Timeline for Expected Value for the Number of Parts of a Random Partition (Considering Only a Portion of the Partition Spectrum)
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S May 12, 2020 at 16:23 | history | bounty ended | ZeroTheHero | ||
| S May 12, 2020 at 16:23 | history | notice removed | ZeroTheHero | ||
| May 12, 2020 at 15:29 | vote | accept | Teferi | ||
| May 11, 2020 at 19:03 | answer | added | Anand | timeline score: 6 | |
| May 5, 2020 at 3:46 | comment | added | Gerry Myerson | If the bounty expires without a good answer, let me suggest posting the question to mathoverflow.net | |
| S May 5, 2020 at 3:30 | history | bounty started | ZeroTheHero | ||
| S May 5, 2020 at 3:30 | history | notice added | ZeroTheHero | Authoritative reference needed | |
| S May 4, 2020 at 3:07 | history | bounty ended | CommunityBot | ||
| S May 4, 2020 at 3:07 | history | notice removed | CommunityBot | ||
| Apr 30, 2020 at 14:44 | comment | added | Teferi | @antkam I am interested in both of those quantities. It seems that there is little information on percentiles for partitions. To get an exact answer, I may need to go back to the drawing board and look at partitions that have a certain number of parts, rather than a fraction of the spectrum. Thanks for taking a look! | |
| Apr 30, 2020 at 13:13 | comment | added | antkam | To be precise, you are not asking about the "expected value of the number of parts of a partition". You are asking about the highest number of parts in the partition. This is exactly the $k$th percentile. I still have no idea how to help though. :( | |
| Apr 30, 2020 at 2:14 | comment | added | Teferi | @antkam Yes, you are correct - we are interested in the expected value of the number of parts (and the highest number of parts) of a partition while only considering the $k^{th}$ percentile of the smallest partitions. It's not obvious how to alter the generating function to consider only the $๐^{๐กโ}$ percentile. | |
| Apr 28, 2020 at 17:51 | comment | added | antkam | [cont'd] Alternatively, are there known theories about families of distributions (indexed by $n$ here) s.t. the growth (w.r.t. $n$) of the mean is similar to the growth of the $k$th percentile? E.g. consider the family $Binomial(n,p)$ - because of CLT, the leading terms are both linear. | |
| Apr 28, 2020 at 17:45 | comment | added | antkam | Excuse me if this is a silly question -- I am new to this. :) Let $X =$ the number of parts in a random partition. Then 1976 result is about the mean $E[X]$, while you're asking about the $k$-th percentile for a fixed $k$, am I right? The 1976 paper (which I only vaguely understand) seems to use a standard technique of differentiating a generating function to find the mean. Is there a similar technique for percentile statistics? Nothing comes to my mind but I'm a newbie at generating functions. | |
| Apr 28, 2020 at 3:00 | history | tweeted | twitter.com/StackMath/status/1254968724492365825 | ||
| S Apr 26, 2020 at 1:06 | history | bounty started | Teferi | ||
| S Apr 26, 2020 at 1:06 | history | notice added | Teferi | Authoritative reference needed | |
| Apr 26, 2020 at 1:04 | history | edited | Teferi | CC BY-SA 4.0 | Added more details; fixed formatting |
| Apr 25, 2020 at 2:08 | history | edited | Teferi | CC BY-SA 4.0 | edited body |
| Apr 24, 2020 at 15:58 | comment | added | Teferi | @joriki Yes, that is the paper I was referring to. | |
| Apr 24, 2020 at 2:19 | comment | added | joriki | Apparently you mean the 1976 paper "The Expected Number of Parts of a Partition of $n$"? This is available online here. | |
| Apr 24, 2020 at 2:12 | comment | added | joriki | You can get the proper font and spacing for $\max$ and $\log$ using \max and \log. For operators that don't have a command of their own, you can use \operatorname{name}. | |
| Apr 23, 2020 at 17:13 | history | asked | Teferi | CC BY-SA 4.0 |