  The Baldoni--Vergne volume and Ehrhart polynomial formulas for flow polytopes
are significant in at least two ways. On one hand, these formulas are in terms
of Kostant partition functions, connecting flow polytopes to this classical
vector partition function fundamental in representation theory. On the other
hand the Ehrhart polynomials can be read off from the volume functions of flow
polytopes. The latter is remarkable since the leading term of the Ehrhart
polynomial of an integer polytope is its volume! Baldoni and Vergne proved
these formulas via residues. To reveal the geometry of these formulas, the
second author and Morales gave a fully geometric proof for the volume formula
and a part generating function proof for the Ehrhart polynomial formula. The
goal of the present paper is to provide a fully geometric proof for the Ehrhart
polynomial formula of flow polytopes.
