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Ordinary hyperspheres and spherical curves

Lin, Aaron and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2020) Ordinary hyperspheres and spherical curves. Advances in Geometry. ISSN 1615-715X (In Press)

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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 ﰀ 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 ﰀ 4.

Item Type: Article
Official URL: https://www.degruyter.com/search?q1=Advances+in+Ge...
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 24 Mar 2020 13:57
Last Modified: 13 Jul 2020 23:32
URI: http://eprints.lse.ac.uk/id/eprint/103821

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