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 
.
