There are two groups of numbers A _ 1, A _ 2, ... a _ n；; If B _ 1, B _ 2, ... B _ N satisfies A _ 1 ≤ A _ 2 ≤...≤ A _ N, B _ 1 ≤ B _ 2 ≤...≤ B _ N, then there are
a_ 1 b_n + a_2 b_{n- 1}+...+ a_n b_ 1
≤a _ 1 b _ { t _ 1 }+a _ 2 b _ { t _ 2 }+……+a _ n b _ { t _ n }
≤a _ 1 b _ 1+a _ 2 b _ 2+a _ n b _ n。
Where t_ 1, t_2, ..., t_n is 1, 2, ..., n if and only if a_ 1 = a_2 =...= a_n or b _1= b.
Sorting inequality is often used to describe the relationship between the products of a set of numbers that have nothing to do with order. The relationship between size can be determined by shilla _1≤ a _ 2 ≤ a _ 3 ≤ ... ≤ a _ n.
When using, a group of numbers are often constructed and solved by forming a product relationship with the original number. It is suitable for proving fractions, products, especially rotational inequalities.
The above rank inequality can also be simply described as: the sum of inverse order and ≤ disordered order and ≤ congruence order.