A Continuous Family of Marked Poset Polytopes

The Minkowski Property and Reflexivity of Marked Poset Polytopes

“…In this paper, we will assume throughout that at least all minimal elements in P are marked: min(P ) ⊆ P * . To a marked poset we associated in [9] a family of polyhedra parametrized by partitions P = C O. Definition 1.2.…”

“…The following result on the Ehrhart equivalence of the marked chain-order polytopes is proved in [9] with the help of a transfer map. Proposition 1.7.…”

“…Remark 3.3. Another proof of this corollary without using the Ehrhart theory can be executed using the transfer map [9]: it suffices to notice that the transfer map preserves not only the lattice points, but also the boundary of the polytope by continuity.…”

“…A first step in this direction has been initiated by the first two authors in [8], where such polytopes are defined under certain restrictions. Later in the joint work with J.-P. Litza [9], this approach is combined with the interlacing one parameter family: we introduced a family interlacing the marked order and the marked chain polytopes, called marked poset polytopes, parametrized by points in a hypercube. In this family, every vertex of the hypercube corresponds to a lattice polytope (called a marked chain-order polytope) and they all have the same Ehrhart polynomial.…”