| dc.contributor.advisor | Suppose that d ≥ 2 and m are fixed. For which n is it the case that any n angles can be realised by placing m points in Rd?
A simple degrees of freedom argument shows that m points in R2 cannot realise more than 2m - 4 general angles. We give a construction to show that this bound is sharp when m ≥ 5.
In d dimensions the degrees of freedom argument gives an upper bound of dm−(d+12)−1dm−(2d+1)−1 general angles. However, the above result does not generalise to this case; surprisingly, the bound of 2m-4 from two dimensions cannot be improved at all. Indeed, our main result is that there are sets of 2m - 3 angles that cannot be realised by m points in any dimension. | |
| dc.contributor.author | Balister, P | en_US |
| dc.contributor.author | Furedi, Z | en_US |
| dc.contributor.author | Bollobas, B | en_US |
| dc.contributor.author | Leader, I | en_US |
| dc.contributor.author | Walters, M | en_US |
| dc.date.accessioned | 2016-08-26T13:12:34Z | |
| dc.date.available | 2015-07-28 | en_US |
| dc.date.issued | 2016 | en_US |
| dc.date.submitted | 2016-07-21T15:08:33.502Z | |
| dc.identifier.issn | 0021-2172 | en_US |
| dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/14877 | |
| dc.description.sponsorship | The first is partially supported by NSF grant DMS 1301614. The second author is partially supported by NSF grant DMS 1301614 and MULTIPLEX no. 317532. The third author’s research supported in part by the Hungarian National Science Foundation OTKA 104343, by the Simons Foundation Collaboration Grant #317487, and by the European Research Council Advanced Investigators Grant 267195. | en_US |
| dc.format.extent | 995 - 1012 | en_US |
| dc.relation.ispartof | ISRAEL JOURNAL OF MATHEMATICS | en_US |
| dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in Israel Journal of Mathematics following peer review. The version of record is available https://link.springer.com/article/10.1007/s11856-016-1370-1 | |
| dc.title | Subtended angles | en_US |
| dc.type | Article | |
| dc.rights.holder | © Springer | |
| dc.identifier.doi | 10.1007/s11856-016-1370-1 | en_US |
| pubs.author-url | https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000382866000020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=612ae0d773dcbdba3046f6df545e9f6a | en_US |
| pubs.issue | 2 | en_US |
| pubs.notes | 12 months | en_US |
| pubs.notes | 12 months from publication date (not yet known) | en_US |
| pubs.publication-status | Published | en_US |
| pubs.volume | 214 | en_US |
