Timeline for From Steiner systems to geometric lattices to matroids
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2019 at 6:22 | vote | accept | M. Winter | ||
| Aug 12, 2019 at 21:45 | comment | added | Richard Stanley | Matroid designs are a matroidal generalization of block designs, including Steiner systems. One reference is nvlpubs.nist.gov/nistpubs/jres/77B/jresv77Bn1-2p15_A1b.pdf, but there are quite a few others. | |
| Aug 12, 2019 at 16:47 | answer | added | LeechLattice | timeline score: 2 | |
| Aug 12, 2019 at 16:15 | comment | added | LeechLattice | @M.Winter I tried to derive a paving matroid from $M_{22}$, and it turned out to have rank 4 and the permutation group $M_{22}$ on 22 points acting on it. | |
| Aug 12, 2019 at 16:10 | comment | added | M. Winter | @Bullet51 My mistake, it was at least 3. Can you explain your intuition behind your statement? I have no idea what all this has to do with each other. | |
| Aug 12, 2019 at 16:09 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Aug 12, 2019 at 16:08 | comment | added | LeechLattice | It's hard to believe that the matroid is really rank 3, as the action of $M_{22}$ on 22 points is 3-transitive. | |
| Aug 12, 2019 at 15:04 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Aug 12, 2019 at 14:59 | comment | added | M. Winter | @Sam Yes, I am interested in the bases. I am probably not aware of the exact way the cryptomorphism goes from lattices to matroids. | |
| Aug 12, 2019 at 14:59 | comment | added | Sam Hopkins | Could you link to the paper you are reading, by the way? | |
| Aug 12, 2019 at 14:58 | comment | added | Sam Hopkins | Just to be clear: you want the matroid realized as a set of bases? (As you are probably aware from reading Wikipedia, geometric lattices and matroids are "the same things." There are many ways to formulate the axioms of matroids that turn out yield isomorphic- or 'cryptomorphic'- structures.) | |
| Aug 12, 2019 at 14:56 | history | asked | M. Winter | CC BY-SA 4.0 |