# The number of strings on essential tangle decompositions of a knot can be unbounded

## TL;DR

This paper constructs an infinite family of knots that can be decomposed into arbitrarily many essential tangles, demonstrating unbounded complexity in their tangle decompositions.

## Contribution

It introduces a new class of knots with unbounded essential tangle decompositions, expanding understanding of knot complexity.

## Key findings

- Existence of knots with arbitrarily high essential tangle decomposition number
- Construction method for such knots
- Implications for knot complexity theory

## Abstract

We construct an infinite collection of knots with the property that any knot in this family has $n$-string essential tangle decompositions for arbitrarily high $n$.