6. Unknotting numberMore 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. |