  Let G be a connected bipartite graph with color classes E and V and root
polytope Q. Regarding the hypergraph (V,E) induced by G, we prove that its
interior polynomial is equivalent to the Ehrhart polynomial of Q, which in turn
is equivalent to the h-vector of any triangulation of Q. It follows that the
interior polynomials of (V,E) and its transpose (E,V) agree.
  When G is a complete bipartite graph, our result recovers a well known
hypergeometric identity due to Saalsch\"utz. It also implies that certain
extremal coefficients in the Homfly polynomial of a special alternating link
can be read off of an associated Floer homology group.
