Twisted torus links that are unlinks

A twisted torus link $T(p,q,r,s)$ is obtained by performing $s$ full twists on $r$ adjacent strands of the $(p,q)$-torus link. In this paper, we classify twisted torus links that are unlinks. We give a complete characterization of all parameter families $(p,q,r,s)$ for which the associated twisted torus link is an unlink.