Timeline for Lattice question
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2017 at 13:18 | history | edited | Francisco Santos | CC BY-SA 3.0 |
added 103 characters in body
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| Feb 4, 2017 at 13:17 | comment | added | Francisco Santos | @Yoav Kallus; You are right... second failed attempt on my side. And in fact your idea is conceptually much simpler. For a smaller (coordinate-wise) example, your $k_3$ can be changed to any vector with odd sum of coordinates and different from $(\pm 1,0)$ or $(0,\pm 1)$. (E.g, $k_3=(3,0)$ or $k_3=(2,1)$ work). | |
| Feb 4, 2017 at 2:46 | comment | added | Yoav Kallus | If I understand the question and your example, this is still not a counterexample to the OP's proposed conjecture: $(2,-1)$ is connected to $(1,2)$ by the vector $(-1,3)$ which is a side of $P$. But I think there is a simpler counterexample: Let $K$ be the Minkowski sum of the segments from the origin to the points $k_1=(1,1)$, $k_2=(1,-1)$ and $k_3=(500,501)$. Let $P$ be the Minkowski sum of only the first two, then $(1,0)\in P$ is not connected to the rest of $P$. | |
| Feb 4, 2017 at 2:02 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Fixed LaTeX typo.
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| Feb 3, 2017 at 17:12 | history | edited | Francisco Santos | CC BY-SA 3.0 |
Edited Feb 3 to correct previous wrong example
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| Feb 2, 2017 at 15:48 | history | answered | Francisco Santos | CC BY-SA 3.0 |