Rearrangement Inequality

I recently read about the Rearrangement Inequality on AOPS , and understood most of it.

If we have two series ( say A & B ) of equal length , then the maximum value of the sum of product of their elements taken two at a time (one from each and not repeated ) is when the numbers to be multiplied are taken from sorted sets and with i=j.

It is easy to see that if there are N sets then we can easily find the maximum value of the sum of product of their elements taken N at a time (one from each and not repeated ) .

I am curious to know is there any general way to find the minimum value ?? All suggestions are welcome and please don't be shy to comment ...

#RearrangementInequality #Inequality #Rearrangement

Easy Math Editor

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Comments

I'm curious what makes you so curious ...

Santanu Banerjee - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$