Ask HN: Wanted: Elementary but surprising group theory result ...

Re:Ask HN: Wanted: Elementary but surprising group theory re... by pmiller2 on Saturday February 12, 2011 @12:38PM (#2210530)

What about (not) Burnside's lemma:

If $G$ acts on a set $X$ and $|X^g|$ denotes the number of elements of $X$ fixed by $g$, then the number of orbits $|X/G|$ is given by

$|X/G| = \frac {1} {|G|} \sum_{g \in G} |X^g|.$

The proof is simple, yet you can count an amazing number of things with it.

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Re:Ask HN: Wanted: Elementary but surprising group theory re... by RiderOfGiraffes on Saturday February 12, 2011 @02:29PM (#2210868)

Ah, now that's more interesting. I'm not sure I can make that readily accessible, but if I consider a specific example (yet to be invented) then maybe I can make it "obviously useful" while still being an abstract result.

I'll have to think about that. Boffo. Good one. Thanks.

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