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 et al gave a linear description of the permutahedron of a series-parallel poset. Unfortunately, their main theorm characterizing the facet defining inequalities is only correct for not series-decomposable posets. The paper does 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, it summarizes briefly results about the corresponding separation problem.
