Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting vertices of integral polytopes defined by facets   We present a number of complexity results concerning the problem of counting
vertices of an integral polytope defined by a system of linear inequalities.
The focus is on polytopes with small integer vertices, particularly 0/1
polytopes and half-integral polytopes.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc