The enumeration of doubly symmetric diagrams for strongly positive amphicheiral knots

TL;DR

This paper develops an enumeration method for prime strongly positive amphicheiral knots using doubly symmetric diagrams, successfully classifying all cases up to 18 crossings and exploring the origins of Gauss words.

Contribution

It introduces a new enumeration strategy for prime knots with doubly symmetric diagrams and classifies all such cases up to 18 crossings.

Findings

All prime strongly positive amphicheiral knots up to 18 crossings are classified.

A new enumeration method for doubly symmetric diagrams is proposed.

The origin and realizability of Gauss words are discussed.

Abstract

This is the second part of the article on doubly symmetric diagrams and strongly positive amphicheiral knots. We develop an enumeration strategy for prime knots given by doubly symmetric diagrams and determine all cases up to 18 crossings in the doubly symmetric diagram. A digression covers the origin of Gauss words for long curves and explains how Gauss marked non-realizable words.