Timeline for On necessary condition for no integer points in polytope
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2017 at 15:09 | vote | accept | Turbo | ||
| Nov 2, 2017 at 15:09 | vote | accept | Turbo | ||
| Nov 2, 2017 at 15:09 | |||||
| Nov 2, 2017 at 15:09 | vote | accept | Turbo | ||
| Nov 2, 2017 at 15:09 | |||||
| Nov 2, 2017 at 15:01 | comment | added | Wlodek Kuperberg | Let us continue this discussion in chat. | |
| Nov 2, 2017 at 15:00 | comment | added | Turbo | I meant $\sqrt2-\epsilon$ at any $\epsilon\in(0,\sqrt2-1)$. | |
| Nov 2, 2017 at 14:59 | comment | added | Wlodek Kuperberg | @Turbo: From your comments I gather that you allow lattice points on the boundary of $K$, even though you said $|K\cap \mathbb{Z}^n|=0$. | |
| Nov 2, 2017 at 14:57 | vote | accept | Turbo | ||
| Nov 2, 2017 at 14:59 | |||||
| Nov 2, 2017 at 14:52 | comment | added | Wlodek Kuperberg | Right. The way the example is constructed, the John's e ellipsoid is a sphere. Of course, the product could use a line segment longer than $d$, in which case some of the axes of the ellipsoid could be arbitrarily long. | |
| Nov 2, 2017 at 14:46 | comment | added | Turbo | yes... but my main argument was about smallest axis smaller than $1$ necessary which is disproved in your case with smallest axis $\sqrt 2$ or $\sqrt k$ in general. | |
| Nov 2, 2017 at 14:43 | history | edited | Wlodek Kuperberg | CC BY-SA 3.0 |
added 2 characters in body
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| Nov 2, 2017 at 14:42 | comment | added | Wlodek Kuperberg | @Turbo: Thanks for the correction. I changed "radius" to "diameter", which is what I meant. | |
| Nov 2, 2017 at 14:39 | comment | added | Turbo | $K_2\times [0,d]^{n-2}$ contains John's ellipsoid with smallest axis $\sqrt2$ (not sphere of radius $d$). | |
| Nov 2, 2017 at 14:36 | history | edited | Wlodek Kuperberg | CC BY-SA 3.0 |
edited body
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| Nov 2, 2017 at 12:50 | history | edited | Wlodek Kuperberg | CC BY-SA 3.0 |
extended construction
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| Nov 2, 2017 at 12:46 | history | undeleted | Wlodek Kuperberg | ||
| Nov 2, 2017 at 2:19 | history | deleted | Wlodek Kuperberg | via Vote | |
| Nov 2, 2017 at 2:17 | history | edited | Wlodek Kuperberg | CC BY-SA 3.0 |
specific example described
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| Nov 2, 2017 at 2:10 | history | answered | Wlodek Kuperberg | CC BY-SA 3.0 |