  Given an Eulerian digraph, we consider the genus distribution of its
face-oriented embeddings. We prove that such distribution is log-concave for
two families of Eulerian digraphs, thus giving a positive answer for these
families to a question asked in Bonnington, Conder, Morton and McKenna (2002).
Our proof uses real-rooted polynomials and the representation theory of the
symmetric group $\mathbb{S}_n$. The result is also extended to some
factorizations of the identity in $\mathbb{S}_n$ that are rotation systems of
some families of one-face constellations.
