Timeline for Bicoloring of $\mathbb{N}^2$, avoiding set of patterns, is the maximal limit density rational?
Current License: CC BY-SA 3.0
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| Oct 8, 2015 at 23:03 | comment | added | Jason Siefken | The density of the distribution of $\gamma_i$ is given by $\phi'$. $5/\log 216 = \int_{1/3}^2 t\phi'(t)\,\mathrm{d} t$ is the expected value. | |
| Oct 8, 2015 at 22:27 | comment | added | Per Alexandersson | Wait, so this average is independent on the actual tiling? That's fascinating! How did you get the $5/\log 216$? Yes, as long as the density of some subset of tiles has irrational density, I believe it should be fine. | |
| Oct 8, 2015 at 18:30 | history | answered | Jason Siefken | CC BY-SA 3.0 |