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)