Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Varchenko-Gel'fand Ring of a Cone   For a hyperplane arrangement in a real vector space, the coefficients of its
Poincar\'{e} polynomial have many interpretations. An interesting one is
provided by the Varchenko-Gel'fand ring, which is the ring of functions from
the chambers of the arrangement to the integers with pointwise addition and
multiplication. Varchenko and Gel'fand gave a simple presentation for this
ring, along with a filtration and associated graded ring whose Hilbert series
is the Poincar\'{e} polynomial. We generalize these results to cones defined by
intersections of halfspaces of some of the hyperplanes and prove a novel result
for the Varchenko-Gel'fand ring of an arrangement: when the arrangement is
supersolvable the associated graded ring of the arrangement is Koszul.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin