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MathGroup Archive 2005

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Re: Partition Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57620] Re: Partition Function
  • From: "Carl K. Woll" <carlw at u.washington.edu>
  • Date: Thu, 2 Jun 2005 05:16:56 -0400 (EDT)
  • Organization: University of Washington
  • References: <d7k3qf$ooq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Shug Boabby" <Shug.Boabby at gmail.com> wrote in message 
news:d7k3qf$ooq$1 at smc.vnet.net...
> hi there,
>
> is there any way to get mathematica to return the actual partitions of
> an integer? the only functions related to this, (e.g.
> http://mathworld.wolfram.com/PartitionFunctionP.html) only return the
> *number* of partitions, not the actual partititons (including
> permutations) themselves.
>
> e.g. for 4, i'd like a function to return
> {{1,1,1,1}, {2,1,1}, {1,2,1}, {1,1,2}, {3,1}, {2,2}, {1,3}, {4}}
>
> with the ordering of the partitions not being important
>
> cheers,
> Shug
>

Needs["DiscreteMath`Combinatorica`"]

Flatten[Permutations /@ Partitions[4], 1]
{{4}, {3, 1}, {1, 3}, {2, 2}, {2, 1, 1}, {1, 2, 1}, {1, 1, 2}, {1, 1, 1, 1}}

Carl Woll 



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