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About four-ball packings

Part of: Discrete geometry

Published online by Cambridge University Press:  26 February 2010

Károly Böröczky Jr
Károly Böröczky Jr
Affiliation:
MTA Matematikai Kutató Intézet, Budapest Pf. 127, 1364 Hungary.
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Abstract

The main object of this note is to prove that in three-space the sausage arrangement is the densest packing of four unit balls. Our method can be used to determine minimal arrangements with respect to various properties of four-ball packings, as we point out in Section 3.

MSC classification

Secondary: 52C17: Packing and covering in $n$ dimensions
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 226 - 232
Copyright
Copyright © University College London 1993

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References

1.Betke, U. and Gritzmann, P.. Über L. Fejes Toths Wurstvermutung in kleinen Dimensionen. Acta Math. Hungar., 43 (1984), 299–307.Google Scholar
2.Böröczky, K. Jr. Some extremal properties of the regular simplex. In Proceedings of the Conference on Intuitive Geometry, Szeged (1991).Google Scholar
3.Fejes Tóth, L.. Research Problem 13. Period. Math. Hungar., 6 (1975), 197–199.Google Scholar
4.Gandini, P. M. and Wills, J. M.. On finite sphere packings. Math. Pannonica, 3 (1992), 19–29.Google Scholar
5.Gritzmann, P. and Wills, J. M.. An upper estimate for the lattice point enumerator. Matematika, 33 (1986),. 197–203.CrossRefGoogle Scholar
6.Groemer, H.. Über die Einlagerung von Kreisen in einen konvexen Bereich. Math Zeitschr., 73 (1960), 285–294.CrossRefGoogle Scholar
7.Hadwiger, H.. Vorlesung über Inhalt, Oberfläche und Isometrie (Springer-Verlag, Berlin, 1957).Google Scholar
8.Oler, N.. An inequality in the geometry of numbers. Acta Math., 105 (1961), 19–48.Google Scholar
9.Kleinschmidt, P., Pachner, U. and Wills, J. M.. On L. Fejes Tóth's ‘Sausage Conjecture’. Isr. J. Math., 47 (1984), 216–226.Google Scholar
10.Wills, J. M.. On the density of finite packings. Acta Math. Hung., 46 (1985), 205–210.CrossRefGoogle Scholar
11.Wills, J. M.. Research problem 35. Periodica Math. Hung., 14 (1983), 332–334.Google Scholar