ominance
المؤلف:
Skiena, S
المصدر:
Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.
الجزء والصفحة:
...
5-1-2022
1529
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 
, ![<span style=]()
{7}" src="https://mathworld.wolfram.com/images/equations/Dominance/Inline16.gif" style="height:15px; width:17px" /> dominates all other partitions, while ![<span style=]()
{1,1,1,1,1,1,1}" src="https://mathworld.wolfram.com/images/equations/Dominance/Inline17.gif" style="height:15px; width:107px" /> is dominated by all others. In contrast, ![<span style=]()
{3,1,1,1,1,}" src="https://mathworld.wolfram.com/images/equations/Dominance/Inline18.gif" style="height:15px; width:81px" /> and ![<span style=]()
{2,2,2,1}" src="https://mathworld.wolfram.com/images/equations/Dominance/Inline19.gif" style="height:15px; width:62px" /> 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.
الاكثر قراءة في نظرية المجموعات
اخر الاخبار
اخبار العتبة العباسية المقدسة
