# A Note on Alexander Polynomials of 2-Bridge Links

## TL;DR

This paper extends existing formulas for the Alexander polynomial of 2-bridge knots and links to a 2-variable case, interpreting it as a walk on a 2D integer lattice, providing a new combinatorial perspective.

## Contribution

It introduces a novel formula for the 2-variable Alexander polynomial of 2-bridge links, generalizing previous one-dimensional interpretations.

## Key findings

- Provides a combinatorial interpretation as a walk on a 2D lattice.
- Extends Hartley's and Minkus's formulas to the 2-variable case.
- Offers a new perspective on link invariants through lattice walks.

## Abstract

A formula for the Alexander polynomial of a 2-bridge knot or link given by Hartley and also by Minkus has a beautiful interpretation as a walk on the integers. We extend this to the 2-variable Alexander polynomial of a 2-bridge link, obtaining a formula that corresponds to a walk on the 2-dimensional integer lattice.