BPS counting for knots and combinatorics on words

@article{Kucharski2016BPSCF,
  title={BPS counting for knots and combinatorics on words},
  author={Piotr Kucharski and Piotr Sułkowski},
  journal={Journal of High Energy Physics},
  year={2016},
  volume={2016},
  pages={1-39}
}
A bstractWe 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-Poincaré series) are solutions to those equations and reproduce generating series that encode BPS invariants. Furthermore, BPS invariants in question are… 
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