Distributive Lattice Polyhedra

Poly-antimatroids are generalization of the notion of antimatroid to multisets. When the underlying set consists of only two elements, such two-dimensional poly-antimatroids correspond to point sets in the integer lattice Z^d. In this research we concentrate on geometrical properties of two-dimensional poly-antimatroids and prove that these sets form distributive lattice polyhedra. Our findings imply that two-dimensional poly-antimatroids have convex dimension 2. Further we investigate geometrical properties of three-dimensional distributive lattice polyhedra.