ABSTRACT
Partially ordered sets, or posets for short, lattices and polytopes play a key role in many modern fi elds of research, such as combinatorics, algebraic geometry, physics and engineering.
A poset P, is a pair P=(S, ≤ ) of a set S together with an order relation ≤ which satisfi es the following conditions for all x, y, z ∈S: • x ≤ x (refl exivity) • x ≤ y and y ≤ x imply x = y (anti-symmetry) • x ≤ y and y ≤ z imply x ≤ z (transitivity)
An element x is minimal if there is no y such that y < x and x is maximal if there is no y such that x < y.
