Cable knots obtained by positively twisting torus knots

초록

The twisted torus knot T(p,q,r,s) is a knot obtained from the torus knot T(p,q) by twisting r adjacent stands fully s times. If r = p or r is a multiple of q, then T(p,q,r,s) is known to be a cable of a nontrivial knot or a torus knot. Assuming that r & NOTEQUAL;p and r is not a multiple of q, we determine the parameters p,q,r,s for which the positively twisted torus knot T(p,q,r,s) is a cable knot.

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