## Partial Order

A Relation '' is a partial order on a Set if it has:

1. Reflexivity: for all .

2. Antisymmetry: and implies .

3. Transitivity: and implies .

For a partial order, the size of the longest Chain (Antichain) is called the Length (Width). A partially ordered set is also called a Poset.

See also Antichain, Chain, Fence Poset, Ideal (Partial Order), Length (Partial Order), Linear Extension, Partially Ordered Set, Total Order, Width (Partial Order)

References

Ruskey, F. Information on Linear Extension.'' http://sue.csc.uvic.ca/~cos/inf/pose/LinearExt.html.