Comments on: The ormat game http://bit-player.org/2010/the-ormat-game An amateur's outlook on computation and mathematics. Thu, 17 May 2012 10:18:16 +0000 http://wordpress.org/?v=2.6.3 By: Gerry Myerson http://bit-player.org/2010/the-ormat-game#comment-3170 Gerry Myerson Mon, 23 Aug 2010 06:56:27 +0000 http://bit-player.org/?p=771#comment-3170 To answer Barry's question, yes, if all the row and column sums are equal, then the matrix is a sum of permutation matrices. The result goes back to Konig, 1915/16, and can be seen as a consequence of Hall's Marriage Theorem. See D Leep and G Myerson, Marriage, magic, and solitaire, Amer Math Monthly 106 (1999) 419-429. To answer Barry’s question, yes, if all the row and column sums are equal, then the matrix is a sum of permutation matrices. The result goes back to Konig, 1915/16, and can be seen as a consequence of Hall’s Marriage Theorem. See D Leep and G Myerson, Marriage, magic, and solitaire, Amer Math Monthly 106 (1999) 419-429.

]]> By: Barry Cipra http://bit-player.org/2010/the-ormat-game#comment-3158 Barry Cipra Fri, 20 Aug 2010 14:34:02 +0000 http://bit-player.org/?p=771#comment-3158 Brian, are you now conjecturing that all your conjectures turn out to be wrong? Your flag-waving approach is much much better than my uppity triangular idea. It gets to a good general result without any messy case-by-case analysis. Well done! Brian, are you now conjecturing that all your conjectures turn out to be wrong?

Your flag-waving approach is much much better than my uppity triangular idea. It gets to a good general result without any messy case-by-case analysis. Well done!

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