Hasse diagram

In the mathematical area of order theory, a Hasse diagram (pronounced HAHS uh, named after Helmut Hasse (1898–1979)) is a simple picture of a finite partially ordered set. Concretely, one represents each member of S as a vertex on the page and draws a line that goes upward from x to y if x < y, and there is no z such that x < z < y. In this case, we say y covers x, or y is an immediate successor of x. Furthermore it is required that the vertices are positioned in such a way that each line meets exactly two vertices: its two endpoints. Any such diagram (given that the vertices are labeled) uniquely determines a partial order, but there are many possible diagrams for specifying a given order.

Related Topics:
Mathematical - Order theory - Helmut Hasse - Partially ordered set - Partial order

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