  We resolve affirmatively some conjectures of Reiner, Stanton, and White
\cite{ReinerComm} regarding enumeration of transportation matrices which are
invariant under certain cyclic row and column rotations.
  Our results are phrased in terms of the bicyclic sieving phenomenon
introduced by Barcelo, Reiner, and Stanton \cite{BRSBiD}.
  The proofs of our results use various tools from symmetric function theory
such as the Stanton-White rim hook correspondence
  \cite{SW} and results concerning the specialization of Hall-Littlewood
polynomials due to Lascoux, Leclerc, and Thibon \cite{LLTUnity}
\cite{LLTRibbon}.
