Timeline for Structure of nonaveraging sets of integers
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2011 at 18:06 | comment | added | Seva | I believe it is not; it is just that $n=30$ is too small a number (in our present context). Consider the following. If $r_3(n)$ (the largest possible size of a progression-free subset of $[1,n]$) is a reasonably smooth function, then we should expect that $r_3(cn)=(c+o(1))r_3(n)$, for any fixed $c>0$. Now, under Conjecture 3, since $B$ is a progression-free subset of $[1,n-t]$ and $|B|=(1/2+o(1))r_3(n)$, we must have $t\le(1/2+o(1))n$. However, in your example $t=19$, which is about $(2/3)n$. | |
| Apr 3, 2011 at 10:33 | comment | added | Ewan Delanoy | The $n=30$ example (where $C$ is empty) is a counterexample to your intuition. | |
| Apr 3, 2011 at 10:30 | vote | accept | Ewan Delanoy | ||
| Apr 3, 2011 at 8:10 | history | answered | Seva | CC BY-SA 2.5 |