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Re: Maximising a sum of matrix elements

• To: mathgroup at smc.vnet.net
• Subject: [mg60182] Re: Maximising a sum of matrix elements
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Tue, 6 Sep 2005 02:27:24 -0400 (EDT)
• Organization: The University of Western Australia
• References: <dfiv7u$p8n$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <dfiv7u$p8n$1 at smc.vnet.net>,
 Colin Pratt <coke101 at blueyonder.co.uk> wrote:

> Given a n x n matrix with positive entries, find the maximum sum involving 
> one and only one entry from each row and column. 

For any square matrix mat,

  MaxSum[mat_?MatrixQ] := Max[Tr /@ Permutations[mat]]

> Is there a simple way to enumerate the n! possible sums?

Yes. 

  Permutations[mat]

does what you want.

The following links may be of interest to you:

  http://answers.google.com/answers/threadview?id=485314
  http://hydrogen.ws.binghamton.edu/~qqiu/thermal/00736189.pdf

Cheers,
Paul

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Paul Abbott                                      Phone:  61 8 6488 2734
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