A twisted torus knot is obtained from a torus knot by performing full twists on some adjacent strands of the torus knot. Morimoto constructed infinitely many twisted torus knots which are composite knots and he conjectured that his knots are all of composite twisted torus knots. We show that his conjecture is almost true by giving a complete list of such twisted torus knots.

中文翻译：

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通过扭转圆环结获得复合结

通过在圆环结的一些相邻股上进行完全捻合而从圆环结获得了圆环结。森本构造了无数个扭曲的圆环结，它们是复合结，他猜想他的结都是复合的扭曲圆环结。通过给出这种扭曲的圆环结的完整列表，我们证明了他的猜想几乎是正确的。