What does permutation mean?
A permutation is a rearrangement of elements in which their order changes but, in its mathematical sense, the elements themselves remain the same. The word is especially important in mathematics, where a permutation is a bijection from a set to itself and forms the basis of permutation groups. In more general contexts, it means any change in the order or arrangement of people, objects, or events: the schedule may simply involve a different permutation of the same activities. The term conveys systematic rearrangement rather than the removal or addition of elements. It is useful when precision matters because it distinguishes changing order from replacing, combining, or selecting things.
nounA rearrangement of the elements of a set, group, or sequence, especially in mathematics. The term can also refer generally to a change in the order or arrangement of things.
- A rearrangement of a set or sequence in which the order of the elements is changed.
- A particular arrangement produced by such a rearrangement.
- A change in the order or sequence of events, items, or elements.
- In mathematics, a bijection from a set to itself, especially in the study of permutations and permutation groups.
"The algorithm considers every permutation of the possible results."
"The six possible permutations of three objects were listed on the board."
"A change in the order of the interviews led to a different permutation of the candidates."
The plural is permutations when referring to separate rearrangements or mathematical arrangements.
"The program tested all 720 permutations of the six objects."
A permutation is the mathematical art of changing everything’s order without changing what is there.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does permutation come from?
The word comes through French permutation, from Latin permutatio, a word meaning “change” or “interchange.” It was formed from Latin permutare, meaning “to interchange” or “to change,” which combines per- with mutare, “to change or move.” The same broad root appears in related English words such as commute and interchange, reflecting a shared sense of exchanging or altering positions.
Related word forms
How permutation is actually used
In mathematics, the word is technical and usually means a rearrangement of a finite set. In general use, it can sound formal or abstract, though it is also used in computing, statistics, and discussions of sequence or order.
Easily confused with permutation
A permutation is an arrangement or rearrangement, while a replacement substitutes one thing for another.
A permutation changes the order of elements, whereas a combination selects elements without regard to their order.