Definition of "permutation" in English

noun

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. (mathematics) 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. (mathematics, combinatorics) 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. (music) A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.