Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson Dirichlet$(\alpha,\theta)$-Bridge Equations and
  Coagulation-Fragmentation Duality   Paper discusses fragmentation coagulation duality formula related to those
already appearing in the literature.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con