In general, we can represent a nite partial ordering set (S, <) using this procedure: Start with the directed graph for this relation. Because a partial ordering is reexive, a loop (a,a) is present at every vertex a. Remove these loops. Next, remove all edges that must be in the partial ordering because of the presence of other edges and transitivity. That is, remove all edges (x,y) for which there is an element z ∈ S such that x ≺ z and z ≺ x. Finally, arrange each edge so that its initial vertex is below its terminal vertex. Remove all the arrows on the directed edges, because all edges point “upward” toward their terminal vertex. These steps are well dened, and only a nite number of steps need to be carried out for a nite partial ordering set. When all the steps have been taken, the resulting diagram contains sufficient information to end the partial ordering. The resulting diagram is called the Hasse diagram of (S,< ), named after the twentieth-century German mathematician Helmut Hasse who made extensive use of them.
Is there another application of Hasse Diagram?