Timeline for Uniformly permutation and the length of a size biased cycle
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2014 at 9:56 | comment | added | Douglas Zare | @Lucia: That indicates a more stringent condition, that for any $u$, the size of the cycle containing $u$ is uniformly distributed, is also not enough to guarantee a uniform distribution. As an example, take then uniform distribution on $S_n$, then map each permutation to the lexicographically first permutation in its conjugacy class, then conjugate by a uniformly random power of $(1 2 ... n)$. For $n \ge 3$ this is not uniformly distributed on $S_n$ but for each $u$, the cycle containing $u$ has a uniformly distributed length. | |
| Sep 2, 2014 at 9:29 | vote | accept | Bati | ||
| Sep 1, 2014 at 17:06 | answer | added | Janne Kokkala | timeline score: 3 | |
| Sep 1, 2014 at 16:23 | comment | added | Lucia | It seems to me that there are $n!$ variables -- the probabilities for each permutation -- but only $n^2+1$ equations. So for large $n$, surely this is false? (Of course the probabilities have to be non-negative ...) | |
| Sep 1, 2014 at 15:07 | history | asked | Bati | CC BY-SA 3.0 |