Hmm. I think my fundamental disconnect here was the idea of permutation as a repeated process. As a formal term it's really ever come up in a discrete mathematics class comparing it with combinations, on the subject of counting. Here we seem to be defining permutation as a function that can be repeatedly applied.
Looks like the first sentence of wikipedia confirms it's an overloaded word:
>In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Looks like the first sentence of wikipedia confirms it's an overloaded word:
>In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.