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MathGroup Archive 2003

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Re: combinatorics problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40110] Re: combinatorics problem
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 21 Mar 2003 02:36:24 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <b59a1e$sb3$1@smc.vnet.net> <b5bjfj$5qv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <b5bjfj$5qv$1 at smc.vnet.net>,
 Paul Abbott <paul at physics.uwa.edu.au> wrote:

> Here is such a function (it still uses pruning so can be made more 
> efficient):
> 
>   <<DiscreteMath`
> 
>    myfunc[l_, p_] := 
>    Module[{pre2, pre3, pre4},     
>       pre2 = Sort /@ Map[Tr, Select[KSetPartitions[l, Length[p]],
>          Sort[Length /@ #] == Sort[p] &], {2}]; 
>       pre3 = Union[pre2];
>       pre4 = Count[pre2, #] & /@ pre3; 
>       Thread[{pre3, pre4}]
>    ]

Here is a simpler version (using Split to do the run length encoding):

   <<DiscreteMath`

   myfunc[l_, p_] :=
   Split[ 
      Sort[
         Sort /@ Map[Tr, Select[KSetPartitions[l, Length[p]], 
            Sort[Length /@ #] == Sort[p] & ], {2}]   
      ]
   ] /. x_?MatrixQ :> {First[x], Length[x]}

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul



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