Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Signed graphs and the freeness of the Weyl subarrangements of type
  $B_{\ell}$   A Weyl arrangement is the hyperplane arrangement defined by a root system.
Arnold and Saito proved that every Weyl arrangement is free. The Weyl
subarrangements of type $A_{\ell}$ are represented by simple graphs. Stanley
gave a characterization of freeness for this type of arrangements in terms of
thier graph. In addition, The Weyl subarrangements of type $B_{\ell}$ can be
represented by signed graphs. A characterization of freeness for them is not
known. However, characterizations of freeness for a few restricted classes are
known. For instance, Edelman and Reiner characterized the freeness of the
arrangements between type $ A_{\ell-1} $ and type $ B_{\ell} $. In this paper,
we give a characterization of the freeness and supersolvability of the Weyl
subarrangements of type $B_{\ell}$ under certain assumption.

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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: eess