Timeline for Lattice points in cross-polytopes
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2013 at 22:22 | comment | added | Noam D. Elkies | Yes I saw it, but had nothing to contribute. In large dimensions we don't know how to pack $l_1$ balls (hyperoctahedra / cross-polytopes) any more densely than $l_2$ (round/Euclidean) balls. | |
| Jun 15, 2013 at 22:18 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Much more experimental data on the pairwise coprime case; faster code
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| Jun 11, 2013 at 20:40 | comment | added | Yoav Kallus | @Elkies, I wonder if you saw this question from a couple of weeks ago, which also seems to be about intersection of cross polytopes with lattices: mathoverflow.net/questions/132165/… | |
| Jun 11, 2013 at 20:32 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Add proof and code
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| Jun 11, 2013 at 20:15 | comment | added | Noam D. Elkies | You're welcome. I'll post the gp code before long. Meanwhile, To enumerate $E \cap {\bf Z}^3$ when $(q_1,q_2,q_3) = (k,k+1,k+1)$, observe that the integer points are those with $\left|x_1\right|+\left|x_2\right|+\left|x_3\right| \leq k$ together with the $4(k+1)$ points with $x_1=0$ and $\left|x_2\right|+\left|x_3\right| = k+1$. | |
| Jun 11, 2013 at 20:09 | comment | added | Oleg Eroshkin | Great! That is quite surprising. I assumed, that is better to look for co-prime $q_i$ for counterexamples. | |
| Jun 11, 2013 at 20:06 | vote | accept | Oleg Eroshkin | ||
| Jun 11, 2013 at 20:03 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |