Poset Dimension

The Dimension of a Poset $P = (X, \leq)$ is the size of the smallest Realizer of $P$. Equivalently, it is the smallest Integer $d$ such that $P$ is Isomorphic to a Dominance order in $\Bbb{R}^d$.

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.