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Partially Ordered Set

A partially ordered set (or Poset) is a Set taken together with a Partial Order on it. Formally, a partially ordered set is defined as an ordered pair $P = (X, {\leq)}$, where $X$ is called the Ground Set of $P$ and $\leq$ is the Partial Order of $P$.

See also Circle Order, Cover Relation, Dominance, Ground Set, Hasse Diagram, Interval Order, Isomorphic Posets, Partial Order, Poset Dimension, Realizer, Relation


Dushnik, B. and Miller, E. W. ``Partially Ordered Sets.'' Amer. J. Math. 63, 600-610, 1941.

Fishburn, P. C. Interval Orders and Interval Sets: A Study of Partially Ordered Sets. New York: Wiley, 1985.

Trotter, W. T. Combinatorics and Partially Ordered Sets: Dimension Theory. Baltimore, MD: Johns Hopkins University Press, 1992.

© 1996-9 Eric W. Weisstein