 2, 3, 4}} .

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