dominant set

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every coordinate of p is at least as large as the corresponding coordinate of q. A partition p_a dominates a partition p_b if, for all k, the sum of the k largest parts of p_a is >= the sum of the k largest parts of p_b. For example, for n = 7, {7} dominates all other partitions, while {1, 1, 1, 1, 1, 1, 1} is dominated by all others. In contrast, {3, 1, 1, 1, 1, } and {2, 2, 2, 1} do not dominate each other.

connected domination number | domatic number | domatic partition | dominating set | domination number | partially ordered set | realizer