Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A weighted cellular matrix-tree theorem, with applications to complete
  colorful and cubical complexes   We present a version of the weighted cellular matrix-tree theorem that is
suitable for calculating explicit generating functions for spanning trees of
highly structured families of simplicial and cell complexes. We apply the
result to give weighted generalizations of the tree enumeration formulas of
Adin for complete colorful complexes, and of Duval, Klivans and Martin for
skeleta of hypercubes. We investigate the latter further via a logarithmic
generating function for weighted tree enumeration, and derive another
tree-counting formula using the unsigned Euler characteristics of skeleta of a
hypercube and the Crapo $\beta$-invariant of uniform matroids.

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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn