Timeline for Which unordered partition of $n$ gives rise to the largest number of ordered partitions?
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Aug 12, 2013 at 18:41 | vote | accept | VSJ | ||
| Aug 11, 2013 at 20:19 | answer | added | Chassaing | timeline score: 2 | |
| Aug 10, 2013 at 3:06 | answer | added | Will Sawin | timeline score: 8 | |
| Aug 9, 2013 at 5:44 | comment | added | Gerry Myerson | You could well be right. Anyway, I retract my $(1/3,1/3,1/3)$ suggestion, which was based partly on misunderstanding the question, and partly on misinterpreting some calculations I did. | |
| Aug 9, 2013 at 4:08 | comment | added | VSJ | @Gerry Myerson: I actually suspect the answer is $(1/4, 1/8, 1/16,.....)$. With some dubious analysis which involves substituting factorials by their stirling approximations, I get that the number of ordered partitions that this particular unordered partition gives rise to is $\approx c2^n$, where $c$ is a constant. This is pretty big! | |
| Aug 9, 2013 at 3:51 | comment | added | Gerry Myerson | The maximum value (but not the partition giving rise to the maximum value) is tabulated at oeis.org/A102462 --- there are also links to related matters (but no answer to the current question). | |
| Aug 9, 2013 at 0:01 | comment | added | Gerry Myerson | Have you done any experiments with small $n$ to get a feel for what goes on here? I suspect it converges to $(1/3,1/3,1/3)$. | |
| Aug 8, 2013 at 21:25 | history | asked | VSJ | CC BY-SA 3.0 |