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# Dominance

The dominance relation on a set of points in Euclidean -space is the intersection of the coordinate-wise orderings. A point dominates a point provided that every coordinate of is at least as large as the corresponding coordinate of .

A partition dominates a partition if, for all , the sum of the largest parts of is the sum of the largest parts of . For example, for , dominates all other partitions, while is dominated by all others. In contrast, and do not dominate each other (Skiena 1990, p. 52).

The dominance orders in are precisely the partially ordered sets of dimension at most .

Connected Domination Number, Domatic Number, Domatic Partition, Dominating Set, Domination Number, Partially Ordered Set, Realizer

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## References

Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Stanton, D. and White, D. Constructive Combinatorics. New York: Springer-Verlag, 1986.

Dominance

## Cite this as:

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