Minimal Links in the Cubic Lattice
How many edges are necessary and sufficient to realize two closed simple curves in the cubic lattice forming a link of a given type ? Let this number be the edge number of the link. We show that the minimal edge number of links is subadditive with respect to the connected sum of links. In addition, we prove the existence of an edge index, which is the average number of edges per component under iterated connected sums of links of a given type. The minimal edge numbers of some simple links are estimated using simulated annealing.
KeywordsBottom Edge Link Type Closed Simple Curf Reidemeister Move Lattice Link
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