Lattice paths and quiver generating series with higher level generators

TL;DR

This paper extends the knots-quivers correspondence by incorporating higher level generators into quiver generating series, exploring their combinatorial structure and relation to BPS numbers.

Contribution

It introduces a generalized framework for quiver generating series with higher level generators and provides new combinatorial interpretations.

Findings

New combinatorial interpretations of generating series coefficients

Relationship established between higher level generators and BPS numbers

Enhanced understanding of the combinatorics underlying the generalized correspondence

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.