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Zbl 0843.57006
Janse van Rensburg, E.J.; Promislow, S.D.
Minimal knots in the cubic lattice. (English)
[J] J. Knot Theory Ramifications 4, No.1, 115-130 (1995). ISSN 0218-2165

Summary: How many edges are necessary and sufficient to construct a knot of type $K$ in the cubic lattice? Define the minimal edge number of a knot to be this number of edges. To what extent does the minimal edge number measure the complexity of a knot? What is the behaviour of the minimal edge number under the connected sum of knots, and what is its limiting behaviour? We consider these questions and show that the minimal edge number may be computed using simulated annealing.

MSC 2000:: *57M25 Knots and links in the 3-sphere
52C99 Discrete geometry

Keywords: knotted polygons; cubic lattice; knot complexity; simulated annealing

Cited in: Zbl 1114.57005

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