Timeline for Distribution of big component of set partitions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2012 at 2:10 | history | edited | Louigi Addario-Berry | CC BY-SA 3.0 |
Fixed an error pointed out by Brendan McKay
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| Jan 10, 2012 at 2:08 | comment | added | Louigi Addario-Berry | Thanks for the comment, Brendan. Pitman has this right; I didn't in my first version of my answer. I'll correct. | |
| Jan 10, 2012 at 1:17 | comment | added | Brendan McKay | Usually cells of set partitions are required to be non-empty. However, this is easy to fix and even helps since partitions into $k$ parts then correspond to the same number $k!$ of ordered partitions. Let $X_1,\ldots,X_k$ be iid random variables with distribution Poisson($\lambda$) conditioned on not being 0. Then their joint distribution conditioned on their sum being $n$ is the joint distribution of the cell sizes of a random partition. This distribution is independent of $\lambda$, so as Louigi says $\lambda$ can be selected to be useful. | |
| Jan 9, 2012 at 19:20 | comment | added | Igor Rivin | Cool, thanks! I will check out the references... | |
| Jan 9, 2012 at 17:18 | history | answered | Louigi Addario-Berry | CC BY-SA 3.0 |