A combinatorial study of partial order polytopes

To each finite set with at least two elements, there corresponds a partial order polytope. It is defined as the convex hull of the characteristic vectors of all partial orders which have that set as ground set. This 0/1-polytope contains the linear ordering polytope as a proper face. The present article deals with the facial structure of partial order polytopes. Our main results are: (i) a proof that the nonadjacency problem on partial order polytopes is NP-complete; (ii) a characterization of the polytopes that are affinely equivalent to a face of some partial order polytope.