# A generating polynomial for the two-bridge knot with Conway's notation C(n,r)

## TL;DR

This paper introduces a generating polynomial that encodes the Kauffman states of two-bridge knots specified by Conway's notation, providing a new algebraic tool for knot analysis.

## Contribution

It constructs an explicit integer polynomial for two-bridge knots with Conway's notation, linking combinatorial knot states to algebraic expressions.

## Key findings

- Polynomial coefficients enumerate Kauffman states
- Provides a new algebraic representation for two-bridge knots
- Facilitates computational analysis of knot invariants

## Abstract

We construct an integer polynomial whose coefficients enumerate the Kauffman states of the two-bridge knot with Conway's notation C(n,r).