Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biquandle Virtual Brackets   We introduce an infinite family of quantum enhancements of the biquandle
counting invariant we call biquandle virtual brackets. Defined in terms of
skein invariants of biquandle colored oriented knot and link diagrams with
values in a commutative ring $R$ using virtual crossings as smoothings, these
invariants take the form of multisets of elements of $R$ and can be written in
a "polynomial" form for convenience. The family of invariants defined herein
includes as special cases all quandle and biquandle 2-cocycle invariants, all
classical skein invariants (Alexander-Conway, Jones, HOMFLYPT and Kauffman
polynomials) and all biquandle bracket invariants defined in previous work as
well as new invariants defined using virtual crossings in a fundamental way,
without an obvious purely classical definition.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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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: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga