Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularity confinement for a class of $m$-th order difference equations
  of combinatorics   In a recent publication, it was shown that a large class of integrals over
the unitary group U(n) satisfy difference equations over $n$, involving a
finite number of steps; special cases are generating functions appearing in
questions of longest increasing subsequences in random permutations and words.
The main result of the paper states that these difference equations have the
\emph{discrete Painlev\'e property}; roughly speaking, this means that, after a
finite number of steps, the solution to these difference equations may develop
a pole (Laurent solution), depending on the maximal number of free parameters,
and immediately after be finite again (``\emph{singularity confinement}''). The
technique used in the proof is based on an intimate relationship between the
difference equations (discrete time) and the Toeplitz lattice (continuous time
differential equations); the point is that the ``Painlev\'e property'' for the
discrete relations is inherited from the ``Painlev\'e property'' of the
(continuous) Toeplitz lattice.

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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn