# Definition talk:Rotation (Permutation Theory)

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What's the difference between a rotation and a permutation? --prime mover 07:42, 2 March 2012 (EST)

- Formally, as stated on PW, the domain of a permutation is an initial segment of $\N^*$, i.e. $\{1,2...,n\}$. In particular, it is fixed. A rotation is a function permuting the indices of any given ordered $n$-tuple of elements of the set $A$. Conceptually this difference isn't huge, but to say that these are identical would be too colloquial. --Lord_Farin 08:30, 2 March 2012 (EST)
- Oh yes of course.
- It depends I suppose on the definition used of Definition:Permutation, which in the context of set theory is "just" a bijection from a set to itself.
- In this context, of course, we're talking of Definition:Permutation on n Letters which does indeed narrow the definition down.
- I've never understood the reason for this complexification, but it's there, that's what you see in the literature.
- I'd recommend this is amplified to make the distinction visible, by stating the fact that the permutation meant is Definition:Permutation on n Letters, and then explaining that a
**rotation**is the same thing as the more general Definition:Permutation. As it is, the concept of what the rotation defines is used quite a lot already in the discussions on the Definition:Symmetric Group, so there's plenty scope for lots of lovely rework here. --prime mover 13:06, 2 March 2012 (EST)