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The Forbidden Number of a Knot

  • CRANS, ALISSA S. ;
  • MELLOR, BLAKE ;
  • GANZELL, SANDY
  • Received : 2014.06.16
  • Accepted : 2014.10.07
  • Published : 2015.06.23

Abstract

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

Keywords

virtual knot;forbidden move;odd writhe

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