Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The enumeration of planar graphs via Wick's theorem   A seminal technique of theoretical physics called Wick's theorem interprets
the Gaussian matrix integral of the products of the trace of powers of
Hermitian matrices as the number of labelled maps with a given degree sequence,
sorted by their Euler characteristics. This leads to the map enumeration
results analogous to those obtained by combinatorial methods. In this paper we
show that the enumeration of the graphs embeddable on a given 2-dimensional
surface (a main research topic of contemporary enumerative combinatorics) can
also be formulated as the Gaussian matrix integral of an ice-type partition
function. Some of the most puzzling conjectures of discrete mathematics are
related to the notion of the cycle double cover. We express the number of the
graphs with a fixed directed cycle double cover as the Gaussian matrix integral
of an Ihara-Selberg-type function.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph