TL;DR
This paper introduces the concepts of positive and negative heights of knotoids, proving their relationship to the unsigned height, and explores polynomial invariants and sequences related to knotoids.
Contribution
It defines positive and negative heights for knotoids, shows they determine the unsigned height, and investigates polynomial invariants and sequences associated with knotoids.
Findings
Positive and negative heights determine the unsigned height.
Polynomial invariants provide lower bounds for signed heights.
Sequences associated with knotoids are studied.
Abstract
The height of a knotoid is a measure of how far it is from being a knot. Here we define the positive and negative parts of the height, and we prove that they determine the unsigned height. Some polynomial invariants provide lower bounds for the signed heights. We also study a set of sequences associated to a knotoid.
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Taxonomy
TopicsMechanics and Biomechanics Studies · Artificial Intelligence in Games