Generalized Reverse Rearrangement Inequality

Hello everyone,

I've been working on my Reverse Rearrangement inequality that you may remember from half a year ago, and I'm happy to say that I have finally proved the general version.

Here is the inequality statement:

Given $n$ similarly ordered positive real sequences $\{a_{i,j}\}_{1\le i\le m}$ for $1\le j\le n$ , the inequality $\prod_{i=1}^m\sum_{j=1}^na_{\sigma_j(i),j}\ge \prod_{i=1}^m\sum_{j=1}^na_{i,j}$ is true where $\sigma_1, \sigma_2, \ldots , \sigma_n$ are $n$ not necessarily distinct permutations of $\{1,2,\ldots, n\}$ .

Here is the paper that contains the proof: General RR

Check it out!

~Daniel

#Algebra #Inequalities #Generalize #Permutations #ReverseRearrangementInequality

Easy Math Editor

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`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`	$\sin \theta$
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Comments

Are you a high school genius or what?! What grades are you? Could you teach me? I'm really amazed on you @Daniel Liu

Figel Ilham - 6 years ago

Thanks for the praise! I'm a freshman in highschool right now. I suppose I could teach you, but you'd have to tell me what sort of thing you want to be taught.

Daniel Liu - 6 years ago

Congo for your achievement.

shivamani patil - 6 years ago

Hey , I'm not able to find the link to the latest Proofathon contest . Can you provide a link here ?

Thanks!

A Former Brilliant Member - 6 years ago

Hello, there have been unexpected delays. Sorry, it will be soon ASAP.

Daniel Liu - 6 years ago

Why isnt it the @Daniel Liu inequality?? :(

David Lee - 6 years ago

Because Generalized Reverse Rearrangement sounds way better. You can help by spreading this thing like Nutella :D

Daniel Liu - 6 years ago

Daniel can you post something on the topic of binomial expansion..... and congrats for the result that u worked on for half of the year

sarvesh dubey - 6 years ago

Hello,

Thanks for the kind words!

I won't be making a binomial expansion paper, but here's a good one you can look at.

Daniel Liu - 6 years ago

Hey, @Daniel Liu I am amazed by your work and want to get in touch so you can hopefully mentor me so that I can delve into higher mathematics head on. I am actually 13 (I messed up during registration) so I want to be as close to your level as I can be when I am your age (I know, its a long shot but a man can dream). Can you please respond to this by giving me your email so we can get in touch.

Aneesh S. - 5 years, 12 months ago

@Aneesh S. – Sorry, but I don't know if I can successfully mentor you. But here are some points: 1) If you haven't tried competition math, see if you can join a local math competition near you. 2) Check out the Art of Problem Solving community at aops.com. This site has many resources to help you get good. 3) Do the practices on Brilliant! 4) You can feel free to ask me any questions about what specific part of math you want to learn, and I can help you.

Daniel Liu - 5 years, 12 months ago

@Daniel Liu – Daniel Liu Well, I have tried competition math and go up to the state level but I want to not only solve problems but make discoveries. Can you please help me with Geometry and Number Theory, I am eager to learn more about those. Can I have your email so we can communicate more?

Aneesh S. - 5 years, 12 months ago

@Aneesh S. – Hey Daniel the paper is marvellous really you had done a great work in mathematics but could you please suggest mE some topics in geometry and number theory as i am very interested in geometry to its inner depths or could you please give me your email pleas

Biswajit Barik - 4 years, 4 months ago

@Biswajit Barik – I suggest getting "Lemmas in Olympiad Geometry". It is quite a good introduction to Olympiad Geometry :)

Daniel Liu - 4 years, 4 months ago

@Daniel Liu – Thank you very much Daniel

Biswajit Barik - 4 years, 4 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}`	$\boxed{123}$