Timeline for Lower bounding the maximum size of sets in a set family with union promise
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 15, 2011 at 18:00 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Jul 15, 2011 at 16:52 | comment | added | Gerhard Paseman | Gowers , $s$ also depends on $m$, but yes. The reason I see for including $n$ is if epsilon is small, we may need some padding to get nontrivial unions with very large $m$. This is one problem where the poster might help out by motivating some of the parameters. I would like to know why the C's are specified before n is mentioned. Gerhard "Email Me About System Design" Paseman, 2011.07.15 | |
| Jul 15, 2011 at 12:51 | comment | added | gowers | So s depends on $\epsilon$ and the sets $C_1,\dots,C_k$? | |
| Jul 15, 2011 at 5:45 | comment | added | Artem Kaznatcheev | Added a more formal statement, hopefully it is clear. Paseman's more informal restatement also works. | |
| Jul 15, 2011 at 5:44 | history | edited | Artem Kaznatcheev | CC BY-SA 3.0 |
added a more formal statement
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| Jul 14, 2011 at 22:07 | comment | added | Gerhard Paseman | I think another way to present it is as follows: Let the C's and epsilon be given. Let m and n be additional parameters large enough to make the following interesting. What is the smallest s among all families such that no S has more than s elements and every union of epsilon times m S's covers one of the C's. One may need large n if epsilon is very small. Gerhard "Email Me About System Design" Paseman, 2011.07.14 | |
| Jul 14, 2011 at 19:59 | comment | added | gowers | With your use of the words "given" and "let" I find it hard to work out exactly how the quantification works in your question. Would it be possible to ask it in a more formal way? | |
| Jul 14, 2011 at 17:33 | history | asked | Artem Kaznatcheev | CC BY-SA 3.0 |