ominance

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 .

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.