TL;DR
This paper introduces a new class of monotonic moves for knots and links that potentially simplifies the process of determining their equivalence by not increasing diagram crossings.
Contribution
It proposes natural generalizations of Reidemeister moves that are conjectured to be complete for computing canonical forms and deciding isotopy.
Findings
Experimentation supports the conjecture of move completeness.
Monotonic moves do not increase the number of crossings.
Potential for more efficient knot and link classification.
Abstract
We propose some natural generalizations of Reidemeister moves that do not increase the number of crossings in the generated diagrams. Experimentations make us conjecture that this class of monotonic moves is complete for computing canonical forms and then deciding isotopy.
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Taxonomy
TopicsRobot Manipulation and Learning · Design Education and Practice · Interactive and Immersive Displays