Lattice paths and quiver generating series with higher level generators (2408.01832v1)

Abstract: The generalized knots-quivers correspondence extends the original knots-quivers correspondence, by allowing higher level generators of quiver generating series. In this paper we explore the underlined combinatorics of such generating series, relationship with the BPS numbers of a corresponding knot, and new combinatorial interpretations of the coefficients of generating series.