Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two knots are not pass equivalent to each other, but the enantiomers of the trefoil knot are pass equivalent. A knot has Arf invariant 0 if the knot is pass equivalent to the unknot and 1 if it is pass equivalent to the trefoil knot.
Pass Equivalent
See also
Arf Invariant, Knot, Knot Move, Pass Move, Trefoil Knot, UnknotExplore with Wolfram|Alpha
References
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 223-228, 1994.Referenced on Wolfram|Alpha
Pass EquivalentCite this as:
Weisstein, Eric W. "Pass Equivalent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PassEquivalent.html