A relation "<=" is a partial order on a set S if it has: 1. Reflexivity: a<=a for all a element S. 2. Antisymmetry: a<=b and b<=a implies a = b. 3. Transitivity: a<=b and b<=c implies a<=c. For a partial order, the size of the longest chain (antichain) is called the partial order length (partial order width). A partially ordered set is also called a poset.
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