Abstract

A knot shadow is a diagram without over/ under information at all crossings. Many knot types are obtained from a knot shadow by assigning over/ under information to each crossing. The purpose of the paper is to observe numbers of knot types obtained from closed 3-braid knot shadows. As a result, we discover that given an arbitary odd integer [Formula: see text], there exists a closed 3-braid knot shadow [Formula: see text] such that the number of [Formula: see text] torus knots is more than that of trivial knots in the knots obtained from [Formula: see text] by assigning over/ under information to each crossing.

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