Timeline for Analogy between Integers and Permutations
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2014 at 11:54 | answer | added | Chassaing | timeline score: 1 | |
| May 22, 2014 at 20:57 | vote | accept | john mangual | ||
| May 21, 2014 at 14:52 | history | edited | john mangual | CC BY-SA 3.0 |
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| May 21, 2014 at 14:41 | answer | added | Chassaing | timeline score: 5 | |
| May 21, 2014 at 12:52 | history | edited | john mangual | CC BY-SA 3.0 |
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| May 21, 2014 at 5:21 | comment | added | Anthony Quas | Probably I'm telling you what you saw already. Apologies if this is the case. | |
| May 21, 2014 at 5:20 | comment | added | Anthony Quas | Having a 1 min glance at the Granville article, it seems to me that the objects are integers and permutation. He factorizes integers into primes and gets a "partition of unity" from that (i.e. $(\log p_1/\log n,\ldots,\log p_d/\log n)$). He factorizes permutations into cycles and gets a partition of unity from that $(\ell_1(\sigma),\ldots,\ell_d(\sigma))$. So I think the analogy is 1) pick a prime of size roughly $e^N$ and find its partition of unity; pick a permutation on roughly $N$ symbols and find its partition of unity. Lo and Behold! they have (roughly) the same distribution! | |
| May 20, 2014 at 23:58 | answer | added | Qiaochu Yuan | timeline score: 6 | |
| May 20, 2014 at 23:53 | comment | added | john mangual | I think the objects are $\mathbb{Z}/p\mathbb{Z}$ actions on the permutation groups $S_n$. | |
| May 20, 2014 at 23:44 | comment | added | Anthony Quas | Do you think it's more than "if you compute certain statistics for (a) prime factorization; and (b) cycle decomposition of permutations, then for large $n$, the distributions are close to the same thing"? | |
| May 20, 2014 at 23:32 | history | edited | KConrad | CC BY-SA 3.0 |
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| May 20, 2014 at 23:18 | history | asked | john mangual | CC BY-SA 3.0 |