Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notions of denseness   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.

33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph