Timeline for What is the maximal diameter of a cell in a particular partition of the simplex?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 21, 2015 at 16:00 | comment | added | Joseph O'Rourke | @User123321: The intuition is that, between two adjacent hyperplanes, the longest cuts are those furthest from the hyperplane's common vertex, because the hyperplanes spread. So perhaps you could prove monotonicity as one hyperplane cuts through the fan of hyperplanes emanating from one vertex. | |
| Dec 21, 2015 at 6:07 | vote | accept | User123321 | ||
| Dec 21, 2015 at 6:04 | comment | added | User123321 | @JosephO'Rourke. Thanks a lot for the diagram and suggestion. I agree (by drawing pictures) that this seems to be the case for $n=3$ and larger $K$ as well. (And, the exact length of this segment can of course be computed analytically for all $K$.) Do you have any further justification for this conjecture? Also, would it help to find (reasonable) upper bounds for this diameter, without nailing it exactly? I edited the question to reflect this, but I am worried that asking for suggestions for upper bounds is too open-ended. | |
| Dec 18, 2015 at 18:53 | comment | added | Joseph O'Rourke | @MoritzFirsching: Thanks. $0.4899$. | |
| Dec 18, 2015 at 16:43 | comment | added | Moritz Firsching | the $\approx\frac{1}{2}$ really is $\frac{\sqrt{6}}{5}$, I guess | |
| Dec 18, 2015 at 13:55 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |