Abstract.
This post shows a diagram, listing a lot of inequalities and showing implications between them.
Inspired by a tweet, I decided to play a bit with Graphviz to create a graph on which inequalities imply which ones. Here’s the result:
Click here to obtain a larger version. Click any box on the image to obtain the Wikipedia page on the inequality.
Tags: Bessel's inequality, Cauchy-Schwarz inequality, generalized mean inequality, Gibb's inequality, Hölder's inequality, inequalities, inequality of arithmetic and geometric mean, inequality of weighted arithmetic and geometric mean, Jensen's inequality, log-sum inequality, Maclaurin's inequality, Mahler's inequality, Minkowski's inequality, Muirhead's inequality, Newton's inequalities, Parseval's identity, Pythagorean means, Rao-Blackwell Theorem, triangle inequality, Young's inequality (on numbers)
Nice idea!
But instead of providing a higher resolution bitmap version, you should publish the .dot source file instead. With it, everyone can create a even bigger one – one other formats like .svg.
I’d happily provide the .dot file, but unfortunately I cannot find the source files anymore… If I happen to find them again, I’ll put them online.
I understand—anyhow, thanks for your rapid response!