Timeline for looking for proof or partial proof of determinant conjecture
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jul 31, 2013 at 1:22 | comment | added | Stefan | @DavidSpeyer : Thanks for all the time you have obviously put into this problem and your partial results. If I solve this problem one way or the other, with a proof or a counterexample, I will edit my question and leave a comment for you, which you will hopefully be notified of in your e-mail. | |
| Jul 31, 2013 at 1:21 | vote | accept | Stefan | ||
| Jul 29, 2013 at 22:36 | comment | added | GH from MO | This is all very nice, but in your special case the final sign should be be $(-1)^{n(n-1)/2}$. The problem comes from the fourth display, where you forgot to multiply $\sum t_i\mu_{\sigma(i)}$ and $\mu_j t_i$ by $-1$. The Lemma and its proof should be updated accordingly. | |
| Jul 29, 2013 at 17:03 | comment | added | Stefan | if your assertion is correct (I have no reason to doubt it, though I don't understand the proof 100%), I am pretty sure that the determinant of the matrix $M$ has the right sign if $\gamma_{n-1}< \mu_1 < \gamma_{n} < \mu_2$ and and $\gamma_n - \mu_1$ is ``really small''. I'd like to extend this to the case where $\gamma_{n-1}< \mu_1 < \gamma_{n} < \mu_2$ and $\gamma_n - \mu_1$ is not necessarily small. | |
| Jul 27, 2013 at 2:14 | history | answered | David E Speyer | CC BY-SA 3.0 |