Faces of maximal chain polytopes

Abstract

The maximal chain polytope $\mathcal{M}(P)$ is associated with a finite poset $P$. For a set of maximal chains $\mathcal{C}$, it is shown that the convex hull of all the points corresponding to elements of $\mathcal{C}$ is not a face of $\mathcal{M}(P)$ if and only if $\mathcal{C}$ has an incomplete guided crown structure. Using this result, several examples, including the dimension of $\mathcal{M}(\mathbf{m}\times \mathbf{n})$, are calculated.

17 pages. Added Section 3; clarified proof of Proposition 2.11; fixed minor errors