The Unapologetic Mathematician

Conjugacy classes in symmetric groups

Let’s work out how symmetric groups act on themselves by conjugation. As I’m writing I notice that what I said before about composition of permutations is sort of backwards. It’s one of those annoying conventions that doesn’t really change anything, but can still be a bit confusing. From here on when we write permutations in cycle notation we compose by reading the cycles from right to left. That is, $(1\,2)(1\,3)=(1\,3\,2)$. Before I was reading them left to right. The new way behaves more like group actions. The exposition comes after the jump.

February 23, 2007

Carny Folk

So the second Carnival of Mathematics is up at Good Math, Bad Math. My first post on Rubik’s Cube is up there, as well as one about algebraic topology at UM regular Mikael Johansson’s place, and one on permutation cycle types at The Universe of Discourse.

That last topic is actually really monumentally important, and I’ll be getting back to it after class and the graduate student seminar today.