Geometry & Topology, Vol. 4 (2000)
Paper no. 9, pages 277--292.
Notions of denseness
Greg Kuperberg
Abstract.
The notion of a completely saturated packing [Fejes Toth, Kuperberg
and Kuperberg, Highly saturated packings and reduced coverings,
Monats. Math. 125 (1998) 127-145] is a sharper version of maximum
density, and the analogous notion of a completely reduced covering is
a sharper version of minimum density. We define two related notions:
uniformly recurrent and weakly recurrent dense packings, and
diffusively dominant packings. Every compact domain in Euclidean space
has a uniformly recurrent dense packing. If the domain self-nests,
such a packing is limit-equivalent to a completely saturated
one. Diffusive dominance is yet sharper than complete saturation and
leads to a better understanding of n-saturation.
Keywords.
Density, saturation, packing, covering, dominance
AMS subject classification.
Primary: 52C15, 52C17.
Secondary: 52C20, 52C22, 52C26, 52B99.
DOI: 10.2140/gt.2000.4.277
E-print: arXiv:math.MG/9908003
Submitted to GT on 4 August 1999.
(Revised 28 September 2000.)
Paper accepted 21 September 2000.
Paper published 8 October 2000.
Notes on file formats
Greg Kuperberg
Department of Mathematics, University of California
One Shields Ave, Davis, CA 95616-8633, USA
Email: greg@math.ucdavis.edu
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