Timeline for Matrix with small elements and prescribed determinant
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 7, 2017 at 23:16 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Apr 7, 2017 at 23:08 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 8, 2017 at 22:52 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 7, 2017 at 13:46 | comment | added | Fedor Petrov | @GerryMyerson Yes, I am not completely satisfied by this double logarithm gap between lower and upper bound. | |
| Feb 6, 2017 at 22:51 | comment | added | Gerhard Paseman | I think he wants a proof that it is O(log p/ log log p). I don't have a proof, but a darned good idea (augmentation) in that direction. Gerhard "It's The Idea That Counts" Paseman, 2017.02.06. | |
| Feb 6, 2017 at 22:10 | comment | added | Gerry Myerson | So, you need something better than just saying it's between $\log p$ and $\log p/\log\log p$? | |
| Feb 6, 2017 at 20:25 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Feb 6, 2017 at 19:12 | comment | added | Fedor Petrov | Yes, but such constructions can not give better bounds, since after an elementary transform the rows of our matrix (almost all of them) have bounded norms. | |
| Feb 6, 2017 at 14:32 | comment | added | js21 | Alternatively, the bound $k = O(\log p)$ can be achieved by writing $p=Q(2)$ where $Q$ is a polynomial with coefficients in $\{ 0 ,1 \}$ (base $2$ expansion), and then by noting that $p = \det(2 I - M)$ where $M$ is the companion matrix of $Q$. The matrix $ 2I - M$ has coefficients in $\{-1,0,1,2,3 \}$. | |
| Feb 6, 2017 at 8:01 | history | asked | Fedor Petrov | CC BY-SA 3.0 |