Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Z^a and Painleve equations   A discrete analogue of the holomorphic map z^a is studied. It is given by a
Schramm's circle pattern with the combinatorics of the square grid. It is shown
that the corresponding immersed circle patterns lead to special separatrix
solutions of a discrete Painleve equation. Global properties of these
solutions, as well as of the discrete $z^a$ are established.

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: econ
3
The categories of this paper are: physics