Timeline for colorings of ${\mathbb Z}^d$ with constraints
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2014 at 17:30 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
added 22 characters in body
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| Jan 13, 2014 at 6:39 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
added 129 characters in body
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| Jan 12, 2014 at 18:12 | comment | added | Wolfgang | I think your construction can even yield a (n+1,k+1) coloring, just using one additional color instead of all the negative ones, and to iterate that, just choose another origin. :) ... and yet, we can still ask if there are "minimal" pairs $(n,k)$ that only allow periodic colorings. | |
| Jan 12, 2014 at 18:10 | comment | added | Anthony Quas | I think periodically repeating $\begin{pmatrix} 0&0&0&1\\1&2&1&2\end{pmatrix}$ is fine. There are only a handful of line directions to check: (1,0), (1,1), (1,2) and (0,1). | |
| Jan 12, 2014 at 17:29 | comment | added | Wolfgang | you are right. Nice idea to swap colors like that - it is so useful to think "out of the box" rather than thinking in terms of affine spaces and the like. | |
| Jan 12, 2014 at 8:14 | history | answered | Aaron Meyerowitz | CC BY-SA 3.0 |