In
order theory, a
Hasse diagram (;
German: ) is a type of
mathematical diagram used to represent a finite
partially ordered set, in the form of a
drawing of its
transitive reduction. Concretely, for a partially ordered set
(S, =) one represents each element of
S as a
vertex in the plane and draws a
line segment or curve that goes
upward from
x to
y whenever
y covers x (that is, whenever
x <
y and there is no
z such that
x <
z <
y). These curves may cross each other but must not touch any vertices other than their endpoints. Such a diagram, with labeled vertices, uniquely determines its partial order.