permutation

[pur-myoo-tey-shuh n] /ˌpɜr myʊˈteɪ ʃən/
noun
1.
the act of permuting or permutating; alteration; transformation.
2.
Mathematics.
  1. the act of changing the order of elements arranged in a particular order, as abc into acb, bac, etc., or of arranging a number of elements in groups made up of equal numbers of the elements in different orders, as a and b in ab and ba; a one-to-one transformation of a set with a finite number of elements.
  2. any of the resulting arrangements or groups.
    Compare combination (def 8b).
Origin
1325-75; Middle English permutacioun (< Middle French permutacion) < Latin permūtātiōn- (stem of permūtātiō) thoroughgoing change. See per-, mutation, permute
Related forms
permutational, adjective
permutationist, noun
Synonyms
1. modification, transmutation, change.
Examples from the web for permutations
  • The technical permutations filled notebooks, then a filing cabinet.
  • Over months, the fastest permutations of sails and trim will be studied.
  • But even gene scientists today say they are struggling with the many permutations of those four molecules.
  • It is about training the brain to see possibilities and permutations in the larger world.
  • There are myriad permutations for drivers clinching wild cards today.
  • Only later did various permutations of the tea party develop additional political planks which are all over the map.
  • Literally millions of billing permutations are possible.
  • In the end, he identified four, though with all kinds of combinations and permutations among them.
  • Winning support for government bills is easiest when there are lots of parties and hence many winning permutations.
  • However, it is not the only solution, and the lifeboat problem has a great many permutations that defeat your simple solution.
British Dictionary definitions for permutations

permutation

/ˌpɜːmjʊˈteɪʃən/
noun
1.
(maths)
  1. an ordered arrangement of the numbers, terms, etc, of a set into specified groups: the permutations of a, b, and c, taken two at a time, are ab, ba, ac, ca, bc, cb
  2. a group formed in this way. The number of permutations of n objects taken r at a time is n!/(n–r)! nPr Compare combination (sense 6)
2.
a combination of items made by reordering
3.
an alteration; transformation
4.
a fixed combination for selections of results on football pools Usually shortened to perm
Derived Forms
permutational, adjective
Word Origin
C14: from Latin permūtātiō, from permūtāre to change thoroughly; see mutation
Word Origin and History for permutations

permutation

n.

mid-14c., from Old French permutacion "change, shift" (14c.), from Latin permutationem (nominative permutatio) "a change, alteration, revolution," noun of action from past participle stem of permutare "change thoroughly, exchange," from per- "thoroughly" (see per) + mutare "to change" (see mutable).