Timeline for Ramsey type theorem
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2018 at 16:14 | vote | accept | Jiayi Liu | ||
| Feb 22, 2018 at 16:14 | comment | added | Jiayi Liu | Yes @gowers. While the proposition does not hold if you replace {0,...,7} by {0,...,5}. | |
| Feb 22, 2018 at 16:05 | vote | accept | Jiayi Liu | ||
| Feb 22, 2018 at 16:14 | |||||
| Feb 21, 2018 at 7:41 | comment | added | Wolfgang | @ThomasBloom OK I see now. Sorry! No swapping of labels allowed... | |
| Feb 19, 2018 at 21:23 | comment | added | Thomas Bloom | Wolfgang: there is a constraint because it says the minimum of $A$ is $2k$, not just that $2k\in A$. For example, with $k=3$ this forces $B=\{7\}$ and $A=\{6\}$. | |
| Feb 19, 2018 at 17:36 | comment | added | Wolfgang | What is the use of the "condition" involving a $k$? The labels 0,...,7 can be swapped wlog, so this is no constraint. | |
| Feb 19, 2018 at 17:11 | answer | added | Adam P. Goucher | timeline score: 8 | |
| Feb 19, 2018 at 15:44 | comment | added | gowers | Maybe worth noting, just to motivate the question, that we cannot take the parity of the minimum element, since that can be the same for all four sets, and we cannot take the parity of the size of the set, since $A$ and $B$ can both have even size. They can also have the same size mod 3 or 4. So a lot of the usual methods for finding counterexamples to Ramsey questions don't work here. | |
| Feb 19, 2018 at 7:21 | comment | added | Jiayi Liu | I wasn't seeking for an algorithm to determine answers for such kind of problems. I only wonder this particular problem. | |
| Feb 18, 2018 at 22:51 | comment | added | Adam P. Goucher | If you negate this question to place it in the existential form 'does there exist $f$ such that for all $A, B, C$ satisfying these properties, at least one of $\{f(C), f(A \cup C), f(B \cup C), f(A \cup B \cup C) \}$ is true and at least one is false?', then it can be written as a conjunction of many 4-variable clauses over $2^8$ variables (the function values). This could be given to a SAT solver and (I suspect) solved almost instantaneously. | |
| Feb 18, 2018 at 15:53 | history | edited | Peter Heinig | CC BY-SA 3.0 |
While question was on top of stack anyway, three edits from slightly strange notation and phrasing to usual phrasing were made.
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| Feb 18, 2018 at 15:21 | history | reopened |
Stefan Kohl♦ Peter Heinig András Bátkai j.c. Yemon Choi |
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| Feb 18, 2018 at 10:58 | comment | added | Peter Heinig | In my opinion one should give the OP the benefit of the doubt that this is a question that they need to know in their mathematical research. It is a sensible question, which can come up in research. It could be equivalently rephrased more catchily as 'Is it true that for every hypergraph $\mathcal{H}$ on the finite ordinal $8$, there exist three disjoint subsets $A$, $B$, $C$ of $8$ such that (0) the sets $C$, $A\cup C$, $B\cup C$, $A\cup B\cup C$ either all are in $\mathcal{H}$ or all are out, and (2) the minimum element of $B$ is one larger than the minimum of $A$, and is at most $7$.' | |
| Feb 18, 2018 at 10:46 | history | edited | Peter Heinig | CC BY-SA 3.0 |
Removed ungrammatical last sentence. Added a question mark at end of proposition. Changed 'correct' to 'true'.
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| Feb 18, 2018 at 8:55 | review | Reopen votes | |||
| Feb 18, 2018 at 13:20 | |||||
| Feb 18, 2018 at 8:41 | comment | added | Jiayi Liu | It's revised now. | |
| Feb 18, 2018 at 8:38 | history | edited | Jiayi Liu | CC BY-SA 3.0 |
added 36 characters in body
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| Feb 17, 2018 at 15:02 | history | closed |
user6976 Andrés E. Caicedo Stefan Waldmann Stefan Kohl♦ Ben McKay |
Needs details or clarity | |
| Feb 16, 2018 at 15:08 | review | Close votes | |||
| Feb 17, 2018 at 15:02 | |||||
| Feb 16, 2018 at 14:48 | history | edited | Jiayi Liu | CC BY-SA 3.0 |
added 4 characters in body; edited tags
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| Feb 16, 2018 at 11:42 | history | asked | Jiayi Liu | CC BY-SA 3.0 |