I don’t have too much to say about permutations, but there are two points that I have often found myself needing to get straight in supervisions. In fact, make that three. Here they are. [Added later: I have just finished the post, and it ended up being longer than I expected.]

1. The first is a confusion that some people have about what a permutation of actually *is*. What could possibly be the trouble, you might ask? Well, let's take the permutation that in cycle notation is written . My guess is that a non-negligible percentage of people reading this have worried about whether this permutation means that you cycle round the *elements* 1, 2 and 4 of the set or the *elements in the places* 1, 2 and 4.

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