The Dimension of a Poset is the size of the smallest Realizer of . Equivalently, it is the smallest Integer such that is Isomorphic to a Dominance order in .
See also Dimension, Dominance, Isomorphic Posets, Realizer
References
Dushnik, B. and Miller, E. W. ``Partially Ordered Sets.'' Amer. J. Math. 63, 600-610, 1941.
Trotter, W. T. Combinatorics and Partially Ordered Sets: Dimension Theory.
Baltimore, MD: Johns Hopkins University Press, 1992.