Lin, Aaron and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2021) Ordinary hyperspheres and spherical curves. Advances in Geometry, 21 (1). 15 - 22. ISSN 1615-715X
Text (Ordinary hyperspheres)
- Accepted Version
Download (239kB) |
Abstract
An ordinary hypersphere of a set of points in real d-space, where no d + 1 points lie on a (d - 2)-sphere or a (d - 2)-flat, is a hypersphere (including the degenerate case of a hyperplane) that contains exactly d + 1 points of the set. Similarly, a (d + 2)-point hypersphere of such a set is one that contains exactly d + 2 points of the set. We find the minimum number of ordinary hyperspheres, solving the d-dimensional spherical analogue of the Dirac-Motzkin conjecture for d ≥ 3. We also find the maximum number of (d + 2)-point hyperspheres in even dimensions, solving the d-dimensional spherical analogue of the orchard problem for even d ≥ 4.
Item Type: | Article |
---|---|
Official URL: | https://www.degruyter.com/view/journals/advg/advg-... |
Additional Information: | © 2021 Walter de Gruyter GmbH, Berlin/Boston. |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 24 Mar 2020 13:57 |
Last Modified: | 08 Nov 2024 20:54 |
URI: | http://eprints.lse.ac.uk/id/eprint/103821 |
Actions (login required)
View Item |