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ON FREE PLANES IN LATTICE BALL PACKINGS

Published online by Cambridge University Press:  22 May 2002

MARTIN HENK ,
GÜNTER M. ZIEGLER  and
CHUANMING ZONG
MARTIN HENK
Affiliation:
Fachbereich Mathematik/IMO, Universität Magdeburg, Universitätsplatz 2, D–39106 Magdeburg
GÜNTER M. ZIEGLER
Affiliation:
Fachbereich Mathematik MA 7–1, Technische Universität Berlin, Strasse des 17. Juni 136, D–10623 Berlin
CHUANMING ZONG
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P. R. Chinacmzong@math08.math.ac.cn
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Abstract

This note, by studying the relations between the length of the shortest lattice vectors and the covering minima of a lattice, proves that for every d-dimensional packing lattice of balls one can find a four- dimensional plane, parallel to a lattice plane, 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 of such ‘free planes’ is far from d.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 3 , May 2002 , pp. 284 - 290
Copyright
© The London Mathematical Society 2002

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