Timeline for Maximal set of non commuting elements in a conjugacy class of $S_8$
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2016 at 15:29 | vote | accept | Maryam | ||
| Mar 3, 2016 at 15:29 | vote | accept | Maryam | ||
| Mar 3, 2016 at 15:29 | |||||
| Feb 20, 2016 at 18:26 | comment | added | user9072 |
While I understand the intent is to be polite, ultimately it may make the conversation for Derek Holt slightly less convenient that you use @Professor Holt as it will not show up in his inbox. To have notification what directly follows @ must match a beginning substring of username (without space). To follow what auto-complete suggests is simplest. If you feel you need to be formal I recommend: do not use an @ as part of the main text, and place the @username at the end or the start as an add-on. Put differently treat @username like an email-address that you cannot alter.
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| Feb 20, 2016 at 18:11 | answer | added | Peter Mueller | timeline score: 8 | |
| Feb 20, 2016 at 16:40 | comment | added | Maryam | As you see in the end of second paper the upper and lower bound for case S_8 are 6908 and 6988. I think if ì can count the set of maximal size for conjugacy class in question, then exact number is achieved. | |
| Feb 20, 2016 at 16:39 | comment | added | Maryam | @Professor holt, this is an old problem to find the maximal non commuting elements in a finite group as you know. My motivation is two paper by Ron Brown with the subject minimal cover of S_n by abelian subgroups and maximal subset of pairwise non commuting elements. | |
| Feb 20, 2016 at 16:30 | comment | added | Peter Mueller | @DerekHolt: I was wrong when I thought I had an argument that $224$ can't be achieved. | |
| Feb 20, 2016 at 16:26 | comment | added | Derek Holt | @Maryam No, $218$ is the largest I have found so far using moderately intelligent random searches, and Peter Mueller now has $222$. As you can see from the comments above, there is an upper bound of $224$ and Peter Mueller thinks he might be able to prove that $224$ is impossible to achieve. So we are getting close to the correct answer. Could you say something about the motivation for this problem? | |
| Feb 20, 2016 at 16:25 | comment | added | Peter Mueller | @Maryam: If I'm not wrong, then I have a clique of size 222 now. | |
| Feb 20, 2016 at 16:08 | comment | added | Maryam | @Professor Holt. Thanks alot. You mean the right number is 218? | |
| Feb 20, 2016 at 15:36 | comment | added | Derek Holt | Now I have one of size $218$. That's getting close! | |
| Feb 20, 2016 at 11:58 | comment | added | Derek Holt | In fact it is not hard to prove the upper bound of $224$ directly because, for each of the $56$ triples $\{a,b,c\}$, you can choose at most $4$ pairwise non-commuting elements $(a,b,c)(x,y)$ and (as in JohnShareshian's answer), the only way to do this is to fix $x$ and use the four possible $y$. | |
| Feb 19, 2016 at 22:09 | comment | added | Peter Mueller | Lovasz's theta upper bound shows that such a clique has size $\le224$, while mcqd (sicmm.org/konc/maxclique) quickly finds a clique of size $200$. | |
| Feb 19, 2016 at 14:59 | history | edited | user9072 | CC BY-SA 3.0 |
minor cleanup
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| Feb 19, 2016 at 13:48 | comment | added | Derek Holt | That sounds difficult! It is a maximal clique problem in a graph with $1120$ vertices, and the complexity of all known algorithms for finding maximal cliques appears to be exponential. By searching at random, I have found such a subset of size $188$, but maybe someone can beat that. | |
| Feb 19, 2016 at 13:04 | history | asked | Maryam | CC BY-SA 3.0 |