Timeline for Maximum conjugacy class size in $S_n$ with fixed number of cycles
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2019 at 4:49 | answer | added | Gerhard Paseman | timeline score: 0 | |
| Jun 11, 2019 at 1:58 | answer | added | Gerhard Paseman | timeline score: 2 | |
| Jun 7, 2019 at 13:27 | history | edited | metallicmural99 | CC BY-SA 4.0 |
Conjecture not true.
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| Jun 7, 2019 at 10:17 | answer | added | Geoff Robinson | timeline score: 2 | |
| Jun 7, 2019 at 6:04 | answer | added | Aaron Meyerowitz | timeline score: 4 | |
| Jun 5, 2019 at 20:09 | comment | added | metallicmural99 | Thanks @GerhardPaseman. I've been trying induction, at least for the "$a_1 \geq \frac{m-1}{2}$" part of my prediction, but it hasn't quite worked out yet.. I'll try the local minimization over a fixed multiset and see how that pans out. | |
| Jun 5, 2019 at 16:55 | comment | added | Gerhard Paseman | Local optimizing suggests (for a fixed multiset of values a_j) that larger values of a_j should belong to smaller j. In particular, choose (1)^8(6)^8 over (3)^8(4)^8. Once you know how to optimize for a fixed multiset, then find a good multiset which adds up to a given m. I think your prediction is on the right track, and that for small m, one large cycle will work. Gerhard "Just Locally Minimize The Denominator" Paseman, 2019.06.05. | |
| Jun 5, 2019 at 16:08 | history | asked | metallicmural99 | CC BY-SA 4.0 |