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.

© 1996-9 *Eric W. Weisstein *

1999-05-26