Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice packings with gap defects are not completely saturated   We show that a honeycomb circle packing in $\R^2$ with a linear gap defect
cannot be completely saturated, no matter how narrow the gap is. The result is
motivated by an open problem of G. Fejes T\'oth, G. Kuperberg, and W.
Kuperberg, which asks whether of a honeycomb circle packing with a linear shift
defect is completely saturated. We also show that an fcc sphere packing in
$\R^3$ with a planar gap defect is also not completely saturated.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org