Timeline for Can the optimal packing density in $\mathbb{Z}^d$ be irrational?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2023 at 11:41 | comment | added | domotorp | And of course "since" was supposed to be "single", but I see that luckily you were more intelligent than me and you've managed to understand my question... | |
| Sep 26, 2023 at 11:55 | comment | added | Arsenii Sagdeev | @domotorp No, I do not have a constuction with several tiles where $d_p$ is irrational either | |
| Sep 26, 2023 at 11:53 | comment | added | Arsenii Sagdeev | @domotorp you are right, I don't see how uncomputablity follows from their preprint, since in Corollary 1.5 they get $d$ and a periodic $E \subset \mathbb{Z}^d$ (that can be distinct from $\mathbb{Z}^d$) as part of the input. So the computability of $d_p(\cdot)$ could be open for each $d\ge2$, but I'm not sure... | |
| Sep 23, 2023 at 21:04 | comment | added | domotorp | Are you sure that it follows from their preprint that the function is uncomputable for $d\ge 3$? Also, if instead of a since $S$, you allow multiple tiles that can be used, then do you have a construction? | |
| Sep 20, 2023 at 8:53 | history | asked | Arsenii Sagdeev | CC BY-SA 4.0 |