  A (t,s)-rack is a rack structure defined on a module over the ring
$\ddot\Lambda=\mathbb{Z}[t^{\pm 1},s]/(s^2-(1-t)s)$. We identify necessary and
sufficient conditions for two $(t,s)$-racks to be isomorphic. We define
enhancements of the rack counting invariant using the structure of (t,s)-racks
and give some computations and examples. As an application, we use these
enhanced invariants to obtain obstructions to knot ordering.
