An nmove on a KL is a local change, where the remaining part of the KL remains unchanged. We say that two KLs, L_{1} and L_{2}, are nmove equivalent if one can be transformed to the other by a finite number of nmoves and their inverses (nmoves) (Przytycki, 2003). Nakanishi's
Conjecture Every knot is 4move equivalent to
an unknot (1979).
The smallest known candidate for a counterexample to Nakanishi's Conjecture is the link
Just as with the unknotting (unlinking) number u(L) and ¥unknotting (unlinking) number u_{¥} (L), a minimal number of n moves required to obtain a knot or link k (k £ [^{n}/_{2}]) from a given KL can be defined as an nmove unknotting (unlinking) number u_{n}(L), taken over all projections of a KL. In fact, in the language of nmoves, unknotting number u(L) is u_{2}(L), and u_{¥} (L) is u_{1}(L). In the case of u_{n}(L) we can make a Conjecture analogous to BernhardJablan Conjecture, and work only with minimum projections at all levels of unknotting (unlinking) process. According to such a Conjecture, the minimal number of nmoves necessary to obtain a knot or link k (k £ [^{n}/_{2}]) from a rational KL given by its Conway symbol, for a given parameter n, can be calculated by the LinKnot function NMoveRat (webMathematica NMoveRat).
