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Radii and the Sausage Conjecture

Published online by Cambridge University Press:  20 November 2018

Károly Bőrőczky Jr.  and
Martin Henk
Károly Bőrőczky Jr.
Affiliation:
MTA Matematikai Kutató Intézet, Budapest, Pf 127, 1364 Hungary, e-mail:h5808bor@ella.hu
Martin Henk
Affiliation:
Mathematisches Institut, Universität Siegen Hölderlinstrasse 3 5900 Siegen Germany e-mail:henk@hrz. uni-siegen.dbp. de
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Abstract

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In 1975, L. Fejes Toth conjectured that in Ed, d ≥ 5, the sausage arrangement is denser than any other packing of n unit balls. This has been known if the convex hull Cn of the centers has low dimension. In this paper, we settle the case when the inner m-radius of Cn is at least O(ln d/m). In addition, we consider the extremal properties of finite ballpackings with respect to various intrinsic volumes.

Keywords

52C1752A40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 156 - 166
Copyright
Copyright © Canadian Mathematical Society 1995

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