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Poset Dimension


The dimension of a partially ordered set P=(X,<=) 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 R^d.


See also

Dimension, Dominance, Isomorphic Posets, Realizer

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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.

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Poset Dimension

Cite this as:

Weisstein, Eric W. "Poset Dimension." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PosetDimension.html

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