Bryant, David, Huber, Katharina T., Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Tupper, Paul F.
(2023)
Diversities and the generalized circumradius.
Discrete and Computational Geometry.
ISSN 0179-5376
(In Press)
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Abstract
The generalized circumradius of a set of points A\subseteq R^d with respect to a convex body K equals the minimum value of \lambda\geq 0 such that a translate of \lambda K contains A. Each choice of K gives a different function on the set of bounded subsets of R^d; we characterize which functions can arise in this way. Our characterization draws on the theory of diversities, a recently introduced generalization of metrics from functions on pairs to functions on finite subsets. We additionally investigate functions which arise by restricting the generalized circumradius to a finite subset of R^d. We obtain elegant characterizations in the case that K is a simplex or parallelotope.
Item Type: | Article |
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Faculty \ School: | Faculty of Science > School of Computing Sciences |
Depositing User: | LivePure Connector |
Date Deposited: | 16 Jan 2023 17:32 |
Last Modified: | 16 Jan 2023 17:32 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/90611 |
DOI: |
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