Timeline for How many ways to partition a group of people?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2014 at 20:29 | vote | accept | anon | ||
| Mar 20, 2014 at 0:26 | comment | added | Zack Wolske | Imperial College seems to have changed their domains and didn't redirect old pages. You can find it via the way back machine, web.archive.org/web/20050308115423/http://www.icparc.ic.ac.uk/… | |
| Mar 19, 2014 at 22:48 | answer | added | Zack Wolske | timeline score: 6 | |
| Mar 19, 2014 at 19:00 | history | edited | anon | CC BY-SA 3.0 |
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| Mar 19, 2014 at 18:48 | comment | added | anon | @ZackWolske - thanks, that is helpful. If I found the Warwick Harvey link that you are referring to, then the actual website is down (at least for now). The computer program looks promising, though I am not very good with tech and don't know how to implement it. If somebody did, I'd be happy to accept that answer, although I would be interested in conceptual discussion - original question edited to reflect that. (As hinted above, I really am just echoing a question I received from a friend not in math so ... I am not a researcher in this topic.) | |
| Mar 19, 2014 at 17:24 | comment | added | Peter Dukes | As another (possibly better) trivial upper bound, you might consider a related problem: constant composition codes with length $70$, composition $[7,7,...,7]$ and minimum distance $60$. I believe if you can upper bound such codes (say by the Hamming bound) then it provides an upper bound in your case. You may have to strengthen it, though, because solutions imply codes but not vice-versa. | |
| Mar 19, 2014 at 15:41 | comment | added | Zack Wolske | Your question is "what is the maximal $k$ which makes SGP ($10-7-k$) solvable". The SGP does not ask for a perfect solution, as the author notes on page 7 of the freely available thesis, and which should be clear from the simpler 10 week solution for 8 groups of 4. The thesis also includes an algorithm in ECLiPSe (page 48) for arbitrary numbers of golfers and groups, an SAT implementation, and gives a link to Warwick Harvey's page listing known (as of 2002) solutions, including 5 compatible partitions for yours. It really deserves more than a glance if you are researching this topic. | |
| Mar 19, 2014 at 15:19 | comment | added | The Masked Avenger | If an edit were given saying something like "the comments showed me this is part of combinatorial design theory, and the Handbook does not have a design with these parameters; does anybody here have better than simple bounds?", I think the question would be received more favorably here. For my account, no editing is needed. | |
| Mar 19, 2014 at 15:11 | comment | added | The Masked Avenger | I like the question, and a reading without context does show that there is a mathematical problem of interest. Given the way it is presented, I am less surprised than Gerry at the close votes: for MathOverflow it appears poorly motivated and unresearched, with no attempt at doing something like finding trivial bounds. Even though it is a good and polite question, minus marks for not having a (conducive to this forum) good presentation. | |
| Mar 19, 2014 at 14:48 | comment | added | anon | @The Masked Avenger - I apologize for the lack of clarity. I anticipated that when I asked "What is the maximal number of compatible partitions you can form," it would be interpreted literally, instead of as "What is a trivial upper bound on the maximal number of compatible partitions you can form." Anyhow, let me clarify now that I am indeed asking for the actual answer to the actual question. That being said, I would certainly be interested in nontrivial upper and lower bounds. | |
| Mar 19, 2014 at 14:43 | comment | added | anon |
@Zack - thanks for the link. It seems interesting, but after glancing through the first one I don't see an answer to the instance of my question, or a way to get compute it. As you yourself point out, the problem is slightly different - the SGP asks for a perfect'' solution, and I am asking for an optimal'' solution. I am unable to see the published paper for subscription reasons. If you have read it, do you know if it addresses methods for my problem?
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| Mar 19, 2014 at 9:58 | comment | added | Zack Wolske | My comment above isn't accurate in this case, since there will be pairs of people who are never in the same group, so it isn't a complete block design. I should also add that the thesis results have been published in Ann. Operations Research (2012), link.springer.com/article/10.1007%2Fs10479-011-0866-7 | |
| Mar 19, 2014 at 9:58 | comment | added | Roland Bacher | This is how participants are ideally assigned to the tables at Oberwolfach conferences. | |
| Mar 19, 2014 at 5:10 | comment | added | The Masked Avenger | It is clear though that there can be a group of at most 11 such mutually compatible partitions, which in itself does not require research mathematics. The only part that does is the part that determines the actual value, and it is unclear from the question if the actual value is needed, or if the elementary estimate will suffice. | |
| Mar 19, 2014 at 3:27 | comment | added | Gerry Myerson | Why the close votes? This isn't high school combinations-and-permutations, it's a question about what turns out to be a significant and difficult research problem in combinatorial designs. | |
| Mar 19, 2014 at 2:39 | comment | added | Zack Wolske | This is an example of a "social golfer problem", which asks for a maximal (70,10,1) block design with parallelism. You can read up on solution methods in this master's thesis, logic.at/prolog/sgp/sgp.html | |
| Mar 19, 2014 at 1:31 | review | Close votes | |||
| Mar 19, 2014 at 10:29 | |||||
| Mar 19, 2014 at 1:26 | review | First posts | |||
| Mar 19, 2014 at 4:54 | |||||
| Mar 19, 2014 at 1:07 | history | asked | anon | CC BY-SA 3.0 |