Timeline for Are there always more conjugacy classes in the kernel of a morphism to $Z_2$ than not?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| May 30, 2021 at 11:21 | comment | added | YCor | Is "more than" meant to be "$\ge$"? If $G$ is abelian and $\phi$ surjective there's indeed equality, as already observed by several users. This applies more generally for $G=H\times A$, $\phi$ trivial on $H$ and surjective on $A$ abelian. Are there other cases? We might expect a proof of $\ge$ to help classify the cases of equality. | |
| May 29, 2021 at 17:18 | comment | added | LSpice | @MarkWildon's answer, referenced above. \\ Name of these notes, referenced by @lambda: Wagner - Introduction to combinatorial enumeration. | |
| May 29, 2021 at 15:48 | history | edited | YCor | CC BY-SA 4.0 |
edited tags, added implicit assumption
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| May 29, 2021 at 11:20 | comment | added | Mark Wildon | My answer below includes a reference to this paper of Gupta sciencedirect.com/science/article/pii/0097316576900510 that gives a bijective proof of the partition identity. | |
| May 29, 2021 at 11:16 | answer | added | Mark Wildon | timeline score: 10 | |
| May 29, 2021 at 10:34 | answer | added | Geoff Robinson | timeline score: 5 | |
| S May 29, 2021 at 4:06 | vote | accept | Clark Lyons | ||
| May 29, 2021 at 2:28 | answer | added | LSpice | timeline score: 11 | |
| May 29, 2021 at 1:21 | comment | added | lambda | The equivalence of this identity with the one in the post linked by David is pretty easy, but it appears in exactly this form as chapter 9 exercise 7 of these notes. My guess is that this one doesn't appear in standard sources because it's straightforwardly equivalent to that better-known identity (attributed to Euler in Andrews's book) even though this formulation is in some ways more natural. | |
| May 28, 2021 at 20:18 | answer | added | Clark Lyons | timeline score: 13 | |
| May 28, 2021 at 12:32 | comment | added | David E Speyer | Regarding the partition identity, see math.stackexchange.com/questions/92191 . | |
| May 28, 2021 at 7:21 | vote | accept | Clark Lyons | ||
| S May 29, 2021 at 4:06 | |||||
| May 28, 2021 at 6:56 | vote | accept | Clark Lyons | ||
| May 28, 2021 at 6:56 | |||||
| May 28, 2021 at 6:29 | comment | added | Gerry Myerson | The stackexchange post is math.stackexchange.com/questions/4153508/… The general rule here is you wait for several days before posting to a second site, and you link the two posts to spare people from duplication of effort. | |
| May 28, 2021 at 3:27 | answer | added | David E Speyer | timeline score: 13 | |
| May 28, 2021 at 2:00 | comment | added | David E Speyer | Partitions with distinct odd parts are in easy bijection with self conjugate partitions. I think I've seen it in that guise but am not sure where. | |
| May 28, 2021 at 1:49 | comment | added | lambda | I have seen that partition identity before, though unfortunately not in a publicly available source. I suspect it is "well known" but I'm not sure off the top of my head the best place to look. | |
| May 28, 2021 at 1:35 | answer | added | Buzz | timeline score: 2 | |
| May 28, 2021 at 0:18 | review | First posts | |||
| May 28, 2021 at 6:43 | |||||
| May 28, 2021 at 0:15 | history | asked | Clark Lyons | CC BY-SA 4.0 |