Timeline for What's the big deal about $M_{13}$?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jul 28, 2014 at 15:30 | comment | added | Nick Gill | @PeterDukes, you should look at the Conway-Elkies-Martin paper to see the precise status of $M_{13}$ as a sharply 6-transitive set. (This is where the notions of universal donor and recipient come in.) As for the connection to codes... I don't know much about these things in general, so can't answer this but I like the sound of it as a possible way of answering my question. | |
| Jul 20, 2014 at 12:56 | comment | added | Peter Dukes | I am curious about two things (which I admit do not directly relate to your question). First, what is the status of $M_{13}$ as a sharply $6$-transitive set? This paper link.springer.com/article/10.1023%2FA%3A1011211907282 claims Conway said it is, but allegedly disproves that it is. I haven't thought about this carefully. Second, assuming $M_{13}$ is not sharp, what is its minimum distance as a permutation code (under Hamming distance)? Stepping in the direction of your question, if the distance is fairly large, is this "code" unique in some sense? | |
| Jul 17, 2014 at 14:47 | history | edited | Nick Gill | CC BY-SA 3.0 |
edited body
|
| Jul 16, 2014 at 22:37 | comment | added | Nick Gill | @quid, thanks! Was editing in too much haste... | |
| Jul 16, 2014 at 22:37 | history | edited | Nick Gill | CC BY-SA 3.0 |
edited body
|
| Jul 16, 2014 at 22:18 | comment | added | user9072 | The name of Scott C. was correct, now it is wrong. I do not edit as you seem in the process of doing so. | |
| Jul 16, 2014 at 22:15 | history | edited | Nick Gill | CC BY-SA 3.0 |
added 292 characters in body
|
| Jul 16, 2014 at 21:36 | history | edited | Nick Gill |
edited tags
|
|
| Jul 16, 2014 at 21:35 | comment | added | Nick Gill | Since 3 people have upvoted Stefan Kohl's comment let me put the question another way, more bluntly: $M_{13}$ is a union of cosets of a permutation group. There are many unions of cosets of permutation groups but we don't usually bother studying them. Why do people bother with $M_{13}$? | |
| Jul 16, 2014 at 20:42 | history | edited | Nick Gill | CC BY-SA 3.0 |
added 141 characters in body
|
| Jul 16, 2014 at 20:40 | comment | added | Nick Gill | @StefanKohl, roughly speaking, I would like to know if $M_{13}$ can be characterized as a subset of a permutation group in some basic way. Alternatively, I would like some context and motivation explaining (from a group theoretic point of view) the construction of $M_{13}$. Hmmm, perhaps that's still too vague... | |
| Jul 16, 2014 at 20:33 | comment | added | Stefan Kohl♦ | What precisely are you actually asking? -- To me your question seems pretty vague. | |
| Jul 16, 2014 at 20:32 | comment | added | Nick Gill | Another possible characterization in a slightly different direction: $M_{13}$ is the only 6-transitive groupoid whose non-trivial elements have support at least $\frac13(n-1)$. | |
| Jul 16, 2014 at 20:24 | history | asked | Nick Gill | CC BY-SA 3.0 |