Adequate Knots

Given a diagram for a knot K, one can form a link consisting of disjoint planar circles by smoothing all the crossings in the positive sense (defined locally, so that the string orientation of the two strands does not affect the choice of smoothing). Suppose that exactly one of the crossing smoothings is changed to negative, and regardless of the choice of crossing point, the number of circles is reduced. Then the diagram is called positive adequate. If a knot has a positive adequate diagram, then it is called a positive adequate knot.

There is the analogous definition of negative adequate, and a knot is called adequate if it satisfies the positive and negative condition.

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