f-vector inequalities for order and chain polytopes

The order and chain polytopes are two 0/1-polytopes constructed from a finite poset. In this paper, we study the f -vectors of these polytopes. We investigate how the order and chain polytopes behave under disjoint unions and ordinal sums of posets, and how the f -vectors of these polytopes are expressed in terms of f -vectors of smaller polytopes. Our focus is on comparing the f -vectors of the order and chain polytope built from the same poset. In our main theorem we prove that for a family of posets built inductively by taking disjoint unions and ordinal sums of posets, for any poset P in this family the f -vector of the order polytope of P is component-wise at most the f -vector of the chain polytope of P.