## Some important theorems from combinatorics

In relation to the problems that I recently presented here – the crocodile dinner problem, the crossing lines problem and its “schoolgirl” formulation – I’d like to reference a few important and beautiful theorems. Unfortunately, combinatorics is one of those branches of mathematics that I have never been exposed to.

**Dilworth’s theorem** http://en.wikipedia.org/wiki/Dilworth%27s_theorem

**König’s theorem** http://en.wikipedia.org/wiki/K%C3%B6nig%27s_theorem_(graph_theory)

(you gotta love wikipedia: “Note that, although Kőnig’s name is properly spelled with a double acute accent, the theorem named after him is customarily spelled with an umlaut”)

**Marriage theorem** http://en.wikipedia.org/wiki/Marriage_theorem , http://www.cut-the-knot.org/arithmetic/marriage.shtml , http://www.cut-the-knot.org/arithmetic/elegant.shtml

Apparently, all these theorems are equivalent.

And “combinatorics” has lots of irrelevant anagrams 🙂

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