Hasse diagram

In mathematics, a Hasse diagram (pronounced HAHS uh) is a simple picture of a finite partially ordered set. One says of two members x and y of a partially ordered set S that "y covers x" if x ≤ y and no element of S is between x and y. The partial ordering is then just the transitive closure of the cover relation. The Hasse diagram of S may then be defined abstractly as the set of all ordered pairs (x, y) such that y covers x, i.e., the Hasse diagram may be identified with the cover relation. Concretely, one represents each member of S as a black dot on the page and draws a line that goes upward from x to y if y covers x.

[An illustration here might be useful.]

For example, if a Hasse diagram was drawn of the poset of all the divisors of a number, partially ordered by divisibility, then the number itself would be at the top of the diagram, the number 1 would be at the bottom, and the smallest (prime) divisors would cover the bottom element.