# Doubly slice odd pretzel knots

## TL;DR

This paper characterizes when certain odd pretzel knots are doubly slice, showing a specific pattern of twist parameters guarantees this property, and confirms these are the only such knots.

## Contribution

It provides a complete classification of doubly slice odd pretzel knots with a specific twist parameter pattern, extending previous work.

## Key findings

- Doubly slice odd pretzel knots occur with a specific twist pattern.
- The paper proves these are the only such knots with that pattern.
- It combines new results with prior work to classify these knots.

## Abstract

We prove that an odd pretzel knot is doubly slice if it has $2n+1$ twist parameters consisting of $n+1$ copies of $a$ and $n$ copies of $-a$ for some odd integer $a$. Combined with the work of Issa and McCoy, it follows that these are the only doubly slice odd pretzel knots.