Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract matrix-tree theorem   The classical matrix-tree theorem discovered by G.Kirchhoff in 1847 relates
the principal minor of the nxn Laplace matrix to a particular sum of monomials
of matrix elements indexed by directed trees with n vertices and a single sink.
In this paper we consider a generalization of this statement: for any k \ge n
we define a degree k polynomial det_{n,k} of matrix elements and prove that
this polynomial applied to the Laplace matrix gives a sum of monomials indexed
by acyclic graphs with n vertices and k edges.

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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th