Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact packings of the plane with three sizes of discs   A compact packing is a set of non-overlapping discs where all the holes
between discs are curvilinear triangles. There is only one compact packing by
discs of size $1$. There are exactly $9$ values of $r$ which allow a compact
packing by discs of sizes $1$ and $r$. We prove here that there are exactly
$164$ pairs $(r,s)$ allowing a compact packing by discs of sizes $1$, $r$ and
$s$.

3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an