Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The solution of the $A_r$ T-system for arbitrary boundary   We present an explicit solution of the $A_r$ $T$-system for arbitrary
boundary conditions. For each boundary, this is done by constructing a network,
i.e. a graph with positively weighted edges, and the solution is expressed as
the partition function for a family of non-intersecting paths on the network.
This proves in particular the positive Laurent property, namely that the
solutions are all Laurent polynomials of the initial data with non-negative
integer coefficients.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph