Timeline for Overlapping sets
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| S Sep 26, 2013 at 10:52 | history | bounty ended | Per Alexandersson | ||
| S Sep 26, 2013 at 10:52 | history | notice removed | Per Alexandersson | ||
| Sep 26, 2013 at 8:34 | vote | accept | Per Alexandersson | ||
| Sep 21, 2013 at 20:20 | comment | added | Per Alexandersson | Ilya Bogdanov Yes, that is true. | |
| Sep 21, 2013 at 20:12 | comment | added | Ilya Bogdanov | Just a remark. The statement about segments of integers holds even if all $F_x$ are divisible by $k$; in this case you may split the family into $k$ `equal' parts. | |
| Sep 21, 2013 at 9:24 | answer | added | domotorp | timeline score: 4 | |
| Sep 20, 2013 at 19:00 | comment | added | Russ Woodroofe | Ah! I missed that F_x was a count, rather than itself a set. Thanks. | |
| Sep 20, 2013 at 8:35 | answer | added | Chassaing | timeline score: 3 | |
| Sep 19, 2013 at 19:12 | comment | added | Gerhard Paseman | You might look at some additional restrictions on F, e.g. E in F implies E has two elements. One small F for which there is no F' is the edge set of a triangle. Characterizing "graphs" F with such a property may turn out to be related to an NP-complete problem. Gerhard "Ask Me About System Design" Paseman, 2013.09.19 | |
| Sep 19, 2013 at 18:27 | comment | added | Per Alexandersson | 2F'_x just means 2 times the number of subsets in F', that contains x. There is some structure on I of course, namely that F_x is even for every x. A simple example is when I is the real numbers and F is some intervals of the form ]a,b] on the real line. Then F_x being even for all x, is just another way of saying that every point in the real line is covered by an even number of intervals in F. It is easy to show that in this case, we can find a subset F' in F, that covers every point x "half as much" as F. | |
| Sep 19, 2013 at 18:04 | comment | added | Russ Woodroofe | What does 2F'_x mean? It looks like maybe you're assuming some kind of structure on I? | |
| S Sep 19, 2013 at 11:39 | history | bounty started | Per Alexandersson | ||
| S Sep 19, 2013 at 11:39 | history | notice added | Per Alexandersson | Draw attention | |
| Sep 17, 2013 at 11:18 | history | asked | Per Alexandersson | CC BY-SA 3.0 |