Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial data of a free arrangement and the Terao conjecture   We present a combinatorial structure of generators of $D(\mathcal{A}).$ This
structure permits us to detect the relationship between the combinatorial
determined property and the singularity of vector field. Consequently, by using
only combinatorial data, we have a basis of the module in free case and that
yields a proof for the Terao's conjecture. We also verify the example of
Ziegler and give a sufficient condition on combinatorial determined property of
generators.

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th