The Signed Weighted Resolution Set is Not a Complete Pseudoknot Invariant

TL;DR

This paper demonstrates that the signed weighted resolution set is not a complete invariant for pseudoknots by analyzing its limitations using Gauss-diagrammatic invariants and local moves.

Contribution

It shows that the signed weighted resolution set cannot distinguish all non-equivalent pseudoknots, revealing its incompleteness as an invariant.

Findings

Signed weighted resolution set is incomplete for pseudoknots

Gauss-diagrammatic invariants help analyze pseudoknot invariants

Flype-like moves affect pseudoknot invariants

Abstract

When the signed weighted resolution set was defined as an invariant of pseudoknots, it was unknown whether this invariant was complete. Using the Gauss-diagrammatic invariants of pseudoknots introduced by Dorais et al, we show that the signed were-set cannot distinguish all non-equivalent pseudoknots. This goal is achieved through studying the effects of a flype-like local move on a pseudodiagram.