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Jul 28, 2013 at 22:37 comment added Igor Rivin @Stefan: $S$ is a subset of the indices. The convention is that we negate all of the $\gamma$ whose indices are in the subset.
Jul 28, 2013 at 22:15 comment added Stefan Thanks for the latest revision to your answer. Knowing that the conjecture is false for negative $B$ may be useful. I do not quite understand the "closed form" at the end, in particular the definition of $\gamma_S$ (what is $S$?).
Jul 27, 2013 at 18:03 history edited Igor Rivin CC BY-SA 3.0
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Jul 25, 2013 at 21:31 comment added Stefan Thanks, that is really impressive. I had never heard of a Cauchy matrix before. By the way, $B \geq 0$ and all the $\gamma$'s are positive and distinct. David Speyer's commment above also looks helpful. I am going to wait a week or so and accept my favorite answer.
Jul 25, 2013 at 21:21 history answered Igor Rivin CC BY-SA 3.0