Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex-Facet Assignments For Polytopes   Motivated by the search for reduced polytopes, we consider the following
question: For which polytopes exists a vertex-facet assignment, that is, a
matching between vertices and non-incident facets, so that the matching covers
either all vertices, or all facets? We provide general conditions for the
existence of such an assignment. We conclude that such exist for all simple and
simplicial polytopes, as well as all polytopes of dimension $d\le 6$. We
construct counterexample in all dimensions $d\ge 7$.

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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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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: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: quant-ph