Notions of denseness

The notion of a completely saturated packing [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

Mathematical Subject Classification 2000

Primary: 52C15, 52C17

Secondary: 52C20, 52C22, 52C26, 52B99

References

Forward citations

Publication

Received: 4 August 1999

Revised: 28 September 2000

Accepted: 21 September 2000

Published: 8 October 2000

Proposed: Robion Kirby

Seconded: Michael Freedman, Walter Neumann

Authors

Greg Kuperberg
Department of Mathematics University of California One Shields Ave Davis California 95616-8633 USA

Volume 4, issue 1 (2000)

Greg Kuperberg