# An independence system as knot invariant

## TL;DR

This paper introduces an independence system associated with knot diagrams, proving it as a knot invariant for alternating knots and exploring its properties and variations across different diagrams.

## Contribution

It defines a new independence system for knot diagrams and establishes its invariance for alternating knots, also analyzing its matroid properties.

## Key findings

- Independence system is a knot invariant for alternating knots
- Some knot diagrams have independence systems that are matroids
- Others do not exhibit matroid properties in their independence systems

## Abstract

In this article, we define an independence system for a classical knot diagram and prove that the independence system is a knot invariant for alternating knots. We also discuss the exchange property for minimal unknotting sets. Finally, we show that there are knot diagrams where the independence system is a matroid and there are knot diagrams where it is not.