Timeline for Neighbor count in sphere packing in N dimensions
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 8, 2020 at 6:44 | comment | added | David Roberts♦ | If you can get a copy of Sphere packing, lattices and groups (doi.org/10.1007/978-1-4757-6568-7) it has a lot of info, not at the right level, perhaps, but with lots of references. Cohn has a nice 2014 survey arxiv.org/abs/1603.05202, predating the work Viazovska (+et al) establishing the d=8,24 cases. See Fig 1 on p53 | |
| Sep 8, 2020 at 6:42 | comment | added | David Roberts♦ | I don't know what you mean by "this packing" in the last paragraph, but I guess you mean that we know the densest packing in 8 and 24 dimensions, as I said. The connections to sporadic (I guess you mean finite simple) groups are not obvious. The symmetries of the Leech lattice form a finite group that maps two-to-one onto the sporadic simple group $Co_1$. It also connects with the other sporadics in the "2nd generation of the so-called Happy Family". | |
| Sep 8, 2020 at 6:34 | comment | added | David Roberts♦ | Why is this the case? Well, for context, we didn't know(1) until the late 90s the optimal packing in 3d. That we now know it in 8 and 24 dimensions is mildly astounding, and due to properties extra special to those dimensions. [(1) depending if you believe that Hales' original proof was enough or not; the referees of his paper couldn't certify his code, hence the more recent formalised proof] | |
| Sep 8, 2020 at 4:41 | review | First posts | |||
| Sep 8, 2020 at 7:52 | |||||
| Sep 8, 2020 at 4:35 | history | asked | John Shedletsky | CC BY-SA 4.0 |