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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.