The dimension of a partially ordered set 
is the size of the smallest realizer of 
. Equivalently, it is the smallest integer 
such that 
is isomorphic to a dominance order in 
.
Poset Dimension
See also
Dimension, Dominance, Isomorphic Posets, RealizerExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Poset DimensionCite this as:
Weisstein, Eric W. "Poset Dimension." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PosetDimension.html