Timeline for Can we color Z^+ with n colors such that a, 2a, ..., na all have different colors for all a?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 30, 2010 at 4:19 | comment | added | Harry Altman | FWIW, I've checked that this approach works when $n\le34$. | |
| May 29, 2010 at 21:57 | comment | added | gowers | Yes, it's clear that it's false in general, but that the set of lattice simplices T that actually turn up in the problem is not at all general: the lengths of the sides are small given the dimension. I now think that this approach is just a rephrasing of what Ewan was proposing. | |
| May 29, 2010 at 20:30 | comment | added | Sergei Ivanov | Your proposed generalization is false. Take the 6 points in $\mathbb Z_+^2$ defined by $x_1+x_2\le 2$. One cannot 6-color this set plus two points: (2,1) and (1,2). | |
| May 29, 2010 at 17:17 | history | answered | gowers | CC BY-SA 2.5 |