Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Coloring Book Approach to Finding Coordination Sequences   An elementary method is described for finding the coordination sequences for
a tiling, based on coloring the underlying graph. We illustrate the method by
first applying it to the two kinds of vertices (tetravalent and trivalent) in
the Cairo (or dual-3^2.4.3.4) tiling. The coordination sequence for a
tetravalent vertex turns out, surprisingly, to be 1, 4, 8 ,12, 16, ..., the
same as for a vertex in the familiar square (or 4^4) tiling. We thought that
such a simple fact should have a simple proof, and this article is the result.
We also apply the method to obtain coordination sequences for the 3^2.4.3.4,
3.4.6.4, 4.8^2, 3.12^2, and 3^4.6 uniform tilings, as well as the snub-632 and
bew tilings. In several cases the results provide proofs for previously
conjectured formulas.

7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat