Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determinant formulas for the $\tau$-functions of the Painlev\'e
  equations of type $A$   Explicit determinant formulas are presented for the $\tau$ functions of the
generalized Painlev\'e equations of type $A$. This result allows an
interpretation of the $\tau$-functions as the Pl\"ucker coordinates of the
universal Grassmann manifold.

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin