Timeline for Sets blocking every $2$-flat in $AG(n,2)$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2016 at 9:52 | comment | added | js21 | Minor remark : the Croot-Lev-Pach-Ellenberg-Gijswijt method, as in dl.dropboxusercontent.com/u/15433464/f3_eng.pdf, gives a worse bound, namely $c = 4 \times 3^{-\frac{3}{4}} \simeq 1,75.$ | |
| Sep 15, 2016 at 9:25 | vote | accept | Seva | ||
| Sep 15, 2016 at 9:22 | comment | added | Ilya Bogdanov | I've added an update with an example. | |
| Sep 15, 2016 at 9:21 | history | edited | Ilya Bogdanov | CC BY-SA 3.0 |
Example added.
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| Sep 15, 2016 at 8:56 | comment | added | Seva | Good! Still, I wonder what are the best bounds known. The immediate probabilistic bound: consider a random set $A$ to which the elements of $\mathbb F_2^n$ are chosen independently with probability $p$, then the expected number of $2$-flats in $A$ is about $2^{3n}p^4$, while the expected size of $A$ is $2^np$; hence, for $p\approx 0.1\cdot 2^{-2n/3}$ we can destroy all $2$-flats removing not too many elements of $A$, and we are still left with, roughly, $2^np$ elements. That is, we get $c=2^{1/3}$ this way. | |
| Sep 15, 2016 at 8:43 | history | answered | Ilya Bogdanov | CC BY-SA 3.0 |