Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces   We consider the problem of enumerating spanning trees on lattices.
Closed-form expressions are obtained for the spanning tree generating function
for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under
free, periodic, and a combination of free and periodic boundary conditions.
Results are also obtained for a simple quartic net embedded on two
non-orientable surfaces, a Moebius strip and the Klein bottle. Our results are
based on the use of a formula expressing the spanning tree generating function
in terms of the eigenvalues of an associated tree matrix. An elementary
derivation of this formula is given.

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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph