Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 501-511 (2002)

On Minimum Kissing Numbers of Finite Translative Packings of a Convex Body

Istvan Talata

Department of Mathematics,Auburn University, 218 Parker Hall, Auburn, AL 36849-5310, USA; Current address: Department of Mathematics, The University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109-1109, USA, e-mail: talata@math.lsa.umich.edu

Abstract: For a convex body $K$, let us denote by $t(K)$ the largest number for which there exists a packing with finitely many translates of $K$ in which every translate has at least $t(K)$ neighbours. In this paper we determine $t(K)$ for convex discs and $3$-dimensional convex cylinders. We also examine how small the cardinalities of the extremal configurations can be in these cases.

Keywords: convex cylinder, convex disc, kissing number, translative packing

Classification (MSC2000): 52C17, 52A10

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