Timeline for Finite field Szemeredi-Trotter theorem with unequal number of points and lines
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2014 at 18:43 | vote | accept | Josh Zahl | ||
| Feb 19, 2014 at 17:34 | vote | accept | Josh Zahl | ||
| Feb 19, 2014 at 18:43 | |||||
| Feb 19, 2014 at 17:34 | comment | added | Josh Zahl | Hi Mark and Terry. First, thanks for the references! If I understand correctly, the trick Mark mentioned allows us to add a line from the point $(1-2\epsilon, 3/2-2\epsilon)$ to the point $(1, 3/2-\epsilon)$. This line has slope $1/2$. (The dual of this line is already present; it is the line from $(1,3/2-\epsilon)$ to $(1+2\epsilon, 3/2+\epsilon)$, which has slope 1. I would be especially happy if there were results that gave us lines passing through $(1,3/2-\epsilon)$ that had slopes better than $1/2$ or $1$ (in the respective directions). It sounds like Terry is not optimistic about this :( | |
| Feb 18, 2014 at 23:58 | comment | added | Terry Tao | Hmm, this trick (together with projective duality to interchange the roles of P and L) widens the slope of the red lines in Josh's diagram a bit (they become parallel to the brown lines), but still doesn't improve upon the trivial bounds once P and L are sufficiently far apart. | |
| Feb 18, 2014 at 23:19 | history | edited | Mark Lewko | CC BY-SA 3.0 |
added 651 characters in body
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| Feb 18, 2014 at 22:40 | history | answered | Mark Lewko | CC BY-SA 3.0 |