Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New lower bound on the Shannon capacity of C7 from circular graphs   We give an independent set of size $367$ in the fifth strong product power of
$C_7$, where $C_7$ is the cycle on $7$ vertices. This leads to an improved
lower bound on the Shannon capacity of $C_7$: $\Theta(C_7)\geq 367^{1/5} >
3.2578$. The independent set is found by computer, using the fact that the set
$\{t \cdot (1,7,7^2,7^3,7^4) \,\, | \,\, t \in \mathbb{Z}_{382}\} \subseteq
\mathbb{Z}_{382}^5$ is independent in the fifth strong product power of the
circular graph $C_{108,382}$. Here the circular graph $C_{k,n}$ is the graph
with vertex set $\mathbb{Z}_{n}$, the cyclic group of order $n$, in which two
distinct vertices are adjacent if and only if their distance (mod $n$) is
strictly less than $k$.

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph