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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:

Jensen's inequality Newton's inequality Rao-Blackwell theorem Log sum inequality Generalized mean inequality Inequality of arithmetic and geometric mean Muirhead's inequality Maclaurin's inequality Gibb's inequality Pythagorean means Young's inequality Inequality of arithmetic and geometric means Hölder's inequality Parseval's inequality Mahler's inequality Cauchy-Schwarz inequality Minkowski's inequality Bessel's inequality Triangle inequality

Click here to obtain a larger version. Click any box on the image to obtain the Wikipedia page on the inequality.

Comments.

John Doe wrote on December 17, 2010:

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.

Felix Fontein wrote on December 19, 2010:

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.

John Doe wrote on December 19, 2010:

I understand—anyhow, thanks for your rapid response!