The HOMFLY Polynomial of a Forest Quiver

TL;DR

This paper introduces a recursive definition of the HOMFLY polynomial for forest quivers and establishes its equivalence with the polynomial of associated plabic links, providing a closed-form expression based on independent sets.

Contribution

It defines the HOMFLY polynomial for forest quivers and proves its equivalence to that of related plabic links, offering a new combinatorial formula.

Findings

HOMFLY polynomial for forest quivers can be defined recursively.

The polynomial matches that of associated plabic links.

A closed-form expression in terms of independent sets is derived.

Abstract

We define the HOMFLY polynomial of a forest quiver $Q$ using a recursive definition on the underlying graph of the quiver. We then show that this polynomial is equal to the HOMFLY polynomial of any plabic link which comes from a connected plabic graph whose quiver is $Q$. We also prove a closed-form expression for the HOMFLY polynomial of a forest quiver $Q$ in terms of the independent sets of $Q$.