Timeline for Estimating a sum over set partitions
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Oct 19 at 0:27 | vote | accept | T. Amdeberhan | ||
| Oct 17 at 18:59 | comment | added | Abdelmalek Abdesselam | Don't close. This is a good question. | |
| Oct 17 at 18:57 | answer | added | Abdelmalek Abdesselam | timeline score: 7 | |
| Oct 17 at 1:19 | comment | added | T. Amdeberhan | @AbdelmalekAbdesselam: N is allowed to increase freely. | |
| Oct 16 at 23:21 | review | Close votes | |||
| Oct 21 at 3:03 | |||||
| Oct 16 at 23:05 | history | edited | Andrés E. Caicedo |
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| Oct 16 at 22:29 | comment | added | Abdelmalek Abdesselam | @T.Amdeberhan: Ok I think I understand, except what is $N$. It is nowhere defined. I also have eyes to see an absolute value is taken on the LHS. | |
| Oct 16 at 21:27 | comment | added | T. Amdeberhan | @AbdelmalekAbdesselam: $N$ and $n$ are different. The formulation is correct. On the LHS, we take the absolute value. | |
| Oct 16 at 21:14 | comment | added | T. Amdeberhan | @PietroMajer: no, it is not a typo. | |
| Oct 16 at 20:50 | comment | added | Pietro Majer | Also, is $D\in C$ a typo? | |
| Oct 16 at 20:08 | comment | added | Abdelmalek Abdesselam | BTW the question (even in need of clarification) looks very interesting to me, because lots of estimates of this kind occur in rigorous statistical mechanics. The main topic here is Moebius inversion in the partition lattice, following Rota, Groeneveld, Penrose,... | |
| Oct 16 at 20:07 | comment | added | Abdelmalek Abdesselam | I believe the sum is over partitions $\sigma$ which are finer than $\rho$. There are lots of problems with the current formulation though. Is $N$ the same as $n$? Should the product be over blocks $C$ of $\rho$ instead of $\sigma$ so then the sum over $D$ is over $\sigma$ blocks inside the block $C$ of $\rho$? Is $|D|$ the number of points in $D$? For the estimate to make sense are we taking the max of the left-hand side over $\rho$?... | |
| Oct 16 at 19:29 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
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| Oct 16 at 19:09 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
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| Oct 16 at 18:57 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
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| Oct 16 at 18:48 | comment | added | Chris McDaniel | What are you summing over here? | |
| Oct 16 at 18:40 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |