Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting prime juggling patterns   Juggling patterns can be described by a closed walk in a (directed) state
graph, where each vertex (or state) is a landing pattern for the balls and
directed edges connect states that can occur consecutively. The number of such
patterns of length $n$ is well known, but a long-standing problem is to count
the number of prime juggling patterns (those juggling patterns corresponding to
cycles in the state graph). For the case of $b=2$ balls we give an expression
for the number of prime juggling patterns of length $n$ by establishing a
connection with partitions of $n$ into distinct parts. From this we show the
number of two-ball prime juggling patterns of length $n$ is $(\gamma-o(1))2^n$
where $\gamma=1.32963879259...$. For larger $b$ we show there are at least
$b^{n-1}$ prime cycles of length $n$.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int