Timeline for A family of subsets with a "gluing" property
Current License: CC BY-SA 2.5
13 events
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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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| Jun 17, 2010 at 4:14 | answer | added | Victor Protsak | timeline score: 1 | |
| Jun 14, 2010 at 9:18 | history | edited | joshuahhh | CC BY-SA 2.5 |
tried to clarify that I'm not talking about a relation
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| Jun 14, 2010 at 9:16 | comment | added | joshuahhh | Oh, I see that I've phrased things confusingly: There is no /relation/ here. "Connected" is a /property/ of a subset. I'll edit to make that a bit more clear... | |
| Jun 14, 2010 at 8:22 | comment | added | supercooldave |
Does it help if you make the relation "connected" explicit and formulate things as a combination of properties of the relation and of the sets the relation connects. For example, the relation is certainly reflexive and symmetric, but not transitive as mentioned below. And if S1 connected S2, then (S1 cup S2) connected (S1 cup S2)... Just an idea.
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| Jun 14, 2010 at 7:46 | history | edited | joshuahhh | CC BY-SA 2.5 |
added 15 characters in body
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| Jun 14, 2010 at 7:45 | comment | added | joshuahhh | @supercooldave: "Maximal connected set" is supposed to mean "one for which no superset is connected". So it's "maximal" in the poset sense. @Kevin Ventullo: That's a good point. I could change the glueability property to apply to any family of subsets with nonempty intersection (instead of just pairs), but for now I think I'll restrict the question to finite sets, which is what I really care about anyway. | |
| Jun 14, 2010 at 7:44 | answer | added | Charles Matthews | timeline score: 3 | |
| Jun 14, 2010 at 7:35 | comment | added | Martin Rubey | Did you look at the exponential principle yet? (chapter 5 of Stanley EC II) Possibly also arxiv.org/abs/0911.3760 | |
| Jun 14, 2010 at 7:30 | comment | added | Kevin Ventullo | Are you assuming S is finite? Otherwise, there need not be any maximal connected sets. For example, take S to be any infinite set, and define the connected sets to be precisely the finite subsets of S. | |
| Jun 14, 2010 at 7:08 | comment | added | supercooldave | What exactly do you mean by 'maximally connected'? In my mind, maximally connected would imply a lot of connectivity, which would mean a lot of overlap between the sets, which would exclude that they are a partition. | |
| Jun 14, 2010 at 7:04 | history | edited | joshuahhh | CC BY-SA 2.5 |
changed grammar slightly, added example
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| Jun 14, 2010 at 6:10 | history | asked | joshuahhh | CC BY-SA 2.5 |