Timeline for An upper bound on the number of sets of parallel lines covering points in a finite plane?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2015 at 1:16 | vote | accept | pxdnr | ||
| S Apr 28, 2015 at 1:16 | history | suggested | Anurag |
added more relevant tags
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| Apr 28, 2015 at 0:48 | review | Suggested edits | |||
| S Apr 28, 2015 at 1:16 | |||||
| Apr 28, 2015 at 0:15 | answer | added | Douglas Zare | timeline score: 3 | |
| Apr 27, 2015 at 22:27 | comment | added | pxdnr | Also, thank you for the hyper-oval example. | |
| Apr 27, 2015 at 22:18 | comment | added | pxdnr | I've updated the question: I've removed the meaningless condition on the cover, and we are looking for upper bounds as a function of $n$, in particular we're interesting in values of $n$ which are much smaller than $|\mathbb{F}|$. Furthermore, we're not including $L_\infty$, although that's not an important restriction. | |
| Apr 27, 2015 at 22:16 | history | edited | pxdnr | CC BY-SA 3.0 |
deleted 25 characters in body
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| Apr 27, 2015 at 16:10 | comment | added | Douglas Zare | Also, the points $\{(0,0),(0,1),(1,0),(1,1)\}$ have $3$ even covers: $L_0, L_1, L_\infty$. | |
| Apr 27, 2015 at 16:08 | comment | added | Douglas Zare | What do you mean, "every point in $P$ is on a line in $L_m$?" Parallel lines partition the points so the condition seems meaningless. Are you looking for upper bounds on the number of even covers as a function of $n$? If you don't restrict the number of points, you can have sets with $|\mathbb{F}|+1 = q+1$ even covers. For example, take a hyper-oval in the projective plane. This has $q+1$ points and every line intersects it in $0$ or $2$ points. Delete a line not intersecting the hyper-oval to get a set with $q+1$ even covers in an affine plane. | |
| Apr 27, 2015 at 11:58 | review | First posts | |||
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| Apr 27, 2015 at 11:52 | history | asked | pxdnr | CC BY-SA 3.0 |