Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BPS counting for knots and combinatorics on words   We discuss relations between quantum BPS invariants defined in terms of a
product decomposition of certain series, and difference equations (quantum
A-polynomials) that annihilate such series. We construct combinatorial models
whose structure is encoded in the form of such difference equations, and whose
generating functions (Hilbert-Poincar\'e series) are solutions to those
equations and reproduce generating series that encode BPS invariants.
Furthermore, BPS invariants in question are expressed in terms of Lyndon words
in an appropriate language, thereby relating counting of BPS states to the
branch of mathematics referred to as combinatorics on words. We illustrate
these results in the framework of colored extremal knot polynomials: among
others we determine dual quantum extremal A-polynomials for various knots,
present associated combinatorial models, find corresponding BPS invariants
(extremal Labastida-Mari\~no-Ooguri-Vafa invariants) and discuss their
integrality.

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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph