Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coarsening polyhedral complexes   Given a polyhedral complex C with convex support, we characterize, by a local
codimension-2 condition, polyhedral complexes that coarsen C. The proof of the
characterization draws upon a surprising general shortcut for showing that a
collection of polyhedra is a polyhedral complex and upon a property of
hyperplane arrangements which is equivalent, for Coxeter arrangements, to Tits'
solution to the Word Problem. The motivating special case, the case where C is
a complete fan, generalizes a result of Morton, Pachter, Shiu, Sturmfels, and
Wienand that equates convex rank tests with semigraphoids. The proof of the
main result also implies a special case of Tietze's convexity theorem. We also
prove oriented matroid versions of our results, obtaining, as a byproduct, an
oriented matroid version of Tietze's convexity theorem.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph