  It is known that the normalized volume of standard hypersimplices (defined as
some slices of the unit hypercube) are the Eulerian numbers. More generally, a
recent conjecture of Stanley relates the Ehrhart series of hypersimplices with
descents and excedences in permutations. This conjecture was proved by Nan Li,
who also gave a generalization to colored permutations. In this article, we
give another generalization to colored permutations, using the flag statistics
introduced by Foata and Han. We obtain in particular a new proof of Stanley's
conjecture, and some combinatorial identities relating pairs of Eulerian
statistics on colored permutations.
