Timeline for sets of partitions associating any two elements exactly once
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 29, 2018 at 6:51 | comment | added | Ed Wynn | You might like to check out Brendan McKay's papers on "isomorph-free exhaustive generation"; also go backward from there (especially Read and Faradzev) and forward (because I don't know what's more recent). If it leads you towards the "nauty" graph-labelling software (as it might), then make sure that you follow links to the most recent version, a collaboration with Adolfo Piperno (pallini.di.uniroma1.it). It's a very interesting area, though not easy. | |
| May 28, 2018 at 19:01 | comment | added | Martin Rubey | Could you please clarify: you write that there is a single klatsch on three elements, but adding the discrete partition would produce another one. Are you excluding the discrete partition? | |
| May 28, 2018 at 18:32 | answer | added | Gerhard Paseman | timeline score: 1 | |
| May 28, 2018 at 17:58 | comment | added | Gerhard Paseman | My best guess is enumeration of combinatorial structures. Based on the previous comment (that enumerating klatsches would solve some tournament design problems), I guess that there are many people who would like to have had such an algorithm in the past. Gerhard "Many May Still Want One" Paseman, 2018.05.28. | |
| May 28, 2018 at 17:48 | comment | added | Gerhard Paseman | Note that for any klatsch K, if it does not have the discrete partition D in it, you can add D to preserve the condition. Apart from D, your condition induces a partition of the two element sets of A, so that there are at most A choose 2 many members of K that are not D, and much fewer if any member of K contains a large subset of (so lots of pairs from) A. It looks like a generalized tournament design. Gerhard "Sort Of Like Board-Gaming Night" Paseman, 2018.05.28. | |
| May 28, 2018 at 17:42 | comment | added | Gerhard Paseman | Sorry, no good suggestions here. I am thinking of finite topologies, combinatorial designs, and enumeration of such structures. From a universal algebraic perspective, you are looking for special antichains in the lattice of equivalence relations on a finite set, in that exactly one member of the chain is over (greater than) any particular minimal member of the lattice (your C in P condition). However I do not know who in order theory has considered this. Gerhard "Not Quite Over My Head" Paseman, 2018.05.28. | |
| May 28, 2018 at 17:16 | history | edited | Asaf Karagila♦ |
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| May 28, 2018 at 14:52 | review | First posts | |||
| May 28, 2018 at 15:27 | |||||
| May 28, 2018 at 14:49 | history | asked | Lisa Vibbert | CC BY-SA 4.0 |