The permutahedron Perm(P) of a poset P is defined
as the convex hull of those permutations that are
linear extensions of P. Von Arnim, Faigle, and
Schrader gave a linear description of the permutahedron
of a series-parallel poset. Unfortunately, their main
theorem characterizing the facet defining inequalities
is only correct for not series-decomposable posets. We
do not only give a proof of the revised version of this
theorem but also extend it partially to the case of
arbitrary posets and obtain a new complete and minimal
description of Perm(P) if P is series-parallel.
Furthermore, we summarize briefly results about the
corresponding separation problem.
