Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial
  Characterization   We showed in the first paper of this series that the generic $C_2^1$-cofactor
matroid is the unique maximal abstract $3$-rigidity matroid. In this paper we
obtain a combinatorial characterization of independence in this matroid. This
solves the cofactor counterpart of the combinatorial characterization problem
for the rigidity of generic 3-dimensional bar-joint frameworks. We use our
characterization to verify that the counterparts of conjectures of Dress (on
the rank function) and Lov\'{a}sz and Yemini (which suggested a sufficient
connectivity condition for rigidity) hold for this matroid.

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The categories of this paper are: nlin
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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: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas