permutation

noun

Etymology: From Middle English permutacioun, permutacyoun, from Old French permutacïon, promutatïon and Medieval Latin permūtātiōnem, accusative of permūtātiō. Morphologically permute + -ation.

1. One of the ways something exists, or the ways a set of objects can be ordered.

   “Which permutation for completing our agenda items makes the most sense?”

2. A one-to-one mapping from a finite set to itself.

   “This permutation takes each element to the one following it, with the last mapped back to the first.”

3. An ordering of a finite set of distinct elements.

   “There are six permutations of three elements, e.g. {abc, acb, bac, bca, cab, cba}.”

4. A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.