Timeline for Find Minimal covering sets for $n\times n\times n$ grid (covering means each grid point has a axis line in common with set)
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2022 at 18:00 | history | tweeted | twitter.com/StackMma/status/1569022964028293120 | ||
| Sep 11, 2022 at 15:05 | answer | added | azerbajdzan | timeline score: 3 | |
| Sep 11, 2022 at 11:54 | answer | added | user293787 | timeline score: 2 | |
| Sep 11, 2022 at 9:25 | comment | added | user293787 | To prove $\Xi(4) \geq 8$ distinguish two cases. Case 1: Every $x$-slice (here $x$ is the first coordinate) contains at least two points of $S$. Case 2: There exists an $x$-slice containing less than $2$ points of $S$. Case 1 implies $|S| \geq 4\cdot 2 = 8$ because there are four $x$-slices. Case 2 implies that in the $x$-slice with less than $2$ points of $S$, at least $9$ points in that slice are not covered by points in that slice, and must be covered by $\geq 9$ points of $S$ that are not in the slice, therefore $|S| \geq 9$. | |
| Sep 11, 2022 at 7:43 | comment | added | Adam | So, for instance, how can we easily prove that $\Xi(4)=8$? | |
| Sep 11, 2022 at 7:40 | history | asked | Adam | CC BY-SA 4.0 |