Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-03T02:57:25.689Z Has data issue: false hasContentIssue false
  • English
  • Français

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. [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)