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Minimal Links in the Cubic Lattice

  • R. Uberti
  • E. J. Janse van Rensburg
  • E. Orlandinit
  • M. C. Tesi
  • S. G. Whittington
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 103)

Abstract

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.

Keywords

Bottom Edge Link Type Closed Simple Curf Reidemeister Move Lattice Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1998

Authors and Affiliations

  • R. Uberti
    • 1
  • E. J. Janse van Rensburg
    • 1
  • E. Orlandinit
    • 2
  • M. C. Tesi
    • 3
  • S. G. Whittington
    • 4
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada
  2. 2.Department of Theoretical PhysicsOxford UniversityUK
  3. 3.Mathematical InstituteUniversity of Oxford, OxfordUK
  4. 4.Department of ChemistryUniversity of TorontoTorontoCanada

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