Algorithmic simplification of knot diagrams: new moves and experiments

@article{Petronio2015AlgorithmicSO,
  title={Algorithmic simplification of knot diagrams: new moves and experiments},
  author={C. Petronio and A. Zanellati},
  journal={arXiv: Geometric Topology},
  year={2015}
}
This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete simplification of a knot diagram D is a sequence of moves that transform D into a diagram D' with the minimal possible number of crossings for the isotopy class of the knot represented by D. The simplification is monotonic if the number of crossings never… Expand
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References

SHOWING 1-10 OF 31 REFERENCES
Automated Reidemeister Moves: A Numerical Approach to the Unknotting Problem
The Enumeration and Classification of Knots and Links
The number of Reidemeister moves needed for unknotting
Unknotting Unknots
A new algorithm for recognizing the unknot
On the bridge number of knot diagrams with minimal crossings
  • Jae-Wook Chung, X. Lin
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
  • 2004
Hard Unknots and Collapsing Tangles
Tait’s conjectures and odd crossing number amphicheiral knots
Embedding knots and links in an open book I: Basic properties
...
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