On Gauss codes of virtual doodles
Andrew Bartholomew, Roger Fenn, Naoko Kamada, Seiichi Kamada
TL;DR
This paper introduces the concept of left canonical Gauss codes for virtual doodles, establishing a unique correspondence between oriented virtual doodles and these codes, thereby advancing the combinatorial understanding of virtual doodles.
Contribution
The paper defines left canonical Gauss codes and proves their uniqueness in representing oriented virtual doodles, providing a new combinatorial tool for their classification.
Findings
Left canonical Gauss codes uniquely represent oriented virtual doodles.
A new method for classifying virtual doodles using Gauss codes.
Enhanced understanding of virtual doodle structures through canonical forms.
Abstract
We discuss Gauss codes of virtual diagrams and virtual doodles. The notion of a left canonical Gauss code is introduced and it is shown that oriented virtual doodles are uniquely presented by left canonical Gauss codes.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Mathematical Dynamics and Fractals