I have two circulant Cayley digraphs: that is, Cayley digraphs *X* = Cay(ℤ/*m*, *S*) and *Y* = Cay(ℤ/*n*, *T*), for odd integers *m* < *n*, and sets with sizes |*S*| = (*m* − 1)/2, and |*T*| = (*n* − 1)/2.

These digraphs are antisymmetric, in that *S* is disjoint from −*S*, and *T* is disjoint from −*T*. (It follows that for each distinct pair of vertices *a,b* in either graph, there is either an arc from *a* to *b*, or vice versa.)

**Question.** What conditions on *m*, *n*, *S*, and *T* must hold for *X* to be an induced directed subgraph of *Y*?