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 _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul