Timeline for Pick a homogeneous set of size $n$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 7 at 8:57 | vote | accept | Joe Miller | ||
| May 6 at 8:54 | answer | added | Ilya Bogdanov | timeline score: 11 | |
| May 1 at 5:29 | comment | added | Joe Miller | @GerryMyerson That's a beautiful example, thanks! This suggests that the rest of my upper bounds are pretty terrible. | |
| May 1 at 1:39 | comment | added | Gerry Myerson | I think $c(3)\le7$, by 2-coloring the points of the Fano plane. For any 2-coloring, there's a monochromatic line. So, sample 123, 145, 167, 246, 257, 347, 356. | |
| May 1 at 1:23 | comment | added | Gerry Myerson | @Rob, ah. I read the "you may sample" and the "as you would like" as permitting, rather than requiring, the samples to be taken at the same time, but, of course, you are right. | |
| May 1 at 1:02 | comment | added | RobPratt | @GerryMyerson The samples must be chosen "all at the same time." | |
| May 1 at 1:01 | comment | added | Gerry Myerson | Homogeneous means monochrome? Anyway, for $n=3$, sample $\{1,2,3\}$. Assume $2$ and $3$ are the same color. Sample $\{2,3,4\}$ and $\{2,3,5\}$. If neither is monochrome, then $\{1,4,5\}$ is. So $c(3)=4$. Am I right? | |
| Apr 30 at 9:10 | history | asked | Joe Miller | CC BY-SA 4.0 |