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6. Unknotting number

More complicated is the question of unknotting numbers [10, 31-35]. For the calculation of unknotting numbers we accepted the folowing Conjecture:

(a) u(1) = 0, where 1 is the unknot; 

(b) u(k) = min u(k-)+1, where the minimum is taken over all knots k-, obtained from a minimal projection of  k by one change of crossing. 

Because by one change of crossing in a knot pq we could obtain only knot (p-2)q or p(q-2), we propose that for the unknoting numbers of knots belonging to the family pq holds the recursion formula: u(pq) = min (u((p-2)q), u(p(q-2)))+1. 

 

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