Re: Listing the partitions of a set

• To: mathgroup at smc.vnet.net
• Subject: [mg65302] Re: [mg65282] Listing the partitions of a set
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 25 Mar 2006 05:17:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Needs["DiscreteMath`Combinatorica`"];

s=SetPartitions[4]

{{{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}}}

s/.{x_?NumberQ}:>x

{{{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}}

Bob Hanlon

>
> From: Richard Palmer <mapsinc at bellatlantic.net>
To: mathgroup at smc.vnet.net
> Subject: [mg65302] [mg65282] Listing the partitions of a set
>
>
> 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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