6. Partition relations graph

6.1 General lattice concept

Let's take a look at the organizational chart (figure 12 ) of a hypothetical company: the segments linking two people represent the "is the superior of" relationship. This is a partial order, i.e. it does not apply to every pair of individuals: A is not B's superior, and vice versa. This partial order induces fairly common notions such as level (of hierarchy), successor (the immediate superior) and predecessor. An important notion is that of the smallest common majorant (or supremum) of two individuals x and y, noted $x.\text{V}.y$...