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On Free Planes in Lattice Ball Packings |
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| Authors: | Henk, Martin Ziegler, Gunter M. Zong, Chuanming |
| Affiliation: | Fachbereich Mathematik/IMO, Universität Magdeburg Universitätsplatz 2, D–39106 Magdeburg Fachbereich Mathematik MA 7–1, Technische Universität Berlin Strasse des 17. Juni 136, D–10623 Berlin School of Mathematical Sciences, Peking University Beijing 100871, P. R. China; cmzong{at}math08.math.ac.cn |
| Abstract: | This note, by studying the relations between the length of theshortest lattice vectors and the covering minima of a lattice,proves that for every d-dimensional packing lattice of ballsone can find a four-dimensional plane, parallel to a latticeplane, such that the plane meets none of the balls of the packing,provided that the dimension d is large enough. Nevertheless,for certain ball packing lattices, the highest dimension ofsuch free planes is far from d. |
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