Cabling sequences of tunnels of torus knots
  This is the second of three papers that refine and extend portions of our earlier preprint, "The depth of a knot tunnel." Together, they rework the entire preprint.   The theory of tunnel number 1 knots that we introduced in "The tree of knot tunnels" yields a parameterization in which each tunnel is described uniquely by a finite sequence of rational parameters and a finite sequence of 0's and 1's, that together encode a procedure for constructing the knot and tunnel. In this paper we calculate these invariants for all tunnels of torus knots. 
Sangbum Cho, Darryl McCullough